Multiple hydraulic fracture treatments in the reservoirs with natural fractures create complex fracture networks. Predicting well performance in such a complex fracture network system is an extreme challenge. The statistical nature of natural fracture networks changes the flow characteristics from that of a single linear fracture. Simply using single linear fracture model for individual fractures, and then summing the flow from each fracture as the total flow rate for the network could introduce a significant error. In this paper we present a semi-analytical model by a source method to estimate well performance in a complex fracture network system. The method solves the problem by considering the fractures as a combined series of slab sources and by superposing the sources under several boundary or flow conditions. The method simulates complex fracture systems in a more reasonable approach. To reflect heterogeneous nature of natural fractures, a stochastic method of generating discrete fracture networks is adopted. The fractal discrete fracture network model (FDFN) incorporates the various scale-dependent data, such as outcrops, logs and cores; and creates more realistic natural fracture networks. FDFN model is combined with the slab source model to build fracture networks first, and then the flow problem in the complex fracture systems is solved. After generating the complex fracture network, each fracture, the analytical solution of superposed slab sources, is applied to predict the overall flow from all of the fractures in the system by considering the effects between the fractures through the superposition principle. The fluid inside the natural fractures flows into the hydraulic fractures, and the fluid of the hydraulic fractures from both the reservoir and the natural fractures flows to the wellbore. Because of the flexibility of the source method, non-orthogonally intersecting fractures are allowed in the system to simulate the geostatistically distributed fracture systems. The non-orthogonal fractures are approximated as a series of either vertical or horizontal sub-fractures, depending on the intersecting angle of the fractures. Simplified example of combined geometries of hydraulic fractures and natural fractures is presented. The methodology developed in this study captures the nature of multiple stage fractured horizontal wells in naturally fractured formations, and can be used to predict fractured well performance. It is relatively simple to apply compared with reservoir simulations. Introduction Since the successful development of Barnett shale in early 2000s due to the implementation of hydraulic fracturing and horizontal well drilling, unconventional reservoirs such as shale and tight sand have become an important additional resource of hydrocarbon energy. As new technology becomes available, multiple-stage fracturing in horizontal wells is now a primary stimulation method to bring economical and technical benefits of unconventional gas wells. Extended fracture network can be created in shale formations by multi-stage fracturing to improve volumetric transmissibility of nano-Darcy reservoirs. Because the fractures created in multi-stage treatments express a stochastic nature, strongly depending on the natural fracture characteristics of the formation, such a fracture system is hard to describe precisely, posting an extreme challenge in modeling of well performances.

Naturally fractured reservoirs constitute a significant portion of oil and gas fields worldwide. Like all reservoirs, waterflooding is routinely used in naturally fractured formations to increase recovery. However, the benefits of waterflooding can be limited due to early water breakthrough via the fractures. Therefore it is imperative to closely monitor the flood progress in these reservoirs. Analyzing transient tests in water injection wells, especially early in the life of the flood can provide valuable information, such as the mobilities in various regions around the well and the location of the flood front. An analytical model to design and analyze falloff transient data in naturally fractured reservoirs is highly desirable so that pressure transient analysis techniques can be applied for monitoring and optimizing secondary recovery projects. In this paper we present a semi-analytical solution for the pressure response during falloff tests in naturally fractured reservoirs under multiphase flow conditions. We consider water injection into an oil reservoir, resulting in two-phase flow. In our model, the radial variation of fluid saturation is modeled as a multibank reservoir with constant saturation in each bank. Each bank has a different relative permeability and compressibility value, corresponding to the fluid saturation in the bank. We model naturally fractured reservoir behavior using Warren & Root's dual porosity model, which is extended to accommodate two-phase and multi-composite reservoirs. We also include capillary pressure effects in the model. The proposed semi-analytical solution was tested and compared against numerical simulation results obtained from commercial simulators. The results have been in excellent agreement, validating our semi analytical approach. Using the proposed solution provides a rigorous and fast method to design and analyze tests. It also allows for using nonlinear regression techniques as opposed to computationally expensive trial and error matching for estimation of reservoir properties. Our analytical model can also be used as a guideline for grid refining in the vicinity of the wellbore and time-step selection in numerical simulators for transient tests analysis. We expect our analytical method will enable operators and engineers to design and analyze falloff tests quickly and accurately in naturally fractured reservoirs.

Multiple hydraulic fracture treatments in reservoirs with natural fractures create complex fracture networks. Predicting well performance in such a complex fracture network system is an extreme challenge. The statistical nature of natural fracture networks changes the flow characteristics from that of a single linear fracture. Simply using single linear fracture models for individual fractures, and then summing the flow from each fracture as the total flow rate for the network could introduce significant error. In this paper we present a semi-analytical model by a source method to estimate well performance in a complex fracture network system. The method simulates complex fracture systems in a more reasonable approach. The natural fracture system we used is fractal discrete fracture network model. We then added multiple dominating hydraulic fractures to the natural fracture system. Each of the hydraulic fractures is connected to the horizontal wellbore, and some of the natural fractures are connected to the hydraulic fractures through the network description. Each fracture, natural or hydraulically induced, is treated as a series of slab sources. The analytical solution of superposed slab sources provides the base of the approach, and the overall flow from each fracture and the effect between the fractures are modeled by applying the superposition principle to all of the fractures. The fluid inside the natural fractures flows into the hydraulic fractures, and the fluid of the hydraulic fracture from both the reservoir and the natural fractures flows to the wellbore. This paper also shows that non-Darcy flow effects have an impact on the performance of fractured horizontal wells. In hydraulic fracture calculation, non-Darcy flow can be treated as the reduction of permeability in the fracture to a considerably smaller effective permeability. The reduction is about 2% to 20%, due to non-Darcy flow that can result in a low rate. The semi-analytical solution presented can be used to efficiently calculate the flow rate of multistage-fractured wells. Examples are used to illustrate the application of the model to evaluate well performance in reservoirs that contain complex fracture networks.