Aqueous Relative Permeability Options (W)

The relative permeability is constant regardless of saturation. 

The Burdine (1953) relative permeability function is described as

Aqueous phase relative permeability can be computed as a function of aqueous saturation from knowledge of the soil-moisture retention function and the pore distribution model of Burdine [1953]. If the van Genuchten and Brooks and Corey soil-moisture retention functions are used, closed-form expressions for fluid phase relative permeability can be derived. Using the van Genuchten soil-moisture retention function, the aqueous phase relative permeability appears as shown:

Using the Brooks and Corey soil-moisture retention function, the aqueous phase relative permeability appears as shown:

The Mualem(1976) relative permeability function is described as

where L = 0.5.

Aqueous phase relative permeability can be computed as a function of aqueous saturation from knowledge of the soil-moisture retention function and the pore distribution model of Mualem [1976]. If the van Genuchten and Brooks and Corey soil-moisture retention functions are used, closed-form expressions for fluid phase relative permeability can be derived. Using the van Genuchten soil-moisture retention function, the aqueous  relative permeability appears as shown:

Using the Brooks and Corey soil-moisture retention function, the aqueous phase relative permeability appears as shown:

The pore scale parameter (aka tortuosity-connectivity coefficient) can be specified to be any value. The default value is 0.5.

There is a minimum saturation for the porous medium.

The Mualem (1976) relative permeability model is used to calculate the vertical permeability and the Polmann (1990) model is used to calculate horizontal permeability.

Polmann (1990) used a stochastic model to evaluate tension-dependent anisotropy.  The Gardner (1958) relationship was used to describe unsaturated hydraulic conductivity as a function of saturated hydraulic conductivity and tension. Using a linear correlation model between the zero-tension intercept and β, Polmann (1990) presented a generalized model that accounts for the cross-correlation of the local soil property (i.e., lnK_s and β) residual fluctuations.  Compared against the uncorrelated lnK_s and β model, the partial correlation of the properties was shown to have a significant impact on the magnitude of the effective parameters derived from the stochastic theory.  The Polmann (1990) equations for deriving the effective parameters for strongly stratified porous media are as shown below.

A modified version of the original Polmann model is implemented in STOMP. This version uses a single segment of the log-linear K(h) function. Because the Polmann model is based on the log-linear hydraulic function, it may be applicable only to a relatively narrow pressure head range over which the parameters are derived.  Extrapolating the derived hydraulic function to other pressure head conditions may cause significant error or even physically incorrect results (e.g., the predicted hydraulic conductivity in the horizontal direction may increase with decreasing saturation, which is physically incorrect). It calculates an anisotropy coefficient (C_an) and the hydraulic conductivity in the horizontal direction (K_h). The modified model also requires user specified maximum (C_an^max) and minimum (C_an^min) limits of the anisotropy coefficient. If computed values of C_an are outside these limits, the values are truncated as shown in the equations below:

The Directional Aqueous Relative Permeability Card can be used to represent anisotropy for several aqueous relative permeability models. Zhang et al. 2003 and Raats et al. 2004 demonstrate the use of Directional Aqueous Relative Permeability with the Modified Mualem model.

Aqueous- and gas-phase relative permeability are computed according to the Fatt and Klikoff [1959] models from the conventionally defined effective aqueous saturation according to equations (1) and (2), respectively.

Aqueous- and gas-phase relative permeability can be computed from modified expressions for effective aqueous saturation according to the empirical model of Corey [1977]. The model of Corey accounts for trapped air through a modification to the definition of the effective aqueous saturation according to equation (1). The Corey functions for aqueous- and gas-phase relative permeability are computed according to equations (2) and (3), respectively.

The free Corey is a modified version of the empirical model of Corey [1977]. The model accounts for trapped air through a modification to the definition of the effective aqueous saturation according to equation (1). The free Corey function for aqueous-phase relative permeability is computed according to equation (2).

This option accepts tabulated relative permeability data. The default is the data of aqueous saturation and aqueous relative permeability data pairs and linear interpolation is used between data points; a cubic spline interpolation scheme can also be specified. Alternately, capillary head vs relative permeability can be provided using the keyword "head." Other interpolation schemes that can be specified for capillary head vs. aqueous relative permeability are log capillary head vs relative permeability, cubic spline, or cubic spline for log capillary head vs relative permeability.