Modeling transient pressure behaviour of a multi-fractured horizontal well in a reservoir with an arbitrary boundary and different fracture networks by considering stress-sensitive effect

Abstract

Combining horizontal drilling together with hydraulic fracturing greatly improves the economic viability of exploiting a tight reservoir, while the stress-sensitive effect raises the significant difficulty to accurately evaluate its well performance. In this paper, a semi-analytical model is proposed to evaluate transient pressure behaviour of a multi-fractured horizontal well (MFHW) in a naturally fractured reservoir with an arbitrary boundary and different fracture networks under stress-sensitive effect. More specifically, the boundary element method coupled with the Pedrosa's transform formulation is used to obtain accurate solutions of the nonlinear equations incorporated with stress-sensitive effect in an arbitrary-shaped reservoir with single-zone or two-zone matrix subsystems. Meanwhile, the Laplace-transform finite difference method can be utilized to semi-analytically deal with the nonlinear fracture subsystems consisting of primary, secondary, and natural fractures by dividing complex fracture networks into small fracture segments. The convergence-skin effect is then introduced to represent the radial flow pattern in hydraulic fractures near a horizontal wellbore. Not only can the effects of stress-sensitivity in the matrix and different fracture subsystems be respectively examined, but also the corresponding pressure responses together with pressure derivative curves are obtained. Such coupled theoretical formulations have been verified and then extended for field applications. The semi-analytical solution is found to be more accurate and reasonable than the solution with the uniform permeability modulus, while the stress-sensitivity has a dominant impact on the intermediate- and late-time flow periods. The convergence-skin effect can be aggravated in the late-time period by considering the inherent stress-sensitivity in a hydraulic fracture, especially at low fracture conductivity. Based on the sensitivity analysis associated with different networks, the initial fracture conductivity in primary and secondary fractures imposes a great impact on the early-stage bilinear flow and fluid feed regimes, while the initial fracture conductivity in natural fractures makes a difference to the transient pressure response in the transition flow regime. As the minimum fracture conductivity in the primary fractures decreases, such an influence becomes more dominant during the late-time flow period. However, the minimum fracture conductivity in secondary and natural fractures has an inappreciable effect on the flow regime. In the late-time flow period, the effect of boundary shape becomes more obvious on the type curves, especially for a relatively small reservoir compared with the size of a horizontal well intercepted by multiple hydraulic fractures. For a reservoir with two-zone systems, the smaller the mobility ratio in the two zones is, the earlier the boundary-dominated flow in the outer zone will commence. Not only does this study facilitate understanding the respective contribution of stress-sensitivity and convergence-skin effect on the well production, but also the newly proposed models can be applied to optimally design a hydraulic fracturing operation under various constraints.