To understand the mechanism of bacterial growth in a reactive transport model inside a bioremediation biobarrier, pore-scale numerical modeling must be performed. An attempt has been made to understand and simulate the growth and decay of indigenous bacteria in a saturated porous medium at pore scale with a known concentration of Cr VI and to predict the increased microbial activity for the transformation of Cr VI to Cr III. Darcy-scale models previously developed could not address the hydrodynamics of the system, and contaminant degradation rates were overpredicted.
In this study, the pore-scale model combines processes such as fluid flow, solute transport with advection and diffusion equations of Cr VI reactive transport. Along with biotransformation of Cr VI and substrate consumption, the model mainly incorporates bacterial growth and decay at a pore scale. The model is divided into three parts, one for each of the processes and is operated on different time scales.
It can also predict the movement and consumption of the substrate and biotransformation of Cr (VI) by bacteria together with the changes in its concentration. FEM: Finite Element Method FVM: Finite Volume Method FDM: Finite Difference Method LBM: Lattice Boltzmann Method PN: Pore Network.
General Introduction
On the other hand, the pore scale is the largest spatial scale at which liquid and solid phase differentiation is possible. Because the pore scale represents the architecture of the pore space where microbial reactions and multicomponent transport take place, it is possible to explain biogeochemical behavior not detected or predicted using other scales. In this study, an attempt was made to understand the pore processes taking place in a biological barrier containing a consortium of Cr (VI)-reducing bacteria.
Purpose and scope of the project
Objectives
Thesis outline
Pore scale modeling of fluid
A multiphase 2D model was developed to simulate fluid flow in a microfluidic model using STAR-CCM+ software, which uses FVM on unstructured meshes and a fluid volume method to implicitly track the interface between two phases. A multicomponent model using LBM was used to numerically solve the equations of fluid flow, solute transport, and bacterial growth to develop a 2D model to simulate the experimental results. Homogeneous reactions were described with local mass action equilibrium relations, while mineral reactions were treated kinetically with boundary conditions on the surface of the mineral.
The model was further improved by including a distribution function boundary condition for the total solute concentration and compared with analytical solutions obtained by FLOTRAN and AQUASIM simulations.
Pore scale modeling of biomass
Gamma distributions and Lagrangian velocity distributions were used to provide parameters quantifying flow changes. A two-dimensional pore network reactive transport model for saturated porous environments was developed to investigate how the physical properties of the medium contribute to nutrient transport mechanisms and their consumption by indigenous microorganisms. The results show that the complex spatiotemporal distribution of nutrients is mainly driven by interactions between system physical conditions, such as mean inherent heterogeneity, baseflow residence time, nutrient input concentrations, and internal biomass decomposition capacity.
Simulation results also showed that the spatial heterogeneity of pore sizes is a more powerful regulator than biomass distribution in controlling the spatial distribution and transport of nutrients. The diffusion term is integrated in parts to reduce the differentiation requirements of the unknown weighted residue. The last term of the above equation at the boundaries (Γ) of the domain (Ω) and 𝒏⃗⃗ is the unit outward normal of the boundary.
Which means that the jth shape function has the value 1 at the jth grid node and is equal to zero at all other nodes. The approximate solution for u is defined as the sum of the product of the unknown nodal values (uj) and the shape function Sj. Where [𝑲] is the NN × NN stiffness matrix, {𝒖} is the unknown column matrix and {𝑭} is the force vector.
Where NEN is the node number of the element = 4 for quadrilateral element and 3 for triangular elements. Since the shape function 𝑺𝒋 is used for both unknown approximation and coordinate transformation, it is known as iso-parametric formulation. Using the chain rule, the ξ and η derivatives of the ith shape function are in terms of the x and y derivatives as follows.
So after substituting the above equations into the stiffness element equation, the following form is obtained. Each element of the local stiffness matrix is therefore calculated and then they are assembled into the global stiffness matrix according to the global node numbers of any element. Appropriate initial and boundary conditions are applied and the matrix equation is solved to obtain the values for the unknown vector.
Model description
Equations used
Fluid flow
Substrate and Chromium transport
Biomass spread and growth
Model inputs
COMSOL Model
Model 1
There is no significant change in biomass concentration up to 12 h, since the point of bacterial inoculation is located beyond the inlet, and the time lag is due to the time required for the bacteria to diffuse near the inlets and then grow. The concentration of Cr (VI) decreases due to advection at the beginning and biotransformation in later stages. This is due to the lag in biomass movement from the inoculation site to the outlet due to the very low velocity.
There is a gradual decrease in the concentration of Cr (VI) at first due to its exit from the model through the outlet and a large decrease later due to biotransformation by bacteria. The gradual decrease of Cr (VI) due to biotransformation by increasing biomass can be observed. A gradual decrease in substrate concentration is seen with an immediate increase in biomass concentration as it nears the inoculation point.
Model 1
There is no change in biomass concentration up to 100 h as the movement of bacteria from the inoculation point to the outlet is very slow due to very low velocities within the model. There is a large increase in biomass growth later, which accounts for a greater decrease in Cr (VI) concentration.
Model 1
A gradual decrease in substrate concentration is seen with increasing biomass concentration after a delay as it is close to the outlet. The model can be improved by modeling the movement of bacteria using cellular automata, thus accounting for its motility (bacterial sliding). Bacterial chemotaxis to pollutant and substrate can also be modeled to improve the directionality of biomass spread.
Clogging due to biomass as well as its attachment and detachment to the pores changes the fluid flow dynamics, incorporation of this aspect in the model can significantly improve. The model can be validated with experimental results and inverse modeling can be done to estimate parameters that are known to check the accuracy and applicability of the model. Pore-scale simulation of biomass growth along the transverse mixing zone of a model two-dimensional porous medium.
Combination of finite element and finite volume methods for effective multiphase flow simulations in highly heterogeneous and structurally complex geological media. A steady-state biofilm model for simultaneous reduction of nitrate and perchlorate, part 1: Model development and numerical solution. A steady-state biofilm model for simultaneous reduction of nitrate and perchlorate, part 2: Parameter optimization and results and discussion.
An improved lattice Boltzmann model for multicomponent reactive transport in pore-scale porous media. Pore-scale hydrodynamics in a progressively trapped three-dimensional porous medium: 3-D particle tracking experiments and stochastic transport modeling. Bench-scale column experiments to study Cr (VI) content in bio-confined aquifers.
