Productivity calculation and distribution of staged multi-cluster fractured horizontal wells

Applying the potential theory and the superposition principle, the authors derived the linear productivity equations of staged multi-cluster fractured horizontal well considering finite and infinite conductivity fractures, respectively. The cluster yields and total yield were obtained by solving these equations numerically. A concrete example is used to analyze the productivity distribution of the fractured horizontal well and the influence of fracture parameters on it. When the fracture conductivities are infinite, the total productivity decreases significantly with the decrease of all fracturesʹ half-lengths; outer fractures near the endpoints of the horizontal wells contribute most to the total productivity, and fractures on the edges contribute more than the middle ones within the same stage. When the fracture conductivities are finite, the contribution of outer fractures near the endpoints of the horizontal wells to the total productivity decreases, and the contribution of middle fractures within each stage increases significantly, but the overall distribution characteristics are in accord with the former case. Fracture conductivities have a great influence on the productivity, but they are not linearly correlated. Three stages and two clusters per stage can ensure high productivity, and during fracturing design, one should try to increase fracture half-lengths and fracture conductivities, especially for outer fractures near the endpoints of the horizontal well, and there exists an optimal value for the fracture conductivities.