A Two-Phase Non-Linear One-Dimensional Flow Model for Reserves Estimation in Tight Oil and Gas Condensate Reservoirs Using Scaling Principles

Abstract

Abstract A common approach to forecast production from unconventional reservoirs is to extrapolate single-phase flow solutions. This approach ignores the effects of multi-phase flow, which exist once the reservoir pressure falls below the bubble/dew point. This work introduces a new two-phase (oil and gas) flow solution suitable to extrapolating oil and gas production using scaling principles. Additionally, this study compares the application of the two-phase and the single-phase solutions to estimates of production from tight oil wells in the Wolfcamp Formation of West Texas. First, we combine the oil and the gas flow equations into a single two-phase flow equation. Second, we introduce a two-phase pseudo-pressure to help linearize the pressure diffusivity equation. Third, we cast the two-phase diffusion equation into a dimensionless form using inspectional analysis. The output of the model is a predicted dimensionless flow rate that can be easily scaled using two parameters: a hydrocarbon pore volume and a characteristic time. This study validates the solution against results of a commercial simulator. We also compare the results of both the two-phase and the single-phase solutions to forecast wells. The results of this research are the following. First, we show that single-phase flow solutions will consistently underestimate the oil ultimate recovery factors for solution gas drives. The degree of underestimation will depend on the reservoir and flowing conditions as well as the fluid properties. Second, this work presents a sensitivity analysis of the PVT properties that shows that lighter oils (more volatile) will yield larger recovery factors for the same drawdown conditions. Third, we compare the estimated ultimate recovery (EUR) predictions for two- and single-phase solutions under boundary-influenced flow conditions. The results show that single-phase flow solutions will underestimate the ultimate cumulative oil production of wells since they do not account for liberation of dissolved gas and its subsequent expansion (pressure support) as the reservoir pressure falls below the bubble point. Finally, the application of the two-phase model provides a better fit when compared with the single-phase solution. The present model requires very little computation time to forecast production since it only uses two fitting parameters. It provides more realistic estimates of ultimate recovery factors and EUR, when compared with single-phase flow solutions, since it considers the expansion of the oil and gas phases for saturated flow. Finally, the solution is flexible and can be applied to forecast both tight oil and gas condensate wells.