Yunhao Zhang’s research while affiliated with University of Regina and other places

In this work, a robust and pragmatic method has been developed, validated, and applied to describe two-phase flow behaviour of a multifractured horizontal well (MFHW) in a shale gas formation. As for a fracture subsystem, its permeability modulus, non-Darcy flow coefficient, and slippage factor have been defined and embedded into the governing equation, while an iterative method is applied to update the gas/water saturation in each fracture segment within discrete fracture networks. For a matrix subsystem, a skin factor on a fracture face is defined and introduced to represent the change in relative permeability in the matrix domain at each timestep, while the adsorption/desorption term is incorporated into the diffusivity equation to accurately calculate the shale gas production by taking the adsorbed gas in nanoscale porous media into account. Then, the theoretical model can be applied to accurately capture the two-phase flow behaviour in different subdomains. The accuracy of this newly developed model has been confirmed by the numerical simulation and then it is extended to field applications with excellent performance. The stress-sensitivity, non-Darcy flow, and slippage effect in a hydraulic fracture (HF) are found to be obvious during the production, while the initial gas saturation in a matrix and HFs imposes an evident influence on the production profile. As for an HF with a high gas saturation, the dewatering stage is missing and water from the matrix can be neglected during a short production time. For the matrix subsystem, a high-water saturation in the matrix near an HF can affect gas production during the entire stage as long as gas relative permeability in the HF remains low. In addition, the adsorption/desorption in the matrix subsystem can increase gas production but decrease water production. Compared to the observed gas/water production rates for field applications, the solutions obtained from the method in this work are found to be well matched, confirming its reliability and robustness.

A semi-analytical technique has been developed, validated, and applied to quantify the pressure behaviour of a multifractured horizontal well (MFHW) in a gas reservoir with discrete fracture networks and an arbitrary boundary. Considering stress-sensitivity and the slippage effect in the matrix subsystem, a pseudo-pressure is incorporated into the gas flow equations. To weaken the strong nonlinearity from such a combined effect, the dual-reciprocity boundary element method (DRBEM) is applied to efficiently and effectively linearize the governing equations by replacing the nonlinear function with a series of particular solutions. Comparing with the boundary element method (BEM), not only can the DRBEM be used to obtain the accurate solution in any space and time domains, but also it is flexible to deal with the nonlinearity restriction in the governing equations. The finite volume method (FVM) is then adopted to simulate gas flow behaviour in the fracture subsystem with different fracture geometries. Not only can the proposed model be applied to a complex fracture network and operating schedules, but also capture complex gas flow behaviour including the Langmuir sorption, slippage effect, and stress-sensitive effect in a gas reservoir with a discrete fracture network and an arbitrary boundary. The mathematical formulations have been validated and then extended to field applications. A strong stress-sensitive effect is found to result in a large pressure drop and offset the permeability-enhancing effect from the slippage effect. In addition, a decrease in pressure drop derived from gas desorption would restrict the stress-sensitive effect. Furthermore, it can be found that each individual factor imposes a significant impact on the linear flow and boundary dominated flow regimes. On the basis of a mutual interference, the combined effect (i.e., stress-sensitivity, slippage effect, and gas adsorption/desorption) may be weaker than that of each individual factor. In the late boundary-dominated flow regime, the effect of boundary shape becomes more obvious on the pressure distribution curves since the pressure wave would reach the boundaries near fractures within a relatively short time.

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.

In this study, a semianalytical technique has been developed to examine stress-sensitive effect on the transient pressure responses of a multiple-fractured horizontal well in an unconventional reservoir with an arbitrary-shape. Considering its arbitrary-shaped boundaries, the boundary element method is adopted to simulate flow behaviour by incorporating the permeability modulus (i.e., stress-sensitive effect) into the governing equation to describe the flow behaviour within the hydraulic fractures. To weaken the nonlinearity of such governing equations in a hydraulic fracture subsystem, a semianalytical approach is used to achieve consistent solutions with good accuracy. The convergence skin effect is introduced to represent the radial fluid-flow pattern in the hydraulic fractures near the horizontal wellbore. Not only can the stress-sensitive effects of hydraulic fractures be examined, but also the corresponding pressure responses together with pressure derivative curves are obtained. The mathematical formulations have been verified and then extended for field applications. The stress-sensitive effect of hydraulic fractures in a box-shaped reservoir with closed boundaries is found to be obvious during the intermediate- and late-time periods. Furthermore, the noticeable stress-sensitive effect in hydraulic fractures occurs earlier by taking the convergence-skin effect into account. A hydraulic fracture with a high permeability modulus is found to result in a positive stress-sensitive effect. Also, sensitivity analysis on pressure responses and their corresponding derivative curves have been performed with respect to the convergence skin effect, boundary shape, maximum distance, and minimum fracture conductivity.