Reservoir Engineering - General - Calculation of Transient Oil Production in a Radial Composite Reservoir

Production of oil by expansion from a cylindrical reservoir composed of two concentric regions of different properties has been determined as a function of time for a reservoir producing at constant terminal pressure. The parameters involved are permeability, porosity, compressibility and oil viscosity. Results agree with those of a generally accepted method for uniform reservoirs when all parameters are taken as uniform. Cumulative production at any given time is reduced below that of the uniform reservoir when a region of considerably lower permeability adjoins the well; cumulative production increases when a high-permeability region adjoins the well. Curves are presented illustrating quantitative effects of these variations. INTRODUCTION Most petroleum reservoirs can be exploited by release of pressure and consequent expansion of underground fluid. During part of the production history of certain reservoirs by this mechanism, fluid compressibility can be considered small and constant. Cumulative fluid produced by this means as a function of time was calculated for a uniform reservoir by van Everdingen and Hurst.l For certain cases where a production well has been damaged or where an acid treatment has been used, a zone of properties different from those of the reservoir may be created around the production well. In such a case, expansion of the reservoir fluid takes place in a system composed of two concentric cylindrica1 regions of different reservoir properties. Such composite systems were studied in connection with heat flow by Jaeger2 who presented a solution for temperature distribution in a radial system with an infinitely large outer radius. Similar heat flow problems have been studied by other authors Oil production from composite reservoirs was studied for constant production rate by Hurst,4 Loucks and Guerrero,5 and Carter.6 THEORY This work considers constant terminal pressure. Cumulative flow is calculated for a composite bounded system in which no flow takes place across the outer boundary (Fig. 1). Since the flow is considered to be purely radial, the problem involves only one space dimension and time. It is convenient to define the following dimen-sionless pressure drops (Fig. 1).