Summary: Due to the low porosity and permeability of the shale matrix, multi-fractured horizontal well (MFHW) is one of the most well-known technologies to promote the withdrawal of shale oil. It is a great challenge to characterize the flow behavior by coupling pre-Darcy flow in pores of the shale matrix and Darcy flow inside fractures, particularly in the radial composite shale reservoir with stimulated reservoir volume (SRV). Because the semi-analytical method can contribute to revealing the flow mechanism of the MFHW, the approach to efficiently obtain a suitable and exact semi-analytical solution becomes a key issue. In this work, to couple the modified point-source solution of the shale matrix with the numerical solution of fractures,we developed a semi-analytical solution to analyze the impact of pre-Darcy flow and SRV properties on the pressure behavior of the MFHW. Moreover, we used a local grid refinement method to verify the accuracy of the newly developed semi-analytical solution. The results show that the radial flow regime in the dimensionless pressure derivative will obviously disappear due to the pre-Darcy flow. Pre-Darcy flow in the SRV zone is adverse to the late production of the MFHW after the pseudolinear flow regime, while pre-Darcy flow in the unstimulated reservoir volume (USRV) zone is beneficial to increase the production during the regional interporosity flow regime. Meanwhile, the “groove” can be recognized from the pressure derivative curves, which mainly depend on the mobility ratio and the storage capacity ratio. In addition, due to the uneven distribution of fractures, the pressure derivative during the pseudoradial flow regime significantly deviates from 1/(2N).

Based on the property discontinuity in the radial direction, this paper develops a new composite model to simulate the productivity of volume fractured wells in naturally fractured reservoirs. The analytical solution of this model is derived in detail and its accuracy is verified by the same model’s numerical solution. Detailed analyses of the traditional transient and cumulative rate are provided for the composite model. Results show that volume fracturing mainly contributes to the early-flow period’s production rate. As interregional diffusivity ratio increases or interregional conductivity ratio decreases, the transient rate at the same wellbore pressure increases. Three characteristic decline stages may be observed on transient rate curves and the shape of traditional rate curves in the middle- and late-flow periods depends on naturally fractured medium and boundary condition. By introducing a new pseudo-steady constant, new Blasingame type curves are also established and their features are more salient than those of traditional rate curves. Five typical flow regimes can be observed on these new type curves. Sensitivity analysis indicates that new Blasingame type curves for varied interregional diffusivity ratio, interregional conductivity ratio, interporosity coefficient and dimensionless reservoir radius, except storativity ratio, will normalize in the late-flow period.

A fractured horizontal well is an effective technology to obtain hydrocarbons from tight reservoirs. In this study, a new semi-analytical model for a horizontal well intercepted by multiple finite-conductivity reorientation fractures was developed in an anisotropic rectangular tight reservoir. Firstly, to establish the flow equation of the reorientation fracture, all reorientation fractures were discretized by combining the nodal analysis technique and the fracture-wing method. Secondly, through coupling the reservoir solution and reorientation fracture solution, a semi-analytical solution for multiple reorientation fractures along a horizontal well was derived in the Laplace domain, and its accuracy was also verified. Thirdly, typical flow regimes were identified on the transient-pressure curves. Finally, dimensionless pressure and pressure derivative curves were obtained to analyze the effect of key parameters on the flow behavior, including fracture angle, permeability anisotropy, fracture conductivity, fracture spacing, fracture number, and fracture configuration. Results show that, for an anisotropic rectangular tight reservoir, horizontal wells should be deployed parallel to the direction of principal permeability and fracture reorientation should be controlled to extend along the direction of minimum permeability. Meanwhile, the optimal fracture number should be considered for economic production and the fracture spacing should be optimized to reduce the flow interferences between reorientation fractures.

Reorientation fractures may be formed in soft and shallow formations during fracturing stimulation and then affect well productivity. The principal focus of this study is on the productivity analysis for a horizontal well with multiple reorientation fractures in an anisotropic reservoir. Combining the nodal analysis technique and fracture-wing method, a semi-analytical model for a horizontal well with multiple finite-conductivity reorientation fractures was established to calculate its dimensionless productivity index and derivative for production evaluation. A classic case in the literature was selected to verify the accuracy of our semi-analytical solution and the verification indicates this new solution is reliable. Results show that for a fixed fracture configuration the dimensionless productivity index of the proposed model first goes up and then remains constant with the increase of fracture conductivity, and optimal fracture conductivity can be determined on derivative curves. Strong permeability anisotropy is a negative factor for well production and the productivity index gradually decreases with the increase of anisotropic factor. As principal fracture angle goes up, horizontal well’s productivity index increases correspondingly. However, the effect of reoriented fracture angle on the productivity index is not as strong as that of principal fracture angle. When reoriented fracture angle is smaller than principal fracture angle, reoriented factor should be as low as possible to achieve optimal productivity index. Meanwhile, well productivity index rises up with the increase of fracture number and fracture spacing, but the horizontal well has optimal reorientation fracture number and fracture spacing to get the economical productivity. Furthermore, the influence of the rotation of one central reorientation fracture on productivity index is weaker than that caused by the rotation of one external reorientation fracture. In addition, the asymmetrical distribution of one or more reorientation fractures slightly affects the productivity index when fracture conductivity is high enough.

Polymer flooding has been proved by many scholars for use in heavy oil reservoirs. However, due to mobility control effects and injectivity, selecting the appropriate solution viscosity is essential. It is difficult to form a deep understanding of the effect and mechanism of polymer flooding using conventional experimental methods with oil recovery as the reference standard, so it is necessary to conduct further study with the aid of simulation methods. In this study, a one-dimensional displacement mathematical model based on the Buckley–Leverett theory was established, and in the range of water–oil viscosity ratio from 0.1 to 0.6, the variation of water saturation along the flow caused by polymer solution was studied. The research results showed that under the action of a polymer solution, compared with water flooding, there was a decreasing region of water saturation along the flow due to oil phase accumulation. The larger the water–oil viscosity ratio, the larger the area of water saturation decline and the greater the degree of water saturation decline, resulting in a better the displacement effect. However, under the condition of oil–phase viscosity of 70 mPa·s, when the water–oil viscosity ratio reached 0.4, the range and degree of water saturation decline along the way no longer changed, all the crude oil that could be swept had been displaced, and the outlet end was close to producing only water, not oil; therefore, further increasing the water–oil viscosity ratio could not increase the oil recovery. At the same time, the increase in pressure had not changed, that is, the increase in pressure had not resulted in the same increase in oil recovery. When the viscosity of oil phase increased to 140 mPa·s, the same rule was displayed, the appropriate water–oil viscosity ratio was also 0.4. The paper analyzed the action mechanism of polymer solution through process description, and the results provided a clear selection method for selecting reasonable polymer solution concentration, as well as a reference for polymer solution range under different crude oil viscosity conditions.