Calculation of Theoretical Productivity Factor

Abstract

A method has been developed whereby one may calculate the productivityfactors of producing formations from a knowledge of the reservoir conditions.Account is taken not only of the heterogeneous character of the gas-oil flowsystem but also of the detailed variations with pressure of the shrinkage andviscosity of the oil, the solubility of the gas in the oil, and even thevariability of the gas viscosity and the deviation of the gas from idealbehavior. Curves are shown giving the results of numerical calculations on theproduction rate as a function of the pressure differential for a highpressureand a low-pressure system, three values of gas-oil ratio being treated in eachcase. Curves are also given showing the variation with distance from the wellof the pressure, oil saturation, and permeability. The effect of connate wateris briefly discussed in relation to the apparently large discrepancies betweenthe calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity ofan oil-bearing formation to produce is well recognized; for it is the compositeand integrated resultant of the physical properties of both the porous mediumand the fluid stream passing through it with respect to the ease with which theparticular petroleum fluids present in the formation can flow through it andinto producing wells. The most direct method of determining the productivity factor of a wellconsists, as is well known, in the simultaneous measurement ofreservoir-pressure differentials and rates of production and the expression ofthe data in terms of rate of flow per unit pressure drop. Actual measurementscarried out in this manner on producing wells have given factors that generallylie in the range of 0 to 100 bb1. per day per pound pressure drop. This widerange arises not only from variations in permeability but also from the varyingsand thickness of producing formations. T.P. 1352