Introduction to Porosity

PETROPHYSICS, VOL. 44, NO. 3 (MAY-JUNE 2003); P. 205–212, 7 FIGURES

TUTORIAL

An Introduction to Porosity 1

Jeffrey R. Hook 

In pri princi nciple ple por porosi osity ty is a ver very y sim simple ple con concep ceptt but bec becaus ausee of the many different ways in which it may be determined it can, in detail, mean many subtly different things. In the vast majority of cases the differences are probably not significant but the competent petrophysicist needs to be aware of  the differences and when they are important. Frequently the same term is used to mean different things; often dependent on the technical discipline discipline of the user user.. In particular, particular, the term effective porosity is in widespread use but means different things to different people. This tutorial is intended to provide an int introdu roducti ction on to the basic concepts concepts of por porosit osity y. It also refle re flect ctss th thee au auth thor’ or’ss opi opini nion on as to themost co comm mmon on usa usage gess of  terms and highlights the differences. A suggestion is made for a terminology that could help to resolve the differences. Thiss disc Thi discussi ussion on of por porosi osity ty sta starts rts by con consid sideri ering ng the theoretical aspects of porosity for an idealized rock and the diff di ffer eren ence cess in a re real al ro rock ck.. Th This is is fo foll llow owed ed by a br brie ieff ex exam amiination of how the porosity of real rocks can be measured. Thes Th esee as aspe pect ctss wi will ll be co cove vere red d in mu much ch gr grea eate terr de deta tail il in ot othe her  r  tutorials in this series. Essentially porosity can be determine mi ned d in tw two o wa ways ys – fr from om co core re an anal alysi ysiss or lo logs. gs.2 It is ne nece cesssary to unders understand tand the diff differenc erences es in the techniques techniques and to  be aware of the meanings applied to each term as used in each technique.

  

V  p V b



V  p V p  V g 

where   is porosity, V  porosity,  V  p p  is void space or pore volume,  V b  is  V  g   bulk volume, and and V  volume.  g  is grain volume. During deposition a sediment will be laid down with  porosity. This is known as primary porosity. For uniform spherical grains there are five idealized arrangements of  grai gr ains ns th that at ma may y be fo form rmed ed—e —eac ach h wi with th a th theo eore reti tica call va valu luee of   porosity. These arrangements are known as simple cubic, orthorho orth orhombi mbic, c, doub double le nest nested, ed, fac face-ce e-cente ntered red cub cubic ic and rhombohedral. Figure 1 shows a cubic packing of uniform spheres of  radius, r  radius,  r , together with a unit cell for this arrangement. The

IDEALIZED ROCKS

Porosity is defined as the ratio of the volume of voids (the spaces between the grains) in a rock to the bulk volume (the overall volume of the voids plus the grains) of that rock  (Amyx et al., 1960)

FIG. 1

Cubic packing of uniform uniform spheres.

Manuscript received by the Editor February 18, 2003 and revised manuscript received April 29 2003. 1 Helix RDS 2 A log in this document means a downhole measurement irrespective of the method of conveyance. ©2003 Society of Professional Well Log Analysts. All rights reserved. May-June 2003

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unit cell is a cube with sides equal to 2r  and hence bulk volume Vb   (2r ) 3  8r 3 . Within the unit cell as depicted in Figure 1 there are eight (1/8) spheres, in other words a single sphere, so that the grain volume  4 V g    r 3 3 and the void, or pore, volume is 4 V p  Vb  Vg   8r 3   r 3   3 and porosity,   , is 4 8r 3   r 3   3 1 . .       0476 8r 3 6 The porosity is independent of the grain size. Figure 2 shows a rhombohedral packing of uniform spheres that is the most compact packing arrangement. According to Fraser and Graton (1935) the porosity of this arrangement is 0.260, again independent of the radius of the uniform spheres. For all the idealized arrangements, in this very simple and unrealistic case of uniform spherical grains, porosity is independent of the size of the grains. In real rocks there will be a range of particle sizes and also the grain shape and angularity will vary. When there is a range of grain sizes the smaller grains can fit in the pore

FIG. 2

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Rhombohedral packing of uniform grains.

spaces between the larger grains and thus reduce the porosity as shown in Figure 3. For non-spherical grains the packing will be very different to those shown above and, in general, the packing will  be much denser and the porosity will be reduced. The idealized packing arrangements considered above are not likely to be present in real packings except over a localized volume. As burial of the sediment progresses, overburden pressure increases and the grains will be rearranged to a more dense packing thereby reducing porosity. Consequently, in real rocks, the arrangement of the grains will differ considerably from the simple cases discussed above which may be considered as upper limits on the possible porosity for intergranular rocks. Conversely, higher porosities can be observed in certain rare circumstances where grain bridging occurs or vugs contribute a large proportion of the porosity. Also, during the process of lithification, porosity will be further reduced by the development of cement and the growth of clay minerals in the pore space. Following deposition and during lithification various processes, chemical and physical, will modify this initial porosity. Eventually, as burial continues and the overburden stress increases, the grain shapes will be altered by pressure dissolution at the grain interfaces leading to a reduction in porosity. The dissolved material may then be re-deposited within the pore space reducing porosity further. Porosity that is created by these processes, such as dissolution of feldspar grains or through dolomitization of car bonates or fracturing, is known as secondary porosity. Factors controlling porosity are 1) grain shape, 2) grain size distribution (sorting), 3) compaction, 4) cementation, 5) clay, 6) dissolution of grains and 7) fracturing.

FIG. 3

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Effect of range of grain sizes on pore volume.

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RESERVOIR ROCKS

In the evaluation of a reservoir the pore volume required for the definition of reserves is that which is available for  the storage of oil, gas and water. This volume must be connected so that hydrocarbons can flow through the rock and  be produced (it must also be connected so that the hydrocar bons could access the pore space in the first place). Connected pore space

Diagenetic processes, or the particular morphology of the constituent grains, can cause some pore space to be disconnected from the majorityof the pore space. These pores cannot then be accessed by hydrocarbons migrating into a reservoir. The porosity which comprises the whole of the pore space, whether connected or not, is referred to as total  porosity. The connected pore space is often referred to as the effective porosity although it may be better described as connected porosity. By definition, this effective porosity must be less than the total porosity. For the majority of reservoirs, particularly sandstone, the difference between this effective (connected) and total  porosity is small. However, in some formations, such as those containing significant quantities of sponge spicules, dolomitised carbonates in which much of the porosity may  be composed of vugs, or oomoldic limestones, the differences can be large. Connected porosity is not necessarily very efficient at transmitting fluids through the formation. For example, vugs can be connected but the connecting pore throats may be so small that flow from or through the vug will be difficult. Porosity then can be large but permeability low. Also dead-end pores, i.e. pores with a single entry throat such as sponge spicules or ooids, will contribute significant  porosity but may be by-passed by flowing fluids.

3. The remainder of the water is free to move. Following the definitions of total and effective porosity as given above under connected pore space, the class of the  pore water is not relevant. However, the electrochemically  bound clay water cannot really be considered to be occupying pore space (defined as non-solid material) that could be available for storage of hydrocarbons. Consequently, when attempting to determine the storage capacity of a reservoir  the clay bound water volume should be excluded. This pore volume (total, or, sometimes, connected, porosity less the clay bound water porosity) is also often referred to as “effective porosity.” Producible fluid pore space

Furthermore the term “effective porosity” is also some times used to describe the pore volume containing “free fluids.” This excludes capillary held water from the pore volume and the porosity becomes a property not of the rock  alone but also that rock’s height above the hydrocarbonwater contact within the reservoir. MEASUREMENT OF POROSITY

Although porosity is a very important parameter in the evaluation of a formation it cannot be measured directly. All the measurement techniques determine some other 

Non-clay pore space

Figure 4 shows a representation of a “real” reservoir rock  in which the matrix is composed of non-spherical grains composed of, say, quartz and feldspar, and where there is no non-connected pore space. Some of the original pore space is occupied by clay mineral particles and the remainder is filled with water and hydrocarbon. There are three classes of pore water. 1. Associated with the clay particles is an amount of electrochemically-bound water (clay-bound water) that is not mobile. The amount of clay bound water held by the clay particles is a function of the salinity of the pore water and the type of clay, with, for example, montmorillonite holding considerably more water than kaolinite. 2. Additional water is held in the small pores and on the surface of the matrix grains by capillary forces. May-June 2003

FIG. 4

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A typical “real” reservoir rock. 207

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 property, which then must be converted to reservoir porosity. Core measurements determine sample volumes in an environment that is not the same as the reservoir. Logs record some property of the formation such as bulk density, which is then related to porosity by some model of tool response. The indirect nature of the measurements leads to many of the problems with comparisons of porosity. When considering the techniques used to determine reservoir porosity the inclusion or exclusion of clay bound water volume becomes important as the different measurement methods treat it in different ways. Porosity in core analysis

Measurement of porosity in the core analysis laboratory essentially consists of taking a sample from the core, extracting the fluids from the sample and then determining two out of the pore volume, grain volume and bulk volume of the sample. The detailed laboratory techniques used will determine exactly what porosity is measured. When examining a core analysis report, it is unlikely that any term other than simply porosity will be encountered. In the world of core analysis the term porosity normally refers to the pore space that can be contacted in the particular technique being used (typically gas injection porosity or fluid re-saturation). Unless the sample is disaggregated this will exclude unconnected pores. If pressed the “core analyst” will refer to this porosity as effective porosity. When the term total porosity is used it will be in relation to a technique in which the core sample has been disaggregated before its  porosity was measured. Then all normally unconnected  pores will be included. Note, however, that there is no reference to the amount of clay bound water retained by any clay minerals in the pore space. The amount of clay bound water retained depends on the detailed sample preparation techniques, in particular the method of drying the samples. If simple oven drying at tem peratures above 100°C is used then it is considered that all clay bound water will be removed and porosity includes all  pore space. If, however, humidity controlled drying at low temperatures is used then it is possible that at least some of  the clay water will remain, thereby reducing the measured  porosity. The precise amount of clay bound water retained is uncertain and whether the condition of the clays in the sample in the laboratory matches that of the clays in the reservoir is a matter for conjecture. Hence, in core analysis,  porosity may or may not include some electrochemically  bound clay water. The detailed analysis technique needs to  be considered to understand the results. Core porosity techniques

Further details of these laboratory measurement tech208

niques can be found in the core analysis tutorial in this series and in “Recommended Practices for Core Analysis” (1998). Gas injection porosity

This technique is also referred to as gas expansion porosity. A known quantity (volume and pressure) of gas, usually helium, is injected into the pore space of a clean, dry core  plug in a sample holder. From the final pressure of the gas the grain volume or pore volume can be estimated. Since the gas flows into the sample pore space this technique must measure effective (connected) porosity but the hydration state of any clay minerals will depend on the drying techniques.  Fluid resaturation porosity

A clean, dry sample of known weight is saturated with a fluid of known density (usually kerosene or brine). The increase in weight gives the pore volume. This measurement gives the effective (connected) porosity since the fluid flows into the pore space. Whether clay bound water is included in the measured porosity depends on the hydration state of the clays when the dry sample is weighed. Summation of fluids porosity

This measurement is performed on core as received in the laboratory not on clean, dry samples. Two core pieces are used in the test procedure. The bulk volume of the first  piece is measured and then a measured volume of mercury is injected to give the gas volume in the sample. The second  piece of core is crushed and the water and oil in the pores is extracted by distillation. The volumes of gas, water and oil are related to the weights of the samples and added to give the pore volume and hence porosity. Porosity as determined in this way must be a combination of total and effective (connected) porosity since one core piece is disaggregated and the other is not. Porosity in log analysis

The simplified view of a “real” reservoir rock given in Figure 4, in which the clay particles can be regarded as  be in g di spe rs ed th ro ug hou t th e roc k le ad s to th e 4-component (matrix, clay, water and hydrocarbon) model depicted in Figure 5. In this figure: V ma volume of matrix grains V dcl  volume of dry clay (an idealized version of the clay matrix shown in Figure 4) V cbw volume of clay bound water  V cl  volume of wet clay (V dcl  + V cbw) V cap volume of capillary bound water  V  fw volume of free water 

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V hyd  volume of hydrocarbon V  pt  total pore volume V  pe effective pore volume (excluding clay-bound water) V b bulk volume of rock. In this model all the pore space is treated as a single entity with no consideration given as to whether the pores are connected or not. There are several logging tools that estimate porosity and they all work by putting energy into the formation from a transmitter and measuring the effect of the formation on the signal detected at a receiver. The effect is determined by some physical property of the formation that is not porosity  but is something related to it, for example the velocity of  sound in the case of the sonic tool. This is an indirect approach to estimating porosity. The way in which each of the components in Figure 5 affects the total response of the logging tool depends on the detailed physical nature of the measurement but, for sim plicity, is often assumed to be a volume-weighted average of the constituent parts.

the fluid contained in them. Thus, included in the pore space are hydrocarbons, free water, capillary held water and chemically bound water attached to clay minerals. With the nomenclature given in Figure 5, total porosity,   t , is given  by

 Effective porosity

Both the density and neutron logging tools essentially respond to all the pore space contained within a volume of  rock. Since gamma rays and neutrons pass through the rock  material, including grains, independently of any flow paths, these logs do not recognize the difference between connected and unconnected pores. The density tool responds to the electron density of the formation, which is closely related to the bulk density, which in turn can be related to either total or effective porosity, as explained above. The neutron tool responds to the hydrogen index of the formation—again closely related to either total or effective  porosity but also influenced by clay type and other factors.

The tool response equation for a logging tool which measures a volume-weighted average of the formation  property, x, is  x log  x ma Vma  x cl Vcl  xw Vw  xhyd V hyd  

 xma Vma  x cl Vcl  xw e Swe  xhyd   e (1 S we ) . It should be noted that the volumes of the various components sum to unity in this equation, i.e., Vma  Vcl  Vw  Vhyd     1. In this equation   e  is the log analysis effective porosity and is the volume that is available for the storage of hydrocarbon. In this case the volume of water that is electrochemically bound to the rock mineral surfaces is excluded from the pore space as discussed above under non-clay pore space. Using the nomenclature in Figure 5,   e, is given by

  e 

V   pe V b



V pt  V cbw V b

  t  

V   pt  V b

.

In neither of these definitions is there any reference to the need for the porosity to be connected. Generally where porosity is derived from logs alone then it is log analysis effective porosity that is estimated. To use the equations given above it is necessary to estimate values for  V cl  and xcl  to give e, or  V dcl  and xdcl  to give t . Since logs are measuring the whole rock as it is in-situ and without any control of the experimental conditions, the wet clay properties can be estimated more easily than dry clay properties by using log data alone and so   e  is normally determined.  Nuclear porosity logs

Sonic, or acoustic, porosity log 

The sonic logging tool measures the velocity of an

.

Total porosity

The response equation can also be written in terms of the total porosity as:  x log  x ma Vma  x dcl Vdcl  xw Vw  xhyd V hyd  

 xma Vma  x dcl V dcl    xw   t Swt  xhyd  t (1 S w t )  . Total porosity,  t , is the ratio of the total volume of pores to the bulk volume of the material regardless of the nature of  May-June 2003

FIG.  5

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4-component petrophysical model of rock.

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acoustic wave that propagates through the rock. Straightfor ward relationships are used to estimate either total or effective porosity. However, since the measurement is based on a  propagating wave, the response is not necessarily a simple volume-weighted average of the components, although the frequently used Wyllie time-average equation is. It is thought that the wave bypasses random events such as vugs, and therefore measures a property that is closer to connected porosity than total porosity.  NMR porosity logs

Current generations of NMR logging tools measure the signal decay curve due to spin-spin relaxation. The initial signal amplitude is related to the number of protons in the  pores and is thought to measure a porosity that is close to a total porosity. The porosity measured is a function of the shortest T 2, the decay constant due to spin-spin relaxation, that can be detected by the tool and this, in turn, depends on the echo spacing. Modern tools that can detect a  T 2  as short as approximately 0.3 ms are thought to include most of the clay bound water in their measurement leading to a porosity that matches reasonably well to helium core porosity. The older tools, which detected  T 2 only as low as approximately 3 ms are thought to measure an effective porosity.  Neither generation of tools, as conventionally run, distinguishes explicitly between connected and non-connected  pores. Further details of the physical principles of the logging tools can be found in the other articles in this series or in Tittman (1986).

the velocity of sound. These responses are converted into  porosity by applying a suitable model or by calibration. Improved estimates will result if several logs are combined and these logs are in turn integrated with other methods of  determining porosity such as core analysis. Combining log measurements reduces the effect of measurement errors in the logs and reduces errors caused by uncertainties in the matrix properties. Also, in some cases, such as gas, the effect on two logs will be opposite and combining the measurements compensates for these effects. Generally, because the experimental conditions can be well controlled and the experiment can be repeated if necessary, core porosity gives the best estimate of “true” porosity and is regarded as the ground truth to which log measurements should be calibrated. Core calibration of logs

For the density log there is a good, predictable, linear  relation between density and porosity. Whether “total” or  “effective” porosity is derived from the logs depends on the details of the parameters used to convert the log reading to  porosity. This relation can be derived from the general tool response equation given above so that, for a clean sand (or a 2-component fluid-matrix mix in which any clay can be regarded as matrix),

 b  ma (1  )   fl    ma  b           fl     ma   ma            b     ma  fl   ma   fl    a b  c

INTEGRATION OF CORE AND LOG POROSITY

All the logging tools described above as determining  porosity actually measure something that is not porosity. The density tool responds to the formation electron density, the neutron tool to the hydrogen index and the sonic tool to

FIG. 6

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Calibration of density log with core data.

To estimate values for  a and c, or   ma and   fl , a linear fit can be applied to a crossplot of core porosity and log density data as in Figure 6. The formation is modeled as a homogeneous entity and constant values of matrix density and fluid density are assumed to be able to represent the formation. A histogram of core sample grain density, shown in Figure 7, can be used to give a value of matrix density,   ma. In this  particular case a value of 2.64 g cm –3 was selected for   ma. This was based on the modal value of the histogram that was considered to best represent the formation. A rock with zero  porosity has a bulk density equal to the matrix density so one point on the relationship between porosity and density can be defined as the point ( ma, 0). A regression line through this point and the density-core porosity data pairs will define the fluid density for the formation as the density at 100% porosity. In this case fluid density,  fl , was esti –3 mated to be 0.93 g cm .

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TABLE  1

Summary of terms.

Porosity type

Pore volume

Measurement technique

Primary porosity

Void volume of a sediment when it was deposited.

Secondary porosity

Void volume that is created by diagenetic processes.

Total porosity (not necessarily connected)

Total void volume. Clay bound water is included in pore volume.

Core analysis (disaggregated sample) density, neutron, NMR logs if dry clay parameters used to derive porosity.

Effective porosity (connected)

Void volume contactable by fluids (connected). Clay bound water is included in pore volume.

Core analysis (competent sample). Possibly sonic log.

Effective porosity (log analysis)

Void volume available for storage of hydrocarbons. Clay bound water is excluded from pore volume. Unconnected pore volume not necessarily excluded from  pore volume. Depends on measurement technique.

Porosity logging tools if wet clay parameters used to derive porosity.

Effective porosity (usually in reservoir simulations)

Void volume available for storage of producible fluids. Clay bound water is excluded from pore volume. Capillary held water is also excluded from pore volume.

No direct technique to measure this. This definition implies that the effective porosity of a rock is a function of its location within a reservoir.

Similar techniques could be applied to the other porosity logs although a more complex nonlinear relationship may  be necessary. SUMMARY

From the above discussion, it can be seen that, although the term porosity has a simple theoretical definition, there are many different meanings attached to the term that are in common use in the oil and gas industry. These meanings are dependent on the method used to determine porosity and the use to which it may be put. A summary of the terms used for  the types of porosity discussed in this article and the techniques used to measure them is given in Table 1. There are many other types of porosity that have not been discussed in this tutorial, such as • fracture porosity: porosity resulting from natural fractures in the rock  • microporosity: porosity resident in small pores, commonly associated with detrital and authigenic clays or  within carbonate grains • intragranular porosity: porosity due to voids within the rock grains. Clearly there is scope for confusion, principally from the extensive use of the term “effective porosity” and the different meanings attributed to it. To attempt to reduce the vagueness of the terminology May-June 2003

used in practice in the hydrocarbon industry it is suggested that the following definitions should be used (Table 2). In this terminology the “log” total and effective porosities are attempts to measure the desired rock properties - total and effective porosity respectively. REFERENCES Amyx, J. W., Bass, D. M., and Whiting, R. L., 1960, Petroleum Reservoir Engineering, McGraw-Hill Book Company.

FIG. 7

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Grain density histogram for data from Figure 6.

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TABLE  2

Proposed terminology.

Total porosity Connected porosity Effective porosity “Log” total porosity “Log” effective porosity

Includes all pore volume, including clay bound water. A property of the rock. Includes only pore volume that can be contacted by fluids at the present time. Clay bound water is included in the pore volume. A property of the rock. Includes only pore volume that has the potential to store hydrocarbons. Clay bound water is excluded from the pore volume. A property of the rock. “log” should be replaced with the particular measurement technique used, (not confined to a downhole measurement). Pore volume includes all void volume including clay bound water. “log” should be replaced with the particular measurement technique used, (not confined to a downhole measurement). Pore volume includes only pores available to store hydrocarbons and excludes clay bound water. Measurement conditions of the log need to be considered, e.g. T 2 cut-off for NMR log.

Fraser, H. J. and Graton, L. C., 1935, Systematic packing of  spheres – with particular relation to porosity and permeability:  Journal of Geology., vol. 43, p. 785–909. Recommended Practices for Core Analysis, 1998, American Petroleum Institute RP 40. Tittman, J., 1986,  Geophysical Well Logging : London (Academic Press).

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ABOUT THE AUTHOR  Jeff Hook   is currently a Consultant Petrophysicist with Helix RDS. His previous experience includes various petrophysical roles with Enterprise Oil and Mobil North Sea Ltd in London and with BNOC/Britoil/BP. His initial experience in the oil industry was with a core analysis service laboratory where he was responsible for the development of analytical techniques and quality assurance of both special and conventional core analysis laboratories. Since  joining the operating sector of the indu stry he has gain ed experience in all aspects of the application of petrophysics ranging from design of data acquisition programmes through single well evaluation to field studies and equity re-determinations. He has authored papers on core analysis, facies and permeability  prediction and application of NMR logs and his current interests include applications of NMR logs and integration of petrophysical and geophysical data. He has played an active part in the activities of the London Petrophysical Society (a chapter of SPWLA) for  many years, and has served as President, Treasurer and V-P Membership. He is currently a Regional Director for SPWLA (Europe Position II).

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