Papers - Engineering Research - Pressure Distribution in Oil and Gas Reservoirs by Membrane Analogy (With Discussion)

The pressure distribution in a producing oil or gas reservoir has been obtained mathematically in a limited number of special cases where the boundary of the reservoirs are simple geometric figures with the wells conveniently located within them. Using some of the previous work as a basis, it can be proved that a number of additional problems of pressure distribution can be solved by use of soap film. This method is particularly applicable to a reservoir drained by a number of wells, or to a reservoir of irregular shape, or to both. Since this method obtains the pressure distribution, it also establishes the drainage boundaries of the wells. This paper derives the analogy between the equation representing the pressure distribution in a reservoir and the equation of the deflected membrane. It also describes the apparatus and the method of operation. The experimental method is employed to solve a problem whose mathematical solution is known and the results compared. These are found to be in good agreement. The method is applicable to any homogeneous liquid, compressible or incompressible, or to a gas, flowing in a reservoir of uniform thickness, permeability and porosity. The flow state may be either the steady state or the transient state wherein the density or pressure of the fluid in the reservoir declines at a constant rate. PRESSURE-DISTEIBUTION PBOBLEM Fluids encountered in the oil reservoir are compressible and expand and move toward the drilled hole where the Dressure is lowest. The loss of fluid from the reservoir lowers the pressure in the more distant parts of the reservoir, permitting the fluids in these parts to expand and move toward the well. The area around the well affected by drainage is increasing continuously, and the density, pressure, and velocity of flow