Saturation Function Card Options (CO2E)

This option uses the van Genuchten (1980) retention function. 

 

 

 where m = 1-1/n. 

the Brooks and Corey (1966) retention is used.

 

the Brooks and Corey (1966) retention is used.

 

This option is used for a fractured medium. The retention properties for both the fracture and the matrix are needed.

Dual porosity functions or equivalent continuum models for aqueous-gas systems relate the gas-aqueous capillary pressure to the bulk aqueous saturation for fractured geologic media through two functions [Klavetter and Peters 1986; Nitao 1988]. One function relates the gas aqueous capillary pressure to the matrix aqueous saturation and the other relates the gas-aqueous capillary pressure to the fracture aqueous saturation. The pivotal assumption associated with the dual porosity function is that the fracture and matrix pressures are in equilibrium. This assumption neglects transient fracture-matrix interactions. Fracture and matrix effective saturations can be computed with either van Genuchten or Brooks and Corey functions above. The bulk aqueous saturation is computed by combining the fracture and matrix aqueous saturations and diffusive porosities:

 

 

where the actual saturations are computed from effective saturations, according to

 

This option considers entrapped gas that is immobile and also reduces the pore fraction for the mobile fluid.

A theoretical model for hysteretic saturation functions for aqueous-gas systems was developed by Parker and Lenhard [1987]. A simplified version of this model, analogous to Kaluarachchi and Parker [1992], has been implemented in the STOMP simulator. The model includes effects of gas entrapment during aqueous-phase imbibition paths. Gas entrapment during aqueous-phase imbibition will depend on the aqueous saturation and current saturation path. The amount of entrapped gas varies linearly between zero and the gas effective residual saturation with the apparent saturation, which varies between the reversal point from main drainage to one. Gas effective residual saturations are computed using an empirical relationship developed by Land [1968] for aqueous-NAPL systems. In this simplified hysteretic model for aqueous-gas systems, gas can be trapped or free, where free gas refers to continuous volumes which advect freely and trapped gas refers to discontinuous ganglia of gas occluded within the aqueous phase. Occluded gas is assumed to be immobile. The apparent aqueous saturation equals the effective aqueous saturation plus effective trapped gas saturation, as shown in the first Equation below. The effective gas saturation equals the effective trapped and free gas saturations, as shown in the third Equation below. In hysteretic systems, the residual saturation is independent of capillary pressure.

 

 

The saturation functions relate gas-aqueous capillary pressure to apparent aqueous saturations, according to the first and second equation, for the van Genuchten and Brooks and Corey functions, respectively. The effective trapped gas saturation is computed according to the forth Equation, which recognizes that entrapped gas cannot exceed the gas present. Land’s parameter for gas-aqueous interfaces is computed according to the fifth Equation.

 

The Haverkamp et al. (1977) retention is used

 

To extend the saturation function below the aqueous residual saturation, functional extensions are required. STOMP-CO2 and -CO2e recognizes the Webb (2000) model. This function works with both the van Genuchten and Brooks and Corey characteristics functions, without requiring additional input as the oven-dried head is assumed to be equal to a capillary pressure of 109 Pa (~105 m).

This option accepts the tabulated retention data. The default is the data of pressure head and saturation data pairs and linear interpolation is used between data points. Other key words such as "water content" if data type is water content and "log" for log-linear interpolation.