Plugging-Nonplugging Pathways Model for Asphaltene Deposition in Single-Phase
Ali and Islam (1997, 1998) considered only asphaltene deposition and resorted to a simplified, single phase formation damage modeling approach according to Gruesbeck and Collins (1982). Here, their model is presented in a manner consistent with the rest of the presentation of this article. Also, a few missing equations are supplied. Note that this model applies for undersaturated oils. The rate of deposition in the plugging paths is given by:
The deposition in the nonplugging paths is expressed by:
The fluid flux in the plugging pathways is given by:
Note that Ali and Islam (1997, 1998) used the original Gruesbeck and Collins (1982) equation, which misses the fp and fnp terms in Eq. 14-48 instead of the corrected Eq. 14-48 given independently by Civan (1992) and Schechter (1992). The flow in the nonplugging pathways is given by:
Following Gruesbeck and Collins (1982), Ali and Islam (1997) assumed fp and fnp as some characteristic values of the porous medium and determined them to match the model predictions to experimental data. The permeability impairments in the plugging and nonplugging pathways were represented by the Gruesbeck and Collins (1982) empirical expressions, given, respectively, by:
where Kpo and Knpo denote the permeabilities of the plugging and nonplugging pathways before damage, and aand β are some adjustable
constants. Ali and Islam (1997) assumed the same concentrations in the plugging and nonplugging pathways. Thus, the mass balance of the suspended particles of asphaltene in the flowing fluid can be expressed as (Civan, 1995, 1996):
In laboratory core tests, the mass rate of phase L added per unit volume of phase L is zero:
The mass rate of asphaltene particles added to phase L is given by:
where Ԑp and Ԑeap denote the retention by filtration and adsorption, respectively. The formulation by Ali and Islam (1997) implies that they expressed the dispersion coefficient as a linear function of the interstitial velocity of the fluid:
where A, is an empirically determined coefficient and VL is the interstitial velocity, given by:
Assuming a constant rate injection of oil into a core plug and constant oil density and applying Eqs. 14-54 through 57, Eq. 14-53 can be written as:
It can be shown that Eq. 14-58 can be reformulated in the form given by Ali and Islam (1997). However, the last term in their equation appears to probably have a typographical error, because o in their equation should be replaced by 3a/3r The same error has been repeated by Ali and Islam (1998). The initial and boundary conditions for Eq. 14-58 are given by:
Ali and Islam (1998) obtained the results presented in Figures 14-48 through 14-50.
References
Acevedo, S., Ranaudo, M. A., Escobar, G., Gutierrez, L., & Ortega, P., "Adsorption of Asphaltenes and Resins on Organic and Inorganic Substrates and Their Correlation with Precipitation Problems in Production Well Tubing," Fuel, Vol. 74, No. 4, 1995, pp. 595-598.
Ali, M. A., & Islam, M. R., "The Effect of Asphaltene Precipitation on Carbonate-Rock Permeability: An Experimental and Numerical Approach," SPE Paper No. 38856, Proceedings of the 1997 SPE Annual Conference and Exhibition, held in San Antonio, Texas, October 1997, pp. 139-146.
All, M. A., & Islam, M. R., "The Effect of Asphaltene Precipitation on Carbonate-Rock Permeability: An Experimental and Numerical Approach," SPE Production and Facilities Journal, August 1998, pp. 178-183.
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, June 12-16, 1988, Calgary, Alberta, 16 p.
Andersen, S. I., Keul, A., & Stenby, E., "Variation in Composition of Subfractions of Petroleum Asphaltenes," Petroleum Science and Technology, Vol. 15, No. 7 & 8, 1997, pp. 611-645.
Chang, F. F., & Civan, F., "Practical Model for Chemically Induced Formation Damage," J. of Petroleum Science and Engineering, Vol. 17, 1997, pp. 123-137.
Chang, C.-L., & Fogler, H. S., "Peptization and Coagulation of Asphaltenes in Apolar Media Using Oil-Soluble Polymers," Fuel Science and Technology International, Vol. 14, No. 1 & 2, 1996, pp. 75-100.
Chang, C.-L., & Fogler, H. S., Langmuir, Vol. 10, 1994, pp. 1749-1758.
Chung, T.-H., "Thermodynamic Modeling for Organic Solid Precipitation," SPE 24851, Proceedings of the 67th Annual technical Conference and Exhibition of the SPE held in Washington, D.C., October 4-7, 1992, pp. 869-878,
Civan, F., "A Generalized Model for Formation Damage by Rock-Fluid Interactions and Particulate processes," SPE 21183 paper, Proceedings of the SPE 1990 Latin American Petroleum Engineering Conference, October 14-19, 1990, Rio de Janeiro, Brazil, 11 p.
Civan, F, "Evaluation and Comparison of the Formation Damage Models," SPE 23787 paper, Proceedings of the SPE International Symposium on Formation Damage Control, February 26-27, 1992, Lafayette, Louisiana, pp. 219-236.
Civan, F, Predictability of Formation Damage: An Assessment Study and Generalized Models, Final Report, U.S. DOE Contract No. DE-AC22- 90BC14658, April 1994.
Civan, F., "A Multi-Phase Mud Filtrate Invasion and Well Bore Filter Cake Formation Model," SPE 28709 paper, Proceedings of the SPE International Petroleum Conference & Exhibition of Mexico, October 10-13, 1994, Veracruz, Mexico, pp. 399-412.
Civan, F., "Modeling and Simulation of Formation Damage by Organic Deposition," Proceedings of the First International Symposium on Colloid Chemistry in Oil Production: Asphaltene and Wax Deposition, ISCOP '95, Rio de Janeiro, Brazil, November 26-29, 1995, pp. 102- 107.
Civan, F. " A Multi-Purpose Formation Damage Model" SPE 31101 paper, the SPE Formation Damage Control Symposium, Lafayette, Louisiana, February 14-15, 1996, pp. 311-326.
Civan, F., "Interactions of the Horizontal Wellbore Hydraulics and Formation Damage," SPE 35213 paper, Proceedings of the SPE Permain Basin Oil & Gas Recovery Conf., March 27-29, 1996, Midland, Texas, pp. 561-569.
Civan, F., Knapp, R. M., & Ohen, H. A., "Alteration of Permeability by Fine Particle Processes," Journal of Petroleum Science and Engineering, Vol. 3, Nos. 1/2, October 1989, pp. 65-79.
DeBoer, R. B., Leerlooyer, K., Eigner, M. R. P., & van Bergen, A. R. D., "Screening of Crude Oils for Asphalt Precipitation: Theory, Practice, and the Selection of Inhibitors," SPEPF, February 1995, pp. 55-61.
Dubey, S. T, & Waxman, M. H., "Asphaltene Adsorption and Desorption From Mineral Surfaces," SPE Reservoir Engineering, August 1991, pp. 389-395.
Gruesbeck, C. and R. E. Collins, "Entrainment and Deposition of Fine Particles in Porous Media," SPEJ, pp. 847-856, December 1982.
Gruesbeck, C. and Collins, R. E., "Particle Transport Through Perforations," SPEJ, December 1982, pp. 857-865.
Gupta, S. P., & Greenkorn, R. A., "Dispersion During Flow in Porous Media with Bilinear Adsorption," Water Resources Research, Vol. 9, 1973, pp. 1357-1368.
Haskett, C. E., & Tartera, M., "A Practical Solution to the Problem of Asphaltene Deposits-Hassi Messaoud Field, Algeria," JPT, April 1965, pp. 387-391.
Houchin, L. R., & Hudson, L. M., "The Prediction, Evaluation and Treatment of Organic Damage Caused by Organic Deposition," SPE 14818 paper, Proceedings of the Seventh SPE Symposium on Formation Damage Control, February 26-27, 1986, Lafayette, Louisiana, pp. 83-90.
Khalil, C. N., Rocha, N. O., & Silva, E. B., "Detection of Formation Damage Associated to Paraffin in Reservoirs of the Reconcavo Baiano, Brazil," Proceedings of the 1997 SPE International Symposium on Oil Field Chemistry held in Houston, Texas, February 18-21, pp. 277-281.
Leontaritis, K. J., "Application of a Thermodynamic-Colloidal Model of Asphaltene Flocculation," presented at the Symposium of Solids Deposition, Area 16C of Fuels and Petrochemical Division, AIChE Spring National Meeting and Petroleum Exposition, March 28-April 1, 1993, Houston, Texas.
Leontaritis, K. J., "The Asphaltene and Wax Deposition Envelopes," Fuel Science and Technology International, Vol. 14, No. 1 & 2, Marcel Dekker, Inc., New York, 1996, pp. 13-39.
Leontaritis, K. J., "PARA-Based (Paraffin-Aromatic-Resin-Asphaltene) Reservoir Oil Characterizations," SPE Paper 37252, Proceedings of the 1997 SPE International Symposium on Oilfield Chemistry held in Houston, Texas, February 18-21, 1997, pp. 421-440.
Leontaritis, K. J., "Asphaltene Near-Wellbore Formation Damage Modeling," SPE Paper 39446, Proceedings of the 1998 SPE Formation Damage Control Conference held in Lafayette, Louisiana, February 18-19, 1998, pp. 277-288.
Leontaritis, K. J., & Mansoori, G. A., "Asphaltene Flocculation During Oil Production and Processing: A Thermodynamic-Colloidal Model," SPE Paper 16258, Proceedings of the SPE International Symposium on Oil Field Chemistry, San Antonio, Texas, January 1987, pp. 149-158.
Leontaritis, K. J., Amaefule, J. O., and Charles, R. E., "A Systematic Approach for the Prevention and Treatment of Formation Damage Caused by Asphaltene Deposition," SPE Paper 23810, Proceedings of the SPE International Symposium on Formation Damage Control, Lafayette, LA, February 26-27, 1992, pp. 383-395.
Lichaa, P. M., "Asphaltene Deposition Problem in Venezuela Crudes, Usage of Asphaltenes in Emulsion Stability," Oil Sands, June 1997, pp. 609-624.
Lira-Galeana, C., & Firoozabadi, A., "Thermodynamics of Wax Precipitation in Petroleum Mixtures," AIChE Journal, Vol. 42, No. 1, January 1996, pp. 239-248.
Manoranjan, V. S., & Stauffer, T. B., "Exact Solution for Contaminant Transport with Kinetic Langmuir Sorption," Water Resources Research, Vol. 32, No. 3, 1996, pp. 749-752.
Mansoori, G. A., "Modeling of Asphaltene and Other Heavy Organic Depositions," Journal of Petroleum Science and Engineering, Vol. 17, 1997, pp. 101-111.
Mansoori, G. A., "Modeling and Prevention of Asphaltene and Other Heavy Organic Deposition in Oil Wells," Paper SPE 27070, proceedings of the International Symposium on Formation Damage Control held in Lafayette, Louisiana, 9-10 February 1994, pp. 9-18.
Mansoori, G. A., "Modeling and Prevention of Asphaltene and Other Heavy Organic Deposition in Oil Wells," SPE 27070 paper, presented at the Third Latin American/Caribbean Petroleum Engineering Conference, April 27-29, 1994, Beunos Aires, Argentina.
Marquardt, D. W, "An Algorithm for Least-squares Estimation of Nonlinear Parameters," J. Soc. Indust. Appl. Math., Vol. 11, 1963, p. 431.
Metzner, A. B., & Reed, J. C., "Flow of Non-Newtonian Fluids—Correlation of the Laminar, Transition, and Turbulent Flow Regions," AIChE J., Vol. 1, No. 4, 1955, pp. 434-440.
Minssieux, L., "Core Damage From Crude Asphaltene Deposition" SPE 37250 paper, 1997 SPE International Symposium on Oilfield Chemistry, February 18-21, 1997, Houston, Texas.
Nghiem, L. X., & Coombe, D. A., "Modeling Asphaltene Precipitation During Primary Depletion," SPE Journal, Vol. 2, June 1997, pp. 170-176.
Philp, R. P., Bishop, A. N., Del Rio, J.-C, and Allen, J., "Characterization of High Molecular Weight Hydrocarbons (>C40) in Oils and Reservoir Rocks," in The Geochemistry of Reservoirs, Cubitt, J. M. and England, W. A. (Eds.), Geological Society Special Publication No. 86, 1995, pp. 71-85.
Ring, J. N., Wattenbarger, R. A., Keating, J. F., and Peddibhotla, S., "Simulation of Paraffin Deposition in Reservoirs," SPE Production & Facilities, February 1994, pp. 36-42.
Schechter, R. S., Oil Well Stimulation, Prentice Hall, Englewood Cliffs, New Jersey, 1992, 602 p.
Sircar, S., Novosad, J., & Myers, A. L., "Adsorption from Liquid Mixtures on Solids, Thermodynamics of Excess Properties and Their Temperature Coefficients," I&EC Fund., Vol. 11, 1972, p. 249.
Speight, J. G., "Asphaltenes in Crude Oil and Bitumen: Structure and Dispersion," Chapter 8, pp. 377-401, in Suspensions: Fundamentals and Applications in the Petroleum Industry, Schramm, L. L. (Ed.), Advances in Chemistry Series 251, American Chemical Society, 1996, Washington, DC, 800 p.
Speight, J. G., "The Chemical and Physical Structure of Petroleum: Effects on Recovery Operations," J. of Petroleum Science and Engineering, Vol. 22, Nos. 1-3, 1999, pp. 3-15.
Speight, J. G., "Solvent Effects in the Molecular Weights of Petroleum Asphaltenes," Preprints ACS, Div. Pet. Chem., pp. 825-832.
Speight, J. G., & Long, R. B., "The Concept of Asphaltenes Revisited," Fuel Science and Technology International, Vol. 14, No. 1 & 2, 1996, pp. 1-12.
Srivastava, R. K., & Huang, S. S., "Asphaltene Deposition During CO2 Flooding: A Laboratory Assessment," Paper SPE 37468, Proceedings of the 1997 SPE Productions Operations Symposium, held in Oklahoma City, Oklahoma, March 9-11, 1997, pp. 617-635.
Sutton, G. D., & Roberts, L. D., "Paraffin Precipitation During Fracture Stimulation," JPT, September 1974, pp. 997-1004.
Wang, S., Civan, F., & Strycker, A. R., "Simulation of Paraffin and Asphaltene Deposition in Porous Media," SPE 50746 paper, SPE International Symposium on Oilfield Chemistry, February 16-16, 1999, Houston, Texas, pp. 449-458.
Weingarten, J. S., & Euchner, J. A., "Methods for Predicting Wax Precipitation and Deposition," SPERE, February 1988, pp. 121-132.
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.
Wojtanowicz, A. K., Krilov, Z. and Langlinais, J. P.: "Study on the Effect of Pore Blocking Mechanisms on Formation Damage," Paper SPE 16233, presented at Society of Petroleum Engineers Symposium, March 8-10, 1987, Oklahoma City, Oklahoma, pp. 449-463.
Yarranton, H. W., & Masliyah, J. H., "Molar Mass Distribution and Solubility Modeling of Asphaltenes," AIChE Journal, Vol. 42, No. 12, December 1996, pp. 3533-3543.
Zhou, X., Thomas, F. B., & Moore, R. G., "Modeling of Solid Precipitation from Reservoir Fluid," Journal of Canadian Petroleum Technology, Vol. 35, No. 10, December 1996, pp. 37-45.
