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Summary Natural fractures are of great significance to the management of petroleum resources, groundwater, and carbon sequestration. Given that many naturally fractured reservoirs have poorly connected fractures, the traditional dual-porosity model like Warren and Root’s model is not reasonable for pressure transient analysis in these reservoirs. Therefore, the objective of this study is to develop a new discrete model (DM) in discretely fractured reservoirs based on a semianalytical approach. The DM comprises three domains: wellbore-connecting (WC) fractures and/or wellbore-isolating (WI) fractures, and matrix. The DM is verified by case studies with numerical simulators for four kinds of discretely fractured reservoirs with (1) WC fracture networks, (2) WI fracture networks, (3) WC and WI fractures, and (4) WI fractures. Results indicate that the pressure transient behaviors in discretely fractured reservoirs can be classified into three types: WC fracture networks, WC and WI fractures, and WI fracture (networks). The special flow regimes of WC fracture networks are fluid supply and pseudoboundary dominated flow. For WC and WI fractures, the special flow regimes are bilinear flow, linear flow, and isolated fracture effect. The early pseudoradial flow and isolated fracture effect (“V-shaped” or “dip”) are the special flow regimes of WI fracture (networks), and they are similar to traditional dual-porosity models like the Warren and Root model. However, the source of “V-shaped” in DM is quite different from that in the Warren and Root model. This paper gives a new insight into the well testing in discretely fractured reservoirs.

SummaryBecause of readily available production data, rate-transient analysis (RTA) is an important method to predict productivity and reserves, and for reservoir and completion characterization in unconventional reservoirs. In addition, multihorizontal well pads are a common development method for unconventional reservoirs. Close well spacing between multifractured horizontal wells (MFHWs) in the multiwell pads makes interference from adjacent MFHWs especially significant. For RTA of production data from multihorizontal well pads, the influence of adjacent MFHWs cannot be ignored. In this work, we propose a semianalytic RTA model for the multihorizontal well pad with arbitrary multiple MFHW properties and starting-production times. Combining Laplace transformation and finite-difference analysis, we obtained a general solution of a multiwell mathematical model to use in RTA. Our model is applicable to cases of multiple MFHWs with different bottomhole pressures (BHPs), varying hydraulic-fracture properties, and different starting-production times. In the solutions, we observe bilinear flow, linear flow, transition flow, and multi-MFHW flow. Rate-normalized pressure (RNP) and its derivative are also affected by multi-MFHW flow. Two case studies revealed that the negative effect of interwell interference on the parent-well productivity is closely related to the pressure distribution caused by the production of child wells.

Summary Fracture networks are extremely important for the management of groundwater, carbon sequestration, and petroleum resources in fractured reservoirs. Numerous efforts have been made to investigate transient behaviors with fracture networks. Unfortunately, because of the complexity and the arbitrary nature of fracture networks, it is still a challenge to study transient behaviors in a computationally efficient manner. In this work, we present a mesh-free approach to investigate transient behaviors in fractured media with complex fracture networks. Contributions of properties and geometries of fracture networks to the transient behaviors were systematically analyzed. The major findings are noted: There are approximately eight transient behaviors in fractured porous media with complex fracture networks. Each behavior has its own special features, which can be used to estimate the fluid front and quantify fracture properties. Geometries of fracture networks have important impacts on the occurrence and the duration of some transient behaviors, which provide a tool to identify the fracture geometries. The fluid production in the fractured porous media is improved with high-conductivity (denser, larger) and high-complexity fracture networks.

Summary In this paper, we present an efficient semianalytical model for pressure-transient analysis in fractured wells by considering arbitrarily distributed fracture networks. The semianalytical model included three domains: matrix, hydraulic-fracture networks, and discrete natural fractures. Using the line-source function, we developed the diffusivity equation for fluid flow in matrix. By applying the vertex-analysis technique, we eliminated the flow interplay at fracture intersections and established the diffusivity equations for fluid flow in hydraulic-fracture networks and isolated natural fractures. The pressure-transient solution of these diffusivity equations was obtained using Laplace transforms and the Stehfest numerical inversion. Results showed that with the discrete natural fractures, a “V-shaped” pressure derivative (the classical dual-porosity feature of naturally fractured reservoirs) emerged. With the hydraulic-fracture networks, the reservoir system would exhibit pressure behaviors such as “pseudoboundary-dominated flow,” “fracture-interference flow,” and “fluid-feed flow.” All these pressure characteristics were dependent on the properties and geometries of natural/hydraulic fractures. In addition, through synthetic field application, we found that different (natural/hydraulic) fracture distributions and geometries had distinct behaviors of pressure derivatives, which may provide an effective tool to identify the properties of randomly distributed natural fractures as well as complex hydraulic fractures in unconventional plays.

Summary Liquid/supercritical carbon dioxide (L/SC-CO2) fracturing is an emerging technology for shale gas development because it can effectively overcome problems related to clay swelling and water scarcity. Recent applications show that L/SC-CO2 fracturing can induce variations in temperature. Understanding of this phenomenon is rudimentary and needs to be carefully addressed to improve the understanding of CO2 thermodynamic behavior, and thus helps to optimize CO2 fracturing in the field. In this paper, we develop a numerical model to assess the impact of thermal effect on fracture initiation during CO2 fracturing. The model couples fluid flow and heat transfer in the fracture, and is verified by a peer-reviewed solution and observation in laboratory experiments. The velocity, pressure, and temperature are calculated at various time to demonstrate the thermodynamic behavior during fracture initiation. A pseudo shock wave is observed, associated with a compression wave and an expansion wave, which finally leads to an increase in temperature in the new fracture and a decrease in temperature in the initial fracture. The thermal stress is derived to investigate the difference between hydraulic fracturing and CO2 fracturing. The results show that thermal stress, resulting from CO2 fracturing initiation, is comparable to the rock strength, which will help induce microfractures, and thus promote the fracture complexity. The formation pressure after CO2 fracturing is also calculated to evaluate the pressure-buildup potential. This work highlights the importance of CO2 expansion during and after fracturing. It is one of the unique features that differs from hydraulic fracturing. For field-design recommendations, to enhance the thermal effect of CO2 fracturing, it is a good strategy to pump CO2 at high pressure and low temperature into the reservoirs with high Young's modulus, low Poisson's ratio, low permeability, and high geothermal temperature (or large depth). This paper does not address the dynamics of fracture propagation under the influence of thermal effect. Rather, it intends to demonstrate the potential of the thermal effect of CO2 fluid in assisting the fracture propagation, and the importance of incorporating the compressibility of CO2 into fracture modeling and operation design. Failing to account for this thermal effect might underestimate the fracture complexity and stimulated reservoir volume.

Summary In this paper, we propose a new model for pressure-transient analysis in multiple-fractured horizontal wells (MFHWs) with consideration of pressure drop along the wellbore. To make the physical model better understood, the whole formation is divided into three parts: (1) reservoir, (2) fracture, and (3) wellbore. With incorporating frictional and acceleration pressure drops, a mathematical model with a finite-conductivity horizontal well (FCHW) is developed. Newton-Raphson iterations are used to solve the mathematical model and obtain the transient-pressure solutions of the MFHW. Model verification is performed by comparing with the solutions from a numerical software. On the basis of the field cases from the Ordos Basin, performance prediction, sensitivity analysis, type-curve matching, and evaluations of uncertainty parameters are conducted. Results show that the contribution of wellbore hydraulics to the total pressure drop increases first and then decreases after reaching the peak value. Ignoring wellbore hydraulics would cause erroneous results during the well-performance forecast. In addition, the dimensionless wellbore pressure of the MFHW increases with an increase in Reynolds number (Re); it decreases as the reservoir/wellbore constant (ChD) increases. Furthermore, the impact of pressure drop on the pressure performance of the MFHW becomes more serious with the increasing Re or the decreasing ChD.

Summary Many researchers are currently seeking conventional geological sequestrations for carbon dioxide (CO2) storage, including saline aquifers, depleted conventional hydrocarbon reservoirs, and unminable coal seams. Only a few researchers have looked into depleted-shale formations for possible CO2 sequestration because of safety and economic reasons. To improve this situation, many measures should be taken. First and foremost, it is of great significance to find a method to estimate the CO2-storage capacity in depleted shale. In this paper, a new analytical method to estimate CO2-storage capacity in shale was developed. First, a trilinear-flow model proposed for the depleted-shale reservoir had a horizontal injection well—namely, a multiple-fractured horizontal well (MFHW)—at a constant injection rate. The model incorporated multiple mechanisms such as Knudson diffusion, gas adsorption, and effect of stress sensitivity. Then, the transient-pressure solution of the injection well was solved by applying mathematical methods of the Pedrosa (1986) substitution and Laplace transform. Subsequently, CO2-storage capacity was evaluated according to the transient-pressure performance of the injection well. After that, model verification and sensitivity analysis were conducted. Finally, we applied the proposed method in a case derived from the New Albany Shale, which had been proved to be a promising candidate for CO2 storage. The results show that good agreements exist between our analytical results and these numerical solutions. The average difference is approximately 3.03%, which shows our methodology is reasonable. Further, it only takes approximately 10 seconds of central-processing-unit (CPU) time with 100 timesteps by use of the proposed approach to estimate the CO2-storage capacity of the study area in the New Albany Shale, which indicates the new approach is rapid. In addition, results of sensitive analysis show that as stress-sensitivity coefficient, adsorption index, and Knudsen diffusion coefficient increase, CO2-storage capacity increases. As storage ratio increases, CO2-storage capacity decreases. This work provides a new approach to the estimation of CO2-storage capacity, which is beneficial to exploit the residual depleted-shale reservoirs as well as decrease CO2 emissions.

Summary In naturally fractured reservoirs, complex fracture systems can easily develop along a horizontal wellbore during hydraulic fracturing. In the fracture systems, multiple, discrete secondary fractures are connected to the multiple-fractured horizontal well (MFHW). Because of the fracture complexity, most studies about performance forecast of such MFHWs highly depend on numerical simulators. In this paper, a new semianalytical approach is proposed to overcome the challenge to analyze the pressure behavior of MFHWs in complex-fracture systems. First, a mathematical model for MFHWs with secondary-fracture networks is established. Then, with Gauss elimination and the Stehfest numerical algorithm (Stehfest 1970), the transient-pressure solution of the mathematical model is solved, and type curves of MFHWs with secondary-fracture networks are obtained. After that, model validation and sensitivity analysis are conducted. It is found that the presented approach can rapidly and accurately generate type curves of MFHWs with secondary-fracture networks. This work provides very meaningful references for reservoir engineers in fracturing evaluations as well as performance estimations of MFHWs in naturally fractured reservoirs.