Abstract:Based on Green 's function and source functions, the analytical solution of pressure in a horizontal well with multiple hydraulic fractures was obtained by using mirror-injection and superposition theorem. At first, pressure drop was derived in three different conditions:infinite surrounding, prescribed flux and prescribed pressure when the top and bottom of the formation were prescribed. Then, new solutions of the wellbore pressure were described assuming that the wellbore of the horizontal well had infinite flow conductivity. According to Stehfest numerical inversion, the pressure drop was derived considering wellbore storage and skin factor. The pressure plots and pressure derivative curves on different conditions in the fracturing horizontal and the influence of fracturing parameters were analyzed. The results show that there are five flow regimes including fracturing linear flow, fracturing radial flow, formation linear flow, system radial flow and bound influence. For a dual porosity model, cross flow exists which flows from matrix system to the fracture system. In dimensionless form, pressure drops when the fracturing number rises. However, when the pressure wave reaches the boundary, the fracturing number has little effect on the flow. The fracture length influences both the time when the fracturing radial flow appears and the pressure drop before forming linear flow. Under the same production time, the longer the fracture length, the later the fracturing radial flow appears and the less the dimensionless pressure drops. The spacing between two fractures influences the time when the fracturing radial flow ends; when the spacing is smaller, the time for fracturing radial flow lasts shorter. The results are verified in engineering application to prove the feasibility of the models.