This paper (SPE 51023) was revised for publication from paper SPE 37030, first presented at the 1996 SPE Asia Pacific Oil & Gas Conference held in Adelaide, Australia, 28-31 October. Original manuscript received for review 16 September 1996. Revised manuscript received 20 May 1998. Revised manuscript approved 9 June 1998.

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 bound reservoir with wells producing at constant rate will exhibit pseudosteady-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 pseudo pressure 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.

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