The effect of reservoir heterogeneity on the productivity of wells in closed depletion reservoirs is investigated. A direct pseudosteady-state equation solution, derived using the divergence theorem, is used to conduct an extensive stochastic simulation study at greatly increased computational efficiency. Dozens of permeability fields corresponding to various Dykstra-Parsons coefficients and correlation lengths are generated using geostatistical simulation techniques. The pseudosteady-state equation is solved by a finite-element method in 2D heterogeneous reservoirs. Pressure drawdown is calculated from the solution. Results are analyzed statistically to examine the effects of geostatistical parameters of reservoir heterogeneity on well productivity during pseudosteady-state.

Analysis of the results show that the properties of the pressure drawdown frequency distribution function are sensitive to structure (well-block permeability) and intensity (Dykstra-Parsons coefficient), but weakly to connectivity (congelation length). Bivariate analysis indicates that the logarithm of pressure drawdown is linearly correlated with the logarithm of the well-block permeability, and that spatial connectivity of permeabilities affects the correlation. Comparison with the behavior of equivalent homogeneous systems provides quantification of an additional pressure loss due to reservoir heterogeneity as a function of Dykstra-Parsons coefficient and correlation length.

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