Petrography and Texture of Petroleum-Bearing Formations 57 ^COMPARISONS^ INTEGRATION (BOUNDARY AND INITIAL CONDITIONS) 1) LABORATORY DATA 2) DATA FILTERING AND SMOOTHING 3) MARQUARDT- LEVENBERG NONLINEAR OPTIMIZATION 4) PARAMETER ESTIMATION VOLUME AVERAGING ETWORK MODEL JUULJUU1_\ x-v unnnnnc \(sj DiDnac ^ v ^ DDDDDDn NETWORKING Figure 3-5. An integrated modeling approach to characterization of porous formation and processes (after Civan, ©1994; reprinted by permission of the U.S. Department of Energy). 58 Reservoir Formation Damage O •o O o [INTERCONNECTED PORES [ DEAD-END PORES ISOLATED PORES Figure 3-6. Interconnectivity of pores. 0.01 O CC O 03 5 DC 10-= 100-= \ X THROATS ASSOCIATED WITH INTERQRANULAR FORES BODIES A—A THROATS 100 I SO so 40 SO CUMULATIVE FREQUENCY (%) Figure 3-7. Typical cumulative pore body and pore throat size distributions in porous formation (after Ehrlich and Davies, ©1989 SPE; reprinted by permission of the Society of Petroleum Engineers). Petrography and Texture of Petroleum-Bearing Formations 59 0.1 1 10 Pore Thraal Radius, microns 1000 Figure 3-8. Typical bimodal pore throat size distributions in porous formation (after AI-Mahtot and Mason, ©1996; reprinted by permission of the Turkish Journal of Oil and Gas). where D is the diameter of the pores approximated by spheres, D m , is the mean pore diameter calculated by: D= DF(D)dD (3-17) and s d is the standard deviation, and D min and D max denote the smallest and largest diameters. Bi-Modal 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: (3-18) 60 Reservoir Formation Damage 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: f(x) = x am (l-x) m / \x am (\-x} m dx I J (3-19) in which jc denotes a normalized diameter defined by: (3-20) £> min and £> max are the smallest and the largest diameters, respectively, a and m are some empirical power coefficients. The mode, x m , and the spread, a 2 , for Equation 3-19 are given, respectively, by: x m =a/(a + and (am + l)(m +1) (3-21) (3-22) 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 mathe- matical 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: dV_ dD l , 0<d<e (3-23) Petrography and Texture of Petroleum-Bearing Formations 61 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: , 0<d<e (3-24) in which V 0 is the constant of integration. Perrier et al. (1996) then considered a range of pore size as £> min <D< D max . Thus, applying Equa- tion 3-24, the total pore volume, V , is given by (Perrier et al., 1996): Vp = V 0 -V%£ 0-25) Because V p =0 for D = D max , Equation 3-24 leads to (Perrier et al., 1996): (3-26) Textural Parameters Nolen et al. (1992) have described the textual appearance of reservoir formation by four parameters: 1. Median grain size, defined as: "max d g = J dF(d)d(d] 2. Grain shape factor, defined as: in which volume and volume based diameter, d v , are given, respec- tively, by: ro/ (3-29) 62 Reservoir Formation Damage and the surface area and surface area based diameter, d A , are given, respectively, by: 1/2 (3-30) Note that y = 1 for spherical particles. 3. Sorting, defined by: 5 = d-d o (3-31) where d g is the average grain diameter, d 0 is the mode diameter, and a is the standard deviation. 4. Packing, which is the volume fraction of the solid matrix, given by: (3-32) where <|) denotes the porosity in fraction. Triangular diagrams, such as shown in Figure 3-9 by Hohn et al. (1994), are convenient ways of presenting the relationships between packing, vvvvvvvvvvvv 75 Cement 25 (incl. coats) Figure 3-9. A ternary chart showing the relationship between packing density, intergranular pore space, and cement in Granny Creek wells nos. 1-9, 11, and 12 (after Hohn et al., ©1994; reprinted by permission of the U.S. Depart- ment of Energy). Petrography and Texture of Petroleum-Bearing Formations 63 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 composi- tion, texture, porosity, and permeability for a typical sandstone reservoir. References 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. 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. 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. Bruggeman, D. A. G. "Berechnung verschiedener physikalischer Konstanten von heterogenen Substanze," Ann. Phys. (Leipzig), Vol. 24, 1935, pp. 636-679. 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. 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. 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. Cinco-Ley, H., "Well-Test Analysis for Naturally Fractured Reservoirs," Journal of Petroleum Technology, January 1996, pp. 51-54. Collins, E. R., Flow of Fluids Through Porous Materials, Penn Well Publishing Co., Tulsa, Oklahoma, 1961, 270 p. 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. 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. 64 Reservoir Formation Damage 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. Ehrlich, R. and Davies, D. K., "Image Analysis of Pore Geometry: Relationship to Reservoir Engineering and Modeling," SPE 19054 paper, Proceedings of the SPE Gas Technology Symposium held in Dallas, Texas, June 7-9, 1989, pp. 15-30. 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. 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. 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 Con- ference, Buenos Aires, Argentina, April 27-29, 1994. 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 per- formed under Contact No. DE-AC22-90BC14657, U.S. Department of Energy, Bartlesville, Oklahoma, May 1994. 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. Kaviany, M., Principles of Heat Transfer in Porous Media, Springer- Verlag, New York, 1991, 626 p. 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. Liu, S., Afacan, A., & Masliyah, J. H., Chemical Engineering Science, Vol. 49, 1994, pp. 3565-3586. 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. Petrography and Texture of Petroleum-Bearing Formations 65 Liu, S. and Masliyah, J. H., Single Fluid Flow in Porous Media, Chem. Engng. Commun., Vol. 148-150, 1996b, pp. 653-732. 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. 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. Nolen, G., Amaefule, J. O., Kersey, D. G., Ross, R., & Rubio, R., "Problems Associated with Permeability and V clay 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. 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. 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. Popplewell, L. M., Campanella, O. H., & Peleg, M., "Simulation of Bimodal Size Distributions in Aggregation and Disintegration Pro- cesses," Chem. Eng. Progr., August 1989, pp. 56-62. 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. 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. Whitaker, S., The Method of Volume Averaging, Kluwer Academic Pub- lishers, Boston, 1999, 219 p. 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. Chapter 4 Petrophysics-Flow Functions and Parameters Summary A review of the petrophysical properties involving formation damage is presented in this chapter. Introduction The distribution and behavior of multiphase fluid systems in petroleum reservoirs are strongly influenced by the petrophysical properties of sedimentary formations. Ucan et al. (1997) state: "Petrophysical properties of multiphase flow systems in porous rock are complex functions of the morphology and topology of the porous medium, interactions between rock and fluids, phase distribution, and flow pattern and regimes. The effect of these properties on the flow behavior is lumped in the form of empirically determined relative permeability and capillary pressure func- tions which are used as the primary flow parameters for the macroscopic description of multiphase flow in porous media." During formation damage, petrophysical properties vary due to rock, fluid, and particle interactions. Therefore, dynamic relationships are required to take the varying petrophysical properties into account in predicting the fluid behavior during formation damage. This chapter presents a review of the primary petrophysical properties that influence the fluid behavior and formation damage in petroleum reservoirs. Wettability Alteration Kaminsky and Radke (1997) stated that the wettability of reservoirs is "loosely defined as the preferential affinity of the solid matrix for either the aqueous or oil phases." 66 [...]... 75 IflflkWalf-We 10 0 I OH- Wat (a) 0 .4 (b) 0.6 0.8 1. 0 0.00 0.0 0.2 0 .4 0.6 0.8 1. 0 0.05 (c) -0 .10 1. 0 Sw Figure 4- 5 Capillary pressure curves for a) 10 0% water-wet and 10 0% oilwet systems, b) three fractionally-wet systems, and c) three mixed-wet systems (McDougall and Sorbie, 19 95 SPE; reprinted by permission of the Society of Petroleum Engineers) 76 Reservoir Formation Damage 1. 0 10 0% WW 66% WW... Using the Centrifuge Method," SPE 2 6 14 8 paper, Proceedings of the SPE Gas Technology Symposium, Calgary, Alberta, Canada (June 28-30 19 93) pp 10 7 -11 7 Amott, E., "Observations Relating to the Wettability of Porous Rock," Trans A/ME, Vol 216 , 19 59, pp 15 6 -16 2 Cassie, A B D., & Baxter, S., "Wettability of Porous Surfaces," Trans Faraday Soc., Vol 40 , 19 44 , pp 546 -5 51 Chang, Y C., Mohanty, K K., Huang,... Vol 14 2, 19 41 , pp 15 2 -16 9 Marie, C M., Multiphase Flow in Porous Media, Gulf Publ Co., Houston, Texas, 19 81, 257 p McDougall, S R., & Sorbie, K S., "The Impact of Wettability on Waterflooding: Pore Scale Simulation," SPE Reservoir Engineering, August 19 95, pp 208- 213 Mohanty, K K., Masino Jr., W H., Ma, T D., & Nash, L J., "Role of Three-Hydrocarbon-Phase Flow in a Gas-Displacement Process," SPE Reservoir. .. Science and Engineering, Vol 20, No 3 /4, pp 12 7 -13 2, 19 98 Robin, M., Rosenberg, E., & Fassi-Fihri, O., "Wettability Studies at the Pore Level: A New Approach by use of Cryo-SEM," SPE Formation Evaluation, March 19 95, pp 11 -19 Sharma, R., "On the Application of Reversible Work to Wetting/Dewetting of Porous Media," Colloids and Surfaces, Vol 16 , No 1, 19 85, pp 87- 91 Sigmund, P M., & McCaffery, F G., "An... Oklahoma City, Oklahoma, March 10 -12 , 19 85, pp 15 7 -16 3 Donaldson, E C., & Crocker, M E., "Characterization of the Crude Oil Polar Compound Extract," DOE/BETC/RI-80/5, NTIS, Springfield, Virginia 2 216 1, 19 80, 27 p Donaldson, E C., Ewall, N., & Singh, B., "Characteristics of Capillary Pressure Curves," Journal of Petroleum Science and Engineering, Vol 6, No 3, 19 91, pp 249 -2 61 Donaldson, E C., Kendall,... and Crocker (19 80)] WI = Iog10 (A +1 A~) (4- 2) Thus, according to Equation 4- 2, as following: porous materials are classified 1 WI > 0, water-wet, 2 WI ~ 0, intermediately-wet, and 3 WI < 0, oil-wet Many studies have reported wettability variation during formation damage due to alteration of pore surface characteristics by rock, fluid, and particle interactions Figure 4 -1, by Donaldson (19 85), shows... Engineering, Vol 18 , Nos 1/ 2, 19 97, pp 1- 19 Civan, R, & Donaldson, E C., "Relative Permeability from UnsteadyState Displacements: An Analytical Interpretation," SPE Paper 16 200, Proceedings of the SPE Production Operations Symposium held in Oklahoma City, Oklahoma, March 8 -10 , 19 87, pp 13 9 -15 5 Collins, E R., Flow of Fluids Through Porous Materials, Penn Well Publishing Co., Tulsa, Oklahoma, 19 61, 270 p Cuiec,... Process," SPE Reservoir Engineering, August 19 95, pp 2 14 -2 21 Neasham, J W., "The Morphology of Dispersed Clay in Sandstone Reservoirs and Its Effect on Sandstone Shaliness, Pore Space and Fluid Flow Properties," SPE 6858, Proceedings of the 52nd Annual Fall Technical Conference and Exhibition of the SPE of AIME held in Denver, Colorado, October 9 -12 , 19 77, pp 18 4 -19 1 Paterson, A., Robin, M., Fermigier, M.,... remains unchanged during formation alteration, Equation 4- 8 can be applied at a reference state and denoted by subscript "0" and at an instantaneous state during formation damages to obtain: 74 Reservoir Formation Damage Pc CcosG . Related to Reservoir Quality, SPE 19 40 7, the SPE Formation Damage Control Symposium held in Lafayette, Louisiana, February 22-23, 19 90, pp. 73-82. 64 Reservoir Formation Damage Defarge, . Recovery," Contract No. AC22-89BC 144 77, in EOR-DOE/BC-90 /4 Progress Review, No. 64, pp. 68- 71, U.S. Department of Energy, Bartlesville, Oklahoma, May 19 91, 12 9 p. Garrison, Jr., J. R., . Engineering Science, Vol. 49 , No. 11 , 19 94, pp. 18 69 -18 78. Liu, S., Afacan, A., & Masliyah, J. H., Chemical Engineering Science, Vol. 49 , 19 94, pp. 3565-3586. Liu, S.,