Colloidally-Induced Fines Release in Porous Media

Journal of Petroleum Science and Engineering, 4 (1990) 213-221 213 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

Colloidally-induced fines release in porous media

Kartic C. Khilar% R.N. Vaidya2 and H.S. Fogler2'3 1Department of Chemical Engineering, Indian Institute of Technology, Bombay Powai, Bombay, 400 076 (India) 2Department of Chemical Engineering, The University of Michigan, Ann Arbor, Michigan 48109-2136 (U.S.A.) (Accepted after revision June 9, 1989)

ABSTRACT

Khilar, K.C., Vaidya, R.N. and Fogler, H.S., 1990. Colloidally-induced fines release in porous media. J. Pet. Sci. Eng., 4: 213-221.

A critical value of the total ionic strength (CTIS) has been found to exist for mixed salt solutions flowing in porous media. If the ionic strength drops below this value, significant amounts of fines are released in-situ due to colloidal forces, causing drastic formation damage. For a NaCI/CaC12 system, the CTIS is strongly dependent on the relative amount of CaC12 present in the solution. The concept of a critical salt concentration (CSC) and the analysis based on DLVO theory has been extended to mixed salt systems to estimate the CTIS. The difference between critical flocculation concentration (CFC), and the present definition of CTIS has been pointed out. Predictions of this analysis are consistent with experimental observations.

Introduction Schofield, 1955; Rowell et al., 1969; Hardcas- tle and Mitchell, 1974; Kolakowski and Mati- Colloidally-induced release and migration in jevic, 1979; Khilar and Fogler, 1984). The lat- porous media is important in numerous pro- est of these studies has addressed the concept cesses such as enhanced oil recovery, migra- of critical salt concentration in detail and an tion of organic waste from landfills, regenera- experimental method has also been proposed tion of filter beds, and erosion of earthen to determine CSC for fines migration in Berea embankments (Khilar and Fogler, 1984, 1987; sandstone (Khilar and Fogler, 1984). The mi- Khilar et al., 1985). The phenomenon of col- grating fines in Berea sandstone were found loidally-induced fines migration is of signifi- predominantly to be kaolinite clay. In addi- cant importance in the petroleum industry as tion, an analysis has been formulated deline- these released fines can migrate and plug re- ating the effects of flowrate, pH, temperature gions in the formation causing damage and and, charge and size of cation on CSC in a sin- hence reduction in production. A number of gle salt system. This analysis is based on DLVO studies using single salt systems (NaC1, KC1, theory of stability of lyphobic colloids and the etc. ) have conclusively shown that colloidally- CSC is analogous to the critical flocculation induced fines release is a threshold type of pro- concentration (CFC) in colloid sol stability cess that can occur when the salt concentra- (Hiemenz, 1986). tion of the flowing solution decreases below a Studies have been reported on colloidally- threshold (or a critical) value known as criti- induced fines migration with a mixed salt sys- cal salt concentration (CSC) (Quirk and tem of NaC1/CaC12 (Quirk and Schofield, 1955; Jones, 1964; Kia et al., 1987b). These 3Author to whom all correspondence should be addressed. studies primarily emphasize the importance of

Nomenclature

a radius of sphere Subscripts A Hamaker constant i,j species, (1,2..) e electronic charge LVA London-Van der Waals F force BR Born repulsion h distance of separation DLR Double layer I total ionic strength HR hydrodynamic k Boltzman constant T total n bulk concentration of ions 7" temperature Acronyms I potential energy CFC Critical Flocculation Concentration y dimensionless potential (Eq. 5c) CSC Critical Salt Concentration _- valency of the ion CTIS Critical Total Ionic Strength DLVO Deryaguin-Landau-Verwey-Overbeek Greek symbols permitivity of medium x Debye Huckel parameter (Eq. 5b) cr Born repulsion parameter zeta potential T surface potential (all in consistent C.G.S. units)

the presence of a minimum amount of Ca 2+ cium ions is greater than a critical value of ions in solution or on the surface of the fines 75%, then the zeta potential is sufficiently re- (clay) to prevent their release and migration. duced for the prevention of colloidally-in- Quirk and Schofield (1955) have observed duced fines release. The surface coverage of that soil permeability decreases due to the clay calcium ions depends strongly on the total swelling* and dispersion when the concentra- ionic strength as well as on the calcium ionic tion of Ca 2+ ions in the mixed salt solution de- fraction or percentage in the solution. Conse- creases below a threshold value of 2.5 × 10 -4 quently, the threshold value of the concentra- M. Their data showed that this threshold value tion of Ca 2+ to prevent fines release must de- is independent of the concentration of Na + in pend on the mole percentage of calcium in the the solution; which is rather unconvincing. solution. Experimental work concerning a crit- Recent work of Kia et al. (1987b) focuses on ical total ionic strength (CTIS) of a mixed salt the amount of Ca 2+ ion on the surface rather system, the percentage of calcium in solution than that in the bulk solution. This is a more and its relationship with the phenomenon of reasonable approach, because the amount of colloidally-induced fines migration has not Ca 2+ ions on the surface of the fines deter- been reported, nor has an analysis been put mines the zeta potential of the fines which in forth that can be used to estimate the CTIS. turn controls the release process. Kia et al. have This information is useful in many chemical, shown that if the solution composition is ad- environmental and petroleum engineering op- justed so that coverage on the surface by cal- erations involving flow of mixed salt solutions through a porous medium. *Reduction in permeability due to clay swelling occurs Continuing our earlier work on the CSC because of reduction in flow cross-sectional area due to (Khilar and Fogler, 1984) we show here that volume changes of the clay. In fines migration, the clay particles detach from the pore walls and migrate with the there exists a critical total ionic strength fluid until they are captured at pore constrictions, thereby (CTIS), below which colloidally-induced fines reducing the flow cross-sectional area. release may occur in Berea sandstone. We have COLLOIDALLY-INDUCED FINES RELEASE IN POROUS MEDIA 215

Berea Sandstone, temperature = 300 K expanded our earlier analysis of the CSC to Ko = I 0 roD, Calcium percentage = 0 254 cm Diameter, 254 cm length, velocity = 19 7 crn/hr mixed salt systems consisting of symmetric and 1.6 unsymmetric electrolytes. In a NaC1/CaCI2 system, the CTIS strongly depends on the rel- O,e ative amount of CaC12 present in the solution o0.e (calcium molar percentage, %Ca). For exam- ple in a 5% calcium and 95% sodium solution, 0.4 Q- tx I~ a tx the CTIS is 0.025 M while it decreases signifi- °Q tOIo-lg- o. I° ° 8- ot: Io.°o o. o.O., cantly to 0.005 M for a 10% calcium and 90% ~)Z~ Z I i ~rz [ I I I I I I sodium solution. As we will soon see the pre- 0 40 80 120 160 200 240 280 320 360 400 dictions using this analysis agree well with the Pore Volumes experimental data. Fig. 2. Measurementof critical ionic strength from relative permeability (Khilar, 1981 ). Measurement of the critical total ionic strength (CTIS) permeability (K/Ko). A typical measurement is shown in Fig. 2 (Khilar, 1981). The value A schematic of the experimental system is of the CSC for different cations, such as Li+, shown in Fig. 1. It consists of a positive dis- K +, NH~-, Cs ÷, have been reported by Khilar placement pump for fluid injection, a Hassler (1981). In our present study, the concentra- cell in which the core is contained and, pres- tions of the ions (Ca :÷ and Na ÷ ) were mea- sure and concentration measuring devices. For sured using specific ion electrodes. The partic- a constant injection rate, the pressure drop ulate content of the effluent was analyzed using across the core was monitored continuously as an Atomic Absorption Spectrometer (AAS)* a function of the ionic strength of the aqueous and a Scanning Electron Microscope (SEM). solution flowing through the core. All the Be- The ionic strength at which the pressure drop rea sandstone samples used for this study were across the core begins to increase and the clay from the same block, having a initial permea- particles appear in the effluent determines the bility of approximately 10 roD. The cores were critical concentration. A similar experimental not fired nor acidized prior to the experi- procedure was used in this work. ments. The Berea samples had a clay content In a typical experiment, a Berea sandstone of approximately 8 wt%, and 75% of which is core (2.54 cm both in diameter and length) kaolinite clay. was vacuum saturated with a NaC1/CaC12 salt The ionic strength of the solution is de- solution of 0.10 M ionic strength (I) and at a creased in a stepwise manner, and this tech- particular mole percent of calcium. The satu- nique has been used successfully (Khilar, 1981; rated Berea sandstone was placed in a core Khilar and Fogler, 1984) to determine the CSC holder and a NaCI/CaC12 salt solution was of various single salt systems. The critical ionic flown through the core at a superficial velocity strength is defined as the ionic strength at of 19.2 cm h- ] ( 15.1 ft day- 1). The tempera- which there is a sharp decline in the relative ture was maintained at 30°C by means of a constant temperature bath. The inlet pH was 4£ in the range 6-7 while the pH of the effluent was found to vary between 8 and 9. As de- Effluent for analysis *The fines that are releasedwere collectedand acidized. t,,i.... -' ..... bLrd o This solution was then analyzedfor Al3+ and Si 4+ concentration using an AAS, and therefore estimate the Fig. 1. Experimentalequipment. amount of fines released. 216 K.C. KHILAR, R.N. VAIDYA AND H.S. FOGLER

Berea sandstone, temperature = 300 K TABLE 1 Ko = 10 roD, Calcium ~ercentage = 5 2.54 cm diameter, 2.54 cm length CTIS for Berea sandstone at different calcium percentage

% Ca % Na CTIS (M) 10 "3 ~' ~ ~ ~ ~ ~'-' ~ ~"" ~ ~ ~ ~" ~

0 100 0.071 5 95 0.025 0.8 10 90 0.005 15 85 << 0.001

0.6 ("4 Ox 0 o C, to obtain a range for the CTIS. Having ob- 0.4 ¸ II II II II II 3: tained a coarse range, the ionic strength was then decreased in small steps within the range 0.2 to determine the CTIS with an accuracy of _ 0.0005 M. Figures 3 and 4 show the values of CTIS 0.0 • i . , • , i 0 40 80 120 160 200 240 280 320 measured at calcium percentages of 5 and 10, and all the results are summarized in Table 1. Pore Volumes One observes from this table that CTIS de- Fig. 3. Measurement ofCTISat 5 mole % calcium and 95 creases as the calcium percentage increases. mole % sodium. That is, even at low ionic strength the fines are Berea sandstone, temperature = 300 K not released at higher calcium percentages. At Ko = 10 mD, Calcium percentage = 10 2.54 cm diameter, 2.54 cm length 15 % calcium/85% sodium, the CTIS could not be obtained as it appears to be much below the detection limit of the system. 1.0 The experimental results can be explained through a qualitative analysis, by comparing 0.8 the zeta potentials (() and the consequent variations in the double layer interactions. The

0.6 zeta potentials of kaolinite and the Berea sandstone are strongly dependent on the ex- X,O ",::l" oc ("4 0 q tent of surface coverage of Ca 2÷ ions (Kia et ,~ ,~, 0.4 0 al., 1987b), which in turn depends on the ion II II II II II II II exchange equilibria between the particles and 0.2 the mixed salt solution (Bolt, 1955; Wilem- sky, 1982). The ionic condition of the fluid can be described by two parameters: the calcium 0.0 0 40 80 120 160 200 240 280 320 percentage and the total ionic strength. The reduction in zeta potential with increasing cal- Pore Volumes cium percentage causes the double layer repul- Fig. 4. Measurement of CTIS at 10 mole % calcium and sive potential to decrease and decreasing the 90 mole % sodium. probability of release. Therefore, the total ionic strength must be reduced to increase the dif- scribed earlier, the ionic strength of the salt so- fuse double layer and increase the probability lution was decreased in a step-wise manner, the of release. Consequently, increasing the cal- ionic strength was first decreased by large steps cium percentage lowers the CTIS. COLLO1DALLY-INDUCEDFINES RELEASE IN POROUSMEDIA 217

Extension of CSC analysis to estimate CTIS order of 5A, the Born repulsive potential is comparable in magnitude to London-Van der The DLVO-type of analysis, used earlier by Waals and Double layer potential. The inclu- Khilar and Fogler (1984) to estimate the CSC, sion of the Born repulsion term makes the pri- is extended to study the effects of calcium per- mary minimum of the interaction potential fi- centage on CTIS. The total energy (Fw) and nite. The existence of the finite primary the total force (FT) are identically zero at minimum has been able to explain the ob- CTIS: served adsorption/desorption of particles from VT=0 (I) surfaces and the flocculation behavior of colloidal suspensions (Hamaker, 1937; Rucken- OVT stein and Prieve, 1976; Feke et al., 1984). Oh --0=FT (2) Equation 3 reduces to: where, h is the distance of separation between the pore wall and the particle. The total poten- WT = VLV A -1- VBR "[- VDLR (3a) tial (FT) can be obtained by simply adding the Some investigators have modeled clay/clay individual potentials: interactions as either having a plate/plate or a I-ZT = VLVA -1- VDLR -1- VBR "-[- VHR (3) cylinder/plate geometry (James and Wil- where: liams, 1982 ). Typically, the clay particles are the order of one micron size and the pore to VLVA London-van der Waals attractive potential; which they are attached have diameters approximately 30-40 microns. Therefore, the in- VDLR Double layer repulsive potential; VBR Born repulsive potential; and teraction between the particle (kaolinite clay) VHR Hydrodynamic repulsive potential. and the sandstone surface (Berea) were mod- It has been shown that, the contribution of eled to have a sphere/plate geometry as done the hydrodynamic potential becomes compa- by previous investigators (Khilar, 1981; rable to the colloidal forces only at very high Sharma et al., 1985). For such a system the flow-rates, that is superficial velocities greater London-Van der Waals potential is given by than 1000 cm h-~ (Cerda, 1988). The experi- (Ruckenstein and Prieve, 1976 ): mental results of Khilar ( 1981 ), listed in Ta- ble 2, also show the weak dependence of veloc- AFln(h+2a~ 2a( h+a ~] (4) ity on the critical salt concentration. Since the L experimental velocities in this study were much lower ( 19.2 cm h- 1), the effect of VHR where A is the Hamaker constant, a is the ra- was neglected. When the distance of separa- dius of the particle, and h is the distance of tion between the particle and the wall is of the separation. The double layer potential can be calcu- TABLE2 lated, under certain approximations, using the following expression of Ruckenstein and CSC various superficial velocities (Khilar, 1981 ) Prieve ( 1976): Superficial velocity CSC molarity (cm h-l ) (M) VDLR = 16e(~)2 a tanh(4 ) tanh(~)e -~h 3.15 0.072 + 0.003 19.7 0.071 + 0.002 568.4 0.071 +0.002 (5) 218 K.C. KHILAR, R.N. VAIDYA AND H.S. FOGLER where: i ~z'~1~nO_2 i2~i (5a) o 2 { 8rce2I~ x =~ ek-T-) (5b) to

Fluid flow" Y~= kT (5c) In these expression: n° bulk concentration of species, i surface potential of surface, j(j= 1, 2 ) >,-- zi valency of species, i e electronic charge uJ

I total ionic strength •-~ o k Boltzmann's constant T absolute temperature E e permittity of the medium (all in cgs units ) The Born repulsion potential (VBR), aC- counts for the short range structural or hydra- L tion forces due to the interaction of particles h, distance of separation with adsorbed fluid layers (Feke et al., 1984). Assuming that these interactions can be line- Ionic strength of A is greater than ionic strength of B arly superimposed, Ruckenstein and Prieve Fig. 5. Interaction potentials showing the critical ionic strength. (1976) obtained the following formula for a sphere-plate interaction geometry: The value of CTIS is determined as the value Aa [- 8a+h 6a-h-] of the ionic strength I for which both the mag- VBR= 7~0 (-~J[(2a+h)7t- (6) nitude and the slope of the VT/kT versus h plot become zero at some distance of separation Here a, is the collision diameter, and is ap- (Eqs. 1 and 2). Figure 5 shows some typical proximately 5-6 •. interaction profiles that may be realized from The ionic strength and the calcium percent- Eqs. 3-6. One observes, that there is more than age (%Ca) are related to the molarities of Na + one situation when the conditions of Eqs. 1 and and Ca 2+ (MNa and Mc,) in the following 2 are satisfied. The first situation arises when manner: the maximum of the interaction potential I = Mr~a + 3Mc, (7) curve satisfies the above conditions, and is shown as curve A. This salt concentration is %Ca = 100 \MN, + 2Mc, J ( 8 ) generally referred to as the critical flocculation concentration (CFC) in colloidal studies re- The total energy of interaction VT was calculated to aggregation of particles. As can be ob- lated by using Eqs. 3-6. The total energy of in- served from Fig. 5, the primary minimum is teraction may be evaluated as a function of the still negative compared to the bulk potential separation distance h for different values of (which is zero), and therefore the escape of ionic strength and at various calcium particles from the primary minimum is percentages. minimal. COLLOIDALLY-INDUCED FINES RELEASE IN POROUS MEDIA 219

Reducing the ionic strength below the CFC The values of zeta potentials were taken from results in the second situation, when the pri- the literature and at the calcium percentage of mary minimum satisfies the conditions of Eqs. 5 and 10, the zeta potentials of kaolinite are 1 and 2. This is shown by curve B in Fig. 5. approximately -16 and -12 mV, respec- This ionic strength will be referred to as the tively, and those of Berea sandstone at -18 critical total ionic strength (CTIS). Lowering and - 14 mV, respectively (Kia et al., 1987a, the ionic strength below the CTIS makes the 1987b). The variation of zeta potential with value of the potential at the primary minimum total ionic strength (excluding the variations greater than the bulk potential. This condition at very low values of I) was found to be very now favors the detachment (or escape) of the weak (Kia et al., 1987a) and was neglected in particles from the primary minimum. The the calculations. A Hamaker's constant, A, of presence of a maximum in the interaction po- 0.6X10 -13 ergs, which lies in the reported tential can slow the rate of release, since the range of 0.30-6.0X 10 -13 ergs for clay-sand- particles have to diffuse over a potential bar- stone systems (Lyklema, 1968 ), was found to rier. For some ionic conditions, a secondary fit the observed experimental data minimum may also be present and this could satisfactorily. also have an effect on the rate of adsorption The variations of interaction potential with and desorption of particles (Ruckenstein, the distance of separation and for different 1978 ). This effect results because the particles ionic strengths can be observed from any of that are released form the primary minimum these two figures. One observes from Fig. 6, the diffuse over the potential barrier and under total interaction potential is negative or at- certain circumstances may be captured in the tractive (no release condition) at high values secondary minimum, thus reducing release of ionic strength, while the potential is posi- rates. From the above discussion, however, it tive or repulsive (favoring release) at lower is evident that, ionic strengths below CTIS will ionic strengths of the order of 0.001 M. lead to the detachment of the clay fines from The variation of total potential with dis- the sandstone surface. These released fines will tance of separation h follows the common diffuse into the bulk and flow with the fluid, trend of decrease in attractive energy as sepa- consequently leading to formation damage. ration distance increases and the occurrence of Figures 6 and 7 show the total energy of in- maximum and minimum depending on the teractions VT as a function of distance of sep- value of the zeta potential, ionic strength and aration h for different values of total ionic Hamaker's constant. Comparing Figs. 6 and 7, strength I at 5 and 10% calcium percentage. one observes that for the same value of ionic

["- 40 ["" 30 Calcium Percentage = 5 Calcium Percentage = l0 > ~ 30' ~ 2o

~ eo. e~ g -~ 10 , •~, 0

~ -10 /'- 0.1M LN "~ 0.1M [--, -10 [.... 2O 0.0 0'.2 0'.4 0'.6 0'.8 1.0 0.0 0'2 0.4 0'.6 0'.8 1,0 x 200 ,~ Distance of Separation, h X 2(10 Distancc of Separation, h Fig. 6. Total interaction potential for different ionic Fig. 7. Total interaction potential for different ionic strengths and 5% calcium in solution. strengths and 10% calcium in solution. 220 K.C, KHILAR, R.N. VAIDYA AND H.S. FOGLER

TABLE 3 strength (CTIS) for a mixed salt system of NaCI/CaC12 flowing through Berea sandstone Comparison of CFC and CTIS at various calcium exists, below which fines are released due to percentages colloidal forces. The value of CTIS is strongly % Ca CFC(M) CTIS(M) CTIS(M) dependent on the relative amount of CaC12 (experimental (predicted) present in the solution. For calcium molar percentage of 15 or higher, the molarity of the 0 0.12 0.071 0.071 5 0.1 0.025 0.035 CTIS is virtually zero, while the maximum 10 0.032 0.005 0.008 value (0.07 M) is at zero calcium percentage. Analysis based on the DLVO theory agree rea- strength/, the interaction potential Vx is more sonably well with measurements. Although this negative (increased attraction) at higher cal- study has been conducted for Berea-NaC1/ cium percentages and decreases (becomes CaC12 system, the measurement technique and negative) with an increase in ionic strength. the analysis developed can be applied to other One also observes from these figures that systems as well. CTIS at 5 and 10% calcium can be taken equal to 0.035 and 0.008, respectively. These corre- Acknowledgements sponding values calculated from DLVO theory compare well with the measured values of O. 025 One of the authors, KCK, thanks the De- and 0.005 M. For 15%Ca/85%Na the calcula- partment of Science and Technology, New tions showed that even at a low ionic strength Delhi, India for financial support (Sanction of 0.001 M, the total energy of interactions is No. DST/STP/83/III) to carry out a part of negative and hence the CTIS is below 0.001 this work. In addition KCK acknowledges with M. The values in Table 3 give the ionic strength thanks the summer visiting faculty position for the CFC and the CTIS, as has been defined offered by the department of Chemical Engi- previously, for various calcium percentages. As neering at The University of Michigan. We also discussed earlier, an increase in concentration gratefully acknowledge the support from the beyond the CFC enhances flocculation, while National Science Foundation grant No. CBT- decreasing below the CTIS favors peptization 8516458. (or detachment) of particles. Although this very good agreement of theo- References retical predictions with data may be somewhat fortuitous, we wish to caution that the quanti- Bolt, G.H., 1955. Ion adsorption by clays.Soil Sci., 79: 267. Cerda, C.M., 1988. Mobilization of quartz fines in po- tative agreement depends on the estimated rous media. Clays Clay Miner., 36 (6):491. Hamaker's constant, which can be determined Grim, R.E., 1968. Clay Mineralogy, McGraw Hill, New accurately with great difficulty. Therefore like York, N.Y., p. 596. most other analyses based on the DLVO the- Erickson, E., 1952. Cation-exchange equilibria on clay ory, this analysis can be considered as semi- minerals. Soil Sci., 74: 103. Feke, D.L., Prabhu, N.D., Mann, Jr., J.A. and Mann, IIl, quantitative predicting the relative change in J.A., 1984. A formulation of the short-range repulsion CTIS at different colloidal conditions for a between spherical colloidal particles. J. Phys. Chem., mixed salt system. 88 (23): 737. Hamaker, H.C., 1937. A general theory of lyophobic colloids. II. Rec. Tray. Chim., 56 ( 1 ): 3. Conclusions Hardcastle, J.H. and Mitchell, J.K., 1974. Electrolyte concentration -- permeability relationships in so- It can be concluded from the presented mea- dium-illite silt mixtures. Clays Clay Miner., 22 (2): surements and analysis that a critical total ionic 143. COLLOIDALLY-INDUCEDFINES RELEASE IN POROUS MEDIA 221

Hiemenz, P.C., 1986. Principles of Colloid and Surface Kolakowski, J.E. and Matijevic, E., 1979. Particle adhe- Chemistry, 2nd ed., Marcel Dekker, New York, N.Y., sion and removal in model systems. J. Chem. Soc. pp. 717-721. Faraday Trans. I., 75 ( 1 ): 65. James, A.E. and Williams, D.J.A., 1982. Particle interac- Lyklema, J., 1968. Principles of the stability of lyophobic tions and rheological effects in kaolinite suspensions, colloidal dispersions in non-aqueous media. Adv. Col- Adv. Colloid Interface Sci., 17:219. loid Interface Sci., 2: 65. Jones, F.O., Jr., 1964. Influence of chemical composition Quirk, J.P. and Schofield, R.K., 1955. The effect of elec- of water on clay blocking of permeability. J. Pet. Tech- trolyte concentration on soil permeability. J. Soil Sci., nol., (Ap.): 441. 6 (2): 163. Khilar, K.C., 1981. The water sensitivity of Berea Sand- Rowel, D.L., Payne, D. and Ahmad, N., 1969. The effect stone. Ph.D. thesis, The University of Michigan, Ann of the concentration and movement of solutions on the Arbor, Mich. swelling, dispersion, and movement of clay in saline Khilar, K.C. and Fogler, H.S., 1984. The existence of a and alkali soils. J. Soil Sci., 20 ( 1 ): 176. critical salt concentration for particle release. J. Col- Ruckenstein, E., 1978. Reversible rate of adsorption or loid Interface Sci., 101: 214. coagulation of Brownian particles-Effect of the shape Khilar, K.C. and Fogler, H.S., 1987. Colloidally induced of the interaction potential. J. Colloid Interface Sci., fines migration in porous media. Rev. Chem. Eng., 4: 66 (3): 531. (1/2)41. Ruckenstein, E. and Prieve, D.C., 1976. Adsorption and Khilar, K.C., Fogler, H.S. and Gray, D.H., 1985. Model desorption of particles and their chromatographic for piping-plugging in earthen structures. ASCE, J. separation, AIChEJ., 22 (2): 276. Geotech. Eng. Div., 111: (7) 833. Kia, S.F., Fogler, H.S. and Reed, M.G., 1987a. Effect of Sharma, M.M., Yortsos, Y.C. and Handy, L.L., 1985. Re- pH on colloidally induced fines migration. J. Colloid lease and deposition of clays in sandstones. SPE 13562, Interface Sci., 118 ( 1 ): 158. Int. Symp. Oilfield and Geothermal Chem., Phoenix, Kia, S.F., Fogler, H.S., Reed, M.G. and Vaidya, R.N., Ariz. 1987b. Effect of salt composition on clay release in Be- Wilemsky, G., 1982. Weak repulsive interactions berea Sandstones. S.P.E. 16254, Production Engineer- tween dissimilar electrical double layers. J. Colloid In- ing, (Nov.) 277. terface Sci., 88( 1 ): 111.