Formation Evaluation MSc Course Notes Paul Glover

Formation Evaluation Dr. Paul W.J. Glover

MSc Petroleum Geology Department of Geology and Petroleum Geology University of Aberdeen UK

Contents Copyright

Formation Evaluation MSc Course Notes

Contents 1.

Introduction

1

2.

Reservoir Fluids

6

3.

Reservoir Drives

19

4.

Coring, Preservation and Handling

33

5.

Porosity

43

6.

Single Phase Permeability

54

7.

Wettability

76

8.

Capillary Pressure

84

9.

Electrical Properties

95

10. Relative Permeability

104

11. Commissioning Studies

131

Abbreviations References

Dr. Paul Glover

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Introduction

Chapter 1: Introduction 1.1

Introduction

This course aims to provide an understanding of the behaviour of fluids in reservoirs, and the use of core analysis in the evaluation of reservoir potential. It is intended to give the end user of special core analysis data an insight into the experimental techniques used to generate such data and an indication of its validity when applied to reservoir assessment. It has been written from the standpoint of a major oil industry operational support group, and is based upon the substantial experience of working in such an environment.

1.2

Core Analysis and other Reservoir Engineering Data

Special core analysis (SCAL) is one of the main sources of data available to guide the reservoir engineer in assessing the economic potential of a hydrocarbon accumulation. The data sources can be divided into field and laboratory measurements as shown in Figure 1.1. Laboratory data are used to support field measurements which can be subject to certain limitations, e.g.: (i)

Fluid saturations may be uncertain where actual formation brine composition and resistivity are not available.

(ii)

Permeability derived from well test data may be reduced by localised formation damage (skin effects) and increased by fractures.

Sedimentological data can be used to predict areal and vertical trends in rock properties and as an aid in the correct choice of core for laboratory measurements. For core analysis to provide meaningful data, due regard must be given to the ways in which rock properties can change both during the coring procedure (downhole), core preservation, and subsequent laboratory treatment.

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Introduction

This report is intended as a guide to the reliability and usefulness of the various RCAL and SCAL techniques generally available, and the ways which these techniques have, and will continue to be, refined in the light of current research. Maximum benefit will only be obtained from core analysis by full consultation between the reservoir engineer and the laboratory core analyst; taking all available data into account.

1.3

Reservoir Fluids and Drives

Hydrocarbon reservoirs may contain any or all of three fluid phases. These are; • • •

Aqueous fluids (brines), Oils, and Gases (hydrocarbon and non-hydrocarbon).

The distribution of these in a reservoir depends upon the reservoir conditions, the fluid properties, and the rock properties. The fluid properties are of fundamental importance, and will be studied in the first part of this course. The natural energy of a reservoir can be used to facilitate the production of hydrocarbon and non-hydrocarbon fluids from reservoirs. These sources of energy are called natural drive mechanisms. However, there may still be producible oil in a reservoir when natural drive mechanisms are exhausted. There exist artificial drive mechanisms that can then be used to produce some of the remaining oil. The type of drive currently operating in a reservoir has a strong control on the evaluation and management of the reservoir. Consequently, drive mechanisms will also be reviewed as part of the course.

1.4

Routine Core Analysis (RCAL)

Routine core analysis attempts to give only the very basic properties of unpreserved core. These are basic rock dimensions, core porosity, grain density, gas permeability, and water saturation. Taken in context routine data can provide a useful guide to well and reservoir performance, provided its limitations are appreciated. These limitations arise because routine porosity and permeability measurements are always made with gases on cleaned, dried core at room conditions. Such conditions are distinctly different from the actual reservoir situation. Thus routine data should be applied to the reservoir state with caution. This is especially true for permeability measurements. Routine core analysis data is cheap, and often form the great majority of the dataset representing reservoir core data. A schematic diagram of common RCAL measurements is given as Figure 1.2. Routine porosity data are generally reliable, being little affected by interactions between minerals and reservoir fluids. Correction for overburden loading is usually all that is required. Routine permeability results can misrepresent the reservoir situation as reservoir fluids often interact with the minerals forming the pore walls. This is frequently the case because these interactions cannot be allowed for in routine measurements. Correction can be only made for the compressibility of gases used. Thus the Klinkenberg correction converts gas permeability to ‘equivalent liquid permeability’ (KL) but still assumes no fluid-rock interaction. An actual liquid, brine or oil, usually gives a lower permeability than KL. If interface sensitive clays are

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Introduction

present in the reservoir, drying can destroy them and KL may be one or two orders of magnitude greater than an actual brine permeability measured on preserved, undried, core. An example of this effect is seen in the Magnus field and was demonstrated by Heaviside, Langley and Pallatt [1]. Permeability is affected by overburden loading to a greater extent than porosity. This must be allowed for when applying routine data to the reservoir situation.

Each of the RCAL measurements made is discussed in detail, covering; the theory, test methods, and limitations of alternative methods. The topics covered will include: Chapter 4. Chapter 5. Chapter 6.

1.5

Unpreserved core cleaning and water analysis. Sample dimension, porosity and grain density measurements. Gas permeability.

Special Core Analysis (SCAL)

Special Core Analysis attempts to extend the data provided by routine measurements to situations more representative of reservoir conditions. SCAL data is used to support log and well test data in gaining an understanding of individual well and overall reservoir performance. However, SCAL measurements are more expensive, and are commonly only done on a small selected group of samples, or if a difficult strategic reservoir management decision has to be made (e.g. to gasflood, or not to gasflood). Tests are carried out to measure fluid distribution, electrical properties and fluid flow characteristics in the two and occasionally three phase situation, and are made on preserved core. A schematic diagram of common SCAL measurements is given as Figure 1.3.

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Introduction

Porosity and single phase gas or liquid permeabilities are measured at overburden loadings so that the room condition data can be corrected. Wettability and capillary pressure data are generated by controlled displacement of a wetting phase by a non wetting phase e.g., brine by air, brine by oil or air by mercury. These systems usually have known interfacial tension (IFT) and wetting (contact) angle properties.

Conversion to the required reservoir values of IFT and contact angle can then be attempted to give data for predicting saturation at a given height within a reservoir. Electrical properties are measured at formation brine saturations of unity and less than unity, to obtain the cementation exponent, resistivity index, and excess conductivity of samples. These are used to provide data for interpretation of down-hole logs. Relative permeability attempts to provide data on the relative flow rates of phases present (e.g. oil and water or gas and water). Fluid flow is strongly influenced by fluid viscosities, and wetting characteristics. Care has to be taken that measurements are made under appropriate conditions, which allow some understanding of the wetting characteristics. The data generated allows relative flow rates and recovery efficiency to be assessed. Each of the SCAL measurements made is discussed in detail in the relevant chapter, covering the theory, test methods, and limitations of alternative methods. The topics covered will include:

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Chapter 4. Chapter 5. Chapter 6. Chapter 7. Chapter 8. Chapter 9.

Chapter 10. Chapter 11.

1.6

Introduction

Preserved core; methods of preservation and requirement for preserved core. Porosity at overburden pressures. Gas and liquid single phase permeabilities at overburden conditions. Wettability determinations; techniques available and limitations of data obtained. Capillary pressure measurements; techniques available and limitations of data obtained. Electrical measurements; resistivity index and saturation exponent, formation factor at room and overburden pressure, and cementation exponent. Relative Permeability; Theory, Techniques available, limitations and application of data. Typical SCAL programmes.

Arrangement of the Text

Effective assessment of reservoirs begins with an understanding of the properties of reservoir fluids, which is covered in Chapter 2. Chapter 3 discusses the various reservoir drives encountered in reservoir management. Chapter 4 discusses coring, core preservation and handling, which is of relevance mainly to SCAL studies. Chapters 5 and 6 cover RCAL porosity and permeability measurements, together with extensions to overburden pressure for SCAL studies. Chapters 7 to 10 cover various wettability, capillary pressure, electrical, and relative permeability measurements commonly practised in SCAL studies. Chapter 11 briefly examines typical SCAL work programmes.

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Chapter 2:

Reservoir Fluids

Reservoir Fluids

2.1 Introduction Reservoir fluids fall into three broad categories; (i) aqueous solutions with dissolved salts, (ii) liquid hydrocarbons, and (iii) gases (hydrocarbon and non-hydrocarbon). In all cases their compositions depend upon their source, history, and present thermodynamic conditions. Their distribution within a given reservoir depends upon the thermodynamic conditions of the reservoir as well as the petrophysical properties of the rocks and the physical and chemical properties of the fluids themselves. This chapter briefly examines these reservoir fluid properties.

2.2 Fluid Distribution The distribution of a particular set of reservoir fluids depends not only on the characteristics of the rock-fluid system now, but also the history of the fluids, and ultimately their source. A list of factors affecting fluid distribution would be manifold. However, the most important are: Depth The difference in the density of the fluids results in their separation over time due to gravity (differential buoyancy). Fluid Composition The composition of the reservoir fluid has an extremely important control on its pressure-volume-temperature properties, which define the relative volumes of each fluid in a reservoir. This subject is a major theme of this chapter. It also affects distribution through the wettability of the reservoir rocks (Chapter 7). Reservoir Temperature Exerts a major control on the relative volumes of each fluid in a reservoir. Fluid Pressure Exerts a major control on the relative volumes of each fluid in a reservoir. Fluid Migration Different fluids migrate in different ways depending on their density, viscosity, and the wettability of the rock. The mode of migration helps define the distribution of the fluids in the reservoir. Trap-Type Clearly, the effectiveness of the hydrocarbon trap also has a control on fluid distribution (e.g., cap rocks may be permeable to gas but not to oil). Rock structure The microstructure of the rock can preferentially accept some fluids and not others through the operation of wettability contrasts and capillary pressure. In addition, the common heterogeneity of rock properties results in preferential fluid distributions throughout the reservoir in all three spatial dimensions. The fundamental forces that drive, stabilise, or limit fluid movement are: • • • • •

Gravity (e.g. causing separation of gas, oil and water in the reservoir column) Capillary (e.g. responsible for the retention of water in micro-porosity) Molecular diffusion (e.g. small scale flow acting to homogenise fluid compositions within a given phase) Thermal convection (convective movement of all mobile fluids, especially gases) Fluid pressure gradients (the major force operating during primary production)

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Reservoir Fluids

Although each of these forces and factors vary from reservoir to reservoir, and between lithologies within a reservoir, certain forces are of seminal importance. For example, it is gravity that ensures, that when all three basic fluids types are present in an uncompartmentalised reservoir, the order of fluids with increasing depth is GAS:OIL:WATER, in exact analogy to a bottle of french dressing that has been left to settle.

2.3 Aqueous Fluids Accumulations of hydrocarbons are invariably associated with aqueous fluids (formation waters), which may occur as extensive aquifers underlying or interdigitated with hydrocarbon bearing layers, but always occur within the hydrocarbon bearing layers as connate water. These fluids are commonly saline, with a wide range of compositions and concentrations; Table 2.1 shows an example of a reservoir brine. Usually the most common dissolved salt is NaCl, but many others occur in varying smaller quantities. The specific gravity of pure water is defined as unity, and the specific gravity of formation waters increases with salinity at a rate of about 0.075 per 100 parts per thousand of dissolved solids. When SCAL measurements are made with brine, it is usual to make up a simulated formation brine to a recipe such as that given in Table 2.1, and then deaerate it prior to use. Table 2.1 Composition of Draugen 6407/9-4 Formation Water Component

Concentration, g dm-3

Pure water NaCl CaCl2.6H2O MgCl2.6H2O KCl NaHCO3 SrCl2.6H2O BaCl2.6H2O

Solvent 34.70 4.90 2.70 0.40 0.40 0.12 0.06 Final pH = 7

Why a connate water phase is invariably present in hydrocarbon bearing reservoir rock is easily explained. The reservoir rocks were initially fully or partially saturated with aqueous fluids before the migration of the oil from source rocks below them. The oil migrates upwards from the source rocks, driven by the differential buoyancy of the oil and the water. In this process most of the water swaps places with the oil since no fluids can escape from the cap rock above the reservoir. However, the water is not completely displaced as the initial reservoir rock is invariably water-wet, leaving the water-wet grains covered in a thin layer of water, with the remainder of the pore space full of oil. Water also remains in the microporosity where gravity segregation forces are insufficient to overcome the water-rock capillary forces. The aqueous fluids, whether as connate water or in aquifers, commonly contain dissolved gases at reservoir temperatures and pressures. Different gases dissolve in aqueous fluids to different extents, and this gas solubility also varies with temperature and pressure. Table 2.2 shows a selection of gases. If gas saturated water at reservoir pressure is subjected to lower

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Reservoir Fluids

pressures, the gas will be liberated, in exactly the same way that a lemonade bottle fizzes when opened. In reservoirs the dissolved gas is mainly methane (from 10 SCF/STB at 1000 psi to 35 SCF/STB at 10 000 psi for gas-water systems, and slightly less for water-oil systems). Higher salinity formation waters tend to contain less dissolved gas. Table 2.2 Dissolution of Gases in Water (dissolved mole fraction) at 1 bar 104 × Xgas @ 1 bar

Gas

Helium Argon Radon Hydrogen Nitrogen Oxygen Carbon dioxide Methane Ethane Ammonium

o

25 C

55oC

0.06983 0.2516 1.675 0.1413 0.1173 0.2298 6.111 0.2507 0.3345 1876

0.07179 0.1760 0.8911 0.1313 0.08991 0.0164 3.235 0.1684 0.01896 1066

Xgas = mole fraction of gas dissolved at 1 bar pressure, i.e.=1/Hgas. Aqueous fluids are relatively incompressible compared to oils, and extremely so compared to gases (2.5×10-6 to 5×10-6 per psi decreasing with increasing salinity). Consequently, if a unit volume of formation water with no dissolved gases at reservoir pressure conditions is transported to surface pressure condition, it will expand only slightly compared to the same initial volume of oil or gas. It should be noted that formation waters containing a significant proportion of dissolved gases are more compressible than those that are not gas saturated. These waters expand slightly more on being brought to the surface. However the reduction in temperature on being brought to the surface causes the formation water to shrink and there is also a certain shrinkage associated with the release of gas as pressure is lowered. The overall result is that brines experience a slight shrinkage (< 5%) on being brought from reservoir conditions to the surface. Formation waters generally have densities that are greater than those of oils, and dynamic viscosities that are a little lower (Table 2.3). The viscosity at high reservoir temperatures (>250oC) can be as low as 0.3 cP, rises to above 1 cP at ambient conditions, and increases with increasing salinity.

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Reservoir Fluids

Table 2.3 Densities and Viscosities for a Typical Formation Water and a Refined Oil Brine Component

Composition, g/l

Pure water NaCl CaCl2.6H2O MgCl2.6H2O Na2SO4 NaHCO3

Solvent 150.16 101.32 13.97 0.55 0.21

Fluid

Temperature, oC

Density, g/cm3

Brine Brine Brine

20 25 30

1.1250 1.1237 1.1208

1.509 1.347 1.219

Kerosene Kerosene Kerosene

20 25 30

0.7957 0.7923 0.7886

1.830 1.661 1.514

Dynamic Viscosity, cP

2.4 Phase Behaviour of Hydrocarbon Systems Figure 2.1 shows the pressure versus volume per mole weight (specific volume) characteristics of a typical pure hydrocarbon (e.g. propane). Imagine in the following discussion that all changes occur isothermally (with no heat flowing either into or out of the fluid) and at the same temperature. Initially the component is in the liquid phase at 1000 psia, and has a volume of about 2 ft3/lb.mol. (point A). Expansion of the system (A→B) results in large drops in pressure with small increases in specific volume, due to the small compressibility of liquids (liquid hydrocarbons as well as liquid formation waters have small compressibilities that are almost independent of pressure for the range of pressures encountered in hydrocarbon reservoirs). On further expansion, a pressure will be attained where the first tiny bubble of gas appears (point B). This is the bubble point or saturation pressure for a given temperature. Further expansion (B→C) now occurs at constant pressure with more and more of the liquid turning into the gas phase until no more fluid remains. The constant pressure at which this occurs is called the vapour pressure of the fluid at a given temperature. Point C represents the situation where the last tiny drop of liquid turns into gas, and is called the dew point. Further expansion now takes place in the vapour phase (C→D). The pistons in Figure 2.1 demonstrate the changes in fluid phase schematically. It is worth noting that the process A→B→C→D described above during expansion (reducing the pressure on the piston) is perfectly reversible. If a system is in state D, then application of pressure to the fluid by applying pressure to the pistons will result in changes following the curve D→C→B→A.

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Reservoir Fluids

We can examine the curve in Figure 2.1 for a range of fluid temperatures. If this is done, the pressure-volume relationships obtained can be plotted on a pressure-volume diagram with the bubble point and dew point locus also included (Figure 2.2). Note that the bubble point and dew point curves join together at a point (shown by a dot in Figure 2.2). This is the critical point. The region under the bubble point/dew point envelope is the region where the vapour phase and liquid phase can coexist, and hence have an interface (the surface of a liquid drop or of a vapour bubble). The region above this envelope represents the region where the Dr. Paul Glover

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Reservoir Fluids

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Reservoir Fluids

vapour phase and liquid phase do not coexist. Thus at any given constant low fluid pressure, reduction of fluid volume will involve the vapour condensing to a liquid via the two phase region, where both liquid and vapour coexist. But at a given constant high fluid pressure (higher than the critical point), a reduction of fluid volume will involve the vapour phase turning into a liquid phase without any fluid interface being generated (i.e. the vapour becomes denser and denser until it can be considered as a light liquid). Thus the critical point can also be viewed as the point at which the properties of the liquid and the gas become indistinguishable (i.e. the gas is so dense that it looks like a low density liquid and vice versa). Suppose that we find the bubble points and dew points for a range of different temperatures, and plot the data on a graph of pressure against temperature. Figure 2.3 shows such a plot. Note that the dew point and bubble points are always the same for a pure component, so they plot as a single line until the peak of Figure 2.2 is reached, which is the critical point.

The behaviour of a hydrocarbon fluid made up of many different hydrocarbon components shows slightly different behaviour (Figure 2.4). The initial expansion of the liquid is similar to that for the single component case. Once the bubble point is reached, further expansion does

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Reservoir Fluids

not occur at constant pressure but is accompanied by a decrease in pressure (vapour pressure) due to changes in the relative fractional amounts of liquid to gas for each hydrocarbon in the vaporising mixture. In this case the bubble points and dew points differ, and the resulting pressure-temperature plot is no longer a straight line but a phase envelope composed of the bubble point and dew point curves, which now meet at the critical point (Figure 2.5). There are also two other points on this diagram that are of interest. The cricondenbar, which defines the pressure above which the two phases cannot exist together whatever the temperature, and the cricondentherm, which defines the temperature above which the two phases cannot exist together whatever the pressure. A fluid that exists above the bubble point curve is classified as undersaturated as it contains no free gas, while a fluid at the bubble point curve or below it is classified as saturated, and contains free gas. Figure 2.6 shows the PT diagram for a reservoir fluid, together with a production path from the pressure and temperature existing in the reservoir to that existing in the separator at the

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Reservoir Fluids

surface. Note that the original fluid was an undersaturated liquid at reservoir conditions. On production the fluid pressure drops fast with some temperature reduction occurring as the fluid travels up the borehole. All reservoirs are predominantly isothermal because of their large thermal inertia. This results in the production path of all hydrocarbons initially undergoing a fluid pressure reduction. Figure 2.6 shows that the ratio of vapour to liquid at separator conditions is approximately 55:45. If we analyse the PT characteristics of the separator gas and separator fluid separately then we would find that the separator pressuretemperature point representing the separator conditions falls on the dew point line of the separator gas PT diagram, and on the bubble point line of the separator oil PT diagram. This indicates that the shape of the PT diagram for various mixtures of hydrocarbon gases and liquids varies greatly. Clearly, therefore it is extremely important to understand the PT phase envelope as it can be used to classify and understand major hydrocarbon reservoirs.

2.5 PVT Properties of Hydrocarbon Fluids 2.5.1 Cronquist Classification Hydrocarbon reservoirs are usually classified into the following five main types, after Cronquist, 1979: • • • • •

Dry gas Wet gas Gas condensate Volatile oil Black oil

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Reservoir Fluids

Each of these reservoirs can be understood in terms of its phase envelope. The typical components of production from each of these reservoirs is shown in Table 2.4, and a schematic diagram of their PT phase envelopes is shown in Figure 2.7.

Table 2.4 Typical Mol% Compositions of Fluids Produced from Cronquist Reservoir Types Component or Property CO2 N2 C1 C2 C3 iC4 nC4 iC5 nC5 C6 s C7+ GOR (SCF/STB) OGR (STB/MMSCF) API Specific Gravity, γAPI ,oAPI C7+ Specific Gravity, γo

Dry Gas

Wet Gas

Gas Volatile Oil Condensate

Black Oil

0.10 2.07 86.12 5.91 3.58 1.72 0.50 -

1.41 0.25 92.46 3.18 1.01 0.28 0.24 0.13 0.08 0.14 0.82

2.37 0.31 73.19 7.80 3.55 0.71 1.45 0.64 0.68 1.09 8.21

1.82 0.24 57.60 7.35 4.21 0.74 2.07 0.53 0.95 1.92 22.57

0.02 0.34 34.62 4.11 1.01 0.76 0.49 0.43 0.21 1.16 56.40

∞ 0

69000 15

5965 165

1465 680

320 3125

-

65.0

48.5

36.7

23.6

-

0.750

0.816

0.864

0.920

Note: Fundamental specific gravity γo is equal to the density of the fluid divided by the density of pure water, and that for C7+ is for the bulked C7+ fraction. The API specific gravity γAPI is defined as; γAPI = (141.5/γo) - 131.5. Dr. Paul Glover

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Reservoir Fluids

2.5.2 Dry Gas Reservoirs A typical dry gas reservoir is shown in Figure 2.8. The reservoir temperature is well above the cricondentherm. During production the fluids are reduced in temperature and pressure. The temperature-pressure path followed during production does not penetrate the phase envelope, resulting in the production of gas at the surface with no associated liquid phase. Clearly, it would be possible to produce some liquids if the pressure is maintained at a higher level. In practice, the stock tank pressures are usually high enough for some liquids to be produced (Figure 2.9). Note the lack of C5+ components, and the predominance of methane in the dry gas in Table 2.4.

2.5.3 Wet Gas Reservoirs A typical wet gas reservoir is shown in Figure 2.9. The reservoir temperature is just above the cricondentherm. During production the fluids are reduced in temperature and pressure. The temperature-pressure path followed during production just penetrates the phase envelope, resulting in the production of gas at the surface with a small associated liquid phase. Note the presence of small amounts of C5+ components, and the continuing predominance of methane in the wet gas in Table 2.4. The GOR (gas-oil ratio) has fallen as some liquid is being produced. However, this liquid usually amounts to less than about 15 STB/MMSCF. Note also the small specific gravity for C7+ components (0.750), indicating that the majority of the C7+ fraction is made up of the lighter C7+ hydrocarbons.

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Reservoir Fluids

2.5.4 Gas Condensate Reservoirs A typical gas condensate reservoir is shown in Figure 2.10. The reservoir temperature is such that it falls between the temperature of the critical point and the cricondentherm. The production path then has a complex history. Initially, the fluids are in an indeterminate vapour phase, and the vapour expands as the pressure and temperature drop. This occurs until the dewpoint line is reached, whereupon increasing amounts of liquids are condensed from the vapour phase. If the pressures and temperatures reduce further, the condensed liquid may reevaporate, although sufficiently low pressures and temperatures may not be available for this to happen. If this occurs, the process is called isothermal retrograde condensation. Isobaric retrograde condensation also exists as a scientific phenomenon, but does not occur in the predominantly isothermal conditions of hydrocarbon reservoirs. Thus, in gas condensate reservoirs, the oil produced at the surface results from a vapour existing in the reservoir. Note the increase in the C7+ components and the continued importance of methane in Table 2.4. The GOR has decreased significantly, the OGR has increased, and the specific gravity of the C7+ components is increasing, indicating that greater fractions of denser hydrocarbons are present in the C7+ fraction.

2.5.5 Volatile Oil Reservoirs A typical volatile oil reservoir is shown in Figure 2.11. The reservoir PT conditions place it inside the phase envelope, with a liquid oil phase existing in equilibrium with a vapour phase having gas condensate compositions. The production path results in small amounts of further condensation, and re-evaporation can occur again, but should be avoided as much as possible by keeping the stock tank pressure as high as possible. Reference to Table 2.4 shows that the fraction of gases is reduced, and the fraction of denser liquid hydrocarbon liquids is increased, compared with the previously discussed reservoir types. Changes in the GOR, OGR and specific gravities are in agreement with the general trend.

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Reservoir Fluids

2.5.6 Black Oil Reservoirs

A typical gas condensate reservoir is shown in Figure 2.12. The reservoir temperature is much lower than the temperature of the critical point of the system, and at pressures above the cricondenbar. Thus, the hydrocarbon in the reservoir exists as a liquid at depth. The production path first involves a reduction in pressure with only small amounts of expansion in the liquid phase. Once the bubble point line is reached, gas begins to come out of solution and continues to do so until the stock tank is reached. The composition of this gas changes very little along the production path, is relatively lean, and is not usually of economic importance when produced. Table 2.4 shows a produced hydrocarbon fluid that is now dominated by heavy hydrocarbon liquids, with most of the produced gas present as methane. The GOR, OGR and specific gravities mirror the fluid composition.

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Reservoir Drives

Chapter 3: Reservoir Drives 3.1 Introduction Recovery of hydrocarbons from an oil reservoir is commonly recognised to occur in several recovery stages. These are: (i) (ii) (iii) (iv)

Primary recovery Secondary recovery Tertiary recovery (Enhanced Oil Recovery, EOR) Infill recovery

Primary recovery This is the recovery of hydrocarbons from the reservoir using the natural energy of the reservoir as a drive. Secondary recovery This is recovery aided or driven by the injection of water or gas from the surface. Tertiary recovery (EOR) There are a range of techniques broadly labelled ‘Enhanced Oil Recovery’ that are applied to reservoirs in order to improve flagging production. Infill recovery Is carried out when recovery from the previous three phases have been completed. It involves drilling cheap production holes between existing boreholes to ensure that the whole reservoir has been fully depleted of its oil. This chapter discusses primary, secondary and EOR drive mechanisms and techniques.

3.2 Primary Recovery Drive Mechanisms During primary recovery the natural energy of the reservoir is used to transport hydrocarbons towards and out of the production wells. There are several different energy sources, and each gives rise to a drive mechanism. Early in the history of a reservoir the drive mechanism will not be known. It is determined by analysis of production data (reservoir pressure and fluid production ratios). The earliest possible determination of the drive mechanism is a primary goal in the early life of the reservoir, as its knowledge can greatly improve the management and recovery of reserves from the reservoir in its middle and later life. There are five important drive mechanisms (or combinations). These are: (i) (ii) (iii) (iv) (v)

Solution gas drive Gas cap drive Water drive Gravity drainage Combination or mixed drive

Table 3.1 shows the recovery ranges for each individual drive mechanism.

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Reservoir Drives

Table 3.1 Recovery ranges for each drive mechanism Drive Mechanism Solution gas drive

Energy Source

Recovery, % OOIP

Evolved solution gas and expansion

20-30

Evolved gas

18-25

Gas expansion

2-5

Gas cap drive

Gas cap expansion

20-40

Water drive

Aquifer expansion

20-60

Bottom

20-40

Edge

35-60

Gravity drainage

Gravity

50-70 A combination or mixed drive occurs when any of the first three drives operate together, or when any of the first three drives operate with the aid of gravity drainage. The reservoir pressure and GOR trends for each of the main (first) three drive mechanisms is shown as Figures 3.1 and 3.2. Note particularly that water drive maintains the reservoir pressure much higher than the gas drives, and has a uniformly low GOR.

3.2.1 Solution Gas Drive This drive mechanism requires the reservoir rock to be completely surrounded by impermeable barriers. As production occurs the reservoir pressure drops, and the exsolution and expansion of the dissolved gases in the oil and water provide most of the reservoirs drive energy. Small amounts of additional energy are also derived from the expansion of the rock and water, and gas exsolving and Dr. Paul Glover

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Reservoir Drives

expanding from the water phase. The process is shown schematically in Figure 3.3. A solution gas drive reservoir is initially either considered to be undersaturated or saturated depending on its pressure: • •

Undersaturated: Reservoir pressure > bubble point of oil. Saturated: Reservoir pressure ≤ bubble point of oil.

For an undersaturated reservoir no free gas exists until the reservoir pressure falls below the bubblepoint. In this regime reservoir drive energy is provided only by the bulk expansion of the reservoir rock and liquids (water and oil). For a saturated reservoir, any oil production results in a drop in reservoir pressure that causes bubbles of gas to exsolve and expand. When the gas comes out of solution the oil (and water) shrink slightly. However, the volume of the exsolved gas, and its subsequent expansion more than makes up for this. Thus gas expansion is the primary reservoir drive for reservoirs below the bubble point. Solution gas drive reservoirs show a particular characteristic pressure, GOR and fluid production history. If the reservoir is initially undersaturated, the reservoir pressure can drop by a great deal (several hundred psi over a few months), see Figures 3.1 and 3.2. This is because of the small compressibilities of the rock water and oil, compared to that of gas. In this undersaturated phase, gas is only exsolved from the fluids in the well bore, and consequently the GOR is low and constant. When the reservoir reaches the bubble point pressure, the pressure declines less quickly due to the formation of gas bubbles in the reservoir that expand taking up the volume exited by produced oil and hence protecting against pressure drops. When this happens, the GOR rises dramatically (up to 10 times). Further fall in Dr. Paul Glover

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Reservoir Drives

reservoir pressure, as production continues, can, however, lead to a decrease in GOR again when reservoir pressures are such that the gas expands less in the borehole. When the GOR initially rises, the oil production falls and artificial lift systems are then instituted. Oil recovery from this type of reservoir is typically between 20% and 30% of original oil in place (i.e. low). Of this only 0% to 5% of oil is recovered above the bubblepoint. There is usually no production of water during oil recovery unless the reservoir pressure drops sufficiently for the connate water to expand sufficiently to be mobile. Even in this scenario little water is produced.

3.2.2 Gas Cap Drive A gas cap drive reservoir usually benefits to some extent from solution gas drive, but derives its main source of reservoir energy from the expansion of the gas cap already existing above the reservoir. The presence of the expanding gas cap limits the pressure decrease experienced by the reservoir during production. The actual rate of pressure decrease is related to the size of the gas cap. The GOR rises only slowly in the early stages of production from such a reservoir because the pressure of the gas cap prevents gas from coming out of solution in the oil and water. As production continues, the gas cap expands pushing the gas-oil contact (GOC) downwards (Figure 3.4). Eventually the GOC will reach the production wells and the GOR will increase by large amounts (Figures 3.1 and 3.2). The slower reduction in pressure experienced by gas cap reservoirs compared to solution drive reservoirs results in the oil production rates being much higher throughout the life of the reservoir, and needing artificial lift much later than for solution drive reservoirs. Dr. Paul Glover

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Gas cap reservoirs produce very little or no water. The recovery of gas cap reservoirs is better than for solution drive reservoirs (20% to 40% OOIP). The recovery efficiency depends on the size of the gas cap, which is a measure of how much latent energy there is available to drive production, and how the reservoir is managed, i.e. how the energy resource is used bearing in mind the geometric characteristics of the reservoir, economics and equity considerations. Points of importance to bear in mind when managing a gas cap reservoir are: • Steeply dipping reservoir oil columns are best. • Thick oil columns are best, and are perforated at the base, as far away from the gas cap as possible. This is to maximise the time before gas breaks through in the well. • Wells with increasing GOR (gas cap breakthrough) can be shut in to reduce field wide GOR. • Produced gas can be separated and immediately injected back into the gas cap to maintain gas cap pressure.

3.2.3 Water Drive The drive energy is provided by an aquifer that interfaces with the oil in the reservoir at the oil-water contact (OWC). As production continues, and oil is extracted from the reservoir, the aquifer expands into the reservoir displacing the oil. Clearly, for most reservoirs, solution gas drive will also be taking place, and there may also be a gas cap contributing to the primary recovery. Two types of water drive are commonly recognised: • Bottom water drive (Figure 3.5) • Edge water drive (Figure 3.5) The pressure history of a water driven reservoir depends critically upon: (i) (ii) (iii)

The size of the aquifer. The permeability of the aquifer. The reservoir production rate.

If the production rate is low, and the size and permeability of the aquifer is high, then the reservoir pressure will remain high because all produced oil is replaced efficiently with water. If the production rate is too high then the extracted oil may not be able to be replaced by water in the same timescale, especially if the aquifer is small or low permeability. In this case the reservoir pressure will fall (Figure 3.1). The GOR remains very constant in a strongly water driven reservoir (Figure 3.2), as the pressure decrease is small and constant, whereas if the pressure decrease is higher (weakly water driven reservoir) the GOR increases due to gas exsolving from the oil and water in the reservoir. Likewise the oil production from a strongly water driven reservoir remains fairly constant until water breakthrough occurs.

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Reservoir Drives

Using analogous arguments to the gas cap drive, it can be seen that thick oil columns are again an advantage, but the wells are perforated high in the oil zone to delay the water breakthrough. When water breakthrough does occur the well can either be shut-down, or assisted using gas lift. Reinjection of water into the aquifer is seldom done because the injected water usually just disappears into the aquifer with no effect on aquifer pressure. The recovery from water driven reservoirs is usually good (20-60% OOIP, Table 3.1), although the exact figure depends on the strength of the aquifer and the efficiency with which the water displaces the oil in the reservoir, which depends on reservoir structure, production well placing, oil viscosity, and production rate. If the ratio of water to oil viscosity is large, or the production rate is high then fingering can occur which leaves oil behind in the reservoir (Figure 3.6).

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3.2.4 Gravity Drainage The density differences between oil and gas and water result in their natural segregation in the reservoir. This process can be used as a drive mechanism, but is relatively weak, and in practice is only used in combination with other drive mechanisms. Figure 3.7 shows production by gravity drainage.

The best conditions for gravity drainage are: • •

Thick oil zones. High vertical permeabilities.

The rate of production engendered by gravity drainage is very low compared with the other drive mechanisms examined so far. However, it is extremely efficient over long periods and can give rise to extremely high recoveries (50-70% OOIP, Table 3.1). Consequently, it is often used in addition to the other drive mechanisms.

3.2.5 Combination or Mixed Drive In practice a reservoir usually incorporates at least two main drive mechanisms. For example, in the case shown in Figure 3.8. We have seen that the management of the reservoir for

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different drive mechanisms can be diametrically opposed (e.g. low perforation for gas cap reservoirs compared with high perforation for water drive reservoirs). If both occur as in Figure 3.8, a compromise must be sought, and this compromise must take into account the strength of each drive present, the size of the gas cap, and the size/permeability of the aquifer. It is the job of the reservoir manager to identify the strengths of the drives as early as possible in the life of the reservoir to optimise the reservoir performance.

3.3 Secondary Recovery Secondary recovery is the result of human intervention in the reservoir to improve recovery when the natural drives have diminished to unreasonably low efficiencies. Two techniques are commonly used: (i) (ii)

Waterflooding Gasflooding

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3.3.1 Waterflooding This method involves the injection of water at the base of a reservoir to; (i) (ii)

Maintain the reservoir pressure, and Displace oil (usually with gas and water) towards production wells.

The detailed treatment of waterflood recovery estimation, mathematical modelling, and design are beyond the scope of these notes. However, it should be noted that the successful outcome of a waterflood process depends on designs based on accurate relative permeability data in both horizontal directions, on the choice of a good injector/producer array, and with full account taken of the local crustal stress directions in the reservoir.

3.3.2 Gas Injection This method is similar to waterflooding in principal, and is used to maintain gas cap pressure even if oil displacement is not required. Again accurate relperms are needed in the design, as well as injector/producer array geometry and crustal stresses. There is an additional complication in that re-injected lean gas may strip light hydrocarbons from the liquid oil phase. At first sight this may not seem a problem, as recombination in the stock tank or afterwards may be carried out. However, equity agreements often give different percentages of gas and oil to different companies. Then the decision whether to gasflood is not trivial (e.g. Prudhoe Bay, Alaska).

3.4 Tertiary Recovery (Enhanced Oil Recovery) Primary and secondary recovery methods usually only extract about 35% of the original oil in place. Clearly it is extremely important to increase this figure. Many enhanced oil recovery methods have been designed to do this, and a few will be reviewed here. They fall into three broad categories; (i) thermal, (ii) chemical, and (iii) miscible gas. All are extremely expensive, are only used when economical, and are implemented after extensive SCAL studies have isolated the reservoir rock characteristics that are causing oil to remain unproduced by conventional methods.

3.4.1 Thermal EOR These processes use heat to improve oil recovery by reducing the viscosity of heavy oils and vaporising lighter oils, and hence improving their mobility. The techniques include: (i) (ii)

Steam injection (Figure 3.9). In situ combustion (injection of a hot gas that combusts with the oil in place, Figure 3.10). (iii) Microwave heating downhole (3.11). (iv) Hot water injection. It is worth noting that the generation of large amounts of heat and the treatment of evolved gas has large environmental implications for these methods. However, thermal EOR is probably the most efficient EOR approach.

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Reservoir Drives

3.4.2 Chemical EOR These processes use chemicals added to water in the injected fluid of a waterflood to alter the flood efficiency in such a way as to improve oil recovery. This can be done in many ways, examples are listed below: (i) Increasing water viscosity (polymer floods) (ii) Decreasing the relative permeability to water (cross-linked polymer floods) (iii) Increasing the relative permeability to oil (micellar and alkaline floods)

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(iv) Decreasing Sor (micellar and alkaline floods) (v) Decreasing the interfacial tension between the oil and water phases (micellar and alkaline floods) An example of chemical EOR is shown in Figure 3.12.

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Chemical flood additives, especially surfactants designed to reduce surface or interfacial tension, are extremely expensive. Thus the whole chemical EOR flood is designed to minimise the amount of surfactants needed, and to ensure that the EOR process is economically successful as well as technically. Chemical flooding is therefore not a simple single stage process. Initially the reservoir is subjected to a preflush of chemicals designed to improve the stability of the interface between the in-situ fluids and the chemical flood itself. Then the chemical surfactant EOR flood is carried out. Commonly polymers are injected into the reservoir after the chemical flood to ensure that a favourable mobility ratio is maintained. A buffer to maintain polymer stability follows, then a driving fluid, which is usually water, is injected. Figure 3.13 shows a typical flood sequence. Note that the mobilised oil bank moves ahead of the surfactant flood, and how the total process has reduced the amount of the surfactant fluid used.

3.4.3 Miscible Gas Flooding This method uses a fluid that is miscible with the oil. Such a fluid has a zero interfacial tension with the oil and can in principal flush out all of the oil remaining in place. In practice a gas is used since gases have high mobilities and can easily enter all the pores in the rock providing the gas is miscible in the oil. Three types of gas are commonly used: (i) CO2 (ii) N2 (iii) Hydrocarbon gases.

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All of these are relatively cheap to obtain either from the atmosphere or from evolved reservoir gases. The high mobility of gases can cause a problem in the reservoir flooding process, since gas breakthrough may be early due to fingering, leading to low sweep efficiencies. Effort is then concentrated on trying to improve the sweep efficiency. One such approach is called a miscible WAG (water alternating gas). In this approach water slugs and CO2 slugs are alternately injected into the reservoir; the idea being that the water slugs will lower the mobility of the CO2 and lead to a more piston-like displacement with higher flood efficiencies. An additional important advantage of miscible gasflooding is that the gas dissolves in the oil, and this process reduces the oil viscosity, giving it higher mobilities and easier recovery. A WAG flood is shown in Figure 3.14.

3.5 Infill Recovery Towards the end of the reservoir life (after primary, secondary and enhanced oil recovery), the only thing that can be done to improve the production rate is to carry out infill drilling, directly accessing oil that may have been left unproduced by all the previous natural and artificial drive mechanisms. Infill drilling can involve very significant drilling costs, while the resulting additional production may not be great.

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Chapter 4: Coring, Preservation and Handling 4.1 Introduction Large financial resources are invested in RCAL and SCAL core analysis programmes, and a wide range of accurate experimental determinations can be carried out. However, cores are expensive to obtain and represent a very dilute sampling of the reservoir rock. It is clear that the samples used in such studies should be as representative as possible of the reservoir rock at depth if the final data is to be credible, and an efficient use of the financial resources devoted to them. Samples of the reservoir rock and the fluids they contain can be, and are commonly, altered by the process of obtaining them (coring, recovery, wellsite handling, shipment, storage, and preparation for experimentation). This chapter gives an overview of the alteration processes that may be at work, together with some of the techniques available to reduce alteration, and preserve the rock and fluid properties. The choice of core preparation techniques is increasingly being made by using pre-screening information on the preserved core. This approach is highly recommended.

4.2 The Coring Process Reservoir rock undergoes changes during the coring process and on storage before reaching the laboratory. The changes which occur are shown in Figure 4.1. Some of the changes are reversible whilst others are irreversible but preventable. In most cases it is possible to leave all or part of the core in a usable state. It is essential to use preserved core for certain SCAL tests and for meaningful assessment of routine data.

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Drilling of the core is invariably carried out at very high bottom hole pressure differentials, thus the core is effectively water-flooded with mud filtrate, and the original contents partly displaced. The outer surface of the core will be invaded by mud particles; the depth of invasion being dependent upon permeability. This zone should be avoided when sampling. The rest of the core will have had its original hydrocarbon content, and formation water displaced by mud filtrate; the extent depending upon the core permeability and original fluid saturations. These changes are not always harmful as the core can usually be restored in the laboratory. More important changes can occur if the rock contains minerals sensitive to water salinity. For example, contact with low salinity water can mobilise poorly adhered clay particles, giving a small possibility that core can arrive in the laboratory with mobilised fines, which are not significantly mobile in the reservoir. In a similar fashion the wetting characteristics of the rock may be altered by surfactant mud additives. These changes are usually unavoidable but if formations are known to be particularly sensitive, it may be possible to modify mud composition and reduce overpressure to minimise damage. For complete preservation of wettability on cores above the transition zone, coring with lease crude is necessary. Water saturation may then also be retained intact, allowing better estimation of initial reservoir oil saturation. For transition and water zone a bland mud formulation will do the least harm to original rock properties.

Drying can be the worst that can happen to core after removal from the barrel. If interface sensitive clays, e.g., fibrous illite are present they can be irreparably damaged by drying (Figure 4.2) and any permeability measurements made on such core will be valueless. Thus it Dr. Paul Glover

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is necessary to preserve some core in the state that it leaves the barrel either by immersion in simulated formation brine or by wrapping in foil and wax. The latter technique is the minimum required for samples intended for wettability measurements, but for straightforward assessment of water zone permeabilities immersion in brine is adequate. The necessity for preserved core will be more fully covered under relevant sections below.

4.3 Plug Sampling and Cleaning (Unpreserved Core) Standard techniques are applied unless the core is very heterogeneous or likely to be damaged by routine cleaning methods. One or one and a half inch diameter sample plugs are drilled and trimmed to between two and three inches long with simulated formation brine as lubricant. If the composition of formation brine is unknown, a five percent sodium chloride brine is used. Plugs are taken at regular intervals (often every 25 cm), parallel to bedding planes for horizontal permeability (see Figure 4.3a). Further plugs normal to the bedding plane are taken if required for vertical permeability. The sampling interval can either, be increased, if the core is from a formation known to be homogeneous; or varied if the core contains thin shaly bands making it difficult to produce intact plugs. Thin shaly bands are avoided unless frequent and representative. Figure 4.3b analyses the suitability of core plugs for homogeneous, thickly bedded and thinly bedded whole core. Tests may also be carried out on full diameter core samples. This is necessary if plug sized samples do not contain a representative pore size spectrum. Fractures, vugs (very large pores) and stylolytes are typical structural features which necessitate measurement on full diameter (whole core) samples. The measurements made are the same as for plug samples, but a special core holder is necessary if horizontal permeabilities are required. Plugs are cleaned by alternate extraction with hot toluene and methanol in Soxhlet extractors (Figure 4.4a and 4.4b) until no further discolouration of solvent occurs. This may take from a few, to several hundred hours depending upon permeability. Low permeability plugs are seldom completely free of residual brine and oil at this stage. Complete removal of residual fluids can only be achieved by prolonged Soxhlet extraction. Cores can also be cleaned by Dr. Paul Glover

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flushing the core with alternate miscible solvents (e.g. toluene (for the oil phase) and methanol (for the water phase)) done hot or cold in a Hassler coreholder (Figure 4.4a; also see section 4.5). Both the aqueous (methanol) and oleic (toluene) cleaning phases exiting the rock can be bulked and submitted for analysis of the amount of water and individual hydrocarbons present.

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Plugs are then dried to constant weight in a humidity controlled oven at 60°C, 40% relative humidity. Humidity controlled drying assists in restoring clays to nearer their reservoir state, and may assist in preventing any further damage. However, the Klinkenberg corrected equivalent liquid permeability from this type of drying process may still be larger than the actual brine permeability due to the destruction of the clay texture. If samples of plugs containing clays that are sensitive to drying are required for SEM analysis (e.g. Figure 4.2), then a sample of the core with the original fluid contents must be critical point dried. Ordinary drying destroys fine clay minerals because the interfacial forces associated with the retreating liquid-vapour interface are high enough to mash the clay structure. Critical point drying involves keeping a small sample of the core at pressure and temperature conditions of the critical point of the fluids. The fluids will then be evaporated from the sample without a liquid-vapour interface, which avoids destroying the fine clay structure. This is an expensive operation because it can take many days to perform on even the smallest sample chip. Consequently, it is almost never carried out for core plugs.

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4.4 Core and Plug Preservation (SCAL Techniques) Preserved core is almost always required for one or more of the following reasons: (i) (ii) (iii) (iv) (v)

Wettability determinations. Prevention of drying of interface sensitive clays. Maintenance of fluid saturations as received at surface. Other SCAL where drying is not desirable. Unconsolidated or relatively uncompacted samples that exhibit strong porosity and permeability reductions with overburden stress.

Several methods of preservation are currently available and a choice can be made if the requirement for preserved core is specified. The methods are: Under simulated formation brine or kerosene, for water and oil zone cores respectively. Cores are either kept under simulated formation brine in polymer containers with an airtight seal at ambient pressure (certain types of spaghetti jars are good for this); see Figure 4.5. Wax coated, for all SCAL purposes and especially wettability and residual oil saturations. This technique, also called ‘seal-peel’, is widely used, and involves wrapping the core in layers of plastic and aluminium foil before being dipped in wax. Cores preserved in this way at the well site can be safely stored for moderately long periods and then be used for almost all SCAL purposes (Figure 4.5). In deoxygenated formation brine or kerosene, for wettability measurements. Samples are kept in anaerobic jars which can be pressurised to 30 psi (Figure 4.5). The freshly cut core pieces are placed in the jars under deaerated simulated formation brine or kerosene, and the jars are then sealed. The remaining air is then purged with nitrogen, which is then raised to 30 psi pressure. The samples are then preserved under reservoir fluid and a blanket of inert gas. Providing that the pressure is maintained, the samples may be stored in this state for long periods. Wrapped in cling film and frozen in solid CO2 for fluid saturation measurements. This is used for unconsolidated Dr. Paul Glover

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core. The samples are cooled using liquid nitrogen and are loaded into special containers. The containers can be transported packed in solid CO2, and stored in special freezers. Plugs can be cut from the core using liquid nitrogen as the cutting fluid, and the plugs are then immediately loaded into special coreholders again, and stored frozen. The sample is thawed out and tested without being removed from the special coreholders in which they were initially loaded.

4.5 Cleaning and Treatment of Preserved Core Treatment of preserved core for the tests mentioned above will be reviewed with the appropriate tests; but in general, sample plugs are drilled and trimmed using deoxygenated formation brine and stored under deoxygenated, depolarised kerosene or brine before testing. There are several methods of cleaning core. The actual method used will depend upon the properties of the core. Usually the optimum method will be clear from pre-screening information on the core. Pre-screening measurements include: • • • • • • •

Core description Core lithology Assessment of consolidation SEM analysis of mineralogy and pore structure Petrographic analysis of mineralogy and pore structure XRD/XRF analysis for bulk and clay mineralogies CT scanning to assess core heterogeneities, Figure 4.6 (cross-bedding, and fractures)

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This information is designed to identify possible problems with; (i) unconsolidated core, (ii) clay sensitivity, (iii) stress sensitivity, (iv) core mineralogical hetereogeneity, (v) core structural heterogeneity (e.g. fractures, vugs, fossils, and cross-bedding). The commoner specialist cleaning methods include: (i) (ii) (iii) (iv)

Critical point drying Cold miscible solvent flushing Hot miscible solvent flushing Direct fluid replacement (oil for oil and brine for brine)

Core cleaning, where appropriate, is most often carried out using miscible solvent flushing techniques. The core if confined in a Hassler holder (Figure 4.4a) and cold solvent flowed through it. Cleaning is usually complete after flowing three 200 ml alternating portions each of methanol and toluene. Under certain circumstances only one portion of each solvent will be used, although it is commoner to use at least three portions of each. This is applied to cores known to contain mobile fines or where it is necessary to retain wettability modifying crude oil components in their existing state. In some circumstances the evolved solvents need to be quantitatively tested using chemical techniques for the water content, and the oil content and composition. In this case special dry methanol is used, and the toluene is replaced with a more efficient solvent such as CS2 (very dangerous) or dichloromethane.

4.6 Unconsolidated Core Unconsolidated core gives rise to particular problems in coring, storage, handling and plugging. Its extremely friable nature means that any rough handling damages the pore structure irreversibly, and samples can turn into a pile of mud in your hand. The most common method of handling, shipping, storage, and plugging this type of core is in a frozen state. The core is frozen with liquid nitrogen or dry ice as soon as it emerges from the coring barrel. It is then placed in a special core holder for the relevant experiment to be carried out. Thawing inside the coreholder, prior to the experiment is only carried out after the sample has been fully supported with the relevant applied confining pressures (see above).

4.7 Water Analysis It is possible to obtain the initial water saturation and water composition from preserved whole core and core plugs by extracting the water. This is done by the Dean and Stark method. Figure 4.7 shows the Dean and Stark apparatus. The preserved sample is placed in a paper thimble in the large glass container and fluxed with hot solvent. The water evaporates, is carried by the solvent vapours into the long straight condenser in the top of the apparatus, cools, condenses and is trapped in the graduated part of the apparatus. The water saturation can be calculated by using the volume of the evolved water and a measurement of the porosity of the rock sample after the extraction process. The composition of the evolved fluids can also be analysed chemically, however, the water compositions more commonly used in SCAL applications derive from wireline formation testing.

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Porosity

Chapter 5: Porosity 5.1 Introduction and Definition Total porosity is defined as the fraction of the bulk rock volume V that is not occupied by solid matter. If the volume of solids is denoted by Vs, and the pore volume as Vp = V - Vs, we can write the porosity as:

V - Vs Vp Pore Volume φ= = = V V Total Bulk Volume

(5.1)

The porosity can be expressed either as a fraction or as a percentage. Two out of the three terms are required to calculate porosity. It should be noted that the porosity does not give any information concerning pore sizes, their distribution, and their degree of connectivity. Thus, rocks of the same porosity can have widely different physical properties. An example of this might be a carbonate rock and a sandstone. Each could have a porosity of 0.2, but carbonate pores are often very unconnected resulting in its permeability being much lower than that of the sandstone. A range of differently defined porosities are recognised and used within the hydrocarbon industry. For rocks these are: (i) (ii) (iii) (iv)

Total porosity Connected porosity Effective porosity Primary porosity

(v) Secondary porosity (vi) Microporosity (vii) Intergranular porosity (viii) Intragranular porosity (ix) Dissolution porosity (x) Fracture porosity (xi) Intercrystal porosity (xii) Moldic porosity (xiii) Fenestral porosity (xiv) Vug porosity

Defined above. The ratio of the connected pore volume to the total volume. The same as the connected porosity. The porosity of the rock resulting from its original depositional structure. The porosity resulting from diagenesis. The porosity resident in small pores (< 2 µm) commonly associated with detrital and authigenic clays. The porosity due to pore volume between the rock grains. The porosity due to voids within the rock grains. The porosity resulting from dissolution of rock grains. The porosity resulting from fractures in the rock at all scales. Microporosity existing along intercrystalline boundaries usually in carbonate rocks. A type of dissolution porosity in carbonate rocks resulting in molds of original grains or fossil remains. A holey (‘bird’s-eye’) porosity in carbonate rocks usually associated with algal mats. Porosity associated with vugs, commonly in carbonate rocks.

It should be noted that if the bulk volume and dry weight, or the bulk volume, saturated weight and porosity of a rock sample is known, then the grain density can be calculated. This parameter is commonly calculated from the data to compare the results with the known grain

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densities of minerals as a QA check. For example the density of quartz is 2.65 g cm-3, and a clean sandstone should have a mean grain density close to this value.

5.2 Controls on Porosity The initial (pre-diagenesis) porosity is affected by three major microstructural parameters. These are grain size, grain packing, particle shape, and the distribution of grain sizes. However, the initial porosity is rarely that found in real rocks, as these have subsequently been affected by secondary controls on porosity such as compaction and geochemical diagenetic processes. This section briefly reviews these controls.

5.2.1 Grain Size The equilibrium porosity of a porous material composed of a random packing of spherical grains is dependent upon the stability given to the rock by frictional and cohesive forces operating between individual grains. These forces are proportional to the exposed surface area of the grains. The specific surface area (exposed grain surface area per unit solid volume) is inversely proportional to grain size. This indicates that, when all other factors are equal, a given weight of coarse grains will be stabilised at a lower porosity than the same weight of finer grains. For a sedimentary rock composed of a given single grain size this general rule is borne out in Figure 5.1 (to the left). It can be seen that the increase in porosity only becomes significant at grain sizes lower than 100 µm, and for some recent sediments porosities up to 0.8 have been measured. As grain size increases past 100 µm, the frictional forces decrease and the porosity decreases until a limit is reached that represents random frictionless packing, which occurs at 0.399 porosity, and is independent of grain size. No further loss of porosity is possible for randomly packed spheres, unless the grains undergo irreversible deformation due to dissolution-recrystallisation, fracture, or plastic flow, and all such decreases in porosity are termed compaction.

5.2.2

Grain Packing

The theoretical porosities for various grain packing arrangements can be calculated. The theoretical maximum porosity for a cubic packed rock made of spherical grains of a uniform

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size is 0.476, and is independent of grain size. The maximum porosity of other packing arrangements is shown in Table 5.1 and Figure 5.2. Table 5.1 Maximum porosity for different packing arrangements Packing

Maximum Porosity (fractional)

Random Cubic Orthorhombic Rhombohedral Tetragonal

≥0.399 (dependent on grain size) 0.476 0.395 0.260 0.302

Figure 5.2 The porosities of standard packing arrangements.

5.2.3

Grain Shape

This parameter is not widely understood. Several studies have been carried out on random packings of non-spherical grains, and in all cases the resulting porosities are larger than those for spheres. Table 5.2 shows data for various shapes, where the porosity is for the frictionless limit. Figure 5.1 shows data comparing rounded and angular grains, again showing that the porosity for more angular grains is larger than those that are sub-spherical. Table 5.2 The effect of grain shape on porosity Grain Shape

Maximum Porosity (fractional)

Sphere Cube Cylinder Disk

≥0.399 (dependent on grain size) 0.425 0.429 0.453

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5.2.4

Porosity

Grain Size Distribution

Real rocks contain a distribution of grain sizes, and often the grain size distribution is multimodal. The best way of understanding the effect is to consider the variable admixture of grains of two sizes (Figure 5.3).

Figure 5.3 The behaviour of mixing grain sizes. Note that a mixture of two sizes has porosities less than either pure phase. The porosity of the mixture of grain sizes is reduced below that for 100% of each size. There are two mechanisms at work here. First imagine a rock with two grain sizes, one of which has 1/100th the diameter of the other. The first mechanism applies when there are sufficient of the larger grains to make up the broad skeleton of the rock matrix. Here, the addition of the smaller particles reduces the porosity of the rock because they can fit into the interstices between the larger particles. The second mechanism is valid when the broad skeleton of the rock matrix is composed of the smaller grains. There small grains will have a pore space between them. Clearly, if some volume of these grains are removed and replaced with a single solid larger grain, the porosity will be reduced because both the small grains and their associated porosity have been replaced with solid material. The solid lines GR and RF or RM in Figure 5.3 represent the theoretical curves for both processes. Note that as the disparity between the grain sizes increases from 6:3 to 50:5 the actual porosity approaches the theoretical lines. Note also that the position of the minimum porosity is not sensitive to the grain diameter ratio. This minimum occurs at approximately 20 to 30% of the smaller particle diameter. In real rocks we have a continuous spectrum of grain sizes, and these can give rise to a complex scenario, where fractal concepts become useful.

5.2.5 Secondary Controls on Porosity Porosity is also controlled by a huge range of secondary processes that result in compaction and dilatation. These can be categorised into (i) mechanical processes, such as stress

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compaction, plastic deformation, brittle deformation, fracture evolution etc., and (ii) geochemical processes, such as dissolution, repreciptation, volume reductions concomitant upon mineralogical changes etc. The effect of stress mediated compaction on porosity will be discussed in section 5.4. The effect of chemical diagenesis is more complex, and is better assessed for any given rock by examination of SEM or optical photomicrographs.

5.3 Laboratory Determinations There are many methods for measuring porosity, a few of which will be discussed below. Several standard techniques are used. In themselves these are basic physical measurements of weight, length, and pressures. The precision with which these can be made on plugs is affected by the nature (particularly surface texture) of the plugs.

5.3.1

Direct Measurement

Here the two volumes V and Vs are determined directly and used in Eq. (1). This method measures the total porosity, but is rarely used on rocks because Vs can only be measured if the rock is totally disaggregated, and cannot, therefore, be used in any further petrophysical studies. This measurement is the closest laboratory measurement to density log derived porosities.

5.3.2

Imbibition Method

The rock sample is immersed in a wetting fluid until it is fully saturated. The sample is weighed before and after the imbibition, and if the density of the fluid ρ is known, then the difference in weight is ρ Vp , and the pore volume Vp can be calculated. The bulk volume V is measured using either vernier callipers and assuming that the sample is perfectly cylindrical, or by Archimedes Method (discussed later), or by fluid displacement using the saturated sample. Vp and V can then be used to calculate the connected porosity. This is an accurate method, that leaves the sample fully saturated and ready for further petrophysical tests. The time required for saturation depends upon the rock permeability.

5.3.3

Mercury Injection

The rock is evacuated, and then immersed in mercury. At laboratory pressures mercury will not enter the pores of most rocks. The displacement of the mercury can therefore be used to calculate the bulk volume of the rock. The pressure on the mercury is then raised in a stepwise fashion, forcing the mercury into the pores of the rock (Figure 5.4). If the pressure is sufficiently high, the mercury will invade all the pores. A measurement of the amount of mercury lost into the rock provides the pore volume directly. The porosity can then be calculated from the bulk volume and the pore volume. Clearly this method also measures the connected porosity. In practice there is always a small pore volume that is not accessed by the mercury even at the highest pressures. This is pore volume that is in the form of the minutest pores. So the mercury injection method will give a lower porosity than the two methods described above. This is a moderately accurate method that has the advantage that it can be done on small irregular samples of rock, and the disadvantage that the sample must be disposed of safely after the test.

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Porosity

The mercury method also has the advantage that the grain size and pore throat size distribution of the rock can be calculated from the mercury intrusion pressure and mercury intrusion volume data. This will be discussed at further length in the section on capillary pressure.

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5.3.4

Porosity

Gas Expansion

This method relies on the ideal gas law, or rather Boyle’s law. The rock is sealed in a container of known volume V1 at atmospheric pressure P1 (Figure 5.5). This container is attached by a valve to another container of known volume, V2, containing gas at a known pressure, P2. When the valve that connects the two volumes is opened slowly so that the system remains isothermal, the gas pressure in the two volume equalises to P3. The value of the equilibrium pressure can be used to calculate the volume of grains in the rock Vs.. Boyle’s Law states that the pressure times the volume for a system is constant. Thus we ca write the PV for the system before the valve is opened (left hand side of Eq. (5.2)) and set it equal to the PV for the equilibrated system (right hand side of Eq. (5.2)):

P1 ( V1 − Vs ) + P2 V2 = P3 ( V1 + V2 − Vs )

(5.2)

The grain volume can be calculated:

P V + P2 V2 − P3 (V1 − V2 ) Vs = 1 1 ( P1 − P2 )

(5.3)

In practice P1, P2 and P3 are measured, with V1 and V2 known in advance by calibrating the system with metal pellets of known volume. The bulk volume of the rock is determined before the experiment by using either vernier callipers and assuming that the sample is perfectly cylindrical, or after the experiment and subsequent saturation by Archimedes Method (discussed later), or by fluid displacement using the saturated sample. The bulk volume and grain volume can then be used to calculate the connected porosity of the rock. Any gas can be used, but the commonest is helium. The small size of the helium molecule means that it can penetrate even the smallest pores. Consequently this

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Porosity

method gives higher porosities than either the imbibition or mercury injection methods. The method itself is very accurate, insensitive to mineralogy, and leaves the sample available for further petrophysical tests. It is also a rapid technique and can be used on irregularly shaped samples. Inaccuracies can arise with samples with very low. Low permeability samples can require long equilibration times in the helium porosimeter to allow diffusion of helium into the narrow pore structures. Failure to allow adequate time will result in excessively high grain volumes and low porosities.

5.3.5

Density Methods

If the rock is monomineralic, and the density of the mineral it is composed of is known, then the pore volume and porosity can be calculated directly from the mineral density and the dry weight of the sample. This method gives the total porosity of the rock, but is of no practical use in petrophysics.

5.3.6

Petrographic Methods

This method is used to calculate the two dimensional porosity of a sample, either by point counting under an optical microscope or SEM, or image analysis of the images produced from these microscopes. Commonly a high contrast medium is injected into the pores to improve the contract between pores and solid grains. This method can provide the total porosity, but is wildly inaccurate in all rocks except those that have an extremely isotropic pore structure. However, it has the advantage that pore types and the microtextural properties of the rock can be determined during the process.

5.3.7

Other Techniques

Other techniques include porosity by (i) analysing all evolved fluids (gas+water+oil) and assuming that their volume is equal to that of the pore space, (ii) CT scanning, and (iii) NMR techniques.

5.3.8

Bulk Volume Measurement

Most of the methods reviewed above require the knowledge of the bulk volume of the rock sample. Three ways are commonly used. These are (i) by using callipers, (ii) using fluid displacement, and (iii) using Archimedes’ method. Vernier Callipers If the rock is a perfect right cylinder with smooth surfaces, then calliper measurements of length and diameter can give quite an accurate bulk volume. In this case several measurements (approx. 10) are made of the length and the diameter, and the arithmetic mean of each is used. Repeatability and accuracy then depend mainly upon surface texture of the sample. Repeat helium expansion determinations of porosity on samples with smooth surface textures where the calliper bulk volume is used should fall within ±0.3 porosity percent regardless of actual porosity. Inaccuracies can arise with samples with very high permeability. High permeability sandstone samples are frequently friable, have large grain and pore sizes, and do not produce smooth surfaced right cylinders when plugs are drilled and accurate bulk volume determination becomes difficult. Straightforward measurement with

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Porosity

vernier callipers is not possible and Archimedes method or other liquid displacement methods have to be used. Fluid Displacement This method notes the displacement of fluid on a graduated scale when the rock sample is placed in a container containing the fluid. If the fluid automatically enters the pores errors will result. The method is commonly carried out with a non-wetting fluid such as mercury, or with other fluids with a sample that has already been saturated. Mercury displacement is carried out in a pyknometer fitted with a calibrated pump (Kobe method Figure 5.4). The sample is immersed in mercury during this test and will give erroneous results where mercury enters samples with very large pores. There is also a tendency to give high bulk volumes if air is trapped where the sample touches the top of the chamber. The Kobe method is used as the first part of the mercury injection method (Section 5.3.3). Archimedes Method The sample is weighed dry, fully saturated with formation brine whose density is accurately known. The saturated sample is then weighed suspended under a balance in air, and again while suspended in the fluid in which it is saturated. The various weight readings, and the density of the fluid allow the bulk volume of any irregular sample to be found accurately. The difference in the weight between the saturated sample suspended in air and that when suspended in the fluid is equal to Vsρf, where ρf is the density of the fluid. There are few sources of significant error in this method, provided no fluid drains from the plug whilst it is weighed in air. The most difficult part is judging how much excess fluid to remove from the surface of the plug. Vuggy limestones present particular problems which may only be overcome by whole core measurements. The contents of vugs exposed on the plug surface may have been disturbed during drilling. Internal vugs may be partially filled with solids from the drilling fluid during the coring process. If exposed vugs are genuinely part of the pore volume, then bulk volume must be obtained by calipering since these will not be taken account of by liquid immersion techniques.

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Porosity

It should be noted that these are all laboratory methods. Well logging utilises several other different techniques, which all have larger errors associated with them. These are based on acoustic, electromagnetic, NMR, and radioactive processes.

5.4 Influence of Stress SCAL porosity measurements have to be done at overburden pressure if they are to be correlated with downhole measurements. These measurements are made using the overburden cell (Figure 5.6) attached to a helium expansion porosimeter. Pore volume changes can also be observed whilst measuring formation factor at overburden pressures. It is not possible to repeat determinations without allowing time for stresses in the core to be relieved. It is conceivable that permanent damage could result when applying overburden to poorly cemented cores, thus if a plug has to be used for a number of tests, overburden measurements should form the later stages of the test sequence. As with routine poroperms, whole core measurements may be necessary if samples are vuggy, fractured or contain stylolytes. The precision of the data obtained is similar to that of routine poroperms. Care has to be taken that samples are given sufficient time to allow compaction to occur at each overburden pressure. The resulting porosity data is usually displayed as a fraction of that at ambient pressure as function of overburden pressure (Figure 5.7), or as pore volume compressibility (pore volume/pore volume/psi), as shown in Figure 5.8.

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Porosity

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Chapter 6: Single Phase Permeability 6.1 Introduction and Definition Permeability is a property of a porous medium that characterises the ease which fluids flow though it in response to an applied fluid pressure gradient. The primary objective for permeability measurements applied to the hydrocarbon industry is that they should be fit for purpose. In this case the purpose is to provide data that can be used in accurate and effective reservoir modelling. If the reservoir model is to be used to help the understanding of a dry gas reservoir at ambient conditions, then horizontal air permeability measurements at ambient conditions will be fine. However, the reservoirs that are of interest are rarely so simple, and it should be our aim to build multi-phase models capable of modelling oil reservoirs at in situ conditions. Fluid permeabilities measured at or corrected to relevant reservoir conditions using relevant fluids are essential inputs if such models are to be representative of the reservoir. The fluid saturation and number of mobile fluids have a great effect on permeability, reducing it below that for a dry rock containing a single fluid. This section will deal with single phase fluid permeabilities. In particular the gas and Klinkenberg permeability measurements that are made as part of RCAL, and the single phase liquid permeabilities that are part of the more complex relative permeability SCAL tests, but which are sometimes carried out on their own as part of RCAL.

6.1.1 Basic Definitions Feynmann once said that, for a scientific measurement to be successful, the scientist or engineer must know exactly what he or she is measuring. This comment has many implications for the scientist. For the reservoir engineer/petrophysicist it requires that the meaning of permeability is understood. So back to basics; permeability characterises the ease with which fluids flows through a medium in response to a fluid pressure gradient. However, permeability is not measured directly, but calculated from other physical measurements with various theoretical and empirical relationships. The dependence on these relationships has the implication that the resulting permeabilities are dependent on various assumptions and boundary conditions. The relationship used in the hydrocarbon industry is the empirically derived Darcy’s Law in 1856, derived using the apparatus shown in Figure 6.1.

q=KA

(P − Pout ) ∆h = K A in L L

(6.1)

where: q = water flow rate A = cross-sectional area of sand pack L = length of sand pack ∆h = difference between the water heights in the manometers in Figure 6.1 (h1-h2) K = A constant of proportionality characteristic of the sand pack (permeability) Pin-Pout = fluid pressure gradient.

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The units of permeability used in the oil industry are the ‘darcy’, D, and the ‘millidarcy’, mD. It is worth noting that the S.I. unit of permeability is in per metres squared (m-2), and shows that there is an implicit spatial scaling of permeability in the measurement itself. This fact is often overlooked when we use core measurements made at core plug scale (core volume approximately 40 cm3), and then happily (and naively) compare it directly with logging measurements, whose scale volume (volume of sensitivity) is 15000 cm3, and model reservoir wide processes, whose scale volume may be approximately 1015 cm3! A permeability of 1 D allows the flow of 1 cm3 per second of water with 1 centipoise, cP, viscosity, through a crosssectional area of 1 cm2, when a pressure gradient of 1 atmosphere pressure per centimetre is applied. (1 D ~ 10-12 m-2.) It should be understood that Darcy’s law, Eq. (6.1), was derived for unconsolidated sand packs, assumes unreactive aqueous fluids with constant properties, and requires correction for the different viscosity of different fluids, and correction for gas slippage (Klinkenberg effect)

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and inertial effects (Forchheimer effect) if used with gaseous fluids. In practice it is applied to all rocks even though it is not clear that this is a valid extrapolation. One should, therefore, always question the accuracy of a core permeability measurement. The law, Eq. (6.1), has been extended for practical use in the following ways: • • • •

Inclusion of a fluid dynamic viscosity so that unreactive fluids other than brines can be used. Rewriting the ∆h term in terms of absolute pressures. Writing the flow rate, q, as volume flow per time (q=V/t). Inclusion of a constant to take account of the units commonly used in measurement.

Thus the working equation for measuring single phase liquid permeabilities in the hydrocarbon industry is:

K( mD) = 1000 µ

L V 1 A t P − P 1 2

(

)

(6.2)

If gas is used we must take account of the compressibility of the gas giving the working equation for measuring single phase gas permeability in hydrocarbon industry RCAL:

K( mD) = 2000 µ where: K µ L A V t q P1 P2 Patm

= = = = = = = = = =

Patm L V A t P2 − P2 2 1

(

)

(6.3)

permeability, (millidarcies, mD) viscosity, (centipoise, cP) plug length (cm) plug cross section (cm2) volume of fluid passed in t seconds (cm3) time (seconds) Flow rate, q=V/t, cm3s-1 inlet pressure (atmospheres absolute) outlet pressure (atmospheres absolute) atmospheric pressure (atmospheres absolute)

Gas permeability measurements are the most common RCAL permeability measurements. These measurements suffer from two problems that are not encountered with liquid permeabilities. These are the Klinkenberg and Forchheimer effects.

6.1.2 The Klinkenberg Effect Darcy’s modified law for gases Eq. (6.3) is not applicable at low gas pressures (gas densities). This is because, at such low pressures, the mean free path of the gas molecules become larger than the pore dimensions. When this happens, the gas cannot be considered to be a continuous medium and fluid mechanics cannot be used reliably. In practice the effect causes measured permeabilities to be overestimated at low pressures (Figure 6.2a). In the low density (gas pressure) limit the permeability is expressed as:

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α K app = K L 1 +   P


(6.4)

Here the apparent or measured permeability Kapp is dependent on the so-called Klinkenberg permeability KL, the gas pressure P and a constant known as the slip factor, α. The standard solution to the problem involves the following steps: • • •

Repeating the measurement of gas permeability, Kapp, at four or five different gas inlet pressures, P1 and gas outlet pressures, P2. Calculating the mean gas pressure in the core for each determination; Pmean = (P1 + P2)/2. Plotting Kapp against 1/Pm.

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The resulting plot is a straight line with a positive gradient (Figure 6.2b). The intersection of the curve with the x-axis at 1/Pm = 0 gives KL . The Klinkenberg permeability is independent of gas pressure, and is effectively the permeability of the gas as P→∞, i.e. the permeability for a near perfect liquid (an infinitely compressed near perfect gas). The values of apparent permeability depend on the type of gas used even though their different viscosities are taken into account in the calculation of apparent permeability. However, the Klinkenberg permeability is independent on the type of gas used as all gases have the same properties in the P→∞ limit (Figure 6.2c). This makes the Klinkenberg permeability very useful, for it can be compared for different samples that had their gas permeabilities measured with different gases at different gas pressures. The Klinkenberg permeability should be approximately the same as the permeability of the rock when 100% saturated with a single phase reservoir liquid such as water or oil. The gradient of the Klinkenberg plot gives the slip factor, which can be used to characterise the rock microstructure. The Klinkenberg correction should be applied to all core analysis measurements without fail.

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6.1.3 The Forchheimer Effect At high gas flow rates (high differential pressures P1-P2), the gas accelerates through pore throats and decelerates in pore bodies sufficiently for the gas inertia to cause turbulence. Darcy’s law is an approximation of Navier-Stokes law, both of which require flow to be laminar. Thus when the flow rate is fast enough for the flow to be turbulent, neither work. In practice such high flow rates are avoided in all core analysis measurements. If they are encountered they show up as underestimates in gas permeability measurements that are recognised as an increase in the gradient of the K versus 1/Pm curve at low values of 1/Pm.

6.1.4 Averaging Permeabilities It has been shown that the most probable permeability behaviour of a heterogeneous porous medium made up of n randomly distributed regions of differing uniform permeabilities, K1 to Kn, is described by the geometric mean of the individual permeabilities, which corresponds to the mode of a log-normal distribution:

K g = n K1 ⋅ K 2 ⋅ K 3 ⋅ ⋅ ⋅ K n

(6.5)

The analysis is extremely complex. However, it is possible to analyse two simple systems of different permeabilities that occur within core analysis and reservoir systems. These are (i) flow through linear beds in series, and (ii) flow through linear beds in parallel. Linear Beds in Series. The system is shown in Figure 6.3a. The beds have a cross-sectional area A that is constant. Each bed has a thickness, Ti , and a uniform permeability Ki. The pressures at the contact between each of the beds, Pi. can be analysed thus:

(P1 − P4 ) = (P1 − P2 ) + (P2 − P3 ) + (P3 − P4 )

(6.6)

Now using Eq. (6.1) with ∆h replaced by the pressure difference, and noting that the thickness of the total unit T is equal to the sum of the individual beds T1 etc., we get:

q T3 q T1 q T2 qT = + + K A K1 A K 2 A K 3 A

(6.7)

Rearranging we find that the mean permeability is the harmonic average of the individual permeabilities:

Kh = n

T

∑ {Ti K i }

(6.8)

i =1

For example analysing Figure 6.3b, where three layers of equal thickness T=1 m have permeabilities 1000 mD, 200 mD, and 1 mD, we get the mean permeability equals 2.98 mD!

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Clearly the permeability is controlled by the smallest permeability because all the fluids that pass easily through the higher permeability layers are held up by the low permeability layer. Linear Beds in Parallel. The system is shown in Figure 6.3c. The beds have a thickness T that is constant. Each bed has a cross-sectional area to flow, Ai , and a uniform permeability, Ki. The pressures at the inlet P1 and outlet P2 of the complete unit will be the same for all layers, but each layer will transport a different fraction qi of the total flow rate qt thus:

q t = q1 + q 2 + q 3

(6.9)

Now using Eq. (6.1), with ∆h replaced by the pressure difference and noting that the total area A = A1+A2+A3, we get:

K A ( Pin − Pout ) K1 A1 ( Pin − Pout ) = + T T K 2 A 2 ( Pin − Pout ) K 3 A 3 ( Pin − Pout ) + T T

(6.10)

Rearranging we find that the mean permeability is the arithmetic average of the individual permeabilities:

n

∑ Ki Ai K a = i=1

A

(6.11)

For example, analysing Figure 6.3d, where three layers of equal area A = 1 m2 have permeabilities 1000 mD, 200 mD, and 1 mD, we get the mean permeability equals 400 mD! The mean permeability falls much more into the mid range because the fluids partition for flow into each of the layers depending on its permeability. In this case, the layer with the highest permeability conducts 83.3% of the flow. For comparison, the geometric mean of equal volumes of 1000 mD, 200 mD, and 1 mD is 10.6 mD, which falls between the two extreme cases analysed above, and represents random arrangement of equal volumes of material with these three permeabilities.

6.1.5 Notes on RCAL Permeabilities Gas permeabilities corrected for the Klinkenberg effect are commonly used, however this measurement provides the most optimistic values of permeability mainly due to the measurement being done for; (i) single phase gas fluids that are not representative of the true reservoir fluids, (ii) low overburden pressures and temperatures that are not representative of the in situ reservoir conditions, and (iii) cleaned dry rocks. Other measurement methods account for these problems, but are more expensive, and often we are asked to use Klinkenberg permeabilities where better measurements are unavailable. It is therefore important for us to understand the factors affecting the determination of permeability

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measurements, such that the quality and relevance to the problem of any permeability dataset can be assessed. The factors affecting core permeability measurements fall into three broad categories; (i) planning errors, (ii) sample errors, (iii) measurement errors, and (iv) analysis errors. Planning errors are the fault of the person who commissions the permeability study. It is very tempting to order a standard routine core analysis study. However, resources and time can be saved by the commissioning manager thinking carefully about the purpose that the data is required for. Klinkenberg permeabilities should not be used to estimate the efficiency of a waterflood, yet some companies do so by correcting them to effective relative permeabilities using rules of thumb that do not take account of the fluids and reservoir wettability adequately. Sample errors are associated with; (i) sampling frequency, location, orientation, type and size; all of which affect how representative the 40 cm3 sample is of the properties of the 1015 cm3 sized reservoir, (ii) the type of drilling fluids, and (iii) the state of preservation and the process of cleaning and drying, which can affect permeability greatly in shaly sandstones. Measurement problems are related to the accurate measurement of pressure and flow, and are dependent both on the initial experimental rig design as well as the permeameter operator. Finally, Analysis problems involve the relevant use of the derived data and close the circle to the planning stage. The indiscriminate lumping together of permeability data from different measurement techniques, bad poroperm cross-plot analysis, and inefficient core-log correlation of poroperm data, all contribute to inaccurate analysis, and almost always are the result of either ignorance of the meaning and limitations of permeability data, or an effort to ‘make do’ with irrelevant data resulting from poor permeability study planning.

6.2 Controls on Permeability 6.2.1

Porosity

There have been several attempts to derive a general relationship between porosity and permeability. In many ways, however, all attempts are bound to fail at a fundamental level since porosity is a scalar measurement and permeability is a vector measurement. Clearly though it is reasonable to assume that permeability should increase with porosity in unfractured reservoirs without significant diagenetic. One of the most well known models linking porosity and permeability is known as the Kozeny-Carman model that considers the porous media to be made up of bundles of capillary tubes. The basic equation is:

K KC = where: KKC c d φ

= = = =

c d2 φ 3

(1 − φ )

2

(6.12)

Kozeny-Carman predicted permeability, mD A constant Median grain size diameter, microns Effective porosity

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Another commonly used empirical model is that of Berg:

K B = d 2 φ 5.1

(6.13)

where KB is the predicted permeability. Although this empirical model has been concocted from a range of rocks and it is clear that the equation may not work on samples from other locations. Recently, a new model has been proposed by Revil, Glover, Pezard and Zamora (RGPZ). This is a non-empirical model that is derived from the fundamental understanding of the electrokinetic properties of rocks, and hold the potential for improved permeability prediction for rocks of different porosities, grain sizes, and pore tortuosities. It is expressed as:

K RGPZ = where: KRGPZ m d a φ

= = = = =

Dr. Paul Glover

d 2 φ 3m 4am

2

(6.14)

RGPZ predicted permeability, D The cementation exponent Median grain size diameter, microns Grain packing index Effective porosity

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Note that all of these models use a grain size diameter to scale the predicted permeability to the size of rock microstructure, and to ensure that the models are dimensionally correct. Figure 6.4 compares the three models described above for a range of clean sandstone, shaly sandstone, and carbonate samples. Lines are placed at 1 mD in Figure 6.4; rocks with permeabilities less than this value are considered to be non-reservoir rock (i.e. unproducible economically).

6.2.2

Bedding

Permeability is a vector property, and as such, is greatly affected by directional heterogeneity within core samples. The commonest cause of such heterogeneities is bedding. It is a general rule that the vertical permeability within a reservoir (i.e. that perpendicular to the bedding) is lower than that in the bedding plane (horizontal permeability). In fact the vertical permeability is often about a third of that in the horizontal direction. It should also be noted that some of the difference between the vertical and horizontal permeabilities results from differences in the way the local stress fields in the vertical and horizontal directions compact pores and close microcracks.

6.2.3

Pore Geometry

Permeability is highly dependent on the tortuosity of the pore fluid flow paths. Tortuosity can be affected by many rock characteristics, including: • • • • • • • • • •

Grain size and its distribution Grain shape Sorting Grain orientation Packing arrangement Degree and type of cementation Amount, orientation and connectivity of micro-fractures Clay content Bedding Diagenesis

The detailed relationships are known only qualitatively, and the relative importance of each vary from rock type to rock type. For example, the permeability of carbonates is primarily controlled by; (i) dissolution porosity, (ii) dolomitization, and (iii) fractures.

6.2.4

The Stress Conditions

Permeability is very sensitive to stresses that compact the rock. This compaction can occur in any direction not just vertically. However, vertical compaction is usually the most important. Indeed the local stress state may be such that dilatancy occurs (formation of fractures) increasing the permeability of the rock. In all cases it is poorly consolidated rocks that are affected to the greatest extent. Figure 6.5a and b show the effect of increasing the hydrostatic confining pressure on the permeability of a rock. Figure 6.5c compares the effect of overburden stress on permeability compared to the effect upon porosity. It can be seen that overburden stress affects permeability much more than porosity. This is because permeability

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is very sensitive to the tortuosity of fluid flow paths through the rock, and such changes are associated with very small changes to the rock porosity Overburden stress compacts the rock pressing the grains together. The size of the pores reduces little, but the pore throats that control the passage of gas between the pores undergo much greater closure, effecting the permeability to a greater extent. The large decreases observed indicate that it is very important to apply corrections to permeabilities measured at low confining pressures before they are considered to be representative of the reservoir, or measure the permeability at reservoir stress conditions in the first place (SCAL). It should also be noted that fracturing (both macroscopic and microfractures), that increases the permeability of the rock samples when measured in the laboratory, can be caused by drilling and concomitant upon the sudden reduction in stress experienced by the rock upon extraction of the core from the well. These fractures can be closed again by measuring the rock at reservoir conditions, but it is very difficult to know how to correct low pressure Klinkenberg permeability determinations for such fracturing.

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6.3 Laboratory Determinations 6.3.1

Steady State Gas Permeability Determinations

Routine permeability measurements are made by confining plugs in Hassler core holders, Figure 6.6, applying nitrogen pressure to one end and measuring flow rate and pressure differential. Figure 6.7 shows a steady state gas permeability rig that is equipped to measure a large range of permeabilities (i.e. gas flow rates). Standard hydrocarbon industry rigs look similar, but have fewer options for measuring upstream pressure and flow rate.

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For plugs having moderate permeabilities, 5-500 mD, repeat determinations at given confining, inlet and outlet pressures should fall within a few percent. Normally four or five consecutive measurements are made at various mean pressures (Pm) to enable a Klinkenberg plot (Figure 6.2b) of permeability vs. 1/Pm to be made. Extrapolation to infinite mean pressure gives the equivalent liquid permeability, KL. Permeabilities above about 500 mD become less precise as the measured pressure differential falls leading to higher experimental errors. High permeabilities also imply large pores, large grains and rough surface texture.

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Very rough surfaces may need wrapping in soft PTFE tape or repair with epoxy to ensure proper sealing by the Hassler sleeve. The sleeve pressure used will depend upon plug surface texture and the hardness of the rubber sleeve. Low permeabilities (less than 5 mD) do not normally present any problems; but for normal reservoir applications, a cut off value of 0.01 mD is applied. Values below this are simply reported as less than 0.01 mD, and are not interesting as a reservoir. In practice rocks with permeabilities less than 1 mD are considered to be non-reservoir rock (i.e. unproducible economically). If cap rocks are being investigated, the actual permeability values will be reported, whatever their permeability. Caution is needed in the handling of friable, poorly cemented samples. Gradual compaction can occur even with sleeve pressures as low as 400 psi. Consequently long equilibration times may be necessary for this type of sample. The first indication of this type of behaviour occurs when carrying out the normal repeat timings of gas flow, when steadily decreasing flow rates are observed.

6.3.2

Unsteady State Gas Permeability Determinations

This is not as standard as the steady state method. It applied a volume of gas at a high initial pressure to one end of the sample and then measures the decay of the pressure as the gas leaks away through the core. One advantage of this method is that it can be used to determine the permeability of very low permeability rocks. It has therefore been used to measure the permeability of cap rocks. It must be said, however, that leakage through cap rocks is now recognised to depend primarily on fractures through the cap rock rather than the permeability of the bulk rock itself, and so these measurements are being done less and less.

6.3.3

Steady State Liquid Permeability Determinations

Permeabilities to oil and water at 100% saturation of each fluid, or of oil in the presence of Swi can also be easily carried out. The saturated samples are placed in a core holder. The required fluid is flowed through the sample, while measuring the steady state volume flow and pressure differential (see Figure 6.8 for a schematic diagram of a typical permeameter set-up). All fluids used should be degassed prior to use. The permeability is calculated from Eq. (6.2). There is no need to institute a Klinkenberg correction, but the data is carefully examined to ensure that the flow is laminar by carrying the test out at various flow rates and checking whether they all give approximately the same permeability. Those high flow rates that are suspected to contain turbulent (Forchheimer) effects are discarded.

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The values of permeability Kw at Sw=1 or Ko at So=1 should be approximately the same as the Klinkenberg permeability, KL. Ko at Sw=Swi and So=1-Sw will be less that that at So=1.

6.4 Data Handling The correlation of core and logging data enable reservoirs to be assessed for production potential. The full description of this process is outwith the scope of this course. However, we will briefly examine some of the issues related to the correlation of core measurements with logs, and the use of permeability measurements in poroperm cross-plots.

6.4.1

Core-Log Comparison

The comparison of porosity and permeability data from core measurements and log methods is important to ensure that there is good agreement between them, allowing the measurements to be used in reservoir modelling with confidence. The process should compare the log and core data on the same log-type display (Figure 6.9). It is usually clear whether one of the curves needs to be depth shifted relative to the other. If a shift is necessary it is usually implemented for the core data, as uncertainties in core depth occur when there is not 100% core recovery

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form the hole. Corrections of 10 to 20 m are not uncommon. When comparing the depth corrected core and log data it is usually clear whether there is a good match between the two. The degree of match is an average determination made by eye as the two measurements will rarely be in very close agreement. This is because the measurements are made by widely varying techniques, with varying scales of measurement. For example, a standard core plug will have a volume of investigation of about 40 cm3, compared to approximately 15000 cm3 for a wireline tool. Additionally, the various methods measure different properties. For example core porosities are usually measurements of effective porosities (with non-connected porosity and clay bound water excluded, and usually avoiding fractures), whereas log derived porosities are generally measurements of total porosity. This results in the log porosities being generally a little higher than the log-derived porosities.

6.4.2

Poroperm Cross-plots

Permeability is of incredible interest to the hydrocarbon industry as it describes how profitable fluids can be extracted from reservoirs. Clearly, any way of predicting permeability is of great interest too. One of the fundamental processes that is applied to permeability data is to plot it on a log-lin permeability-porosity diagram (Figure 6.10). Often there is a relationship within a given rock unit, and differences between rock units can be useful in the analysis of the reservoir. The main aims are:

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• •


To estimate permeability where only porosity data is available (e.g. In Figure 6.10, a conglomerate with a porosity of 13.3% has a permeability of 100 mD). To establish a porosity cut-off below which the reservoir is unproductive (e.g. the data in Figure 6.10 has porosity cut-offs of 5.3% in the conglomerate and 10.7% in the sandstone, corresponding to a permeability of 1 mD..

This method is very powerful if used in an homogeneous formation, but can produce remarkably erroneous results if carried out badly. There are a few points to bear in mind when using cross-plots: • • • • •

Some positive correlation between porosity and permeability exists for non-fractured, nonvuggy rocks with the same degree of diagenesis (Figure 6.11). The estimation method is based on a mathematical correlation that only takes account of porosity and permeability. No other factors are taken account of (e.g. diagenesis, fractures, vugs). The log permeability scale can generate large permeability errors. The cross-plot should be done for each individual rock unit if the relationship is to be valid. Doing a cross-plot for the whole reservoir is a waste of time. Individual cross-plots for each mineralogy/lithology and/or based upon grain and pore size information from mercury porosimetry. Individual permeability zones can also be delineated by plotting the distribution of permeabilities on a lin-log plot. This results in a log-normal distribution for well controlled permeability data (see section 6.1.4). If the distribution is unimodal (Figure 6.12a) then a cross-plot for all the data will be valid. If the distribution is multimodal (Figure 6.12b) then a cross-plot must be done for the data belonging to each of the

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• •


unimodal populations making up the multi-modal dataset (3 in the case of Figure 6.12b). There are statistical tests that can distinguish which population a sample belongs to, e.g. the Kolmogorov-Smirnoff test. Some rocks do not produce a clear relationship (e.g. commonly carbonates). There is no physical basis for this type of plot. In fact reference to Eqs. (6.12) to (6.13) indicates that a log-log plot would be more appropriate, and Eq. (6.14) indicates that a linlin plot of permeability against φ3m/m2 would provide the best results.

There are two other important points to bear in mind. First, for the cross-plot to be the most valid, it should be done with permeabilities and porosities that are representative of the reservoir. This means that the permeabilities should be Klinkenberg corrected, and both permeabilities and porosities should be corrected to reservoir stress conditions. Any derived permeabilities are then the permeabilities for complete saturation of the rock with the test fluid, and will need to be reduced to relative permeabilities if required. If drill stem test permeabilities are used, then these will have been made in the presence of multi-phase fluids, and it is important to know more about the fractions of each fluid present and the wettability of the rock before valid deductions can be made. The second point is that the porosities from core measurements are effective porosities, whereas those from log measurements are commonly total porosities. If data from both sets are to be used, then they must be reconciled Dr. Paul Glover

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before use. Figure 6.13 shows the typical ranges of poroperm relationships for various lithologies and rock microstructure.

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Wettability

Chapter 7: Wettability 7.1 Introduction and Definition There exists a surface tension between a fluid and a solid, in the same way that a surface tension exists between an interface between two immiscible fluids (cf. the surface tension on water under air that is sufficient to support the weight of a needle.). When two fluids are in contact with a solid surface, the equilibrium configuration of the two fluid phases (say air and water) depends on the relative values of the surface tension between each pair of the three phases (Figure 7.1). Let us denote surface tension as γ, and solid, liquid and gas as s, l, and g respectively. Each surface tension acts upon its respective interface, and define the angle θ at which the liquid contacts the surface. This is known as the wetting (or dihedral) angle of the liquid to the solid in the presence of the gas. Equilibrium considerations allow us to calculate the wetting angle from the surface tensions:

γ lg cos θ = γ sg − γ sl

(7.1)

This is known as Young’s equation (1805). Table 7.1 shows some contact angles and surface tensions for common fluids in the hydrocarbon industry. Table 7.1 Contact angles and interfacial tension for common fluid-fluid interfaces Interface

Air-Water Oil-Water Air-Oil Air-Mercury

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Contact Angle, θ, degrees

cos θ

Interfacial Tension, dynes/cm

0 30 0 140

1.0 0.866 1.0 -0.765

72 48 24 480

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Wettability

Note that: • •

If γsg > γsl , then cosθ > 0 and θ <90o. If γsg < γsl , then cosθ < 0 and θ >90o.

For a stable contact | cosθ | ≤ 1, or equivalently | γsg - γsl | ≤ γgl . This inequality is not satisfied when γlg + γsl < γsg, when liquid covers the whole solid surface. Alternatively, when γlg + γsg < γsl, the gas displaces the liquid away from the surface completely. Figure 7.2 shows a range of different wetting conditions.

When one fluid preferentially covers the surface, it is called the wetting fluid, and the other fluid is called the non-wetting fluid. The origin of these surface tensions arises in the different strengths of molecular level interactions taking place between the pairs of fluids. For example a quartz sandstone grain generally develops greater molecular forces between itself and water than between itself and oils. Clean sandstones are therefore commonly water wet. However, should that same grain have been baked at high temperatures in the presence of oil at depth, then (i) its surface chemical structure can be altered, or (ii) the surface itself can become coated, in such a way that results in the grain having greater molecular interaction with oils than water, and hence become oil wet. IMPORTANT NOTE Properly measured wettabilities on well preserved core and core plugs should form the initial step in choosing relative permeability test methods.

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Wettability

7.2 Laboratory Determination There are several methods for determining wettability of a rock to various fluids. The main ones are: (i) Microscopic observation This involves the direct observation and measurement of wetting angles on small rock samples. Either a petrographic microscope or SEM fitted with an environmental stage is used. The measurements are extremely difficult, and good data relies more on luck than judgement. (ii) Amott wettability measurements This is a macroscopic mean wettability of a rock to given fluids. It involves the measurement of the amount of fluids spontaneously and forcibly imbibed by a rock sample. It has no validity as an absolute measurement, but is industry standard for comparing the wettability of various core plugs. (iii) USBM (U.S. Bureau of Mines) method. This is a macroscopic mean wettability of a rock to given fluids. It is similar to the Amott method but considers the work required to do a forced fluid displacement. As with the Amott method, it has no validity as an absolute measurement, but is industry standard for comparing the wettability of various core plugs. (iv) NMR longitudinal relaxation and other wettability methods. These are briefly summarised in Table 7.2. Table 7.2 Summary of Wettability Measurement Techniques Measurement Technique

Physical Observation

Amott and Amott-Harvey

Amounts of oil and water imbibed by a sample spontaneously and by force. Work required to imbibe oil and water. Microscopic examination of the interaction between the fluids and the rock matrix. Changes in longitudinal relaxation time. The distribution of grains at water/oil or air/water interfaces. Displacement of the non-wetting fluid from a glass slide. Shape and magnitudes of Kro and Krw curves. Resistivity logs before and after injection of a reverse wetting agent. Adsorption of a dye in an aqueous solvent.

U.S. Bureau of Mines (USBM) Microscopic examination Nuclear Magnetic Resonance Flotation method Glass slide method Relative permeability method Reservoir logs Dye adsorption

The first two methods are the commonest within the oil industry and are described in greater detail in the next two sections.

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7.2.1

Wettability

Amott Wettability Measurements

Wettability measurements by the Amott method give a guide to the relative oil or brine wetting tendencies of reservoir rocks. This can be crucial in the selection of relative permeability test methods to generate data relevant to the reservoir situation. It is not always possible to reproduce reservoir wettabilities in room condition relative permeability tests. However, an appreciation of the difference between reservoir and laboratory wettabilities can assist in interpretation of laboratory waterfloods. The Amott method (Figure 7.3) involves four basic measurements. Figure 7.4 shows the data produced with the water wetting index given by AB/AC and the oil wetting index by CD/CA. (i) (ii) (iii) (iv)

The amount of water or brine spontaneously imbibed, AB. The amount of water or brine forcibly imbibed, BC. The amount of oil spontaneously imbibed, CD The amount of oil forcibly imbibed, DA

Figure 7.4 shows the initial conditions of the sample (point X) to be oil saturated at Swi. The spontaneous measurements are carried out by placing the sample in a container containing a known volume of the fluid to be imbibed such that it is completely submerged (steps 1 and 3 in Figure 7.3 for water and oil respectively), and measuring the volume of the fluid displaced by the imbibing fluid (e.g. oil in step 1 of Figure 7.3). The forced measurements are carried out by flowing the ‘imbibing’ fluid through the rock sample and measuring the amount of the displaced fluid (steps 2 and 4 in Figure 7.3), or by the use of a centrifuge. The important measurements are the spontaneous imbibitions of oil and water, and the total (spontaneous and forced) imbibitions of oil and water. Water-wet samples only spontaneously imbibe water,

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Wettability

oil-wet samples only spontaneously imbibe oil, and those that spontaneously imbibe neither are called neutrally-wet. The wettability ratios for oil (AB/AC) or water (CD/CA) are the ratios of the spontaneous imbibition to the total imbibition of the each fluid.

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Wettability

In general use the samples to be measured are centrifuged or flooded with brine, and then flooding or centrifuging in oil to obtain Swi. The standard Amott method is then followed. At the end of the experiment the so called Amott-Harvey wettability index is calculated:

SpontaneousWaterImbibition SpontaneousOilImbibition − TotalWaterImbibition TotalOilImbibition AB CD = − AC CA

Index=

(7.2)

Wettability indices are usually quoted to the nearest 0.1 and are often further reduced to weakly, moderately or strongly wetting. The closer to unity the stronger the tendency.

7.2.2

USBM Wettability Measurements

This method is very similar to the Amott method, but measures the work required to do the imbibitions. It is usually done by centrifuge, and the wettability index W is calculated from the areas under the capillary pressure curves A1 and A2:

W=log

A1 A2

(7.3)

where, A1 and A2 are defined in Figure 7.5. Note that in this case the initial conditions of the rock are Sw=100%, and an initial flood down to Swi is required (shown as step 1 in Figure 7.5), although either case may be necessary for either the Amott or USBM methods. Figure 7.6 shows typical USBM test curves for water wet, oil wet and neutrally wet cores.

7.2.3

USBM and Amott Technique Comparison

Warning. While both methods are common within the oil industry, they show remarkable differences especially near the neutral wettability region. In general, the Amott method is probably the most reliable and accurate especially in the neutral wettability region. A comparison of the two methods, together with contact angles, is given in Table 7.3. Table 7.3 Comparison of the Amott and USBM Wettability Methods

Amott wettability index water ratio Amott wettability index oil ratio Amott-Harvey wettability index USBM wettability index Minimum contact angle Maximum contact angle

Dr. Paul Glover

Oil Wet

Neutral Wet

Water Wet

0 >0 -1.0 to -0.3 about -1 105o to 120o 180o

0 0 -0.3 to 0.3 about 0 60o to 75o 105o to 120o

>0 0 0.3 to 1.0 about 1 0o 60o to 75o

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7.3

Wettability

Sample Preservation and the Effect on Wettability

Sample preservation, preparation, storage and test conditions are important since wettability is sensitive to oxidation of crude oil and to temperature. Preservation of samples at the well-site is generally by wrapping in foil and wax coating. The process should be carried out as soon as possible after removal of the core from the barrel. Samples are drilled and trimmed with deaerated, simulated depolarised kerosene prior to testing. Tests carried out to assess reservoir wettability must be made on preserved core at a temperature high enough to ensure that any wax present in the residual core remains in solution. If the wax precipitates, it will tend to increase the oil wetting tendency of the core. Room condition wettabilities may only apply to reservoirs containing wax free crude or cleaned cores from laboratory tests.

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Wettability

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Capillary Pressure

Chapter 8: Capillary Pressure 8.1 Introduction and Theory Capillary pressure data are required for three main purposes: • • •

The prediction of reservoir initial fluid saturations. Cap-rock seal capacity (displacement pressures). As ancillary data for assessment of relative permeability data.

Capillary pressures are generated where interfaces between two immiscible fluids exist in the pores (capillaries) of the reservoir rock. It is usual to consider one phase as a wetting phase and the other as a non-wetting phase. However, intermediate cases occur which can greatly complicate the picture. The drainage case, i.e. a non-wetting phase displacing a wetting phase applies to hydrocarbon migrating into a previously brine saturated rock. Imbibition data is the opposite to drainage, i.e. the displacement of a non-wetting phase by a wetting phase. Thus, the drainage data can usually be used to predict non-wetting fluid saturation at various points in a reservoir, and the imbibition data can be useful in assessing the relative contributions of capillary and viscous forces in dynamic systems. The basic relationship (Figure 8.1) between capillary pressure, interfacial tension, contact angle and pore radius is given by

Cp =

2 γ cos θ .A a

(8.1)

where; Cp γ θ a A

= = = = =

capillary pressure (psi) interfacial tension (dynes/cm) contact angle (degrees) pore radius (microns) 145 x 10-3 (constant to convert to psi)

Applying this to a water wet rock having a broad spectrum of pore entrance radii, oil migrating into water filled pores under a given pressure differential will only enter pores larger than those indicated by ‘a’ in Equation (8.1). Thus for oil introduced at 2 psi into a system having γ = 40 dynes/cm and θ = 0 (water wet), oil will only enter pores larger than

2 =

2 x 40 x 1 x 145 x 10 −3 a

(8.2)

giving a = 5.8 µm. If capillary pressure data are available for a given system, it should be possible to convert to another system of known θ and γ. This is expanded in Section 8.2.

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Capillary Pressure

8.2 Mercury Injection These tests can only be carried out on cleaned, dried test plugs. They are initially immersed in mercury at <10-3 mm Hg vacuum within the apparatus sketched in Figure 8.2. The pressure in the system, effectively the differential across the mercury/vacuum interface, is raised in stages. The volume of mercury which has entered the pores at each pressure is determined from volumetric readings, and the proportion of the pore space filled can be calculated. This gives the curve shown in Figure 8.3. Further readings can be taken as the pressure is lowered to provide data for the imbibition case from Swi to Cp = 0 at point A in Figure 8.3. The volume of mercury injected into the pores at a given pressure is usually expressed as a proportion of the total pore space, and is presented as a pore size distribution (Figure 8.4) or converted to oil or gas-brine data using appropriate contact angles and interfacial tensions. Typical conversions are given below:-

C p (gas - brine) = C p (Air - Hg)

72 cos 0o 480 cos 130

o

(8.3)

= 0.233 C p (Air - Hg)

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C p (oil - brine) = C p (Air - Hg)

Capillary Pressure

25 cos 30o 480 cos 130

o

(8.4)

= 0.070 C p (Air - Hg)

Further conversion to height above oil, or gas-water contact is possible from

C p = hg ( ρ w - ρ o )

(8.5)

Displacement pressures for the assessment of cap rock seal capacity can be assessed from the capillary pressure curves. Care has to be used and allowance made for the effect of surface irregularities. This is especially true of samples with small total pore volumes, i.e. less than 1 ml that are typically the case with cap rock samples. Approximate permeabilities can also be calculated from pore size distribution data; but care has to be taken to exclude the contribution of surface irregularities, since a small number of large pores disproportionately increases the calculated permeability. The data presented in Figure 8.4 shows the effect of surface irregularities at pore throat diameters greater than 10 microns.

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Capillary Pressure

Mercury injection has the following disadvantages: (i) It is a destructive test. (ii) It is carried out on dried core which allows for no fluid-surface interactions. (iii) It can cause collapse of accumulations of grain surface coating minerals. The latter two effects lead to low implied connate water saturations. The data obtained apply to a system containing a fully wetting phase and a fully non-wetting phase. The capillary pressure data obtained will not necessarily apply to pores containing fluids showing partial wetting preferences. The advantages of the technique are that it is rapid (about three hours per sample) and irregular samples can be used. A drainage capillary pressure curve can be produced in a matter of hours and in certain circumstances drill cuttings can provide useful data.

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Capillary Pressure

8.3 Porous Plate Method 8.3.1

Gas-Brine Systems

This technique is generally applied in the drainage mode to air-brine systems starting with test plugs which are initially brine saturated. The capillary pressure is applied across the test plug and a brine saturated porous plate. The high displacement pressure of the porous plate allows brine from the plug to pass through, but prevents flow of the displacing fluid (normally air). The apparatus is shown in Figure 8.5. Plugs are removed at intervals and weighed until weight (and therefore fluid) equilibrium is attained. The pressure applied is then increased and the process repeated until a full curve of about six points is obtained. In this method care has to be taken to maintain good capillary contact between the test plug and the porous plate. This is assisted by using a paste of filter-aid and brine between the plate and a filter paper. The test plug is positioned on the paper and a lead weight placed on the plug to keep it solidly in place. There is also the danger that the water in the sample will be

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Capillary Pressure

evaporated by the gas pressure. To avoid this the input gas can be saturated with water by bubbling it through a reservoir of water prior to use, and keeping a beaker of water inside the porous plate pressure vessel.

The resulting data is presented as (i) air-brine capillary pressure versus brine saturation (Figure 8.6), (ii) converted to oil-brine data (Figure 8.7), or (iii) as saturation versus height above oil (or gas) - water contact.

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Capillary Pressure

The disadvantages of the porous plate method are that it is time consuming, needing up to twenty days for equilibration at each pressure. Also, capillary contact with the porous plate may be lost at high pressures. This causes erroneously high connate water saturations to be implied. Imbibition measurements are not generally attempted. The advantage of the method is that the test plug has at least one representative fluid in place, i.e. the brine. This ensures that brine mineral interactions e.g. clay swelling, which affect pore size and surface states, are taken account of. This is a large advantage over the mercury method, which cannot take account of clay-water interactions.

8.3.2 Oil Brine Systems It is more difficult to make oil-brine measurements than air-brine. For a fully water-wet system, oil-brine drainage capillary pressure data can be inferred from air-brine data. Actual oil-brine drainage capillary pressure can be measured using a Hassler cell fitted with a brine saturated disc (see Figure 8.8). An initially brine saturated test plug is subjected to an oil pressure at the inlet face, and the volume of brine produced (oil taken up) observed at the outlet. Once equilibrium is achieved (this may take 1-3 weeks), the pressure is increased and the process repeated until a full curve is obtained. Care has to be taken that the displacement pressure of the disc is not exceeded, leading to brine displacement from the disc as well as the test plug. This can only be checked and allowed for by weighing the disc before and during the course of the experiments. The disadvantages of the method are basically the same as for the gas-brine case, but with added complications if test plug wetting characteristics differ from those of the reservoir. The method is limited to approximately 50 to 100 psi depending upon disc characteristics. Imbibition measurements are extremely difficult and are limited to about 25 psi.

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Capillary Pressure

The advantages of the method are that, if the wetting characteristics are as in the reservoir, then representative data should be obtained for both mixed and oil wet systems.

8.3.3

Other Methods

There are several other more advanced methods of measuring capillary pressure that are currently being investigated by the hydrocarbon industry. All use a core in a Hassler or similar coreholder under confining pressure. The major ones are: (i) The Dynamic Method This involves injecting the two fluids into a rock core simultaneously, and producing one behind a semi-permeable membrane. (ii) The Semi-Dynamic Method This involves injecting a single fluid, while a membrane at the far end of the rock is washed with the other fluid. This method can be used to measure the complete drainage and imbibition parts of the capillary pressure curve. (iii) The Transient Method This method is technologically complex, and involves the measurement of saturation and pore fluid pressures simultaneously during fluid injection into the sample.

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Capillary Pressure

8.4 Centrifuge Method The centrifuge method is widely advocated by US companies. It relies upon increasing the gterm in the equation;

Cp = h g (ρ w - ρ o ) ,

(8.6)

by spinning the core plug at a known radius and rpm. The average capillary pressure is then given by:

C p ( psi) = 7.9x10 −8 ( ρ1 − ρ 2 ) R 2 ( rb2 − rt2 )

(8.7)

where ρ1 and ρ2 are the densities of the two phases present and rb and rt are the radii of rotation of the bottom and top of the core respectively. For the oil-brine drainage cycle, brine saturated test plugs are immersed in oil in specially designed holders. Starting at a low rpm setting, the amount of brine expelled from the plug is noted for a given rate of rotation. The volumes are measured in the following manner. A calibrated glass vial is attached to the end of the sample. The volume of fluid being deposited in this vial can be read while the centrifuge is spinning fast using a stroboscope. The rate is then increased in stages and produced brine volumes are recorded for each rotation speed to give the drainage curve. The imbibition curve can then be followed by stopping the centrifuge allowing spontaneous imbibition to occur to point A at Cp = 0 (Figure 8.3). The fluid in the imbibition cell is then changed from brine to oil, and the portion of the curve from A (Cp) = 0 to Sor (Figure 8.3) can then be followed by recording the volume of oil produced at several increasing rates of rotation. The main disadvantage of the centrifuge method is that a capillary pressure gradient is applied which must inevitably give rise to a saturation gradient. This will be more exaggerated at low pressures. The advantages of the centrifuge method are that it is rapid, a full drainage and imbibition cycle being complete in a matter of days, and that oil-brine data can be obtained, hopefully, under representative wetting conditions. Centrifuges can also be operated at elevated temperatures (up to 150°). Differences in wetting characteristics should be taken into account when applying laboratory data to the field. Thus air-brine and mercury-air data obtained on cleaned core will represent a fully water wet system for the drainage case. They may not adequately describe a mixed or oil wet system. The closest one can get to this situation, on a routine basis, is with an actual oilbrine system when one would expect to find lower Swi values than a water wet system.

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Capillary Pressure

8.5 Applications of Methods The applications of the various major methods described above are given in Table 8.1. Table 8.1 Parameters associated with various capillary pressure measurement methods. Range

Method Mercury Hg - Air

Drainage Imbibition

Porous Plate Air - Brine Oil - Brine

Sw = 1 to Swi Swi to Cp=0, Cp=0 to Sor Cp=0 to Sor As sample

Swi to Cp=0

Sample wetting state Sw precision Pressure limit, psi Elapsed time

Centrifuge Air - Brine Oil - Brine

Water wet tends low 1150 1-2 days

tends high 70-100 3 months

tends high 70-100 3 months

not known 1000-2000 1-3 days

Cp=0 to Sor

not known 1-3 days

8.6 Capillary Pressure Prediction (Leverett Method) The Leverett ‘J’ function is an attempt to correlate capillary pressure with pore structure (defined in terms of porosity and permeability). The basic capillary model predicts that to displace a wetting phase with a non-wetting phase then:

Cp =

2 γ Cos θ . a

(8.8)

For a simple capillary model, the mean hydraulic radius, a, is given by:

 K a=2 2 ε   θ

12 (8.9)

Combining Eq. (8.8) and (8.9) we get;

12

 K Cp   θ γ cos θ

=

1 2ε

(8.10)

from which the Leverett ‘J’ function is defined:

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Capillary Pressure

12

 K Cp   θ J= γ cos θ

(8.11)

or;

 K J = 0.217 C p   θ

12 (8.12)

where Cp is in psi, γ is in dynes/cm, and K is in mD. Given a typical J curve, the capillary pressure curve for a material of similar pore structure can be calculated for a given value of θ and K.

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Chapter 9: Electrical Properties 9.1 Introduction Laboratory measurements of electrical properties (formation factor and resistivity index) are intended to complement those made during down hole logging operations. The data are used to refine values of n, a and m in Eq. (9.1) and (9.2) below:

F =

Ro a = m Rw φ

(9.1)

where; F Ro Rw a φ m

= = = = = =

Formation factor Resistivity of brine saturated rock Resistivity of brine Constant Porosity Cementation exponent

and,

I=

Rt 1 = R o S nw

(9.2)

where; I Rt n

= = =

Resistivity index Resistivity of rock at Sw < 100% Saturation exponent

Without prior laboratory data, n is generally assumed to have a value of 2. Typically, laboratory derived data gives values between 1.7 and 2.4 (Figure 9.1). Equations (9.1) and (9.2) are empirical in nature. They are generally adhered to by ‘clean’ samples, but where clays (usually described as shales in this context) are present large deviations can occur. Empirical corrections for shale effects, i.e. for m to m* and n to n* are possible but the best procedures are in doubt. The shale effect, which is primarily due to enhanced surface conduction in the high surface area clays, can now also be corrected for using fundamental theory, but the governing equations for the physical processes involved are complex. As with other SCAL tests, samples should be prepared and brought to the initial brine saturated state without drying. The displacing phase used in resistivity index measurements is air, thus these tests are carried out in conjunction with air-brine capillary pressure measurement, most commonly using the porous plate method.

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9.2 Formation Factor Formation factor is a function of porosity and pore geometry and is defined above in Eq. (9.1). Laboratory measurements are made at room conditions or at overburden conditions, the apparatus is sketched in Figures 9.2 and 9.3 respectively. Normally plugs require 2 weeks for equilibration with formation brine. For room condition tests, measurements are made at intervals of a few days until constant values are obtained. In the case of overburden measurements, it is possible to flow brine through the plug in the cell and equilibrium is achieved more rapidly. Overburden resistance measurements are made at increasing pressures, but time has to be allowed for equilibrium to be achieved. This is generally due to varying rates of compaction under overburden pressures and, in the case of low permeability samples, it can take many hours for brine to be fully expelled. Rates for compaction vary according to material, 24 hours often being required for full equilibration. Repeat determinations cannot be made without allowing plugs sufficient time to relax back to the unconfined state. This can take many weeks and in some cases, where the pore structure is irreversibly damaged, the rock never returns to its initial state. Once a rock has been used for resistance measurements at high overburden pressures, it should never be used for further study for this reason. Overburden formation factor measurements are generally combined with pore volume compressibility determinations.

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The actual electrical measurements of resistance in themselves are very precise (better than 0.1%), but care has to be exercised in setting up the plug for the measurements. The most important thing is that the electrodes at each end of the sample do not have any electrical connection except through the rock. This may seem obvious and trivial to arrange, but this one proviso causes the greatest difficulty when setting up a plug to be measured either at high overburden pressures, during rare triaxial deformation experiments, or using high electrical frequencies. The first and second of these situations arises from the need to electrically isolate the electrodes at each end of the sample from each other and the pressure vessel. Insulation is shown schematically in Figure 9.3, but in reality it is not always easy to arrange a robust electrically insulating and pressure-proof leadthrough. In the last situation, it is the capacitance of the leadthroughs and the pressure vessel itself that causes the problems. Even though there is no direct conductive connection, high frequency current can leak from one electrode to the other through the body of the pressure vessel by charge induction, even though there is an insulator in between.

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High quality in-phase and out-of-phase resistance (conduction, and permittivity) measurements can be made anywhere in the frequency range from DC to 10 MHz using impedance analysers. The whole range of frequencies is generally used in academic rock physics, where the technique is called impedance spectroscopy. In the oil industry, only one frequency is used. This is usually 1 kHz, or near it, and is usually taken as the frequency at which the out-of-phase component of the resistance is minimised, i.e. the frequency at which the conduction is most ohmic. Note that this frequency avoids the highest frequencies where current leakage can be a problem. It also avoids the low frequencies, where electrode polarisation can be a problem. The electrodes are commonly made of platinum gauze, upon which a fine dendritic structure of amorphous black platinum has been electro-deposited. This increases the surface area of the electrodes by several orders of magnitude, helping to reduce electrode polarisation effects to negligible values. Often a pad of filter paper soaked in the pore fluid is inserted between the rock and the platinum electrode to (i) homogenise the current flow, (ii) improve the electrical connection, and (iii) avoid conductive minerals channelling current into the rock. For room condition tests, care has to be taken to remove excess surface moisture from the plug (so that the conduction along the plug surface is not measured) and to ensure that just sufficient brine is contained in the electrode ends to give good contact. Contact problems are

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less pronounced in the overburden cell as brine is flowed through the system before measurements are taken, and good electrical contact is assisted by the hydrostatic load on the end pieces. Plug surface conduction is removed by placing the plug in a rubber sleeve, which is squeezed tightly onto the plug by the confining pressure. The main measurement is sample resistance, r. This is clearly dependent upon the length, L, and the cross sectional area, A, of the sample. In order to compare samples, the resistance, length and cross sectional area of the sample are used to calculate the resistance per unit length and per unit cross sectional area of the sample rock; this is called the resistivity, R:

R = r

A L

(9.3)

Note from Eq. (9.1) that the resistivity of the pore fluid is also required. This can be done in a standard dip cell, but this method is prone to large systematic errors. More commonly a specially designed fluid cell is used (Figure 9.4). This cell is connected to the same impedance analyser as used for the main measurements, and at the same frequencies. The fluid resistance obtained in this way is converted to a fluid resistivity by multiplication by a cell constant, that varies from cell to cell, and with temperature and pressure. The cell constant is obtained by calibrating the cell with fluids of accurately known composition and resistivity.

The precision of measurement is dependent upon operator skills and sample permeability. For lower permeability samples (with small pores) repeat determinations should fall within a few percent. For friable, high permeability samples repeatability is poorer, and in extreme cases room condition tests may be impossible due to too rapid drainage of fluid from the sample.

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Cementation exponent, m, for a particular sample can be calculated directly from Eq. (9.1) if it is assumed that a=1. More commonly, cementation exponent for a group of samples is calculated graphically using a minimum of 10 samples covering a wide a permeability range as possible. A typical data set is shown in Figure 9.5. Equation (9.1) can be rewritten as:

log F = log a - mlog φ

(9.4)

A log-log plot of formation factor against porosity gives a straight line, with a gradient equal to the negation of the cementation exponent, and with a y-intercept at φ=1 equal to log (a). It is common to see cementation data from a best fit through the data giving both m and a, but most commonly the linear regression is forced through (φ=1, F=1) corresponding to a=1.

Some typical overburden measurements are shown in Figure 9.6.

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9.3 Resistivity Index This involves similar measurements to formation factor except that resistance is measured at values of Sw less than 100%. Plots of resistivity index and Sw give n, the saturation exponent (Figure 9.7). The methods of desaturation include porous plate and centrifuge, thus resistivity index measurements are conveniently combined with air/brine capillary pressure measurements. Note that Eq. (9.2) can be written as:

log I = 1 - n log Sw

(9.5)

So the saturation exponent, n, is the negation of the gradient of the log I versus log Sw plot (Figure 9.7 shows typical data), and that the line should always pass through (Sw=1, I=1). The practical considerations for these electrical measurements are similar to those for formation factor, except that the tendency for brine to drain from the plug is essentially removed because of the lower saturations. The electrical measurements can be performed to better than 0.1% and saturation changes determined to ± 0.5 Sw%. Care has to be taken to avoid evaporation losses during desaturation and measurement of resistance. Plugs are stored in closed weighing bottles and only removed for the minimum possible period.

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9.4 Shale Effects Very little data is available on the reproducibility of m and n. Repeat determinations of n by a skilled operator should result in good agreement, probably within a few percent. Plots of Sw versus resistivity index often give very good straight lines, but this is not always the case. Some scatter is likely at high values of Sw (above 80%) and at low values (below 20%). The reasons for this are not well understood. Scatter at high values of Sw is difficult to account for; but at low values of Sw it could be due to genuine clay effects, i.e. ‘excess’ conductivity of clays, or to water vapour loss and concentration of brine in the test plug. Correction of m and n to m* and n* is still under general discussion within the industry. These are generally corrected from cation exchange capacity (CEC), which can be obtained from laboratory measurements on crushed rock. Unfortunately, the values obtained for CEC can depend upon the amount of crushing the core has been subjected to, and the method used. It is possible that measurement of formation factor at various salinities can give a better guide to correction of m and n. A plot of core conductivity against brine conductivity (Figure 9.8) can give a value for BQV/F*, which has then at least been obtained from direct electrical measurements on intact core with the fluids of interest in place.

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This topic requires deeper discussion than can be covered here, but it should be borne in mind that the relationships between electrical properties and saturations are empirical; linear relationships cannot always be expected. A more comprehensive discussion on the accuracy of electrical measurements are given in

references [2] and [3].

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Relative Permeability

Chapter 10: Relative Permeability 10.1

Introduction and Definition

Routine permeability measurements are made with a single fluid filling the pore space. This is seldom the case in the reservoir situation except in water zones. Generally, two and sometimes three phases are present, i.e. oil, water, and occasionally gas as well. Here one would expect the permeability to either fluid to be lower than that for the single fluid since it occupies only part of the pore space and may also be affected by interaction with other phases. The concept used to address this situation is called relative permeability. The relative permeability to oil, Kro, is defined as:

K ro =

K eo effective oil permeability = K base permeability

(10.1)

K ew effective water permeability = K base permeability

(10.2)

Similarly we can define:

K rw = K rg =

K eg K

=

effective gas permeability base permeability

(10.3)

The choice of base permeability is not, in itself, critical provided it is consistently applied. Conversion from one base to another is a matter of simple arithmetic. However, experimentally, the base permeability is usually chosen as that measured at the beginning of an experiment. For example, an experiment may start by measuring the permeability to oil in the presence of an irreducible water saturation in the core. Water is then injected into the core, and the oil permeability and water permeabilities measured as water replaces oil within the core. The base permeability chosen here, would most commonly be the initial permeability to oil at Swi. Laboratory measurements are made by displacing one phase with another (unsteady state tests see Figure 10.1) or simultaneous flow of two phases (steady state tests Figure 10.2). The effective permeabilities thus measured over a range of fluid saturations enable relative permeability curves to be constructed. Figure 10.3 shows an example of such a curve from an unsteady state waterflood experiment. At the beginning of the experiment, the core is saturated with 80% oil, and there is an irreducible water saturation of 20% due to the water wet nature of this particular example. Point A represents the permeability of oil under these conditions. Note that it is equal to unity, because this measurement has been taken as the base permeability. Point B represents the beginning water permeability. Note that it is equal to zero because irreducible water is, by definition, immobile. Water is then injected into the core at one end at a constant rate. The volume of the emerging fluids (oil and water) are measured at

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the other end of the core, and the differential pressure across the core is also measured. During this process the permeability to oil reduces to zero along the curve ACD, and the permeability to water increases along the curve BCE. Note that there is no further production of oil from the sample after Kro=0 at point D, and so point D occurs at the irreducible oil saturation, Sor. Note also that Kro + Krw ≤ 1 always.

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It must be stressed, however, that these curves are not a unique function of saturation, but are also dependent upon fluid distribution. Thus the data obtained can be influenced by saturation history and flow rate. The choice of test method should be made with due regard for reservoir saturation history, rock and fluid properties. The wetting characteristics are particularly important. Test plugs should either, be of similar wetting characteristics to the reservoir state, or their wetting characteristics be known so that data can be assessed properly.

Rigs for relperm measurement are often varied in design depending upon the exact circumstances. Figure 10.4 shows an example of a typical rig piping diagram. The fluid flow lines would be nylon or PTFE tube for ambient condition measurements (fluid pressures up to a few hundred psi, and confining pressures up to 1500 psi), and stainless steel for reservoir condition measurements (fluid pressures of thousands of psi, confining pressures up to 10,000 psi, and temperatures up to 200oC). These latter experiments are extremely complex, timeconsuming, and expensive especially if live fluids are to be used. The mean saturation in the core is measured by collecting and measuring the volume of time-spaced aliquots of the evolving fluids. However, there are various successful methods of monitoring the saturation of the various fluids inside the core during the experiments. These are:

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(i) GASM (Gamma Attenuation Saturation Monitoring). Commonly used by BP, this uses doped oil or water phases to attenuate the energy of gamma rays that travel through the core perpendicular to the flood front. Each gamma source/detector pair measures the instantaneous water and oil, or gas and oil saturation averaged over a thin cross section of the core. Up to 8 pairs are used to track the fluid saturations in the core during an experiment, giving a limited resolution. Modern techniques use a single automated motorised source/detector pair. (ii) X-Radiometry. Commonly used by US companies. It is similar to GASM, but uses xrays instead of gamma rays. (iii) CT Scanning. Uses x-rays and tomographic techniques to give a full 3D image of the fluid saturations in the core during an experiment. The spatial resolution is about 0.5 mm, but is extremely expensive, and measurements can be made only every 5 minutes or so. (iv) NMR Scanning. A very new application that is similar to the CT scanning. It has an increased resolution, but is even more expensive. The first two methods are commonly used, whereas the last two are rarely used due to their cost.

10.2

Oil-brine relative Permeability Theory

Three cases will be considered: (i) Water-wet systems (ii) Oil-wet systems, and (iii) The intermediate wettability case. It should be remembered that in water-wet systems capillary forces assist water to enter pores, whereas in the oil wet case they tend to prevent water entering pores. Many reservoir systems fall between the two extremes, which does nothing to make laboratory water-flood data easier to interpret. However, a knowledge of the two extreme cases allows misinterpretation of intermediate data to be minimised. Consideration must be given to flow rates. Close to the well bore, advance rates will be high, further away, rates can be very low. This can be modelled in laboratory tests; but in the case of oil wet systems, there is a tendency for low recoveries to be predicted due to end effects, i.e. retention of wetting phase at test plug outlet face.

10.2.1 Water Wet Systems Consider a water-wet pore system at Swi (generally 15 to 30%) some distance from well bore such that flow rates are low, typically advancing at 1 ft/day. This is equivalent to about 4 cc/hr in a typical laboratory waterflood. The following sequence occurs as water migrates into the rock:

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(i)

Figure 10.5. Initially at Swi, water is the wetting phase and will not flow. Kro = 1 and Krw = 0.

(ii)

Figure 10.6. Water migrates in a piston like fashion, tending to displace most of the oil ahead of it.

(iii) Figure 10.7. As water saturation increases oil flow tends to cease abruptly, and Sor is reached. (iv) Figure 10.8. Dramatically increasing the water flow rate (bump) has very little effect on oil production or Krw. This is because capillary forces provide most of the energy required for displacement of the oil. If floods are carried out at too high a flow rate on water-wet cores the trapping mechanisms present in the reservoir are not allowed to occur. Instead of entering small pores preferentially by capillary forces, the water flows at a relatively higher velocity through larger pores, thus tending to bypass ‘groups’ of smaller pores containing oil. The Sor value obtained may then differ from the true reservoir situation.

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Water wet systems are usually adequately described by low rate floods, and do not exhibit end effects to any significant extent. Water wet data are characterised by: (i) Limited oil production after water breakthrough. (ii) Generally good recoveries. (iii) Low Krw values at Sor. Some typical data are presented in Figures 10.9 and 10.10. Points to take note of are the limited amount of incremental data obtained (although this may be extended by using viscous oils). This is caused by the rapid rise in water cut and the very short period of two phase flow typical of water wet systems.

10.2.2 Oil Wet Systems Consider water entering an oil-wet pore system containing (typically) very low water saturations. The sequence of events from Swi is illustrated by Figures 10.11 to 10.14 as follows:

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(i)

Figure 10.11. Capillary pressure considerations indicate that an applied pressure differential will be required before water will enter the largest pore. The actual pressure differential required is dictated by Eq. (8.1).

(ii)

Figure 10.12. Water flows through the largest flow channels first, Kro falls and Krw rises rapidly.

(iii) Figure 10.13. After large volumes of water have flowed through the system, Sor is reached. This equilibrium is attained slowly giving the characteristic prolonged slow production of oil after early water breakthrough. If waterfloods on oil wet core are carried out at too low a flow rate there may be inappropriate retention of oil at the outlet face of the test plug. This is illustrated in Figure 10.14. At the end of a low rate flood, Krw and the amount of oil produced are relatively low. If the flow rate (and hence the pressure differential) are increased at this stage, substantial further oil production occurs and Krw increases significantly. This situation does not model processes occurring in the reservoir and should be avoided by appropriate choice of waterflood rate at the beginning of the experiment.

Typical high rate valid oil wet data are shown in Figure 10.15 and 10.16.

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10.2.3 Intermediate Systems Data from intermediate wetting rock-fluid systems can be difficult to assess, especially if a single test mode has been used to obtain data. It is usually necessary to carry out a variety of flood modes to fully assess end effects and rate dependence. A low rate flood followed by a high rate bump flood will usually give an indication of the extent of end effects. Flow reversal may indicate whether low recoveries are due to pore scale end effects evenly distributed within the test plug. Steady state tests may be necessary to fully define the shape of the relperm curves. Typical intermediate wettability relperm data are shown in Figures 10.17 and 10.18. The shape of the relperm curves is significantly different for the high and low rate floods. However, the volume of oil produced is similar.

Figure 10.19 shows steady state data obtained from a core containing mobile kaolinite fines. These were mobilised during the prolonged simultaneous flow of oil and brine during the steady state test sequence. They have caused the water relative permeability to be suppressed. Figures 10.17, 10.18 and 10.19 contain data obtained on the same test plug and illustrate the need for more than one test made in obtaining valid relative permeability data. Note also that

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the data points are more reasonably spaced and are less scattered for the steady state test, but there are fewer of them. The steady state test is more controlled because it takes much longer to carry out, but the length of time required to come to equilibrium at each flow rate ratio (at least a few days compared to less than one day for a whole unsteady state test) results in fewer data points being taken.

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10.2.4 Relative Permeability Calculations This section includes: (i)

Calculation of relative permeability from laboratory waterflood data and the basic equations from Johnson Bossler & Nauman (JBN). (ii) Prediction of fractional flow from relperm curves and capillary pressure data. (iii) Fractional flow from transition zones. (iv) Variation of fractional flow with viscosity ratio. I.

Calculation of Relative Permeability from Waterflood Experiments: JBN Analysis.

The experimental data generally recorded includes: Qi ∆p ∆pi Qo Qw

= = = = =

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Quantity of displacing phase injected Pressure differential Pressure differential at initial conditions Volume of oil produced Volume of water produced

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These data are analysed by the technique described by Johnson, Bossler and Nauman (see reference list [4]), which is summarised below. Three calculation stages are involved: (a) (b) (c)

The ratio Kro/Krw. The values of Kro and hence Krw. The value of Sw.

The method is aimed at giving the required values at the outlet face of the core which is essentially where volumetric flow observations are made. (a)

Kro/KrW The average water saturation (Swav)is plotted against Qi:

It can be shown that the fractional flow of oil, at the core outlet is given by:

fout =

d S wav d Qi

(10.4)

Together with:

fout =

(b)

1 K µ  1 +  rw o   K ro µ w 

(10.5)

Kro A plot of ∆p/∆pi against Qi is used to obtain the injectivity ratio IR:

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IR =

∆p i 1 ∆p Q i


(10.6)

Kro is obtained by plotting 1/QiIR versus 1/Qi;

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and using the relationship;

1 K ro = fout d (1 / Q i I R ) d (1 / Q i )

(10.7)

Knowing Kro/Krw from (a) above, then Krw can be calculated. (c)

Using Welges correction to convert average saturations to outlet face saturations (Swout);

Swout = Swav − fout Q i

(10.8)

Thus Kro and Krw can be plotted against Swout to give the normal relative permeability curves. II.

Prediction of Fractional Flow

Fractional flow can be predicted from capillary pressure data and relperm curves. Capillary pressure data gives the saturations expected, and the relperm curves provide the values for Krw and Kro at that saturation. Water cut can then be calculated. Water and oil cuts are defined as follows:

Water Cut % =

Water production x 100% Total production

(10.9)

and

OilCut % =

Oil production x 100% Total production

(10.10)

Using the radial flow equations;

Qo =

2π K eo H t Pd R  µ o ln  e   Rw 

(10.11)

and;

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Qw =

where;

Ht Pd

= =

2π K ew H t Pd R  µ w ln  e   Rw 


(10.12)

Thickness of the producing zone being considered. Drawdown pressure.

But from equations 10.1 and 10.2;

K eo = K ro K

(10.13)

K ew = K rw K

(10.14)

and

Thus, since the fractional water cut, fw, is defined as;

fw =

Qw Qo + Q w

(10.15)

we can say:

fw =

III.

1 µ K 1 + w ro µ o K rw

(10.16)

Fractional Flow from Transition Zones

Transition zones or zones with Sw at some value greater than Swi may present problems with unsteady state tests. It may not be possible to perform an unsteady state waterflood starting at Sw values greater than Swi, i.e. where the initial oil saturation is lower than the irreducible saturation attained at ‘infinite’ capillary pressure. The steady state test may be more applicable in such cases. This situation frequently exists in transition zones before production is started. When production commences the oil/water flow ratio should correlate with steady state water drainage test data, i.e. carried out with Sw increasing. This is the most probable direction in which saturation last changed to place the reservoir in its discovery state. IV. Variation of Fractional Flow with Viscosity Ratio For cases where capillary forces are negligible, it can be shown that the fractional flow of water increases as the viscosity of water decreases relative to the oil viscosity. Using the term mobility, defined as:

M ro for oil phase = K ro / µ o Dr. Paul Glover

(10.17)

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M rw for water phase = K rw / µ w

(10.18)

the Mobility Ratio λ = M ro / M rw

(10.19)

Eq. (10.16) is then expressed as:

fw =

1 1+ λ

(10.20)

Thus fw decreases as µw is increased or as µo is decreased. The effect is shown in Figure 10.20.

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10.3 Laboratory Tests Available There are at least ten usual variations of room condition tests, and each can also be done at full reservoir conditions of confining pressure, fluid pressure, and temperature with live fluids (Table 10.1). Table 10.1 Common Laboratory Relperm Tests Type Oil/brine imbibition Oil/brine drainage Oil/brine imbibition Oil/brine drainage Gas/brine drainage Gas/brine imbibition Gas/oil drainage Gas/oil imbibition Gas/oil drainage Gas/oil imbibition

Mode

Sw

So

Sg

Steady state Steady state Unsteady state Unsteady state Unsteady state Unsteady state Unsteady state Unsteady state Unsteady state Unsteady state

Increasing Decreasing Increasing Decreasing Decreasing Increasing Sw=0 Sw=0 Sw=Swi Sw=Swi

Decreasing Increasing Decreasing Increasing So=0 So=0 Decreasing Increasing Decreasing Increasing

Sg=0 Sg=0 Sg=0 Sg=0 Increasing Decreasing Increasing Decreasing Increasing Decreasing

The most representative and costly test is the reservoir condition waterflood. This is carried out on core which has been restored to full reservoir conditions of temperature, overburden loading, fluid contents (live crude) and wettability. Limited numbers of these tests are performed to assess more economical room condition waterflood data. In view of the large number of possibilities, detailed discussion here will be limited to those most frequently studied, i.e. water-floods, steady and unsteady state, gas/brine drainage and imbibition, and gas/oil drainage and imbibition.

10.3.1 Oil-Brine Relative Permeability This is the most frequently requested relative permeability test. It attempts to simulate the displacement of oil by a rising oil-water contact or a waterflood. The choices of test mode available are unsteady state or steady state, and each has its limitations and advantages. In general terms unsteady state tests are less time consuming than steady state tests, but can suffer from uneven saturation distributions (end effects). Displacement rates can be modified to accommodate wettability characteristics to some extent, and to model reservoir flow rates. Steady state tests can be set up to avoid end effects but are more time consuming, requiring time to reach equilibrium at each chosen oil/brine flow ratio.

10.3.2 Oil-Brine Unsteady State Test Procedure Cleaned cores at Swi are confined in a Hassler or other type of core holder fitted with a breakthrough detector and subjected to a constant brine flow. Data recorded are incremental oil and brine production (in calibrated vials), the pressure differential across the core, and the brine breakthrough point. The data are used to calculate the relative permeability characteristics by using the Johnson, Bossler and Naumans technique.

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The normal full test sequence is as follows: (i)

Miscibly clean core by flushing alternately with toluene and methanol; measure weight saturated with methanol. (ii) Saturate with formation brine without drying; measure weight saturated with brine. (iii) Measure Kew at Sw=1. (iv) Flood down to Swi at a suitable differential pressure. (v) Measure Keo at Swi. (vi) Carry out waterflood, recording pressure differential, incremental oil and water production, etc. (data required for JBN analysis). (vii) Use JBN analysis to calculate Keo, Kew, Kro, and Krw for various Swout and Swav. (viii) Measure Kew , and calculate Krw at Sor before and after bump. (ix) Clean, dry, measure KL and φ. Flooding down to Swi is carried out in a Hassler or other type of core holder fitted with a capillary pressure disc. This process may take several weeks, but has the advantage over centrifuge techniques that even saturation distributions are obtained. Oil wet and intermediate systems tend to flood to typically low values of Swi more rapidly, and at lower pressure differentials than water wet systems. Figures 10.9, 10.15 and 10.17 show example data for water-, oil- and intermediate wet cores.

10.3.3 Oil-Brine Steady State Test Procedure These differ from the unsteady state tests in that oil and brine are flowed simultaneously through the test plug at a fixed ratio until equilibrium is attained, Figure 10.2 (constant pressure differential). The saturations were traditionally determined by demounting the plug and weighing, but are now done using one of the methods discussed at the end of section 10.1. The process is repeated with various oil/brine ratios, changing to suit the expected reservoir history, to build up complete relative permeability curves (e.g., Figure 10.19). The effective permeabilities are simply calculated using Darcy’s Law. The disadvantages of steady state tests are that they are more time consuming both in manhours and elapsed time than unsteady state floods. It usually takes at least 24 hours for each flow ratio to equilibrate, but this can extend to 72 hours for low permeability samples or samples made from several core plugs abutted to each other to form a long test sample. Estimation of saturation can be difficult for friable samples if grain loss occurs each time the plug is removed for weighing. The methods of measuring fluid saturations in situ overcome this problem. Steady state tests have the advantage that end effects (which can affect certain unsteady state tests) are eliminated. The test core is mounted between mixer heads made from adjacent core material. These have similar wetting characteristics to the test plug and allow the correct flow regime to fully establish itself before the test plug is entered. End effects then occur in the outlet end piece instead of the test plug.

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10.3.4 Gas-Brine Relative Permeability Tests Unsteady state tests are most common due to difficulties handling injection of gas over long periods in steady state tests. Consequently, this section will only deal with unsteady state gasbrine relperm tests. The drainage cycle, i.e. gas displacing brine, models gas injection into a brine saturated zone. Full relative permeability curves are generated and more importantly, gas permeability at irreducible brine saturation. The imbibition cycle models movement of a gas/water contact into the gas zone. Imbibition tests cannot be set up to give the full relative permeability curves, but do give brine permeability at trapped gas saturation and the actual trapped gas saturation itself. Typical gas-brine drainage and imbibition data are shown in Figures 10.21 and 10.22.

The drainage test is performed by flowing gas (saturated with water vapour to ensure that the gas does not evaporate the brine) into a brine saturated plug. Incremental gas and brine production and pressure differential are recorded. Relative permeability curves can then be calculated using JBN analysis.

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Figure 10.22 Gas/Brine Relative Permeability Data Plug Code

3 5 12

KL, mD

12.8 411 103

Drainage

Imbibition

Kew at Sw=100 % mD

Keo at Swi, mD

Kro at Swi, mD

Sw at End of Test

Sg at end of Test

Kew at Sgi, mD

Krw at Sgi, mD

Sg at end of test

Sw at end of test

4.3 165 50

5.2 87 44

1.21 0.53 0.88

0.38 0.42 0.21

0.62 0.58 0.79

0.21 1.48 1.05

0.05 0.01 0.02

0.53 0.19 0.48

0.47 0.81 0.52

Imbibition data are obtained by recording the pressure differential across the core as brine is flowed into the test plug initially at S=Swi+Sg. As the initially dominant gas phase is replaced by more viscous water, the pressure differential rapidly increases to a maximum. It then falls slowly as gas dissolves in the flowing brine. This dissolution is unavoidable to some extent, but can be reduced by equilibrating the injected brine with the gas at pressure prior to injection. It should be noted that the injected brine will not completely displace the gas, and a trapped gas saturation will always remain. The maximum pressure differential is recorded and used to calculate Krw at residual (trapped) gas saturation. Krw at trapped gas saturation can be surprisingly low, values of 0.02 to 0.1 being frequently recorded. It is interesting to consider the reservoir situation which is slightly, but significantly, different from the laboratory technique. In the reservoir water migrates into the gas zone as pressure declines, but unlike the core test, the gas saturation does not necessary decline. It tends to remain high or increase slightly, since the trapped gas expands as pressure falls. This maintenance or even increase in Sg tends to keep Krw low or reduce it even further. This scenario operates in many reservoirs even if some of the gas migrates onwards and upwards.

10.3.5 Gas-Oil Relative Permeability Tests Unsteady state tests can be performed in both drainage and imbibition modes. The drainage mode (gas displacing oil) models gas advance into an oil zone, and usually yields full relperm curves. The imbibition cycle provides data for an oil zone advancing into a gas cap but only end point permeability and trapped gas saturation are obtained. It is worth considering the mechanism occurring as an oil reservoir is depleted to a pressure below its bubble point. The process which occurs is represented in Figures 10.23, 10.24 & 10.25. (i)

Referring to Figure 10.23. Initially gas forms in discrete, immobile bubbles, which reduces Kro very significantly. (ii) Figure 10.24. As pressure falls further, the gas saturation increases. The bubbles eventually become connected and give rise to a significant gas permeability. The saturation at which gas becomes mobile is termed the critical gas saturation. Krg rapidly increases and Kro further declines. The relative flow rate of oil is further reduced by the lower viscosity and higher mobility of the gas. (iii) Figure 10.25. Eventually the oil droplets become discontinuous and only gas is produced.

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Laboratory gas-oil relative permeability tests are performed in a similar manner to the gasbrine tests. If required, the tests can be performed with connate water present, but this requires that brine saturated cores be flooded to Swi with oil prior to gas flooding. The relative merits of tests with and without connate water have not yet been fully investigated. It can be argued that the connate water will be immobile and this has been found to be true in some experiments. However, where connate water is present we have noticed that Krg tends to show a more concave upwards curve than when it is absent. The situation is very complex, but could possibly be affected by the wetting characteristics of the rock. The effect is shown in Figures 10.26 & 10.27.

10.3.6 Relative Permeability Data Treatment Interpretation and use of relative permeability data to predict individual well or reservoir performance can be complicated by lateral variations in rock properties. Thus, although the laboratory tests can adequately describe the behaviour of a particular test plug, modelling of a well or reservoir performance may require modified relative permeability data. Correlations of overall curve shape, cross-over points, recovery at a given produced volume, brine permeability at residual oil saturation etc., must all be made with reference to lithology, permeability, and initial fluid saturations. Choice of test method will be governed by application of data, i.e. high flow rate for near the well bore, and low flow rates away from the well bore. As stressed previously, no one test method can fully describe a system and choice of data will be influenced by laboratory scale limitations; in particular, end effects in oil wet cores and problems sometimes caused by wettability alterations and mobile fines. Good petroleum engineering reports should highlight any experimental difficulties encountered and indicate the most reliable data. However, it is often impossible to assess service company data since flow rates are seldom constant and ∆p/∆pi versus Qi curves are not reported. If you are ever in a position to commission this type of work, ensure that provision of this information is part of the contract.

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Commissioning Studies

Chapter 11: Commissioning Studies 11.1 Introduction It is not easy to specify RCAL and SCAL programmes on a general basis. Each reservoir (or well) has to be considered on its own merits. The numbers of each particular test required will depend on the permeability/porosity distribution. The range of tests required will depend on previous experience with the particular reservoir rock/fluid combination under study. Where previous experience is available and there is good agreement between routine core analysis, log and well performance data, the numbers of tests and possibly scope can be reduced. Where anomalies exist it will be advantageous to increase coverage of some parameters and possibly introduce special test sequences to assess the more unusual core and fluid interactions connected with formation damage. The more common reservoir situations encountered are summarised below. In each case it is the SCAL that has been concentrated upon. Routine core analysis commissioning is usually done by internal protocol. For example, plugging every foot wherever the strength of the core fabric allows it, basic chemical cleaning, and then He porosity and gas permeability on the core plugs. Sometimes Hg porisimetry, CT scanning and petrographic analyses are also carried out on a small number of plugs. When commissioning a SCAL study the FIRST step is to review ALL the RCAL data that has already been obtained. The RCAL information effectively provides a pre-study that will help identify possible problems in carrying out the SCAL work. These problems may include (i) swelling clays, (ii) friable and unconsolidated core, (iii) drilling fluid contamination, (iv) mobile fines, etc. Also, it is important to seek the technical advice and expertise of: v Anyone with experience of the rock properties for the field in question. v The technical staff and managers carrying out the work. v Any other individual or source that may provide data that could help save expensive mistakes. Remember time is money, but if corners are cut such that the real requirements are not well defined, or data that you already have is not used, or possible problems with the rocks are not recognised, then more money will be wasted. SCAL data is very expensive to collect. Hence, ask yourself the following points during SCAL commissioning: 1. 2. 3. 4. 5.

What data do you have already from RCAL? What other knowledge is there that you can draw upon? What is the type of field, drive and hydrocarbon? What do you want to do with the SCAL data? Will your projected SCAL campaign provide sufficient data for the purpose it was designed - Is it fit for purpose? 6. Is there any information that would be missing? If it is required, commission it! 7. Is there a specified test that will not tell you any further information concerning the field? If there is drop it!

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8. Have you commissioned sufficient cores of each type of test to provide a reliable and representative coverage of the well section of interest? If you do not know how to judge this, get advice! 9. Does the data you have flag any possible problems with the particular rock to be analysed? If there are problems you must talk to the people carrying out the tests. They should be warned of problems, and in most cases will be able to advise you on the best technical approach to either overcome, avoid or minimise the problem. 10. Does the service company know your needs sufficiently well to provide good and informed service? Good communications leads to better data! 11. Have you asked the service company managers and technical staff for their expert advice? 12. Do you know the timescale for the scheduled work, and is it fixed? If not fix it – SCAL tests are of known duration and can be scheduled well. 13. Have you specified the errors that are acceptable on the measurements? To do this you will need to communicate with the service company. Ensure that measurement errors, which always occur, are sufficiently small or manageable that the data is fit for purpose. 14. Have you specified the data to be provided in a format that will the of best use to you, i.e., on CD-ROM in Excel format as well as a written report? A little time spent planning can save an enormous amount of money.

11.2 Dry Gas Reservoirs These represent the simplest case but the relative importance of the suggested tests (Figure 11.1) will depend upon the nature of the reservoir. Particular care should be taken with highly fractured reservoirs where gas/brine contacts move rapidly. Measurement of trapped gas saturation is particularly important here. With sandstone reservoirs brine permeability in the water zone may be significantly lower than indicated by routine measurements. This can be readily assessed from a relatively small number of tests on preserved water zone cores.

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Figure 11.1 Basic SCAL Programme for a Dry Gas Reservoir 100’ Thick with a Single Facies Type Test Sequence

1 2

3

4 5 6

7

Drill, trim and clean by flushing as many plugs as are obtainable from preserved core (up to 60) Capillary pressure (air-brine) Resistivity index Saturation exponent Formation factor Cementation factor Formation factor at overburden pressure Pore volume compressibility at overburden pressure Brine permeability at overburden pressure Ambient condition relative permeability gas floods Drainage and imbibition cycles Water zone permeabilities Brine permeabilities of preserved core - plug samples Clean by routine methods Routine porosity (He method) KL gas permeability Plug description, thin section, and SEM studies to link SCAL properties with sedimentological characteristics Typical cost

Number of Tests Proposed

Typical Charge per Test (Manhours)

As required

-

10-20

15

10-20

12

10

30

5

6

As required

-

As required

-

700-1000 man-hours (approximately £800,000)

11.3 Oil Reservoir without Gas Cap The situation with oil reservoirs becomes more complex than a dry gas reservoir as: (i) (ii)

Transition zones are usually from a more significant portion of the reservoir. Flow characteristics and relative permeabilities are strongly influenced by wettability.

The static tests, i.e. capillary pressure, resistivity index, formation factors etc., are basically straightforward, (Figure 11.2). However, dynamic tests, i.e. relative permeability, are more complicated, and choice of type and test mode depends upon wettability. Wettability measurements should be considered as an essential preliminary to choice of relative permeability test. If waterflooding is envisaged then wettability is extremely important, as will be water zone brine permeabilities on preserved core.

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Figure 11.2 Basic SCAL Programme for an Oil Reservoir 100’ Thick with a Single Facies Type

1 2

3

4 5 6

7

8

9

Test Sequence

Number of Tests Proposed

Typical Charge per Test (Manhours)

Drill, trim and clean by flushing as many plugs as are obtainable from preserved core (up to 60) Capillary pressure (air-brine) Resistivity index Saturation exponent Formation factor Cementation factor Formation factor at overburden pressure Pore volume compressibility at overburden pressure Brine permeability at overburden pressure Wettability tests on preserved and cleaned core Ambient condition relative permeability tests (mode chosen depending on wettability measurements) Reservoir condition waterfloods. Possibly in preference to (5 above) depending on the characteristics of the core Water zone permeabilities Pore throat size distribution measurements by mercury injection Clean by routine methods Routine porosity (He method) KL gas permeability Plug description, thin section, and SEM studies to link SCAL properties with sedimentological characteristics Typical cost

As required

-

10-20

15

10-20

12

6 10-15

15 30

Up to 6

120

5

10

As required

-

As required

-

700-1700 man-hours (approximately £1,400,000)

11.4 Oil Reservoir with Gas Cap The static tests are basically the same as for 11.2 above. Choice of dynamic relative permeability tests will depend upon the expected movement of oil/water and gas/oil contacts. If expansion of the gas cap into the oil zone is envisaged, gas-oil relative permeability at connate water tests are desirable. Similarly if the reservoir is being waterflooded for pressure maintenance or to reduce gas cap size; the imbibition gas/oil test will provide valuable data on oil permeability at trapped gas saturation and the trapped gas saturation itself.

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11.5 Gas-Condensate The flow regimes and saturation changes which occur in condensate reservoirs are among the most difficult to model in the laboratory, and are extremely rare.

11.6 Formation Damage The term formation damage generally describes permeability reduction brought about by: (i) (ii) (iii) (iv)

Movement of fines. Introduction of particulate matter. Introduction of incompatible fluids. Introduction of fluids upsetting desired relative permeability behaviour.

It is especially difficult to specify a general scheme of formation damage tests. The particular reservoir fluids, minerals, saturation change directions, and introduced fluid compositions should be considered when defining a programme. Two situations will therefore be briefly covered which illustrate the means of damage detection and the applicability of single and two phase tests. The cases considered here are poor and declining injectivity in a water injection well, and formation damage caused by drilling muds.

11.6.1 Poor and Declining Injectivity The possibilities here are: (i) Particulate matter in injection water. (ii) Mobile fines within reservoir rock. (iii) Incompatible waters causing clay swelling. These processes can be tested for by the following methods: (i)

The problem of particulate matter in injection water should be taken care of by proper filtration but could be tested for with on site core tests. The tests however tend to be pessimistic and indicate greater permeability decline rates than are encountered downhole.

(ii)

The presence of mobile fines can be detected fairly readily in the laboratory. Permeability to liquids (brines) are observed and plotted against throughput. Changes occur with throughput and flow direction when fines move to block pore throats, Figure 11.3.

(iii) The sensitivity of a formation to brine composition can be assessed by core throughput tests with changing brine compositions, Figure 11.3. Simple clay swelling effects are observed as reversible permeability changes. However, it is possible that some particles become dislodged during the tests and then behave as mobile fines.

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10.6.2 Drilling Mud Formation Damage A recent study indicated that single phase (liquid) permeability tests cannot necessarily be relied upon to predict formation damage for a two phase situation. Single phase tests indicated that oil based mud filtrate permeability was greater than for water based mud filtrate, implying permeability damage by the water based mud. However, when the mud filtrates were displaced with gas, the effective gas permeabilities were the same in both instances. This case has been simplified, as other factors, such as relative permeability, fluid saturations and volume throughput required to achieve recovery of gas permeability; also need to be considered when interpreting the permeability data.

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Abbreviations

Abbreviations A B Cp FF,F E Ht Kbrine Kg KL Ko Keo Kr Kro Krw KSFW Kw Kew l ,L m m* Mr n n* P, p Pc Pd Pm Qo Qi Qv Qw Re RCAL Relperm Ro Rw Rt SCAL So Sor Sgt Sw Swi t

Dr. Paul Glover

Cross sectional area Specific Counterion Activity (Waxman-Smits) Capillary Pressure Formation factor Tortuosity factor Producing zone thickness Brine permeability Gas permeability Equivalent liquid permeability (Klinkenberg corrected gas permeability) Oil permeability Effective oil permeability Relative permeability Relative permeability to oil Relative permeability brine Permeability to simulated formation water Brine/water permeability Effective brine/water permeability Length Cementation factor Cementation factor (corrected) Mobility Saturation exponent Saturation exponent (corrected) Pressure Capillary pressure (psi) Drawdown pressure Mean flowing pressure Volume oil produced Volume water injected Cation exchange capacity meq/ml Volume water produced Effective reservoir radius Routine core analysis Relative Permeability Core resistivity Brine resistivity (or wellbore diameter) Core resistivity at reduced Sw Special Core Analysis Oil saturation Residual oil saturation Residual trapped gas saturation Brine saturation Initial brine saturation Time (secs)

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Abbreviations

Abbreviations continued V, v γ λ θ φ ρο ρω µο µω

Dr. Paul Glover

Volume Interfacial tension Mobility ratio Contact angle Porosity Oil density Brine density Oil viscosity Water (brine) viscosity

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Selected References

Selected References [1]

Permeability Characteristics of Magnus Reservoir Rock. Heaviside, Langley and Pallatt, 8th Formation Evaluation Symposium Trans. Mar. 1983. London.

[2]

Errors in Laboratory Measurements of Formation Resistivity Factor”, by A.E. Worthington. S.P.W.L.A. 16th Annual Logging Symposium 4-7 June 1975.

[3]

Comments on obtaining Accurate Electrical Properties of Cores, by Hoyer, S Spann. S.P.W.L.A. 16th Annual Logging Symposium 4-7, June 1975.

[4]

Calculation of Relative Permeability from Displacement Experiments, Johnson, Bossler and Nauman, Pet. Trans. AIME (1959), 216, p.370.

[5]

EHRLICH, R., CRABTREE, S.J., HORKOWITZ, K.O. & HORKOWITZ, J.P. 1991. Petrography and reservoir physics 1: objective classification of reservoir porosity. The American Association of Petroleum Geologists Bulletin, 75, 1547-1562. Abstract: Porosity observed in thin section can be objectively classified using a combination of digital acquisition procedures and pattern recognition algorithms. Pore types are derived from the frequency distributions of sizes and shapes of patches of porosity exposed in thin section. Each pore type is represented by a characteristic distribution of sizes and shapes found in thin section. Most sandstone reservoirs contain fewer than six pore types. Much of the variability in reservoir physics is associated with changes in pore type abundance. The advantages of this approach to porosity classification are (1) the criteria for classification are objectively defined, (2) classification procedure is rapid, accurate, and precise, (3) pore types are understood easily in terms of conventional genetic classification schemes, and (4) pore type data are related strongly to petrophysical properties.

[6]

MCCREESH, C.A., EHRLICH, R. & CRABTREE, S.J. 1991. Petrography and reservoir physics 2: relating thin section porosity to capillary pressure, the association between pore types and throat size. The American Association of Petroleum Geologists Bulletin, 75, 1563-1578. Abstract: Porosity in reservoir rocks is configured into a few types of pores whose size and shape are controlled by depositional fabric and processes. The size, shape, and abundance of each pore type can be objectively determined from thin section using image analysis and pattern recognition procedures. Each pore type tends to be associated with a limited range of throat sizes. The association between pore type and throat size can be determined using regression procedures linking pore type data obtained from thin section with capillary pressure data. To do so, a set of samples is required wherein the association between pore type and throat size is fixed, but where pore type proportions vary between samples. This condition is met by a sample suite representing reservoir facies from a single core or, in many cases, from a single field. The relationship between pore type and throat size is an effective means to relate reservoirs in terms of the efficiency of the porous to multiphase flow. Parameters derived from the relationship can be used to construct accurate physical models that subdivide physical response in terms of the contributions of each pore type.

[7]

EHRLICH, R., ETRIS, E.L., BRUMFIELD, D., YUAN, L.P. & CRABTREE, S.J. 1991. Petrography and reservoir physics 3: physical models for permeability and formation factor. The American Association of Petroleum Geologists Bulletin, 75, 1579-1592. Abstract: Permeability and formation factor are physical properties of porous rocks useful for assessing reservoirs. Neither property varies consistently as porosity varies. The relationship of both properties to porosity is complex, being sensitive to the structure of the porous microstructure, i.e., the sizes of pore throats, the numbers and sizes of pores, and the relationships between pores and throats. Physical models to account for these factors require parameters that describe physically relevant properties of the microstructure. A partial characterization of the relationship between pores and throats is embodied in the relationship between pore type and throat size. This relationship is derived by combining data obtained from thin sections, from which pore types are derived via image analysis, and mercury injection porosimetry, which quantifies throat size information. Parameters derived from such a combination are

Dr. Paul Glover

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Selected References

sufficient to construct simple physical models for permeability and electrical conductivity (inverse formation factor). These models assume a porous medium that has large numbers of flow paths parallel to the potential gradient, such that flow has little tortuosity (i.e., flow parallel to bedding). The contributions of each pore type to permeability and electrical conductivity are computed. Calculated values are close to measurement values. A constant of proportionality is the same for all samples from a reservoir, but can vary between reservoirs, is required, and must have values ranging (for sandstones) from about 2.5 to 3.5 for permeability and 5.0 to 7.0 for conductivity. These values are consistent for an efficiently packed fabric. One result of such modeling is a physical model of Archie's cementation exponent m as the ratio of the logarithms of the cross sectional throat area to pore area (per unit area). [8]

WARDLAW, N.C. & TAYLOR, R.P. 1976. Mercury capillary pressure curves and the interpretation of pore structure and capillary behaviour in reservoir rocks. Bulletin of Canadian Petroleum Geology, 24, 225-262. Notes: A classic on this subject. Explains the reasons behind various aspects of injection and withdrawal curves, by looking at SEM of rocks studied.

[9]

VAVRA, C.L., KALDI, J.G. & SNEIDER, R.M. 1992. Geological applications of capillary pressure: a review. The American Association of Petroleum Geologists Bulletin, 76, 840-850. Notes: Important discussion of interpreting mercury injection porosimetry results.

[10]

PITTMAN, E.D. 1992. Relationship of porosity and permeability to various parameters derived from mercury injection-capillary pressure curves for sandstones. The American Association of Petroleum Geologists Bulletin, 76, 191-198. Notes: As mercury injection tests are expensive and not abundant, derives relationships using multiple regression on large database of samples. Empirical equations make it possible to construct pore aperture radius distribution curves from core analysis porosity and permeability.

[11]

BLIEFNICK, D.M. & KALDI, J.G. 1996. Pore geometry: control on reservoir properties, Walker Field, Columbia and Lafayette counties, Arkansas. The American Association of Petroleum Geologists Bulletin, 80, 1027-1044. Notes: An oolite carbonates sequence. Useful discussion on interpreting mercury injection porosimetery results.

[12]

RINGROSE, P.S., SORBIE, K.S., FEGHI, F., PICKUP, G.E. & JENSEN, J.L. 1993. Relevant reservoir characterisation: recovery process, geometry and scale. In Situ, 17, 55-82. Notes: With miscible-gas flood, large-scale geometry may be more important than the internal small-scale structure. With waterflood, small-scale structure likely to be dominant. Emphasises must think not only about the rock but also the fluids and the recovery process.

[13]

CORBETT, P.W. & JENSEN, J.L. 1993. Quantification of variability in laminated sediments: a role for the probe permeameter in improved reservoir characterization. In: NORTH, C.P. & PROSSER, D.J. (eds) Characterization of fluvial and aeolian reservoirs. Geological Society special publication 73, London, 433-442.

[14]

HUANG, Y., RINGROSE, P.S. & SORBIE, K.S. 1995. Capillary trapping mechanisms in water-wet laminated rocks. SPE Reservoir Engineering, 10, 287-292. Abstract: Most floods in sandstone cores are performed either in almost homogeneous samples or else in core samples of uncertain heterogeneity. As a result, the interaction of small-scale sedimentary heterogeneity with the fluid mechanics of water-oil displacement cannot be adequately understood or quantified. The results are reported from low-rate, drainage-imbibition floods in a 20 x 10 x 1 cm slab or cross-laminated heterogeneous sandstone. The laminated aeolian sandstone was characterized by detailed

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Selected References

probe permeameter mapping prior to setting it in a resin cast. The distribution of porosity, permeability, irreducible water, and residual oil saturation were subsequently monitored using CT scanning techniques. The low-rate imbibition floods show that between 30 and 55% of original oil may be trapped in isolated high permeability lamina. This work shows the importance of recognizing the role of core-scale heterogeneity in the laboratory measurement of waterflood behavior, i.e., the interaction of capillary forces with rock structure. The practice of performing high-rate floods on rock samples assumed to be heterogeneous is unwise and can lead to erroneous conclusions. The work has major implications for (1) 2-phase petrophysical measurements, (2) the assessment of residual/remaining oil, and (3) multiphase flow scaleup. [15]

MCDOUGALL, S.R. & SORBIE, K.S. 1992. Network simulations of flow processes in strongly wetting and mixed-wet porous media. In: CHRISTIE, M.A., DA SILVA, F.V., FARMER, C.L., GUILLON, O., HEINEMANN, Z.E., LEMONNIER, P., REGTIEN, J.M.M. & VAN SPRONSEN, E. (eds) ECMOR III: Proceedings of the third European conference on the mathematics of oil recovery. Delft University Press, Delft, Netherlands, 169-181. Notes: Deriving 2-phase flow parameters such as relative permeability and capillary pressure from microscopic considerations.

[16]

MCDOUGALL, S.R. & SORBIE, K.S. 1995. The impact of wettability on waterflooding: pore-scale simulation. SPE Reservoir Engineering, 10, 208-213.

[17]

PICKUP, G.E., RINGROSE, P.S., JENSEN, J.L. & SORBIE, K.S. 1994. sedimentary structures. Mathematical Geology, 26, 227-250.

Permeability tensors for

Abstract: Accurate modeling of fluid flow through sedimentary units is of great importance in assessing the performance of both hydrocarbon reservoirs and aquifers. Most sedimentary rocks display structure from the millimeter or centimeter scale upward. Flow simulation should therefore begin with grid blocks of this size in order to calculate effective permeabilities for larger structures. Several flow models for sandstones are investigated, and their impact on the calculation of effective permeability for single phase flow is examined. Crossflow arises in some structures, in which case it may be necessary to use a tensor representation of the effective permeability. Conditions are established under which tensors are required, e.g., in crossbedded structures with a high bedding angle, high permeability contrast, and laminae of comparable thickness. Cases where the off-diagonal terms can be neglected, such as in symmetrical systems, are also illustrated. The method of calculating tensor permeabilities may be extended to model multiphase flow in sedimentary structures.

Dr. Paul Glover

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Formation Evaluation MSc Course Notes Paul Glover

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