Effects of Ionic Strength on Fine Particle Clogging of Soil Filters

M. G. Hajra, S.M.ASCE1; L. N. Reddi, M.ASCE2; L. A. Glasgow3; M. Xiao, S.M.ASCE4; and I. M. Lee5

Abstract: The effects of ionic strength of the permeating fluid on the clogging of soil filters and drainage layers are addressed using both experimental and modeling investigations. In the experimental phase, a sandy soil representative of soil filters was permeated with pore fluids containing kaolinite particles. The ionic strength of the solutions was changed using different concentrations of NaOH and KCl. The permeability reductions of the soil filter were determined by varying pore fluid and particle suspension parameters. Higher ionic strength caused more flocculation of the kaolinite particles and resulted in more rapid reduction of permeability. In the modeling phase, a physical ␪ clogging model developed previously by the authors, was used to account for the ionic strength effects. A lumped parameter 0 was used in the model to account for the ionic strength of the pore fluid and the several interparticle forces, for example gravitational, inertial, ␪ hydrodynamic, electric double layer, and van der Waals forces. The effect of the lumped parameter 0 on the permeability reduction was found to be greater than the effect of the sizes of the influent particles. For the same ionic strengths, NaOH resulted in larger flocs of kaolinite particles than KCl, and caused more rapid reduction in permeability. DOI: 10.1061/͑ASCE͒1090-0241͑2002͒128:8͑631͒ CE Database keywords: Filters; Drainage; Permeability; Flocculation; Clogging.

Introduction petroleum engineering ͑Gray and Rex 1965; Muecke 1979; Bagh- dlklan et al. 1989͒; and ͑3͒ ‘‘sealing of liners’’ of canals, reser- Soil filters and drainage layers are used to provide stability to voirs, and lagoons in hydraulic and agricultural engineering ͑Bar- numerous geotechnical and geoenvironmental infrastructure sys- rington et al. 1987a,b͒. tems. Current practice in filter design is based on a comparison of Permeability reduction due to fine particle accumulation oc- the particle sizes of the soil filter and the base soil. Previous curs through two different mechanisms: ͑1͒ particles larger in size studies document that accumulation of colloid-sized particles in than a given pore size of the filter media are trapped by the pore porous media may cause more than 1 order of magnitude reduc- throat thus reducing the cross-sectional area available for fluid tion in permeability of filters and drainage layers ͑Reddi et al. flow, and ͑2͒ particles smaller than the diameter of the pore throat 2000͒. Reddi et al. ͑2000͒ also show that permeability can be are deposited on the pore walls causing a gradual reduction of the reduced even when the migrating particles are smaller than the pore radii. The latter is a dominant mechanism when interparticle majority of the soil filter pores. The concentration of particles in attractive forces exist between the porous medium and the fines. the pore stream was found to affect the rate of permeability re- These include gravitational, inertial, hydrodynamic, electric duction. Fine particle clogging in porous media also has been double layer, and van der Waals forces. Laboratory studies show studied in several engineering disciplines in addition to geotech- that permeability reduction occurs in formations containing non- nical and geoenvironmental engineering. Examples include: ͑1͒ expandable clays, such as illite or kaolinite, often caused by elec- ͑ wastewater filtration ͑McDowell-Boyer et al. 1986; Amirtharajah trostatic changes due to pH of the permeating fluid Mungan ͒ ͑ ͒ 1988; Tobiason and O’Melia 1988͒; ͑2͒ oil recovery processes in 1965 . Baghdlklan et al. 1989 concluded that ionic strength and pH of the fluid affected the permeability reduction when clays were injected into unconsolidated sand packs. These studies sug- 1Formerly, Doctoral Research Assistant, Dept. of Civil Engineering, gest that permeabilities of filters and drainage layers can be sig- 2118 Fiedler Hall, Kansas State Univ., Manhattan, KS 66506. 2Professor and Head, Dept. of Civil Engineering, 2118 Fiedler Hall, nificantly affected by the ionic conditions of the fluid media. Kansas State Univ., Manhattan, KS 66506. In an attempt to address the effects of ionic strength on particle 3Professor, Dept. of Chemical Engineering, 105 Durland Hall, Kansas deposition in porous media, Rege and Fogler ͑1988͒ developed a ␪ State Univ., Manhattan, KS 66506. network model where a single lumped parameter 0 was used to 4Formerly, Doctoral Research Assistant, Dept. of Civil Engineering, characterize the conditions for capture. They found that condi- 2118 Fiedler Hall, Kansas State Univ., Manhattan, KS 66506. tions favoring greater deposition result in relatively high values of 5Professor, Dept. of Civil Engineering, Korea Univ., Seoul 136-701, ␪ 0 . They also predicted that if the pore size distributions and/or Korea. ␪ the particle size distributions were changed, a fixed value of 0 Note. Discussion open until January 1, 2003. Separate discussions would be adequate to model all the simulations. But the relative must be submitted for individual papers. To extend the closing date by effect or importance of migrating particle/floc size and ␪ in fine one month, a written request must be filed with the ASCE Managing 0 Editor. The manuscript for this paper was submitted for review and pos- particle accumulation was not addressed in that study. Also, an sible publication on August 21, 2000; approved on February 19, 2002. experimental validation of such a modeling approach had not This paper is part of the Journal of Geotechnical and Geoenvironmental been attempted. Engineering, Vol. 128, No. 8, August 1, 2002. ©ASCE, ISSN 1090- In this paper, the effects of ionic strength of the permeating 0241/2002/8-631–639/$8.00ϩ$.50 per page. liquid on permeability reduction of soil filter media are addressed.

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 2002 / 631 Fig. 1. Influent particle size distributions for different ionic strengths

The relative effect of the influent particle size distribution or floc mained undisturbed at the time of analysis. As seen in Fig. 1, size of the particles and the ionic strength of the fluid ͑represented NaOH resulted in larger aggregates than KCl for the same ionic ␪ ͒ by 0 in the model on permeability reduction is investigated in strength. Moreover, higher ionic strengths caused greater floccu- this study. In the first part of the paper, an extension of the ex- lation of the kaolinite particles and shifted the size distributions perimental investigation reported in Reddi et al. ͑2000͒ is de- toward larger sizes. scribed. In the second part, the experimental results are used to Fig. 2 shows a schematic of the flow apparatus. The influent validate a modeling approach. suspension was prepared in a tank at a desired particle concentra- tion ͑0.5 g/L͒ for all the experiments. NaOH or KCl was then added to the influent to change the ionic strength of the solution Experimental Materials and Methods to the desired value. Influent samples were collected from the tank at regular time intervals for particle size distribution analy- Experiments were conducted using a sandy soil ͑hereafter re- ses. A continuous peristaltic flow pump, operated through a com- ͒ ferred as filter sand with the particle size characteristics: D60 puter, was used to pump the particle suspension from the influent ϭ ϭ ϭ 1.25 mm, D30 0.5 mm, and D10 0.25 mm. The porosity of tank into the soil sample at a constant rate of 50 mL/min. The the filter sand in the experiments was 29%. The hydraulic con- flow rate from the soil was also measured independently by col- ductivity of the soil corresponding to this porosity was 3.6 lecting the discharge into a graduated cylinder, to ensure accuracy ϫ10Ϫ2 cm/s, which was determined using a constant-head per- of the flow rate. A pulse dampener was used at the inlet flow line meability test with tap water as the permeant liquid. Kaolinite was to minimize any pulses caused by the pump. A magnetic stirrer at used to prepare the influent particulate suspension. Sodium hy- the base of the pulse dampener prevented particle settling and droxide ͑NaOH͒ and potassium chloride ͑KCl͒ were added to the deposition. The pressure drop across the soil sample, caused by influent suspensions to change the ionic strength of the permeat- gradual particle accumulation, was recorded using a differential ing fluid. Two different concentrations of NaOH ͑0.001 and 0.01 pressure transducer connected to a computerized data acquisition M͒ and KCl ͑0.01 and 0.1 M͒ were used. Fig. 1 shows the differ- system. The effluent coming out of the soil sample was passed ences in particle size distributions of particulate suspensions re- through a continuous-flow turbidimeter to record the turbidity sulting from the addition of these electrolytes. These size distri- values in terms of nephelometric turbidity units ͑NTUs͒. At regu- butions were measured using a charge coupled device camera lar time intervals, effluent samples were collected for particle size ͑with an 8 mm video tape recorder͒ attached to a transmitted light and particle number distribution analyses. Each experiment was microscope. The images were digitized and then analyzed with stopped when the pressure drop across the soil sample and the both a Bausch and Lomb® image analyzer and Sigma Scan Pro® effluent turbidity attained steady value. Darcy’s law was used to software. The suspensions were used directly in the analyses determine the permeability of the filter media using the recorded without adding any dispersing agents. The ionic condition and the pressure difference values across the soil sample and the flow rate flocculated structure of the influent and effluent samples thus re- of the pump.

632 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 2002 Fig. 2. Schematic of experimental setup

Results and Discussion strength caused greater flocculation of the kaolinite particles and resulted in larger aggregates. This resulted in more rapid reduc- The results for a representative experimental run with 0.01 M tion of permeability for the higher ionic strength scenarios. This NaOH in the influent suspension are shown in Fig. 3. The perme- finding was supported by the microscopic images of the influent ability values of the sample, normalized by the initial permeabil- samples. ity, and the effluent particle concentrations in terms of turbidity Fig. 5 shows the digitized microscopic images of the influent values, are plotted against pore volumes. The permeability was samples for 0.001 M NaOH, 0.01 M NaOH, 0.01 M KCl, as well reduced by 1 order of magnitude in about 50 pore volumes. After as tap water. A comparison of Figs. 5͑a and b͒ shows that the 100 pore volumes, the effluent turbidity reached a steady value of flocculation of kaolinite particles is greater with 0.01 M NaOH. 140 NTU, which is far less than the influent turbidity value, in- The larger flocs generated in the presence of 0.01 M NaOH block dicating continuous particle accumulation in filter pores. Fig. 4 the pore spaces, resulting in a more rapid reduction of permeabil- shows a comparison of the permeability profiles for all the differ- ity. With 0.001 M NaOH, the flocs are smaller in size but greater ent ionic strength conditions. For a given solution, higher ionic in number; i.e., a few large flocs can have a more adverse affect

Fig. 3. Results from representative experimental run with 0.01 M NaOH and Kaolinite clay suspension

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 2002 / 633 Fig. 4. Comparison of permeability reduction profiles for different ionic strength conditions

Fig. 5. Microscopic video images of influent with: ͑a͒ 0.001 M NaOH, ͑b͒ 0.01 M NaOH, ͑c͒ 0.01 M KCl, and ͑d͒ tap water

634 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 2002 Fig. 6. Variation of turbidity with pore volumes upon permeability than a larger number of small flocs. The ionic Fig. 6 shows the normalized turbidity profiles for the different strength is defined by ionic strength conditions. T represents the effluent turbidity at any given time and T represents the influent turbidity. For the case of 1 0 Iϭ ͚ m z2 (1) 0.01 M NaOH, it is seen that T/T reached a steady state value of 2 i i 0 0.2 after about 100 pore volumes. The turbidity never reached the ϭ ͑ ͒ where mi ,zi molality moles of solute per kg of solvent and influent turbidity value because of continued particle deposition charge for the ith ionic species, respectively. For dilute aqueous inside the soil sample. This was also observed in the experiments solutions, molality and molarity are nearly equal; so for a 0.01 M using tap water. KCl solution, IХ0.01 m. A comparison of Figs. 5͑a and b͒ shows that at the same ionic strength, NaOH promotes larger flocs than does KCl. The Debye length lD is defined by 4␲e2 Ϫ1/2 Mathematical Modeling l ϭͫ ͚ N z2ͬ (2) D ␧␬t i i A mathematical model was developed to account for the ionic where eϭfundamental unit of electronic charge; ␧ϭdielectric strength effects on filter clogging. The model is an extension of ␬ϭ ϭ ͑ ͒ constant; Boltzmann constant; t temperature K ; and Ni , that developed previously ͑Reddi et al. 2000͒ for physical clog- ϭ zi number of ions per unit volume and charge corresponding to ging. The soil filter medium is idealized as an ensemble of paral- the ith species, respectively. Therefore, for both 0.01 M NaOH lel capillary tubes of various diameters. To estimate the changes and 0.01 M KCl, the thickness of the ionic atmosphere would be in its permeability due to pore clogging, the Kozeny hydraulic ϫ Ϫ8 about 30 Å (30 10 cm). The promotion of flocculation by radius model is used. To simulate time-dependent reductions in NaOH is likely due to changes in the electrokinetic potentials of the pore diameters as a result of clogging, the particle deposition the edges of the particles, which are very sensitive to pH. James rate in each pore tube is expressed as a product of the flow rate in and Williams ͑1982͒ showed that the electrokinetic potentials of the pore tube ͑estimated using the Poiseuille law͒, particle con- the faces of kaolinite plates were unaffected by pH changes in the centration in the pore fluid, and particle capture probability. For a presence of NaCl, whereas the potentials of the edges of the plates change significantly with pH. Fig. 5͑d͒ illustrates the par- full description of the modeling approach for physical clogging, ͑ ͒ ticulate suspension prepared with tap water only. Greater floccu- see Reddi et al. 2000 . ͑ lation of kaolinite occurred in tap water than in the KCl solution, The particle capture probability approach Stein 1940; Rege ͒ but less than in the NaOH solution. Tap water contains many and Fogler 1988 , used in the physical clogging model, was re- different ionic species including Naϩ,Kϩ,Al2ϩ,Fe3ϩ, etc. The tained in this study. This approach is ideal for evaluation of depo- multivalent cations are known to effectively promote flocculation sition of particles passing through pores larger than themselves. It of negatively charged clays; this effect is described qualitatively conceptualizes that the probability of particle capture is equiva- by the Schulze–Hardy rule ͑Weber 1972͒. The presence of these lent to the fraction of total flow in the annulus of a pore tube species controls the relative degree of flocculation shown in Fig. between r and (rϪ␪a), and expresses the probability of capture 5͑d͒. as

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 2002 / 635 ␪a 2 ␪a 3 ͑ ͒ϭ ͫͩ j ͪ Ϫͩ j ͪ ͬ p ri ,a j 4 ri ri ␪ 4 a j ϩͩ ͪ (3) ri ϭ ϭ where ri radius of ith pore tube; a j radius of ith particle; and ␪ϭa lumped parameter that takes into account the effect on depo- sition of several interparticle forces such as gravitational, inertial, hydrodynamic, electric double layer, and van der Waals forces. According to Rege and Fogler ͑1988͒, a higher value of ␪ sug- gests that the surface conditions are favorable for deposition, be- cause particles in a relatively large annulus can be captured. Fac- tors that affect the value of ␪ are fluid velocity, ionic strength, fluid properties, and particle density and concentration. They pos- tulated the following exponential expression for ␪: ␯͑r ͒ ␪ϭ␪ Ϫ i 0 expͫ ␯ ͬ (4) cr ␪ ϭ ␯ where 0 a constant, dependent on ionic conditions; (ri) ϭ ␯ ϭ velocity of flow in the ith diameter pore tube; and cr a criti- Fig. 7. Variation of probability of particle capture with respect to cal velocity beyond which the hydrodynamic force is so high that floc size and ␪ ␯ 0 no particle deposition is likely. For filter soils, cr is close to 0.1 cm/s ͑Reddi et al. 2000͒. ␪ The value of 0 is primarily affected by changes in the ionic increased. The three-dimensional path due to NaOH and KCl strength of the permeating fluid. Rege and Fogler ͑1988͒ sug- shown in this figure will be discussed subsequently. gested a range of 2.5–10 for systems with bentonite suspensions and KCl concentrations ranging from 0.0 to 0.01 M. They sug- gested that when conditions for deposition are favorable ͑e.g., Application of Model ͒ ␪ relatively high ionic strength , 0 should have a higher value. A three-dimensional graph of Eq. ͑3͒ is shown in Fig. 7 to demon- The model was applied for the experimental conditions of this ␪ strate the relative importance of floc size and 0 on the probabil- investigation. The pore size distribution of the filter sand, deter- ity of capture. The floc size, represented by a, was varied from 0 mined in the previous study ͑Reddi et al. 2000͒, was used as input ␮ ␪ to 80 m. The value of 0 was varied from 0 to 80. The pore size in the model. The influent particle size distributions, which varied of the soil was kept constant at 1,000 ␮m. It is seen that the for the different ionic conditions, were also used to simulate the ␪ probability of capture increases if the floc size a, 0 , or both, are particle deposition process within the soil filter. The critical ve-

Fig. 8. Results from representative model calibration with kaolinite suspension and 0.001 M NaOH

636 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 2002 ␪ Table 1. 0 Values Obtained using Model Calibration for Different sults, are shown in Table 1 along with the pH of the solution and Ionic Strengths the median size of the influent kaolinite particles. Using these Median size values, a three-dimensional path of the increase in probability of of influent kaolinite particle capture is plotted with respect to the floc size a and the ͑␮ ͒␪ ␪ ͑ ͒ Ionic strength pH of solution flocs m 0 lumped parameter 0 for all the different ionic conditions Fig. 7 . The effect of ␪ on the probability of capture is seen to be greater Tap water 8.6 3.6 4 0 relative to the effect of the floc sizes, for the ionic conditions 0.001 M NaOH 9.6 8.5 20 chosen in this study. 0.01 M NaOH 11.1 14.0 75 Fig. 9 shows a comparison between experimental and model- 0.01 M KCl 7.2 9.0 4 ing results for two different concentrations 0.5 and 1.0 g/L of 0.1 M KCl 7.5 10.2 10 ␪ Kaolinite in tap water. The optimal value of 0 for tap water is 4. ␪ The same value of 0 successfully predicts the permeability pro- file for the two different concentrations of kaolinite suspension. locity ␯ used in Eq. ͑4͒ is difficult to measure. Sensitivity analy- cr Figs. 10 and 11 show a comparison of the experimental results sis of the model ͑with respect to ␯ ͒ was made in a previous cr with the model output for all the different ionic strength condi- study ͑Reddi et al. 2000͒.A␯ value of 0.1 cm/s was found to be cr tions. The satisfactory agreement between model output and the valid for the filter sand used in this study; therefore all the mod- experimental observations seen in these figures shows that the eling computations were made here with ␯ ϭ0.1 cm/s. cr physical clogging model could be used satisfactorily to take ionic To study the effect of ionic strength on the reduction of per- strength effects into account when the lumped parameter ␪ is meability values, simulations were performed with different val- 0 used. Since the values of ␪ used here were generated using ues of ␪ . An increase in ␪ caused more favorable conditions for 0 0 0 model calibration with experimental results, a generalized ex- deposition, resulting in rapid reduction in the permeability values. trapolation of the model beyond the conditions and constraints in This is evident from Fig. 8, which corresponds to 0.001 N NaOH. this study is not warranted. The model results did not agree with The model computations were made with the influent particle size experimental observations in the case of 0.01 M NaOH, even distribution discussed earlier, and ␪ values ranging from 5 to 20. 0 when ␪ is increased further. This corresponds to the case of the This range of ␪ is consistent with those suggested by Rege and 0 0 largest floc sizes measured in this study. The flocs formed in this Fogler ͑1988͒ for the range of ionic strengths addressed in this case could be entirely blocking the liquid-conducting pores at the study. As seen in the figure, the permeability reduction was influent end. These flocs could be much larger than those ob- greater and more rapid as the value of ␪ increased. A ␪ value of 0 0 served in the effluent; therefore, the floc sizes a used in the model 20 gave results that were closest to the experimental data. When might not be representative of those trapping the pores in the soil the ionic strength was increased to 0.01 M NaOH, a ␪ value of 0 column. 75 gave the best correlation with experimental data. Thus when conditions for deposition are favorable ͑relatively high ionic ͒ ␪ Conclusions strength , a higher value of 0 should be used. A similar result ␪ was found with KCl. The optimal values of 0 for which the The permeability results from the experiments conducted with model’s performance matched closest with the experimental re- kaolinite suspensions showed significant differences due to ionic

Fig. 9. Experimental results versus model predictions for different concentrations of kaolinite in tap water

JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 2002 / 637 Fig. 10. Experimental results versus model predictions for 0.001 M NaOH, 0.01 M NaOH, and tap water

strength conditions of the permeating particle suspensions. In The physical clogging model developed earlier could be em- general, an increase in ionic strength led to a more rapid reduction ployed to take ionic strength effects into account using a lumped ␪ ␪ in permeability, because of the larger floc sizes associated with parameter 0 in the model. Although the values of 0 were ob- high ionic strength. Also, the presence of a few larger flocs/ tained using model calibration with experimental results, the trend particles in the influent suspension caused more rapid reduction in in the values is consistent—higher ionic strengths are associated ␪ permeability than a larger number of smaller sized flocs. For the with higher 0 . The modeling investigation also revealed that the same ionic strength, the rate and extent of permeability reduction effect of the ionic condition of the pore fluid, represented by the ␪ was greater with NaOH than with KCl, because of the differences lumped parameter 0 in the model, on permeability reduction is in flocculation behavior of kaolinite with these two agents. more important than the size of the influent particles/flocs.

Fig. 11. Experimental results versus model predictions for 0.01 M KCl and 0.1 M KCl

638 / JOURNAL OF GEOTECHNICAL AND GEOENVIRONMENTAL ENGINEERING / AUGUST 2002 Acknowledgments caused by clay dispersion and migration.’’ Proc., 14th Clay Minerals Soc. North American Clay Minerals Conf., Univ. of California, Ber- The work reported in this paper was funded in part by the Na- keley, Berkeley, Calif. tional Science Foundation ͑Grant Nos. CMS-9713708 and INT- James, A. E., and Williams, D. J. A. ͑1982͒. ‘‘Particle interactions and 9734804͒ and by Korea Science and Engineering Foundation ͑No. rheological effects in kaolinite suspensions.’’ Adv. Colloid Interface 985-1200-001-2͒. Some financial support was also provided by Sci., 17, 219–232. McDowell-Boyer, L. M., Hunt, J. R., and Sitar, N. ͑1986͒. ‘‘Particle the Agricultural Experiment Station at the Kansas State Univer- ͑ ͒ ͑ ͒ transport through porous media.’’ Water Resour. Res., 22 13 , 1901– sity Contribution No. 99-374-J . The support from these agencies 1921. is gratefully acknowledged. The writers also wish to thank the Muecke, T. W. ͑1979͒. ‘‘Formation fines and factors controlling their anonymous reviewers for their constructive criticism of this work. movement in porous media.’’ JPT J. Pet. Technol., 144–150. Mungan, N. ͑1965͒. ‘‘Permeability reduction through changes in pH and salinity.’’ Trans. Soc. Min. Eng. AIME, 234, 1449–1453. References Reddi, L. N., Xiao, M., Hajra, M. G., and In, M. L. ͑2000͒. ‘‘Permeability reduction of soil filters due to physical clogging.’’ J. Geotech. Geoen- Amirtharajah, A. ͑1988͒. ‘‘Some theoretical and conceptual views of fil- viron. Eng., 126͑3͒, 236–246. tration.’’ J. Am. Water Works Assoc., 36–46. Rege, S. D., and Fogler, H. S. ͑1988͒. ‘‘A network model for deep bed Baghdlklan, S. Y., Sharma, M. M., and Handy, L. L. ͑1989͒. ‘‘Flow of filtration of solid particles and emulsion drops.’’ AIChE J., 34͑11͒, clay suspensions through porous media.’’ SPE Reservoir Eng., 213– 1761–1772. 220. Stein, P. C. ͑1940͒. ‘‘A study of the theory of rapid filtration of water Barrington, S. F., Jutras, P. J., and Broughton, R. S. ͑1987a͒. ‘‘The sealing through sand.’’ D.Sc. dissertation, Massachusetts Institute of Technol- of soils by manure. I. Preliminary investigations.’’ Can. Agric. Eng., ogy, Cambridge, Mass. 29͑2͒, 99–103. Tobiason, J. E., and O’Melia, C. R. ͑1988͒. ‘‘Physicochemical aspects of Barrington, S. F., Jutras, P. J., and Broughton, R. S. ͑1987b͒. ‘‘The sealing particle removal in depth filtration.’’ J. Am. Water Works Assoc., of soils by manure. II. Sealing mechanisms.’’ Can. Agric. Eng., 29͑2͒, 80͑12͒, 54–64. 105–108. Weber, W. J. ͑1972͒. Physicochemical processes for water quality control, Gray, D. H., and Rex, R. W. ͑1965͒. ‘‘Formation damage in sandstones Wiley-Interscience, New York.

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