Pressure Distribution in Unsaturated Oil Reservoirs

The pressure distribution in a reservoir producing an incompressible fluidby radial flow in a horizontal structure is a simple logarithmic function useddaily by reservoir engineers. The assumption of an incompressible liquid isequivalent to assuming that pressure is maintained constant at the well radiusand at some external ?radius of drainage,? or, in other words, that the entireflow into the well passes across the external radius. In most cases a well issurrounded by other wells draining adjoining areas so that the ?radius ofdrainage? is not a line of constant pressure with flow equal to the flow intothe well but rather a contour of zero pressure gradient across which no flowoccurs, production being due to the expansion of the liquid within thearea. The radial flow steady state pressure distribution for this case does not seemto be extensively used despite the fact that the mathematical analysis has beengiven in detail and the results are simple and generally applicable. The objectof this discussion is to develop this result from a physical rather than amathematical viewpoint, thereby aiding intuition in judging circumstances towhich it may be applicable. If the production rate at a well in an unsaturated reservoir is maintainedconstant while no flow occurs across the outer radius a steady state will soonbe reached in which the flow rate or pressure gradient is constant with time atall points in the reservoir. To preserve such a condition it is necessary thatthe pressure decline at the same rate at all points in the reservoir, that is, the curves of pressure versus radial distance at successive times are allparallel. Then each unit volume of oil is expanding at the same rate andcontributing an equal share to the production. T.N. 61