Assisted history matching and graphical methods for estimating individual layer properties from well testing data in stratified reservoirs with multilateral wells

One of the main purposes for conducting well tests is to obtain information about reservoir parameters, such as its permeability and the existence of skin effects. Determining individual layer properties from pressure transient data in multilayer reservoirs is challenging, since pressure behavior is influenced by the properties of all layers. This work presents three methods for estimating layer properties from well testing data in multilayer reservoirs with multilateral wells. First, we extend two existing graphical straight-line methods for estimating individual layer properties in multilayer systems with vertical wells to stratified reservoirs with multilateral horizontal wells. These techniques are the rate-normalized pressure analysis and the delta transient method. Both methods require a clear identification of radial flow regimes, which may not occur in a practical case. Additionally, we show that a computer-assisted history matching method based on the Nelder–Mead optimization algorithm can also be used to evaluate layer permeabilities and skin. This optimization method does not rely on the identification of any specific flow regime. Estimates obtained from the graphical methods were used as initial guess for the assisted history matching. The proposed techniques are applied on a set of synthetic well-test cases, where pressure and layer flow-rate profiles are computed from an existing analytical model. Results show that all three methods are able to yield good estimates for layer properties if both early- and late-time radial flow are observed. In cases where only one of the radial flow regimes is identified, then the NM algorithm provides the best results, showing that the assisted history matching improved the estimates provided by the graphical method.