Succession-of-States Model for Calculating Long-Time Performance of Depletion Reservoirs

Abstract

Summary This study presents a new finite-element approach for directly calculating pseudosteady-state flow behavior for wells in depletion systems. The approach allows for spatially dependent reservoir properties, complex reservoir geometries, and multiple wells. Results are verified against long-time transient solutions reported in the literature for several regularly shaped systems. The paper also demonstrates application of the approach to field-scale problems. Results show that this approach provides a fast and accurate method for modeling the long-time behavior of depletion reservoirs. The approach is particularly applicable to single-phase volumetric gas reservoirs. A bounded reservoir with wells producing at constant rate will exhibit pseudo steady-state behavior after the end of typically short-lived infinite-acting and transition flow periods. This study develops a new approach for directly calculating pseudosteady-state flow behavior without solving the full time-dependent form of the diffusivity equation. This approach can be applied to the linearized forms of the diffusivity equation for either single-phase liquid or gas flow. A finite-element method is used that allows for spatially dependent reservoir properties, complex reservoir geometries, and multiple wells. The first part of this paper presents a verification of the approach by comparing results for some regularly shaped systems against full-transient solutions reported in the literature. For the simulation of field-scale problems with multiple wells of differing production rates, a well model based on a near-wellbore approximation of the pseudopressure distribution during pseudosteady-state is introduced to reduce the concentration of elements near wells. The second part of the paper demonstrates application of the direct pseudosteady-state concept to actual reservoir problems. To account for rate changes during extended production periods, the pseudosteady-state equation was solved successively for each flow period and combined with an overall reservoir material balance analysis. Results from this study show that this approach provides a fast and accurate method for modeling the long-time behavior of various types of reservoirs under depletion conditions. The approach is particularly applicable to single-phase volumetric gas reservoirs.