Petrographical Characteristics

The petrographical parameters are facilitated to quantitatively describe the texture or appearance of the rock minerals and the pore structure. The fundamental parameters used for this purpose are described in the following.

Fabric and Texture

Lucia (1995) emphasizes that "Pore space must be defined and classified in terms of rock fabrics and petrophysical properties to integrate geological and engineering information." Fabric is the particle orientation in sedimentary rock (O'Brien et al., 1994). Defarge et al. (1996) defined: "Texture, i.e., the size, shape, and mutual arrangement of the constitutient elements at the smaller scale of ... sedimentary bodies, is a petrological feature that may serve to characterize and compare" them.

Lucia (1995) points out that: "The pore-size distribution is controlled by the grain size in grain-dominated packstones and by the mud size in mud-dominated packstones." Lucia (1995) explains that: "Touching-vug pore systems are defined as pore space that is:

(1) significantly larger than the particle size, and

(2) forms an interconnected pore system of significant extent"


Porosity, (j), is a scalar measure of the pore volume defined as the volume fraction of the pore space in the bulk of porous media. The porous structure of naturally occurring porous media is quite complicated. The simplest of the pore geometry is formed by packing of near-spherical grains. When the formation contains different types of grains and fractured by stress and deformation, pore structure is highly complicated. For convenience in analytical modeling, the porous structure of a formation can be subdivided into a number of regions. Frequently, a gross classification as micropores and macropores regions according to Whitaker (1999) and Bai et al. (1993) can be used for simplification. However, in some cases, a more detailed composite description with multiple regions may be required (Cinco-Ley, 1996; Guo and Evans, 1995). Such descriptions may accommodate for natural fractures and grain packed regions of different characteristics. The various regions are considered to interact with each other (Bai et al., 1995).

Spherical Pore Space Approximation

For simplification and convenience, the shapes of the pore space and grains of porous media are approximated and idealized as spheres. The pore volume can be approximated in terms of the mean pore diameter, D, as:

File:Geological and petrophysical classification of the carbonate rock interparticle pore structure.png
Geological and petrophysical classification of the carbonate rock interparticle pore structure
File:Geological and petrophysical classification of the rock vuggy pore structure.png
Geological and petrophysical classification of the rock vuggy pore structure
Then, given the bulk volume, VB, the porosity is expressed by:
File:Porosity is expressed.png
Porosity is expressed
The pore surface is given by:

The specific pore surface in terms of the pore surface per pore volume is given by:

The expressions given above for a spherical shape can be corrected for irregular pore space, respectively, as (Civan, 1996):
File:Spherical shape can be corrected for irregualr pore space, respectively.png
Spherical shape can be corrected for irregualr pore space, respectively
where Cl,C2,...,C5 are some empirical shape factors. Similarly, for the spherical idealization of a particle, the specific surface defined as the contact surface per volume sphere is given by: This can be corrected for irregular particle shape as:
File:Irregular particle shape.png
Irregular particle shape
where C6 is a shape factor.

Area Open for Flow

Areosity or areal porosity is the fractional area of the bulk porous media open for flow (Liu and Masliyah, 1996). Liu and Masliyah (1996) point out that, frequently, the areal porosity has been taken equal to the volumetric porosity of porous media.
File:Volumetric porosity.png
Volumetric porosity
File:Isotropic porous media.png
Isotropic porous media

They emphasize that Equation 3-11 performs well for models considering a bundle of straight hydraulic flow pathways and nonconnecting constricted pathways. Whereas, for isotropic porous media, Liu et al. (1994) recommend that the areal porosity should be estimated as:


Tortuosity is defined as the ration of the lengths, Lt and L, of the tortuous fluid pathways and the porous media:

Liu and Masliyah (1996a, b) recommend the Bruggeman (1935) equation for consolidated porous media of porosity (|) < 0.45. They point out that the latter may have a variable accuracy and, therefore, tortuosity should be measured.

Interconnectivity of Pores

Davies (1990) classified the pore types in four groups:

Pore Type 1: Microspores, generally equant shape, less than 5 microns in diameter. These occur in the finest grained and shaly portions of the sand.

Pore Type 2: Narrow, slot like pores, generally less than 15 microns in diameter, commonly slightly to strongly curved. These represent reduced primary intergranular pores resulting from the reduction of original primary pores by extensive cementation.

Pore Type 3: Primary intergranular pores, triangular in shape, twenty-five to fifty microns maximum diameter. These are the original primary intergranular pores of the rock which have been affected only minimally by cementation.

Pore Type 4: Solution enlarged primary pores: oversized primary pores, fifty to two hundred microns maximum diameter produced through the partial dissolution of rock matrix.

File:Thin-section images of various pore types.png
Thin-section images of various pore types

Frequently, for convenience, pore space is perceived to consist of pore bodies connecting to other pore bodies by means of the pore necks or throats as depicted. Many models facilitate a network of pore bodies connected with pore throats.

However, in reality, it is an informidable task to distinguish between the pore throats and pore bodies in irregular porous structure (Lymberopoulos and Payatakes, 1992). Interconnectivity of pores is a parameter determining the porosity of the porous media effective in its fluid flow capability. In this respect, the pores of porous media.

The sketched are classified in three groups:

1. Connecting pores which have flow capability or permeability (conductor),

2. Dead-end pores which have storage capability (capacitor), and

2 Non-connecting pores which are isolated and therefore do not contribute to permeability (nonconductor).

File:Description of the pore volume attributes.png
Description of the pore volume attributes

The interconnectivity is measured by the coordination number, defined as the number of pore throats emanating from a pore body. Typically, this number varies in the range of 6 < Z < 14 (Sharma and Yortsos, 1987). For cubic packing, Z = 6 and <J> = 1 - n/6. The coordination number can be determined by nitrogen sorption measurements (Liu and Seaton, 1994).

Pore and Pore Throat Size Distributions

Typical measured pore body and pore throat sizes, given by Ehrlich and Davies (1989) The mathematical representation of the distribution of the pore body and pore throat sizes in natural porous media can be accomplished by various statistical means. The three of the frequently used approaches are the following:

1. Log-Normal Distribution (not representative)

2. Bi-Model Distribution (fine and course fractions)

3. Fractal Distribution

Log-Normal Distribution:

Because of is simplicity, the log-normal distribution function given below has been used by many, including Ohen and Civan (1991):

File:Log-normal distribution function.png
Log-normal distribution function
File:An integrated modeling approach to characterization of porous formation and processes.png
An integrated modeling approach to characterization of porous formation and processes
File:Interconnectivity of pores.png
Interconnectivity of pores.
File:Typical cumulative pore body and pore throat size distributions.png
Typical cumulative pore body and pore throat size distributions
File:Typical bimodal pore throat size distributions in porous formation.png
Typical bimodal pore throat size distributions in porous formation

Bi-Modal Distribution.:

File:Mathematical representation of the size distribution.png
Mathematical representation of the size distribution

Typically, the pore body and pore throat sizes vary over finite ranges and the size distributions can display a number of peaks corresponding to various fractions of pore bodies and pore throats in porous media. If only two groups, such as the fine and coarse fractions, are considered, a bi-modal distribution function according to Popplewell et al. (1989) can be used for mathematical representation of the size distribution:

File:P-distribution function in the following modified from.png
P-distribution function in the following modified from
File:The differential pore size distribution can be written in terms of the pore diameter.png
The differential pore size distribution can be written in terms of the pore diameter

where D denotes the diameter, f\(D) and /2(^) are the distribution functions for the fine and coarse fractions, and w is the fraction of the fine fractions. Popplewell et al. (1988, 1989) used the p-distribution function to represent the skewed size distribution, because the diameters of the smallest and the largest particles are finite in realistic porous media. For convenience, they expressed the P-distribution function in the following modified from:

Chang and Civan (1991, 1992, 1997) used this approach successfully in a model for chemically induced formation damage.

Fractal Distribution: Fractal is a concept used for convenient mathematical description of irregular shapes or patterns, such as the pores of rocks, assuming self-similarity. The pore size distributions measured at different scales of resolution have been shown to be adequately described by empirically determined power law functions of the pore sizes (Garrison et al., 1993; Verrecchia, 1995; Karacan and Okandan, 1995; Perrier et al., 1996). The expression given by Perrier et al. (1996) for the differential pore size distribution can be written in terms of the pore diameter as:

File:Integrating Equation distribution.png
Integrating Equation distribution

where, D denotes the pore diameter, V represents the volume of pores whose diameter is greater than D, d is the fractal dimension (typically 2 < d < 3), e is the Euclidean space dimension (e = 3) and (3 is a positive constant. Thus, integrating Equation 3-23, Perrier et al. (1996) derived the following expression for the pore size distribution.

Textural Parameters

File:The textual appearance of reservoir formation by four parameters.png
The textual appearance of reservoir formation by four parameters
File:Triangular diagrams.png
Triangular diagrams

Nolen et al. (1992) have described the textual appearance of reservoir formation by four parameters:

1. Median grain size, defined as:

and the surface area and surface area based diameter, dA, are given, respectively, by:

2. Grain shape factor, defined as:

3. Sorting, defined by:

4. Packing, which is the volume fraction of the solid matrix, given by:

File:A ternary chart showing the relationship between packing density, intergranular pore space.png
A ternary chart showing the relationship between packing density, intergranular pore space

density, cement, and intergranular volume at various locations of reservoir formations. Such diagrams provide useful insight into the heterogeneity of reservoirs. Coskun et al. (1993) shows the relationships between composition, texture, porosity, and permeability for a typical sandstone reservoir.


1. Al-Mahtot, O. B., & Mason, W. E., "Reservoir Description: Use of Core Data to Identify Flow Units for a Clastic North Sea Reservoir," Turkish Journal of Oil and Gas, Vol. 2, No. 1, February 1996, pp. 33-43.

2. Bai, M., Elsworth, & Roegiers, J. C., "Multiporosity/Multipermeability Approach to the Simulation of Naturally Fractured Reservoirs," Water Resources Research, Vol. 29, No. 6, 1993, pp. 1621-1633.

3. Bai, M., Bouhroum, A., Civan, F., & Roegiers, J. C., "Improved Model for Solute Transport in Heterogeneous Porous Media," J. Petroleum Science and Engineering, Vol. 14, 1995, pp. 65-78.

4. Bruggeman, D. A. G. "Berechnung verschiedener physikalischer Konstanten von heterogenen Substanze," Ann. Phys. (Leipzig), Vol. 24, 1935, pp. 636-679.

5. Chang, F. F., & Civan, F., "Modeling of Formation Damage due to Physical and Chemical Interactions between Fluids and Reservoir Rocks," SPE 22856 paper, Proceedings of the 66th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, October 6-9, 1991, Dallas, Texas.

6. Chang, F. F., & Civan, F., "Predictability of Formation Damage by Modeling Chemical and Mechanical Processes," SPE 23793 paper, Proceedings of the SPE International Symposium on Formation Damage Control, February 26-27, 1992, Lafayette, Louisiana, pp. 293-312.

7. Chang, F. F., & Civan, F., "Practical Model for Chemically Induced Formation Damage," J. of Petroleum Science and Engineering, Vol. 17, No. 1/2, February 1997, pp. 123-137.

8. Cinco-Ley, H., "Well-Test Analysis for Naturally Fractured Reservoirs," Journal of Petroleum Technology, January 1996, pp. 51-54.

9. Collins, E. R., Flow of Fluids Through Porous Materials, Penn Well Publishing Co., Tulsa, Oklahoma, 1961, 270 p.

10. Coskun, S. B., Wardlaw, N. C., & Haverslew, B., "Effects of Composition, Texture and Diagenesis on Porosity, Permeability and Oil Recovery in a Sandstone Reservoir," Journal of Petroleum Science and Engineering, Vol. 8, 1993, pp. 279-292.

11. Davies, D. K., "Image Analysis of Reservoir Pore Systems: State of the Art in Solving Problems Related to Reservoir Quality, SPE 19407, the SPE Formation Damage Control Symposium held in Lafayette, Louisiana, February 22-23, 1990, pp. 73-82.

12. Defarge, C., Trichet, J., Jaunet, A-M., Robert, M., Tribble, J., & Sansone, F. J., "Texture of Microbial Sediments Revealed by Cryo-Scanning Electron Microscopy," Journal of Sedimentary Research, Vol. 66, No. 5, September 1996, pp. 935-947.

13. Ehrlich, R. and Davies, D. K., "Image Analysis of Pore Geometry: Relationship to Reservoir Engineering and Modeling," SPE 19054 paper, roceedings of the SPE Gas Technology Symposium held in Dallas, Texas, June 7-9, 1989, pp. 15-30.

14. Ertekin, T., & Watson, R. W., "An Experimental and Theoretical Study to Relate Uncommon Rock-Fluid Properties to Oil Recovery," Contract No. AC22-89BC14477, in EOR-DOE/BC-90/4 Progress Review, No. 64, pp. 68-71, U.S. Department of Energy, Bartlesville, Oklahoma, May 1991, 129 p.

15. Garrison, Jr., J. R., Pearn, W. C., & von Rosenberg, D. U., "The Fractal Menger Sponge and Sierpinski Carpet as Models for Reservoir Rock/ Pore Systems: I. Theory and Image Analysis of Sierpinski Carpets and II. Image Analysis of Natural Fractal Reservoir Rocks, In-Situ, Vol. 16, No. 4, 1992, pp. 351-406, and Vol. 17, No. 1, 1993, pp. 1-53.

16. Guo, G., & Evans, R. D., "Geologic and Stochastic Characterization of Naturally Fractured Reservoirs," SPE 27025 paper, presented at 1994 SPE III Latin American & Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, April 27-29, 1994.

17. Hohn, M. E., Patchen, D. G., Heald, M., Aminian, K., Donaldson, A., Shumaker, R., & Wilson, T, "Report Measuring and Predicting Reservoir Heterogeneity in Complex Deposystems," Final Report, work performed under Contact No. DE-AC22-90BC14657, U.S. Department of Energy, Bartlesville, Oklahoma, May 1994.

18. Karacan, C. 6., & Okandan, E., "Fractal Analysis of Pores from Thin Sections and Estimation of Permeability Therefrom," Turkish Journal of Oil and Gas, Vol. 1, No. 2, October 1995, pp. 52-58.

19. Kaviany, M., Principles of Heat Transfer in Porous Media, Springer- Verlag, New York, 1991, 626 p.

20. Liu, H., & Seaton, N. A., "Determination of the Connectivity of Porous Solids from Nitrogen Sorption Measurements—III. Solids Containing Large Mesopores," Chemical Engineering Science, Vol. 49, No. 11, 1994, pp. 1869-1878.

21. Liu, S., Afacan, A., & Masliyah, J. H., Chemical Engineering Science, Vol. 49, 1994, pp. 3565-3586.

22. Liu, S., & Masliyah, J. H., "Principles of Single-Phase Flow Through Porous Media," Chapter 5, pp. 227-286, in Suspensions, Fundamentals and Applications in the Petroleum Industry, Advances in Chemistry Series 251, L. L. Schramm (ed.), American Chemical Society, Washington, DC, 1996a, 800 p.

23. Liu, S. and Masliyah, J. H., Single Fluid Flow in Porous Media, Chem. Engng. Commun., Vol. 148-150, 1996b, pp. 653-732.

24. Lucia, F. J., "Rock-Fabric/Petrophysical Classification of Carbonate Pore Space for Reservoir Characterization," AAPG Bulletin, Vol. 79, No. 9, September 1995, pp. 1275-1300.

25. Lymberopoulos, D. P., & Payatakes, A. C., "Derivation of Topological, Geometrical, and Correlational Properties of Porous Media from Pore-Chart Analysis of Serial Section Data," Journal of Colloid and Interface Science, Vol. 150, No. 1, 1992, pp. 61-80.

26. Nolen, G., Amaefule, J. O., Kersey, D. G., Ross, R., & Rubio, R., "Problems Associated with Permeability and Vclay Models from Textural Properties of Unconsolidated Reservoir Rocks," SCA 9225 paper, 33rd Annual Symposium of SPWLA Society of Core Analysts, Oklahoma City, Oklahoma, June 15-17, 1992.

27. O'Brien, N. R., Brett, C. E., & Taylor, W. L., "Microfabric and Taphonomic Analysis in Determining Sedimentary Processes in Marine Mudstones: Example from Silurian of New York," Journal of Sedimentary Research, Vol. A64, No. 4, October 1994, pp. 847-852.

28. Perrier, E, Rieu, M., Sposito, G., & de Marsily, G., "Models of the Water Retention Curve for Soils with a Fractal Pore Size Distribution," Water Resources Research Journal, Vol. 32, No. 10, October 1996, pp. 3025-3031.

29. Popplewell, L. M., Campanella, O. H., & Peleg, M., "Simulation of Bimodal Size Distributions in Aggregation and Disintegration Processes," Chem. Eng. Progr., August 1989, pp. 56-62.

30. Sharma, M. M. and Yortsos, Y. C., "Transport of Particulate Suspensions in Porous Media: Model Formulation," AIChE J., pp. 1636-1643, Vol. 33, No. 10, Oct. 1987.

31. Verrecchia, E. P., "On the Relation Between the Pore-Throat Morphology Index ("a") and Fractal Dimension (DJ) of Pore Networks in Carbonate Rocks-Discussion," Journal of Sedimentary Research, Vol. A65, No. 4, October 1995, pp. 701-702.

32. Whitaker, S., The Method of Volume Averaging, Kluwer Academic Publishers, Boston, 1999, 219 p.

33. Winsauer, W. O., Shearin, H. M., Masson, P. H., and Williams, M. "Resistivity of Brine Saturated Sands in Relation to Pore Geometry," Bull. Amer. Ass. Petrol. Geol., Vol. 36(2), 1952, pp. 253-277.