Transient pressure behavior of multi-stage fractured horizontal wells in stress-sensitive tight oil reservoirs

Abstract

Due to well-developed natural fractures, tight oil reservoirs always described as stress sensitive dual media reservoir. So far, the pressure distribution model for multi-stage fractured horizontal well (MFW) in stress sensitive reservoir is almost solved by numerical method. This paper gives the semi-analytical solution to this problem. Firstly, with consideration of stress sensitivity, a transient pressure behavior model of MFW was established. Using perturbation transform, Laplace transform, image theory and superposition principle the mathematical model was solved. Finally, by applying stehfest numerical inversion and perturbation inverse transform, we get the transient pressure for MFW in the time domain.According to the result of calculation, the flow process of MFW can be identified as six regimes: Ⅰ linear flow, Ⅱ the first radial flow, Ⅲ double radial flow, Ⅳ radial flow in the natural fractures system, Ⅴ cross flow, Ⅵ radial flow in the entire reservoir. Stress-sensibility primarily influences the latter five stages. The well bore dimensionless pressure drop is several times larger comparing with the situation that don't take the stress sensitive into account, and the dimensionless pressure drop derivative curve will tilte up in the later flow process, showing the characteristic of closed boundary. Accordingly, the calculating error will be larger and can mislead the interpretation of well testing.