A Mathematical Model for Predicting Long-Term Productivity of Channel-Fractured Shale Gas/Oil Wells

This study focuses on the development of an analytical model to predict the long-term productivity of channel-fractured shale gas/oil wells. The accuracy was verified by comparing productivity calculated by the proposed model with numerical results. Sensitivity analysis was conducted to analyze significant parameters on the performance of channel fracturing. Field application of the model was conducted using production data obtained from an Eagle Ford Formation dry gas well, which was completed using channel fracturing. The procedure for estimating reservoir and stimulation parameters from production data was provided. The results indicated that the equivalent fracture width obtained from our model is consistent with the inversion of cubic law. Comparison with numerical simulations demonstrated that the proposed model might under- or overestimate well productivity, with mean absolute percentage error (MAPE) values of less than 8%. Sensitivity analysis indicated that, with the increase of fracture width, fracture half-length, and matrix permeability, the productivity of channel-fractured wells increases disproportionately. In addition, well productivity will increase as the ratio of the pillar radius to the length of channel fracture decreases, provided that the proppant pillars are stable and the fracture width is held constant. Under the conditions of smaller fracture width and larger matrix permeability, the effect of using channel fracturing to increase well productivity is more significant. However, as the fracture width becomes large, the benefits of channel fracturing will diminish. The case study indicated that the shale gas productivity estimated by the proposed model matches well with field data, with MAPE and R-2 of 12.90% and 0.93, respectively. The proposed model provides a basis for optimizing the design of channel fracturing.