Exercise: Modeling Aerobic Biodegradation of Hydrocarbons
Objective
The purpose of this exercise is to gain hands-on experience in modeling aerobic biodegradation
of fuel hydrocarbons (BTEX) based on three simple approaches, i.e., instantaneous reaction, 1storder kinetics and Monod kinetics. The simulation code used in this excise is MT3D’99,
however, the same exercise can be carried out using RT3D or BIOPLUME III.
Problem Description
The sample problem considered in this exercise involves two-dimensional transport from a
continuous point source in a confined aquifer under steady-state flow conditions. The model grid
consists of 46 columns, 31 rows and 1 layer and is aligned with the flow direction along the x
axis (see Figure 1). The flow model is surrounded by constant-head boundaries on the east and
west borders and no-flow boundaries on the north and south borders. The head values at the
constant-head boundaries are arbitrarily chosen to establish the required hydraulic gradient. One
injection well is located at column 16 and row 16. The injection rate is sufficiently small so that
the flow field remains approximately uniform. The model parameters used in the simulation are
listed below:
Cell width along rows  x  = 10 m
Cell width along columns  y = 10 m
Layer thickness  z  = 10 m
Groundwater seepage velocity  v  = 1/3 m/day
Porosity () = 0.3
Longitudinal dispersivity = 10 m
Ratio of transverse to longitudinal dispersivity = 0.3
Volumetric injection rate = 1 m3/day
Simulation time  t  = 730 days (2 years)
Assume that the injected water contains hydrocarbon (species 1) with a constant concentration of
1000 ppm (mg/L). Further assume that the background concentration of oxygen (species 2) in
the aquifer is 9 ppm. The background oxygen concentration is modeled by setting the initial
concentration of species 2 to 9 ppm in all model cells and by assigning 9 ppm to the species 2
concentration of the inflow from the constant-head boundary. Hydrocarbon and oxygen are
assumed to react instantaneously; the stoichiometric ratio for the reaction is approximately 3.0.
The calculated concentrations for hydrocarbon and oxygen at the end of the two-year simulation
period are shown in Figure 2. The maximum concentration of hydrocarbon is approximately 50
ppm at the injection point, as shown in Figure 2(a). The oxygen plume is depleted where the
concentration of hydrocarbon is above zero as in Figure 2(b). The TVD scheme is chosen for
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solving the advection term while all other terms are solved by the explicit finite-difference
option.
Point source at (16,16)
HC=1000 ppm; O2=0
v =1/3 m/day
Constant-head boundary
Mass flux outflow boundary
Constant-head boundary
Specified mass flux boundary
O2=9 ppm, HC=0 ppm
No-flow boundary
No-flow boundary
Figure 1. Illustration of the conceptual model and numerical model grid.
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300
250
Y Axis (m)
200
150
100
50
(a) BTEX
50
100
150
200
250
300
350
400
450
Y Axis (m)
300
250
Y Axis (m)
200
150
100
50
(b) Oxygen
50
100
150
200
250
300
350
400
450
Figure 2. Calculated
concentration
distributions at 730 days
assuming instantaneous
reaction between BTEX
(top) and oxygen
(bottom).
X Axis (m)
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VMOD Notes on Flow Simulation
1. Create a new model with a name like ‘exercise3’ and save it in a new subdirectory:
No of Columns=46
Xmin=0
Xmax=460
No of Rows=31
Ymin=0
Ymax=310
No of Layers=1
Zmin=0
Zmax=10
Unit for Length: meter
Unit for Time: day
Unit for Conductivity: m/day
Unit for Pumping rate: m3/day
Unit for Mass: kg
Unit for Concentration: mg/L
Do not check the box “Set up transport model”.
2. Under the ‘Properties’ menu, set the following default properties:
Kx = 10 m/d
Ky = Kx
Kz = 1 m/d
Ss = 0. [specific storage for transient flow in a confined aquifer]
Sy = 0.3 [specific yield for transient flow in an unconfined aquifer]
Eff. Por. = 0.3 [effective porosity]
Tot. Por. = 0.3 [total porosity]
3. Under the ‘Properties’ menu, select Dispersion:
Longitudinal dispersivity = 10.0 m to layer 1.
4. Under Layer Options,
Make sure Horiz/Long=0.3; Vert/Long=[not used]; and Diff Coeff.=0.
5. Under the ‘Boundaries’ menu, assign Constant-Head Boundary
At the left-hand border with head=4.5 (code 1), from days 0 to 730 and
at the right-hand border with head=0 (code 2), from days 0 to 730.
Check: v  K
hleft  hright
4.5  0
1
 10
 m/day
L
0.3  450 3
6.. Then, under the ‘Wells’ menu, assign
an injection well at Column 16 and Row 16 from days 0 to 730 with flow rate = 1 m3/d;
and a pumping well at Column 31 and Row 16 days 0 to 730 with flow rate = 1 m3/d.
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7. Go the Main menu and select RUN. Under the ‘MODFLOW’ menu,
Click on the ‘Steady-State’ run type.
Select the ‘Layers’ submenu and toggle the layer type for all layers into Type-0
(confined).
Select the ‘Solver’ submenu and change the solver from the default ‘WHS’ to ‘PCG2’.
8. Translate and run ‘MODFLOW’ only, under ‘steady-state’ mode, and check calculated
head distribution as well as flow balance.
VMOD Notes on Transport Simulation
1.. Return to the main menu. Then go to ‘SETUP’, and
Select ‘Numerical Engines’ and define a MT3D99 simulation with ‘linear isotherm
(equilibrium-controlled)’ and Instantaneous Reactions with two species as in
Designation
Component Description
Mobile
SCONC
SP1
BTEX
Component 001
yes
0
0
Oxygen
Component 002
yes
0
0
Note: the sorption option is selected but SP1(Kd) is set to zero so that it is equivalent to
no sorption. This must be done because VMOD appears to have a bug; without the
sorption option, VMOD does not seem to generate the chemical reaction input file.
Also in the same screen under the ‘Model Params’, input the value 3.0 as the yield
coefficient between BTEX and Oxygen.
2. Go back to the INPUT screen. Under Properties, select Initial Concentration and
Assign initial BTEX concentration to zero everywhere in the grid;
Assign initial Oxygen concentration to 9 mg/L everywhere in the grid.
3. Go to ‘OVERLAY’ screen, and turn on ‘Pumping Wells’ to display them. Then, under
Boundaries, select ‘Point Source’ and
Assign concentration at the injection well at Row 16 and Column 16
Start(day)
End(day)
BTEX Conc. (mg/L) O2 Conc (mg/L)
0
730
1000
0
and assign concentration at the constant-head boundary on the left-hand side (Column 1):
Start(day)
End(day)
BTEX Conc. (mg/L) O2 Conc (mg/L)
0
730
0
9
4. Go to the RUN screen and under the MT3D99 menu,
Select the Advection submenu, and select TVD and set the Courant number to 0.75.
Then, select the Output/Time Step submenu, and set the total simulation time to 730 days.
5. Translate and Run both MODFLOW and MT3D99, and in the OUTPUT screen,
Check the concentration distribution for both BTEX and O2 at the end of simulation. Set
the contour levels for BTEX to 1, 5, 10, and 25; and 1 and 5 for Oxygen. Select different
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contour colors to overlay the two plumes. The BTEX plume should be similar to Figure
2(a), while the Oxygen plume similar to Figure 2(b). You can also export the calculated
concentration values along Row 16 and Column 30, respectively, to external ASCII files.
Which, when plotted using Excel, should be similar to those shown in Figures 3 and 4.
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BTEX
Concentration (ppm)
50
O2
40
30
20
10
0
0
100
200
300
Longitudinal Distance (m)
400
Figure 3. Calculated BTEX and O2 concentrations along the flow direction (Row 16).
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Concentration (ppm)
10
8
6
4
BTEX
2
O2
0
0
50
100
150
200
250
300
Transverse Distance (m)
Figure 4. Calculated BTEX and O2 concentrations normal to flow direction (along Column 30).
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Comparison with First-Order and Monod Kinetics
Next, we will try to simulate the aerobic biodegradation of BTEX using single-species, firstorder and Monod kinetics, and compare the simulated BTEX plumes with Figure 2(a).
First, go to the Main menu, and from the ‘SETUP’ menu, select ‘Numeric Engines’. Create a
new ‘Variant’ of the MT3D’99 model with ‘linear isotherm (equilibrium-controlled)’ and ‘firstorder decay’. What is the first-order rate coefficient that would lead to a reasonable match
between the simulated plume and Figure 2(a)?
Next, go to the Main menu, and from the ‘SETUP’ menu, select ‘Numeric Engines’ again.
Create a new ‘Variant’ of the MT3D’99 model with ‘linear sorption (equilibrium-controlled)’
and ‘Monod kinetics. Note that Monod kinetics is a nonlinear reaction, which requires the
outer iteration number to be greater than 1. Assign a value of 10. What are the two Monod
kinetics parameters that would lead to a reasonable match between the simulated plume and
Figure 2(a)?
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