the effect of bacterial generation on the transport of radionuclide in porous media

Pergamon Ann. Nucl. Energy. Vol. 24, No. 9, pp. 721-734, 1997

0 1997 Elsevier Science Ltd. All rights reserved Printed in Great Britain.

PII: SO306-4549(97)00007-g 0306-4549/97 $17.00 + 0.00

THE EFFECT OF BACTERIAL GENERATION ON THE TRANSPORT OF RADIONUCLIDE IN POROUS MEDIA

BYOUNG SUB HAN and KUN JAI LEE

Korea Advanced Institute of Science and Technology Department of Nuclear Engineering

373-1 Kusong-Dong, Yusong-Gu Taejon, Republic of Korea 305-701

(Received 16 September, 1996)

Abstract - The purpose of this paper is to provide a methodology to develop a predictive model based on a conceptual three-phase system and to investigate the influence of bacteria and their generation on the radionuclide transport in porous media. The mass balance equations for bacteria, substrate and radionuclide were formulated. To illustrate the mode1 simply, an equilibrium condition was assumed to partition the substrate, bacteria and radionuclide concentrations between the solid soil matrix, aqueous phase and bacterial surface. From the numerical calculation of radionuclide transport in the presence of bacteria, it was found that the growth of bacteria and supplied primary substrate as a limiting or stimulating growth factor of bacteria are the most important factors of the radionuclide transport. It was also found that, depending on the transport of bacteria, the temporal and spatial distribution of the radionuclide concentration was significantly affected. The model proposed in this study will improve the evaluation of the role of the bacteria to the transport of radionuclide in groundwater systems. Furthermore, this model can be usefully utilized in analyzing the important role of colloidal particulate on the overall performance of radioactive waste safety. 0 1997 Elsevier Science Ltd. All rights reserved.

1. INTRODUCTION

Recently, radionuclide transport in deep geologic systems has become an important subject to fully estimate the safety of a radioactive waste repository. The reason is that many countries are considering deep geologic system at depths of a few tens of meter for LLW and up to more than a kilometer for HLW as one of the potential radioactive waste repositories. However, most of the radionuclide migration studies in a potential repository have been focused on the transport of dissolved forms of radionuclide through flowing groundwater and some studies start to deal with colloidal particulate facilitated radionuclide transport. However, no studies on the effect of specific particulate generation on the transport of radionuclides was carried out.

Zajic (1969) showed the presence and activity of microbes are important in the uranium biochemical cycle. Pederson (1987) confirms the existence of microbial populations in deep ground water in granitic rock and the average number of bacteria is determined to be 3x105 bacteria per ml. West et al.(l982, 1985) and West and McKinley( 1985) showed that microbial contamination of nuclear waste repositories is inevitable and cannot be precluded from even a very deep repository for high-level waste. The environment of such a repository is likely to be characterized by the limited sources of available energy and nutrients which would constrain the maximum possible bacterial activity.

The significance of colloidal particle facilitated subsurface contaminant migration has been reviewed by McCarthy and Zachara (1989). They noted that since the composition of mobilized colloidal particles is

721

122 Byoung Sub Han and Kun Jai Lee

similar to that of immobile soil particles in a groundwater reservoir, colloids can adsorb contaminants in a similar fashion and maintain them in the mobile phase. A number of field observations have demonstrated the earlier arrival of colloidal tracers than solute tracers in fractured and porous media is published. Harvey et al. (1989) found that microspheres can travel more rapidly than bromide in a column that has a secondary pore structure. Toran et al. (1988) imposed an artificial fracture within a laboratory sand column and also observed an early breakthrough of colloids compared to other conservative tracers.

Many models on the microbial processes mainly focused on the repositories for LLW and ILW (Arter et al., 1991, Colasanti et al, 1991, Mckinley and Grogan, 1991). Rao and Jessup (1983) reviewed mathematical models of microbes that describe the importance of dispersion, advection, sorption, and transformation on the movement of chemicals in soil. Corapcioglu and Haridas (1985) described the migration of bacteria in porous media as a complex combination of two mobile phases (bacteria and substrata) and one stationary phase. Homberger et al. (1992) conducted a laboratory column experiment and concluded that the model of Corapcioglu and Haridas (1985) can successfully describe some of the important characteristics of the transport of bacteria through porous media. Mills et al. (1991) gave a summary of modeling approaches developed for colloidal-sized particle transport and presented a test model for particle/metal transport in porous media. A methodology has been developed to predict maximum microbial activity levels based on nutrient and energy mass balances (McKinley et al., 1985;Grogan and McKinley, 1990). Based on the predicted microbial activity, the consequences of microbial growth for a repository can be estimated.

In natural environments, a number of relationships exist between individual microbial species, microbes and their surrounding environments. The interrelationships of the various microbes within a groundwater biological system in a deep geologic medium, however, are continuously changing, and the dynamic state is dominated. The composition of the radionuclide transport system is governed by the geochemistry and geohydraulic equilibrium state created by the associations and interactions of all individual constituents in the system. Environmental changes temporally upset the equilibrium. However, it will be reestablished, possibly in modified form, as the microbial population shifts to adjust to the new circumstances. Among the scenarios of safety assessment of the repository, the drilling of boreholes will usually introduce drilling fluids in the aquifer system. As the boreholes stand open in contact with surface waters, then surface waters with organic materials are eventually introduced into the repository. Together with the boreholes, the building of the repository may introduce external micro-organisms and organic materials to the repository. This process will change the geochemical and geohydraulic equilibrium of natural environments, and it will induce bacterial growth.

As the radionuclides are sorbed or desorbed on the bacteria and soil matrix (Pederson et al., 1991), the migration of radionuclides can be effected by the presence of bacteria themselves and their growth which supplies other carriers. If the majority of the bacteria are growing on the surface of a flowing media during the migration, the retardation phenomena will be changed too. But, previous models which do not include the effect of colloidal particulate generation during the transport possibly have either under-estimated or over- estimated the bacteria-mediated radionuclide transport. In this study, a new model based on a conceptual three phase system was developed, and the investigation of the influence of bacteria and their generation on the radionuclide transport in the porous media was conducted.

2. MATHEMATICAL MODELLING

The presence of bacteria and bacterial generation can influence the radionuclide transport through groundwater in different ways. Free living bacteria constitute mobile suspended particles which may have a radionuclide sorbing capacity higher than that of the surrounding medium. Then the radionuclide transport will be enchanced. On the other hand, if the majority of the bacteria are growing in bio-accumulations on the surface of the surrounding medium, transport of radionuclides may be retarded. The possible interactions between the substrate, bacteria and radionuclides considered in this study are illustrated in Figure 1.

Effect of bacterial generation 723

lmobile Phase Mobile Phase

~~------_-_-_-_-_-,_-_-_-----_~_-_-_,

I I

I SUPPlY

I Bacteria

generation generation

P” hn

i (adsorbed on Bacteria)

obile Carrier

Figure 1. Partition of substrate, bacteria and radionuclide within porous media

2.1 BACTERIA MIGRATION AND DEPOSITION IN POROUS MEDIA

The mass balance equation of the one-dimensional transport of bacteria suspended both in aqueous phase and captured on the solid matrix in homogeneous porous media can usually be written as

E + 43s -=-V.J+R,-R, it d

where, C is the number density of bacteria (kg/m-$ pc is the density of bacteria (kg/&), S is the mass fraction of bacteria associated with the solid matrix, 0 is the porosity, t is the time (s), J is the total mass flux of bacteria (kg/mzs), and Rp Rd are the rates of growth and decay of bacteria (kg/mJs), respectively.

The specific mass discharge of bacteria is the sum of the fluxes of hydrodynamic dispersion, diffusion, sedimentation, chemotaxis and advection,

(2)

where D is the dispersion coefficient of bacteria (m2/s), V is the pore water velocity (m/s), Vg is the sedimentation velocity (m/s), and V, is the chemotaxis velocity (m/s). The dispersion coefficient of bacteria takes into account activated random movement, diffusion, and hydraulic dispersion. If there is no flocculation, the sedimentation of bacteria is negligible due to the proximity of the density of bacteria to that of water. The contribution of chemotaxis is insignificant in the absence of a macroscopic substrate concentration gradient. Therefore, the specific mass discharge can be simplified as

J = -BDVC + eve (3)


The growth of bacteria is assumed to follow Monad’s equation (Monod, 1942). Nutrients required for bacteria growth can be present in groundwater. Since the bacterial growth in a groundwater environment is usually slow, Monad’s equation can be used. If bacteria can grow at the same rate in the deposited state as well as in the suspension, a generalized Monad’s equation can be written as

where p is the specific growth rate (I/s). The functional relationship between p and nutrient concentration was proposed by Monod. Of the same form as the Langmuir adsorption isotherm, it states that

where P,,,~ is the maximum growth rate (I/s) achievable when CF >> K; and the concentration of all other essential nutrients is unchanged (I/s), CF is the concentration of the nutrients (kg/&), and Ki is the value of the substrate concentration where the specific growth rate has half of its maximum (kg/m3) value. For low levels of substrate concentrations where CF is much smaller than Ki, and the bacterial mass concentration is approaching a steady state, the Monad’s equation can be simplified as

p = kc,

where k is the first-order generation rate (l/s).

(6)

The death of bacteria is known as a first-order irreversible reaction, the decay term in the above equation can be expressed as

R, = k,E+ k,pp (7)

where kd is the specific decay rate (l/s).

If the adsorption of bacteria on a solid surface is instantaneous and reversible,

S= K,C (8)

where KI is the equilibrium distribution coefficients for the bacteria with solid surface (d/kg).

Then the substitution of equations (3) - (8) yields

where R is the retardation coefficient of bacteria

(10)

However, evidence is accumulating that adsorption of bacteria is a rate-limited and non-equilibrium process in which the adsorption rate is limited by chemical reaction and diffusive mass kinetics. Such a non- equilibrium phenomena has been identified as an increase of the distribution coefficient with time in batch sorption experiments and as an unsymmetrical breakthrough curve in column and field studies, characterized by a slow approach to the steady-state cell densities as well as elution from tailing. The experimental results


presented by Gannon et al. (1991) show that bacteria can move through a homogenous porous medium with significant retention after the initial stage. It suggests that once the finite number of retaining sites of the porous media are saturated, bacteria can move through the porous medium without any significant retention. However, since the equilibrium isotherm cannot take into account the retention capacity, a kinetic equation that describes the attachment and detachment of bacteria in porous media may be written as

Q= k,tXZ-k,p,S (11)

where kfand k,. are the forward and reverse rate constant (d/kg s), respectively.

2.2 SUBSTRATE TRANSPORT IN POROUS MEDIA

The balance equation for substrate in a porous media can be expressed as :

%S, =, -+-=-v.(-BDVC,; +evc,)-R, a a (12)

where pb is the dry bulk density of solid (kg/d), SF is the mass fraction of adsorbed substrate per unit mass of solid, CF is the mass of the substrate per unit volume (k&d) and RF is the rate of substrate consumption by bacterial growth (kghds). The rate of substrate consumption, RF, can be expressed as

R, = pY-‘[K+p,o] (13)

where Y is the cell yield which is the mass of cells produced per unit mass of substrate removed.

For heterogeneous populations of wastewater origin, Gaudy and Gaudy (1980) determined the I’ value ranging from 0.29 to 0.68. A value of 0.5 would be a fairly good average value. Sykes et al. (1982) has determined 0.04 for a landfill study. If the adsorption of substrate on solid surface is instantaneous,

s,; = K,C, (14)

where K2 is the equilibrium distribution coefficients for the substrate with solid surface (d/kg).

Substituting equations (13) (14) into equation (12) gives

6’R, %$ = V (BDVC, - WC,) - pUy-‘QRC (15)

where Rfis the substrate retardation coefficient

R, =I+& e

2.3 RADIONUCLIDE TRANSPORT AND RETARDATION

The mass balance of radionuclide transport in the aqueous phase is formulated as:

&S, &@2 +L=-V+6’DVC, +Wc,)+Q,, +Q,, -,+X2, +pbS,) a a

(16)

(17)


where C, is the concentration of radionuclide adhered in the aqueous phase (kg/&), S, is the mass fraction of radionuclide adhered on a solid surface (kg/&), and Qac and Qas are the net rates of radionuclide sorption on free bacteria and adhered bacteria, respectively. Qoc and Qas represent the mass transfer terms in equation (17) such as

If the adsorption of radionuclide on a solid surface is instantaneous,

s, = K& (20)

where K3 is the equilibrium distribution coefficients for the radionuclide with solid surface (m).

Substituting equation (20) into (17) gives

BR, % = -V ’ (- QDVC, +W,)+Q, +Qm -~@R,Ca

where R, is the radionuclide retardation coefficient

R, cl++

The mass balance for radionuclide adhered to a mobile bacteria surface is expressed as :

aeoc -=-V.(d)-Q,,-Q,,-~~~

a

and the mass balance for radionuclide adhered to bacteria sorbed on the solid surface is given by

(21)

(22)

(23)

(24)

where S, S, are the mass fractions of radionuclide adhered to a free bacteria surface per unit mass of free bacteria and radionuclide adhered to sorbed bacteria, respectively, while Qcs is the net rate of radionuclide sorbed on adhered bacteria on a solid surface.

Q,, = k,tbC - k,p,o,S (25)

We assumed a constant flow velocity and that the bacteria moves with a velocity equal to that of the aqueous phase. Furthermore, we assume that the adsorption of the radionuclide on a carrier surface is instantaneous and the adsorption sites on mobile and immobile carriers are in equilibrium with the aqueous phase. Justification of this equilibrium assumption was investigated by Jennings and Kirkner (1984).

CT = K4Cs (26) a* = K5Cs (27)

where K4, KS are the equilibrium distribution coefficients for the radionuclide with mobile and immobile carriers, respectively.

With the substitution of equations (18), (19) into equations (23) (24) and linear adsorption isotherms

Effect of bacterial generation

equations (26), (27) into equation (21) with an assumption of constant flow velocity, V yields,

721

R ao : (K,+PAW$ & 1 DV’C, -(l+ K,C)VX, -il(l+ K,C)R,C,

’ a l+K,C ’ Zf l+K,C + K, (DVC . VC, - C, . VJ/B) t

(28)

where Rt is the new retardation factor of radionuclide

R = Ro + KC +- PJ,WI~ I l+K,C

The total retardation coefficient in equation (29) reduces to the conventional retardation coefftcient, R,,

when the carrier concentration approaches zero.

Equations (9), (15) and (28) constitute the set of governing equations of bacteria mediated radionuclide transport with three unknowns. However, another level of simplification is achieved if equations (9) and (IO) are substituted into equation (27). Then, the rearrangement yields

R rfi,+(P~K1(K5-K4)/~)C K= I DV*C, - (1 + K,C)V VC, - A(1 + K,C)R,C,

’ a l+K,C ’ tz l+K,C + K,(DVCX, + RC’,C(p-k,))

(31)

The second term of the LHS and the last term of the RHS has been derived from the temporal and spatial variations of carrier concentrations, respectively.

The retardation coefficient can be rearranged as

I P~K, + p,K,‘K,C R, =l+; l+K,C (32)

where the term K,’ is the distribution coefficient of the bacteria between the aqueous phase and the solid

matrix, i.e., K,’ = K,p, /pb . The term K,‘K, in equation (32) represents the retardation of the radionuclide by the bacteria accumulation. If the bacteria has the same distribution coefficient of sorption by a solid matrix

as that of the radionuclide, then Rt would be the same as the conventional retardation coefficient R as in equation (22). If there is no carrier, i.e., without the presence of bacteria, equation (31) is reduced to the conventional radionuclide transport equation with the conventional retardation coefficient R. If there is no bacteria, equation (3 1) reduces to the conventional advection/dispersion equation with the conventional retardation coefficient. If K3 >>Kl: as is the general case of the transport of colloid particles, the effect of immobile bacteria on the transport will be insignificant and Rt will be quite smaller than R. Equation (32) clearly shows that radionuclide transport has been retarded by a factor of (D-K&)-l due to the presence of bacteria. In the case of significantly large radionuclide adsorption on the surface of the bacteria (K3 <<KI ‘). the retardation will be enchanced.


3. NUMERICAL SOLUTIONS FOR MODEL EQUATIONS

The complete set of governing equations describing the substrate-bacteria mediated radionuclide with the equilibrium conditions can be expressed in a one-dimensional form with an assumption of constant flow velocity and the same flow velocity and dispersion coefftcients as groundwater

(33)

(35)

Equations (33)-(34) constitute the complete set of governing equations with two unknowns CF and C,. It seems that determining the analytical solution of the complete set of partial differential equations would be impossible. However, in constant substrate conditions, an analytical solution of bacteria transport equation subjected to the following boundary and initial conditions,

C(x,t) = co C(x,t) = 0

C(x,t) = 0

&(x,1) = c;

at x=0

at t=O

atx=oO

(36.a)

(36.b)

(36.~)

(36.d)

can be obtained as follows

C=~exp(kx)Jexp(-a(,~-lz,i)enp(-<* - v2x2/4<*)d< k

(37)

Rx2 3 a=-4Dr2 p P=P~,,

c; K, + C; ’

C’i is the constant concentration of

substrate.

In a condition of constant bacterial concentration, the analytical solution of the transport of radionuclide subject to boundary and initial conditions

can be obtained as follows

Co(x,f)= C,“e-” at x=0 (38.a)

C,(x,t) = 0 at t=O (38.b)

C,(x.t)=O atx=oO (38.~)

Cix,t) = co (38.d)

Co = $exp( m - A(1 + K,CO)r)jexp(-<* - v2x2/4<*)d< k

(39)


0.5 D

, D’= l+K,CO ’

Co is the constant concentration of bacteria.

Numerical solutions of equations (33)-(34) are obtained by a fully implicit finite difference method. Since equations (33) and (34) can be obtained independently of equation (35), solutions of C, have been obtained by using the solutions of CF and C. As seen in Figure 2, the numerical results of the fully implicit FDM show an excellent match with the analytical solutions given by equations (37)-(39).

2.a) Equation (37)

-m; 2.b) Equation (39)

Figure 2. Comparison of analytical solution (symbol) with numerical solution (line)

Following the partial verification of the numerical solutions, numerical simulations of equations (33)-(35) have been employed to simulate the transport of radionuclide in the presence of bacterial growth with boundary and initial conditions (36.a)-(36.c), (38.a)-(38.c) and

C,.(x,t) = CF. C,(x,t)=O CF(XJ) = 0

at x=0

at t=O

at x=00

(43.a)

(43.b)

(43.c)

4. RESULTS OF THE MODEL

The proposed bacteria-mediated radionuclide transport model has been applied to simulate the migration of radionuclide through porous media. In this study, the effect of bacterial growth and parameters that governs bacterial growth in waste repository conditions are investigated. The effects of other parameters are relatively well studied by many authors. Based on literature study on the bacterial behavior with surrounding environments, numerical analyses are conducted. Table 1 shows the values of parameters we used in numerical illustrations.

Parameter

e PC

Pb D V

Pmax Ki kd

Tablel. Reference parameters

Value Parameter Value 0.1 Y 0.1

1.7 g/cm3 a lop5 I/yr

1 .OO 1 g/cm3 Co 0.01 kgh 10-j mz/yr

1 m/yr IOJ I/yr

I 0m4 g/cm3 10 I/yr

C#

KI K2

K3 K47 KS

.J

0.1 kg/m5 0.1 m-r/kg

0.00 I mj/kg

0.01 mj/kg 10 m-‘/kg


In this study, the initial amount of bacteria represents the bacteria introduced by human activity or indigenous population at the starting time of the numerical illustration. Pedersen (1993) reviewed the characteristics of the deep subterrain biosphere and reported a range of from 103 up to 108 bacteria/ml bacteria are present in groundwater or sediment. Ghiorse and Wilson (1988) compiled the total numbers of bacteria from many different, mostly shallow, pristine groundwater sites and reported a range from 103 up 108 microbes/ml. In this study, the number of bacteria in groundwater at repository conditions are 108 bucteridcm3. It was conservatively assumed that the bacteria would have an average weight of lo-16 kg. This gave the bacterial concentration at 10-2 kg/m3.

The distribution coefficients for the radionuclides on bacteria have been measured by many experiments. In this study, we use 10 m3/kg. The equilibrium distribution coefficients for the bacteria with solid surface represents the correlation between the numbers of attached and free bacteria. But, there is no positive correlation. Instead, a negative correlation can be anticipated, because the higher the tendency of a bacterial population to attach, the lesser percentage of the population will be unattached. In this study, we choose the value of 0.1 m3/kg for the equilibrium distribution coefficients for the bacteria with a solid surface. This gave about 100 times (density of bacteria x the equilibrium distribution coefficients for the bacteria with solid surface) more attached bacterial population.

Gaudy et al. (1971) reported the value of Ki and pmar for the heterogeneous microbial population of sewage-origin growing on glucose as 1 O-4 g/ml and 0.38 hr-1, respectively. Gaudy and Gaudy (I 980) noted that the smaller the value of Ki, the more closely Monad’s equation will be able to reproduce the curve of growth.

There are considerable differences in the values of kd in the literature. The value of kd for heterogeneous microbial populations in municipal sewage varies from 0.025 to 0.098 hr1 (Gaudy and Gaudy, 1980). But, deep groundwater bacteria is known to be more resistant to environmental changes and might survive longer (l-6 months) than sewage bacteria. In this study, we use the value of 10-4 g/ml, 103 yr1 and 10 yr-1 for Ki, ,umer and kd, respectively.

For heterogeneous populations of waste water from various carbon sources, the value of Y ranges from 0.29-0.68 (Gaudy and Gaudy, 1980). Sykes et al. (1982) has determined 0.04 for a landfill study. We use 0.1 as a central value of various studies. For the other parameters, we use the values : B-0.1, pc=l .7 g/cm37 pb=l.OOl g/cm33 D=5 m2/yr, v=l m/yr, K2=0.001 m3/kg, K3=0.01 m3/kg.

(a) (W Figure 3. Variations of substrate and bacterial concentration (with and without bacterial generation).

(a) temporal; x = 1 m, (b) spatial; t = 50yr

Figure 3 shows the temporal and spatial variations of substrate and bacteria in the aqueous phase. As seen in these figures, with reference parameters, the presence of bacterial generation increases the bacterial concentration and decreases substrate concentration by consumption. As the reference retardation factor of substrate (~10) is smaller than that of bacteria (&lOOO), the approach time of substrate at a specified distance is shorter than that of bacteria (Figure 3.a). The early decrease of substrate concentration in figure 3.b (bacterial growth case) can be interpreted as the effect of substrate consumption by bacteria which move slowly than substrate.


(a) 09 Figure 4. Spatial variations of bacteria (a) and radionuclide (b) at t=SOyr and sensitivity to

bacterial generation rate

rmllyr

(a) (b)

Figure 5. Temporal variations of bacteria (a) and radionuclide (b) at x=1 m and sensitivity to bacterial generation rate

Figure 4 and 5 present the spatial and temporal variation of bacteria and radionuclide concentration and their sensitivity to the bacterial generation rate. In these figures, the early or late migration of bacteria and radionuclide can be explained with the retardation factor. Although, the retardation factors of bacteria (equation 10) and radionuclide (equation 35) have no direct correlation with the bacterial generation rate, these values have indirectly corelated with bacterial growth and decay rates. The larger the value of net growth of the bacteria (growth-decay), the higher the concentration of bacteria within the porous media. Then the bacteria retardation factor that has a bacterial concentration term in the denominator of equation (IO) gets larger values. But, the total retardation factor (equation 35) needs some parametric interpretation. The difference between equation (21) and (35) is the retardation induced by bacteria. If we subtract equation (2 I) from (35), retardation induced by carriers can be introduced as

1 (P~K,K, - RJW$ R’ = R, - R, = i

l+K,C (44)

If the radionuclide sorption parameter on the surface of free and attached carriers has the same value as in the reference values, the retardation or acceleration can be decided by the values of KI and K3. In this study, as KI > K3, the increase of the retardation of the radionuclide was observed as the value of bacterial concentration increases.

Byoung Sub Han and Kun Jai Lee 732

mm)

(a) astance

W Figure 6. Spatial variations of bacteria (a) and total mobile radionuclide (b) at t=lOOyr

and sensitivity to Kl

r a- F ,,' ;.' c lb70 -K;=lO I(;,,/

_' /

-mbacl&!zcesml ,:’

K, =O.l $ : ’

---.--Kl= 5 -K,=lO 5

Occaa1~ ’ ’ / 0 XI 40 Bo La rm 01 1 10 rm

TWYO nlme(yr)

(4 00 Figure 7. Temporal variations of bacteria (a) and total mobile radionuclide (b) at x=10 m

and sensitivity to Kl

Figure 6 and 7 present the spatial and temporal variation of concentrations of bacteria and total mobile radionuclide which can be defined as the sum of radionuclides in the aqueous phase and the adsorbed phase in bacteria (C&l+Kd)) and their sensitivity to the equilibrium distribution coefficients for bacteria with solid surface (KI). If the other parameters in equation (44) are constant, the change of K1 governs the retardation process. As seen in figure 6.a and 7.a, the larger the tendency of bacterial attachment, the lower the possibility of bacterial loss by diffusion and advection. Thus the generation of bacteria which is in proportion to the bacterial concentration increases.

5. CONCLUSIONS

In this study, we present a mathematical model to describe the transport of radionuclide in groundwater in the presence of bacterial activity. There is much evidence that shows the existence of bacteria and their movement through the subsurface, thereby providing a mobile solid phase for radionuclide migration. As radionuclide interact with bacteria, their mobility can be significantly reduced in the presence of such carriers. Governing equations of such interactions were obtained by modeling the system as a three-phase porous medium with two solid phases (mobile bacteria and stationary soil matrix). The model consists of mass balance equations for bacteria, substrate and radionuclide. For a simple illustration of the model, equilibrium isotherms are assumed to partition the substrate, bacteria and radionuclide concentrations between the solid soil matrix, aqueous phase and bacterial surface. This simplifies the mathematical complexity of the model, resulting in modified retardation coefficients reflecting the presence of a mobile carrier. Following the benchmarking of the numerical solution with analytical solutions of ideal cases, numerical illustrations were conducted for one-dimensional porous.


It has been shown that the presence of bacteria and their growth alter the transport of radionuclide transport in groundwater depending on the state of bacterial activity. The degree of acceleration or retardation was determined by the conditions of the substrate, bacteria and radionuclide transport processes.

In this study, we illustrate the most simple case of substrate-bacteria-mediated radionuclide transport. However, there are many processes in the bacteria-mediated radionuclide transport in groundwater such as secondary utilization of nutrients, bacterial production of complexing agents, and bio-film development. These processes need further experimental and modeling study.

The model proposed in this study could help to evaluate the role of bacterial activity in groundwater systems. Furthermore, this model would be useful in analyzing the importance of colloidal particulate on the overall performance of radwaste repository’ safety.

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