Semi-analytical model of multi-stage fractured horizontal well productivity considering time-dependent fracture conductivity

At present, the models for calculating the productivity of multi-stage fractured horizontal well are researched more, but few productivity formulas consider the effect of the timeliness of fracture conductivity on the productivity. Laboratory experiments and field practice show that the fracture conductivity changes continuously over the time in the process of actual production. In this paper, the reservoir seepage model was solved by means of the source function method, and the reservoir seepage model considering the change of fracture conductivity over the time was solved discretely by means of the finite difference method. Then, both of them were coupled based on the boundary condition that the flow rate and pressure at the contact plane of fracture and oil reservoir are equal. In this way, the semi-analytical model of multi-stage fractured horizontal well productivity considering long-term fracture conductivity was established. The simulation calculation results show that the flow conductivity decreases over the time and it is a nonnegligible factor in the productivity prediction and analysis, for it can change the distribution of seepage field in oil reservoirs and the distribution of flow rate and pressure inside the fractures to make more fluid flow into the well through the fractures near the wellbore. This newly established model and the calculation results in this paper play an important role in guiding reservoir productivity prediction and actual production.