Transient Response in Arbitrary-Shaped Composite Reservoirs

Use of regular-shaped analytical models to history match geometrically complex reservoirs may provide misleading results, especially in situations where the transients are in the transition regime. In this regime, the transients are somewhere between infinite- acting and fully boundary-dominated flows. This means that some, but not all, of the reservoir boundaries influence flow dynamics. As a result, analytical models are unable to accurately capture the effects of the geometrically complex reservoir boundaries; the more irregular the reservoir or drainage area geometry is, the greater its influence on well performance, and, therefore, the greater the deviation of analytical models from field behavior. The boundary element method (BEM) has been used to model arbitrary-shaped reservoirs; its input data requirement is similar to that of analytical models. In this paper, we present the Laplace-transform BEM formulation within a framework that lends itself to developing the solution for arbitrary-shaped and/or composite reservoirs of increased complexity than is currently available in literature, thus eliminating the need for first-principle derivations. The focus here is on two-dimensional flow of a slightly compressible fluid. Our formulation is not only useful for investigating the influence of complex reservoir geometries on well performance, but also for history matching and forecasting multiwell performance, for studying the effect of large-scale reservoir heterogeneities, and for simulating mixed reservoir boundary conditions (including no-flow and constant-pressure boundaries). It permits modeling different well completion types, including hydraulically fractured vertical wells and multiply-fractured horizontal wells. In addition to modeling the response of rate-controlled wells, we also provide solution for pressure-controlled wells.