Pressure transient analysis of multi-stage fractured horizontal wells in boxed reservoirs

A new analytical solution of fluid unsteady flow was presented for wells with finite-conductivity vertical fractures by determining impact functions of fracture conductivity. Based on the new solution, the transient pressure distribution of a fractured horizontal well with multiple finite-conductivity vertical fractures was obtained using the principle of superposition. Calculation results show the pressure transient behavior of fractured horizontal wells under the condition of constant bottom rate. In the ideal fracture arrangement, flow patterns occur in the order of early bilinear flow → early linear flow → middle radial flow → middle linear flow → late pseudo steady state. Uneven length of fractures with equal conductivity and uniform arrangement may affect the transform of early linear flows from earlier bilinear flows and the premature birth of middle radial flows. Nonuniform arrangement of fractures with even length and equal conductivity may influence middle radial flows. Different conductivity of fractures with equal length and uniform arrangement shortens the period of bilinear flows and lengthens the linear flows. Increase in the number of fractures with even length, equal conductivity and uniform arrangement accelerates pressure drops in the reservoir, shortens the period of middle radial flows and lengthens the middle linear flows. Increase in length of all fractures shortens the period of middle radial flows and results in absence of radial flows. It is demonstrated that the horizontal well with multiple vertical fractures may improve fluid flow patterns.