Modeling commingled reservoirs with pressure-dependent properties and unequal inital pressures in different layers: Analytical solutions and software development

Numerical simulators have been used as comprehensive reservoir analysis tools for reservoir engineers to study reservoir performance. However, numerical simulators are time-consuming and difficult for most engineers to use. This is especially true when a multilayer reservoir with each layer having different features is studied. In some situations when approximate analytical solutions can be found, the computer software based on these analytical solutions can become a very efficient reservoir analysis tool.; The purpose of this research is to introduce a simple but comprehensive analytical method for modeling the performance of a commingled (multilayer) reservoir system with pressure dependent fluid properties in each layer. It is assumed that there is only one well in the center of the system. Reservoir engineers who understand (1) how to solve single-layer reservoir problems, (2) superposition, and (3) Duhamel's theorem (continuous superposition) can follow the derivations and use the results to model multilayer reservoir systems. To take into account the variation of fluid properties, a new approach is presented to apply pseudo-pressure and pseudo-time concepts to each layer of a multilayer system. With this approach, reservoir engineers can readily modify an analytical model for slightly compressible liquids to model commingled gas reservoir systems. Based on this analytical model, an analytical computer simulator is developed that reservoir engineers can use to model the performance of commingled reservoirs with unequal initial pressures in different layers. This analytical simulator allows each layer to be (1) either homogeneous or dual porosity, (2) either hydraulically fractured or with radial flow (with skin), and (3) either finite or infinite in extent. This analytical simulator can be used to predict future performance, match past performance, and to assist in the analysis of pressure transient tests. A major advantage of this simulator is that it requires far less computer time than conventional finite-difference simulators to solve the same problems. A numerical simulator has been used to verify this analytical model.; This dissertation also presents a new technique to model pressure buildup performance of a commingled reservoir following constant pressure production. This has been a difficult problem historically.