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Variable Density Flow (VDF) Package Advanced Translation Settings

The Variable Density Flow (VDF) package is an integral part of the SEAWAT engine as it defines the relationship(s) between fluid density and solute concentration(s).  The VDF package is required to run a SEAWAT model simulation.  Numerous options and settings are supported as part of the translation settings in Visual MODFLOW Flex and are described below.

 

Settings for the VDF package are divided into high-level settings that are always required as part of the VDF package and low-level settings that are required (or not) based on the high-level settings.  High-level settings are located in the VDF group of the advanced package table, while low-level settings are displayed as needed in the form area below.  For more complete explanation of the input settings for the VDF package, please refer to p16-19 of the SEAWAT V4 Manual (Langevin et. al., 2007).

 

 

 

 

Variable Density - Theory

In SEAWAT, fluid density is estimated as a linear function of the concentration of one or more solute species, temperature, and pressure head:

 

 ρ = ρ(ref) + Σ ẟρ/ẟCi · [ Ci -  Ci (ref) ] + ẟρ/ẟT · [ T -  T(ref) ] + ẟρ/ẟl · [ l - l(ref) ]

 

 where:

 

ρ is the fluid density [M/L3]

ρ(ref) is the reference fluid density [M/L3]

Ci is the concentration of the ith species [M/L3]

Ci (ref) is the reference concentration, or the concentration at which the fluid density = ρ(ref) [M/L3]

ẟρ/ẟCi is the density/concentration slope, or change in density per unit change in solute concentration of the ith species [ - ]

T is the temperature [Θ]

T(ref) is the reference temperature, or the temperature at which the fluid density = ρ(ref) [Θ]

ẟρ/ẟT is the density/temperature slope [M/L3·Θ]

l is the pressure head [L]

l(ref) is the reference pressure head, or the pressure head at which the fluid density = ρ(ref) [L]

ẟρ/ẟl is the density/pressure head slope [M/L4]

 

Commonly used values for the VDF package

Variable

Reference Value

Slope

Setting Location

Density

1,000 kg/m3 *

n/a

VDF Translation Settings

Salt Concentration

0 mg/L

0.714

 

Temperature

25 oC

-0.375 kg/m3 / oC

 

Pressure Head

0 m

4.46x10-3 kg/m4

VDF Translation Settings

Source: Langevin et al. (2007)

*See Table A.2 in Viessman and Lewis (2003) or similar hydrology/engineering reference textbook for more precise values

 

VDF High-Level Settings

 

Density Option

The density option is a flag (MT3DRHOFLG) that defines which species contribute to the relationship of concentration-derived variable fluid density.  The options are:

 

Calculate density from salt only: salt is assumed to be the first species as defined in the modeling objectives [MT3DRHOFLG=1] [default]

Calculate density from multiple species: species defined with non-zero density slope values as defined in the modeling objectives will be included in the variable density calculations [MT3DRHOFLG=-1]

Uncoupled simulation using pre-calculated density: density will be estimated using input values from a specified .UCN file [MT3DRHOFLG=0]

 

 

Internodal Density Calculation Algorithm

The Internodal Density Calculation Algorithm is a flag (MFNADVFD) that determines the method for calculating the internodal density values used to conserve

fluid mass. The options are:

 

central-in-space algorithm (MFNADVFD = 2)

upstream-weighted algorithm (MFNADVFD = 0)

 

 

Variable Density Water Table Correction

This option represents a flag (IWTABLE) that is used to activate the variable-density water-table corrections (Guo and Langevin, 2002).

 

correction applied (IWTABLE = 0)

correction not applied (IWTABLE = 1)

 

Initial Time Step

A variable for the length of the first transport timestep, used to start the simulation if both of the following two conditions are met: 1) the IMT Process is active, and 2) transport timesteps are calculated as a function of the user-specified Courant number (the MT3DMS input variable, PERCEL, is greater than zero)

 

 

VDF Low-Level Settings

 

Coupling Iteration Radio Selection (NSWTCPL)

If the model simulation is setup to dynamically calculate variable density flow (i.e. MT3DRHOFLG<>0), then this option sets the parameters that define the feedback link that between flow and transport caused by the relationship between solute concentrations and fluid density.  The options are as follows:

 

Implicit coupling using DNSCRIT - density is only (re)calculated:

oat the first transport step of the simulation,

oat the last transport step of a given MODFLOW timestep, or

owhen the maximum density change at a cell is greater than the fluid density convergence criteria

 

Explicit Coupling with one iteration - flow and transport will be explicitly coupled using a one-timestep lag.

 

 

Explicit Coupling with multiple iterations - flow and transport will be explicitly coupled using a one-timestep lag.  Density will be recalculated up to is the maximum number of non-linear coupling iterations for the flow and transport solutions.

 

Note: The explicit coupling option is normally much faster than the iterative option and is recommended for most applications

 

Maximum Number of implicitly coupling iterations (NWSTCPL)

SEAWAT will stop execution if the maximum number of iterations has been reached and convergence between flow and transport has not occurred.

 

 

Minimum/Maximum Fluid Density

Calculated density values will be truncated if they fall below the minimum fluid density or above the maximum fluid density.  If a value of zero is entered for the minimum and maximum fluid density, then SEAWAT will not truncate to a lower and an upper range of calculated density values, respectively.

 

 

Reference Fluid Density

The reference fluid density is the density at the reference concentration, temperature, and pressure. See Theory Section above.

 

 

Fluid Density Convergence Criteria (DNSCRIT)

The fluid density convergence criteria (DNSCRIT) is a user-specified density value [M/L3]. If explicit coupling with multiple iterations is selected, then DNSCRIT is the convergence criterion, in units of fluid density [M/L3], for convergence between flow and transport. If the maximum fluid density difference between two consecutive implicit coupling iterations is not less than DNSCRIT, the program will continue to iterate on the flow and transport equations, or will terminate if NSWTCPL is reached. If implicit coupling is selected, DNSCRIT is the maximum density threshold, in units of fluid density. If the fluid density change (between the present transport timestep and the last flow solution) at one or more cells is greater than DNSCRIT, then SEAWAT will update the flow field (by solving the flow equation with the updated density field).

 

 

Density vs Pressure Head Slope (DRHODPRHD)

Density vs Pressure Head Slope (DRHODPRHD) is the slope of the linear equation of state that relates fluid density to the height of the pressure head (in terms of the reference density). A value of zero, which is typically used for most problems, inactivates the dependence of fluid density on pressure.  See Theory Section above.

 

 

Reference pressure head (PRHDREF)

Reference pressure head (PRHDREF) is the reference pressure head. This value should normally be set to zero. See Theory Section above.

 

 

Uncoupled Simulation Pre-calculated Density Options

If the Density Option is set is set to uncoupled (MT3DRHOFLG=0), then you will have the option of using:

 

the reference fluid density or

density from a .UCN file

 

If choosing the latter option, you can enter or browse to .UCN file that contains the densities to be used.  The .UCN file must be based on a grid of the same dimensions and have the same number of timesteps as the simulation in which it is to be used.

 

 

 

 


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