Predicting and Optimizing the Productivity of Multiple Transverse Fractured Horizontal Wells in Ultra-low Permeability Reservoirs

predicting and optimizing the productivity of horizontal wells is essential to reservoir engineering designation. However, existing mathematical models and evaluation methods did not include the impact of the threshold pressure gradient and the pressure-sensitive effect which cannot be ignored in ultra-low permeability reservoirs. The objective of this paper is to present a method considering the threshold pressure gradient and the pressure-sensitive effect, thus predicting and optimizing the productivity of multiple transverse fractured horizontal wells (MFHW) in ultra-low permeability reservoirs becomes available. The new method couples the non-Darcy elliptical flow, which considers the threshold pressure gradient and the pressuresensitive effect in the reservoir region, the Darcy linear flow in the fractured region, and the Darcy radial flow to the horizontal wellbore in the fractured region respectively. Based on the equality radius mode and the pressure superposition theory, the evaluation methods for the productivity of multiple transverse fractured horizontal wells are presented. In addition, the new method is validated by comparing with field data, results confirm that those formulas are precise and practical, and the evaluation method is reliable. Based on an example of productivity analysis for a multi-fractured horizontal well, the effects of some factors, such as threshold pressure gradient, coefficient of deformation and fracture parameters (fracture number, fracture length, conductivity, uniformity of fractures length and intervals), on the productivity were studied. The results show that the greater the threshold pressure gradient, the greater the effect of it on multi-fractured horizontal well productivity, so the threshold pressure gradient must be accounted to evaluate the MFHW productivity in ultra-low permeability reservoirs. Also, the greater the coefficient of deformation, the greater the effect of it on MFHW productivity, and the affection of coefficient of deformation on productivity is related to producing pressure drop, and the greater the pressure drop, the larger the influence of deformation coefficient on producing rate, thus for strongly pressure-dependent reservoir, we’d better conduct an optimization design for feasible producing pressure drop. In the given condition, the optimal fracture number of the horizontal well is 4～5, the half length of fracture is about 120 m, and the conductivity is 4.8 D•cm. The fractures with longer length, lower conductivity, variable length and placed in unequal interval are favorable for homogeneous oil reservoir. This paper provides reservoir engineers with a reliable and practical method to predict and optimize the productivity of multiple transverse fractured horizontal wells in ultra-low permeability reservoirs.