An Analytical Approach for Below the Bubble Point, Black-Oil System Production Analysis and Optimization

The ability to predict well inflow performance for varying well and reservoir conditions is important when optimizing production. Many methods exist to estimate a well’s current productive capacity (IPR curve) and extensions to the methods are available for predicting future well performance. The extensions to predict future inflow performance behavior account for changes in relative permeability and assume an average reservoir pressure. The applicability and accuracy of the methods depends on knowledge of reservoir parameters which may be difficult to obtain in low permeability reservoirs. Several authors have presented methods of analyzing and history matching well performance. These methods typically yield reservoir parameters which may be used in the well inflow performance methods in order to investigate the results of varying well production parameters. These methods are particularly useful in low permeability settings where interpretable welltest data may be difficult to obtain or prohibitively expensive. Currently, the analytical history matching approach is most accurate when applied to single-phase systems. Predictions of black oil reservoir performance below the bubble point can exhibit large error since depletion of the total reservoir energy is not accounted for using the constant gas-oil ratio approach typical for these methods. This paper presents a method to analyze well performance of black oil systems below the bubble point. The method incorporates a material balance approach to account for changing gas-oil ratios as the reservoir is depleted. Prediction of future well performance is also presented. Along with reservoir characterization, another benefit of the method is the ability to construct IPR curves at any point in order to optimize production. The proposed method uses a pseudo pressure transform to account for changes in fluid properties as the reservoir pressure is depleted. Relative permeability changes can be incorporated in the pseudo pressure transform. Comparisons to finite difference simulation results and actual productio data are presented. Comparisons of future IPR curves generated by other methods are also presented.