|Theme||Visible||Selectable||Appearance||Zoom Range (now: 0)|
Summary This paper presents a hybrid numerical/analytical model for the pressure-transient response of a finite-conductivity fracture intercepted by a horizontal well. The model dynamically couples a numerical fracture model with an analytical reservoir model. This approach allows us to include finer details of the fracture characteristics while keeping the computational work manageable. For example, the fracture may have irregular shape, nonuniform width, and variable conductivity, and the well may not intersect the fracture at its geometric center. In this paper, we use the hybrid model to investigate the effects of fracture properties on the pressure-transient characteristics of a single, finite-conductivity horizontal-well fracture. The single horizontal-well-fracture model can be extended easily to multiply fractured horizontal wells by superposition. The model also can be used to compute the pseudoskin caused by the effects of nonideal fracture geometry, variable conductivity, and flow choking around the wellbore and to investigate the influence of fracture properties on the performance of horizontal wells. Introduction Fracturing horizontal wells is a common practice in tight formations (Moller 1988; Yost and Overbey 1989). Choking of flow around the horizontal well and fracture, however, strongly influences the flow characteristics and reduces the productivity of the fracture (Soliman et al. 1990). Fig. 1 shows the pressure surface on the fracture plane for a square hydraulic fracture intercepted by a horizontal well. The apex of the surface indicates the well intersection, and the increased pressure gradients around the well highlight the choking effect. This aspect of transverse hydraulic fractures emanating from horizontal wells is different from vertical wells. In addition, different fracture geometries may cause horizontal-well-fracture flow regimes that are different from those for vertical-well fractures (Fig. 2). If the fracture is a long rectangle, for example, linear flow dominates the flow convergence in the fracture after a short period of radial flow. Nonrectangular or noncircular fracture geometries may lead to unconventional flow regimes. The effects of flow-choking, fracture geometry, and variable conductivity in a horizontal-well fracture influence the rate of pressure change until pseudoradial flow is established. As confirmed by our results in this paper, the pseudoskin approach provides a good approximation only for the pressure-transient responses of long, rectangular, horizontal-well fractures beyond the fracture radial-flow period. For the other fracture geometries, the pseudoskin approach is appropriate only after the onset of pseudoradial flow. Therefore, the pseudoskin approach suggested in the literature (Soliman et al. 1990; Raghavan et al. 1997; Chen and Raghavan 1997) to incorporate the flow-choking effect into vertical-well-fracture models (Cinco-Ley et al. 1978; Cinco-Ley and Samaniego 1981; Cinco-Ley and Meng 1988; Ozkan and Raghavan 1991a) should not be extended beyond its suggested application. The objective of this paper is to present a model that can be used to understand the pressure-transient performance of a single, finite-conductivity horizontal-well fracture without the simplifying assumptions used in the literature (Soliman et al. 1990; Raghavan et al. 1997; Chen and Raghavan 1997; Larsen and Hegre 1991; Larsen and Hegre 1994; Guo and Evans 1993; Horne and Temeng 1995). In this model, the fracture flow is numerically simulated and dynamically coupled with an analytical reservoir-flow solution. Compared with a fully numerical approach, using an analytical solution for reservoir flow reduces the computational work and allows us to concentrate on the details of the fracture flow. For example, the fracture can have an irregular shape because of geological complexities, and conductivity can be variable within the fracture because of nonuniform gel and proppant placement or a nonplanar fracture profile. Although not included in this paper, non-Darcy flow in the fracture aggravated by flow convergence around the wellbore can be considered easily by a simple modification of the transmissibilities in the numerical model. The model presented in this paper is not limited to transverse horizontal-well fractures, either. Because the wellbore is represented as a source term in the fracture grid, several grids may include the wellbore source terms to simulate the appropriate intersection of the wellbore and the fracture plane (Fig. 3). Inherent in the numerical modeling of fracture flow, however, are the gridding, timestepping, and wellbore representation issues. This paper concentrates on the solution for a single, finite-conductivity, horizontal-well fracture. The procedure for extending the single-fracture solutions to multiply fractured horizontal wells has already been explained in the literature (Raghavan et al. 1997; Chen and Raghavan 1997) and is briefly discussed in Appendix A for completeness.
Wanjing, Luo (China University of Geosciences (Beijing)) | Changfu, Tang (Exploration Research Institute, Anhui Provincial Bureau of Coal Geology, Hefei, and Hefei Research Center of Shallow Geothermal Engineering and Technology)
Summary Fracture distributions (simple or complex fractures), fracture-conductivity heterogeneity (uniform or varying conductivity along the fracture), and flow regimes inside the fracture (Darcy or non-Darcy flow) are the three main issues that have been widely investigated for transient-pressure analysis of vertical fracture systems. In this study, we focus on the latter two issues by proposing a semianalytical solution to discuss the transient-pressure behaviors of a varying-conductivity fracture under non-Darcy-flow condition. First, a general fracture-flow equation is established for the uniform-/varying-conductivity fracture under Darcy/non-Darcy flow. Second, for the case of a varying-conductivity fracture, a dimension transformation and an unequal-length-discretization model are proposed to obtain the pressure solution. Then, the transient-pressure response for the case of non-Darcy flow in the fracture can be also obtained by use of an iterative procedure in each timestep in the Laplace domain. It is shown that results from our solutions agree very well with those reported in the literature (Guppy et al. 1982; Poe et al. 1992). Third, the transient-pressure behaviors of the varying-conductivity fracture under Darcy- and non-Darcy-flow condition are discussed in detail. Results show that non-Darcy flow in the fracture mainly reduces the effective conductivity and the transient-pressure curve follows the curve of an equivalently constant conductivity except for the case of extremely small conductivities. The pressure behaviors of varying-conductivity fractures depend on the value of average conductivity, the distribution of conductivity along the fracture, and the maximum-minimum-conductivity ratio. The presence of the varying conductivity not only affects the effective conductivity in the early and late times, but also changes the shape of the pressure curve, especially for the high-conductivity fracture in the early time. It is very difficult to accurately estimate the fracture parameters by well test for most of the cases of varying conductivities under non-Darcy flow in the fracture.
Wang, Junlei (Research Institute of Petroleum Exploration and Development) | Jia, Ailin (Research Institute of Petroleum Exploration and Development) | Wei, Yunsheng (Research Institute of Petroleum Exploration and Development) | Qi, Yadong (Research Institute of Petroleum Exploration and Development)
Semi-analytical modeling is an efficient method to obtain the transient response of fracture network. Since the fracture width is very small compared to the length, most semi-analytical models regard the fracture panel as 1D linear flow with a continuous line source along which the exchange of influx rate is nonuniformly distributed. In contrast, the purpose of this paper is to explicitly represent realistic finite-volume fractures where the flow pattern is two-dimensional and captures the details of the flow exchange between the porous media and fracture. A methodology similar to the boundary element method (BEM) is developed to simulate the transient pressure behavior for discretely and contiously fractured media. Numerous case studies are presented to validate the approach in comparison to full numerical simulation and existing solutions published in the literature. Case studies also demonstrate its capability to simulate different types of fractured medium.
He, Youwei (China University of Petroleum) | Cheng, Shiqing (China University of Petroleum) | Qin, Jiazheng (China University of Petroleum) | Chen, Jianwen (Changqing Oilfield Company) | Wang, Yang (China University of Petroleum) | Feng, Naichao (China University of Petroleum) | Yu, Haiyang (China University of Petroleum)
Abstract It is observed that production rates decline quickly and water-cut rises to 90% only after two or three years’ production for many multifractured horizontal wells (MFHWs) in China. Reliable measurements are critical to assess production performance and diagnose water-breakthrough positions to arrange the subsequent operations (e.g. stimulation and water plugging). Although production-logging test (PLT) is an effective method for production performance evaluation, the MFHW might be scrapped during the test and PLT is also expensive for an MFHW. To solve this problem, this paper proposes an approach to determine the production contribution of individual fracture and locate water-breakthrough segments along horizontal wellbore by combination of well testing and electrical resistance tomography (ERT). Firstly, a well testing model is developed to model pressure behavior of an MFHW intercepted by asymmetric fractures with arbitrary locations, unequal conductivity and production. Secondly, model validation demonstrates the accuracy of the well testing model proposed in this paper. Thirdly, sensitivity analysis shows that early-radial flow becomes remarkable as spacing between producing fractures or numbers of producing fractures decrease. N* is defined to characterize the number of mainly producing hydraulic fractures (NMPHF), and the value of N* depends on fracture properties (e.g. half-length, spacing, conductivity) besides the NMPHF. Fourthly, the well testing model is applied to estimate the flow profile through history matching of bottomhole-pressure (BHP) data. Fifthly, the introduction of ERT method solves the difficult to distinguish oil and water profile compared with well testing method, enables us to monitor the water-breakthrough locations and reduces the multiplicity of well testing interpretation in well performance evaluation. Finally, this method has been successfully applied to Changqing Oil Field, and results obtained by well testing and ERT method coincide with PLT, which enable petroleum engineers to carry out stimulation strategies to improve production performance and decrease the water-cut of MFHWs.