Permeability and Porosity Reduction by Swelling
Contents
Porosity Reduction by Swelling
Based on the definition of the swelling coefficient, Civan and Knapp (1987) expressed the rate of porosity change by swelling of porous matrix as: where § is porosity, t is time, S is the rate of water absorbed per unit bulk volume of porous medium. Civan 1996 developed an improved equation assuming that the rate of porosity variation by swelling is proportional to the rate of water absorption and the difference between the instantaneous and the terminal or saturation porosities:
from which the porosity variation by swelling can be expressed by:
where ksw is the formation swelling rate constant, t is the actual time of contact with water. Therefore, the swelling rate constant can be determined by fitting Eq. 2-27. However, due to the lack of experimental data, the application of Eq. 2-28 could not be demonstrated. It is difficult to measure porosity during swelling. Permeability can be measured more conveniently. Ohen and Civan (1993) used a permeability-porosity relationship to express porosity reduction in terms of permeability reduction.
Permeability Reduction by Swelling
Civan and Knapp (1987) assumed that the rate of permeability reduction by swelling of formation depends on the rate of the water absorption and the difference between the instantaneous permeability and terminal permeability that will be attained at saturation as: where asw is the rate constant for permeability reduction by swelling, from which the permeability variation by swelling is obtained as:
Civan and Knapp (1987) and Civan et al. (1989) have confirmed the validity of Eq. 2-31 using the Hart et al. (1960) data for permeability reduction in the outlet region of a core subjected to the injection of a suspension of bacteria. Because bacteria is essentially retained in the inlet side of the core, the permeability reduction in the near-effluent port of the core can be attributed to formation swelling by water absorption. The best linear, least-squares fit of Eq. 2-31 to Hart et al. (1960) data using Eq. 2-9 for S yields (Civan et al., 1989): [[File:Best linear, least-squares ormula.png|thumb|400px|Best linear, least-squares formula]] with (Kt/K0) = 0.57 and B = 2asw(cl -c0)Jo/n = QMhr~{/2 with a correlation coefficient of R2 = 0.93 the Hart et al. (1960) data can also be correlated using Eq. 2-6 for S. In this case, the best fit is obtained using the parameter values of A = asw (q - c0)/h = 0.95, h^D = 1, and Kt/K0 = 0.57. Ngwenya et al. (1995) conducted core flood experiments by injecting an artificial seawater into the Hopeman (Clashach) sandstone. They report that the core samples used in their experiments contained trace amounts of clays. Therefore, they concluded that the effect of clay swelling, and entrainment and deposition of clay particles to permeability impairment would be negligible.
Consequently, it can be concluded that the swelling of some constituents of the sandstone formation should be contributing to permeability reduction. The best least-squares linear fit of Eq. 2-31 was obtained using Eq. 2-9 for 5 with the parameter values of B = asw (c, - c0)/h = 0.038hr~1/2 and (KtIK0} = 0.087 with a correlation coefficient of R2 = 0.89. The best fit of Eq. 2-31 using Eq. 2-6 for 5 was obtained using the parameter values of A = asw (cl - c0)/h = 0.035, hjD = 1, and KtIK0 = 0.087. Hart et al. (1960) and the Ngwenya et al. (1995) experimental data does not permit etermining whether Eqs. 2-6 or 9 with Eq. 2-31 better represents the data. Because Eq. 2-6 led to successful representation of the other data correlated in the preceding sections, it is reasonable to assume that Eq. 2-6 should also represent the permeability reduction data equally well. Therefore, Eq. 2-6 may be preferred over Eq. 2-9.
Graphical Representation of Clay Content
The distribution of clays can be conveniently depicted by Lynn and Nasr-El-Din (1998). Lynn and Nasr-El-Din (1998) classified reservoir formations having less than 1 wt. % total clay and permeability higher than one Darcy as the high quality, and the low quality vice versa. Amaefule et al. (1993) measured the formation quality by the reservoir quality index defined as:
Hayatdavoudi Hydration Index (HHI)
The Hayatdavoudi hydration index (HHI=[O/OH]) is defined as the ratio of the oxygen atoms to hydroxyl groups in clays and it controls the enthalpy or free energy of the clays available for the work of swelling by hydration (Hayatdavoudi, 1999, 1999). Hence, higher hydration index is indicative of more clay swelling, according to (Hayatdavoudi, 1999, 1999):
where G, H, S, T, and R denote the free energy, enthalpy, entropy, absolute temperature, and the universal gas constant, respectively. Hayatdavoudi (1999) shows that all clays possess some degree of the work of swelling and therefore classification of different clays as swelling or non-swelling has no significance.
References
[1] Amaefule, J. O., Kersey, D. G., Norman, D. L., & Shannon, P. M., "Advances in Formation Damage Assessment and Control Strategies," CIM Paper No. 88-39-65, Proceedings of the 39th Annual Technical Meeting of Petroleum Society of CIM and Canadian Gas Processors Association, Calgary, Alberta, June 12-16, 1988, 16 p.
[2] Amaefule, J. O., Altunbay, M., Tiab, D., Kersey, D. G., & Keelan, D. K., "Enhanced Reservoir Description: Using Core and Log Data to Identify Hydraulic (Flow) Units and Predict Permeability in Uncored Intervals/Wells," SPE 26436 paper, Proceedings of the 68th Annual Technical Conference and Exhibition of the SPE held in Houston, Texas, October 3-6, 1993, pp. 205-220.
[3] Ballard, T. J., Beare, S. P., & Lawless, T. A., "Fundamentals of Shale Stabilization: Water Transport through Shales," SPE Formation Evaluation, June 1994, pp. 129-134.
[4] Blomquist, G. C., & Portigo, J. M., "Moisture, Density and Volume Change Relationships of Clay Soils Expressed as Constants of Proportionality," Bull. Highway Res. Board, No. 313, 1962, pp. 78-91.
[5] Brownell, W. E., Structural Clay Products, Springer-Verlag, New York, 1976, 231 p.
[6] Bucke, D. P., & Mankin, C. J., "Clay-Mineral Diagenesis Within Interlaminated Shales and Sandstones," /. Sedimentary Petrology, Vol. 41, No. 4, December 1971, pp. 971-981.
[7] Carslaw, H. S., & Jaeger, J. C., Conduction of Heat in Solids, Second ed., Oxford University Press, 1959, 510 p.
[8] 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.
[9] Chang, F. F., & Civan, F., "Practical Model for Chemically Induced Formation Damage," /. of Petroleum Science and Engineering, Vol. 17, No. 1/2, February 1997, pp. 123-137.
[10] Chenevert, M. E., "Shale Alteration by Water Adsorption," JPT, September 1970, pp. 1141-1148.
[11] Chilingarian, G. V., & Vorabutr, P., Drilling and Drilling Fluids, Developments in Petroleum Science, 11, Elsevier Scientific Publishing Co., New York, 1981.
[12] Civan, R, "Predictability of Formation Damage: An Assessment Study and Generalized Models," Final Report, U.S. DOE Contract No. DE-AC22- 90BC14658, April 1994.
[13] Civan, F., "Modeling and Simulation of Formation Damage by Organic Deposition," Proceedings of the First International Symposium on Colloid Chemistry in Oil Production: Asphaltenes and Wax Deposition, ISCOP'95, Rio de Janeiro, Brazil, November 26-29, 1995, pp. 102-107.
[14] Civan, F., "A Multi-Purpose Formation Damage Model," SPE 31101, Proceedings of the SPE Formation Damage Symposium, Lafayette, LA, February 14-15, 1996, pp. 311-326.
[15] Civan, F, "Interactions of the Horizontal Wellbore Hydraulics and Formation Damage," SPE 35213, Proceedings of the SPE Permian Basin Oil & Gas Recovery Conf., Midland, TX, March 27-29, 1996, pp. 561-569.
[16] Civan, F., "Model for Interpretation and Correlation of Contact Angle Measurements," Jour. Colloid and Interface Science, Vol. 192, 1997, pp. 500-502.
[17] Civan, F., "Interpretation and Correlations of Clay Swelling Measurements," Paper SPE 52134, Proceedings of the 1999 SPE Mid-Continent Operations Symposium, 28-31 March 1999, Oklahoma City, OK.
[18] Civan, F., & Knapp, R. M., "Effect of Clay Swelling and Fines Migration on Formation Permeability," SPE Paper No. 16235, Proceedings of the SPE Production Operations Symposium, OKC, 1987, pp. 475-483.
[19] Civan, F., Knapp, R. M., & Ohen, H. A., "Alteration of Permeability by Fine Particle Processes," J. Petroleum Science and Engineering, Vol. 3, Nos. 1/2, October 1989, pp. 65-79.
[20] Collins, E. R., Flow of Fluids Through Porous Materials, Penn Well Publishing Co., Tulsa, Oklahoma, 1961, 270 p.
[21] Crank, J., The Mathematics of Diffusion, Oxford University Press, London, 1956, 347 p.
[22] Degens, E. T., Geochemistry of Sediments (A Brief Survey), Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1965, 342 p.
[23] Ezzat, A. M., "Completion Fluids Design Criteria and Current Technology Weaknesses, SPE 19434 paper, the SPE Formation Damage Control Symposium held in Lafayette, Louisiana, February 22-23, 1990, pp. 255-266.
[24] Grim, R. E., "Modern Concepts of Clay Minerals," Jour. Geology, Vol. 50, No. 3, April-May 1942, pp. 225-275.
[25] Grim, R. E., Clay Mineralogy, McGraw-Hill, New York, New York, 1953, 384 p.
[26] Hart, R. T., Fekete, T., & Flock, D. L., "The Plugging Effect of Bacteria in Sandstone Systems," Canadian Mining and Metallurgical Bulletin, Vol. 53, 1960, pp. 495-501.
[27] Hayatdavoudi, A., "Changing Chemophysical Properties of Formation and Drilling Fluid Enhances Penetration Rate and Bit Life," Paper No. SPE 50729, Proceedings of the SPE International Symposium on Oil Field Chemistry held in Houston, Texas, 16-19 February 1999, pp. 273-285.
[28] Hayatdavoudi, A., private communication, 1999.
[29] Hughes, R. V., "The Application of Modern Clay Concepts to Oil Field Development," pp. 151-167, in Drilling and Production Practice 1950, American Petroleum Institute, New York, NY, 1951, 344 p.
[30] Khilar, K. C., Fogler, H. S., "Water Sensitivity of Sandstones," SPEJ, February 1983, pp. 55-64.
[31] Kia, S. F., Fogler, H. S., & Reed, M. G., "Effect of Salt Composition on Clay Release in Berea Sandstones," SPE 16254, February 1987.
[32] Ladd, C. C., "Mechanisms of Swelling by Compacted Clay," in Highway Research Board Bulletin 245, High Research Board, National Research Council, Publication 731, Washington, D.C., 1960, pp. 10-26
[33] Liu, X., Civan, F, & Evans, R. D., "Correlation of the Non-Darcy Flow Coefficient, J. of Canadian Petroleum Technology, Vol. 34, No. 10, 1995, pp. 50-54.
[34] Lynn, J. D., & Nasr-El-Din, H. A., "Evaluation of Formation Damage due to Frac Stimulation of Saudi Arabian Clastic Reservoir," J. of Petroleum Science and Engineering, Vol. 21, Nos. 3-4, 1998, pp. 179-201.
[35] Mancini, E. A., "Characterization of Sandstone Heterogeneity in Carboniferous Reservoirs for Increased Recovery of Oil and Gas from Foreland Basins," Contract No. FG07-90BC14448, in EOR-DOE/BC- 90/4 Progress Review, No. 64, pp. 79-83, U.S. Department of Energy, Bartlesville, Oklahoma, May 1991, 129 p.
[36] Mohan, K. K., & Fogler, H. S., "Colloidally Induced Smecticic Fines Migration: Existance of Microquakes," AIChE J., Vol. 43, No. 3, March 1997, pp. 565-576.
[37] Mondshine, T. C., "A New Potassium Based Mud System," Paper No. SPE 4516, 48th Annual Fall Meeting of SPE of AIME, October 1973.
[38] Mondshine, T. C., "New Technique Determines Oil Mud Salinity Needs in Shale Drilling," Oil and Gas J., July 14, 1969.
[39] Mungan, N., "Discussion of An Overview of Formation Damage," JPT, Vol. 41, No. 11, November 1989, p. 1224.
[40] Nayak, N. V, & Christensen, R. W., "Swelling Characteristics of Compacted Expansive Soils," Clay and Clay Mineral, Vol. 19, No. 4, December 1970, pp. 251-261.
[41] 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, 1977, pp. 184-191.
[42] Ngwenya, B. T., Elphick, S. C, & Shimmield, G. B., "Reservoir Sensitivity to Water Flooding: An Experimental Study of Seawater Injection in a North Sea Reservoir Analog," AAPG Bulletin, Vol. 79, No. 2, February 1995, pp. 285-304.
[43] Norrish, K., "The Swelling of Montmorillonite," Discussions Faraday Soc., Vol. 18, 1954, p. 120.
[44] Ohen, H. A., & Civan, E, "Simulation of Formation Damage in Petroleum Reservoirs," SPE 19420 paper, Proceedings of the 1990 SPE Symposium on Formation Damage Control, Lafayette, Louisiana, February 22-23, 1990, pp. 185-200.
[45] Ohen, H. A., & Civan, F., "Simulation of Formation Damage in Petroleum Reservoirs," SPE Advanced Technology Series, Vol. 1, No. 1, pp. 27-35, April 1993.
[46] Osisanya, S. O., & Chenevert, M. E., "Physico-Chemical Modelling of Wellbore Stability in Shale Formations," J. of Canadian Petroleum Technology, Vol. 35, No. 2, February 1996, pp. 53-63.
[47] Pittman, E. D., & Thomas, J. B., "Some Applications of Scanning Electron Microscopy to the Study of Reservoir Rock," SPE 7550 paper, November 1979, pp. 1375-1380.
[48] Reed, M. G., "Formation Permeability Damage by Mica Alteration and Carbonate Dissolution," JPT, September 1977, pp. 1056-1060.
[49] Rogers, 1963.
[50] Sahimi, M., Flow and Transport in Porous Media and Fractured Rock, VCR, Weinheim, 1995, 482 p.
[51] Schechter, R. S., Oil Well Stimulation, Prentice Hall, Englewood Cliffs, New Jersey, 1992, 602 p.
[52] Seed, H. B., Mitchell, J. K., & Chan, C. K., "Studies of Swell and Swell Pressure Characteristics of Compacted Clays, Bull. Highway Res. Board, No. 313, 1962, pp. 12-39.
[53] Sharma, M. M., & Yortsos, Y. C., "Fines Migration in Porous Media," AIChE J., Vol. 33, No. 10, 1987, pp. 1654-1662.
[54] Simpson, J. P., "Drilling Fluid Filtration Under Simulated Downhole Conditions," SPE Paper 4779, 1974, 14 p.
[55] Weaver, C. E., & Pollard, L. D., The Chemistry of Clay Minerals, Elsevier, New York, 1973, 213 p.
[56] Welton, J. E., "SEM Petrology Atlas," American Association of Petroleum Geologists, Tulsa, Oklahoma, 1984, 237 p.
[57] Wild, S., Kinuthia, J. M., Robinson, R. B., & Humphreys, I., "Effect of Ground Granulated Blast Furnace Slag (GGBS) on the Strength and Swelling Properties of Lime-Stabilized Kaolinite in the Presence of Sulphates," Clay Minerals, Vol. 31, 1996, pp. 423-433.
[58] Wojtanowicz, A. K., Krilov, Z., & Langlinais, J. P., "Experimental Determination of Formation Damage Pore Blocking Mechanisms," Trans, of the ASME, Journal of Energy Resources Technology, Vol. 110, 1988, pp. 34-42.
[59] Wojtanowicz, A. K., Krilov, Z., & Langlinais, J. P., "Study on the Effect of Pore Blocking Mechanisms on Formation Damage," Paper SPE 16233 presented at Society of Petroleum Engineers Symposium, Oklahoma City, Oklahoma, March 8-10, 1987, pp. 449-463.
[60] Zhou, Z., "Construction and Application of Clay-Swelling Diagrams by Use of XRD Methods," JPT, April 1995, p. 306.
[61] Zhou, Z., Gunter, W. D., Kadatz, B., & Cameron, S., "Effect of Clay Swelling on Reservoir Quality," Paper No. 94-54, Journal of Canadian Petroleum Technology, Vol. 35, 1996, pp. 18-23.
[62] Zhou, Z., Cameron, S., Kadatz, B., & Gunter, W. D., "Clay Swelling Diagrams: Their Applications in Formation Damage Control," SPE Journal, Vol. 2, 1997, pp. 99-106.
