Rate-transient analysis (RTA) methods have historically been used to characterize multi-fractured horizontal wells (MFHWs) during transient linear flow in order to estimate the total effective fracture area. A primary complication in linear flow analysis is the incorporation of multi-phase flow, as well as pressure-dependent rock properties, into the calculations. A new linear flow analysis technique is presented in the current study which can be applied to tight/shale systems with multi-phase flow and pressure-dependent rock properties. In recent work, the authors developed a semi-analytical model for analysis of early-time production data of tight oil reservoirs during transient linear flow. The model assumes two-phase flow of oil and gas in the reservoir. However, there are numerous documented cases of tight oil reservoirs that exhibit high water-oil ratios (WORs) throughout their production history. This fact necessitates the inclusion of water production into RTA to ensure accurate hydraulic fracture characterization. In the current work, the model development is revisited to account for all flowing phases (oil, gas and water). The proposed technique is fundamentally based on the application of the Boltzmann transformation technique and development of modified pseudovariables, which are critical for linearizing the diffusivity equation for describing multi-phase flow. The combination of these techniques allows the liquid-solution analogy to be applied to the transient linear version of the diffusivity equation. In the current work, it is demonstrated that, through application of the Boltzmann transformation, the highly nonlinear partial-differential equations (PDEs) governing three-phase flow through porous media can be converted to three nonlinear ordinary-differential equations (ODEs). The proposed approach has the important advantage of providing the relationship between saturation and pressure, which is used to evaluate pseudopressure. Similar to the approach of Perrine (1956), the solution to the individual ODEs can be combined through defining total mobility, total compressibility and total flow rate to determine the linear flow parameter, ??√?. The presented model provides a theoretical framework for analyzing production data considering a variety of reservoir fluid systems and variability in relative permeability. The robustness of this innovative approach is tested through comparison with more rigorous numerical simulation. Through comparison with numerical simulation, it is concluded that the estimated pressure- saturation relationship is robust. Average relative errors in ??√? estimation using the new methodology are calculated to be less than 12% for all the simulated cases presented in this study. The new technique should serve as a useful tool for petroleum engineers responsible for forecasting tight oil wells exhibiting the complexities of multi-phase flow and pressure-dependent rock properties.
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