A general compositional rescaled-exponential model for multiphase boundary-dominated performance analysis

Hydrocarbon reservoir performance forecasting is an integral component of the resource development chain and is typically accomplished via reservoir modeling using either numerical or analytical methods. Although complex numerical models provide rigorous means of capturing and predicting reservoir behavior, reservoir engineers also rely on simpler analytical models to analyze well performance and estimate reserves when uncertainties exist. Arps, for example, empirically demonstrated that certain reservoirs may decline according to simple, exponential, hyperbolic, or harmonic relationships; such behavior, however, does not extend to more complex scenarios, such as multi-phase reservoir depletion. Due to this limitation, an important research area for many years has been to transform the equations governing flow through porous media in such a way as to express complex reservoir performance in terms of closed analytical forms. In this work, it is demonstrated that rigorous compositional analysis may be coupled with analytical well performance estimations for reservoirs with complex fluid systems, and that the molar decline of individual hydrocarbon fluid fractions can be expressed in terms of rescaled-exponential equations for well performance analysis. This work demonstrates that, by the introduction of a new partial pseudo-pressure variables, it is possible to predict the decline behavior of individual fluid constituents of a variety of gas condensate reservoir systems characterized by widely varying richness and complex multi-phase flow scenarios. A new four-region flow model is proposed and validated to implement gas-condensate deliverability calculations at late times during variable bottomhole pressure production. Five case studies are presented to support each of the model capabilities stated above and validate the use of liquid-analog rescaled-exponentials for the prediction of production decline behavior for each of the hydrocarbon species.