﻿ Numerical Modeling Workflow - Finite Difference Grids > Translation Settings > SEAWAT > VSC Package

Viscosity (VSC) Package Advanced Translation Settings

The Viscosity (VSC) package is the package in SEAWAT that defines the relationship between solute concentration(s) and temperature with viscosity.  The VSC package is optional to run a SEAWAT model simulation and can be turned off by setting Run=No in the advanced settings, if desired.  Numerous options and settings are supported as part of the translation settings in Visual MODFLOW Flex and are described below.

For a more complete explanation of the input settings for the VSC package, please refer to p20-22 of the SEAWAT V4 Manual (Langevin, et. al., 2007). The theoretical basis of how viscosity is used in SEAWAT is discussed on page 6 of the SEAWAT V4 Manual.

Please Note: The VSC package can only be used with the LPF internal flow package.

Viscosity - Theory

Unlike fluid density, a linear approximation of viscosity does not adequately represent the effect of temperature over the range of typical/natural conditions on dynamic viscosity.   For this reason, an alternative equation for dynamic viscosity has been implemented in SEAWAT:

μ = μ(ref) + Σμ/ẟCi · [ Ci -  Ci (ref) ] + μ(T)

where:

μ is the fluid dynamic viscosity* [M/L·T]

μ(ref) is the reference fluid dynamic viscosity [M/L·T]

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

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

μ/ẟCi is the viscosity/concentration slope, or change in viscosity per unit change in solute concentration of the ith species [L2/T]

T is the temperature [Θ]

μ(T) is the viscosity/temperature function - see below.

* Note: The governing equations implemented in SEAWAT use dynamic viscosity. For simplicity, subsequent references to viscosity refer to dynamic viscosity (rather than kinematic viscosity).

Values for the viscosity/concentration slope for each species (μ/ẟCi) and the reference concentrations (Ci (ref)) are set at the Define Modeling Objectives Step (if variable density is the selected flow type). The available/published empirical relationships between viscosity and temperature are tabulated below:

Temperature/Viscosity Functions available in the VSC package

Option

Equation

A1

A2

A3

A4

A5

Linear

--

--

--

--

--

Voss (1984)

2.934 x 10-5

10

248.37

133.15

--

Pawlowski (1991)

1.0 x 10-3

1

1.5512 x 10-2

-20

-1.572

Guo and Zhao (2005)*

0.168

--

--

--

--

Source: after Langevin et al. (2007)

NOTES:

all equations are based on base units of L=meters, M=kilograms, Θ=degrees Celsius

Guo and Zhao (2005) is applicable to oil rather than water at a temperature range of 5oC ≤ T ≤ 170oC.

Viscosity - Settings

Viscosity Option (MT3DMUFLG)

The viscosity option is a flag (MT3DMUFLG) that defines which species contribute to the relationship of concentration-derived variable fluid viscosity.  The options are:

Calculate viscosity from salt only: salt is assumed to be the first species as defined in the modeling objectives [MT3DMUFLG=1] [default]

Calculate viscosity from multiple species: species defined with non-zero viscosity slope values as defined in the modeling objectives will be included in the viscosity calculations.  This option also enables more advanced options to model the effects of temperature on viscosity [MT3DMUFLG=-1]

Use specified viscosity: viscosity will be estimated using a default value or input values from a specified .UCN file [MT3DMUFLG=0]

Minimum/Maximum Fluid Viscosity (VISCMIN/VISCMAX)

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

Reference Viscosity (VSCREF)

The reference fluid viscosity is the viscosity at the reference concentration and temperature.

Viscosity vs. Temperature

If a species has been designated as the temperature species as part of a variable density simulation at the Define Modeling Objectives and the Viscosity Option is set to calculate viscosity from multiple species, then the viscosity vs. temperature options described in the theory section above will be shown:

In this case, you may select one of the four viscosity/temperature relationships: Simple linear, Voss (1984), Pawlowski (1991), or Guo and Zhang (2005).  The table below will be populated with the associated number of fitting parameters (A1 - A5, as applicable) set to the respective defaults.

Specified Viscosity Settings

If the Viscosity Option is set is set to uncoupled (MT3DMUFLG=0), then you will have the option of using:

the reference viscosity,

read specified viscosity from a .UCN file

read concentration from .UCN file and convert to viscosity using linear expression

If choosing either of the last two options, you can enter or browse to .UCN file that contains the file to be used for the respective option. 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.