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The Chevron Basic Formation Evaluation Course Please select the topic on the left that you would like to see.
Formation Evaluation Formation Evaluation generally thought of as the practice of identifying and quantifying hydrocarbons and reservoir parameters from rock and downhole measurements. Data involved in this practice can come from a wide variety of sources.
wireline logs (open hole, cased hole and production logs) MWD (measurement while drilling) mudlogs core and fluid analysis formation testing
Many different types of measurements are made in our attempt to define reservoir properties. These measurements span many types of energy some focus on rock properties other are more sensitive to the fluids. Many have been developed for special logging conditions like oil-based mud. Add to this the fact that logging tools have been around since the 1920s and that there have historically been 3 to 5 logging companies constantly adding new tools with new capabilities and we end up with a staggering number of tools and measurements all with subtle differences in their interpretation.
The measurements are an almost always-indirect measurement that is to say they do not measure the exact property we are after. Over the years a long list of
equations and techniques have been developed to get from log measurements to reservoir properties. Knowing which ones to choose under what conditions is what sometimes termed the "art" of Formation Evaluation. It should also be noted that all too often calculations are done with a specific question in mind and that may not be appropriate for all situations. The log analysis methods may involve many aspects depending on the questions and the time permitted from overlays and quick looks to mineral modeling requiring computers and detailed understanding of the tools. The techniques employed to answer a simple question are not the same as those required to quantify some reservoir parameter with a high degree of certainty. 1. 2. 3. 4. 5. 6. 7.
Will the well produce? If so, will it be oil, gas, or both? Will production include some water? Qualitatively, how much production? What is the depth of the permeable beds? What are the thicknesses of those beds? What is the estimated porosity and saturation of those beds?
Wireline Logging A wireline log is the product of a survey operation, also called a survey, consisting of one or more curves. which provides a permanent record of one or more physical measurements as a function of depth in a well bore. Well logs are used to identify and correlate underground rocks, and to determine the mineralogy and physical properties of potential reservoir rocks and the nature of the fluids they contain. In general a log is the physical paper recording the information, however it has come to also mean digital curves.
1. A well log is recorded during a survey operation in which a sonde is lowered into the well bore by a survey cable. The measurement made by the downhole instrument will be of a physical nature (i.e., electrical, acoustical, nuclear, thermal, dimensional, etc.) pertaining to some part of the wellbore environment or the well bore itself. 2. Other types of well logs are made of data collected at the surface; examples are core logs, drilling-time logs, mud sample logs, hydrocarbon well logs, etc. 3. Still other logs show quantities calculated from other measurements; examples are movable oil plots, computed logs. etc.
Depth Comtrol The most fundamental measurement provided by wireline logging contractors is depth. A description of subsurface reservoirs is not of much value if an accurate reference to depth location is not available. Depth control is therefore extremely important to the success of any logging or completion operation. Contractors specify standards as a function of well depth, wireline cable size, and mud weight. However, in general, all recorded logs are expected to be within to be within a controlled tolerance of 1 ft/10,000 ft (0.3 m/3000 m) of measured depth. Methods for marking the wireline (usually with magnetic marks), knowing the exact distance of the cable makeup to a tool's measure point (including logging head, bridle, etc.), and the distance to the first mark from the downhole end of the cable are all part of the measuring system. In addition, stretch charts for different cable sizes, mud weights, etc. are given for borehole depth, and logging engineers are expected to dedicate themselves to performing depth measurements as accurately as possible. Wireline log depths are considered the standard for well depth accuracy. Scales and Reading Logs Today, the presentation of logs varies as a function of the type and number of services recorded. Tracks represent protions of the log reserved for certain linear or logarithmic scales and grid. Logarithmic scales are generally used for
resistivity data and may occupy one or two tracks. Other log data are generally recorded linearly and may occupy one or two tracks. Track 1 is generally used for control curves (SP, GR, caliper, etx.), but it is also used for quick-look interpretation information. Porosity-sensitive data such as density, neutron, and acoustic are often recorded linearly across two tracks. Resistivity can occupy one or two tracks but is generally recorded on a logarithmic scale and grid. An important parameter related to depth is the time marker. To the left of Track 1, a small flag, pip, or gap in the grid is used to indicate time. If calibrated properly, the time marker occurs every 60 sec and can be used to indicate logging speed. This marker is important to log quality control and should be checked periodically for accuracy. Furthermore, a controlled and constant logging speed is important to several log measurements. Headers Hole sizes to certain depths are recorded on the driller's log. Driller depths for casing strings already in the well are also recorded. These data should be printed clearly on wireline log headers. It is also common practice for the logging engineer to record the logged depth of casing strings. Log depths should never be intentionally falsified for any reason. If the log is not recorded to a depth sufficiently shallow to determine the logged casing depth, the designated block on the
header should be left blank. The driller's total well depth should also be recorded. Date and times for each logging run after circulation should also be recorded on the header. Bottomhole temperature should be recorded with maximum reading thermometers on each logging run, and these data should be recorded on the log header. Other data, such as the surveyed elevations of ground level, derrick floor, sea floor, height above mean sea level, kelly bushing, or similar reference points to depth measurements, should be recorded on the log header. It is important that these data be accurate because the logs can be subpoenaed as legal documents. These data are also commonly placed on a log tail. The completeness and accuracy of header information is a fundamental responsibility of the field logging engineer. That engineer's name is also permanently recorded on the header . The REMARKS section of the log header is used to record any unusual circumstances observed during the logging operation. This includes reasons for a poor quality log not being rerun, why an SP curve was not recorded, etc. It is the logging engineer's space for explaining any unusual circumstance . Perhaps the properties of the drilling fluid adversely affect the log measurements. If so, it should be mentioned in the REMARKS section. It is also important to record tool series numbers, any additional components, and tool numbers on the header. This information is often a helpful clue to interpretative questions and troubleshooting tool problems.
Permeability The ability of fluids to flow through a formation is a key parameter in determining the rate at which any given reservoir will produce fluids. Fluid flow through a formation is governed by three key factors:
1. The nature of the fluid. o this refers to the thickness or viscosity of the fluid o more viscous fluids resist flow and have reduced relative flow rates and vice versa 2. The amount of differential force exerted on the fluid. o increased pressure differential increases flow rates Note: Neither of these factors are governed by rock matrix properties, but are determined by reservoir properties. 3. The geometry of the flow paths through the rocks. o this property is determined by rock matrix properties 4. Rock geometry refers to two separate rock properties. o physical size and orientation of the rock through which the flow is characterized o physical arrangement of the pore spaces within the rock that the fluid will flow through
Flow rate is expressed in the following generalized relationship: Flow Rate = f(Fluid properties, Differential Pressure, and Rock Geometry) The mathematical expression for this relationship is known as Darcy's Law:
q = ( A/ ) x (d /dx) where
q = volume flux (volume per unit time in cc/sec for linear flow) = permeability constant in darcys A = cross sectional area in cm2 = fluid viscosity in centipoises d /dx = hydraulic gradient; the difference in pressure, p, in the direction of flow, x, in atm/cm Permeability is governed by: 1. The size of the flow passages. o As the size of the flow passages decreases, the permeability of the rock decreases. Generally, permeability decreases as grain size decreases 2. The interconnectivity of the pore spaces. o As the interconnectivity of the pore spaces is reduced the permeability decreases; this implies that permeability generally decreases with the an increase in cementation. 3. The tortuosity of the flow paths. o As the tortuosity of the flow path increases, the permeability decreases, implying that the permeability is generally decreased s the heterogeneity of the sorting increases. 4. The molecular and chemical interaction between the fluid and the rock surface. o As the molecular bonding between the fluid and the rock surface increases, the permeability decreases.
The permeability of any rock is affected by the attributes of the matrix; the most important characteristics which affect the ease of fluid flow are: 1. Grain size o As the grain size is decreased, permeability is decreased as a result of a reduction in the effective pore size and the increase in the total surface area per unit volume. o Increased surface are causes an increase in the amount of fluid bound by chemistry to the surface; which in turn reduce the amount of pore space available for fluid flow. 2. Packing o As packing efficiency is increased, permeability is decreased. o Tortuosity of the flow paths is increased because the packing of the grains results in longer effective pore paths. 3. Sorting
o
As the uniformity of sorting decreases, the permeability is decreased because of smaller effective flow passages and the increased tortuosity of the flow paths.
Absolute Permeability (k) is the permeability of a rock when fully saturated with a single fluid. Effective Permeability (ke) is the measure of the permeability of a rock to a specific fluid at a defined saturation in the presence of another fluid. Relative Permeability is defined as the ratio between the effective permeability of a rock to a given fluid at a partial saturation and the permeability of that rock at 100% saturations; this is the same as the effective permeability divided by the relative permeability.
Porosity
Porosity is a measurement of the capacity of rock to contain fluids. From the well logging perspective the rock matrix is the solid material, composed of discrete particles or grains, that when lithified, does not consume available space. The small voids that the rock matrix is unable to fill comprise the porosity. That space will be occupied by water, oil, gas, or other liquids. Porosity is defined as the fraction of the volume not occupied by rock matrix. Mathematically, porosity is expressed by the following equation. Porosity = Bulk Volume - Matrix Volume / Bulk Volume Since rock porosity is essentially determined by the ability of matrix particles to fit together, the matrix characteristics of grain size, sorting, cementation, angularity (roundness), and overlying pressure have a great influence on the amount of porosity present in any given rock.
Two fundamental attributes influence porosity:
The manner in which the grains are packed The degree to which the grains are sorted
Packing The concept of packing is best demonstrated by using the simplified particle shape of spheroids as seen in the figure below. If a sphere of radius r were placed in a cube with a dimension of 2r, then the porosity of that cube can be accurately computed using the above definition where: Total volume = (2r)3 and Matrix Volume = 4/3 r3 Therefore: Porosity =[ 8r3-(4/3) r3] /8r3= 47.6% If we take a series of these spheroids and pack them in a formation using cubic packing as seen below, the formation would have exactly 47.6% porosity. Additionally, if we were to change the diameter of the sphere, but maintain all spheres of the same diameter with cubic packing, the formation would always have the same porosity. If the same spheres are now stacked using rhombic packing, the porosity would decrease to 39.5% because the grains fit closer together. If the grains were packed using rhombohedral packing the porosity would be further reduced to 26%. Parallel cases can be made for non-spherical grain
shape with similar results. Packing affects the efficiency with which grains can fill bulk volume and is a controlling factor in determination of porosity. Sorting The concept of sorting can also be demonstrated with the same spherical grain concepts. If we were to take the same cube and grain shown in Figure 1 and add very small diameter spherical grains in the porous space in the corners, the total porosity of the cube would be obviously reduced. The characteristic of nonuniform sorting has the effect of reducing porosity when all other factors are held constant. Changing grain size when all grains have uniform size has no effect upon the porosity, but increasing the variability of grain size acts to reduce porosity.
Capillary Pressure & Reservoir Quality
The mechanisms controlling the movement and distribution of immiscible fluids (oil, water, and gas) within a rock, on both the pore and reservoir scales are primarily related to the properties of the fluids and the geometries of the pore systems of the rock.. For oil to enter a structure,
water must be displaced. We will find that oil will never succeed in completely displacing the original water within the structure, and where water displacement by oil is the greatest, a residual water saturation will exist which is a function of the rock properties. Furthermore, the amount of oil, which can be recovered economically by primary production and water flooding, varies enormously from less than 10% to more than 80% of the initial oil in place. The distribution and producibility of hydrocarbons can also vary significantly at different levels in the same reservoir. To understand the processes responsible for these large variations, a basic knowledge of the mechanisms controlling the movement and distribution of fluids (oil, water, and gas) within a rock on both the pore and reservoir scales are required. Contributing factors include the nature of the rock-pore system (the shapes and connectivity of pores and throats, surface area, surface roughness, and electrical charge of the pore walls), the phase behavior and properties of the fluids under reservoir conditions (viscosity, interfacial tension, density, and wettability), and the forces that cause the fluids to move within the reservoir (gravity, viscous and capillary forces). Laboratory measurements of capillary pressure, the pressure required to displace a single fluid phase in a multiphase fluid system, provides useful information, which can be related to reservoir conditions to allow us to understand and predict better the occurrence of hydrocarbons in a reservoir, such as water saturation distributions (initial water saturation, and residual oil saturation), fluid levels (oil / water contact, etc.), and water flood responses.
As permeability and sorting increase, the capillary pressure required to reach irreducible water saturation decreases, and the shape of the capillary pressure curve changes from a lazy curve to a sharp, quick buildup. In the case of the well-sorted, permeable rock, a small increase in capillary pressure results in the filling the volumes connected by large pore-throats (the larger portion of the rock pore volume). A large increase in capillary pressure is required to fill those remaining pore volumes connected by the remaining smaller pore-throats. The net results is a capillary pressure curve with a sharp buildup. For the poorer sorted, less permeable rocks, the pore throats are smaller and, therefore, higher capillary pressures are required to reach a water saturation relative to the well sorted, permeable rocks. Key Points 1. As sorting and grain size decrease, capillary pressure increase. 2. The shape of a capillary pressure curve is related to permeability and sorting. As K and sorting increase, the transition from 100% water saturation to minimum water saturation is sharper. 3. Capillary pressure curves represent the properties of a single discrete sample. Caution is required when extrapolation to the reservoir scale. 4. Irreducible water saturation (Swi) is the condition where a non-wetting phase cannot further displace wetting fluid. It is also a measure of the amount of hydrocarbon that can be stored in a pore system. 5. Residual oil saturation (Sor) is a measure of the ultimate amount of hydrocarbon that can be recovered from a system. 6. Both Swi and Sor can vary dramatically between reservoirs, and their values are critical endpoints for the evaluation of a reservoir. 7. The shape of a capillary pressure curve is related to permeability and sorting. As K and sorting increase, the transition from 100% water saturation to minimum water saturation is sharper. 8. Capillary pressure curves represent the properties of a single discrete sample. Caution is required when extrapolation to the reservoir scale.
1. 2. 3. 4.
Capillary pressure curves can be associated with significant fluid levels in a reservoir: the Free Water Level (FWL) is where capillary pressure is zero. above the FWL both oil and water coexist. the first occurrence of mobile oil is the oil-water contact, (however, other oil-water contact definitions are used). 5. above the critical water saturation level only oil is produced. 6. between the FWL and the irreducible water saturation level is the transition zone.
Resistivity General Resistivity Principle The term resistivity (or conductivity) is a general property of materials, as opposed to resistance, which is associated with the geometric form of the material. The relationship of resistivity to the basic electrical properties of current and voltage are described by Ohm's law:
V=IR where current I flows through a material with resistance R, and is associated with a voltage drop V. Resistivity R is composed of two parts -- one is material dependent, and the second is purely geometric (e.g. the length of the sample divided by the surface area of electrical contact plates). From this it follows that
dimensions by which resistivity may be described are Ohmm/m2 (or, more popularly, Ohm-meters). As illustrated, a material of resistivity of one Ohm-meter with dimensions of one meter on each side will have a total resistance, face-to-face, of one Ohm. Or, in other words, a one meter cube of formation rock placed between two electrodes of one square meter each defines a resistivity of one Ohm-meter. Conductivity, the inverse of resistivity (C = 1/R), may be divided into two general types of interest: electrolytic and metallic. Electrolytic conductivity relies on the presence of dissolved salts in a liquid such as water. Metallic conductivity is related to the presence of metals, and is a factor in well logging in ore bodies or, more commonly, with clays or accessory minerals such as pyrite, or graphite. Most rocks are , in essence, insulators and any detectable conductivity usually results from the presence of electrolytic conductors (brine) in the pore space. The conductivity of rocks is primarily of electrolytic origin. It is the result of the presence of water or a combination of water and hydrocarbons in the he pore space in a continuous phase. The actual conductivity will depend on the resistivity of the water in the pores and the quantity of water present. To a lesser extent, it will depend on the lithology of the rock matrix, its clay content, and its texture (grain size, and the distribution of pores, clay, and conductive minerals). Finally, conductivity of a sedimentary formation will depend strongly on temperature (increasing temperature increases electrolytic conductivity). Logging-Related Applications
Determination of water (oil) saturation in the pore spaces of formation rock. Determination of porosity in known water-filled formations. Stratigraphic correlation of rock sequences between nearby wells. Characterization of borehole and formation fluids for environmental correction of neutron logs.
Resistivity of Water
As we have seen dry rocks are generally very good insulators. Resistivity is a function of the geometry of water in the rock and the resistivity of that water. When two metal electrodes are connected to a source of electric current and immersed in a salt solution as in , then an electric potential will exist between the electrodes. The positively charged cations will be attracted to the negatively charged electrode and the negatively charged anions will be attracted to the positively charged electrode. The force on each ion will depend on the voltage level and the charge of the ion. The velocity of the ion will depend on the opposition it encounters moving through the solution. This opposition is determined in turn by the fluid viscosity and the effective size of the ion. The conductivity of a solution has been found to depend on: 1. Charge and size of the ions 2. Ion concentration 3. Viscosity of the solvent
The viscosity of water is controlled by the extent of hydrogen bonding between water molecules and consequently, is a strong function of temperature. Accordingly, the electrical conductivity of aqueous solutions increases sharply with increasing temperature. (The conductivity of metals actually decreases with temperature.) The above nomograph shows the electrical resistivity as a function of concentration in parts per million and temperature in degrees Fahrenheit. It is derived from data on NaCl solutions such as that published in the International Critical Tables.
Arps observed that this data can be approximated by the equation listed in . This relationship is easy to use on a calculator. Consequently, the temperature conversion part of is seldom needed. The charts and equations we have used to convert between salinity and resistivity for different temperatures are applicable strictly only to NaCl solutions. When a brine contains ions other than NaCl, adjustments to these charts and equations are needed. The contribution to conductivity of nonNaCl ions can be converted to equivalent amounts of NaCl using multipliers than be more or less than 1. An important assumption in
this conversion is that the temperature dependence of all ion solutes is the same as that of an NaCl solution of equivalent salinity. This assumption seldom leads to significant errors.
Archie Water Saturation The resistivitiy of a rock with hydrocarbon and connate water is a function of the amount and distribution of water and hydrocarbon, and the resistivity of the water. The most widely recognized water saturation equation is generally called the "Archie equation". It is really the result of two empirical relationships observed by G.E. Archie of Shell Oil.
The first is the relationship between the porosity of a water saturated sample and it's resistivity. In the laboratory, measured the resistivity of numerous specimens having a wide range of porosity values and differing connate water resistivities. Archie's work concluded that from
a plot of Rw versus Ro plotted data indicate: 1. Any Rw increase causes a corresponding increase in Ro for a given porosity 2. At a given Rw, porosity decreases as Ro increases 3. At any given porosity, the ratio of Ro to Rw is constant, regardless of the Rw value
The ratio of rock resistivity (Ro) to connate water resistivity (Rw) is formation factor (F), and F is also a function of porosity. Therefore, Ro = FRw or F = Ro/Rw
F = a/m a the intercept generally taken as 1 (but some empirical equations use other values) m commonly called the cementation exponent generally around 1.8 - 2 for sandstones The second relationship defines how the resistivity of a rock saturated with water changes as oil as water is replaced by oil.. Oil saturation, (usually expressed as water saturation) is: Rt/Ro = Sw-n
Swn = (aRw)/mRt where:
Rw is the formation water resistivity Rt is the true formation resistivity F is the formation resistivity factor n is the saturation exponent and lab measurement derived from core usually around 2
Key Points 1. Accuracy of the Archie equation depends on the accuracy of the input parameters; Rw, F and Rt and porosity. 2. This equation is not constrained, values greater than one can be calculated. 3. n can only be measured from core. 4. a and m can be measured from core or back calculated in a wet zone 5. This is the basic water saturation method from resistivity all shaly sand models have this as their basis
Well Log Analyst View of Lithology Lithology has an effect on almost every log reading. The densityneutron log readings are different in a 30% porosity dolomite versus a 30% porosity sandstone. Once you know the lithology, you can calculate an accurate porosity as well as gain an appreciation for the fluids occupying the pore space in the rock. Knowing the lithology also makes log interpretation useful for geological interpretation. Wireline log lithology can help a geologist or geophysicist fine-tune a stratigraphic section, interpret a depositional environment, or validate the mud log. Log Analyst Rock Classification Model Geologists separate rocks on the basis of increasing size of the fragments that make up the rock. Usually when litholog descriptions are used by geologists they do not imply any particular mineral composition; i.e., a consolidated beach sand consisting of calcite grains is a sandstone to most geologists.
Log analysts usually subdivide rocks differently than geologist. The primary division for log analysts is between carbonates/evaporites and clastics. Carbonates include all limestones, dolomites and evaporites. The calcite "sandstone" of the geologist is a carbonate rock to a log analyst. Clastic rocks, rocks that have been derived by erosion of pre-existing rocks, transported and deposited by water and wind include shales, siltstones, sandstones, and coarsergrained rocks such as grits, cobblestones, or conglomerates. The reason for this terminology is that well logs generally give little information about grain size of rocks coarser than the shale fraction, particularly if they are completely watersaturated. However, lithologies can readily be distinguished by most well logs because of the quite different mineralogy. Using Log Data to Determine Lithology Simple lithologic determination can be done with just one curve like the SP or gamma ray. It can be quite accurate if you already know something about the rock types. If there is more than two rock types present, you need more information than just one curve. More complex lithologic determination can be done with multiple log measurement crossplot techniques (Density/Neutron, Density/Sonic, Neutron/Sonic, MN Plots, or Mid-Plots). Also, the mud log and conventional and sidewall cores can give additional information about the rock type to aid in the wireline log interpretation. There is nothing better than having the rock in your hand. Logging Tools Measure Bulk Properties Logs measure bulk properties of the matrix, clays, and pore fluids in the rock. Log readings are affected by variations in
the abundance and type of matrix, clays, and fluids. Determining the matrix lithology requires the formation evaluationist to separate the effects of the fluids on the log readings from those of the porosity. This is possible because different types of measurements respond to different rock properties. The sonic log is sensitive to the acoustic travel time of the rock, the density log is sensitive to the electron density, and the neutron log is sensitive to the hydrogen density. The petrographer uses the term matrix to describe the minerals present between the framework grains. The formation evaluationist uses the term matrix to describe the framework grains and uses the term clays to describe the minerals between the matrix grains. The figure compares the petrograher and Formation Evaluationist view of the term "Matrix" and the bulk properties measured by logging measurements.
Clays and Shales The term "clay" can have several different meanings. One meaning is a grain size term, any thing less than two microns in size. As it relates to formation evaluation clays are a family of sheet silicate minerals that are found in many sedimentary environments. There are many clay minerals but they are typically classified into 4 main groups; kaolinite, chlorites, illites and smectites. Clays have some very unique properties which effect responses on wireline logs and therefore make their quantification extremely important. Clay surface areas (often expressed as CEC) are typically six to seven orders of magnitude greater than that of sandstone grains. This becomes important for two reasons: 1. the number of possible reaction sites available in the pore space increases, resulting in an increase in matrix conductivity. 2. the amount of water that can be held by capillary forces in the additional micropore space is increased; since this water is immobile, it is not produced, however, it will show up on logs complicating the decision-making process.
Clays vs. Shales One of the most confused set of terms in formation evaluation is clay and shale. We often use these terms interchangeably and cause much confusion. Shale is a rock term referring to a sedimentary rock with > 60% clays sized particles usually but exclusively clay minerals. Most shales are made up of 55 to 90% clay minerals with remained being quartz, feldspar, rock fragments and some organic material. Many log evaluation techniques try to account for clay effects without having any direct information about the clay minerals so these techniques use the shale properties (something that is measured on the log)as a first approximation of clay properties." Shale corrections" are used for all types of
measurements but they are an attempt to account for the adverse affects of clays. Over 80% of all sedimentary rocks are shales, with the remainder being about 60% sandstone and 40% carbonate. Clay minerals, including the several varieties of mica, usually make up about 60% of shales, with the remainder being mostly fine-grained fragments of those minerals occurring in sandstones that best survive weathering.The fractions of the common clay minerals range greatly for shales of different geological ages. Clay mineralogy is related to depositional history, diagenetic processes, depth of burial, rock age and other factors. Older shales show increasing amounts of illite, and less smectite and other expanded clays. Detrital vs Authigenic Clay minerals are almost always a significant part of any clastic depositional system. So clays can be laid down with sand grains usually as alternating sand and shale sequences or more mixed if the or bioturbated . Once deposited mineralogy can continue to change dewatering chemical substitution Key Points 1. Shales are not made up of exclusively of clay minerals 2. The clays in sands may not be the same as the clays in the shales 3. Different clays have varying effects on log measurements 4. For some log measurements the distribution of clay is as important as the type of clay mineral 5. Chlorite and Kaolinte have higher OH content and therefore stronger effect the thermal neutron 6. Illite is the only clay mineral with strong radioactive component 7. All have OH- in the crystal structure 8. Montmorillonites can expand in the presence of fresh water
Evalution of Sandstones Reservoirs The primary formation evaluation objectives in both carbonate and clastic rocks are similar, for example, the identification, quantification, and producibility of hydrocarbons. Problems related to formation evaluation of sandstones are varied and numerous; clay effects on logs, evaluation in fresh water reservoirs, and evaluation problems caused during the drilling of the well. Sandstones range from massive, clean, well-sorted and unconsolidated to thin-bedded, shaly and/or calcareous, poorly sorted and well indurated. Reservoir characteristics for productive sands can have an equally wide range. Characterization of Sandstone Reservoirs Sandstones range from massive, clean, well-sorted and unconsolidated to thinbedded, shaly and/or calcareous, poorly sorted and well indurated. Reservoir characteristics for productive sands can have an equally wide range. The average porosity of sandstone reservoirs is perhaps double the average porosity for carbonate reservoirs. In some prolific carbonate producing provinces, maximum average reservoir porosity is less than ten percent. Typically, sandstone reservoirs with low porosity do not have enough permeability for commercial production of anything but gas (unless they are fractured). Sandstones typically have narrow permeability ranges. Sandstone permeabilities up to several darcies are not uncommon. The exception are thin-bedded laminated shaly sands.
Evaluation Problems in Sandstone Reservoirs 1. Sandstones are usually deposited initially in muddy water, and always contain some fine material that includes clay minerals. Some sandstones have been winnowed by currents or winds, and most (but never all) of the fine fraction containing the clay minerals has been removed. Other sandstones have been dumped with very little sorting by the geological processes that deposited them so that they have a wide range of grain sizes, often including up to 30% or more clay-size material. 2. Sandstone interpretation problems caused by clays are often aggravated by the presence of fresh formation waters. Very fresh formation waters are almost unknown in producing carbonate reservoirs, whereas productive sandstone with reservoirs water salinities of less than 5000 ppm are not uncommon. 3. When holes are drilled in harder consolidated rocks, they remain close to the drilled diameter due to the more competent nature of the rocks. Drill cuttings are usually representative of the rocks being drilled. Conventional core can be used, but sidewall coring is less successful. Packer seats can be obtained, permitting drillstem testing when porosity is encountered. Much of the evaluation is accomplished during drilling and before logs are run. In contrast to that; in soft, unconsolidated sandstone have poor hole conditions that limits evaluation during drilling. Wells are evaluated mostly at total depth using wireline logs, plus hydrocarbon logs and sidewall samples. Conventional coring is often unsuccessful. However, a plastic sleeve core barrel may not only improve recovery, but also minimize trauma to the core during handling. Open hole drillstem tests are often unsafe, and packer seats are commonly unobtainable. Wireline formation tests are used to determine reservoir fluid content and pressures. Often they are inconclusive because of bad hole conditions or deep invasion. If a potential productive zone is found by these methods, it is tested by completing the well and production testing.
Summary of Clastics VS. Carbonates
Clastics and Carbonates have different reservoir properties and the log analyst uses different formation evaluation methods.
Comparison of Carbonate and Sandstone Reservoir Parameters Sandstones
Parameter
Carbonates
10%
Minimum Porosity
2%
38%
Maximum Porosity
50%
10 Darcies
Maximum Permeability
>> 10 Darcies
Always
Conductive Solids
Rare
Common
Fresh Formation Water
Rare
1. Formation evaluation and drilling problems associated with sandstone reservoirs, and the methods developed to solve them, can be quite different from those related to carbonate rocks. 2. Sandstones range from massive, clean, well-sorted and unconsolidated to thin-bedded, shaly and/or calcareous, poorly sorted and well indurated. Reservoir characteristics for productive sands can have an equally wide range. 3. Problems related to formation evaluation of these sandstones are varied and numerous; some are similar to carbonate problems, while others are unique to sandstones. The average porosity of sandstone reservoirs is perhaps double the average porosity for carbonate reservoirs. In some prolific carbonate producing provinces, maximum average reservoir porosity is less than ten percent. 4. Typically, sandstone reservoirs with such low porosity do not have enough permeability for commercial production of anything but gas (unless they are fractured). On the other hand, some chalk carbonate reservoirs have porosity greater than any found in sandstones. 5. Sandstones typically have narrower permeability ranges than carbonates. Sandstone permeabilities up to several darcies are not uncommon, but nothing comparable to the huge permeabilities of coarsely vugular and cavernous carbonates are found in clastic rocks. 6. Problems unique to sandstone reservoirs are mostly due to two factors: Sandstones are usually deposited initially in muddy water, and always contain some fine material that includes clay minerals. 7. Carbonate reservoir rocks are almost always deposited in very clear water, because this is the environment most favorable to the living organisms that create the minerals. 8. Some sandstones have been winnowed by currents or winds, and most (but never all) of the fine fraction containing the clay minerals has been removed.
9. Other sandstones have been dumped with very little sorting by the geological processes that deposited them; resulting in a wide range of grain sizes, often including up to 30% or more clay-size material. 10. Sandstone interpretation problems caused by clays are often aggravated by the presence of fresh formation waters.Very fresh formation waters are almost unknown in producing carbonate reservoirs.Productive sandstone reservoirs with water salinities of less than 5000 ppm are not uncommon.
Evaluation Methods Comparison Carbonates vs. Sandstones Formation Evaluation Method
Value in Sandstones
Value in Carbonates
Wireline Logs
Not always diagnostic
Usually reliable
Mud Logging
Essential
Very Useful
Conventional Cores
Poor recovery
Widely Used
Plastic Sleeve Cores
Valuable
Rarely Used
Sidewall Cores
Essential
Some Use
Wireline Tester
Essential
Widely Used
Drillstem Testing
Difficult and Dangerous
Widely Used
Testing Through Casing
Often Necessary
Occasionally Required
'Shaly Sand' Interpretation Problems
Common
Rare
Borehole Terminology An idealized borehole is a cylinder of uniform diameter filled with a drilling mud "ideal" for logging conditions. Most wireline tools developed for openhole formation evaluation have been optimized to operate in 8" borehole.
As the drill bit penetrates geological horizons in the subsurface, drilling fluid is introduced to that formation for the first time. Mud pressure, penetration rate, and the porous, permeable nature of the rock being penetrated are variables largely responsible for the eventual profile of invasion. In general, wells are drilled with pressure slightly overbalanced to contain reservoir pore pressure and avoid potential blowouts. Impermeable rocks do not experience invasion; however, low-porosity rocks with some permeability are often invaded deeply because available pore spaces to accept the penetrating fluids are widely spread around the borehole. Rock with high porosity and high permeability normally demonstrates shallow invasion because there is more pore volume near the borehole to accept invading fluids.
Logging Terminology in the Borehole Standard terminology is used to refers to the resistivites and saturations of these regions as shown. The flushed zone immediately adjacent to the borehole is at most, a few inches (centimeters) beyond the borehole wall and essentially contains only mud filtrate (Rmf) as occupying fluid . The flushed zone has unique resistivity (Rxo) and saturation (Sxo) values. Most native fluids and gases are flushed farther into the formation, and those that remain are called residual or immovable. Oil reservoirs typically demonstrate residual oil saturations of 15% to 40%, but trapped residual waters are not uncommon, especially in carbonate reservoirs. As time passes, some of the mud filtrate continues to migrate laterally into the formation; i.e., it begins to commingle with native reservoir fluids and form a transition zone between the flushed zone and undisturbed reservoir rock . Water saturation in this transition zone (Si) can vary considerably if the reservoir contains hydrocarbons. A water-bearing horizon will continue to exhibit 100% water saturation, but the commingled waters have differing salinities or resistivities (Rz). The resistivity of the invaded zone (Ri) will therefore differ from that of the flushed zone and virgin zone beyond. The length of time the formation is exposed to the borehole fluid pressures influences the depth of invasion, but permeability and porosity also influence the lateral distance of invasion. A hypothetical view of the diameter of invasion in formations that are somewhat heterogeneous illustrates the effects of porosity and permeability. Diameter of invasion (di) represents the lateral interval encompassing the borehole that is affected by invading drilling fluid, whereas the diameter of flushing (dxo) is much smaller. The virgin reservoir rock has a resistivity (Ro) if it is 100% water bearing, but if the formation contains any hydrocarbon, it has a higher value of resistivity (Rt). The native connate water has its unique resistivity (Rw) or salinity that affects resultant calculations of
water saturation (Sw); i.e., Sw decreases as the volume of oil or gas increases. Resistivity increases as nonconductive hydrocarbon replaces conductive formation waters in the pore space.
Geothermal Gradient
Temperatures at depth can be estimated by using the geothermal gradient if one knows the mean surface temperature and the geothermal gradient. Subsurface temperatures normally increases with depth, and the rate of increase with depth is called the geothermal gradient, defined as:
GG = 100(Tf-Tm)D where GG = geothermal gradient (°F/100 ft), Tf = formation temperature (°F), Tm = mean surface temperature for a given area (°F), D = depth of formation of interest (ft). This equation can also be written as:
Tf = Tm + GG(D/100) and allows an estimate of formation temperature. Charts are available to estimate formation temperatures using a geothermal gradient as shown below:
Mean surface temperature data are usually provided by governmental agencies. In many countries, maps for different seasons are available. Obviously, extreme cold at the surface will affect temperature at very shallow depths (< 1,000 ft), but extreme heat at the surface will also affect the temperature gradient in very shallow wells. Thermal Conductivity of Rocks (10-3 calories/cm/°C) Shale 2.8-5.6 Gypsum 3.1 Water 12-14 Sandstone 3.5-7.7 Anhydrite 13 Air 0.06 Porous Limestone 4-7 Salt 12.75 Oil 0.35 Dense Limestone 6-8 Sulphur 0.6 Gas 0.065 Dolomite 9-13 Steel 110 Quartzite 13 Cement 0.7 The geothermal gradient is a function of the thermal conductivity of the rocks in the subsurface (see table below). A chart with several gradients is provided for estimating temperature (see chart above), but recall that gradients are seldom constant. Temperature surveys have been used effectively to identify different lithology layers from temperature gradient changes (see figure below). Certain geological structures, such as salt domes or reefs, overpressured zones, and different geological ages are factors that cause changes in the geothermal gradient. In one area of the Rocky Mountains (USA), the gradient increases from 1.1 to 1.4 when going into Paleozoic rocks from the younger rocks above.
Key Points 1. Formation temperature and heat conductivity are important to formation evaluation because all resistivity data are temperature dependent. 2. Geothermal gradient is a function of the thermal conductivity of the rocks in the subsurface 3. Geothermal gradients are seldom constant. 4. Extreme cold at the surface will affect temperature at very shallow depths (< 1,000 ft). 5. Extreme heat at the surface will affect the temperature gradient in very shallow wells.
6. Temperature surveys have been used effectively to identify different lithology layers from temperature gradient changes. o salt domes or reefs o overpressured zones o different geological ages 7. Thermal conductivity of water does not change appreciably with increasing salt concentration. 8. The effects of pore fluids on gross conductivity is relatively small for rocks of low to moderate porosity. 9. Thermal conductivity of clays tends to vary inversely with the water content. o In overpressured zones, the higher pore pressure causes higher porosity that accounts for more fluid volume. o Geothermal gradients are typically larger in massive shale formations that overlay reservoir rocks. o Geothermal gradients are usually reduced considerably in aquifers. o Overpressured, high-porosity shales represent a geothermal anomaly.
Temperatures in a Drilling Borehole
The process of circulating drilling fluids (mud) creates a very complex temperature distribution along the borehole - deep zones are cooled while shallow zones are heated. Geothermal measurements are made in boreholes which have temperaturedepth profiles different from the geothermal profile. This is largely due to heat transfer caused by fluid flow (e.g., circulation of drilling mud, upward flow of produced reservoir fluids, downward flow of injection fluids) as seen from the figure below:
Tempertures in a static well During the period of time required to pull pipe (drill pipe) and start logging, the annular (annulus)and drill pipe fluids (mud) mix and heat transfer continues between the borehole and formation. The borehole temperature profile changes from that shown previously and becomes fairly linear with depth, except near total depth, as shown in figure below. At point X, the borehole temperature is equal to the formation temperature and no heat transfer occurs. With the passage of additional time, the borehole fluid (mud) cools above point X and warms below point X as both borehole regions approach thermal equilibrium with the formation.
Formation Temperatures from Logs
We can estimate true formation temperature by making temperature readings on each tool run. We then extrapolate, using a technique similar to the Horner plot used in pressure prediction. Although continuous temperature measuring devices are readily available, most borehole temperature estimates are made from maximum-reading thermometers attached above wireline logging tools. Except in areas such as steam drives, where the normal geothermal gradient is disrupted, this maximum temperature reading is assumed to coincide with the bottom of the hole.
The cooling effect of circulating drilling mud on formations prior to logging can reduce measured bottom hole temperature from thermometer readings by 20°F to 80°F below actual formation temperature. Thus, the BHT recorded on the log header is always lower than true, or static, formation temperature. Since the rise in temperature is similar to a rise in pressure, Timko and Fertl (1972) suggested that BHT data can be analyzed in a manner similar to the Horner pressure-buildup technique. The basic concept predicts a straight-line relationship on semilogarithmic paper of BHT in °F (from well log heading) vs the ratio of t/(t + t), where t= time in hours after circulation stopped; t = circulating time in hours for well conditioning. Extrapolation of this straight line to a ratio of t/(t + t)= 1.0 determines true static formation temperature as shown in the figure below.
Borehole Cross Sections
Borehole cross sections are measured to assure that logging measurements are valid, to correct logging measurements calibrations for downhole conditions, and to compute hole volumes for cement design.
Borehole size or gauge has been measured with caliper logs for many years. The caliper logs used on different tools respond differently in the same non-cylindrical borehole. Borehole cross sections are often described as circles and ellipses because only these shapes can be defined from the one or two dimensions usually available from one logging run. Studies of multi-arm calipers indicate that borehole elongation is preferentially in one direction while the section at right angles tends to stay in gauge. The borehole also tends to be more rugose in the direction of maximum elongation.
Standard Caliper Log Configurations 1. One arm calipers also serves as an eccentering device. o Tend to seek the longest dimension of the borehole cross section, especially if the long axis is in a vertical plane. o If the contact with borehole is steel it is considered to cut through mudcakes. If the contact is rubber, it reads borehole minus one mudcake thickness. 2. Two arm calipers, extend equidistant from a centralized tool body. o Tend to record the long axis of out-of-round holes. o All borehole contacts are rubber and measurement is considered as borehole minus two mudcake thickness.
3. Three arm calipers, center the tool body. o Maintain their arms equidistant from the body of the tool and measure only one diameter,somewhere between the minimum and maximum of the noncircular section.
4. Four arm calipers, consisting of two calipers at right angles to each other. o Four-arm calipers typically use two pairs of arms that extend independently of each other. One pair seeks the long dimension of an out of round hole, the other measures the dimension at right angles.
5. Six-arm devices, which use six independent arms, spaced at 60o angles, allowing the characterization of irregular shaped boreholes. o Six-arm calipers have each arm independent, allowing the arms to characterize the hole shape regardless of the relative position of the tool body. An advantage to this design is that significant pressure is not required to make a measurement, thereby reducing tool drag and irregular tool motion.
Tool Contact In addition to the number of arms, the nature of the tool contact also affects the caliper response when a hole is not cylindrical or has mudcake. Devices that have small contact area can detect smaller borehole irregularities. Contact pressure is usually high enough to cut through any mudcake (steel pads). Pad type devices have somewhat larger pad contact area and when operated at lower contact pressures will override mudcake (rubber pads). Changes in hole shape may not be sensed if the borehole irregularities are changing rapidly and are smaller than the pad dimensions, depending on how the tool contacts the borehole wall.
Invasion
Drilling muds are typically designed so the hydrostatic pressure of the mud column exceeds formation pressure. This pressure overbalance causes mud to
enter permeable formations while at the same time depositing solid particles from the mud system on the borehole wall, forming a filter cake (hmc). The time required to build up sufficient mudcake is a function of specific formation properties and drilling fluid properties, especially solid particles within the mud system. Formation of the filter cake prevents further filtrate invasion and formation damage while maintaining wellbore stability. In most mud systems, invasion is expected. These invading mud particles alter formation composition, and invading mud filtrate alters formation salinity and saturation. As a result of this invasion, some logging measurements reflect drilling altered properties rather than true formation properties. Separating the part of the logging response that comes from the invasion altered region from the part derived from unaltered formation is a major task in well log interpretation. The control of the mud surge and particle migration is primarily dependent on two things: 1. Maintaining a good size distribution of solid particles in the mud 2. Keeping the drilling fluid-formation pressure overbalance as low as possible.
The porosity of a formation needs to be considered in predicting invasion depth. Given the same filtrate losses into equally thick intervals:
Invasion will be deeper in the formation with a lower porosity; high filtration and low porosity cause "deep invasion". Low filtration and high porosity cause shallow invasion.
For most realistic conditions, invasion cannot be eliminated, only slowed. So, prospective intervals should be evaluated as soon as possible. The depth of investigation of a logging tool determines how much the measurement is affected by invasion. Evaluation of water saturation from electrical properties requires an accurate determination of uninvaded formation resistivity or conductivity. Ideally, a deep sensing resistivity (or conductivity) log (RLD) is designed to respond to unaltered formation resistivity (Rt) without being influenced by any of the following:
Mud column (Rm) Mudcake (Rmc) Mud impregnated zone (Rim) Flushed zone (Rxo); immediately adjacent to the borehole wall and essentially contains only mud filtrate (Rmf) Transition zone (Ri) Annulus (Ran)
Invasion Profiles 1. Step 2. Transition 3. Annular
Affects of Invasion on Water Saturation Calculations If invasion is extensive and the deep resistivity log (RLD) is responding partially to an invasion altered region; without invasion corrections, Sw calculations are affected as follows;
Hydrocarbon saturation will be overestimated when Rxo > Rt Hydrocarbon saturation will be underestimated when Rxo < Rt
Hydrocarbon saturation may be underestimated if RLD is significantly affected by a low resistivity annulus. Some formations may be so deeply invaded that saturation evaluation is not possible
Corrections for invasion and determination of depth of invasion require an accurate flushed zone resistivity for even the simplest cases. For more complex and deep alterations, additional measurements with intermediate depths of investigation are required. Key Points
The pressure overbalance in the borehole causes mud and mud filtrate to "invade" the borehole wall. Mud cake slows fluid and solid invasion into the formation; some muds contain material which affects log readings. Mudcake is formed from the solids in the drilling mud. Ideally mudcake should form quickly and have low permeability to reduce invasion. Deeper invasion occurs in lower porosity. Prospective intervals should be evaluated as soon as possible after drilling. The depth of investigation of a logging tool determines how much the measurement is affected by invasion.
Spontaneous Potential The Spontaneous Potential, commonly abbreviated SP, is a measurement of the naturally occurring electrical potentials in the wellbore as a function of depth. It is one of the oldest logging measurements and in today's environment one of the most under utilized measurements. It is sensitive to grain size, permeability and fluid content. SP is somewhat less quantitative than other measurements, however if used carefully it can provide a wealth of information.
Basic Measurement Principles The recording of the SP is the measured potential difference between a single passive moving electrode in the wellbore and a reference electrode, usually located at the surface in the mud pit, or attached to the casing head, or in sea water. There are three possible sources of the electrical potential which contribute to the SP; they are: 1. The electrochemical, Ec potential ,made up of the.membrane and liquid junction potentials 2. The electrokinetic, Ek. potential. (sometimes called streaming potential)
The sum of these different potentials results in a measurement that is not absolute but relative. The potential sensed by the SP electrode is the voltage drop across the mud in the borehole and is typically reported in mv. Since the SP requires a current path in the mud it will not function in an oil based mud. There also be little or no signal if there is no potential difference between the borehole and the formation i.e. where Rmf=Rw. The maximum normally encountered SP is called the static SP (SSP). The SSP is the amount of deflection observed when the SP electrode passes from a position inside a very thick, porous, permeable, clean water sand to a point well within a thick uniform shale. The SSP is the value of the SP that is predicted by the following equation: SP = -Klog (aw/amf) ; where:
aw = the activity of the formation water amf = is the activity of the mud filtrate K = constant Several factors can contribute to less than maximum deflection 1. Insufficient bed thickness causes the effective resistance of the sand to increase because of the corresponding reduction in the cross sectional area of the sand. 2. Increased borehole diameter, the effective resistance of the mud decreases because of the increase of the cross sectional area of the borehole.
3. Deep invasion the interface between the liquid junction and the membrane junction is moved deeper into the formation; which increases the effective resistance of the sand because of the increased path length to the borehole. 4. Presence of hydrocarbons increases the effective resistance of the sand because oil and/or gas have a much higher resistivity than water resulting in a greater drop of potential across the sand, resulting in a suppression of the SP deflection 5. Presence of clay restricts the migration of Cl- ions and assists the migration of Na+ ions due to the predominant negative charge of the clay 6. Significantly reduced porosity and permeability
The shape of the SP curve approaching or leaving the sand/shale boundary is controlled by the relative resistivities of the mud, sand, and shale, an inflection point is observed at the bed boundary interface. This inflection point may be shifted to closure to one formation or another depending on relative resistivities but the inflection point represents the bed boundary. Applications
differentiate permeable from non-permeable formations determine bed boundaries and bed thickness determine formation water resistivity, Rw can be used to calculate Rw in wet zones estimate the volume of shale, Vsh
Borehole and Quality Considerations 1. SP's are very sensitive to extraneous electrical fields which can be caused by welding or other rig electrical equipment, residual magnetism from the cable drum, or atmospheric electrical charges. 2. Unresponsive SP's can be caused by poor grounding of the surface electrode 3. Streaming potentials can caused by under or overbalanced mud columns with differential pressure into or out of the formation. 4. The SP is a relative measurement and drifts with salinity and temperature changes, practice in older logs was for the field engineer to manually bring the SP back on scale. These scale changes are generally obvious but may confuse interpretation. 5. Hydrocarbon causes suppression of the SP signal 6. Thin beds affect SP development how much depends on the resistivity of the formation and the contrast between Rw and Rmf 7. SPs are often base adjusted to remove shifts and drift this needs to be done carefully so as not to introduce anomalous readings
Key Points 1. Variations in SP are the result of the electric potential between the wellbore and the formation as result of the difference is the Rmf and Rw 2. In most wellbore environments, where salinity of the formation water is greater than the salinity of the mud or mud filtrate(Rw
expected SP development opposite relatively high salinity formations is negative. The deflection will be positive if Rw>Rmf. 3. The SP requires a conductive fluid in the borehole, therefore cannot the SP can not be run in non-conductive mud systems or air or gas drilled wells. 4. The SP response of shales is relatively constant and follows a straight line, known as the shale baseline. SP deflection is measured from the shale baseline. 5. If Rmf Rw the SP will not deflect from the shale baseline.
Gamma Ray Log The gamma ray log is probably the most widely run logging measurement. It is used to distinguish lithologies particularly sand from shale. It is a relatively simple measurement and works in open hole or cased so it is the primary measurement for deep control and correlation.
Measurement Principles Gamma Rays are bursts of high energy electromagnetic waves which are emitted spontaneously by some radioactive elements. Nearly all of the gamma radiation encountered in the earth is emitted by the radioactive potassium isotope of atomic weight 40 and the radioactive elements of the uranium and thorium
series. For the most part these elements are found in minerals and solid organic material so almost all the signal comes from the rock matrix and not from the fluid.(some exceptions do occur, usually tracers or radioactive salts added to muds) The gamma ray log is a passive measurement. Gamma rays from the logging environment strike the detector either a solid state crystal (NaI or CsI), or a Geiger Mueller gas chamber and the incident gamma rays produce a signal which is recorded as counts/second. The counts are converted to API units, a standard defined for gamma ray logs and units used to display this measurement. The higher the API the more gamma ray counts recorded. Gamma rays are only slightly attenuated by mud , casing and cement so the measurement can be made under most open and cased hole situations. Applications 1. To distinguish shale beds from other lithologies 2. Semi quantitative calculation the volume of shale and/or clay in reservoir rocks; this assumes the clean zones do not contain radioactive minerals, i.e., granite wash, micaceous sands, radioactive carbonates. o Vsh = (Grzone- Grclean)/(Grshale- Grclean) o Other nonlinear equations are used in some areas 3. Correlation and depth control log, between wells and for logging runs in the same well 4. ID zones of fluid flow (often leaves radioactive scale),fractures, and radioactive tracers
Borehole and Quality Considerations 1. Hole Size o increased borehole diameter attenuates the detector response by moving the tool farther from the formation 2. Position of the tool in the borehole, eccentered tools are closer to the borehole wall 3. Variations in the mud system o bentonite, a clay mineral, is used widely as a gel additive and contains significant amounts of Th an U. o Potassium salts (KCL) are frequently used for clay stabilization o Barite weighting material tends to shield the detectors from the formation by increasing the photoelectric absorption of gamma rays 4. Variations in casing size and weight o Casing properties such as, thickness, material, grade and its position in the hole, as well as the cement properties introduce variations in the energy spectra. 5. Variations in porosity can have effect more rock material means more counts
Key Points
2. 3. 4. 5. 6. 7.
1. Gamma Ray logs are lithology logs that measure the natural radioactivity of a formation Because radioactive material is concentrated in shale, shale has high gamma ray readings and generally sands and carbonates have low gamma ray readings; exceptions are granite wash, micaceous sands, and radioactive carbonates. The gamma ray provides bed information in those environments where the SP is not diagnostic, i.e., salt muds, oil based muds, air or gas drilled holes, and cased holes. Vertical resolution is affected by logging speed, but is approximately 2' at a logging speed of 1800 feet/hr. The gamma ray is a statistical measurement not every wiggle on the curve is significant. In general the tools that are run the slowest give the better readings. Depth of investigation of the gamma ray is approximately 10 - 12 ". The gamma ray log is nearly always recorded in track 1 of the log display. It is scaled so that low radioactivity is near the left side of the track and increases to the right toward the depth column.
Acoustic Logging Acoustic logging uses various forms of sound wave propagation. The acoustic logging principle is related to seismic exploration methods, since both derive data from wave travel times. Types of acoustic measurements include:
Measurement of compressional wave travel times for porosity determination. Recording of full waveforms for differentiating compressional, shear, and Stoneley (Tube) wave travel times. Characterization of the borehole environment (cement evaluation or televiewer imaging of the borehole wall). Integration (summation) of interval transit times as an aid to interpretation of seismic data.
The basic acoustic log is a recording, versus depth, of the time, t (delta-t), required for a compressional sound wave to traverse one foot of formation. Known as interval transit time, t is the reciprocal of compressional wave velocity, and is usually expressed in terms of micro-seconds per foot. The interval transit time for a given formation depends on its lithology and porosity. Dependence on porosity, when lithology is known, makes the acoustic log very useful in formation evaluation.
Measurement Principle The most commonly used borehole compensated acoustic logs use receivers positioned three feet and five feet from each transmitter. Long-spaced tools are sometimes used having transmitter-receiver spacings of 10 feet or more. When one of the transmitters is pulsed, a sound wave is generated and travels through the borehole fluid to the borehole wall, where it is refractedalong the wall, reflected back across the fluid column to two receivers, and recorded as the elapsed time required for the first compressional wave arrival. The difference in the travel (arrival) times between the two receivers, which are a known distance apart, represents the acoustic velocity through the formation. This is known as acoustic interval transit time (t), the time interval representative of the distance between the two receivers expressed in micro-seconds per foot. Each rock type has a characteristic acoustic velocity. Voids in the rock slow the transit time, allowing porosity to be calculated. A knowledge of lithology and fluid type allows porosity to be calculated by empirical means. The speed of sound through the tool body and through the borehole fluid is less than that in the formation. As a result, direct tool body and fluid waves do not interfere with the desired measurement. A knowledge of fluid travel time and lithology is needed to calculate porosity.
Applications for Acoustic Logs
Porosity determination Gas detection Detection of fractures Calibration of seismic and log information Abnormal pressure detection Fracture detection Preparation of synthetic seismograms using the acoustic and density log combination to compute reflection coefficients. Acoustic compressional arrivals may also be compared to shear arrivals or Stoneley arrivals to determine the mechanical properties (competency) of rock or to derive an estimate of permeability. It is also possible to empirically relate comparisons of compressional and shear arrivals to lithology. The advanced technology required to generate and record shear and Stoneley waves is present only is special tools which have been available only since about 1990.
Key Points
Sound velocities are determined by the bulk modulus, shear modulus, and bulk density of the formation. The borehole compensated acoustic signal will be relatively stronger than the long spaced acoustic signal because its source-receiver spacings are significantly less than that of the long spaced tool. However, the long spaced acoustic measurement is better designed to investigate virgin rock in the presence of significant invasion, due to deeper sound penetration. The depth of investigation for both the standard and long-spaced acoustic tools is, however, very shallow. The vertical resolution of the acoustic measurement is determined by the transmitter receiver spacings. The interval transit time of a formation increases in the presence of hydrocarbons. The phenomena of cycle skipping occurs when gas, fractures or other anomalies attenuate the transmitted signal below the triggering threshold of the receiver. There are three key equations which estimate porosity from sonic logs: o Wyllie Time-Average equation o Wyllie Time-Average equation with compaction correction in poorly consolidated rocks, and o Raymer-Hunt-Gardner equation
Density Log Density measurements are used primarily to calculate formation porosity when lithology is known. When combined with other porosity logs, density measurements are used for the detection of gas, evaluation of shaly sands, and lithology identification. Compensated density tools measure the in-situ bulk formation density, RHOB, recorded in (g/cm3). Additionally, a correction curve, deltarho is also recorded (gm/cm3), that reflects the correction to rhob required to compensate for the effect of mudcake. Density Log Measurement Principle The basic tool employs a radioactive source (Cs137; Eg = 663keV) of gamma rays and two detectors. The two sodium iodide scintillation detectors are located at fixed distances and are shielded from the source. The emitted gamma rays collide with electrons in the formation, losing some of their energy to the electrons this interaction is known as Compton scattering(the more electrons the more Compton scattering). The gamma rays from Compton scattering are detected at both the long-spaced (LS) and short-spaced (SS) detectors. The rate of gamma ray attenuation is a function of the electron density of the formation which is closely related to bulk density for the most common elements. The output curve is usually designated RHOB or RHOZ.
The short spaced detector is sensitive to the mud cake thickness and a correction chart, called a spine and ribs relates the count rates at both detectors to a mud cake thickness. This is used to calculate the necessary correction for mudcake .This correction usually appears on the log and is termed or (rho).Corrections are applied to the bulk density in real time during the logging
operation and are used for QC. When lithology is known density measurements are used to calculate formation porosity. Because of the relatively low energy of the gamma ray source, the penetration power of the gamma rays limits the depth of investigation to several inches. As a result, under most conditions the density tool sees primarily flushed zone. Applications:
Determine formation porosity by assuming the fluid density in the pore space and the matrix density contribute to the total bulk density in an additive manner;
= (
matrix -
log)/ (
matrix -
fluid)
Identify lithology when run with other porosity tools. Indicate gas and determine gas saturation when run with neutron logs. Qualitative and quantitative shale identification
Borehole and Quality Considerations
Borehole Size- since density is a pad measurement the borehole size is not really an issue unless it is larger than the arm can reach, however the pad shape is optimized for an 8 inch borehole if it is larger or smaller the detector senses less of the formation and should be corrected. This correction assumes a circular borehole. Borehole rugosity will prevent good pad contact Loss of pad contact will lead to reading mud density and will be seen as a high porosity anomoly rho is the correction applied for mudcake thickness values > .2 gm/cc. should be considered questionable
Key Points
Density measurements are primarily used to calculate formation porosity when lithology is known. Density response to gas is to lower Rhob Density response to shale can vary depending on clay type and degree of compaction
Because the density is a pad tool, the measurement is very sensitive to the rugosity in the borehole. Because of the relatively low energy of the gamma rays source, the penetration power of the gamma rays limits the depth of investigation to several inches. The vertical resolution of the density measurement is ~ 2' at a logging speed of 1800 ft/hr. The depth of investigation is approximately 4". The counting statistics improve as more gamma rays reach the detector , lower RHOB, higher porosity. RHOB is generally considered a good measurement if delta Rho <.2 gm/cc
Photo-Electric Effect The photoelectric or PE measurement is not a separate service but is recorded at the same time as the modern density measurement. It is used as a rough lithology indicator. Measurement Principle The photoelectric effect (PEF) is an integral part of energy window density logging. While the traditional compensated density tool is based entirely on Compton scattering of gamma rays by electrons, the litho-density (Z-density) energy window measurement is based on both Compton scattering, and the photoelectric absorption of gamma rays by electrons. The photoelectric effect occurs when a gamma ray collides with an electron and is absorbed in the process, so all of its energy is transferred to the electron. The probability of the reaction taking place depends on the energy of the incident gamma ray and the type of atom. The photoelectric absorption index of an atom increases with increasing atomic number, Z, providing a rough correlation with lithology.
Pe = (0.1 X Z)3.6
While the Compton scattering occurs over a wide energy range, the photoelectric effect occurs only with low energy gamma rays (less than about 0.5 Mev). Gamma rays are emitted from the tool with an energy of 662 keV and are scattered by the formation, losing energy until they are absorbed through the photoelectric effect. The photoelectric absorption coefficient is virtually independent of porosity, with only a very slight decrease in the coefficient as porosity increases. The fluid content of the formation also has little effect. Simple lithologies, such as pure sandstone, anhydrite, etc., can be read directly from logs using the Pe curve (PEF) alone. Because the Pe of a mixed mineralogy does not combine volumetrically, a new parameter, U, was developed for interpretation purposes. U represents a macroscopic linear cross-section and specifies the absorption of a given thickness of material. It is defined as: U = Pe (Rhob) The most common lithologies and their corresponding characteristic PEF, Rhob and U values are below: Pe Rhob
U
Quartz Sand 1.81 2.64
4.78
Salt (Halite) 4.65 2.04
9.68
Limestone
5.08 2.71
13.77
Anhydrite
5.05 2.98
14.95
Dolomite
3.14 2.88
9.00
Recent Advances Newer measurements (specifically Schlumberger's Platform Express) integrate the density and PE measurements they are solved for by error minimization
modeling the counts from 11 energy windows from three different detectors ( long and short spaced as well as a mud detector). Application
Lithology identification in clean formations. Clay mineralogy differentiation and identification in combination with Th/K ratio from spectral gamma ray log.
Borehole and Quality Considerations
Strongly affected by presence of heavy elements, primarily barite, in drilling mud and invaded filtrate. PEF may be normalized to compensate for barite, but as the magnitude of the shift increases, inconsistencies in invasion profile tend to render the normalized PEF substantially unreliable.
Key Points
PEF is a useful direct lithology indicator for common rock mineralogies. PEF may also be plotted vs. Th/K ratio to differentiate and identify clay minerals. U may be calculated for use in definitive lithology cross-plotting (U versus Rhoma, e.g. chart CP-21).
Neutron Porosity
There many types of neutron logging however thermal neutron porosity tools are perhaps the most widely utilized. This type of Neutron measurement is used primarily to calculate formation porosity when lithology is known. When combined with other porosity logs, neutron measurements are also used for lithology identification, evaluation of shaly sands, and gas detection in both open and cased hole. Neutron logs primarily measure hydrogen ion concentration and are, therefore, sensitive to fluid-filled pore space, but are also influenced strongly by clays. Measurement Principle Neutrons are electrically neutral particles, each having a mass almost identical to the mass of a hydrogen atom. High-energy (fast) neutrons are continuously emitted from a radioactive source which is mounted in the logging sonde. These neutrons collide with nuclei in the formation. With each collision, the neutron loses energy. The amount of energy lost per collision depends on the relative mass of the nucleus with which the neutron collides. The greatest energy loss occurs when the neutron strikes a nucleus of nearly equal mass. The most common nucleus of this type is that of hydrogen. Collisions with nuclei of dissimilar mass do not slow down the neutron very much. Thus, the slowing-down of neutrons depends primarily on the amount of hydrogen in the formation.
Within a few microseconds, the neutrons have been slowed by successive collisions to epithermal and thermal velocities, corresponding to energies of from 100 down to 0.025 electron volts. They then move (diffuse) randomly, without losing any more energy, until they are captured by the nuclei of receptive atoms such as chlorine, hydrogen, silicon, etc. The capturing nucleus emits a high energy gamma ray. Depending on the type of neutron logging tool, either the gamma rays of capture or the neutron concentrations themselves are counted by one or more detectors in the sonde. The traditional CNL log detects thermal neutrons, however, some newer CNL tools incorporate "dual porosity" measurements which include both epithermal and thermal detectors. The Compensated Neutron Tool (CNL) The measurement configuration of the traditional compensated neutron tool is shown in the above figure. Fast (high energy) neutrons are produced by a source located near the bottom of the tool. The source consists of 16 curies of americium housed in a beryllium container. The interaction of gamma rays emitted by the americium with the beryllium produces high energy neutrons which radiate into the formation. Two thermal neutron detectors are spaced about 30 and 60 cm. above the source. The ratio of count rates from these near and far detectors are measured and transformed into a value for formation porosity. The ratio varies with porosity, but there is also significant influence from lithology because the matrix contributes to the slowing down and capture of the neutrons. Therefore, to accurately derive porosity from the near/far count ratio, lithology must be known. The ratio measurement reduces borehole effects, and increases depth of investigation relative to a single detector system. The CNL tool is de-centralized by means of a bow spring, and standard tool diameter is 3-3/8." It must be run in liquid-filled boreholes, which may be either open or cased. The CNL may be combined with other tools including density, sonic, resistivity, caliper and gamma ray.
Applications of Neutron Porosity
Determine formation porosity in fluid-filled, open or cased boreholes Identify lithology when combined with other porosity logs Indicate formation gas Calculate shale volume Facilitate inter-well stratigraphic correlation
Borehole and Quality Considerations
If the tool is not eccentered properly, and the tool loses contact with the borehole wall, accuracy is severely affected and porosity reads too high . Hole caves (wash-outs) are the primary cause of tool eccentering problems. Dry gas substantially reduces apparent porosity. Porosity values sensitive to many borehole effects , many offsetting if corrects are applied ,all should be applied not just some. Shale causes greatly increased apparent porosity.
Key Points
Neutron curve is presented in porosity units of some lithology (usually appropriate for the area, i.e. ss for Gulf of Mexico), most charts and many calculations require neutron values in limestone units. Neutron logs respond to the amount of hydrogen in the formation. Thus, in clean formation, when pores are filled with oil or water, the log reflects porosity. In the CNL tool, sandstone, limestone and dolomite produce different count rate ratios in rock of identical porosity, making it necessary to know lithology in order to obtain correct porosity. The Compensated Neutron Log (CNL) was designed to reduce environmental effects inherent in neutron logging, improve performance in washed-out hole, and to be capable of running in combination with other logs. When formation and borehole conditions differ from calibration conditions (as they almost always do), corrections must be applied to obtain accurate porosity values, however, these are generally small (one to two porosity units). All corrections to apparent neutron porosity are specific to tool type and service company. The CNL has the deepest depth of investigation of all common neutron tools. At 22 porosity units, the tool sees about 10 inches into the formation (that is, 90% of the signal comes from 10 inches or less). The depth of investigation decreases with increasing porosity (the opposite of the density log). Vertical resolution varies with logging speed. At a logging speed of 1800 ft./hr. vertical resolution is about three feet, and may be improved to a maximum resolution of about 11/2 ft. by further reducing logging speed. Neutron porosity is strongly affected (increased) by shale. Correction requires combining with other logs. Displacement of water or oil by gas or steam will, in general, result in lower apparent measured neutron porosity. Compensated neutron logs are normally run in combination with density and gamma ray tools.
Nuclear Magnetic Resonance Log The NMR log is probably one of the most fundamentally different advances in logging measurements in the last decade. The NMR measurement is sensitive to porosity (independent of lithology) and is also capable of distinguishing pore size distribution which is very indicative of permeability and irreducible water content. Measurement Principles NML is dependent on the alignment of the magnetic moment of protons (hydrogen nuclei) with an impressed magnetic field. Protons tend to align themselves with the magnetic field; and when it is removed or changed the proton precess (much like a spinning top) to align with the orientation of the new magnetic field. This proton precession produces a radio frequency signal. As the protons align with the new magnetic field the signal dies away at a rate which is indicative of it the proximity of the hydrogen to interring forces. By slightly delaying the time of measuring, the hole signal is minimized. The signal from hydrogen associated with fluids in large open pores dies away slowly, from small pores it dies away faster, and hydrogen bound in clays and on clay surfaces dies away very fast (in fact too fast to measure).Gas gives a low signal because of its low hydrogen content. The total amplitude of this radio frequency signal then represents the portion of the rock with fluid free to move, generally dubbed FFI or free fluid index.
Permanent magnets in the NMR tool create a static magnetic field that gives rise to a net magnetization among hydrogen nuclei . A pulsed radio frequency signal rotates the net magnetization 90° away from the static magnetic field . After the RF pulse is removed, the protons precess back to their original state, emitting a radio signal whose strength is proportional to the fluid content of the rock. There are two tools avaliable at this time with different capabilities and processing techniques. Schlumberger's CMR is a pad tool with very fine bed resolution. Haliburton's MRIL is senstive to a volume around the dounut shaped volume around the borehole. The free fluid index (FFI), the volume of free fluid that is not bound electrically or chemically to the clay lattice, to rock surfaces, or to some other mineral lattice includes free oil and water but excludes irreducible water; therefore,
FFI = (1 - Siw) . Siw is found by comparing FFI to ,
Siw = 1 - (FFI/) . FFI can be compared to e, and since it is not affected by water bound to matrix lattice, it is an effective device in hydrated minerals (gypsum, carnalite, polyhalite and clays).
In addition to measuring the total signal of hydrogen decay processing can be done which can extract the relative contribution to the total signal from multiple decay rates. This T2 distribution as it is called relates very closely to the pore size distribution. .
Applications 1. 2. 3. 4. 5.
Effective porosity, e (%) Irreducible water saturation, Siw (%) Residual oil saturation, Sor (%) Heavy oil recognition Estimate of permeability, k
Borehole and Quality Considerations 1. magnetic or paramagnetic minerals in the formation can interfere with the measurement 2. The CMR pad tool is very sensitive to borehole rugosity 3. The MRIL tool is sensitive to large hole size and washouts
Key Points 1. FFI is generally considered to effective porosity of a rock , the different between this and total porosity measurements is termed irreducible
2. T2 distribution can be related to pore size distribution 3. Gas is generally not not see as porosity
Resistivity Logs (General)
The first well log was a resistivity tool, which recorded hand-posted point by point measurements. The contrast in resistivity between non-conductive hydrocarbons and conductive formation water is the basis for quantitative saturation calculations. Many different types of resistivity logs have been developed over the years to investigate different types of formations at different depths of investigation under different logging conditions. There are many ways to classify them , shallow vs. deep, focused vs. unfocused, or induced vs. electrode. below in one useful scheme. Often these measurements will be run in different combination to investigated to possibility of invasion and to find the most appropriate value for Rt.
Conductivity, the inverse of resistivity (C = 1/R), may be divided into two general types: electrolytic and metallic. Electrolytic conductivity relies on the presence of dissolved salts in water. Metallic conductivity is related to the presence of metals, and is a factor in well logging in ore bodies or accessory minerals such as pyrite, or graphite. Most rocks are , in essence, insulators and any detectable conductivity usually results from the presence of electrolytic conductors (brine) in the pore space. The conductivity of rocks is primarily of electrolytic origin. It is the result of the presence of water or a combination of water and hydrocarbons in the pore space in a continuous phase. The actual conductivity will depend on the resistivity of the water in the pores and the quantity of water present. In wet zones this means the porosity and in hydrocarbon bearing zones the amount of water is determined by the height of the column and the irreducible water saturation. To a lesser extent, it will depend on the lithology of the rock matrix, its clay content, and its texture (grain size, and the distribution of pores, clay, and conductive minerals). Finally, conductivity of a sedimentary formation will depend strongly on temperature (increasing temperature increases electrolytic conductivity). Logging-Related Applications
Determination of water (oil) saturation in the pore spaces of formation rock. Determination of porosity in known water-filled formations. Stratigraphic correlation of rock sequences between nearby wells. Characterization of borehole and formation fluids for environmental correction of neutron logs.
Key Points
For logging purposes, resistivity is measured in terms of Ohm-meters/meter2, which is related to a theoretical one meter cube of formation residing between one meter square plate electrodes. Resistivity measurements use Ohm's law to measure the voltage drop due to resistance. Resistivity measurements combine a proportional mixture of formation rock, and pore space fluids. In formation rocks most measured conductivity (resistivity) is proportional to the volume of water and/or hydrocarbon in the pore spaces, and the volume of the pore spaces themselves. Resistivity generally varies strongly in inverse proportion to temperature change. As a rough rule of thumb, resistivity roughly drops by half when rising from 75 deg. F. to 200 deg. F.
Array Induction Logs A new generation of induction measurement termed array induction uses many combinations of transmitter and receiver spacings to more accurately map resistivity profiles. The biggest advantages are:
More depths of investigation for better lateral characterization, with less dependence on resistivity Cave (wash-out) effect (more apparent with enhanced resolution software and tools, and with high formation-to-mud resistivity contrasts). Better estimates of Rt in the presence of deep invasion or complex transition zones.
Measurement Principle
Array Induction (ARI) tools, are multiple array logging systems which abandon the concept of fixed-focus sensors, and are constructed of eight independent arrays with main coil spacings ranging from 6 in. to 6 ft. Exceptional stability is maintained over full temperature and pressure ranges through the use of a metal mandrel and ceramic coil forms; there are no fiberglass supporting structures in the tool as there were in standard induction tools. The approach is to recombine multiple arrays to produce a set of measurements at several depths of investigation and then invert the measurements radially to obtain an estimate of Rt. The figure below shows the coil configurations of the tools. Each array consists of a single transmitter coil and two receivers. Nonlinear processing methods have been developed that use each of the measurements, combining them in such a way as to focus the log response at a desired region in the formation that does not change as formation conductivity changes. Several output logs can be presented, each focused to a different distance into the formation. Each of the new logs is a combination of several array measurements, and all are interpretable as induction logs with full environmental corrections. The logs are virtually free of cave effect and can be used to provide Rt estimates with no built-in assumptions about the invasion profile. Applications 1. 2. 3. 4.
Determine (after appropriate environmental corrections) true formation resistivity, Rt. Detection of hydrocarbons (water and oil saturation). Detection of fluid levels (e.g. oil/water contacts). Porosity determination in water-filled formations of known salinity, and limited mud filtrate invasion. 5. Stratigraphic correlation between nearby wells.
Environmental Corrections
The process of log formation in the AIT family of tools is to correct all raw array signals for borehole effects. This process is based on a forward model of the arrays in a circular borehole, and it includes an exact description of the tool in the model. The logs are formed as weighted sums of the raw array measurements, and an accelerometer is included in the tool string as a standard feature for logging speed correction. Dip correction of AIT logs is similar to that of the Phasor. Although the dip correction can, in principle, be run in real time, the lack of accurate apparent-dip information at the wellsite is a practical limitation. The process is at present a computer center product. As with the Phasor processing for dip, the method is limited to angles less than 60°. Key Points
Full borehole corrections are derived from external measurements over a wide range of Rt/Rm contrasts, and applied through non-linear software algorithms. Short-array information can be used to solve for effective borehole parameters in extremely difficult situations. The five logs have median depths of investigation of 10, 20, 30, 60 and 90 in. Median responses are constant both vertically and radially over a wide range of formation conductivities. The vertical resolution of each log is closely matched to that of the others. Three vertical resolution widths are available: 1, 2 and 4 ft. The determination of invasion is improved in both oil- and water-base mud systems. This includes an accurate Rt estimate and a quantitative description of the transition zone. Resistivity and saturation images of the formation can be produced. Signal processing utilizes non-linear algorithms which rely on accurate downhole mud resistivity (Rm) sensor measurements (which leads to an important log quality control check -- temperature corrected downhole Rm should be compared to an independent manual Rm surface measurement). Traditionally induction tools have been limited to fresh mud in which Rxo > Rt invasion characteristics are expected. The radial processing algorithm for the AIT family of tools, unlike the DIL tools, works as well for Rxo < Rt as for Rxo > Rt within limits. The main limitation to using AIT tools in salty muds remains the ability to do accurate borehole corrections.
Induction Logging The induction logging tool was originally developed to measure formation resistivity in boreholes containing non-conducting mud systems (oil-based muds and airdrilled boreholes).Unlike electrode type measurement this type of tool generates a secondary current in the formation rather try and push a current through the mud column. It is the primary resistivity tool used in fresh water and low salinity brine mud systems. The induction tool works best when the borehole fluid is an insulator (low salinity water, oil, gas or air). The tool also works well when the borehole contains conductive mud, providing that the mud is not too salty, the formations too resistive (less than a hundred Ohm-m), or the borehole diameter too large. Measurement Principle The principles of the standard induction tool are best demonstrated by considering a sonde with two coils, a transmitter and a receiver. A high-frequency alternating current of constant intensity is sent through the transmitter coil which creates an alternating magnetic field. This magnetic field induces eddy currents in the formation surrounding the borehole. These eddy currents flow in circular
ground loops coaxial with the transmitter coil and create, in turn, a magnetic field that induces a voltage in the receiver coil. Induction tools differ from electrode devices in three distinct ways: 1. Coils instead of electrodes are used as receivers to measure potential and transmitters to energize the formation. 2. The coils in induction devices are not in physical contact with the mud column as are electrode devices. 3. The frequency of the alternating current used in induction devices is significantly higher than that of the electrode devices.
The Dual Induction Log (DIL) consists of a deep reading induction measurement (ILD), a medium reading induction measurement (ILM), and a shallow focused measurement, either a laterolog-8 (LL8) or a spherically focused measurement (SFL). The operating frequency of 20 kHz was chosen as a compromise between two requirements: 1. The frequency must be high enough to avoid noise problems in resolving the received signals. 2. The frequency must not be so high as to cause significant nonlinear dependence of the response of the tool on formation conductivity.
Because the alternating current in the transmitter coil is of constant frequency and amplitude, the ground loop currents are directly proportional to the formation conductivity. The principle of the measurement is that the voltage induced in the receiver coil is proportional to the ground loop currents, and, therefore, proportional to the formation conductivity (R signal). A second signal, the direct coupling between the transmitter and receiver coils, is also received. However, it can be distinguished and ignored (X signal). Applications 1. 2. 3. 4.
Determine (after appropriate environmental corrections) true formation resistivity, Rt. Detection of hydrocarbons (water and oil saturation). Detection of fluid levels (e.g. oil/water contacts). Porosity determination in water-filled formations of known salinity, and limited mud filtrate invasion. 5. Stratigraphic correlation between nearby wells.
Borehole and Quality Considerations 1. Borehole size effects -- The radial geometric factor of the tool indicates that the borehole region of the induction tool contributes to the total signal reported by the induction tool., but the geometrical contribution of the borehole is very small for tools that measure deep into the formation. However, when the conductivity of the borehole is very large compared to the formation conductivity, the borehole signal can become very large. 2. Shoulder bed effects -- The vertical geometric factor shows that the shoulders should contribute significantly to the response of the induction tool, especially when there are resistive beds with conductive shoulders. 3. Invasion -- The invaded zone can affect the response of the induction tool. Invasion correction is accomplished through the use of the radial geometric equation.
Key Points 1. Depth of investigation is reduced as formation conductivity increases. 2. Usually it is assumed that the deep induction reading is equal to the true formation resistivity, Rt. Conditions where this assumption is not valid include these: o Very large boreholes o Salt muds o Formations with thin beds o Large shoulder bed resistivity contrasts o Abnormally deep invasion 3. The upper end of the measurement range was chosen to be that resistivity corresponding to an error of plus or minus 20% in the measured conductivity. For the conventional induction tool, accuracy is plus or minus 2 mS/m, and the upper limit value is 100ohm-m. 4. As the values of either Rxo or Rt change, the calculated value of diameter of invasion also changes. Generally, as the borehole environment becomes more conductive, the diameter of investigation decreases. 5. As the conductive bed becomes more resistive and/or the shoulders become more conductive, vertical resolution decreases
Laterolog Tools The early laterolog tools (LL3, LL7, and LL8) and the current Dual Laterolog provide a means of measuring a resistivity profile as a function of depth in situations where salt mud systems are used and where formation resistivity is high. This tool consists of both deep laterolog (LLD) and shallow laterlog (LLS) measurements, and usually run with a Rxo measurement using a pad microresistivity device, MSFL , attached to the lower portion of the tool. This combination of measurements allows one to make, in some instances, corrections for the effects of invasion.
Measurement Principle Laterolog devices measure the resistivity of the formation by focusing a beam of current emitted from the tool into the formation and then measuring the properties of the current and the voltage potentials associated with that current. The deep and shallow measurements are made simultaneously, at two different frequencies: 35 Hz for the deep and 240 Hz for the shallow. The principles of current focusing used in the laterolog devices is based in the principle that current flows only where a potential exists. Each of the various types of laterolog tools employ different numbers and configurations of electrodes, but in each arrangement, the survey or measure current electrode (Ao) is centered between electrodes that are at the same potential. The survey current flows orthogonal to the lines of constant potential generated. Two types of focused resistivity devices have been developed, the guard electrode system and the point electrode system. The resistivity response of each of these systems is directed towards a measure of Rt. Applications 1. 2. 3. 4.
Determine true formation resistivity, Rt. Detection of Hydrocarbons Estimation of Recoverable or Moveable, Hydrocarbons Detection of Fluid Levels
5. Identification of Permeable Zones 6. Fracture Detection. 7. Correlation Applications
Borehole and Quality Considerations 1. Borehole size effect Laterolog measurements rely on the borehole fluid to provide an electrical connection between the electrodes and the formation; if the borehole fluid is resistive compared to the formation, borehole effects will be large 2. Shoulder bed effects The influence of the shoulders increases as the resistivity of the mud increases with respect to the resistivity of the shoulders and when the shoulder bed resistivity contrasts with the zone of interest. 3. Delaware effect This is a false increase in resistivity that occurs when the current return and voltage reference for the measurement are made in the borehole opposite a massive resistive bed. 4. Anti-Delaware effect This is a false decrease in resistivity that occurs when the bucking current source and return electrodes are both in the borehole opposite a massive resistive bed. 5. Groningen effect This is a false increase in resistivity that occurs when the current return is on the surface and the voltage reference for the measurement is made in the borehole opposite a massive resistive bed. 6. Invasion This is based on a model using the pseudo-geometric concept; borehole effects are neglected so that the model contains only the three parameters: diameter of invasion (di), resistivity of the invaded zone (Rxo), and the resistivity of the uninvaded zone (Rt).
Key Points
Vertical resolution of LLD and LLS is approximately 2 feet, however the LLS responds more strongly to the region around the borehole. Depth of Investigation (Figure 19 in Resistivity) Laterologs give a sharp definition of bed boundaries regardless of mud resistivity. Most often they are used in hard-rock (high-resistivity) formations as the primary resistivity measurement. Laterolog devices are designed to respond to higher resistivities and are reasonably accurate up to and beyond 2000 ohm-m. Laterolog tool accuracy begins to diminish slightly below 1 ohm-m, but these tools maintain their sensitivity to changes in resistivity at lower values. For invaded beds, when Rxo < Rt, laterologs show much better resolution of bed boundaries. Mud resistivity should be less than formation resistivity. Effects due to enlarged holes are not so severe for low resistivity muds, except for very extreme conditions (as indicated by the Dual Laterolog borehole charts). Laterologs can suffer from artifacts such as the Groningen effect (high resistivity overlying low), from current digitization errors in extremely high-resistivity formations, and from voltage digitization errors and frequency effects in extremely low resistivity formations
Spherically Focused Log The Schlumberger spherically focused log (SFL) is a focused electrode device that uses a different focusing technique than the laterolog and was designed to provide a shallow resistivity measurement when run in combination with the induction devices. Measurement Principle Focusing is used to enforce an approximately spherical shape on the equipotential surfaces within the formation in spite of the presence of the borehole. Borehole effect is virtually eliminated for hole diameters up to 10 in., yet investigation of the tool is kept shallow enough that its response is, in the majority of cases, mostly from the invaded zone.
Environmental Effects 1. Borehole size effect when the borehole is very large, the volume investigated will include portions of the borehole and corrections can become very large and unreasonable 2. Shoulder bed effects the SFL is affected by shoulders in a manner similar to laterologs 3. Invasion effects the SFL is typically used as a shallow investigation device with run with induction tools the pseudo-geometric factor equation for the SFL can be simultaneously solved with geometric response equations for the two induction measurements to determine Rxo, Rt, and diameter of invasion
Key Points 1. The SFL will not operate in non-conductive beds. 2. The SFL was a replacement to the shallow laterolog measurements.
3. Depth of investigation of the SFL is approximately 2’. 4. Vertical resolution of the SFL is approximately 2’.
Normal Devices In the early days of electrical logging, all resistivity measurements were made with unfocused electric logs, normals and laterals commonly referred to as conventional devices. In recent years the only widespread uses of either of those are the normal devices used in conjunction with the induction log (that is, the socalled IES, or Induction Electrical Survey) and in measurement while drilling (MWD). Measure Principles A resistivity-measuring system using a "normal" electrode configuration. A constant current is passed between a current electrode on the sonde (A electrode) and one at the surface (B electrode) while the potential difference is measured between another on the sonde (M electrode) and a reference electrode (N electrode). The "spacing" is the difference between the A and M electrodes. Usually spacing of about 16 inches is used for a the short normal and 64 inches for the medium or long normal. The measure point is midway between the A and M electrodes. A normal device has a depth of investigation said to be about twice the AM spacing. The normal is an unfocused device which produces a symmetrical curve which has been particularly useful in correlation and in determination of lithology.
Formation detail can be increased by decreasing the AM spacing, but depth of investigation suffers. Two normal measurements have historically been run in electrical surveys: 1. The short normal has a 16 in. spacing (AM = 16 in.) o this gives a vertical resolution approximately equal to the induction tools run in conjunction with the normals on the IES o the short normal is directed toward an estimate of Rxo. 2. A long normal having a spacing of 64 in. (AM = 64 in.). o The long normal is directed toward a measurement of Rt.
Key Points
The spacing of the tool controls the vertical resolution of the normal device beds with a thickness less than the critical spacing (bed thickness, h = AM) the normal resistivity indicates a conductive bed (i.e., resistivity reversal). As the AM spacing is increased to obtain deeper investigation, the bed thickness must be greater in order to obtain a response representative of the formation of interest. As the thickness of the bed increases beyond the AM spacing, the tool senses the resistive bed. But Ra should always be considered minimum resistivity when resistivity contrast is high, the current flow is highly distorted, and the apparent resistivity recorded by the normal tool must be corrected. For the case of conductive beds, the opposite occurs and the conductive bed is identified; however, apparent resistivity is always greater than the true resistivity. Normal responses cannot be used to determine formation resistivity when the borehole fluid is nonconductive, bed thickness is equal to or less than the AM spacing, and when Rt/Rm is high because the current distortion becomes too large to adequately correct Ra.
Lateral Device Found on many old logs the lateral curve is one of the most difficult to interpret. Only a few spacing sizes were used in the USA,(typically deep reading) however a suite of lateral devices of varying spacings was the standard resistivity measuremnt in logging programs in the former Soviet Union
Measurement Principles A resistivity measuring system using a "lateral" electrode configuration. A constant current is passed between an electrode A on the bridle and a distant
electrode B, while the potential difference is measured across two electrodes, M and N, located on the sonde. The MN distance is small compared to the AO spacing, which is the distance between the current electrode and the midpoint between the potential-measuring electrodes, typically about 18 feet 8 inches. A short lateral sometimes uses a spacing of 6 to 9 feet. The potential electrodes described above are located below the current electrodes, but on the reciprocal sonde the functions are interchanged so that potential electrodes are above the current electrodes. The measure point is the midpoint between the two electrodes separated by the shortest distance (i.e., MN electrodes; or, AB electrodes on the reciprocal sonde). The lateral device has a deeper depth of investigation than the normal devices with which it is generally used, but has the disadvantage that it requires thick homogeneous beds for optimum usefulness and produces an unsymmetrical curve. So that only one resistivity value (Ra) will be considered to represent the formation resistivity (that isan Ra value corrected to an Rt value representative of the entire bed). For thick beds, the lateral curve will define one of the bed boundaries depending on the actual electrode arrangement. Applications 1. Delineation of Rt when bed thickness is known
Key Points 1. The lateral is a deep reading curve but values do represent Rt at every depth 2. Asymmetrical curve, bed boundaries must be determined from other measurements
Volume of Shale Recognition of, and correction for, the effect of clay on observed log responses is the major sandstone formation evaluation problem. Clay affects the response of most logging tools, some much more than others. Neutron, density, and resistivity interpretations must all take into account clay effects. Ideally to properly correct for these effects one should know the percentage and the types of clays present. However for most logging situations the amounts can only be roughly estimated and the clay properties usually lumped together lumped together. Most techniques normalize the volume calculations by taking the bulk clay properties from a nearby shale zone assuming that shale is mostly clay. Hence we use the term Vshale rather than Vclay. Many types of measurements can be used to calculate a Vsh . Usually a linear or nearly linear relationship is derived between "clean" formation and shale and volume of shale is scaled in between. SP , separation between neutron and density porosity, and most commonly the GR and used for this calculation. Each
technique has its own assumptions but all have one major assumption in common.
The clays in the reservoir are the same as the clays in the shales. In many areas this is a reasonable first assumption but the diagenic processes operating on sand and shale can be quite different. In many cases clays in sands are authigenic (grown in place) and reflect temperature, pressure and chemistry at the time of formation and not the source rock the sediments came from. Even if clays in the sands and shales are similar it is unlikely that any point on the log represents pure clay or clay free reservoir. Which makes choosing the end points difficult. Distribution of Clay in Sandstones The second assumption that comes with making a Vsh calculation is that "shale" is even distributed within the reservoir . The basic framework for a sandstone consists of quartz or other inert minerals. Shale and clay can be distributed in this framework in several ways. The three most common subdivisions of shale are: Structural Shale The shale occurs as rock grains, usually derived by erosion and redeposition of older shales. Structural shale should not affect either the porosity or permeability of the rock. Theoretically, structural shale should affect log response the same as dispersed shale
without lessening the rock porosity (as other shale distributions invariably do). Structural shale examples may be scarce because shale rock particles usually do not survive transportation over any considerable distance. Laminated Shale Shale is distributed in discrete thin beds interbedded with sandstone. The beds are too thin for logging tools to determine the parameters of each bed. Instead, an averaged reading is obtained. As a further complication, the interbedded sands themselves may be either clean or shaly. Dispersed Clay Clay (not shale), the most commonly occurring, is found throughout the porosity as pore filling, grain coating, crystalline overgrowths, discrete crystals, etc., within the sandstone framework. Dispersed shale can plug porosity almost completely, reducing at least the effective porosity to zero.
Shale Volume (Vsh) from Gamma Ray Quantitative evaluation of shale content using gamma ray data assumes that no radioactive minerals other than clays are present (or that no radioactive minerals that are not in the shales are present). The gamma ray shale index (IGR) is defined as -
IRG = GR - GRcn / GRsh - GRcn where:
GR = log response in zone of interest (API units), GRcn = log response in a zone considered clean, shale free (API units), and GRsh = log response in a shale bed (API units).
IGR has been empirically correlated to fractional volumes of shale in otherwise clean reservoir rock to provide a correction to the linear IGR response in rocks from some areas. Curve 1 on the chart represents the linear IGR response from zero to 100% shale and yields an upper limit of shale content in any formation. The other curves represent non linear relations denoted by the name of the author of the study which proposed these relations, Stieber and Calvier. Note that the non linear relationships tend to lower the shale volume for a given GR value. Which relationship to use is not a simple subject. Much depends on local rock types, chemistry and age. Which formula to use is also somewhat dependent on how the end point values for sand and shale baseline are chosen. If much is know about an area and the clay content of the sands and shales are understood good estimates for linear endpoints can be made . Otherwise a non linear relationship can be used so as not to over estimate shale in the reservoir. The Stieber relationship is a common nonlinear Vsh used in the Gulf of Mexico were Vsh = (0.5 IGR/1.5-IGR) Usually endpoints for this calculation are picked from the cleanest sands and cleanest shales found in the zone of interest.
Volume of Shale - Neutron-Density Volume of shale calculated from the separation of the density neutron is arrived at somewhat differently than when calculating Vsh from the gamma ray and the SP. If the proper grain density and neutron matrix are chose, the density and neutron curves should overlay in a clean sand zone. Maximum separation will be observed in a shale. This separation can be used to establish the shale endpoint. Linear interpolation can then be performed between the two endpoints of maximum and minimum separation.
Vsh = ( N - D )/( Nsh
- Dsh)
The terms in the numerator are the values in the zone of interest while the denominator is the difference between the neutron and density readings in the zone believed to be 100% shale. Key Points 1. The matrix of the reservoir must be known and constant. 2. This method assumes that the same clays are present in both
the sands and shales. 3. Errors in this method result from: variations in matrix properties influence of hydrocarbons changes in shale properties.
Volume of Shale Spontaneous Potential The SP measurement can give reliable indications of shale volume, however, measurement resolution can be a problem when using the SP in this way. Remember that SP is a relative not an absolute measurement For many combinations of rock type, porosity, mud and formation water resistivities there is little dynamic range between the reservoir and the surrounding shales, making this calculation extremely sensitive to error. The SP probably does not respond linearly with increasing clay content. It is more sensitive to permeability and as such as the clay content increases it will be initially very sensitive and will approach a shale reading even before the clay percentages are that of the shales.
These factors preclude the use of the SP as the sole shale indicator for a reservoir. It is recommended that other shale indicators be used along with the SP when determining shale volumes. Volume of shale from the SP is calculated as follows:
Key Points 1. Thin beds affect SP response, therefore contrast between Rmf and Rw is very important. 2. As the ratio of Rmf/Rw approaches unity, SP resolution diminishes quickly. 3. Formation hydrocarbons will reduce SP deflections; so these zones will appear to have higher Vsh values. 4. Interbedded clay laminae within a sand body can have an averaging affect of the total SP deflection. 5. A linear calculation method is used for determining Vsh but the true function is probably not linear. 6. Even silty shales or very clay rich sands may have the same SP deflection as true shales.
Log-Derived Porosity () Wireline Porosity While porosity can be determined from a variety of wireline tools, density, neutron and acoustic are by far the most commonly used. It is important to recognize that no log makes a direct measurement of porosity, and all log measurements used to derive porosity have advantages and limitations.
Primary, Secondary and Effective Porosity Porosity is defined as the ratio of pore volume to bulk volume. When determining porosity from wireline data, an understanding of the relationship between pore volume and the physics of the measurement technique is necessary since porosity is based on an indirect measurement. Total Porosity - All void space in a rock and matrix whether effective or noneffective. Total porosity includes that porosity in isolated pores, adsorbed water in grain or particle surfaces, and associated with clays. It does not include water of crystallization wherein the water molecule becomes part of the crystal structure.
Effective Porosity - The interconnected pore volume available to free fluids, excluding isolated pores and pore volume occupied by adsorbed water. In petroleum engineering,
practices, the term porosity usually means effective porosity.Unfortunately this term that seems so simple is poorly used and qualified in petrphysics, effective can also mean that portion of porosity where the water's resistivity is not effected by the clay charge. By definition the effective porosity of shales is zero. This definition is purely a log analysis definition and may have little or no relationship to the previous definition. Total Porosity - The sum of the primary (intergranular or intercrystalline) porosity and the secondary (vugs, fissures, and fractures) porosity. Primary Porosity - Porosity remaining after the sediments have been compacted but without considering changes resulting from subsequent chemical action or flow of waters through the sediment.
Secondary Porosity - Post depositional porosity, the additional porosity created by chemical changes, dissolution, dolomitization, fissures, and fractures.
Density Porosity The proportionality of weight is a direct method of determining reservoir rock porosity, but the matrix density must be known. For example, a pure limestone with 2% porosity will weigh about the same as a pure dolomite with 10% porosity. Density tools are considered the most reliable porosity-sensitive devices; their measurements are more sensitive to porosity than to lithology. Neutron logs respond more to lithology change. In a clean formation with known matrix density, ma, having a porosity, , that contains a fluid of average density, f, the formation bulk density will be: ma = f + (1 - ) ma Solving for :
= ( ma - log)/ ( ma - f) Key Points 1.
2.
3. 4.
5.
ma values commonly used are:
quartz - 2.648 g/cm3 calcite - 2.710 g/cm3 dolomite - 2.850 g/cm3 anhydrite - 2.977 g/cm3 halite - 2.032 g/cm3 oil - 0.850 g/cm3 gas - 1.325 - 0.188 g/cm3 The density of the fluids in reservoir rocks in generally accepted as that of the mud filtrate corrected to formation temperature; these densities range from 1.0 to 1.1 and depend on the salinity , temperature and pressure of the mud. f of 1.0 g/cm3 (fresh water filtrates) f of 1.1 g/cm3 (saltwater filtrates) Residual hydrocarbons in the region investigated by the tool may affect density readings. f oil, therefore affects on may be unappreciable gas < , therefore will read too low. Shales may raise or lower density porosity, depending on whether the shale density is higher or lower than the matrix density. shale densities tend to be lower at shallow depths where compacting forces are not large The bulk density of shale increases with compaction; departure from this trend is observed in overpressured zones where shale density decreases with increasing depth.
6. The density tool requires skid contact with the borehole wall, therefore measurement of porosity is affected by enlarged boreholes. 7. The density tool investigates approximately 25% of the formation surrounding the wellbore; in heterogeneous formations the bulk density measured by the tool may not be representative of the formation.
Porosity from Acoustic Measurements Sonic porosity is derived from the measurement of the interval transit time of a compressional wave traveling through the formation. The following equations are most frequently used to calculate sonic porosity. Wyllie Time-Average Equation The Wyllie Time-Average equation is used widely to obtain porosity in consolidated sandstones and carbonates with intergranular or intercrystallline porosity. While the empirical time-average equation works for hard rocks, it does not predict reliable porosity in poorly consolidated rocks, gas zones, rocks with unusual textures like vuggy carbonates. Porosity derived from the time-average equation in vuggy carbonates is often lower than density porosity. The difference in these two values is sometimes called secondary porosity and is used as an empirical indicator for vugs. The Wyllie Time-Average equation requires as input the measured compressional transit time (t log), estimates of the rock matrix transit time (t ma), and of the pore fluid transit time (t fl). Reasonable porosity values
are usually obtained with normal values of tma and t fl in well-consolidated, brine-saturated rocks if their composition and texture are typical.
Wyllie Time-Average with Compaction Correction Application of a compaction correction improves the accuracy of the Wyllie TimeAverage porosity in poorly consolidated sand-shale sequences. This correction is 100/t sh, where t sh is the compressional transit time in adjacent shale stringers.
Raymer-Hunt-Gardner Equation A linear relation between and t compressional does not predict porosity accurately over its entire range, particularly for values over 20%. In 1980, Raymer, Hunt, and Gardner developed a nonlinear empirical equation, which may be used on a regional basis to relate measured compressional transit time to porosity with improved accuracy. Their quadratic equation is approximated by the form:
where c = 0.4 to 1.0 (0.685 in Schlumberger processing)
1. Porosity increases the interval transit time of sound through the rock. 2. tfluid is usually 189 ( sec/ft); in salt muds a lower value of 185 ( sec/ft) is often used. 3. In high porosity sandstones, > 30%, with low water saturation, and very shallow invasion, t values may be greater than those in the same formation when water saturated.
4. Acoustic travel time in rock matrix is influenced considerably by the following: Rock type as chemical composition varies. Compaction Confining pore pressure. 5. Interval transit time is increased due to the presence of hydrocarbon. 6. Shale increases t by slowing down the acoustic signal; therefore a shale correction is required; this correction depends on whether the shale is laminar or dispersed. 7. The interval transit time of a formation increases in the presence of hydrocarbons. 8. The phenomena of cycle skipping occurs when gas, fractures or other anomalies attenuate the transmitted signal below the triggering threshold of the receiver. 9. Sonic porosity calculated in consolidated sandstones and carbonates with intergranular porosity (grainstones) or intercrystalline porosity (sucrosic dolomites) reflects only matrix porosity. 10. Sonic porosity calculated in formations with vuggy or fracture porosity reflects secondary porosity and is generally too low when calculated with the time-average equation. In this type of rock additional porosity measurements are required to determine primary porosity. 11. t matrix values commonly used:
sandstone 55.5 - 51.0 sec/ft limestones 47.6 - 43.5 sec/ft dolomites 43.5 sec/ft anhydrite 50.0 sec/ft salt 67.0 sec/ft casing 57.0 sec/ft
Sonic-Density Crossplot Crossplots of sonic t and D have poor resolution of porosity and reservoir rock. However, these crossplots are helpful when attempting to clarify sand-shale mixtures.
Key Points 1. Poor lithologic and porosity resolution compared to the neutron-density and neutronsonic crossplots. 2. Used primarily for evaluating sand-shale sequences. 3. Any error in the choice of the lithology pair from the sandstone-limestone-dolomite group results in a large porosity error. 4. Small errors in the transit time or bulk density can result in large errors in both the porosity and lithology analysis. 5. The wide separation seen of the corresponding mineral points for salt, gypsum, and anhydrite make this crossplot very effective for distinguishing evaporite minerals. 6. Depth adjustment of the sonic to density, if the data are acquired on different trips in the hole, is very important.
Neutron-Density and Crossplot Porosity Neutron density crossplot porosity charts were constructed for clean, liquid saturated formations and boreholes filled with water or water based mud. This chart should not be used for air or gas filled boreholes. Additional charts are available for the sidewall neutron tools. The separation between the quartz, limestone, and dolomite lines indicate good resolution for these lithologies. Points for the common evaporites, salt and anhydrite, are also identified.
Key Points 1. Errors in choosing the matrix pair does not result in a large error in the porosity value. only applies when shale and gypsum are not present 2. Neutron porosity is always shown in limestone units. 3. Most commonly used for quick lithology determination. 4. Points that plot between the lithology lines can be assumed to have a matrix approximately proportional to the distance between the two lithology lines. 5. Points from a sandstone that lie to the right of the sandstone line are usually shaly.
6. Gas in the pores can cause the points to plot above the sandstone line. If lithology is known, the correction for gas is parallel to the gas correction line back to the matrix line.
Neutron and density logs are often used together, the chart method is common, but other equations are also used. Usually they involve some type of averaging to account for the effect of clays and of gas on these logs. Typically RHOB will be converted to density porosity and neutron porosity will be in the apporopiate matix. Simple average
neutron + density / 2
Sum of the Squares Method
(( neutron
2
+
density 2) / 2) 1/2
Gulf Coast Method (more emphisis on density)
neutron + density
The neutron - density porosity is often termed total porosity, perhaps because integrating the neutron it is obviously higher than would be expected in shaly sands. One method for correcting this is to subtact the portion of the porosity that related to clay or in this case shale. This new term is often dubbed effective although it may have no relation the the effective pore space the correction is usually in the right direction.
effective = total (1-Vsh)
Rw from SP
The steps in estimating formation water resistivity from the SP are: 1. Decide on the "shale base line", the reference from which the SP is measured.
2. Read the maximum deflection from the base line (maximum is used because most sources of error cause the SP to read low). 3. Calculate temperature at depth of interest. Use linear interpolation between surface temperature and recorded BHT if no better temperature data is available. 4. Decide is a streaming potential (Ek) correction should be made,. Subtract any streaming potential from a negative SP, and add it to a "reversed" SP. 5. Calculate Rmf at Formation Temperature (Use Arps Formula or Schlumberger Chart Gen-9). 6. Find Rmfe at formation temperature from Rmf, using Schlumberger chart Sp-2 7. Find Rmfe/Rwe , using Schlumberger chart Sp-1, or solving: o Ec = (61 + .133 T F) log (Rmfe/Rwe) 8. Find Rw (at Formation Temp.) from using Rwe , chart Sp-2.
Only experience in a specific area will tell you how accurate the answer is likely to be. Generally the calculated Rw will be usefully accurate if the following apply: 1. Formations are thick enough for full SP development, and are electrically non-shaly. 2. Rmf is less than 1 ohm-meter (preferably less than .5 ohm-meter) so that streaming potentials are not high. 3. Formation waters are principally NaCl, and salinities are not less than 10,000 ppm.
Beyond these limitations, the SP can normally be used quantitatively only by applying empirical methods that have been found to work when checked against drillstem test or production test recoveries of uncontaminated formation water. Sources of Error There are many potential sources of error when making Rw estimates from the SP. Users should be aware of them, and of how large the effects can be, to use the curve intelligently. Fortunately, the errors are seldom all additive, and frequently they largely cancel each other. Below is a list of the principal assumptions used in the SP theory that may not be true, and that may not be adequately corrected for: 1. Mud filtrate, assumed to be a NaCl solution, seldom is. Errors are greatest for fresh muds. 2. Formation water, also assumed to be NaCl, usually is if
3. 4. 5. 6.
7. 8.
waters are more saline than about 10,000 -20,000 ppm. Fresher waters have a wide range of composition, and deviate most from NaCl composition for the freshest waters, usually of meteoric origin. Very saline water can have significant concentrations of divalent ions, particularly calcium and magnesium. Activity and resistivity are assumed to have a linear relationship. This introduces large errors from very salty waters, particularly above 100,000 ppm. Streaming potentials can be a major part of the SP if muds are more resistive than 1 ohm-meter, and/or if the hydrostatic pressure due to the mud is much higher than formation pressure. The total static potential (SSP) may be higher than the observed SP used in calculations. The error is important in highly resistive and/or thin beds. Mud filtrate invasion can lower the recorded SP, because of very deep invasion so the electrochemical cell is far from the borehole, and the SP currents are largely in the formation. Very shallow invasion at logging time (because invaded fluids have dissipated) can produce a shale potential across the mud cake that can largely cancel the normal SP. Clay minerals that are electrically charged (almost any clay except some kaolins) will reduce the SP sharply for quite low concentrations. SP theory assumes that adjacent shale beds are perfect shale membranes, impervious to anions. If this is not true, the measured SP will be lowered.
With so many potential sources of error, plus the fact that the SP is often recorded carelessly, it is surprising that the curve is as useful as it is. In many prospecting and producing areas, quite good Rw values can be obtained by using the simplified theory given here. Simple empirical corrections can often be derived from local experience, that permit even more reliable answers.
Rwa (apparent water resistivity) The apparent water resistivity is a very useful and widely used calculation. It can used as an input to the water saturation calculation, or as a quicklook technique for identifying potential hydrocarbon zones. Starting with the Archie water saturation equation
If water saturation is assumed to be 100%, and solving for Rwa the equation reduces to:
Most users set a =1 so:
To use as quick look technique Rwa = Rw only in 100% wet formations; in hydrocarbon bearing formations, Rwa computed from the above equation will be greater than Rw. Key Points & Assumptions 1. The Rwa technique assumes that Rdeep = Rt invasion must be shallow enough that the deep resistivity is true resistivity 2. Rw (or salinity) is relatively constant 3. Lithology and shale effects are negligible 4. Zone selected for calculation are assumed to be 100% water saturated 5. Rwa has advantages over other sources of Rw , because is calculated from the same tools in the same environment the final saturation will not be subject to errors of a, and m.
Water Saturation Water saturation, Sw, is the fraction (or percentage) of the pore volume of the reservoir rock that is filled with water. It is assumed that, unless otherwise known, that the pore volume not filled with water is filled with hydrocarbon. Determining Sw is one of the basic objectives of well logging. Although Sw can be determined by any number of methods, specific circumstances affect or limit the accuracy of each method and it is crucial to use the appropriate method.
Sw is a function of: 1. Type of pore space, connected or isolated 2. Amount of pore space 3. Grain size 4. Homogeneity or heterogeneity of the reservoir matrix and pore throats 5. Relation of vertical permeability to horizontal permeability 6. In-situ pressure and temperature 7. Capillary functions 8. Wettability of the matrix 9. Type of reservoir drive 10. Shape & size of the reservoir , hie ght of column 11. Structural/stratigraphic trap mechanism
Several measurements and petrophysical parameters are essential in deriving accurate saturation values from log data: 1. Reliable and accurate resistivity and temperature values for drilling fluids and formation waters 2. Resistivity values recorded by an appropriate resistivity device; accurate determination Rt Rxo Ri 3. Reliable and accurate porosity information 4. Adequate formation factor to porosity relation 5. Adequate exponential for saturation determination 6. Awareness and/or correction for conductive formation minerals
Numerous methods are available to calculate water saturation; they are: 1. Quick Look Methods Rwa Formation Factor Ratios
Hingle Pickett 2. Rock Parameters, Empirical Relationships, Integration of CEC Data Archie Dual Water Indonesian Model Simandoux Juhasz
QUICK-LOOK METHODS TO DETERMINE SATURATIONS There are many quick-look methods for recognizing hydrocarbon-bearing horizons and estimating their saturation. These methods are used mainly to provide reasonably accurate porosity and saturation data at the well site to facilitate decisions on running casing and testing or abandoning the well. Today's well-site computers present quick-look logs with much less effort than required with earlier analog units. Some of the drawbacks to these methods are listed below. 1. Experience and interpretative abilities of well-site personnel 2. Availability of necessary well-site computer capabilities 3. Availability of important and sometimes critical parameters needed for an accurate analysis 4. Any combination of the above Several older and relatively simple interpretation methods are still available in some form today. These include simple resistivity overlay techniques (Rwa, FR/FAC,
FR/FD) and Rxo/Rt methods.
Rwa Technique A real-time Rwa curve has been available for more than 25 years. Knowledge of
Rw in certain reservoir rocks permits a quick comparison of that value to the recorded Rwa. When logging through a water-wet horizon, the Rwa value should be similar to the known Rw. If Rw is not known, the Rwa curve is often used to establish Rw for specific horizons if some or all the reservoir is believed to be 100% water bearing. Rwa is simply a mathematical rearranging of the Archie equation; i.e. –
Rwa Technique A real-time Rwa curve has been available for more than 25 years. Knowledge of
Rw in certain reservoir rocks permits a quick comparison of that value to the recorded Rwa. When logging through a water-wet horizon, the Rwa value should be similar to the known Rw. If Rw is not known, the Rwa curve is often used to establish Rw for specific horizons if some or all the reservoir is believed to be 100% water bearing. Rwa is simply a mathematical rearranging of the Archie equation; i.e. –
If F = a/m and Ro = F Rw, then Rw = Ro/F. If Rt > Ro, a similar calculation can be made but an apparent Rw will be calculated if the zone is not water bearing –
Rwa = Rt / F Rind / F , where F is determined from porosity-sensitive log data and the proper formation factor-to-porosity relationship. In sandstone reservoirs, the F = 0.62/2.15 (or
F = 0.81/2) relationship is commonly input. Deep-induction values are generally used as the apparent Rt value. Porosity is often determined from acoustic t, density b, or density-neutron crossplot data. An Rwa >> Rw indicates a water saturation less than 100%. Saturation can be calculated easily by using
. Obviously, invasion must be sufficiently shallow such that the deep-resistivity measurement is not affected; porosity determination and the formation factor relationship must be relatively accurate. In addition, the following requirements are necessary in order to successfully implement continuously recorded Rwa techniques – 1. Rw must be relatively constant or vary in a consistent and predictable manner over the interpreted depth intervals. 2. Lithology should be consistent, predictable, and known (sand-shale sequences are best). 3. Permeable horizons should be essentially shale free, or at worst, have similar shaliness characteristics. Quick estimates of saturation can usually be made if the following Rw to Rwa comparative values are used – Sw (%) Rwa 2 times the value of Rw:
71
Rwa 3 times the value of Rw:
57
Rwa 4 times the value of Rw:
50
Rwa 8 times the value of Rw:
35
Rwa 16 times the value of Rw:
25
Rwa 25 times the value of Rw:
20
Rwa 40 times the value of Rw:
16
A nomogram converting Rwa to Sw is also available (Fig. 6-12).
Fig. 6-12 Chart for converting Rwa to Sw
Several years ago, Rmfa traces were recorded with the Rwa information. The Rmfa trace was used as a check for invasion, productivity index, and flushing, if the mud was not salt-saturated. Apparent mud-filtrate resistivity (Rmfa) is determined by
Rmfa = Rxo / F , where Rxo values are from a microresistivity device. However, many of the quicklook traces used are shallow-resistivity measurements (e.g., short normal).
Comparisons of the Rwa and Rmfa curves led to the following interpretative conclusions – 1. If Rwa Rmfa or Rwa < Rmfa, shallow invasion occurred, and the Rwa estimates of producibility are probably accurate. 2. If Rwa > 3Rw and Rmfa > Rmf, this confirms the Rwa indication of producible hydrocarbons. 3. If Rmfa Rmf and Rw < Rwa Rmf, deep invasion is suspected, and favorable
Rwa values should be further investigated. The Rwa method is considered an Archie approach to saturation because porosity and resistivity values are used. The Rwa to Rmfa comparison is comparable to the resistivity ratio methods discussed previously (Chapter 3).
Formation Factor Ratios as a Quick-Look Technique A continuous computed trace can also be made that compares formation factor ratios of resistivity to porosity. The deep-resistivity measurement is converted to
F along with the formation factor conversion from a porosity device. The deep resistivity is considered an adequate Rt measurement and is converted to waterfilled porosity, w, which in turn, is converted to Fdeep. Porosity determined from t (or other porosity derivations) in the accepted local manner is converted to formation factor. Typically, Archie's F = 1/2 or the Humble or equivalent conversion is used to obtain formation factor. In areas where invasion and flushing is sufficiently deep, a pseudomovable oil plot is often made using an F curve converted from a shallow-resistivity device (Fig. 6-13). The separation between the deep and shallow F curves is an index of movable hydrocarbons, whereas the separation between the shallow F and the porosity-derived F (acoustic data in the example) represents residual hydrocarbons. A logarithmic scaler can be used to quickly estimate Sw by fixing the 100% grid on the porosity-
derived F trace and reading the Sw value where the deep resistivityderived F trace crosses the scaler.
Fig. 6-13 Pseudomoveable oil plots can be constructed from ratios of recorded or manually constructed
A different approach and presentation converts the porosity-derived F trace to an Ro trace. The deepresistivity measurement (and microresistivity data, if available)
remains as recorded. The Ro curve is created by shifting the F curve along the logarithmic grid by an amount of resistivity equal to Rw, thus making it an Ro trace. In water-bearing horizons, the deep resistivity and Ro trace should overlay almost exactly. If Rw is not known, the deep-resistivity and Ro curves can be normalized in known water-bearing horizons, and Rw can then be calculated by knowing the value of F at the point it overlays a deep-resistivity curve in the water-bearing zone, Rw = Ro/F.
RESISTIVITY VS. POROSITY CROSSPLOTS There are several methods for comparing resistivity to porosity on crossplots; the two most common plots are the Hingle and Pickett plots. Both methods have versatility in that they not only eventually lead to a more accurate Sw solution but also help resolve other parameters necessary to successful log evaluations. Many companies routinely use these methods to plot the necessary reservoir data on each well and then use that data as a control on subsequent wells. The control may be to identify inaccurate log measurements, to recognize gradual changes from well to well, or to accumulate fieldwide statistical data that can be molded into a uniform control for more detailed field studies.
Hingle Plot Originally, this was a plot of resistivity/conductivity vs. acoustic t values.93 It was quickly applied to resistivity vs. density data, resistivity vs. neutron data, resistivity vs. crossplot porosity, and microresistivity (Rxo or Ri) vs. porosity sensitive devices. The basic premise is to plot data points of either resistivity or conductivity on the ordinate vs. measurements from a porosity-sensitive device (such as t) on the abscissa. For example, a t scale of 50 and 110 (left to right) might be imposed on the x-axis to fit acoustic log data, and the y-axis might be scaled from 0
upwards to 2000 mmhos conductivity on the left of the plot and from upwards to 0.5 ohm-m resistivity on the right of the plot (y-axis). On the U.S. gulf coast, the deep-induction measurement is typically taken as Rt and plotted against the data from the porosity-sensitive device. Sensitivity of the log data (minimum to maximum values of the different measurements) is used to employ adequate scaling. Scales can be selected differently (Fig. 6-3) depending on locales.
Fig. 6-3 Hingle plot scale selection for t, b, etc. can be adjusted to fit specific reservoir conditions.
After ensuring that two different sets of log data are on depth, the analyst plots several data points from the zone of interest. Data points from the water leg of a reservoir are very important and should be plotted (Fig. 6-4).
Fig. 6-4 Hingle plots allow Rw and Vm to be determined from adequate resistivity and acoustic data.
If a large number of points are plotted, a shotgun pattern usually forms. If Archie's saturation equation is combined with Archie's formation factor relationship, the saturation equation can be written as
. If m and n are equal to 2 and a = 1, then .
This equation demonstrates that if Rw remains constant, Sw is proportional to and Sw is equivalent to the bulk volume water per unit of measured volume. When induction and acoustic data are used, the data plotted (Fig. 6-4) can also be used to determine Rw and matrix velocity, Vma, if sufficient points are available and if water-bearing intervals are included on the crossplot. A line is projected through the points found to the left and upper part of the pattern (NW points). The line is presumed to be Ro if a deep-resistivity device is used (e.g., deep induction). The projected line can be extended downward (SW direction) to the abscissa, and the point of intersection will give an estimate of tma, zero porosity. The t scale across the x-axis can then be scaled in terms of porosity for the tma value determined from the Hingle plot. This is a useful plot when tma or Vma are unknown; however, control points from the Ro line should be definitive. This requires some spread in the plotted values of resistivity and t. Obviously, difficulty will be encountered if a water-wet zone (Ro) was not available from the logs. The plot remains useful if Ro control points are not present. A knowledge of lithology allows the analyst to assume tma or Vma using conventional values for sandstone, limestone, or dolomite. If Rw is unknown, the Hingle plot can also be used to determine connate water resistivity. If the NW line was projected through data points representative of Ro, the resistivity of any data point can be divided by the formation factor value –
Rw = Ro/F The porosity is typically scaled using conventional values for matrix, tma = 55.6 µsec/ft with acoustic data in sandstone or ma = 2.71 g/cm3 for density data in limestone, etc. (Fig. 6-5). A grid scale for formation factor (F) can be set up below the porosity scale utilizing the proper transform, F = 1/2 or F = 0.62/2.15 (Fig. 6-5).
Fig. 6-5 Scales for porosity-sensitive devices are selected to fit the sensitivity of reservoir parameters.
Saturation lines can also be drawn across the Hingle plot after the Ro line is established. For example, a 50% Sw line will have ordinate resistivity values four times greater than ordinate resistivity values of the Ro line (Fig. 6-6). When
several Sw lines are constructed, Sw can be determined quickly for any data point on the plot.
Fig. 6-6 Lines representing specific saturation values can be established on the Hingle plot.
The proportionality between and
can also be written as –
. Based on the previous equation, if deep resistivity is representative of Ro, Sw = 1, and the ordinate becomes an inverse square root scale of resistivity vs. porosity, all Ro points fall on a straight line defined by
. Points corresponding
to other constant values of Sw will also fall on a straight line (50% Sw line demonstrated earlier). The Hingle plot remains a functional part of log analysis today because it is a convenient method to determine the necessary matrix parameter for converting density, acoustic, and neutron data to porosity. If a microresistivity (Rxo) device is available, the plot can be used in a similar manner to determine Sxo, water saturation of the flushed zone. The x and y coordinates do not change, and the same plot can be utilized. Rxo values are plotted with the porosity-sensitive data using a different code
for the data
points. Sxo = 100% should be represented by a line projected through the points that fall in the NW section of the plot. The Sxo = 100% line will differ from the
Sw = 100% line if Rw and Rmf differ. Hingle plots are routinely constructed with data acquired from the zones of interest in discovery, appraisal, and development wells. Such plots establish petrophysical markers from well to well and serve as a well-site guide to log quality. The plots can also be implemented in computer crossplot routines.
Pickett Plot Calculating water saturation involves several steps – 1. Obtain a porosity value from log data or core 2. Use an estimated or laboratory-determined m value to establish a formation resistivity factor relationship 3. Calculate a Resistivity Index (I) from the relationship of Rt/Ro or Rt/F Rw 4. Calculate Sw from the relationship Sw–n = I
Despite the development of sophisticated logging technology, log analysts still face challenges in determining accurate Sw values. Although errors can be caused by uncertainties in the knowledge of Rw, determination of , and correct determination of Rt, incorrect m values can also lead to significant error. Undoubtedly, the n exponent also has significance in saturation results, and it is discussed later in this chapter. As previously discussed, one method of estimating Resistivity Index utilizes a log-log plot of resistivity vs. porosity. Crossplotted data points identify graphically the location of water-saturated zones149,150 and data from hydrocarbon zones demonstrate departure away from the water zones. The concept has been fundamental to log analysis for many years, but Pickett's intent was to convert the amount of pattern distortion to accurate estimates of water saturation without knowing many parameters (e.g., Rw or m) normally required. Hingle plots require a knowledge of the m exponent. Pickett's approach began with consideration of the basic equation for true resistivity –
Rt = –m Rw I The parameters are by now familiar with the exception of the (–) superscripts and the Resistivity Index (I). I is related to Sw through the empirical relation –
I = Sw–n , where n is the saturation exponent. Pickett took the logarithm from both sides of the equation and converted it to the linear relation –
log Rt = log aRwI – m log On a log-log plot of Rt versus , this equation represents a family of straight lines with slopes of –m, and intercepts of a RwI on the resistivity abscissa where = 100% on the ordinate. The equation for the water-bearing zone on the plot is –
log Ro = log aRwI – m log , where Ro represents the resistivity of those sediments whose pores are 100% filled with water of resistivity Rw, and I = 1. Pickett's routine is important because it is not necessary to know m or Rw in advance of estimating Sw. These equations
demonstrate that the crossplotted log data will exhibit a straight line for those data sets having the same Rw and a constant I. A linear group of points should be found that represent 100% Sw. Any points having the same porosity value but increasing resistivities will have I values equal to the ratio of their resistivities to the resistivity of the water-bearing line at that porosity. If Rw is known, and the Archie relationship a/m = Ro/Rw is acceptable, an Ro line can be extrapolated through the water-bearing data points of the log-log plot (Fig. 6-7). If Rw is well documented, the a term can be defined by solving the Ro = aRwI equation (reading the value at the point where the Ro line intersects the abscissa at the top of the chart). The slope of the Ro line is representative of the m exponent, negative because of the slope direction. The slope –m is easily resolved by utilizing the x and y coordinates and the logarithmic scale (y = mx + b is the equation of a line). The negative sign (–) for m is normally ignored in conventional log analysis.
Fig. 6-7 Pickett plots can be used to determine values of a, m, and formation factor.
Sw can be determined graphically by using an Rw index. Water saturation charts for any given Rw and known m and n values are easily constructed.105 The log-log plot of porosity vs. resistivity is used as the basic crossplot. A "water scaler" overlay for known m and n values is then indexed. For demonstration purposes,
m and n values of 2 and Rw = 0.04 ohm-m are used. The chart is constructed using the following steps – 1. Define the maximum and minimum Sw lines with any four arbitrarily chosen points (Fig. 6-8). The 100% line is chosen using two points ( = 10% with Ro = 4 ohm-m and = 3% with Ro = 44 ohm-m) and a 10% Sw line is established using two other control points ( = 10%, Rt = 400 ohm-m and = 30%, Rt = 45 ohm-m). 2. Place a logarithmic scaler (Fig. 6-9) between the minimum and maximum
Sw lines and scale the intermediary Sw lines parallel to the minimum and maximum Sw lines. The completed water scaler is then printed on transparent material for overlay purposes. 3. Using the example values, place the transparency over the log-log grid with the index on the Ro = 4 ohm-m, = 10% control point because
Rw = 0.04 ohm-m (Fig. 6-10). The completed chart can then be reproduced (Fig. 6-11). Separate charts can be constructed for different Rw values or for differing values of m or n.
Fig. 6-8 Pickett plot versatility permits rapid Sw determination by using an Rw index to construct a saturation scaler.105
Fig. 6-9 A completed transparent saturation scaler can be used as a quicklook overlay on Pickett plot data.105
Fig. 6-10 The overlay technique can be used to create a chart for specific reservoirs – Example with Rw = 0.04 and = 10% as a control point.105
Fig. 6-11 A completed Sw chart for Rw = 0.04 ohm-m105
DUAL-WATER MODEL Another commonly used saturation equation suggests that a water-saturated shaly sand formation behaves as though it contains two types of water: water near the clay (bound water, Bw) and water removed from the clay surfaces (free water, Fw). Free and bound water are said to behave as conductors in a parallel electrical circuit;33 therefore, the true water conductivity is –
Cw = CFw eff / t + CBw Bw / t The equation can also be written in terms of resistivity –
Rw = t (RFw RBw) / (RBw e + RFw Bw) . Freewater (Fw) resistivity is determined by conventional methods in clean, waterbearing reservoirs. RBw is more difficult to determine because Ro, among other factors, depends on Qv. If selected RBw values result in hydrocarbon saturations occurring in zones considered 100% shale, RBw is probably too low. If Sw values exceed 100%, RBw is probably too high. From a practical log analysis standpoint, there is little argument that the influences of water conductivity in shaly reservoir rocks must be considered in saturation calculations. Several years ago, salinity comparisons of interstitial water in shales and adjacent sands were made and typically demonstrated low salinity in the shale.67,181 Several laboratory experiments showed that mineralization of solutions expelled from shale decreased progressively as overburden pressure increased. As a result, concentrations of interstitial solutions from shales are expected to be lower than the free water around and between the sand grains. Oil production from reservoirs surrounded by overpressured shale sequences has shown that produced waters demonstrate decreasing salinity with time. This may be caused by an influx of fresher waters from the shales.
INDONESIAN MODEL This saturation model is not restricted to Indonesia but acquired the name because of the geographical locale to which it was first adapted.163 At the time, Sw results in Indonesian shaly sand reservoirs were often over-estimated. It was recognized that several parameters affect true resistivity (Rt) – total effective porosity (e), connate water resistivity (Rw), water saturation (Sw), clay content (Vcl), and clay resistivity (Rcl). Earlier laboratory efforts of several investigators had shown that Rt – Sw relationships were affected mostly by the contribution of clay. The conductive influence of the clay affected not only Vcl and Rcl but also Sw. Several Rt – Sw equations were investigated by making frequency crossplots of
Vcl estimates and computed Sw values. The quality of the Sw results was assumed satisfactory if water-bearing formations exhibited a concentration of Sw values near 100% (allowing slight, statistical scatter above and below the 100% value) over the entire range of Vcl values. Points corresponding to water-bearing formations should delineate a clear vertical trend centered on 100% Sw (Fig. 614), and horizons containing hydrocarbons should exhibit data substantially lower than 100% Sw.
Fig. 6-14 Crossplot of computed results demonstrates a clear vertical trend at high Vclay content in water-bearing intervals.
The best results were obtained with a very complicated equation –
The idea expressed is that conductivity of shaly formations depends on three terms, two of which are the conventional conductive network of clays (Vcl – Rcl) and the porosity-formation water network (Rt – Rw). The third term represents the
additional conductivity resulting from crosslinkage of the two networks, as suggested some 20 years earlier.49,50 A simplified version usually provides adequate Sw results if Vcl does not exceed 50%:
As with any saturation equation, the accuracy of input values , Vcl, Rcl, Rt, Rw, a,
m, and n must be within a certain tolerance.
