A density-diffusivity approach for the unsteady state analysis of natural gas reservoirs

The traditional approach employed in the analytical analysis of unsteady state responses for natural gas reservoirs is firmly based on recasting the non-linear pressure diffusivity equation in terms of pseudo variables or pseudofunctions—namely, pseudo-pressure and pseudotime—able to render the equation amenable to analytical treatment. Because the pseudofunction-based approach succeeds in linearizing the diffusivity equation and generating the required benchmark analytical solutions, the implementation of pseudo-variables is understood to be essential to unsteady state analysis of natural gas reservoirs. In this study, the authors propose an approach for the analytical solution of unsteady flow in natural gas reservoirs based on the use of the density-diffusivity equation. To demonstrate its validity and range of application, the authors discuss analytical arguments and perform numerical simulations to corroborate its performance for some of the most widely used inner boundary conditions (BCs): constant pressure and constant rate production. By implementing the concept of depletion-driven dimensionless parameters, the proposed density-diffusivity approximation is able to successfully describe reservoir unsteady behavior while keeping all variables involved in the analysis firmly grounded on physical intuition. In addition, it is shown that the proposed approach also provides a new avenue for the interpretation of liquid type-curves in gas analysis and the iteration-free estimation of original gas in place based on the analysis of boundary-dominated production data.

► A successful density-diffusivity equation based approach is proposed.
► Approach circumvents the use of pseudo-pressure during natural gas analysis.
► Proposed model successfully handles a variety of boundary conditions of interest.
► Provides a new avenue for interpretation of liquid type-curves for natural gases.
► Yields an iteration-free estimation of reserves (OGIP) for natural gas reservoirs.