The gas pseudopressure and pseudotime have significantly improved the accuracy of the gas reservoir engineering analysis. However, the cumbersome calculations involved in evaluation of the pseudo-functions have hindered their application in gas engineering practice. This paper introduces simple analytical expressions for evaluation of the gas pseudopressure and pseudotime. The analytical expressions have been developed with aid of the polynomial regression analysis. polynomial regression analysis. The polynomials provide a quick, yet accurate method of calculating gas pseudo-functions. The comparison of the values determined from the polynomials and the published values of the psuedopressure and pseudotime indicate only 0.3 percent difference. This is well within the range of accuracy for engineering analysis.
The polynomials can significantly enhance the utilization of the gas pseudo-function in gas reservoir engineering applications and the gas reservoir simulation.
The partial differential equation (PDE) governing the gas flow through porous media is non-linear due to the dependency of gas properties on pressure. Therefore, a general solution for gas flow in porous media does not exist. In the past, simplifying assumptions have been made to solve the PDE which has led to familiar pressure squared (P2) solution. In order to obtain an accurate solution however, the PDE must be linearized. The introduction of two functions known as pseudopressure (Pp) and pseudotime (ta) has provided the basis for linearization of PDE. The evaluation of the pseudo-functions however, require numerical integration pseudo-functions however, require numerical integration because the analytical expressions for z-factor, viscosity, and compressibility in terms of pressure are not available. As a result, the gas pseudo-function are not convenient to use and their application in gas engineering analysis have been hindered.
The objective this paper is to develop a simple and accurate method of determining the gas pseudo-function through polynomial regression. The availability of polynomials provides the engineer with a quick method for polynomials provides the engineer with a quick method for gas reservoir data analysis.
The gas pseudopressure as defined below takes into account the variation of gas viscosity and z-factor with pressure: pressure:(1)