A Note on Transient Two-Phase Flow Calculations

Abstract

Introduction Since the appearance of the paper, "Solution of the Equations of Unsteady State Two-Phase Flow in Oil Reservoirs," by W. J. West, W. W. Garvin, and J. W. Sheldon," a twofold investigation of this subject has been carried out. One objective of the investigation has been to determine the feasibility of solving such problems on a medium-size computer such as the Datatron, and the other objective has been to investigate the application of such calculations to experimental and theoretical petroleum reservoir research. In the first Datatron calculations, the fluid and rock properties published by West, et al, were used, together with the published equations describing the system. Details of the formulation not given in the original paper are discussed in the Appendix to this note. Reference should be made to the subject paper for the complete equations and definition of symbols. An unexpected result of this investigation was the discovery that the linear solution published by West was in error. Thus, in addition to describing the Datatron solutions and to discussing certain numerical difficulties which will be encountered if one uses the published method of solution, the purpose of this note is to indicate the nature of this error. Linear Flow Since the linear case requires a minimum amount of scaling, a fixeddecimal point Datatron program was written for the one-dimensional flow problem and an attempt was made to duplicate the solution described by West. As a check on the accuracy of the solution, the cumulative production at each time step was calculated using the two methods described in the Appendix. Satisfactory agreement was observed with the differences in these two values of the order of two parts in 50,000. It should be noted that the mass balance check as described is of questionable value, particularly with regard to the well pressure and saturation. This is especially true in the radial solution where pressure and saturation values near the well bore would make only a negligible contribution to the numerical integration.