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BIO1D documentations
BIO1D

Overview

BIO1D is a one-dimensional modeling code which simulates biodegradation and sorption in contaminant transport.  Our objective was to provide an interactive, user-friendly software package to serve as an educational tool for understanding the relative importance of various physicochemical and biochemical processes.

Applications

BIO1D may be applied to solute transport problems involving a reactive substrate. The reactions may include aerobic and anaerobic degradation and/or adsorption described by linear, Freundlich, or Langmuir isotherm. Figure 1 shows the simulation at a waste site in Conroe, Texas, and is based on an earlier study by Borden, et al. (1984).

BIO1D Figure 1

Figure 1. Simulation of aerobic biodegradation at Conroe site, Texas

The code may be used in conceptualization mode for many applications to help determine the importance of transport processes. The applications can involve a number of reactive substrates such as organic solvents and petroleum products. In addition, because anaerobic degradation is considered, non-organic solutes, such as radionuclides with decay can be simulated. The code will be especially useful for analyzing laboratory data from column experiments.

Model Features

  •  Advective and dispersive transport of a hydrocarbon and an electron acceptor (e.g., oxygen)
  •  Aerobic biodegradation using modified Monod function
  •  Anaerobic biodegradation using Michaelis-Menten kinetics
  •  First-order degradation for both substances
  •  Linear, Freundlich, and Langmuir adsorption isotherms for both substances
  •  Dirichlet, Neumann, and Cauchy boundary conditions modified to include first-order degradation
  •  Cumulative mass balance report

Limitations

  •  Transport is one-dimensional.
  •  The flow field is uniform (constant velocity).
  •  Material properties of both substances are uniform throughout the medium.
  •  Only one reactive substrate is considered per simulation.
  •  Microbial density is assumed constant.

Governing Equations

A summary of the equations solved in BIO1D is presented below.

BIO1D equations 1 and 2

where

S substrate concentration in the pore fluid (ML-3);
O oxygen concentration in the pore fluid (ML-3);
D longitudinal hydrodynamic dispersion coefficient (L2T-1);
x distance (L);
V interstitial velocity (LT-1), assumed uniform;
B(S,O) biodegradation term (ML-3T-1), expressed as a function of the dependent variables S and O;
F ratio of oxygen to substrate consumed;
A(S) substrate adsorption term;
A(O) oxygen adsorption term; and
t time (T).

Aerobic Biodegradation (Monod Function)

BIO1D equation 3

where

B(S,O) aerobic biodegradation term, a function of substrate and oxygen concentration (ML-3T-1);
M microbial mass (ML-3) assumed constant;
K maximum substrate utilization rate per unit mass of micro organisms (T-1);
ks substrate half-saturation constant (ML-3);
kO oxygen half-saturation constant (ML-3);
Smin minimum substrate concentration that limits growth and decay (ML-3); and
Omin minimum oxygen concentration that limits growth and decay (ML-3).

Anaerobic Biodegradation (Michaelis-Menten Kinetics)

BIO1D equation 4

where the terms, Mn, kn, and kSn are counterparts of M, k and kS under anaerobic conditions. As a special case, Mn, kn, and kSn may be set equal to M, k, and kS, respectively.

First-Order Decay

BIO1D equation 5

where uS is a first-order degradation coefficient (T-1).

Linear Adsorption Isotherm

BIO1D equation 6

where

rb bulk mass density of the porous medium (ML-3);
phi effective porosity; and
Kd distribution coefficient (L3M-1).

Freundlich Adsorption Isotherm

BIO1D equation 7

where

Kf rate constant; and
n Freundlich isotherm exponent.

Langmuir Adsorption Isotherm

BIO1D equation 8

where

b constant; and
K maximum sorption capacity of solid.

Uncoupled Simulation Option

When the biodegradation option is not used, the equations (1) and (2) are uncoupled and may be solved simultaneously. Two sets of input values are used for all parameters except those defining the grid and time steps. This permits a wide range of possible comparison studies. Some are listed below.

  • Different velocities. This is an indirect way of comparing the effect of two hydraulic conductivity values. Figure 2 illustrates a field application of BIO1D where the predicted breakthrough curves are bracketed with two estimates of clay permeability. Similarly, hydraulic gradients may also be used for comparison.

BIO1D Figure 2
Figure 2. Varying clay permeability

  •  Different dispersion coefficients
  •  Different adsorption rates. BIO1D is an excellent tool for comparing two isotherms, or varying coefficients of the same isotherm. Figure 3 illustrates a study on varying Freundlich isotherm exponent.
  •  Different first-order rates. As a special case, one of the decay rates may be set to zero.
  •  Different boundary conditions. Three types of boundary conditions with built-in first order degradations are available. In field situations, boundary conditions are not always clearly understood. Thus the importance of assumptions made at the boundary may be studied.

BIO1D Figure 3

Figure 3. Uncoupled simulation option; Varying Freundlich isotherm constant

Interactive Pre-processor

A pre-processor has been built into BIO1D which enables the user to prepare input data interactively. The preparation includes features such as inputting new data and storing them in a disk file, or reading data from a file and editing them. The pre-processor has built-in error recovery procedures to forgive most input errors made by a user during interaction.

For the first-order decay and linear, Freundlich, or Langmuir adsorption isotherms, definitions found in the literature are not always uniform. The pre-processor provides the user with alternative definitions, and the user may select the one that is most familiar. Figure 4 illustrates the definitions available for linear isotherm. The user may define the isotherm in terms of linear isotherm coefficient, distribution coefficient and bulk density, or retardation factor. Many such useful features may be found throughout the interaction.

BIO1D Figure 4

Figure 4. BIO1D data preparation: Alternative definitions.

Run-Time Options

Taking advantage of the single-user microcomputer environment, many simulation options are provided at run-time. A run-time monitor as illustrated in Figure 5 is displayed and updated constantly as the simulation progresses. The user may run the simulation for a certain time period, monitoring its behavior, and then choose a different set of run-time options for the rest of the simulation. The options include printing concentrations, cumulative mass balance information, and selecting plotting intervals. Advanced debugging options such as iteration information, nodal mass balance tables, displacement matrices, and matrix solver monitors are also available at run-time. These options can be useful when the processes simulated are highly nonlinear, or if the results of the simulation show unusual behavior.

BIO1D Figure 5

Figure 5. BIO1D run-time monitor.

The advanced debugging options may also be used by students learning numerical methods. Every step of the nonlinear iterative solution scheme used in BIO1D may be monitored by the user. The Peclet and Courant stability numbers are displayed automatically during data preparation, and a stop watch (Figure 5) is activated to measure the CPU time during the simulation. These features are useful in understanding the effects of varying the input parameters such as, grid spacing, time step size, and convergence criteria which are associated with the numerical solution.

Graphical Results

Concentration vs. distance at a certain time, or concentration vs. time (or pore volume) at any node may be plotted. Concentration may be plotted in linear or log scale. Figures 1, 2 and 3 illustrate these options. Plots may be previewed on the screen and sent to any of the plotters listed under hardware {link}. For comparative studies, hard copy plots from uncoupled simulation runs (eg., Figures 2 and 3) can be readily used in reports.

Verification Tests

The features available in BIO1D have been tested in a systematic manner. A variety of problems have been selected to test major options in biodegradation, adsorption, and boundary conditions. The data files for the above problems have also been carefully prepared to test many of the minor options (grid spacing, plotting, etc.) available in BIO1D. Table 1 shows the features tested by the problem sets A through F.

Table 1. BIO1D features tested

FEATURES
PROBLEM SETS
Advection / Dispersion
A
B
C
D
E
F
Degradation - aerobic
- anaerobic
- first-order
 



B

 
 
 

F
F
F

Uncoupled simulation
 
 
 
D
 
 
Adsorption - linear
- Freundlich
- Langmuir
 
B

C


D



E
 
Bounday condn. - Dirichlet
- Neumann
- Cauchy
A


 
B*

C*


D*


E*


F


Solution - tridiagonal
- pentadiagonal
A

B

C

 
D
E

 
F
Grid - uniform
- variable
A

B

C

D

E


F
Plots - C vs. X
- C vs. T
- C vs PV
A


 
B

 

C
 

D
 

E
F

Features that are not yet tested may also be identified from this table. A description of each test along with a complete list of corresponding input and output files of the BIO1D simulations are presented in the BIO1D documentation.

Documentation

The documentation for BIO1D is comprehensive. It is divided into two major parts. The first part covers the theoretical aspects of BIO1D which include: derivation of the mathematical model; development of the numerical solution; and verification tests. The second part serves as the Userís Manual for the code. The sections included are: step-by-step installation instructions; three guided tours to familiarize the user with the data preparation, simulation, and plotting of the results; detailed input data instructions; interpretation of output; and error conditions and handling.

Hardware

BIO1D runs any PC compatible computer.  As it is a DOS program, special configuration files are supplied for running BIO1D with Windows 2000 or XP. A generic HP LaserJet printer is supported for plotting results.

Availability

BIO1D is available from CertainTech, Inc.  Please contact us at sales@certaintech.com.

 

 Copyright (c) 2005 by CertainTech, Inc.