Kinetics of Bacterial Degradation of Benzylamine ... - ACS Publications

Ephraim, J.; Alegret, S.; Mathuthu, A,; Bicking, M.; Mal- colm, R. L.; Marinsky, J. A. Enuiron. Sci. Technol. 1986,. Perdue, E. M. Geochim. Cosmochim...
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Environ. Sci. Technol. 1991, 25, 240-245

Perdue, E. M.; Reuter, J. H.; Ghosal, M. Geochim. Cosmochim. Acta 1980, 44, 1841-1851. McKnight, D. M.; Thorn, K. A.; Wershaw, R. L.; Bracewell, J. M.; Robertson, G. W. Limnol. Oceanogr. 1988, 33, 1527-1541. Ephraim, J.; Alegret, S.; Mathuthu, A,; Bicking, M.; Malcolm, R. L.; Marinsky, J. A. Enuiron. Sci. Technol. 1986, 20, 354-366. Perdue, E. M. Geochim. Cosmochim. Acta 1978, 42, 1351-1358. Fuchs, W. Brennst. Chem. 1927,8, 337-352. Ihnatowicz, A. Prace Glownego Inst. Gorn. Komun. (Engl. Transl.) 1952, 125, 3. Brooks, J. D.; Sternhell, S. Aust. J . Appl. Sci. 1957, 8, 206-221.

Pergamon: Oxford, 1966; pp 129-141. (20) Gamble, D. S. Can. J. Chem. 1973,51, 3217-3222. (21) Martell, A. E.; Smith, R. M. Critical Stability Constants; Plenum: New York, 1977; Vol. 3. (22) Perdue, E. M.; Reuter, J. H.; Parrish, R. S. Geochim. Cosmochim. Acta 1984, 48, 1257-1263. (23) MacCarthy, P. Colorado School of Mines, personal com-

munication, 1988. (24) Blom, L.; Edelhausen, L.; Van Krevelen, D. W. Fuel 1957, 36, 135-153. (25) Stumm, W.; Morgan, J. Aquatic Chemistry, 2nd ed.; John Wiley and Sons: New York, 1981; p 135. (26) Gamble, D. S. Can. J . Chem. 1970, 48, 2662-2669. (27) Gamble, D. S.; Langford, C. H. Enuiron. Sci. Technol. 1988, 22,

Schnitzer,M.; Gupta, U. C. Soil Sci. SOC.Am. Proc. 1965, 29, 274-277.

Schnitzer, M.; Khan, S. U. Humic Substances in the Enuironment; Marcel Decker: New York, 1972; pp 37-41. Wright, J. R.; Schnitzer,M. Trans. Int. Congr. Soil Sci. 7th 1960, 2, 120-127. Dubach, P.; Metha, N. C.; Jakab, T.; Martin, F.; Roulet, N. Geochim. Cosmochim. Acta 1964, 28, 1567-1578. Holtzclaw, K. M.; Sposito, G. Soil Sci. SOC.Am. J . 1979, 43, 318-323. Van Dijk, H. In The Use of Isotopes in Soil Organic Matter Studies; report of the FAO/IAEA Technical Meeting;

1325-1336.

(28) Dzombak, D. A.; Fish, W.; Morel, F. M. M. Enuiron. Sci. Technol. 1986,20, 669-675.

Receiued for review May 1,1990. Accepted August 27, 1990. This study was supported by federal funds from the United States Department of Energy under Grant DE-FG06-89ER60845 and by funds from the United States Geological Survey ( U S G S ) under Agreement 14-08-001 -A-0410. The contents d o not necessarily reflect the views or policies of the USGS, nor does mention o f trade names or commercial products constitute an endorsement for use.

Kinetics of Bacterial Degradation of Benzylamine in a Montmorillonite Suspension Michael E. Mlllert and Martin Alexander* Institute for Comparative and Environmental Toxicology, Bradfield Hall, Cornel1 University, Ithaca, New York 14853

rn A model was developed for the biodegradation by nongrowing microbial populations of sorbed organic chemicals that are readily desorbed. The model requires inputs in the form of parameters provided by separate measurements of the adsorption isotherm under aseptic conditions and the rate of biodegradation in the absence of sorbent. The only parameter that must be provided by the data to be simulated is the fraction of carbon from the test compound that is incorporated into microbial cells or retained by the sorbent. The model was tested with benzylamine as test compound, a bacterial isolate able to mineralize the chemical, and montmorillonite as sorbent. Benzylamine mineralization by high cell densities of the bacterium was slower in the presence of montmorillonite than in the absence of the clay. Experimental curves for bacterial mineralization of benzylamine in well-dispersed suspensions of montmorillonite were reproduced by the model with standard deviations of usually less than 4%. Introduction

The degradation of organic pollutants in soils and natural waters is frequently the result of microbial activity. However, the sorption of organic compounds by constituents of soil and sediment may reduce the availability of organic molecules to microorganisms, thereby slowing the degradation. Reductions in the rate and extent of biodegradation have been attributed to the sorption of par+Presentaddress: CDM, 10 Cambridge Center, Cambridge, MA 02142. 240

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athion ( I ) , glyphosate ( 2 ) ,and atrazine and linuron (3)to soil; dodecylbenzenesulfonates ( 4 ) to soils and clays; and diquat to lake sediments (5). Information on the kinetics of biodegradation is important to predict the changes in concentration of chemicals with time as well as to understand how microorganisms transform organic compounds that are sorbed. Kinetic data allow the prediction of whether pollutants will be present at hazardous levels in the future or by the time they are transported to areas containing populations of sensitive species. Although attention has been given recently to the kinetics of biodegradation of sorbed chemicals (6-IO), the topic remains relatively unexplored. Clays are major sorbents in soils and sediments. Montmorillonite, an expanding lattice clay, has a great capacity for adsorption, especially of cationic compounds that bind reversibly to the negatively charged magnesium-aluminosilicate sheets of the clay (11). Benzylamine adsorbs to montmorillonite through its protonated amino nitrogen, whose pK, is 9.33 (12, 13). Well-dispersed montmorillonite in suspension provides mostly external clay surfaces, so that the majority of adsorbed molecules are exposed to the aqueous environment. The present study was designed to investigate the kinetics of biodegradation of benzylamine sorbed by montmorillonite in dilute suspension. The goal was to develop a theoretical model for the biodegradation of a sorbed chemical in a well-defined system containing a single species and, in future studies, apply the information to more complex natural environments. The findings should be useful in characterizing biodegradation in environments with high clay contents.

0013-936X/91/0925-0240$02.50/0

0 1991 American Chemical Society

Experimental Methods Bacterial Culture. The benzylamine-degrading bacterium was isolated from Kendaia clay loam by incubating a few grams of soil in 100 mL of an inorganic salts solution (0.8 g of KZHP04, 0.2 g of KHZP04, 0.1 g of (NH4)$04, 0.1 g of CaC1,.2H20, 0.1 g of MgS0,-7H20, and 0.01 g of FeC13.6H20per liter of doubly deionized water) amended with 50 mg of benzylamine/L. The enrichment was incubated for 2 days a t 30 "C on a rotary shaker operating at 120 rpm. After three serial transfers to fresh media, the suspension was streaked on half-strength Trypticase-soy agar, and the activity of cultures derived from single colonies was tested in sterile salts solution amended with 25 mg of benzylamine/L. The loss of benzylamine was confirmed by measurements of the change in absorption of the compound at its maximum (256 nm) using a Hitachi U-2000 UV-visible spectrophotometer. The bacterium used is a motile, Gram-negative rod, 1-2 pm in length, with polar flagella. The bacterium, one of the Pseudomonadaceae, grows in media with a maximum benzylamine concentration of 500 mg/L. When grown on glucose, the isolate retained its benzylamine-degrading activity as determined by measurements of the UV spectra of a SUSpension of the cells in a salts solution containing benzylamine as sole carbon source. Large numbers of cells were obtained by growing the cultures in the salts solution supplemented with 10 g of glucose and 25 mg of benzylamine per liter. The cells were collected by centrifugation a t 12000 g a t 5 "C for 15 min in a Sorvall RC2-B centrifuge, washed with phosphate buffer (pH 6.5-7.0), centrifuged again, and resuspended in salts solution. The inoculum size was standardized by measurements of optical density a t 550 nm. Preparation of Clay-Benzylamine Complex. Sodium-montmorillonite from Crook County, WY, was obtained from the Clay Minerals Society Source Clays Repository, Columbia, MO. The clay was further purified by gravity settling in deionized water t o remove particles larger than 1 pm, flocculation with NaC1, and centrifugation followed by dialysis to remove excess Na ions. The clay was then lyophilized. Its cation-exchange capacity was 1.29 mequiv/g. Clay suspensions were prepared aseptically by adding sterile, doubly deionized water to a weighed portion of dry clay and stirring overnight. The clay-organic complex was formed upon addition of clay suspension (10 g/L) to benzylamine (0.95-25 mg/L final concentration) dissolved in sterile one-tenth strength inorganic salts solution. The resulting suspension was allowed to equilibrate overnight a t 30 "C on a rotary shaker operating a t 120 rpm. Methylene[14C]benzylamine was added to the claybenzylamine suspension at concentrations of 4.5-14.0 pg/L to give 4000-12000 dpm/mL. Subsamples were removed and mixed with Liquiscint scintillation cocktail (National Diagnostics, Manville, NJ), and the radioactivity was determined with a Beckman LS 7500 liquid scintillation counter. The amount of benzylamine complexed with clay and other particulate matter was calculated from the difference in radioactivity measured before and after filtration of the samples through sterile 0.22-pm pore-size nylon syringe filters (MSI, Westboro, MA). The clay suspensions were light in color and did not alter the efficiency of counting radioactivity. Adsorption Measurements. Benzylamine in 10% salts solution was sterilized by passage through sterile 0.22-pm pore-size cellulosic membranes (MSI) before the addition of clay. The adsorption isotherm was measured by making duplicate tubes of sterile clay suspension (1.0 g/L) with

total benzylamine concentrations (including radiolabeled compound) ranging from 0.01 to 100 mg of benzylamine per g of clay per liter, The tubes were left overnight on a reciprocating shaker, and then the total concentration of benzylamine and the amount in solution were measured by liquid scintillation counting. Desorption rates were measured by dilution. For a 10fold dilution, 10 mL of a radiolabeled clay-benzylamine suspension was added to 90 mL of inorganic salts solution that was vigorously stirred. At regular intervals, subsamples were analyzed for total and solution-phase benzylamine by scintillation counting. Measurements were made until desorption established a new equilibrium as determined by the observation of no further change in benzylamine concentration in the solution phase. Biodegradation Measurements. Sterile benzylamine in 10% salts solutions, together with small amounts of radiolabeled compound, was added to 250-mL Erlenmeyer flasks fitted with Teflon-lined screw caps. Sterile suspensions of montmorillonite were added to half of the flasks to provide a final clay concentration of 1.0 g/L, and the flasks were equilibrated overnight a t 30 "C. One each of the clay-containing and clay-free flasks was not inoculated, while a t zero time, a portion of washed cells was added to the other flasks by sterile pipet. The final volume in each flask was 100 mL. All flasks were incubated at 30 "C on a rotary shaker operating a t 120 rpm. At regular intervals, subsamples were removed, and half were passed through sterile 0.22-pm pore-size nylon syringe filters (MSI). The unfiltered and filtered liquids were acidified to pH 2 with 0.4% HC1 and purged with a steady stream of air to remove 14C02. The radioactivity remaining in suspension then was determined by liquid scintillation counting. Chemicals, Benzylamine, 99% purity, was purchased from Aldrich Chemical Co. (Milwaukee, WI). Methylene[14C]benzylamine hydrochloride from Amersham Corp. (Arlington Heights, IL) had a specific activity of 58 mCi/mmol. All chemicals were used without further purification. Doubly deionized water was prepared by passing house-deionized water through a Milli-Q-grade water system (Millipore, Bedford, MA). Data Analysis. Nonlinear regression analyses were performed by the NLIN procedure (with METHOD= MARQUARDT) of SAS version 5 (1985) on an IBM 4381 mainframe computer. The procedure fits an equation by minimizing the sum of the squares of the deviations from the data using the Gauss-Newton method. Necessary inputs are the experimental data, the model equation, parameter names, estimated parameter values, and partial derivatives of the model with respect to the parameters. Numerical models were written in Fortran 77 and compiled and run with MacFortran (Absoft Corp., Auburn Hills, MI) on a Macintosh personal computer.

Results and Discussion Adsorption Isotherm. Montmorillonite suspensions were thoroughly dispersed to provide a maximum number of exposed clay surfaces. Measurements were then made of the isotherm for benzylamine adsorption. The isotherm was "S"-shaped, with a considerable percentage of benzylamine adsorbed in the range of concentrations measured (Figure 1). The adsorption mechanism should be reversible cation exchange, but a mathematical description of this system by a series of equilibrium cation-exchange equations (14 ) was found to be complicated with a large number of unknown parameters. However, clays have a strong preference for binding organic over inorganic cations (25). Thus, Environ. Sci. Technol., Vol. 25,

No. 2, 1991

241

80

i-

a

A

I

=a

c 40 -

a C

B

0

20 40 Solution concentration (rng benzylamine per g clay per L)

Figure 1. Adsorption isotherm at 25 "C for benzylamine in suspensions containing 1 .O g of montmorillonite/L in one-tenth strength inorganic salts solution. Total benzylamine concentrations ranged from 0.01 to 100 mg of benzylamine per g of clay per liter and included 4000 dpm/mL from added radiolabeled benzylamine. The solid line represents the best fii to eq 2: n = 1.39,K = 56.26mg/g-L, and A = 13.17 mg1g.L.

it is assumed that benzylamine adsorption is the dominant process. Any adsorption of dissolved molecules that approaches saturation with increasing concentration can be approximated by a Langmuir adsorption isotherm (16,17): y = KC/(A

+ C)

(1)

where y is the amount sorbed, C is that chemical free in solution, and K and A are constants. The experimental curve, however, was characterized by an initial concave-up portion, which is believed to result from additional binding energy from intermolecular attraction (van der Waals forces) between neighboring adsorbate molecules, as has been observed with other monofunctional organic molecules on soil minerals (18, 19). As the total concentration of benzylamine increased, the attraction became stronger as a result of the greater number and closer proximity of sorbed neighbors, leading to a higher adsorption affinity. As the surface became filled, adsorption leveled off at the maximum coverage,K. Thus, the latter part of the curve was concave-down as surface saturation became more important than the relative weak intermolecular forces. Giles et al. (20,211 included sorbate intermolecular attraction by introducing it into the Langmuir equation through a concentration-dependent activation energy term. Although this approach did not work for the data of the present study, the concept of an additional concentration dependence was added empirically by requiring the original Langmuir isotherm (eq 1) to become a function of the concentration of free chemical raised to some power greater than 1:

+ Cn)

y = KCn/(An

(2)

where n > 1 and the constant A was also raised to the nth power to keep the same units for A and C. Equation 2 reproduced the characteristic shape of the data and provided a best fit with n = 1.39, as illustrated in Figure 1. Desorption Rate. Dilution of a montmorillonite-benzylamine suspension in a 10% salts solution containing no benzylamine caused the organic chemical to desorb from the clay until a new equilibrium was established. TWO starting concentrations were tested by 10-fold dilutions of (1) 10 g of clay with 250 mg of benzylamine per liter and (2) 1.0 g of clay with 25 mg of benzylamine per liter of 242

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01 0

40

20

1

60

Time (h) Figure 2. Biodegradation of benzylamine in the absence of clay (open

symbols) and in the presence of montmorillonite (1.0g/L) suspensions (solid symbols). The flasks contained (A) 0.95 mg of benzylamindl and 3.5 X lo7 cells/mL, (B) 10 mg of benzylamine/L and 8.8 X lo7 cells/mL, and (C)25 mg of benzylamine/L and 2.5 X lo8 cells/mL. The experiment in (C) was conducted with duplicate flasks (circles and squares).

suspension. In both experiments, equilibrium was reached within 0.7-2.0 min, before the first measurement could be made. Thus, assuming first-order desorption kinetics, the desorption half-life was less than 1.0 min under these conditions. Biodegradation. To assess only the effects of sorption and mineralization, growth of the bacteria was minimized by using high cell densities relative to the low concentrations of substrate. Biodegradation was measured in homogeneous solutions and in suspensions of 1.0 g of montmorillonite/L a t benzylamine concentrations of 0.95, 10, and 25 mg of benzylamine per g of clay per liter. Mineralization was determined as the loss of radioactivity from radiolabeled benzylamine added to the medium. Radioactivity in solution did not decline in any of the sterile controls. Mineralization was confirmed by the disappearance of all UV bands in the absorption spectrum. Degradation of benzylamine at the three concentrations was slower in the presence than the absence of clay (Figure 2). The effect of clay was more pronounced a t higher benzylamine concentrations. The data from the study of benzylamine a t 25 mg/L was used to test a mechanistic theory of biodegradation under these conditions of high bacterial numbers, reversible adsorption of substrate, and fast desorption. Before further examination of biodegradation in suspensions of clay, the transformation was first examined in the absence of sorbent, but all other factors were the same. Biodegradation in the Absence of Clay. Under the experimental conditions with little or no bacterial growth because of high cell densities (i.e,, 2.5 X lo8 cells/mL) and a relatively low substrate concentration (25 mg of benzylamine/L), the kinetics of mineralization are expected to be first order (22). Biodegradation curves for benzylamine at initial concentrations of 25 and 4.4 mg/L and 2.5

X lo8 cells/mL, when plotted as the percentage of 14C remaining, were almost superimposable, with exponential decay rate constants in agreement to within 18%. Thus, the rate of substrate disappearance was proportional to the benzylamine concentration, indicating first-order kinetics: -dS/dt = kS (3)

where S is substrate concentration (measured as the fraction of radiolabel remaining since the beginning of the experiment multiplied by the substrate concentration) and k is the first-order rate constant. Integration over time yields the exponential form for substrate concentration:

S = Soe-kt (4) where So is the initial concentration. In the present study, it was not the substrate itself that was measured but the 14C remaining in the reaction mixture after the removal of 14C02. Because a portion of carbon from the degraded compound was incorporated into microbial cells, the measured counts included parent compound, organic products, and incorporated label. Simkins and Alexander (22) described bacterial uptake of radiolabel by assuming that a constant fraction, {, of the metabolized chemical was incorporated into cells: I = {(So - S ) (5) Thus, assuming that the where I is incorporated label. yield of organic products was negligible, which is reasonable since some metabolic products are more readily biodegraded than the parent compound (23), the 14C remaining during the incubation represents the sum of 14C remaining from the parent compound and 14Cin the cells: ['4C] = s + I = {So + (1 - {)S (6) Substitution of eq 4 into eq 6 results in an equation for the time dependence of radiolabel concentration. [14C] = {So + (1- {)Soe-kt (7) Biodegradation of benzylamine a t 25 mg/L in the absence of clay with a population of 2.5 X lo8 cells/mL is shown in Figure 3 (line A and associated points). The measured 14C concentrations are expressed as the corresponding benzylamine concentrations. The data were successfully fit to eq 7 as shown in Figure 3, line A to yield the parameters { = 0.0802 and k = 0.189 h-l (half-life 3.67 h). Biodegradation with Clay Adsorption. Only benzylamine in the solution phase was assumed to be available for biodegradation for the following reasons. Dissolved benzylamine was freely available since the adsorption equilibrium partitioned a significant fraction of the chemical into the solution phase at all concentrations. The system was essentially a t equilibrium with respect to adsorption and desorption, since these surface reactions were instantaneous compared to the relatively slow biodegradation rates. While biodegradation was occurring, the amount of benzylamine bound to particulate matter (clay and bacteria) increased compared to that in sterile conditions because of the presence of the bacteria. The microorganism did not appear to cause facilitated desorption and therefore was assumed not to have altered the claybenzylamine adsorption equilibrium. Thus, adsorption presumably only served to decrease the concentration of biologically available substrate. Based on the above assumptions, a model was derived for benzylamine biodegradation in suspensions of montmorillonite using only data obtained from measurements of the benzylamine-clay adsorption isotherm and the rate constant for biodegradation in the absence of clay. With

I

0 '

0

I

40 Time (h)

80

Flgure 3. Biodegradationof 25 mg of benzylamine/L in the absence (A) and presence (B) of clay. The data for clay-free suspensions from Figure 2C (shown as open circles) were fit to eq 7, and the solid line (A) represents the theoretical curve: k = 0.189 h-', { = 0.0802, and S o = 25 mg/L. The data from Figure 2C, with clay, are represented by solid circles. Curve B was generated by the numerical model detailed in the text, with isotherm parameters n = 2, K = 29.21 mg/g.L, and A = 5.68 mg/g.L; with kinetic parameters k = 0.189 h-', { = 0.16, and S o = 25 mg/g-L; and At = 0.1 h.

only substrate from the solution phase available to the bacterial cells, degradation is assumed to be first order, but the rate is proportional to the concentration in the solution phase, C: - d S / d t = kC

(8) where k is the first-order rate constant for biodegradation in the absence of clay. The total substrate concentration a t any time is the sum of substrate in the adsorbed and in the solution phases: S=q+C (9) The clay-bound chemical, q, can be estimated by the best fit of the isotherm data to the modified Langmuir equation (eq 2), which is substituted into the mass balance formula (eq 9) to yield

S = KCn/(An+ Cn) + C

(10)

The adsorption equation (eq 10) and the differential equation for biodegradation (eq 8) must be combined to solve for total substrate, S , in time. The resulting expression cannot be solved in closed form, so a numerical method was employed following the basic outline of Holm et al. (24). Since only dissolved substrate was assumed to be available for biodegradation, the loss of total substrate should equal the loss of chemical from solution: - d S / d t = - dC/dt and by substituting from eq 8

(11)

-dC/dt = kC (12) Integration of eq 1 2 over a very small time interval, At, yields (13) C(t + At) = C(t)e-kAt where C(t) is the free substrate concentration a t time t. The decrease in substrate concentration resulting from biodegradation in the interval At is defined by C(t + At) = C(t) - AC(t) with substitution from eq 13 to yield

(14)

Environ. Sci. Technol., Vol. 25, No. 2, 1991 243

AC(t) = C ( t ) ( l- e-kAt)

(15)

Finally, since A S = AC by eq 11

AS(t) = C ( t ) ( l- e-kAt) (16) which provides the basis for the numerical solution. The solution-phase concentration, C, is important for the calculation and is obtained numerically from the isotherm (eq 10) KC'/(A' C') C-S =0 (17)

+

+

by Newton's iterative method (25)with an initial estimate of C = S/2. Newton's method allows fast convergence for all values of S. The computational model proceeds from the initial substrate concentration, So,in four steps: (1)calculation of nonsorbed substrate, C; label incorporated into cells, Z (eq 5); and total label remaining, [14C]= S + I; (2) increase of time by At and computation of A S (eq 16); (3) updating of total substrate, S = S - AS; and (4)return to step 1. The procedure is repeated until the desired time interval is spanned. If At is short, the amount of substrate degraded, AS, is small, and the model system is always close to adsorption equilibrium, which is required for a valid calculation. As At decreases, the model-generated curve depicting degradation coverges to its limit for an infinitesimal time interval. For the current data, only slight improvements were observed with At less than 0.1 h. An additional assumption is implicit in the numerical model. Radiolabel remaining in the reaction medium was assumed to be the sum of residual benzylamine and the 14C incorporated into cells. At the end of an experiment, biodegradation was complete, and only incorporated 14C was assumed to remain. The sorbent was not expected to affect the final amount of 14C. However, in laboratory experiments in which degradation in the presence and absence of clay was compared, up to twice as much 14C remained in the suspensions containing clay. The additional 14Cmay represent a fraction of substrate irreversibly bound to the clay, perhaps bonded directly to aluminum oxide that is exposed at the edges of the clay particles. In application of the model, the incorporated fraction, {, successfully accounted for the remaining label, regardless of its final form. Thus, { is an empirical parameter quantifying radiolabel left after biodegradation is complete, and it must be chosen separately for each biodegradation experiment. With adsorption-isotherm parameters from eq 2, a first-order rate constant of k = 0.189 h-l for biodegradation in the absence of clay and 16% incorporation of label, the model-generated curve of remaining 14Cversus time followed the experimental data quite well. If the isotherm data were confined to the concentrations of benzylamine used in the experimental tests of biodegradation (0-25 mg of benzylamine per g of clay per liter), the best fit to the isotherm equation (eq 2) yielded another set of parameters with an optimal exponent n = 2. As shown in Figure 3 (line B and associated points), the numerical model provided the most accurate biodegradation curve (as determined by the standard deviation of the fitted curve from the data) with these parameters. The model-generated curves were quite sensitive to changes in any of the parameters. Equation 7 for biodegradation in the absence of clay was used successfully to fit curves for benzylamine biodegradation obtained with a number of benzylamine concentrations and cell densities. The resulting kinetic parameters and standard deviations of the fitted curves are given in Table I. The numerical model for biodegradation with clay adsorption simulated biodegradation curves obtained 244

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Table I. Kinetic Parameters S0,O mg/L

Bo,* lo6 cells/mL

clay, g/L