An improved mathematical model of gas-water two-phase flows in fractured horizontal wells accounting for physical contact behaviors of fractures with total factor characteristics

In water-bearing gas reservoirs, water existence affects gas production performances due to two-phase flows occurring in matrix and fracture systems. Under the background of staged multi-cluster fractured horizontal wells, this work focuses on an improved gas-water two-phase flow model accounting for physical contact behaviors of fractures with total factor characteristics. Combining a point-convergence method with fractal theory and applying Laplace transform and Stehfest numerical inversion, analytical solutions of this proposed model are solved to validate against the field production data and numerical simulation results. Subsequently, the analytical nephograms of formation pressure and water saturation at different stages are given for the first time, throughout which formation pressure and water saturation distributions at different locations of the fractured reservoir embedded with segmented multi-cluster tree-shaped fracture networks are visually exhibited. The results demonstrate that draining area evolution is limited to each segment at early stage and mid-stage, whereas these multi-cluster segments are really integrated into the whole draining area at late stage. Thus, the moving boundary of fracture-controlled unit is also delineated based on water saturation nephograms and expands with continuous production from 65 to 180 m in the y axis direction, contributing to the effective fracturing area for a high productivity. Furthermore, the share of free gas and adsorbed gas are 83% and 17% at early stage, while free gas and adsorbed gas account for 57% and 43% of total gas at the late stage. Those findings contribute to high-efficient and sustainable development of unconventional gas resources.