Gas Relative Permeability Card Options (GT)

the relative permeability is constant regardless of saturation. 

The Burdine (1953) relative permeability function is described as

 

 

Gas phase relative permeability can be computed as a function of gas 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 gas phase relative permeability appears as shown:

 

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

 

The Mualem(1976) relative permeability function is described as

 

where L = 0.5.

Gas phase relative permeability can be computed as a function of gas 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 gas  relative permeability appears as shown:

 

 

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

 

Dual porosity functions or equivalent continuum models [Klavetter and Peters 1986; Nitao 1988] relate bulk fluid phase relative permeabilities to the those for the fracture and matrix according to the equation below.

 

 

Dual porosity models require the assumption that fracture and matrix fluid pressures are in equilibrium, which inherently neglects transient fracture-matrix interactions. Fracture and matrix relative permeabilities are computed from either the Burdine or Mualem models using either the van Genuchten or Brooks and Corey soil moisture retention functions.

In these functions the effective gas and gas saturations are replaced with the corresponding values for the fracture and matrix components of the soil. For example the fracture and matrix gas relative permeabilities for the Burdine model with the Brooks and Corey soil-moisture retention function are shown below.

 

the Fatt and Klikoff (1959) model

 

Gas-phase relative permeabilities can be computed from modified expressions for effective gas saturation according to the empirical model of Corey [1977]. The Corey's curves account for trapped air through a modification to the definition of the effective gas saturation according to:

 

 

The Corey function for gas phase relative permeability is computed according to:

 

The free Corey model is a modified version of the empirical Corey [1977] model. The model accounts for trapped air through a modification to the definition of the effective aqueous and gas saturations:

 

 

The free Corey function for gas-phase relative permeability is computed according to:

 

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 and gas saturations:

 

The modified Corey function for gas-phase relative permeability is computed according to:

 

Tabulated relative permeability.