Description of Fluid and Species Transport
The preceding treatment of the porous media impairment phenomena implies that the suspended particle and dissolved species concentrations may be different in the plugging and nonplugging pathways. Then, separate sets of balance equations are required for the plugging and nonplugging pathways. Consequently, the numerical solution would require highly intensive computational effort. However, this problem can be conveniently circumvented by assuming that there is hydraulic interaction between these pathways (i.e., they are not isolated from each other).
1. The mass balances are considered for the following four pseudocomponents
a. Gas
b. Oil
c. Suspended paraffins and asphaltenes
d. Dissolved paraffins and asphaltenes
2. Total thermal equilibrium energy balance is considered
3. Non-Newtonian fluid description using the Rabinowitsch-Mooney equation is resorted
4. The Forhheimer equation for the non-Darcy flow description is used
5. The average flow is defined as a volume fraction weighted linear sum of the flow through the plugging and nonplugging paths according to Gruesbeck and Collins (1982)
6. The average permeability is defined as a volume weighted linear sum of the permeabilities of the plugging and nonplugging paths according to Gruesbeck and Collins (1982)
a. In the plugging paths, a snowball deposition effect is represented by an exponential decay function
b. In the nonplugging paths, a gradual pore size reduction, represented by the power law function, is considered
7. The precipitation of the asphaltene and paraffin is predicted, applying Chung's (1992) thermodynamic model for non-ideal solutions to determine the cloud point and the quantity of the precipitates to be formed.
The total mass balance of the gas component is given by:
The first, second, and third terms respectively represent the accumulation, transport, and well production. Assuming that the oil component exists only in the liquid phase and does not vaporize into the gas phase, the oil component mass balance is given by:
for which Ring et al. (1994) assumed woL = 1.0. Considering that organic precipitates only exist in the liquid phase, because it is the wetting phase
for these particles, the suspended paraffin and asphaltene particle mass balances are expressed by:
If the particle density, pp, is assumed constant, and the suspended particle content is expressed by the volume fraction of organic substance (paraffin or asphaltene), σpL, according to Eq. 14-95, then Eq. 14-94 can be simplified as:
Note that both Ring et al. (1994) and Civan (1996) neglected the term on the right, representing the dispersion of particles. The mass balances of the paraffin and asphaltene dissolved in oil is given by:
S is the saturation, p is the density, t is the time, x is distance, u is the volume flux, σp L is the volume fraction of the organic precipitates in the liquid phase, wp,L denotes the mass fraction, xiL is the mole fraction of organic dissolved in the oil, Mi is the molecular weight and DiL is the dispersion coefficient. 3ԑ,/3t represents the volume rate of retention of organic deposits in porous media determined according to Eqs. 14-68, 69, and 76.
Assuming that the various phases are at thermal equilibrium at a temperature of Tv = TL = Ts = T , the total porous media energy balance is given by:
where U and H are the internal energy and enthalpy, respectively, q is the energy loss, p is pressure, k denotes the thermal conductivity, and T is temperature. Ring et al. (1994) simplified Eq. 14-98 as:
The first, second, and third terms represent the accumulation, convection, and conduction heat transfer. The last terms represent the heat carried away by production at wells, heat losses into formation surrounding the reservoir and the external heat losses. The deposition of organic precipitates in porous media reduces the flow passages causing the fluids to accelerate. Therefore, Darcy's law is modified as following, considering the inertial effects, according to the Forchheimer equation (Civan, 1996):
where K is the permeability, PJ is the fluid pressure, and the non-Darcy number is given by:
where β is the inertial flow coefficient, and py and |iiy denote the density and viscosity of a fluid phase J. Note that the formulations presented here are applicable for jnultidimensional cases encountered in the field if 3/3x is replaced by V • and a vector-tensor notation is applied.
Phase Transition
The source terms appearing on the right of Eqs. 14-92 through 99 are considered a sum of the internal (rock-fluid and fluid-fluid interactions) and external (wells) sources. When the oil is supersaturated, the internal contribution to the source terms in Eq. 14-94 is determined as the excess quantity of organic content of oil above the organic solubility at saturation conditions determined by Chung's (1992) thermodynamic model:
Civan (1995) carried out case studies similar to Ring et al. (1994) using the Sutton and Roberts data (1974). Figure 14-51 shows a comparison of the predicted and measured permeability impairments by paraffin deposition for below and above bubble point pressure cases. Note that, above the bubble point pressure, only the liquid phase exists and there is more severe formation damage. Whereas, below the bubble point pressure, both the liquid and vapor phases exist and there is less severe formation damage.
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," , 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.
