Analytical Model for Rate Transient Analysis in Low-Permeability Volatile Oil Reservoirs

This paper presents a simple yet rigorous analytical solution for two-phase (gas-oil) flow in closed volatile oil reservoirs. The solution includes all flow regimes over the life of a multi-fractured horizontal well, including the usually long-duration early transient flow followed by the transition and the boundary-dominated flow regimes. The solution will be particularly useful in rate transient analysis of production data and production forecasting for horizontal wells with multiple fractures in ultra-low permeability reservoirs, such as shales. We formulated the governing, non-linear partial differential equations (PDEs) for simultaneous gas-oil flow with an inner boundary condition of constant bottom-hole pressure (BHP). We then defined pseudo-variables to transform the non-linear PDEs to linear forms. By developing deterministic models for calculation of fluid properties using multi-regression analysis of PVT data and relative permeability curves, we were able to find analytical solutions by the separation of variables method for specified initial and outer boundary conditions. We obtained a production rate-time relation which can be used to generate type curves or to provide a basis for history matching production data and forecasting future production. Under constant bottom-hole pressure producing condition, the resulting solutions that describe the relationship between dimensionless rate and dimensionless two-phase pseudotime indicate a complicated decline with an exponential relation inside an infinite series. We validated the solutions through comparisons with compositional simulation using commercial software; the satisfactory agreements demonstrated the accuracy and utility of the analytical solutions. Our results indicate that the production performance in multi-phase flow is far different than performance in single-phase flow, and that formation properties interpreted using techniques appropriate for single-phase flow can be seriously in error when applied to two-phase flow situations. Finally, we found that our analytical solution yielded reasonable interpretations of actual field data from the Midland Basin.