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. We statistically assigned a fracture network of natural fractures, based on the spacing between fractures and fracture geometry. 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. The finite conductivity of hydraulic fractures is modeled by additional pressure drop inside the fracture, but it is neglected in natural fractures. 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.

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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.

In tight gas reservoirs, horizontal wells have been used to increase reservoir contact and hydraulic fracturing has been applied to further extend the contact of the reservoir. Point source solution has been used to describe the flow behavior. The method was advanced to the volumetric sources, and pressure change inside the source was considered. We have developed a method that can predict horizontal well performance, and the model can also be applied for fractured horizontal wells. The method solves the problem by superposing a series of slab sources under transient or pseudo-steady state flow conditions. The principle of the method comprises calculation of the semi-analytical response of a rectilinear reservoir with closed outer boundaries. The slab source approach assigns the source a geometry dimension, similar to the volumetric source method, but has the solution similar to the point source method by neglecting the effect of the flow inside the source. When solving the source problem the pressure/flow effect inside source is considered sequentially by superposition principle over multiple sources. The pressure response is integrated over time to provide continuous pressure behavior. Flow effect inside of fractures can be studied by dividing the fracture into several segments, and each can be treated as a slab source. The method is validated by comparison with the results of analytical solutions of horizontal wells with uniform flux and infinite conductivity, and fractured wells with uniform flux, finite or infinite conductivity. The method provides an effective tool for horizontal well design and well stimulation design for gas reservoirs. In this paper, we present the details of model development. The examples will be used to illustrate how the model can help to optimize wellbore and fracture design. The method in this paper is more accurate compared with conventional point-source solution, and can handle the transaction from transient flow to pseudo-steady state flow smoothly. The results of the study show that in low permeability formation, hydraulic fracturing has more impact on horizontal well performance.