Mathematical Model for Rate Transient Analysis with Additional Interface Skin for Fractured Horizontal Well With Weak Fluid Supply

Abstract

This paper develops a mathematical model for rate transient analysis in multi-stage fractured horizontal wells with considering weak fluid supply. A new concept of additional skin factor is introduced in the proposed model to characterize the fluid supply. Then, the mathematical model are solved by using the perturbation transformation, point source integration method, Laplace transform, and numerical inversion, while the fracture flow equations are solved by fracture discretization and superposition principle. First, the flow regimes of multi-stage fractured horizontal wells with considering weak fluid supply are identified based on the rate transient behaviors, including wellbore storage and skin effect, bilinear flow, linear flow, pseudo-radial flow in the fractured zone, interface skin effect, pseudo-radial flow in the original zone, and boundary-dominated flow. The effect of additional interface skin makes the double logarithmic curve of production rate appear an abrupt "overlap". The results of the sensitivity study show that the abrupt "overlap" becomes more obvious with the increase of the fracture conductivity, fracture number, the stress sensitivity coefficient, especially the interface skin. Finally, the proposed mathematical model is used to perform a case study on the production data of actual tight-gas wells from the Ordos Basin. The interface skin factor, fracture half-length, fracture conductivity, and boundary radius are evaluated. Through the proposed model, the characteristics of weak fluid supply in tight gas reservoirs are fully understood.