This paper covers the theory and present state of development of anapparatus for the nonmathematical analysis of complex problems of reservoir andwell behavior.
At the present stage of development of this apparatus, it is capable ofsolving the waterdrive problem of any reservoir performance for which amathematical solution has been presented in the literature, either on the basisof steady or unsteady-state flow analysis.
The theory is presented for the extension of the scope of this analyzeralong the lines of the present development. The resulting apparatus should beable to solve reservoir-performance problems previously thought too difficultfor practical solution by mathematical means.
As an illustration of its operation and present scope, the analysis of areservoir problem and synthesis of expected performance is presented.
In this method of analyzing problems of petroleum-reservoir and wellbehavior, the porous continuum of the reservoir is assumed to be divided intosmall blocks, or units. Each block is assumed to be small enough so that for amaterial balance on the fluids in the block an average pressure for the blockcan be used. In analyzing reservoir behavior from this point of view bymathematical means, a set of simultaneous difference equations would beobtained (two for each block), which must be solved or combined into a partialdifferential equation. In the method to be described here, instead of solvingthese sets of equations analytically, electrical units are constructed, whichwill behave in respect to the flow of electricity exactly as the reservoirunits behave under various conditions of fluid flow. The electrical units arethen wired together in the same way that the reservoir units are connectednaturally by virtue of their geometrical locations and shapes.