Transient Productivity Index for Numerical Well Test Simulations
G. Blanc, D. Y. Ding, A. Ene, T. Rahon, D. Rahon, 1999. "Transient Productivity Index for Numerical Well Test Simulations", Reservoir Characterization—Recent Advances, Richard A. Schatzinger, John F. Jordan
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The most difficult aspect of numerical simulation of well tests is the treat-ment of the bottom-hole flowing (BHF) pressure. In full-field simulations, this pressure is derived from the well-block pressure (WBP) using a numerical productivity index that accounts for the grid size and permeability, and for the well completion. This productivity index is calculated assuming a pseudo-steady-state flow regime in the vicinity of the well and is therefore constant during the well production period.
Such a pseudo-steady-state assumption is no longer valid for the early time of a well test simulation as long as the pressure perturbation has not reached several grid-blocks around the well. This paper offers two different solutions to this problem:
The first solution is based on the derivation of a transient numerical productivity index (TNPI) to be applied to Cartesian grids.
The second solution is based on the use of a corrected transmissibility and accumulation term (CTAT) in the flow equation.
The representation of the pressure behavior given by both solutions is far more accurate than the conventional one, as shown by several validation examples presented in the following pages.