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Background on Flow and Transport Properties

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The following sections present an overview of the property zone parameters required for flow and transport models in Visual MODFLOW Flex.

A steady-state groundwater flow model requires conductivity and initial heads property values for each active grid cell in order to run a flow simulation, while transient flow models also require storage properties for each active grid cell. Similarly, a transport model requires various model and species parameter values for each active grid cell in order to run a transport simulation. Upon creating a Visual MODFLOW Flex project, the default flow and transport parameter values are assigned to every grid cell in the model domain. This will ensure the model has the minimum data required to run a simulation. However, in most situations, the flow and transport properties will not be uniform throughout the entire model domain, and it will be necessary to assign different property values to different areas of the model.

Heterogeneous property values are supported by Visual MODFLOW Flex using either Constant Value Property Zones, or Distributed Value Property Zones. These two different approaches are described below.

 

Constant Value Property Zones

The Constant Value Property Zones approach is the most simple and straight-forward, and can be used for all model properties supported by Visual MODFLOW. Different model properties are accommodated by grouping grid cells sharing the same property values into “property zones”. Each property zone will (normally) contain a unique set of property values, and is represented by a different grid cell color.

The Constant Value Property Zones approach requires the development of a conceptual model, whereby each hydrostratigraphic unit of the model is assigned a uniform set of property values. For example, consider an aquifer where there is pumping test data and slug test data indicating a range of horizontal conductivity values from 1x10-4 cm/s to 5x10-4 cm/s at different locations within the aquifer. The conceptual approach would assign a uniform Kx and Ky value of 2.5x10-4 cm/s to the entire aquifer. This value would be adjusted up or down for calibration purposes within the range of values reported. If a reasonable calibration cannot be achieved using this conceptual model, it may be necessary to sub-divide this region into several zones to accommodate local irregularities in the flow pattern. However, almost all modeling textbooks strongly recommend starting out simple at first, getting as close a solution as possible, and then making the model more complex, if necessary.

 

Distributed Value Property Zones

The Distributed Value Property Zones approach is available for flow properties (conductivity, storage, and initial Heads), and most transport properties (e.g. initial concentrations, longitudinal dispersivity, sorption parameters). This approach is a little more complicated than the constant value property zone approach because it involves linking a property zone to one or more parameter distribution arrays containing data interpolated from scattered observation points. When a property zone is linked to a distribution array, the property values assigned to each grid cell within that zone are calculated by multiplying the zone parameter value with the corresponding value from the parameter distribution array. If the grid spacing from the model does not match the grid spacing from the distribution array, a bivariate interpolation scheme is used to calculate the appropriate parameter value at the center of the model grid cell using the four nearest data nodes in the parameter distribution array.

 

Flow Properties

 

Conductivity

Kx - Hydraulic conductivity in the direction of the model X-axis

Ky - Hydraulic conductivity in the direction of the model Y-axis

Kz - Hydraulic conductivity in the direction of the model Z-axis

 

These conductivity parameters may be defined on a cell-by-cell basis using constant property values and/or distributed property values. When importing or assigning the conductivity property zones, Visual MODFLOW Flex will require valid data for each of the above parameters.

 

Anisotropy

The reason Visual MODFLOW Flex prompts for both Kx and Ky is because there are two options for defining the horizontal anisotropy of the Conductivity property zones:

 

Anisotropy by layer

Anisotropy as specified

 

Note: The anisotropy option is set in Translation settings. (see Anisotropy for more details).

If the 'Anisotropy by layer' option is used, the Kx value will determine the conductivity in the X-direction, and the specified anisotropy ratio (Ky/Kx) for each layer will be used to calculate the Ky value for each grid cell.

If the 'Anisotropy as specified' option is used, the model will use the Kx and Ky values defined for each property zone.

Storage

Ss - specific storage

Sy - specific yield

Eff. Por - effective porosity

Tot. Por - total porosity

                                     

Specific Storage (Ss) is defined as the volume of water that a unit volume of aquifer releases from storage under a unit decline in hydraulic head due to aquifer compaction and water expansion. Visual MODFLOW Flex determines the primary storage coefficient (sf1) for MODFLOW based on the user defined Specific Storage parameter. The primary storage coefficient is calculated by Visual MODFLOW to be equal to the specific storage multiplied by the layer thickness (Specific Storage x thickness = Primary storage coefficient). Please NOTE that Specific Storage is not used in Steady State simulations.

Specific Yield (Sy) is known as the storage term for an unconfined aquifer. It is defined as the volume of water that an unconfined aquifer releases from storage per unit surface area per unit decline in the water table. For sand and gravel aquifers, specific yield is generally equal to the porosity. MODFLOW uses Ss or Sy depending on the layer type assigned by the user (please refer to "Layer Type Settings"). For an unconfined layer, MODFLOW uses Sy to determine storage volumes. For a confined layer, Ss is used. For a variable layer, MODFLOW will check the head value of the cell to determine if it is confined or not. If you do not have measured parameter values for Sc and Sy it is recommended that you refer to literature values as a default.

Effective Porosity (Eff. Por) is the pore space through which flow actually occurs, and is used by MODPATH to determine the average linear groundwater velocities for use in time-dependent capture zones and time markers along pathlines. This term is not used for MODFLOW simulations.

Total Porosity (Tot. Por) is the percentage of the rock or soil that is void of material, and is used by MT3D/RT3D/SEAWAT (by default) to determine the chemical reaction coefficients, and for calculating the average linear groundwater flow velocity in the particle tracking solution schemes. A different porosity is used for MT3D/RT3D/SEAWAT than for MODPATH because MT3D accounts for additional transport and reactive processes, such as dispersion. The total porosity term is not used for MODFLOW simulations.

These storage parameters may be defined on a cell-by-cell basis using constant property values and/or distributed property values. When importing or assigning the storage property zones, Visual MODFLOW Flex will require valid data for each of the above parameters.

 

Note: MODFLOW-SURFACT supports the time-varying material properties (TMP1) package (as an add-on) where the flow properties may change over time, as discussed here.

 

Initial Heads

In order to start solving the flow simulation, flow engines require an initial “guess” for the head values in the model.  A good initial guess for the starting heads of the simulation can reduce the required run time significantly, while a poor initial guess can increase run times or lead to stability and/or convergence issues. The Initial Head values are also used to calculate drawdown values, as measured by the difference between the starting head and the calculated head.

 

Vadose Zone

The vadose zone object is only available when an unsaturated flow model (MODFLOW-2005 with the unsaturated zone flow (UZF) package or MODFLOW-SURFACT) is selected in the Modeling Objectives workflow step.

The vadose zone, or unsaturated zone, extends from the land surface to the water table. The vadose zone typically has a lower hydraulic conductivity because some of the pore space is filled with air, and the soil moisture in the vadose zone only travels through the wetted cross-section of the pore space. The relative proportion of air to water in the pores can vary, and consequently the hydraulic properties of the porous media can also vary.

In general, soil moisture in the vadose zone is under tension, and it travels through the vadose zone due to total soil-moisture potential (the sum of the elevation potential, and the pressure head). The pressure head is a function of the volumetric water content of the soil, and depends upon whether the soil has previously undergone wetting or drying. The relationship between pressure head and volumetric water content for a particular soil is known as a soil-water characteristic curve. Using the experimental soil-water characteristic curve and the soil hydrologic parameters, the movement of water in the vadose zone can be determined using the BCF4 package in MODFLOW-SURFACT or the UZF package in MODFLOW 2005. A sample index of soil properties is given below:

 

Table: Sample Index of Soil Hydraulic Properties by Soil Texture*

Soil Type

Sand
[%]

Clay
[%]

Bulk Density

[g/cm3]

Field Capacity

[cm3/cm3]

Wilting Point

[cm3/cm3]

Porosity Fraction

[-]

Saturated Hydraulic Conductivity

[cm/s]

Slope of Retention Curve
[log space] **

Alpha parameter

[cm-1] ***

sand (s)

94.83

2.27

1.49

0.08

0.03

0.43

0.0107

4.1

0.145

loamy sand (ls)

85.23

6.53

1.52

0.15

0.06

0.42

0.003

3.99

0.124

sandy loam (sl)

69.28

12.48

1.57

0.21

0.09

0.4

0.0015

4.84

0.075

silt loam (sil)

19.28

17.11

1.42

0.32

0.12

0.46

0.0011

3.79

0.02

silt (si)

4.5

8.3

1.28

0.28

0.08

0.52

0.0023

3.05

0.016

loam (l)

41

20.69

1.49

0.29

0.14

0.43

0.0005

5.3

0.036

sandy clay loam (scl)

60.97

26.33

1.6

0.27

0.17

0.39

0.0007

8.66

0.059

silty clay loam (sicl)

9.04

33.05

1.38

0.36

0.21

0.48

0.0015

7.48

0.01

clay loam (cl)

30.08

33.46

1.43

0.34

0.21

0.46

0.0005

8.02

0.019

sandy clay (sc)

50.32

39.3

1.57

0.31

0.23

0.41

0.0003

13

0.027

silty clay (sic)

8.18

44.58

1.35

0.37

0.25

0.49

0.0008

9.76

0.005

clay (c)

24.71

52.46

1.39

0.36

0.27

0.47

0.0009

12.28

 

* Source: " Average hydraulic conductivity properties of ARS soil texture classes", draft dated February, 2000 by J. Schaake. This expanded the work of others and included a total of 2128 soil samples. Wilting point is the fractional water content at 15 bar tension; field capacity is the fractional water content at 1/3 bar tension.

 

* Used in Campbell’s equation. ref: Coby et al., A Statistical exploration of the relationship of soil moisture characteristics to the physical properties of soils, Water Resources Research 20(6): 682-690, 1984.

 

** Average values of the van Genuchten soil parameters obtained by experimental means (Carsel and Parrish, 1988) and also reported on page 180 in Contaminant Hydrogeology book by C. W. Fetter (1999). You may want to consider also the ROSETTA code for estimating the unsaturated soil hydraulic properties which can be downloaded from the US Salinity Laboratory website: http://www.ussl.ars.usda.gov.

 

 

Figure: Soil texture classes triangle.

 

Source: Agriculture and Food Canada, 2017 (http://sis.agr.gc.ca/cansis/taxa/cssc3/chpt17.html)

 

Unsaturated Flow - UZF Package

In order to solve the variably saturated flow problem using the UZF package, it is necessary to specify the relationship of relative permeability (Krw) versus water phase saturation (θ), and pressure head (ψ) versus water phase saturation (θ).  Flow through and storage in the unsaturated zone is estimated in the UZF package using a kinematic wave approximation of Richard's equation using the method of characteristics.  The approach includes the assumptions that flow in the unsaturated zone is driven by gravity, that negative potential gradients are ignored, and that flow is vertical through a homogenous column of soil.  The Brooks-Corey function is used to estimate the relationship between relative hydraulic conductivity and water saturation:

 

 

where:

Krw is the relative hydraulic conductivity [L/T]

ε is the Brooks-Corey exponent [-]

Se is the effective water saturation [-]

θ is the current water saturation, which is a function of pressure head [-]

θr is the residual water saturation [-]

 

The parameters are entered as follows:

EPS - (Brooks-Corey exponent ε) controls the air-entry pressure - the smaller the α value, the larger the capillary fringe above the water table.  Gravels and sands have a large α while clayey soils have a small α.

THTi - (initial water saturation θi ) initial water content in the vadose zone.

THTs - (residual water saturation θr) depends upon several factors of the soil including packing. Residual saturation values are generally low for sands and gravels and high for clayey soils. Residual saturation typically ranges from 0.01 to 0.4.

 

The BCF4 package in MODFLOW SURFACT can solve for variably saturated flow in the vadose zone in three dimensions using the Brooks-Corey equation described above or using the Van Genuchten (1980) equation for relative permeability:

 

 

where:

ɣ is an empirical parameter [dimensionless] and is related to empirical parameter β as follows:

 

The relationship of the pressure head (ψ) [L] to relative saturation is described by van Genuchten (1980) using the following equation:

 

 

 

where:

α is an empirical parameter [1/L]

β is an empirical parameter [-]

hc is the capillary pressure [L] and is related to pressure head (ψ)  and elevation (z) by ψ = hc + z

 

Depending on the saturation model selected, the primary inputs for simulating groundwater flow in the vadose zone using MODFLOW-SURFACT are the van Genuchten parameters (α, β, and θr ) and the Brooks-Corey parameter (ε).  The Brooks-Corey and van Genuchten empirical parameters can be measured in the laboratory for a given soil by plotting a soil-water characteristic curve.

The parameters are entered as follows:

VANAL - (van Genuchten α parameter) controls the air-entry pressure - the smaller the α value, the larger the capillary fringe above the water table.  Gravels and sands have a large α while clayey soils have a small α.

VANBT - (van Genuchten β parameter) controls how rapidly the saturation drops from unity to residual, and is an indicator of the grain size distribution. For larger values of β, the saturation drops rapidly with head (uniform grain size distribution), while for smaller values of β, the drop is more gradual (grain-size, and therefore pore size is more varied). β is greater than unity, but typically can be from 1.3 to 6, depending upon the soil.

VANSR - (residual water saturation θr) depends upon several factors of the soil including packing. Residual saturation values are generally low for sands and gravels and high for clayey soils. Residual saturation typically ranges from 0.01 to 0.4.

Brook - (Brooks-Corey ε)  is the Brooks-Corey empirical exponent.  It must be greater than zero (default value is 0.5).

 

The BCF4 package in SURFACT can also be used to simulate vapor flow through the vadose zone.  Pressure head in the air phase (Pa) and total head in the air phase (hap) are related as follows:

 

where

ρw is density of water [L3/T]

ρa is the density of air [L3/T]

g is the gravitational acceleration constant [L/T2]

h is the total head in the air phase [L]

z is the elevation [L]

 

Soil vapor flow options for MODFLOW-SURFACT simulations are set using the advanced settings for the BCF4 package in the Translation Settings workflow step. These are initially based on the project defaults for physical constants in the Model Defaults tab (found under File / Project Defaults / Model Defaults) and include the following:

RHOWPw) is density of water [L3/T]

PHOAPa) is the density of air [L3/T]

VISWw) is the viscosity of water [M/LT]

VISGa) is the viscosity of air [M/LT]

COMPWATw) compressibility of water [LT2/M]

COMPAIRa) compressibility of air [LT2/M]

ATMGP (Patm) is the standard atmospheric pressure [M/LT2]

GRAV (g) is the gravitational acceleration constant [L/T2]

 

Transport Properties

If no transport engine variant has been selected, the Transport Properties options will be disabled. If a transport engine has been selected then the following properties must be defined.

Initial Concentration

In many cases, the historical conditions of the site are unknown, and the contaminant source has been removed or remediated. In such cases, the groundwater contamination is still present and the mass transport simulation must be run forward in time, starting from the existing conditions, to predict the potential downstream impacts. The Initial Concentration properties define the existing conditions of each chemical species at the start of the simulation period.

Initial Concentrations must be defined for each chemical species that you have defined in the Define Modeling Objectives; the default value is 0.  

Model Parameters

Model parameters consist of material properties associated with the geologic units that are independent of the constituent species to be modeled.  The specific model parameters required as part of each simulation is defined by the retardation model and reaction model selected as part of the Define Objectives workflow step.

 

Retardation Model - Model Parameters

 

Bulk Density

Soil Bulk Density is used to calculate the retardation coefficient for each chemical species according to the following formula:

 

where:

 

Ri = Retardation Coefficient of Species i [-]

 

ρb = Soil Bulk Density [M/L3]

 

n = Effective Soil Porosity [L3/L3] à [-]

 

Kd(i) = Distribution Coefficient of Species i [L3/M]

 

The retardation coefficient is used to calculate the ‘retarded’ flow velocity (VR(i)) of each chemical species according to the following formula:

 

 

where:

 

VR(i) = Retarded Flow Velocity of Species i [L/T]

 

V = Average Linear Groundwater Flow Velocity [L/T]

 

Ri = Retardation Coefficient of Species i [-]

 

The retarded flow velocity is used to calculate the advective transport of each species.

Unless otherwise specified during the setup of the transport model, the default soil Bulk Density value for any new model created is 1700 kg/m3.

If no sorption method is selected in the current transport variant, then no Bulk Density values are required for the simulation, and all of the options in the left-hand toolbar will be disabled.

 

Reaction Model/Modules - Model Parameters

The reaction modules associated with RT3D may require model parameter values and settings to be selected at the Define Modeling Objectives workflow step, these include:

Instantaneous aerobic degradation of BTEX [IREACT=1];

Six-Species, First-Order, Rate-Limited, BTEX Degradation using Sequential Electron Acceptors [IREACT=3];

Rate-Limited Sorption [IREACT=4];

Double-Monod Model [IREACT=5];

Sequential First-Order Decay [IREACT=6]; and

Aerobic/Anaerobic PCE/TCE Dechlorination [IREACT=7]

 
where IREACT is a flag in the RT3D RCT package file whose value determines which reaction module is active in the transport model run.

Note: yield values associated with several reaction modules in RT3D are defined on a mg/L basis. To be consistent the user must use mg/L units for all concentrations when using these reaction modules. See additional notes for each reaction module.

 

Instantaneous aerobic degradation of BTEX

 

Parameter

Caption

Description

Default

Units

Constant /

Spatially Variable

Node in Model Explorer

RC1

Y_O2/BTEX

Stoichiometric ratio of oxygen (consumed) to BTEX

3.14

[ - ]

Const

n/a

Stoichiometry

* Note: By changing the value of RC1 instantaneous reactions between any other chemicals can be simulated using this module

 

 

Six-Species, First-Order, Rate-Limited, BTEX Degradation using Sequential Electron Acceptors

 

Parameter

Caption

Description

Default

Units

Constant /

Spatially Variable

Node in Model Explorer

RC1

Cmax_Fe2+

Maximum concentration of Fe2+

0

[M/L3]

Const/Var

R3-3(Reduction Capacities)

RC2

Cmax_CH4

Maximum concentration of CH4

0

[M/L3]

Const/Var

RC3

K_O2

Hydrocarbon decay rate via aerobic process

0

[1/T]

Const/Var

R3-3(Rates)

RC4

K_NO3

Hydrocarbon decay rate via denitrification

0

[1/T]

Const/Var

RC5

K_Fe3+

Hydrocarbon decay rate via iron reduction

0

[1/T]

Const/Var

RC6

K_SO4

Hydrocarbon decay rate via sulfate reduction

0

[1/T]

Const/Var

RC7

K_CH4

Hydrocarbon decay rate via methanogenesis

0

[1/T]

Const/Var

RC8

Ks_O2

Half-saturation constant for oxygen

0.5

[M/L3]

Const/Var

R3-3(Saturations)

RC9

Ks_NO3

Half-saturation constant for nitrate

0.5

[M/L3]

Const/Var

RC10

Ks_Fe3+

Half-saturation constant for Fe3+

0.5

[M/L3]

Const/Var

RC11

Ks_SO4

Half-saturation constant for sulfate

0.5

[M/L3]

Const/Var

RC12

Ks_CH4

Half-saturation constant for methane

0.5

[M/L3]

Const/Var

RC13

Ki_O2

Inhibition coefficient for the oxygen reaction

0.01

[M/L3]

Const/Var

R3-3(Inhibitions)

RC14

Ki_NO3

Inhibition coefficient for the nitrate reaction

0.01

[M/L3]

Const/Var

RC15

Ki_Fe3+

Inhibition coefficient for the Fe3+ reaction

10

[M/L3]

Const/Var

RC16

Ki_SO4

Inhibition coefficient for the sulfate reaction

0.01

[M/L3]

Const/Var

RC17

Y_O2/BTEX

Stoichiometric ratio of oxygen (consumed) to BTEX

3.14

[ - ]*

Const

n/a

Stoichiometry

RC18

Y_NO3/BTEX

Stoichiometric ratio of nitrate (consumed) to BTEX

4.9

[ - ]*

Const

RC19

Y_Fe/BTEX

Stoichiometric ratio of Fe2+ (produced) to BTEX

21.8

[ - ]*

Const

RC20

Y_SO4/BTEX

Stoichiometric ratio of sulfate (consumed) to BTEX

4.7

[ - ]*

Const

RC21

Y_CH4/BTEX

Stoichiometric ratio of methane (produced) to BTEX

0.78

[ - ]*

Const

* Note: Yield values are on a mg/L basis; to be consistent, the user must use mg/L units for all concentrations when using this reaction module

 

 

 

Rate-Limited Sorption

 

Parameter

Caption

Description

Default

Units

Constant /

Spatially Variable

Node in Model Explorer

RC1

K_mt

Mass-transfer rate coefficient

0

[1/T]

Const/Var

R3-4(Sorption)

RC2

Kd

Linear partitioning coefficient (Kd)

1

[L3/M]

Const/Var

 

 

 

Double-Monod Model

 

Parameter

Caption

Description

Default

Units

Constant /

Spatially Variable

Node in Model Explorer

RC1

μ_m(w)

Specific utilization rate

0

[1/T]

Const/Var

R3-5(Rates)

RC2

Ks_d

Monod half-saturation constant for electron donor

0.5

[M/L3]

Const/Var

R3-5(Saturations)

RC3

Ks_a

Monod half-saturation constant for electron acceptor

0.5

[M/L3]

Const/Var

RC4

Y_x/d

Biomass produced per unit of electron donor utilized

0

[ - ]

Const

n/a

Stoichiometry

RC5

Y_a/d

Electron acceptor used per unit of electron donor utilized

0

[ - ]

Const

RC6

K_decay

First-order bacterial death or decay rate

0

[1/T]

Const/Var

R3-5(Rates)

RC7

K_attach

First-order bacterial attachment rate

0

[1/T]

Const/Var

RC8

K_detach

First-order bacterial detachment rate

0

[1/T]

Const/Var

* Note: This reaction module describes a general double Monod model. By setting appropriate yield and kinetic constants, users can model any type of biological systems. Kinetic constants for an aerobic system are given in Clement et al. (1998), and for an anaerobic denitrifying system are given in Clement et al. (1997). Also see Taylor and Jaffe (1990); Hornberger et al. (1992); Zysset et al. (1994); and Reddy and Ford (1996).

 

 

Sequential First-Order Decay

 

Parameter

Caption

Description

Default

Units

Constant /

Spatially Variable

Node in Model Explorer

RC1

K_A

PCE first-order degradation rate

0

[1/T]

Const/Var

R3-6(Rates)

RC2

K_B

TCE first-order degradation rate

0

[1/T]

Const/Var

RC3

K_C

DCE first-order degradation rate

0

[1/T]

Const/Var

RC4

K_D

VC first-order degradation rate

0

[1/T]

Const/Var

RC5

Y_tce/pce

Yield coefficient, TCE/PCE

0.792

[ - ]*

Const

n/a

Stoichiometry

RC6

Y_dce/tce

Yield coefficient, DCE/TCE

0.738

[ - ]*

Const

RC7

Y_vc/dce

Yield coefficient, VC/DCE

0.644

[ - ]*

Const

* Note: Yield values are on a mg/L basis; to be consistent, the user must use mg/L units for all concentrations when using this reaction module

 

Aerobic/Anaerobic PCE/TCE Dechlorination

 

Parameter

Caption

Description

Default

Units

Constant /

Spatially Variable

Node in Model Explorer

RC1

Kp

Sequential (anaerobic) reaction rate for PCE

0

[1/T]

Const/Var

R3-7(Rates)

RC2

Kt1

Sequential (anaerobic) reaction rate for TCE

0

[1/T]

Const/Var

RC3

Kt2

Aerobic decay rate for TCE

0

[1/T]

Const/Var

RC4

Kd1

Sequential (anaerobic) reaction rate for DCE

0

[1/T]

Const/Var

RC5

Kd2

Aerobic decay rate for DCE

0

[1/T]

Const/Var

RC6

Kv1

Sequential (anaerobic) reaction rate for VC

0

[1/T]

Const/Var

RC7

Kv2

Aerobic decay rate for VC

0

[1/T]

Const/Var

RC8

Ke1

Sequential (anaerobic) reaction rate for ETH

0

[1/T]

Const/Var

RC9

Ke2

Aerobic decay rate for ETH

0

[1/T]

Const/Var

* Note: All the yield values are fixed internally; to be consistent, use mg/L units for all species concentrations.

 

Species Parameters

The Species Parameters include the Sorption and Reaction parameters used by the selected transport settings. The available parameters will depend on what sorption and reaction settings you selected in the Modeling Objectives workflow step. The parameters presented in the Species Parameters Database window are from the parameters listed in the Species Parameters Tab in the Modeling Objectives workflow step.

If no sorption or reactions are selected in the current transport variant, then no sorption or reaction parameters are required for the simulation, and there will not be an option for "Species Parameters" at the Define Properties workflow step.

The parameters are described by retardation model and reaction model below.

 

Retardation Model - Species Parameters

The list of parameters required for each species based on each retardation model is provided below, associated base units are provided in square brackets [ ], where L signifies length (e.g. meters, feet), M signifies mass (e.g. kilograms, pounds), and T signifies time (e.g. seconds, days, years).

 

A tabulation of which retardation model is supported by each of the transport engines is provided in the Define Modeling Objectives workflow step.   For more detailed documentation on each of the retardation model parameters, please refer to the documentation of the relevant transport engine (i.e. MT3DMS, RT3D, SEAWAT, or MODFLOW-SURFACT).

 

Linear Isotherm (equilibrium controlled)

Kd is the distribution coefficient [1/(M/L3)]

 

         

Freundlich (equilibrium-controlled)

Kf is the Freundlich constant [1/(M/L3)a]

 

a is the Freundlich exponent [-]

 

Langmuir (equilibrium-controlled)

Kl is the Langmuir is constant  [1/(M/L3)]

 

S is the total concentration of sorption sites available [-]

 

First order kinetic sorption (non-equilibrium)

Kd is the distribution coefficient [1/(M/L3)]

 

K_mass is the first-order kinetic mass transfer coefficient [1/T]

 

Dual-domain mass-transfer without sorption

SCONCIM is the initial concentration in the distribution coefficient  [1/(M/L3)]

 

K_mass is the first-order kinetic mass transfer coefficient [1/T]

 

Dual-domain mass-transfer with linear sorption in mobile domain

SCONCIM is the initial concentration in the immobile domain [M/L3]

 

Kd is the distribution coefficient for the mobile domain [1/(M/L3)]

 

K_mass is the first-order kinetic mass transfer coefficient [1/T]

 

Dual-domain mass-transfer (with the same linear sorption in mobile and immobile domains)

SCONCIM is the initial concentration in the immobile domain [M/L3]

 

Kd is the distribution coefficient for both the mobile and immobile domain [1/(M/L3)]

 

K_mass is the first-order kinetic mass transfer coefficient [1/T]

 

Dual-domain mass-transfer (with different linear sorption in mobile and immobile domains)

SCONCIM is the initial concentration in the immobile domain [M/L3]

 

Kd is the distribution coefficient for the mobile domain [1/(M/L3)]

 

K_mass is the first-order kinetic mass transfer coefficient [1/T]

 

KdIm is the distribution coefficient for the immobile domain [1/(M/L3)]

 

Dual-domain mass-transfer with nonlinear sorption in mobile domain

SCONCIM is the initial concentration in the immobile domain [M/L3]

 

Kf is the Freundlich constant for the mobile domain [1/(M/L3)a]

 

a is the Freundlich exponent for the mobile domain [-]

 

K_mass is the first-order kinetic mass transfer coefficient [1/T]

 

Dual-domain mass-transfer (with the same nonlinear sorption in mobile and immobile domains)

SCONCIM is the initial concentration in the immobile domain [M/L3]

 

Kf is the Freundlich constant for both the mobile and immobile domain [1/(M/L3)a]

 

a is the Freundlich exponent for both the mobile and immobile domain [-]

 

K_mass is the first-order kinetic mass transfer coefficient [1/T]

 

 

Dual-domain mass-transfer (with different linear sorption in mobile and immobile domains)

SCONCIM is the initial concentration in the immobile domain [M/L3]

 

Kf is the Freundlich constant for the mobile domain [1/(M/L3)a]

 

a is the Freundlich exponent for the mobile domain [-]

 

K_mass is the first-order kinetic mass transfer coefficient [1/T]

 

KfIm is the Freundlich constant for the immobile domain [1/(M/L3)aim]

 

aim is the Freundlich exponent for the immobile domain [-]

 
 

Reaction Model - Species Parameters

The list of parameters required for each species based on each reaction model is provided below, associated base units are provided in square brackets [ ], where L signifies length (e.g. meters, feet), M signifies mass (e.g. kilograms, pounds), and T signifies time (e.g. seconds, days, years).

 

A tabulation of which reaction model is supported by each of the transport engines is provided in the Define Modeling Objectives workflow step.   For more detailed documentation on each of the retardation model parameters, please refer to the documentation of the relevant transport engine (i.e. MT3DMS, RT3D, SEAWAT, or MODFLOW-SURFACT).

 

NOTE: The RT3D reactions have specific default species for each of its associated reaction modules.  Selecting a reaction module specific to RT3D will reset the species list and all associated species and model parameters.

 

First-Order Irreversible Decay

K_mobile is the first-order decay rate coefficient for dissolved constituents in both the mobile and immobile domain [1/T]

 

K_sorbed is the first-order decay rate coefficient for sorbed constituents in both the mobile and immobile domain [1/T]

 

 

Note: First-order decay rate coefficients can be derived from half-life values, which are more commonly available. Concentrations that follow first-order decay can be shown to change over time by the equation:

 

 

where:

 

Ct is the concentration of the constituent at time t [M/L3]

C0 is the initial concentration of the constituent [M/L3]

k is the first order decay rate [1/T]

t is elapsed time [T]

 

When the constituent concentration reaches half of its initial concentration (i.e. Ct = 0.5 x C0), the equation above can be rewritten as:

 

k = ln 2 / t1/2

 

where:

 

k is the first order decay rate [1/T]

t1/2 is the half-life of the constituent C [T]

 

Zeroth-Order Irreversible Decay

K_mobile is the zeroth-order decay rate coefficient for dissolved constituents in both the mobile and immobile domain [1/T]

 

K_sorbed is the zeroth-order decay rate coefficient for sorbed constituents in both the mobile and immobile domain [1/T]

 

 

RT3D Reaction Modules

When selecting one of the reaction modules associated with RT3D:

Instantaneous aerobic degradation of of BTEX;

Six-Species, First-Order, Rate-Limited, BTEX Degradation using Sequential Electron Acceptors;

Rate-Limited Sorption;

Double-Monod Model;

Sequential First-Order Decay; or

Aerobic/Anaerobic PCE/TCE Dechlorination

 

The Absolute Tolerance (ATOL) and Relative Tolerance (RTOL) species parameters will be added for each species.  These tolerance parameters are used by the differential equations solver in RT3D to control convergence errors while solving the applicable reaction model.  Setting ATOL(i) = 0.0 results in a pure relative error test on  Species i, while setting RTOL(i) = 0.0 results in a pure absolute error test on Species i. For practical problems, the following rules of thumb may be used to set ATOL and RTOL values:

 

set RTOL(i) = 10-(m+1), where m is the desired number of significant digits for concentration output for species i (Ci )

set ATOL(i) to a small value at which the absolute value of Ci is essentially insignificant (typically between 10-6 to 10-9)

Note: that RTOL + ATOL > 0

 

Caution: Actual (global) errors may exceed the local tolerances, so choose ATOL(i) and RTOL(i) conservatively.

 

Longitudinal Dispersion

Dispersion is a physical process that tends to ‘disperse’, or spread, the contaminant mass in the X, Y and Z directions along the advective path of the plume, and acts to reduce the solute concentration. Dispersion is caused by the tortuosity of the flowpaths of the groundwater as it travels through the interconnected pores of the soil.

 

Dispersion is calculated using the equation:

 

 

where:

 

D is the Dispersion Coefficient [L2/T]

is the longitudinal dispersivity [L]

VL is the longitudinal velocity of flow along the plume migration pathway [L/T]

is the horizontal dispersivity [L]

VH is the horizontal velocity of flow along the plume migration pathway [L/T]

is the vertical dispersivity [L]

VV is the vertical velocity of flow along the plume migration pathway [L/T]

D* is the diffusion coefficient [L2/T]

|v| is the magnitude of seepage velocity [L/T]

 

MT3DMS, RT3D, SEAWAT, and SURFACT calculate the Dispersion Coefficient for the mass transport model using the following parameters:

Longitudinal Dispersivity for each transport grid cell

Ratio of Horizontal to Longitudinal Dispersivity for each layer

Ratio of Vertical to Longitudinal Dispersivity for each layer

Molecular Diffusion Coefficient for each layer

 

Longitudinal Dispersion can be defined using the regular set of tools provided for most parameters (i.e. cell-by-cell, by layer/row/column, or using polylines/polygons/data objects). The Longitudinal Dispersion can also be defined on a layer-by-layer basis  by right-clicking the Longitudinal Dispersion object in the model tree and selecting the Dispersion Parameters option.

 

 

The following dialog will appear:

 

 

Longitudinal Dispersion can also be defined based on property zones by right-clicking the Longitudinal Dispersion object in the model tree and selecting the Edit Property Zones... option.  The absolute values of the horizontal and vertical dispersion parameters will be adjusted according to the property zone values.

 

 

For SEAWAT models, you can specify a diffusion coefficient for each species using the MDCOEFF variable at the define modeling objectives step.  The values will be used if the Multi-diffusion option is set to true in the Advanced Settings for the DSP package in the Translation step.

 

 


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