Calculation of Transient Oil Production in a Radial Composite Reservoir

Production of oil by expansion from a cylindrical reservoir composed of twoconcentric regions of different properties has been determined as a function oftime for a reservoir producing at constant terminal pressure.. The parametersinvolved are permeability, porosity, compressibility and oil viscosity. Resultsagree with those of a generally accepted method for uniform reservoirs when allparameters are taken as uniform. Cumulative production at any given time isreduced below that of the uniform reservoir when a region of considerably lowerpermeability adjoins the well; cumulative production increases when ahigh-permeability region adjoins the well. Curves are presented illustratingquantitative effects of these variations. INTRODUCTION Most petroleum reservoirs can be exploited by release of pressure andconsequent expansion of underground fluid. During part of the productionhistory of certain reservoirs by this mechanism, fluid compressibility can beconsidered small and constant. Cumulative fluid produced by this means as afunction of time was calculated for a uniform reservoir by van Everdingen andHurst.1 For certain cases where a production well has been damagedor where an acid treatment has been used, a zone of properties different fromthose of the reservoir may be created around the production well. In such acase, expansion of the reservoir fluid takes place in a system composed of twoconcentric cylindrical regions of different reservoir properties. Suchcomposite systems were studied in connection with heat flow byJaeger2 who presented a solution for temperature distribution in aradial system with an infinitely large outer radius. Similar heat flow problemshave been studied by other authors;3 Oil production from compositereservoirs was studied for constant production rate by Hurst,4Loucks and Guerrero,5 and Carter.6 THEORY This work considers constant terminal pressure. Cumulative flow iscalculated for a composite bounded system in which no flow takes place acrossthe 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 todefine the following dimensionless pressure drops (Fig. 1).