This paper presents the development, validation, and application of new approximate (semi-analytical) solutions for the wellbore pressure and fractional flowrate responses of commingled layered reservoirs without interlayer cross/low (crossflow is only permitted in the wellbore, not in the reservoir). These formulations use "basis" pressure drop relations for each layer as a mechanism to create multilayer solutions in the Laplace domain and due to the choice of these basis relations; the formulation can be analytically inverted into the real domain. This process provides a direct (albeit approximate) solution for multilayer reservoir systems. The basis relations include a "constant" pressure case and "linear" pressure case. In addition to these methods, we also provide a "Total Pressure/Rate Averaging" (TPRA) formulation which is used to provide an average rate and pressure response for each layer.
These semi-analytical solutions can be used to construct well test or production profiles in a simple computational environment (e.g., a spreadsheet). These solutions can also be used to diagnose well test and production data in terms of layered reservoir behavior. The "linear" pressure case (non-zero intercept) gives the best performance however, from a practical standpoint, the algebra involved limits this approach to 2-layer reservoir case. The TPRA formulation is very consistent, but not as accurate as the other solutions however; the TPRA formulation is easily be extended to n-layers.