A method for calculating the effective non-Darcy flow coefficient and relative permeabilities for gas/brine systems is presented. The capillary pressure is considered to account for the end-effect. This method is applicable to linear displacement in laboratory cores.

The computational model was developed by extending the Civan and Donaldson1  model to include the non-Darcy effect and interfacial drag between the gas and liquid phases. For this purpose Darcy’s law was replaced by the Forchheimer equation modified for two-phase systems by Tutu et al. (see Schulenberg and Muller2 ). Second, a pseudo-pressure formulation was carried out to transform the compressible gas flow and the slightly compressible brine flow equations to incompressible fluid type equations. This serves as a convenience in the calculations. Third, an input-output formulation of the model equations is facilitated for direct calculation of the non-Darcy factors and the relative permeabilities of the gas and the brine phases from the measurements of the pressure differential and the effluent gas to brine ratio. A detailed description of the calculation procedure for implementation on personal computers is presented. Also, the unsteady-state and steady-state differential formulations are developed for comparison purposes.

This method for the calculation of non—Darcy factors simultaneously with the relative permeabilities is essential for the analysis of gas reservoirs involving gas/brine systems. In particular, the simulation of water coning around vertical and horizontal wells where non-Darcy flow may be significant represents an important application of the results presented in this paper.

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