Parameters for Computing Pressure Gradients and the Equilibrium Saturation of Gas-Condensate Fluids Flowing in Sandstones
Authors: Ham Jerry D. , Brill James P. , Eilerts C. Kenneth 
Published: December 2007

Abstract
Data obtained by flowing two-phase fluids through sandstone cores were used to develop empirical equations for computing the pressure gradients and liquid saturations that will occur during the recovery of gas-condensate fluids like those in the Gulf Coast area. Equilibrium saturation may be computed for a given pressure, velocity, and liquid/gas ratio of flow. For this purpose, the minimum liquid flow saturation at high pressures, S, was developed for characterizing a core and a fluid. The effects of saturation on the mobility for Darcy flow and on the coefficient for non-Darcy flow are considered in an equation with parameters in addition to the Klinkenberg and Forchheimer coefficients. All parameters for these equations may be determined parameters for these equations may be determined either by routine measurements or by correlations.

Introduction
Fluid properties required for computing the transient flow of gas-condensate fluids and data obtained to meet this need were discussed at the 1966 SPE-AIME Fall Meeting. In the following year Dranchuk and Kolada described a means of analyzing laboratory data for nonlinear parameters pertaining to flow of gases. Gewers and Nichol pertaining to flow of gases. Gewers and Nichol investigated the effect of liquid saturation on the non-Darcy-flow term of the pressure-gradient equation. Modine and Fields used this kind of information to simulate turbulent flow in gas wells. An equation is needed for computing a more realistic value of the pressure gradient for flowing two-phase fluids than is possible with the Darcy equation. An equation is needed to compute as a boundary condition the liquid saturation possible in the porous medium near flowing wells. This paper describes two such equations that give effect paper describes two such equations that give effect to pressure, fluid velocity, liquid/gas ratio, and saturation. Seven parameters each required for the pressure-gradient and saturation equations may be pressure-gradient and saturation equations may be calculated by means of correlation equations that utilize routinely measured core properties.

Concepts and Equations
The Darcy equation was modified to include the Klindenberg effect "slip flow" and the Forchheimer coefficient to represent "inertial" or "turbulent" flow of gases in dry porous media,(1)
By controlling the velocity (u) and pressure (p), measuring the gradient (dp/dx) and the viscosity [mu(p)], and calculating the density [p(p)], the properties k, b, and beta were determined for properties k, b, and beta were determined for representative cores by least-squares methods. As a step in the modification of Eq. 1 to obtain an equation applicable to the flow of two-phase fluids, mobility, A, for a two-phase fluid must replace the ratio of a known permeability to a viscosity, for the gas phase(2)
The quantities k and mu(p) are to have the same* significance as in Eq. 1, except that mu(p) is the viscosity of a single-phase saturated gas. Relationships of liquid- and gas-phase mobilities, lambda and lambda, to fluid mobility, lambda, have been described in Appendix C of a previous publication. Briefly, lambda = lambda + lambda = f(S, p, F, u) k/mu(p). Now mu(p) is the viscosity of the flowing fluid mu under steady-state conditions only when F = 0.