A multi-linear transient pressure model for multistage fractured horizontal well in tight oil reservoirs with considering threshold pressure gradient and stress sensitivity

Abstract In general, tight oil reservoirs has a numerous tiny and complicated throats, and ultra-low permeability, which leads to a low-velocity non-Darcy flow when the fluid flows in tight reservoirs. The permeability of tight oil reservoirs is no longer a constant, but a variable, which is dependent on reservoir pressure. In other word, the tight oil reservoir is stress sensitive media. The low-velocity non-Darcy flow and stress sensitivity will greatly affect the bottom hole pressure response. So, the low-velocity non-Darcy flow and stress sensitivity should be taken into consideration when researching the transient pressure behaviors of multistage fractured horizontal wells. Currently, there are many researches on transient pressure behaviors of the multistage fractured horizontal well, but none of these researches has taken the low-velocity non-Darcy flow and stress sensitivity into consideration simultaneously. In this paper, threshold pressure gradient and permeability modulus are used to characterize the low-velocity non-Darcy flow and stress sensitivity, respectively. And, a multi-linear transient pressure model of multistage fractured horizontal well with considering low-velocity non-Darcy flow and stress sensitivity is established. The Pedrosa's transformation, perturbation theory, Laplace transformation and stehfest numerical inverse are used to solve this transient pressure model. The novel model is verified by comparing the result of proposed model with that of Ekaterina Stalagorova's model. According to the dimensionless pressure derivative curve, the flow process can be identified as six regimes: ①the main fracture linear flow stage, ②the first transition flow stage, ③dual-linear flow stage, ④the second transition flow stage, ⑤the formation linear flow stage, ⑥the boundary flow stage. Finally, the effects of threshold pressure gradient, permeability modulus and fracture density of stimulated reservoir on dimensionless pressure derivative are analyzed. This research provides theoretical support for correctly understanding the flow law of multistage fractured horizontal well.