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Production data analysis is a crucial tool for evaluating fracture parameters in deep shale multistage fractured gas wells. However, the complex fluid transport mechanisms within nanoscale pores and the two-phase flow of gas and water in reservoirs after hydraulic fracturing introduce significant uncertainty in the analysis results. This study proposes a two-phase flow production data analysis method for evaluating the properties of fractures in shale gas wells. We first establish an analytical model for predicting the productivity of gas–water two-phase in shale gas wells. Subsequently, we employ the fixed-point iteration method to simultaneously solve the two-phase material balance equations to calculate the average reservoir pressure and gas saturation, thereby updating the pseudopressure and pseudotime at each time step. Finally, we develop a high-pressure isothermal adsorption model to correct the apparent permeability model considering multiple fluid transport mechanisms and incorporate it into the productivity calculation. It is worth noting that the shale matrix is divided into organic and inorganic components. The organic pores account for bulk gas transport, surface diffusion, desorption, and high-pressure isothermal adsorption, while the inorganic pores consider bulk gas transport and the influence of a flowable adsorbed water film. Both models integrate real gas effects and stress dependence. The results indicate that the productivity prediction model can simultaneously analyze production data from early linear flow and late boundary-dominated flow. The diagnostic plots of two-phase flow regimes in field cases exhibit straight lines with slopes of 0.5 and 1, respectively. The microscale transport mechanisms of gas play a crucial role in gas well productivity modeling. Under high-pressure conditions, the bulk gas rapidly occupies the space of adsorbed gas, resulting in a reduction in the thickness of the adsorption layer, and consequently decreasing the apparent permeability affected by surface diffusion. Neglecting the influence of high-pressure adsorption may overestimate the true apparent permeability of shale reservoir pores. Therefore, it is recommended to utilize high-pressure isothermal adsorption models to characterize gas adsorption behavior. The real gas effect and stress dependence become more prominent under high-pressure conditions, but as the reservoir pressure decreases, the impact of various gas transport mechanisms on gas production gradually increases. The model proposed in this study has demonstrated high accuracy and computational efficiency through comparison with numerical simulation cases. Application to field cases in the Sichuan Basin, China, further validates the reliability and practicality of the proposed model, providing a theoretical basis for dynamic analysis of shale gas well production and numerical modeling of two-phase flow.
Bai et al. (Fri,) studied this question.