Reservoir Formation Damage Episode 2 Part 1 ppsx

232 Reservoir Formation Damage in which =G' U np= U (10-189) (10-190) because all flow goes through the plugging pathways. The fact that the cumulative amounts of deposits reach certain limiting values as shown in Figure 10-25 is indicative of attainment of such equilibrium conditions. Note, however, that the amounts shown in Figure 10-25 are the cumulative amounts including the amount of deposits in the plugging pathways. Therefore at equilibrium £=£„+£ (10-191) //—Constant-Pressure-Difference Tests Constant pressure tests are more representative of the producing well conditions. Gruesbeck and Collins (1982) flowed suspensions of glass particles through sand packs at constant pressure differences by applying relatively high pressure difference to a column of fine sand pack and relatively low pressure difference to a column of coarse sand pack. The results are reported in Figure 10-27. In the fine sand packs, they observed more deposition near the injection side, and the mean permeability of the sand JT 1.0 0.8 0.6 0.4 i 0.2 g 0.0 • Cj 9.5x10-* oc g C| J£ ^ IS 100 200 PORE VOLUMES 300 4 8 12 16 PACK LENGTH. CM Figure 10-27. Constant pressure deposition and entrainment of 5-10 mm diameter glass beads in a pack of (a) 177-210 mm diameter sand grains subjected to 900 kPa/m pressure gradient and (b) 250-297 mm diameter sand grains subjected to 450 kPa/m pressure gradient (after Gruesbeck and Collins, ©1982 SPE; reprinted by permission of the Society of Petroleum Engineers). Single-Phase Formation Damage by Fines Migration and Clay Swelling 233 pack decreased to zero. Because, in the fine sand pack, almost all the pathways are of the plugging type. Whereas, in coarse sand packs, the deposition tended to occur almost uniformly along the sand pack and the mean permeability of the sand pack decreased to an equilibrium value. Because, in the coarse sand pack, most of the pathways are of the nonplugging types. Gruesbeck and Collins (1982) state that their computer simulation produced results similar to measurement reported in Figure 10-27. Civan et al. (1989), and Ohen and Civan (1990, 1993) also simulated these experiments successfully. Consolidated Core Tests. Gruesbeck and Collins tested Berea and field cores. First, the Berea cores were tested using 1. 2% KCl brine in a dry core (single phase system) 2. 2% KCl brine and white oil at a 50/50 ratio in a dry core (two phase system) 3. white oil in a dry core (single phase system) 4. white oil in a core at connate 2% KCl brine saturation (two phase) Cores were tested at various constant injection rates over a period of time determined by a prescribed, cumulative pore volume amount of the injection fluid. During each test, the pressure difference was measured and the permeability was calculated using Darcy's law. Typical results obtained using a 2% KCl brine in a Berea core are presented in Figure 10-28. As can be seen, the permeability remained unchanged at the low flow rate of 0.0367cm 3 /-?, while it decreased further at each of the increased high flow rates of 0.0682, 0.1002, 0.1310, and 0.1702cm 3 /s. The final permeability values attained after each of the high flow rates are used to calculate the permeability reductions from the initial state, which are then plotted against these high flow rates as shown in Figure 10-29. The results shown in Figure 10-29 are indicative of surface particle removal, similar to Figure 10-24. They stated that the removal of indigeneous particles in the cores from the pore surface and subsequent redeposition at the pore throats caused the permeability reduction. Second, core samples were taken from an oil field, indicating an abnormal decline of productivity in some wells. These cores were tested using 1. white oil in a dry core 2. white oil in a core at connate 2% KCl brine saturation. The experimental results presented in Figure 10-30 indicate a trend similar to Figure 10-29. 234 Reservoir Formation Damage 80 ~ M E a. E 40 0.29 100 200 300 400 500 600 700 PORE VOLUMES 800 900 1000 1100 Figure 10-28. Effect of fluid velocity on the entrainment and redeposition of fines in a 3.81 cm diameter and 3.0 cm long Berea core during a 2% KCI solution injection (after Gruesbeck and Collins, ©1982 SPE; reprinted by permission of the Society of Petroleum Engineers). 30 25 20 10 2% KCI BRINE 1SOPAR M - 2.6 mPa s ISOPARM AT CONNATE 2% Kd BRINE SATURATION .02 .04 .06 .OB .10 .12 .14 INTERSTITIAL VELOCITY. u/</> j; CM/S .16 .18 Figure 10-29. Permeability reduction as a function of the interstitial velocity determined using the Figure 10-28 data (after Gruesbeck and Collins, ©1982 SPE; reprinted by permission of the Society of Petroleum Engineers). The results presented in Figures 10-29 and 10-30 indicate that the indigeneous particles of Berea and field cores are water wet. This is apparent by the effect of the two phases on the critical velocity values required to initiate particle mobilization. The implication of this is that variation of the fluid system from oil to oil/water can reduce the critical Single-Phase Formation Damage by Fines Migration and Clay Swelling 235 j -0.25 1,5 ISOPAR M 2.6 mPa s •4- ISOPAR M AT CONNATE 2% KCi BRINE SATURATION 0.10 0.20 0.30 INTERSTITAL VELOCITY. u/<£j, CM/S 0.40 Figure 10-30. Permeability reduction as a function of the interstitial velocity determined using a 3.81 cm diameter and 3.0 cm long field core sample (after Gruesbeck and Collins, ©1982 SPE; reprinted by permission of the Society of Petroleum Engineers). velocity, induce surface particle mobilization, and increase permeability damage in the near well bore formation. References Cernansky, A., & Siroky, R. "Deep-bed Filtration on Filament Layers on Particle Polydispersed in Liquids," Int. Chem. Eng., Vol. 25, No. 2, 1985, pp. 364-375. Cernansky, A., & Siroky, R., "Hlbkova Filtracia Polydisperznych Castic z Kvapalin na Vrstvach z Vlakien," Chemicky Prumysl, Vol. 32 (57), No. 8, 1982, pp. 397-405. Civan, F. "A Generalized Model for Formation Damage by Rock-Fluid Interactions and Particulate Processes," SPE Paper 21183, 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., & Knapp, R. M. "Effect of Clay Swelling and Fines Migration on Formation Permeability," SPE Paper No. 16235, Proceedings of the 236 Reservoir Formation Damage SPE Production Operations Symposium, Oklahoma City, Oklahoma, 1987, pp. 475-483. Civan, F. "A Multi-Phase Mud Filtrate Invasion and Well Bore Filter Cake Formation Model," SPE Paper No. 28709, Proceedings of the SPE International Petroleum Conference & Exhibition of Mexico, October 10-13, 1994, Veracruz, Mexico, pp. 399-412. 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. 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. "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. Civan, F. "A Multi-Purpose Formation Damage Model," SPE 31101, Proceedings of the SPE Formation Damage Symposium, Lafayette, Louisiana, February 14-15, 1996, pp. 311-326. Civan, F. "Interactions of the Horizontal Wellbore Hydraulics and Formation Damage," SPE 35213, Proceedings of the SPE Permian Basin Oil & Gas Recovery Conf., Midland, Texas, March 27-29, 1996, pp. 561-569. Gruesbeck, C, & Collins, R. E. "Particle Transport Through Perforations," SPEJ, December 1982b, pp. 857-865. Gruesbeck, C., & Collins, R. E. "Entrainment and Deposition of Fine Particles in Porous Media," SPEJ, December 1982a, pp. 847-856. Khilar, K. C., & Fogler, H. S. "Colloidally Induced Fines Migration in Porous Media," in Amundson, N. R. & Luss, D. (Eds.), Reviews in Chemical Engineering, Freund Publishing House LTD., London, England, January-June 1987, Vol. 4, Nos. 1 and 2, pp. 41-108. Khilar, K. C., & Fogler, H. S. "Water Sensitivity of Sandstones," SPEJ, February 1983, pp. 55-64. 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. Metzner, A. B., & Reed, J. C. "Flow of Non-Newtonian Fluids—Corre- lation of the Laminar, Transition, and Turbulent Flow Regions," AIChE J., Vol. 1, No. 4, 1955, pp. 434-440. Nayak, N. V, & Christensen, R. W. "Swelling Characteristics of Com- pacted Expansive Soils," Clay and Clay Mineral, Vol. 19, No. 4, December 1970, pp. 251-261. Ohen, H. A., & Civan, F. "Predicting Fines Generation, Migration and Deposition Near Injection and Production Wells," Proceedings of the Single-Phase Formation Damage by Fines Migration and Clay Swelling 237 First Regional Meeting, American Filtration Society, Houston, Texas, October 30-November 1, 1989, pp. 161-164. Ohen, H. A., & Civan, F. "Simulation of Formation Damage in Petroleum Reservoirs," SPE Advanced Technology Series, Vol. 1, No. 1, April 1993, pp. 27-35. Ohen, H. A., & Civan, F. "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. Schechter, R. S., Oil Well Stimulation, Prentice Hall, Englewood Cliffs, New Jersey, 1992, 602 p. Seed, H. B., Woodward, Jr., R. J., & Lundgren, R. "Prediction of Swelling Potential for Compacted Clays," /. Soil Mech. Found. Div., Proc. Am. Soc. Civ. Eng., 88(SM3), June 1962, pp. 53-87. Wojtanowicz, A. K., Krilov, Z., & Langlinais, J. P. "Study on the Effect of Pore Blocking Mechanisms on Formation Damage," SPE 16233 paper, presented at Society of Petroleum Engineers Production Opera- tions Symposium, Oklahoma City, Oklahoma, March 8-10, 1987, pp. 449-463. Wojtanowicz, A. K., Krilov, Z., & Langlinais, J. P. "Experimental Deter- mination of Formation Damage Pore Blocking Mechanisms," Trans, of the ASME, Journal of Energy Resources Technology, Vol. 110, 1988, pp. 34-42. Chapter 11 Two-Phase Formation Damage by Fines Migration Summary Most reservoirs contain multi-phase fluid systems. Formation damage processes in such reservoirs are more complicated because of the effects of the relative wettabilities of fine particles and formation, interface transport, relative permeabilities, and capillary pressures. There are only a few models available for multi-phase systems. These models have been developed for and tested with two phase laboratory core flow data. This chapter discusses the additional processes on top of those involving single-phase formation damage that need to be considered for multi-phase formation damage by fines migration. A systematic analysis and formu- lation of the relevant processes involving fines migration and formation damage during two-phase fluid flow through sedimentary formations is presented, as well as applications to typical laboratory core damage tests. The formulation can be readily extended for the multi-phase and multi-dimensional systems and the actual fluid conditions existing in reservoir formations. Introduction Several investigators including Muecke (1979), Sarkar (1988), and Sarkar and Sharma (1990) have determined that fine particles behave differently in a multi-phase fluid environment and formation damage follows a different course than the single-phase systems. However, the reported studies on the two-phase formation damage are very limited. Sutton and Roberts (1974) and Sarkar and Sharma (1990) have experi- mentally observed that formation damage in two-phase is less severe than in single-phase. Liu and Civan (1993, 1995, 1996) have shown that two-phase 238 Two-Phase Formation Damage by Fines Migration 239 formation damage requires the consideration of other factors, such as the wettability affect and partitioning of particles between various phases. In this chapter, mutual interactions and affects between the two-phase flow systems, fine particles, and porous matrix are described mathe- matically to develop a predictive model for formation damage by fines migration in two-phase systems flowing through porous formations. The formulation is carried out by extending the Liu and Civan (1993, 1994, 1995, 1996) model for more realistic applications. The tests and case studies used by Liu and Civan (1995, 1996) are presented for demon- stration and verification of the model. Although the model presented here involves some simplifications pertaining to the laboratory core damage experiments, it can be readily modified and generalized for the actual conditions encountered in petroleum reservoirs. Formulation The equations describing the various aspects for formation damage by fines migration during two-phase fluid flow through porous formations are formulated here. However, the formulation can be extended readily to multi-phase fluid systems. It is safe to assume that the gas phase does not carry any solid particles (i.e., it is nonwetting for all particles). For convenience in modeling, the bulk porous media is considered in four phases as schematically depicted in Figure 11-1: (1) the solid matrix, (2) the wetting fluid, (3) the nonwetting fluid, and (4) the interface region. These phases are indicated by S, W, N, and /, respectively. The porous matrix is assumed nondeformable. Therefore, it is stationary and its volumetric flux is zero. The wetting and nonwetting phases flow at the volumetric fluxes denoted, respectively, by u w and U N . The interface region is located between the wetting and nonwetting phases and is assumed to move at a flux equal to the absolute value of the difference between the fluxes of the wetting and nonwetting phases (i.e., its flux is «/ = U W -U N \). The various particles involving the formation damage are classified as (1) the foreign particles introduced externally at the wellbore, (2) the indigeneous particles existing in the porous formation, and (3) the particles generated inside the pore space by various processes, such as the wettability alteration considered in this chapter. Another classification of particles is made with reference to the wettability as (1) the wetting particles, (2) the nonwetting particles, and (3) the intermediately wetting particles. These particles are identified, respectively, by wp, np, and ip. The latter classification is more significant from the modeling point of view. Because, as explained by Muecke (1979), the wettability affects the behavior of these particles in a multi-phase fluid system. By means of 240 Reservoir Formation Damage Solid matrix nS, Non-wetting surface \ Pore body wS, Wetting surface Pore throat Figure 11-1. Multi-phase system in porous media. experimental investigations, Muecke (1979) has observed that particles tend to remain in the phases that can wet them. Ku and Henry, Jr. (1987) have shown that intermediately wet particles accumulate at the interface of the wetting and nonwetting phases, because they are most stable there. Therefore, in the following formulation, an interface region contain- ing the intermediately wet particles is perceived to exist in between the wetting and nonwetting phases as schematically indicated in Figure 11-1. Further, it is reasonable to consider that the wettability of some particles may be altered by various processes, such as asphaltene, paraffin, and inorganic precipitation or by other mechanisms such as the turbulence created by rapid flow in the near-wellbore region. Consequently, these altered particles should tend to migrate into the phases that wet them as inferred by the experimental studies of Ku and Henry, Jr. (1979). In addition to the particles, the various phases may contain a number of dissolved species. The salt content of the aqueous phase is particularly important, because it can lead to conditions for colloidally induced release of clay particles when its salt concentration is below a critical salt concentration (Khilar and Fogler, 1983). For convenience in formulation, the locations for particles retention can be classified in three categories: (1) the wetting pore surface, (2) the nonwetting pore surface, and (3) the pore space behind the plugging pore Two-Phase Formation Damage by Fines Migration 241 throats. These regions are denoted by wS, nS, and tS, respectively, as indicated schematically in Figure 11-1. The areal fractions of the wetting and nonwetting sites can vary as a result of the various rock, fluid, and particle interactions during formation damage, such as by asphaltene, paraffin, and inorganic deposition. Therefore, a parameter f ks indicating the fraction of the pore surface, that is wetting for species k, is introduced in the formulation. Because the applications to describe and interpret the laboratory core damage data, conducted at mild temperature and pressure conditions are intended, the formulation is carried out for one-dimensional flow in homogeneous core plugs, isothermal conditions, and incompressible particles and fluids. This allows the use of a simplified formulation based on volumetric balances and a fractional flow concept. However, the derivation can be readily extended for compressible systems encountered at the prevailing elevated pressure conditions of the reservoir formations. Fluid and Species Transport Assuming incompressible species, the volumetric balance of species j transported via phase J through porous media is given by: (11-1) J = W, N, /, wS, nS, tS and j = w,«, wp, np, ip where e y indicates the volume fraction of phase J in porous media, o ;7 is the volume fraction of species j in phase /, u } is the volumetric flux of phase J through porous media and q jJL represents the volume rate of transfer of species j from phase J to phase L. D- } denotes the coefficient of dispersion of species j in phase /, and p y is the density of phase J, which varies by its composition even if the individual constituent species may be considered incompressible, jc and t denote the distance along the flow direction and time. The dispersion term for particles is usually neglected. The volumetric rate of particle lost per unit bulk media by various processes is given by: tjJL (11-2) in which q ju denotes the volume rate of transformation of species j type to species / type in phase J expressed per unit bulk volume. Summing [...]... respectively: a* a* \iw (11 -14 ) i a* ds a* ™* (11 -15 ) 24 4 Reservoir Formation Damage Note that the saturations add up to one: SW+SN =1 (11 -16 ) Therefore, adding Eqs 11 -14 and 11 -15 yields the following equation: NndwkrW +• K V-N + a* dPcNW vSw dSw dx dx (11 -17 ) dt where the total volumetric loss of particles from the two-phase system is given by: q = qw+qN (11 -18 ) Eqs 11 -14 and 17 can be solved simultaneously... -Ptv =\n N (11 -28 ) (11 -29 ) As a result of substituting Eqs 11 -27 and 11 -28 , Eq 11 -5 can be simplified as (Civan, 19 96): a dx • n\ 3~ t sme) = -^ dx dt (11 -30) Determination of Species Concentrations in Various Phases Once the phase saturations are determined, then the species concentrations can be determined by solving the following equation obtained by combining Eqs 11 -1 and 11 -3: (11 - 31) J = W, N,... below can be implemented: krN (11 -24 ) Under these conditions, Eqs 11 -20 and 22 , respectively, become: 24 6 Reservoir Formation Damage and MS w (11 -26 ) 1 + (M -1) SW Consequently, Eq 11 -19 can be simplified significantly by substituting Eqs 11 -25 and 11 -26 In addition, the non-Darcy effect can be neglected by substituting (11 -27 ) AU =1. 0 ; J = W,N The end-point relative permeabilities and fluid densities may... the first approach, Eq 11 -8 is substituted into Eq 11 -3 to obtain: a* ; J=W >N \*-J The capillary pressure is defined as the difference between the nonwetting and wetting phase pressures according to: PCNW ~ PN (11 - 12 ) Pw The phase / volume fraction is given by: (11 -13 ) where (() is porosity and S} is the saturation of phase J Thus, substituting Eqs 11 - 12 and 11 -13 into Eq 11 -11 yields the following... Civan (19 93, 19 95, 19 96) assumed v\e = 1 , fjs = 1 and $ * constant and used (iy - icrj J ~ \Uj - ucrjj Note &,.,.„ = 0, when I.< icrj or u, < ucrJ hjJjS J J (11 -50) Two-Phase Formation Damage by Fines Migration 25 1 Porosity and Permeability Variation The porosity is expressed by (Liu and Civan, 19 96): J S j *JSj (11 - 51) and the permeability is estimated by (Liu and Civan, 19 96) (11 - 52) Filter Cake Formation. .. Formation Damage Table 11 -1 Core Test Data for Fines Migrations* Data Core without ROS Core diameter (cm) Core length (cm) Initial porosity (fraction) Initial permeability (Darcy) Residual oil saturation End-point relative permeability Injection velocity (cm/s) Water viscosity (cp) Core with ROS 2. 54 8.30 0 . 21 0.0654 0.0 1. 0 4. 31 x 10 "4 1. 0 2. 54 8.30 0 . 21 0.0 825 0.367 0.038 4.31X10" 4 1. 0 * Information... and Ursin (19 92) were used to analyze formation damage due to particle invasion The two samples were labeled as Core #26 and Core #27 in the Eleri and Ursin (19 92) study Prior to flow tests, the core samples 25 4 Reservoir Formation Damage 1. 7- o I 1. 4H £ 1. 3H '0.3 0.35 0.4 0.45 0.5 0.55 0.6 Pore Volume of Injected Fluid « Experiment 0.65 0.7 Simulation Figure 11 -3 Pressure drop across an undamaged core... residual oil Sarkar (19 88) conducted a laboratory test using a Berea core of 8 .27 cm in length to investigate fines migration in two-phase flow The core porosity and permeability initially were 0 . 21 fraction and 0. 12 2 Darcy, respectively The core saturated with crude oil was displaced with 3% Two-Phase Formation Damage by Fines Migration 25 3 0 .1 I" 0. 01 5 2 0.0 01 " 0.5 1 1.5 2 2.5 Pore Volume of Injected... continuity given by Eq 11 -3 Civan's (19 96) formulation based on Richardson's (19 61) formulation can be modified as the following to include the loss terms and inertia flow affect in the saturation equation: (11 -19 ) for which the capillary and gravity dispersion coefficients are given, respectively, by: _ V krN dP,cNW dS (11 -20 ) Two-Phase Formation Damage by Fines Migration 24 5 (11 - 21 ) The zero capillary... can be expressed by (Gruesbeck and Collins, 19 82, Civan, 19 96): =d (11 -35) subject to the initial condition (11 -36) Liu and Civan (19 96) assumed the porosity change is negligible in Eq 11 -35 (i.e., (}) = constant) In Eq 11 -35, ktiJtS denotes the rate Two-Phase Formation Damage by Fines Migration 24 9 constant for deposition by pore throat plugging Civan (19 90, 19 96) proposed a dimensionless correlation . respectively: (11 -14 ) a* i w i a* a* ds a* ™* (11 -15 ) 24 4 Reservoir Formation Damage Note that the saturations add up to one: S W +S N =1 (11 -16 ) Therefore, adding Eqs. 11 -14 and 11 -15 . Eqs. 11 -20 and 22 , respectively, become: 24 6 Reservoir Formation Damage and MS w 1 + (M -1) S W (11 -26 ) Consequently, Eq. 11 -19 can be simplified significantly by substituting Eqs. 11 -25 . fraction is given by: (11 - 12 ) (11 -13 ) where (() is porosity and S } is the saturation of phase J. Thus, substituting Eqs. 11 - 12 and 11 -13 into Eq. 11 -11 yields the following