Application of the heat-flow equation to the problem of unsteady flow of fluids in the petroleum reservoirs



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Past studies of the flow of fluids in petroleum reservoir flow systems indicate that a condition of unsteady flow exists in the reservoir flow system during production of the petroleum reserve. Several methods for treating this type of problem involve analytical solutions based on the classical theory of the conduction of heat in solid bodies. The general applicability of the heat-flow approach to the problem of unsteady flow of fluids in petroleum reservoirs has been studied, and the limitations of the heat-flow treatment have been discussed. Four particular solutions of the heat-flow equation (which are especially useful for treating reservoir flow problems) have been shown and their general utility indicated. The possibility of extending the useful range of previously used techniques to include treatment of compressible fluids was studied, and a method for accomplishing this has been presented. A useful method for obtaining mathematical approximations to experimental curves has been described and its utility illustrated.