Practice of Mass Transport Model Application for Biogeochemical Redox Process in Aquifer

Abstract

Biogeochemical reduction processes are active in alluvial aquifers, because organic carbon which is indispensable for bacteria growth is abundant. As a result of reduction process, significant changes of groundwater quality take place; denitrification, reduction of manganese dioxide, iron-hydroxide, sulfate, arsenate, and methane are well known as reduction processes in an anaerobic groundwater condition. Therefore, the prediction of redox environment in an aquifer is a key subject in order to understand how the groundwater quality is affected. If the mechanism of groundwater quality formation in aquifer scale is systematically understood, impacts caused by accidents or illegal dumping can be predicted, and subsequently, an appropriate management of aquifer will be established. In the present paper, quantitative discussions are made by the numerical simulations applied for the one-dimensional column experiment and two-dimensional fresh-salt water mixing zone. Recommendation and the future subject are presented through the results of two numerical simulations.

1. Introduction

Groundwater quality is strongly affected by aquifer matrix and varies in space and time. Dissolution from base rocks and minerals, ion exchange, adsorption/desorption, decay and biological degradation are the major processes which should be taken into consideration when the characteristics of groundwater quality are discussed. Hydrological and hydrogeochemical factors are needed to be simultaneously considered because the chemical species are affected by the groundwater flow also. The application of the combined mass transport model with groundwater flow is therefore useful for analyzing the above processes quantitatively.

The bacteria mediated geobiochemical processes are significant amongst above processes, specifically in alluvial aquifers where human activity is intensive and impact of various waste is frequent; nitrate pollution is serious for drinking water. Dissolved manganese and iron released in the anaerobic aquifer are often the causes of unpleasant taste for drinking. Furthermore, sulfate and arsenite detected in anaerobic environment are both harmful for living beings [1, 2]. Compared to the remarkable applications of the bacteria technology in the field of medical treatment and food industry, its application to the field scale geochemical study is yet limited. As the authors view, the papers by Kinzelbach and Schäfer [2], Lensing et al. [3], and Hunter et al. [4] have contributed to widen the modeling approaches to bacteria mediated processes taking place in aquifers. Their researches based on the hydrogeological coupled with bacteria mediated processes seem to be useful for better understandings of groundwater chemistry.

The present paper introduces two results of the numerical simulation. The one-dimensional numerical simulation for the column experiment is shown; the effect of the saw dust (organic carbon) as the electron donor for the enhancement to activate sequential reduction processes is discussed. The good agreement has been demonstrated through the detail comparisons with the measured concentration changes of the reduced species [5].

The other result demonstrates qualitative study of the reducing process for the fresh-salt water lens in a sand spit aquifer. The numerical simulations for the two-dimensional unsaturated-saturated groundwater flow and the sequential reducing processes are presented. The numerical solution presents the two-dimensional spatial distributions of several geochemical species. Moreover, the distributions of all species which are considered in the redox modeling are presented along a selected bore hole. The result shows that the modeling approach is also useful to understand the mechanism of groundwater quality in fresh and salt water regions [6].

2. Model Formulation

2.1. Conceptual Model

The developed model describes the simulation of solute transport and biological processes in porous media by considering the interactions between electron acceptors (O₂, NO₃₋, Mn²⁺, Fe²⁺, and SO₄₂₋) and electron donor (CH₂O). The model also describes the release of metabolic products (Mn²⁺, Fe²⁺, and HS⁻). Figure 1 shows the chemical species considered in the redox model and species exchange between different phases. The saturated porous media volume of each element is divided into three phases, the water or liquid as a mobile phase, the bacterial or biofilm as a biophase, and the remainder materials as a matrix phase. The biophase is assumed to include all bacterial metabolism processes. The organic matter is assumed to be present in matrix phase and it can dissolve into the mobile phase. Exchange processes are considered between the different model phases: (i) the mobile phase and the biophase, (ii) the mobile phase and the matrix phase, and (iii) the biophase and the matrix phase.

Figure 1 

Chemical species considered in the redox model and species exchange between different phases.

The model also explains the bacterial growth using double Monod kinetic equation, which is applied to defined four functional bacterial groups (𝑋₁, 𝑋₂, 𝑋₃, and 𝑋₄). The bacterial group 𝑋₁ uses oxygen under aerobic conditions and nitrate under anaerobic conditions as electron acceptors. Under anaerobic conditions bacterial groups 𝑋₂, 𝑋₃, and 𝑋₄ use MnO₂, Fe(OH)₃, and sulfate as electron acceptors, respectively.

2.2. Flow and Transport

This section describes mathematical equations which govern the two-dimensional water flow and transport of solute in porous media. For the one-dimensional column experiment, the flow rate can be constant if the hydraulic head at the inlet and outlet is maintained and clogging by bacteria growth is negligible [5]. On the other hand, the governing equations for the two-dimensional groundwater flow can be written as [6]𝐶_𝑤+𝛼_𝑜𝑆𝜕𝜕ℎ𝑡=−𝜕𝜕𝑥𝑢−𝜕𝜕𝑣𝑦,(1) where 𝐶_𝑤 is specific moisture capacity, 𝛼_𝑜 is switch number which takes to 0 for unsaturated condition or 1 for saturated condition, 𝑆 is specific storage coefficient, ℎ is pressure head, 𝑡 is time, 𝑢 and 𝑣 are Darcy’s velocities in the 𝑥 and 𝑦 directions, respectively𝑢=−𝑘𝜕ℎ𝑣=−𝑘𝜕ℎ𝜕𝑥,𝜕𝑦+𝜌𝜌_𝑓,(2) where 𝑘 is hydraulic conductivity, 𝜌 and 𝜌_𝑓 are salt water density and fresh water density, respectively.

The fundamental two-dimensional partial differential equation governing the advective-dispersive solute transport of contaminants considering reaction part in the porous media can be written as [6]𝑑𝐶_𝑖𝑑𝑡=𝜕𝜕𝐶𝑡^𝑖+𝑢^𝜕𝐶_𝑖𝜕𝑥+𝑣^𝜕𝐶_𝑖=1𝜕𝑦𝜃_mob𝜕𝜕𝑥𝜃^mob𝐷_𝑥𝑥𝜕𝐶_𝑖𝜕𝑥+𝜃^mob𝐷_𝑥𝑦𝜕𝐶_𝑖+1𝜕𝑦𝜃_mob𝜕𝜕𝑦𝜃^mob𝐷_𝑦𝑦𝜕𝐶_𝑖𝜕𝑦+𝜃^mob𝐷_𝑦𝑥𝜕𝐶_𝑖𝜕𝑥+²_𝑗=1𝑆_𝑖,𝑗,(3) where 𝐶_𝑖 is dissolved concentration of species 𝑖 in the mobile phase, 𝜃_mob is the water content, 𝑆_𝑖,𝑗(𝑗=1,2) is chemical or biochemical reaction term; for 𝑗=1 or 2, the dissolved species are exchanged with biophase or matrix phase explained below.

The dispersion coefficient tensor 𝐷, dependent on the real pore velocities, has the following components: 𝐷_𝑥𝑥=𝛼^𝐿𝑢^2𝑉+𝛼^𝑇𝑣^2𝑉+𝜏×𝐷^𝑀𝐷_𝑦𝑦,=𝛼^𝑇𝑢^2𝑉+𝛼^𝐿𝑣^2𝑉+𝜏×𝐷^𝑀𝐷_𝑥𝑦,=𝐷_𝑦𝑥=𝛼^𝐿−𝛼_𝑇𝑢^𝑣^𝑉,(4) where 𝛼_𝐿 and 𝛼_𝑇 are microscopic dispersion lengths for longitudinal and transverse directions, 𝑢^ and 𝑣^ are components of real pore velocities calculated by 𝑢^=𝑢/𝜃_mob and 𝑣^=𝑣/𝜃_mob, 𝑉 is absolute velocity calculated by 𝑉=√𝑢^2+𝑣^2, 𝜏 is tortuosity, and 𝐷_𝑀 is molecular diffusion coefficient.

2.3. Exchange Processes

The source-sink term 𝑆_𝑖,𝑗 describes solute exchange between model phases. The solute exchange driving force is the difference between the concentrations of the species in different phases. The following equations describe the linear solute exchange when boundary film theory between the phases is applicable.

The exchange of solute between the mobile phase and the biophase 𝑆_𝑖,1 is expressed as𝜃_mob𝑆_𝑖,1=𝛼(1−𝑛)𝑎⋅𝜃^mob𝜃_bio√𝐷_𝐿𝜃_bio+𝜃_mob𝐶_bio=𝛼_−𝐶_mob𝜃_mob𝐶_bio−𝐶_mob.(5)

The exchange of solute between the mobile phase and the matrix phase 𝑆_𝑖,2 is expressed as𝜃_mob𝑆_𝑖,2=𝛽(1−𝑛)𝑎⋅𝜃^mob𝜃_mat√𝐷_𝐿𝜃_mat+𝜃_mob𝐶_mat=𝛽_−𝐶_mob𝜃_mob𝐶_mat−𝐶_mob,(6) where 𝐶_bio and 𝐶_mat are concentrations of solute in the biophase and in the matrix phase, respectively, 𝛼 and 𝛽 are exchange coefficients between the phases, 𝛼^ and 𝛽^ are simplified exchange coefficients, 𝑛 is porosity, 𝑎 is diameter of uniform soil particle and 𝜃_bio, and 𝜃_mat are specific volume of bio and matrix phases, respectively.

The low solubility of solid electron acceptors like Fe(OH)₃ and MnO₂ at near neutral pH values restricts their dissolution to values much too low. This assumption allows for the often observed microbial growth under iron and manganese reducing condition [3, 7]. It is assumed that the MnO₂ and Fe(OH)₃ reducers use extracellular complex agent to access the solid electron acceptors [8]. Therefore, the mass exchange rate of MnO₂ or Fe(OH)₃ into the biophase is expressed by 𝑆_3,bio𝜃_bio𝑆_3,bio=𝛾(1−𝑛)𝑎⋅𝜃^bio𝜃_mat√𝐷_𝐿𝜃_bio+𝜃_mat𝐶_mat=𝛾_−𝐶_bio𝜃_bio𝐶_mat−𝐶_bio,(7) where 𝛾 is exchange coefficient between the matrix and biophases and 𝛾^ is its simplified exchange coefficient.

2.4. Biochemical Reactions

The growth of bacteria is considered only in the biophase. The growth of different groups of bacteria in the biophase is formulated by double Monod kinetic equation [9]𝜕𝑋𝜕𝑡=𝑣^max⋅IT_𝑖⋅𝐶¹𝐾₁+𝐶₁⋅𝐶²𝐾₂+𝐶₂𝑋,(8) where 𝑣_max is maximum growth rate. The bacterial growth is limited by the inhibition term represented by IT_𝑖=IC_𝑖/(IC_𝑖+𝐶_𝑖) for the inhibiting species 𝑖, 𝐶_𝑖 is its concentration and IC_𝑖 the inhibition constant, 𝐶₁ is electron donor concentration in biophase, 𝐶₂ is electron acceptor concentration in biophases, 𝐾₁ is electron donor half-saturation constant, 𝐾₂ is electron acceptor half-saturation, and 𝑋 is bacteria concentration.

The decay of bacterial population is described by the first order rate equation𝜕𝑋𝜕𝑡=−𝑣^dec𝑋,(9) where 𝑣_dec is constant decay rate. The net growth of bacterial population is the summation of (8) and (9).

The growth of bacteria population can increase based on one or more respirative pathways. For example, most of aerobic bacteria is facultative in an anaerobic environment and can also grow under denitrifying condition. The switching between aerobic and anaerobic conditions of bacteria groups depends on the oxygen concentration in their nearby environment, and can be written as [10]𝐹O₂_bio=0.5−1𝜋tan⁻¹O₂_bio−O₂_thres×𝑓_s1,(10) where 𝐹([O₂]_bio) is a switching function, [O₂]_bio is concentration of oxygen O₂ in the biophase, [𝑂₂]_thres is threshold concentration of oxygen O₂, and 𝑓_s1 is slope of the switch function.

Bacterial activity in the porous media is mainly driven by the net decomposition of available organic carbon, which provides the energy to the bacteria [4]. Also, it is known that the bacteria uses only dissolved organic carbon chemically defined as CH₂O and the utilizable portion of dead bacteria as electron donors [3]. The model is extended to include the simulation of organic carbon released from matrix phase, the initial concentration of releasable organic carbon from matrix phase can be written as follows:CH₂O^Omat=𝑅𝑀𝑛^CH2O,(11) where 𝑅 is the organic carbon coefficient and 𝑀_CH2O is total mass of carbon in matrix phase.

As a result of bacteria growth, metabolic products are released. They are related to bacterial growth via a production factor as [7]𝜕𝑃_bio𝜕𝑡=𝑃1_𝑃𝜕𝑋𝜕𝑡−𝛼^𝑃_bio𝑃_𝑝−𝑃_mob,=𝑆𝑇𝑌^𝑂𝐶1−𝑌_𝑂𝐶,(12) where 𝑃_mob and 𝑃_bio are the concentration of a metabolic product in mobile phase and biophase, 𝑃_𝑃 is the production factor, 𝑆𝑇 is the stoichiometric coefficient (𝑂𝐶/𝐶), 𝑌_𝑂𝐶 is the yield coefficient.

Based on (12), a typical equation representing the total change of iron in the biophase can be expressed by𝜕𝜕𝑡=𝜃^bio1Fe²⁺_bio𝑃_Fe2+𝜕𝜃^bio𝑋₃𝜕𝑡_grow−𝛼^𝜃_bioFe²⁺_bio−Fe²⁺_mob.(13)

3. Application to One-Dimensional: A Column Experiment

3.1. Column Experiment

The column experiment was carried out using transparent resin columns of 45 cm height and 10 cm internal diameter. The wire mesh (0.1 mm) and the filter paper (ADVANTEC no. 6) were placed at the bottom of each column. The top and the bottom of the column were closed using transparent resin plates with tubes (20 mm diameter) inserted for the flow inlet and outlet.

The columns were packed up to a height of 30 cm with soil and sawdust. The first column was packed with 100% soil, while the second column was packed with a mixture of sawdust (50%) and soil (50%). The secondary treated wastewater was constantly supplied at the top of the two columns for 56 days and the average temperature was measured at 22°C. The secondary treated municipal wastewater was supplied for the experimental period from Wajiro Wastewater Treatment Plant of Fukuoka City, Japan. The packed soil was collected from actual paddy field and sawdust was collected from local wood factory. Table 1 [11] shows the chemical concentration of the injection wastewater and the chemical components of paddy soil and sawdust.

Table 1 

Chemical components of materials.

The water level of waste water was maintained at 60 cm depth above the soil sawdust surface throughout the experiment by using the influent tank installed above the columns. The average flow rate was 0.009 cm³/s and 0.011 cm³/s for soil and soil-sawdust columns, respectively.

Influent and effluent samples were collected daily in glass bottles and then chemical composition was analyzed. The cation concentrations were measured by the atomic absorption spectroscopy (ParkinElmar Japan, 3100 model), while anion concentrations were measured by the ion chromatography (Yoko Analytical Systems model). Electric conductivity, oxidation reduction potential, dissolved oxygen and pH were measured by electrode (DKK-TOA). Hydraulic heads were measured using piezometers located at 0, 5, 10, 20, and 30 cm below the sand-sawdust top surface of the each column. The values of piezometers were used for the calculation of hydraulic conductivity. The hydraulic conductivity of the columns was calculated from flux and water head by using Darcy’s law. Flux was measured by the discharge rate of effluent from the outlet.

3.2. Model Setup

The developed model was applied to the one-dimensional column experiment to describes the interactions between O₂, NO₃₋, Mn²⁺, Fe²⁺, and SO₄₂₋ as electron acceptors and CH₂O as electron donor and bacterial growth along of the column. The organic matter source used in the present experiment is sawdust which presents in matrix. The oxidation of organic carbon is paralleled by a sequence of reduction reaction which is presented in Table 2 [11]. The principal pathways of electron acceptors are aerobic respiration, denitrification, manganese reduction, iron reduction, and sulfate reduction. The model defines five redox reactions mediated by four different bacterial groups 𝑋₁, 𝑋₂, 𝑋₃, and 𝑋₄. Bacterial group 𝑋₁ uses oxygen under aerobic conditions and nitrate under anaerobic conditions as electron acceptor. Under anaerobic conditions bacterial groups 𝑋₂, 𝑋₃, and 𝑋₄ use MnO₂, Fe(OH)₃, and sulfate as an electron acceptor, respectively.

Table 2 

Sequence of reduction reaction.

The one-dimensional advection dispersion differential equation with various reaction terms is solved numerically using the method of characteristics. The reaction part represented by (5) and (6) is calculated by the concentration difference obtained at the previous time step.

The model of solute transport with biological processes is highly complex, as it involves a large number of parameters. To determine the parameters values, sensitivity analysis is needed. The sensitivity analysis adopted in this application is the adjustment of parameters by increasing and decreasing their base values by one order of magnitude.

The discretization condition, hydraulic parameters, and exchange coefficients are presented in Table 3. The discretization is chosen such as it meets the numerical stability criteria (Courant number = 𝑢^×Δ𝑡/Δ𝑥≤1, grid number = Δ𝑥/𝛼_𝐿≤2).

Table 3 

Discretization, hydraulic parameters, and exchange coefficients.

The bacterial growth in the model is assumed to follow the Monod-type kinetics [9]. The maximum growth rate, yield coefficient, inhibition constant and decay rate of all bacterial groups are presented in Table 4. The decay rate is set to 15% of the maximum growth rate. The yield coefficients of the different bacterial groups were chosen according to the energy gain of the mediated redox reaction [3]. Therefore, the yield coefficient is highest for the aerobic bacteria and lower for the anaerobic bacteria.

Table 4 

Biogeochemical parameters used for the two-dimensional redox model.

3.3. Results and Discussion

Applicability of the developed model was checked by comparing the simulated results with the experimental data. The model simulated the two columns using the different values of parameter listed in Tables 3 and 4. The simulated concentrations of the electron acceptors such as oxygen, nitrate, manganese, iron, and sulfate, while the electron donor such as organic carbon agree well with the measured concentrations at the depth of 30 cm as shown in Figures 2 to 7.

Figure 2 

Measured and simulated O2 concentrations for two columns.

The experimental results show that the column packed with soil alone having the low permeability (1.45×10⁻³ cm/sec) yielded reduction in electron acceptors, while the column packed with a mixture of 50% soil and 50% sawdust of relatively higher permeability (7.39×10⁻² cm/sec) showed higher reduction in electron acceptors. The effect of sawdust is more visible in the enhancement of bacterial groups 𝑋₃ and 𝑋₄, which reduced the Fe(OH)₃ and sulfate concentration.

Figure 2 shows the oxygen concentration as a function of time. The observed and simulated values show that oxygen was decreased very rapidly, which is due to the early start of aerobic and denitrifying bacteria group 𝑋₁ to consume oxygen as electron acceptor and organic carbon as electron donor. The rapid approach of steady state of oxygen concentration was reasonably reproduced with the model. The important parameter affecting the oxygen and nitrate concentration was the maximum growth rate of aerobic and denitrifying bacteria.

The nitrate concentration as a function of time is shown in Figure 3. The reduction of nitrate ion with time was simulated using the present model. The numerical solution shows comparable trend with the experiments. It may be apparent that the group of aerobic and denitrifying bacteria 𝑋₁ in the model starts to oxides the organic carbon with nitrate as an electron acceptor when oxygen concentration becomes limited. Switching between aerobic and anaerobic metabolism of bacteria 𝑋₁ was considered to take place at the oxygen threshold concentration at 0.015 mmol/L. The observed and simulated data depict that the nitrate concentration from the soil-sawdust column is little higher than that of soil column, especially during the first twenty days and then after that no significant deference is seen between the two columns. The higher nitrate concentration from the soil-sawdust column would be resulted by high ammonium release from sawdust. Besides, higher water flow rate in the soil-sawdust column may be related, as Guerra et al. [12] demonstrated that the increases in flow velocity rate decreases the detention time necessary for denitrification.

Figure 3 

Measured and simulated NO3− concentrations for two columns.

Figure 4 shows manganese concentration as a function of time. The oxidation of organic carbon with MnO₂ as electron acceptor is catalyzed by anaerobic bacteria 𝑋₂ in the model. As a result, Mn²⁺ ion is released in mobile phase. The overall manganese reduction rate can be directly derived from the observed increase in dissolved Mn²⁺ if the cation exchange with other cations is negligible. The exchange coefficient 𝛾^ in (7) for the matrix phase into biophase is found to be very small (0.00005/day), indicating that manganese reduction is limited by the availability of MnO₂. The observed and simulated data show that the Mn²⁺ concentration of soil-sawdust column is a little higher than that of soil column during the first ten days then the Mn²⁺ concentration of soil-sawdust column becomes lower than that of soil column, which is probably due to the faster reduction by enhanced organic carbon in soil-sawdust column.

Figure 4 

Measured and simulated Mn2+ concentrations for two columns.

Figure 5 shows the iron concentration as a function of time. Under anaerobic conditions bacterial group 𝑋₃ oxides the organic carbon with matrix Fe(OH)₃ as an electron acceptor. The bacteria group 𝑋₃ reduces Fe(OH)₃ and subsequently Fe²⁺ is released. The most important model parameter was the exchange coefficient between matrix Fe(OH)₃ and microbially available Fe(OH)₃ in the biophase. The observed and simulated data show that the Fe²⁺ concentration of soil-sawdust column is higher than that of soil column, which is also probably the rapid reduction by enhanced organic carbon in soil-sawdust column compared with soil alone.

Figure 5 

Measured and simulated Fe2+ concentrations for two columns.

Figure 6 shows the experimental data and simulated sulfate concentration as a function of time.

Figure 6 

Measured and simulated SO42− concentrations for two columns.

Figure 7 

Measured and simulated CH2O concentrations for two columns.

The group of sulfate reducing bacteria 𝑋₄ in the model uses sulfate as an electron acceptor under anaerobic conditions. The observed and simulated results of sulfate concentration show a smaller decrease in the column packed with soil only, while significant decrease in sulfate concentration was observed in the column packed with soil sawdust. This may be attributed to the continuous supply of organic carbon from sawdust to the column. The temporal development of sulfate reduction in the columns is successfully reproduced with the model. The important model parameters were the exchange coefficient between mobile sulfate and microbially available sulfate in the biophase and the maximum growth rate of sulfate reducer bacteria.

Figure 7 shows the simulated organic carbon concentration as a function of time. The organic carbon concentrations for both soil column and soil-sawdust column were measured only once on 36th day of experiment. (Note that however, more frequent measurement of organic carbon concentration seemed necessary in the present experiment because significant changes in both columns took place.) The effect of soil-sawdust column on the carbon concentration increase shows approximately 50% as compared with the column packed with soil alone.

The simulated concentration is in good agreement with the measured values. The concentration of organic carbon of soil column increased in the first two days due to the little consumption by bacteria, after that the concentration of organic carbon decreased for next three days due to high growth of aerobic bacteria after that gradually approaches an equilibrium state. The model is able to calculate the relative contribution of the four bacterial groups to the total number of electrons transferred to organic carbon during the time of column experiment. The groups of aerobic and denitrifying bacteria 𝑋₁ contributed 68.5% of the transferred electrons. Anaerobic bacteria groups 𝑋₂, 𝑋₃, and 𝑋₄, which consume MnO₂, Fe(OH)₃, and sulfate as an electron acceptor, contribute 11%, 13.7%, and 6.7% of the transferred electrons, respectively.

Figures 8 and 9 show the four bacterial growths with time at different depths for soil and soil-sawdust columns. Initially the bacteria tend to be acclimated to the new environmental conditions (pH, temperature, nutrients, etc.). Then, their population increase rapidly with time at an exponential growth in numbers, and the growth rate increases with time. After that with the exhaustion of nutrients and build-up of waste and secondary metabolic products, the growth rate has slowed down to the point where the growth rate equals the death.

Figure 8 

Simulation of bacterial growth versus time at different depths for the column packed with soil.

Figure 9 

Simulation of bacterial growth versus time at different depth for the column packed with soil sawdust.

Figure 10 shows the distribution of the four bacterial groups along the column. The aerobic bacteria 𝑋₁ grow first. As long as the oxygen concentration exceeds 1.5×10⁻² mmol/L, the metabolism of the anaerobic bacteria is inhibited. Afterwards the manganese reducers 𝑋₂ begin to grow, but their activity is limited by the higher availability of manganese. The iron reducers 𝑋₃ grow, and their activity increased by the high availability of iron. At the last half part of the column, the sulfate reducers bacteria group 𝑋₄ increases their activity, which is due to the limited concentration of oxygen and nitrate and high concentration of sulfate and available organic carbon as electron donor. The sulfate reducers bacteria group 𝑋₄ in the model begins to grow with high rate at depth 10 cm, when most part of the column becomes anaerobic.

Figure 10 

Simulated distribution of bacterial population along the soil column after 30 days.

4. Application to a Costal Aquifer

Coastal groundwater biogeochemistry is becoming a popular topic among the groundwater researchers due to its vital role in the groundwater property change. Bacteria mediated reduction is one of the important processes which should be considered seriously in such kind of research activities. However, numerical approaches to simulate the distribution of reduced species in the coastal subsurface environment are not yet common in the field of hydrogeological modeling. In the present section a qualitative discussion is presented for a selected coastal aquifer. Geochemical properties of the groundwater in a coastal aquifer would change with the depth from aerobic state to anaerobic state. The bacteria mediated redox reactions are significant in the geochemical property changes of the subsurface water in a coastal aquifer. The availability of oxygen and other electron acceptors such as NO₃₋, MnO₂, Fe(OH)₃, and SO₄₂₋ with the organic carbon as the electron donor encourage the different bacteria to activate and form reduced environments in the subsoil. The gradual decrease of oxygen with the depth allows bacteria to use other electron acceptors and form Mn²⁺-, Fe²⁺- and HS⁻-rich reduced environments. The salt water below the mixing zone is almost anaerobic in the coastal aquifer, and bacteria mediated reduction processes are dominant. Depending on the availability of organic carbon, a sequence of redox zones of increasing redox potential may develop at the down gradient of the aquifer; reduction zones of oxygen, NO₃₋, MnO₂, Fe(OH)₃, and SO₄₂₋ can be developed if the organic carbon and corresponding electron acceptors are present in the aquifer under the bacterial mediation.

4.1. Site Description

Jinno et al. [13] researched on the geochemical properties of groundwater of the unconfined aquifer at Kujyukurihama coast in Chiba prefecture, Japan by analyzing the major ions (Figure 11). Salt water in the unconfined aquifer at Kujyukurihama coast has −380 mV oxidation-reduction potential at 8.0 m below the surface of the sand pit and the groundwater environment in the salt water region of the aquifer was considerably reduced. The measurements conducted at different depths of this particular aquifer show high concentrations of reduced species in the anaerobic salt water region. As shown in Table 5, location (C) shows high DOC concentration.

Table 5 

Measured chemical species at the site.

Figure 11 

Location of the Kujyukurihama coast in Chiba prefecture, Japan.

4.2. Model Setup

Firstly, a two-dimensional density dependent solute transport model is applied to obtain the steady state for the freshwater/salt water distribution and velocity distribution [6]. The groundwater properties in the subsurface of coastal aquifers are changed with depth according to the chloride concentration. In the shallow region, the water quality is close to the freshwater and in the deep region it is similar to the reduced salt water. However, the black coloured salt water with hydrogen sulphide odour is observed at the site when sand spit was excavated. This implies the precipitation of iron sulphide. Besides, precipitation of iron hydroxide can occur when the aerobic fresh water meets with the reduced salt water at the mixing zone. It is, therefore, necessary to include the following reactions with kinetic of precipitation rate:

Precipitation reaction for hydrogen sulphide: Fe²⁺+HS⁻⟶FeS+H⁺.(14)

The corresponding precipitation reaction rate𝑆_FeS=𝐾_FeSFe²⁺[HS⁻],(15) where 𝑆_FeS is the rate of precipitation in mol/L/sec. 𝐾_FeS is the reaction rate coefficient in L/mol/sec. [Fe²⁺] is the concentration of Fe²⁺ in mol/L. [HS⁻] is the HS⁻ concentration in mol/L.

Precipitation reaction of iron hydroxide4Fe²⁺+O₂+8OH⁻+2H₂O⟶4Fe(OH)₃.(16)

Equation (16) represents that 1 mol/L of Fe²⁺ and (1/4) mol/L of oxygen are consumed to precipitate 1 mol/L of Fe(OH)₃.

The rate of the precipitation of Fe(OH)₃ can be expressed by [1]𝑆_Fe(OH)3=𝐾_Fe(OH)3Fe²⁺[OH⁻]²P_O2,(17) where 𝑆_Fe(OH)3 is the rate of precipitation in mol/l/sec. P_O2 is the oxygen partial pressure in atm.

Equations (15) and (17) are added to the right side of the Fe²⁺ transport equation (see (3)) as a sink term as𝜕Fe²⁺𝜕𝑡+𝑢^𝜕Fe²⁺𝜕𝑥+𝑣^𝜕Fe²⁺=1𝜕𝑦𝜃_𝑤𝜕𝜕𝑥𝜃^𝑤𝐷_𝑥𝑥𝜕Fe²⁺𝜕𝑥+𝜃^𝑤𝐷_𝑥𝑦𝜕Fe²⁺+1𝜕𝑦𝜃_𝑤𝜕𝜕𝑦𝜃^𝑤𝐷_𝑦𝑦𝜕Fe²⁺𝜕𝑦+𝜃^𝑤𝐷_𝑦𝑥𝜕Fe²⁺+𝜕𝑥₂_𝑗=1𝑆_𝑖,𝑗−𝑆_Fe(OH)3−𝑆_FeS.(18)

Similar modifications of the corresponding mass balance equations for HS⁻ and O₂ in mobile phase, Fe(OH)₃ and FeS in matrix phase are done depending on the stoichiometric coefficient in (14) and (16).

The initial distributions of the chemical species required for the two-dimensional redox model is assumed relative to the steady state chloride distribution which is obtained from the two-dimensional density dependent solute transport flow shown in Figure 12 [6]. The initial distribution of each chemical species accompanied with the steady state velocity distribution is input to the redox model in the simulation of bacteria mediated reduction.

Figure 12 

Steady state chloride distribution (%) and velocity distribution for the two-dimensional density dependent solute transport model (selected cross-section of Kujyukurihama beach, Chiba, Japan).

4.3. Results and Discussion

In the selected aquifer, a layer of organic carbon has been found at the 12 m bottom. Therefore, in the numerical simulation, a 4 m thick organic carbon layer is assumed. This layer continuously supplies organic carbon for bacteria growth. In the numerical model, the matrix phase is considered as the organic carbon provider for the bacterial metabolism which takes place in the biophase. The precipitated Fe(OH)₃ and FeS are assumed to deposit in the matrix phase. The behaviors of aerobic and anaerobic bacteria under assigned organic carbon distribution are simulated for ten years. The numerical results of bacterial growth show reduction of electron acceptors and consumption of organic carbon. Figure 13 shows the schematic diagram where the redox model is applied. The redox model parameters are listed in Table 6. The precipitate rate coefficient for Fe(OH)₃ or FeS is assigned by large number, because precipitation takes place quickly compared to reduction processes. Table 7 shows the assumed initial distribution of chemical species for redox model.

Table 6 

Biogeochemical parameters used for the two-dimensional redox model.

Table 7 

Initial chemical species distribution for redox model.

Figure 13 

Schematic representation of the numerical model.

4.3.1. Aerobic Oxidation, Denitrification, and Growth of Bacteria 𝑋₁

Figure 14(a) shows the aerobic and denitrifying bacteria growth for ten years. Bacteria 𝑋₁ grow until 30 days and then the growth gradually decreases. After 2 years of calculation, the bacteria 𝑋₁ growth is not significant. According to Figure 14(a), however, bacteria 𝑋₁ growth is dominant in the freshwater region (Figure 12) and no or less growth can be seen in the anaerobic salt water region of the aquifer. The gradual decrease of CH₂O in the aerobic freshwater region is the main reason for the decrease in bacteria 𝑋₁ growth after 30 days. Due to the consumption of CH₂O in the freshwater region of biophase by bacteria 𝑋₁, CH₂O in the freshwater region of the matrix phase decrease. This process is reasonably simulated as shown in Figure 15(a). The growth of bacteria 𝑋₁ in the freshwater region is controlled by the available CH₂O. As a result of continuous infiltration of rainwater with the assumed 8 mg/L of O₂ concentration, there is enough O₂ for bacteria 𝑋₁ growth. However, there is no CH₂O supply for the freshwater region. Therefore, when the available CH₂O is consumed, the growth of bacteria 𝑋₁ hinders. Moreover, in Figure 16(b), NO₃₋ concentration decreases gradually due to the denitrifying process of bacteria 𝑋₁. Denitrification is rapid in the O₂ low deeper area especially the elevation below 10.0 m. The concentration variations of O₂ and NO₃₋ with the metabolism of bacteria 𝑋₁ imply that the redox model can simulate the growth of aerobic and denitrifying bacteria under the available CH₂O appropriately. Figure 17 shows the spatial distribution of O₂ after 10 years of simulation.

Figure 14 

Numerical results for aerobic and anaerobic bacterial growth (along borehole no. 4).

Figure 15 

Numerical results for concentration variations of the matrix phase species (along borehole no. 4).

Figure 16 

Numerical results for concentration variations of the mobile phase species (along borehole no. 4).

Figure 17 

Simulation results for the spatial distribution of O2 after 10 years.

4.3.2. Reduction of MnO₂ and Growth of Bacteria 𝑋₂

Bacteria 𝑋₂ reduce MnO₂ to Mn²⁺ under anaerobic conditions. Figure 14(b) shows the growth of MnO₂ reducing bacteria 𝑋₂. The decrease of MnO₂ in the matrix phase (Figure 15(b)) corresponds well with the bacteria 𝑋₂ growth which is shown in Figure 14(b). Figure 16(d) shows the concentration of formed Mn²⁺ in mobile phase. Bacteria 𝑋₂ growth is significant in the anaerobic salt water region of the aquifer. Constant CH₂O layer provides abundant electron donor environment which is favorable for bacterial growth. According to Figure 14(b), the bacteria 𝑋₂ growth increases up to 30 days. After that bacteria 𝑋₂ growth in the CH₂O layer becomes lower. The reason for that is the availability of MnO₂. Bacteria 𝑋₂ use available MnO₂ in the organic carbon region. Availability of CH₂O and MnO₂ under anaerobic condition is favorable for the growth of bacteria 𝑋₂. However, gradual consumption of MnO₂ in the CH₂O layer forms a low MnO₂ region, and then the bacteria 𝑋₂ growth in this area becomes low. After the consumption of all available MnO₂, the growth of bacteria 𝑋₂ becomes zero. Availability of CH₂O and MnO₂ in the anaerobic region is the determining factors for bacteria 𝑋₂. Redox model is able to simulate the growth of bacteria 𝑋₂ appropriately under the assigned conditions. Figure 18 depicts the simulation results for the spatial distribution of formed Mn²⁺ after 10 years.

Figure 18 

Simulation results for the spatial distribution of Mn2+ after 10 years.

4.3.3. Reduction of Fe(OH)₃, the Growth of Bacteria 𝑋₃ and Reprecipitation of Fe(OH)₃

The reduction of Fe(OH)₃ occurs in the anaerobic region due to the metabolism of bacteria 𝑋₃ in the redox model. Figure 16(e) shows the formation of Fe²⁺ in the mobile phase due to the reduction of Fe(OH)₃ in the biophase. Figure 14(c) shows the bacteria 𝑋₃ growth for ten years while in Figure 15(c) shows the concentration changes of Fe(OH)₃ in the matrix phase. Up to 30 days, the growth of bacteria 𝑋₃ increases and after that it starts to decrease in the constant CH₂O layer region. The decrease of the growth of bacteria 𝑋₃ in the constant CH₂O layer is due to the consumption of Fe(OH)₃ in the bottom of the aquifer. Even the Fe(OH)₃ in the CH₂O layer, becomes zero after 90 days, still there are some Fe(OH)₃ above the CH₂O layer. Therefore, bacteria 𝑋₃ grows in that region until all the Fe(OH)₃ is reduced by bacteria 𝑋₃. In the region above constant CH₂O layer, the determining factor is the availability of CH₂O for bacteria 𝑋₃ growth while in the CH₂O layer bacteria growth is determined by the availability of Fe(OH)₃. The reprecipitation of formed Fe²⁺ takes place in the mixing zone, where O₂ becomes available. The reduction of Fe(OH)₃ takes place in the lower part of mixing zone and anaerobic salt water region of the aquifer at different rates according to the availability of CH₂O and Fe(OH)₃. The formed Fe²⁺ moves to the mixing zone with the advective flow and meets O₂ and precipitates as Fe(OH)₃. The reprecipitation of Fe(OH)₃ is highlighted as the increase of Fe(OH)₃ concentration in the matrix zone. In Figure 15(c), the gradual increase of Fe(OH)₃ concentration in the mixing zone region (elevation between 6.0 m to 10.0 m) depicts the precipitation of Fe(OH)₃. The Fe²⁺ concentration increases around the 6.0 m elevation in the mobile phase (Figure 16(e)) is due the reduction of precipitated Fe(OH)₃ in bottom edge of the mixing zone. However as a result of precipitation along the mixing zone, the concentration of Fe(OH)₃ is increased. In the aerobic region, there is no growth of bacteria 𝑋₃ to reduce available Fe(OH)₃. Therefore, Fe(OH)₃ can be seen in the aerobic region of the simulation results. The numerical results for the bacteria 𝑋₃ and reduction/reprecipitation of Fe(OH)₃ convince that the redox model simulates the bacteria 𝑋₃ growth and its related processes appropriately for available conditions. It is interesting to check the bacteria 𝑋₃ distribution in the cross-section, because 𝑋₃ is expected to reside along the mixing zone when reduction of Fe(OH)₃ is almost completed and Fe²⁺ is then transported toward the mixing zone. Figures 19 and 20 depict the spatial distribution of Fe(OH)₃ and 𝑋₃, respectively after ten years of simulation. As expected, 𝑋₃ resides below the high matrix zone of Fe(OH)₃.

Figure 19 

Simulation results for the spatial distribution of Fe(OH)3 after 10 years.

Figure 20 

Simulation results for the spatial distribution of 𝑋3 after 10 years.

4.3.4. Reduction of 𝑆𝑂₄₂₋, Growth of Bacteria 𝑋₄, and Precipitation of FeS

The growth of bacteria 𝑋₄ is determined by the availability CH₂O and SO₄₂₋. In the deeper part of the aquifer, especially in the organic carbon rich regions, there are abundant amount of SO₄₂₋ and CH₂O available to make a favorable condition for the growth of bacteria 𝑋₄. As a result of SO₄₂₋ reduction HS⁻ is formed. Figure 16(g) shows the formation of HS⁻ in the mobile phase. HS^- in the mobile phase increases and consequently FeS starts to precipitate in the region, where Fe²⁺ and HS^- are available. Figure 15(d) shows the precipitation of FeS in the matrix phase. FeS precipitation is significant at elevations below 6.0 m. Mobile phase SO₄₂₋ concentration profile is shown in Figure 16(f). The decrease of SO₄₂₋ in the mobile phase and the increase of HS⁻ emphasize the bacteria 𝑋₄ growth and reduction of SO₄₂₋. Bacteria 𝑋₄ growth is shown in Figure 14(d). Bacteria 𝑋₄ growth increases up to 270 days and after that gradually it becomes to a stable with time in the CH₂O layer region. The reduction of SO₄₂₋ will continue due to the availability of SO₄₂₋ and CH₂O in the constant CH₂O layer. In the Kujyukurihama beach, there is a low permeable alluvial deposit with organic carbon at the 12.0 m below the sea level. Table 5 shows high concentration of S²⁻ in the salt water region of the aquifer. These two observations provide a solid evidence for the reduction of SO₄₂₋ in this particular aquifer under the anaerobic bacteria mediation. Figures 21 and 22 show the spatial distributions of SO₄₂₋ and precipitated FeS for 10 years of simulation.

Figure 21 

Spatial distribution of SO42− after 10 years of calculation.

Figure 22 

Spatial distribution of FeS after 10 years of calculation.

5. Conclusion

The results of the column experiment and the numerical solution demonstrate that the consumption of oxygen by bacteria 𝑋₁ took place within a few days and the subsequent reducing processes by bacteria 𝑋₂, 𝑋₃, and 𝑋₄ became active for approximately one week later. On the other hand, in the sand spit, the reducing processes under the assumed initial and boundary conditions seem to last several years. These differences arise from the different scale between the laboratory and field hydrogeological conditions. Besides, the parameters used in the reduction processes are not completely same as shown in Tables 4 and 6 for the one-dimensional and in the two-dimensional simulations. However, two examples encourage the present modeling approach to be useful for groundwater management, specifically in the alluvial aquifer where groundwater quality is a crucial matter or enhancement of groundwater resources is planned. It can be also emphasized that the field sampling should be appropriately planned so that the modeling approach to be reliable for the practical application.

The results of the present numerical study also demonstrate that appropriate sampling frequency, locations, and chemical species could be determined in order to make efficient analyses of groundwater basins, where various management targets are planned.

Acknowledgment

The authors express the gratitude to Professor Tosao Hosokawa of Faculty of Engineering of Kyushu Sangyou University, Fukuoka, Japan, who provided his valuable experimental data.