Fracture Design Research Articles

Effect of Hydration under High Temperature and Pressure on the Stress Thresholds of Shale

The stress threshold of deep reservoir shale subjected to fracturing fluid immersion is an important factor affecting fracture initiation and propagation during fracturing. However, little information has been reported on the effect on shale of soaking at high temperature and high pressure (HTHP). In this study, immersion tests and triaxial compression tests were carried out at reservoir temperature and in-situ stress on the downhole cores with different mineral compositions. The characteristics of stress thresholds, i.e., crack initiation stress (σci), crack damage stress (σcd), and peak deviator stress (σp), of shale affected by the different times of soaking with low-viscosity fracturing fluid (a) and the different viscosity fracturing fluids (a, b, and c) were investigated. The results show that hydration at HTHP has a significant softening effect on the stress thresholds (σci, σcd, σp) of reservoir shale, but the softening rate varies for samples with different mineral compositions. The crack initiation stresses of quartz-rich and clay-rich shales treated with different soaking times and different soaking media remain almost unchanged in the range of 47 to 54% of the corresponding peak strength, while the crack initiation stresses of carbonate-rich shales are significantly affected. The ratio σcd/σp of quartz-rich shale is significantly affected by the different viscosity fracturing fluids (a, b) and the different times of soaking with low-viscosity fracturing fluid (a), while clay- and carbonate-rich shales are less affected. The results of this study can provide a reference for the fracturing design of deep shale gas development.

Experimental investigation on mode I fracture characteristics of Longmaxi formation shale after cyclic thermal shock and high-temperature acid etching treatments

Fracture toughness is a key parameter for shale hydraulic fracturing design, which directly affects the fracture initiation pressure. In this paper, the influence of cyclic thermal shock and high-temperature acid etching on the Mode I fracture of Longmaxi Formation shale was investigated. The crack propagation was obtained by using acoustic emission (AE) and digital image correlation (DIC) techniques. Meanwhile, the fracture surface morphology and microstructure of the specimens were analyzed using white light interferometer and scanning electron microscope (SEM). The experimental results demonstrate that cyclic thermal shock severely degrades the nominal strength and fracture toughness of shale. The average fracture toughness is found to be only 0.67 MPa·m0.5, which accounts for a reduction of 25.9 %. AE analysis reveals that microfracture is the dominant mechanism, with the highest amplitude of AE source only 78 dB. The critical strain value of the fracture propagation zone (FPZ) is determined to be 1.35 ‰, and SEM images indicate that along-crystal fracture is the primary fracture mechanism. On the other hand, the shale specimen subjected to high-temperature acid-etching treatment exhibits an average fracture toughness of 0.86 MPa·m0.5, with the AE source amplitude reaching 86 dB. The critical strain value of the FPZ was measured to be 2.38 ‰. The fracture surface appears smooth and is mainly characterized by perforated-crystal rupture. The findings of this study not only enhance our understanding of shale mode I fracture toughness but also provide valuable insights for optimizing process parameters to reduce initiation pressure in deep shale formations.

Fracture Initiation and Propagation in the Hot Dry Rock Subject to the Cyclic Injection Hydraulic Fracturing Treatment

Cyclic injection hydraulic fracturing is a promising way for the geothermal energy exploitation by reactivating the fractures in geothermal reservoir. However, fracture initiation and growth induced by cyclic injection schemes have been inadequately studied for hot dry rock (HDR), and the cyclic injection fracturing optimized often by experience. For this reason, the initiation and propagation of hydraulic fractures in the HDR under different cyclic injection methods were determined by experiment research for hydraulic fracturing. The results show that the cyclic frequency and injection rate play different roles in the stimulation of HDR. The cyclic injection with low frequency-low pressure can create more branched fractures, forming a short but complex hydraulic fracture network. However, when high flow-high frequency injection method is subjected, the branch fractures formed are significantly reduced, but each branch fracture can be fully expanded. To fully exploit the advantages of different injection methods, a numerical model that contains a fracture network was established with PFC software, and an alternating cyclic injection scheme with synergistic control of the cyclic frequency and injection rate was proposed. The comparison results indicated that the alternating cyclic injection method can effectively improve the fracturing effect in the HDR. The stimulation area of the alternating cyclic injection method is about 2.3 times and 2.7 times that of the low flow-low frequency and high flow-high frequency injection methods, respectively. The method presented here can be adopted to optimize the fracture growth regime and provide a scientific basis for EGS hydraulic fracturing design.

Feasibility study of energy storage using hydraulic fracturing in shale formations

Electric energy storage is currently the primary solution for addressing the intermittency and fluctuation of renewable energy sources. Traditional energy storage methods often struggle to simultaneously meet the demands of long storage duration, large capacity, high efficiency, and low cost. In this study, we present and verify the feasibility of a new energy storage method that utilizes hydraulic fracturing technology to store electrical energy in artificial fractures. Our study analyzed factors that impact energy storage capacity and efficiency, which provides a theoretical basis for optimizing hydraulic fracturing design for energy storage. This study also shows a promising direction for transforming depleted shale oil and gas wells into energy storage wells.

Visualization and characterization of experimental hydraulic fractures interacting with karst fracture-cavity distributions

Karst fracture-cavity carbonate reservoirs, in which natural cavities are connected by natural fractures to form cavity clusters in many circumstances, have become significant fields of oil and gas exploration and exploitation. Proppant fracturing is considered as the best method for exploiting carbonate reservoirs; however, previous studies primarily focused on the effects of individual types of geological formations, such as natural fractures or cavities, on fracture propagation. In this study, true-triaxial physical simulation experiments were systematically performed under four types of stress difference conditions after the accurate prefabrication of four types of different fracture-cavity distributions in artificial samples. Subsequently, the interaction mechanism between the hydraulic fractures and fracture-cavity structures was systematically analyzed in combination with the stress distribution, cross-sectional morphology of the main propagation path, and three-dimensional visualization of the overall fracture network. It was found that the propagation of hydraulic fractures near the cavity was inhibited by the stress concentration surrounding the cavity. In contrast, a natural fracture with a smaller approach angle (0° and 30°) around the cavity can alleviate the stress concentration and significantly facilitate the connection with the cavity. In addition, the hydraulic fracture crossed the natural fracture at the 45° approach angle and bypassed the cavity under higher stress difference conditions. A new stimulation effectiveness evaluation index was established based on the stimulated reservoir area (SRA), tortuosity of the hydraulic fractures (T), and connectivity index (CI) of the cavities. These findings provide new insights into the fracturing design of carbonate reservoirs.

Mechanical characteristics and reservoir stimulation mechanisms of the Gulong shale oil reservoirs, the northern Songliao Basin

Shale oil of the Qingshankou Formation of the Gulong Sag, the northern Songliao Basin, represents the first attempt at large-scale development of pure-shale-type shale oil in China. By integrating the multi-scale refined reservoir characterization with macro-micro-scale mechanical testing, it is clarified that the Gulong shale is characterized by high clay mineral content, high rock plasticity, highly-developed bedding, and prominent mechanical anisotropy. A three-dimensional (3D) fracture propagation model of hydraulic fracturing was built for the Gulong shale, which fully captures the hydraulic fracture distribution pattern affected by the high bedding density, in-situ stress, and fracturing treatment parameters. Our research showed that due to influences of bedding, hydraulic fracturing in the Gulong shale forms a complex fracture morphology featuring the main fracture with multiple perpendicular branches that have different lengths (like the outdoor directional TV antenna); however, the vertical propagation of fractures is inhibited, and the fracture height is commonly less than 10 m. The limited stimulated reservoir volume (SRV) is the main problem facing the fracturing stimulation of the Gulong shale oil. Bedding density has vital effects on fracture morphology, so case-specific fracturing designs shall be developed for shale intervals with different bedding development degrees. For reservoirs with well-developed bedding, it is suggested to properly increase the perforation cluster spacing and raise the volume and proportions of viscous fluids of the pad, so as to effectively promote vertical fracture propagation and improve reservoir stimulation performance. This study integrates multi-scale fine reservoir characterization and macro-micro-scale mechanical testing, as well as the construction and numerical simulation of hydraulic fracturing models for high-density layered shale reservoirs, providing a new approach and methodological framework for the fracturing research of high-density layered shale reservoirs.

Modeling Usage of Degradable Fluid-Loss Additive Revamps Fracturing Design

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 210633, “Multimaterial Multiphysics Modeling Coupled With Post-Fracturing Production-Flow Simulations: Revamping Hydraulic Fracturing Design Strategy,” by Abdul Muqtadir Khan, SPE, Vadim Isaev, and Ludmila Belyakova, SPE, Schlumberger. The paper has not been peer reviewed. _ With the aid of a multiphysics simulator, the authors recently presented a novel use of a degradable fluid-loss additive (DFLA) as a fracture geometry additive to reduce the pad volume while achieving the same geometry. In this complete paper, the authors extend advanced slurry flow modeling with production simulation to propose the optimal design strategy for fracturing, which may challenge current treatment-design conventions. A novel work flow was developed, with four coupled working blocks of laboratory, slurry flow modeling, production analysis, and machine learning. The new digital framework proposes solutions for the limitations of current methodology. Introduction Across different generations, multiple fluid additives have been introduced to target specific treatment objectives; one of these that has been available for years, but that has been underused, is fluid-loss additive (FLA). Theoretical and field bases have been presented for its use in the following applications: - Conventional prolific reservoirs to mitigate high fluid loss and create sufficient fracture geometry - Tight gas formations with high tectonic influence to mitigate poroelastic effects and fissure-dependent enhanced leakoff - Unconventional reservoirs to avoid repression during production - Openhole wells to control multiple fracture initiation - Multipad wells to avoid interwell communications and fracture hits - Fracturing treatments aimed at optimizing and reducing crosslinked pad volume Despite these benefits, the primary issue of using an FLA is its potential to damage fracture conductivity and the reservoir. Some developments of nondamaging FLA have been presented but are either operationally complex or difficult to use. This subject requires special attention to investigate damage and production loss through laboratory studies, numerical models, and machine-learning models and define a tailored strategy with DFLA. Digital Framework for Treatment Design The authors present an end-to-end work flow from chemistry development to an automated FLA-assisted fracturing design tailored for a specific reservoir and well. The framework is broadly split into three blocks: laboratory testing, fracture modeling, and production modeling. These blocks can be sensitized together with multiple case runs and a large digital database. This data set then can be subjected to regression and classification algorithms. With enough data built in the toolbox, a fully coupled data- and physics-based forward model can be created that can output the fracture design with DFLA type, concentration, and pad volume with inputs of reservoir properties and pore-throat descriptions. The tool infrastructure is built to allow the model to retrain and update with real field data addition. In the first block, multiple laboratory tests evaluate DFLA performance. The laboratory tests include static and dynamic leakoff tests to evaluate reduction in spurt loss and wall-cake building leakoff coefficient with varying concentrations of DFLA in the fracturing fluid. Additionally, core-flow tests are performed to understand the effect of DFLA on regained permeability and validate the postulation of its nondamaging nature.

3D Integrated Model-Driven Work Flow Developed for Shale Hydraulic Fracturing

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 212406, “3D Integrated G&G Model-Driven Mitigation Work Flow on Screenout, Frac Hits, and Casing Deformation in Ultradeep Shale Hydraulic Fracturing,” by Jianfa Wu and Bo Zeng, PetroChina, and Lipeng Wang, SLB, et al. The paper has not been peer reviewed. _ The Longmaxi shale gas play in China is unique because of multiple tectonic deformations in its geological history. While its hydraulic fracturing design has matured after a decade-long evolution, the success of every well cannot be ensured without considering heterogeneity. To address these challenges, a multidisciplinary team was formed to work on a pad; through the team’s efforts, designed proppant volume achieved zero casing deformations, fewer screenouts, and weaker fracture hits. The key to effective mitigation was continuous 3D geological and geomechanical (G&G) modeling through ongoing iterations with field data. Background The Longmaxi shale play in the Sichuan Basin is approximately 20 000 km2 and is buried between 2000 and 4500 m. This play has more than 10 trillion m3 of gas reserves and is made up of shallow and deep reservoirs. Currently, the operator has moved to the deeper Luzhou and Chongqing blocks buried at a depth greater than 3500 m. Nearly 200 horizontal wells per year are planned in the next 5 years. A fracture hit with tens of MPa increase was observed. Four casing failures were observed on 32 of the wells in this block, which made the unstimulated length more than 200 m and cost an extra $300,000 for interventions in each problematic well. While the risk of screenout, fracture hit, and casing deformation is common, risk levels vary for different reservoirs. No work flow is available that could be developed to identify and reduce these hazards. In this study, ultradeep shale gas at Pad X, buried almost 3900 m in the Luzhou Block, was selected to recognize and mitigate these risks (Fig. 1), where four wells were positioned 300 m apart. The lateral length of X-1 is roughly 1000 m, while the rest of the wells are roughly 1900 m in length. 3D G&G Modeling By combining seismic interpretation, seismic inversion, petrophysical analysis, and 1D geomechanical modeling while adhering to the Longmaxi-Wufeng Shale modeling technique used in neighboring blocks, the authors established a G&G model with dimensions of 40×40×0.5 m for the Luzhou Block. The pad model was refined to 8×8×0.5 m by using well logs to better characterize the variations in stage level. Natural Fractures. 3D surface seismic data was the only reliable source available to predict natural fractures in the shale and design the fracturing job, though the uncertainty was unavoidable. To display fault-/fracture-system characteristics, seismic attributes, including variance, ant tracking, and curvature were examined.

Numerical Simulation of Fracture Flow Interaction Based on Discrete Fracture Model

Hydraulic fracturing of horizontal wells is a common method for enhancing production in low-permeability and unconventional oil reservoirs. However, due to the interference between fractures, issues such as decreased production and water channeling often occur in hydraulic fracturing of horizontal wells. Therefore, studying how to mitigate the effects of fracture interference is of great significance for optimizing hydraulic fracturing design and improving oil and gas recovery rates. In this paper, an oil–water two-phase discrete fracture model was established, and the grid dissection was carried out by using the optimization method to obtain a triangular grid that can finely characterize the fracture in geometry. Then, typical discrete fracture models were designed, and the influences of the fracture permeability ratio, absolute fracture scale, oil–water viscosity ratio, and fracture length on the fracture flow interference were investigated separately. The degree of fracture interference was evaluated using the fracture fractional flow rate ratio, remaining oil saturation, and sweep efficiency. This study verified fracture interaction and identified that the threshold value of the fracture permeability ratio is 9 to classify the degree of interference. Sensitivity analysis shows that the absolute size of the fracture has a significant impact on fracture interference, while the impact of the oil–water viscosity ratio and fracture length on fracture interference is relatively small.

Fracture Toughness Testing of Brittle Laminated Geomaterials Using Hollow Double-Wing Slotted Specimens.

The fracture toughness of shale is a key parameter guiding hydraulic fracturing design and optimization. The hollow double-wing slotted (HDWS) specimen is a typical specimen configuration for measuring the mode I fracture toughness of rock. The calibration of the shape factor (f) is the basis for accurately obtaining the fracture toughness of rocks. In this study, the influences of crack length, hole size, and the anisotropy of elastic parameters on f for specimens with three typical bedding orientations-arrester (A), divider (D), and short-transverse (ST) orientations-are systematically investigated using finite element software. The numerical simulation results support the following findings. The mode I f increases monotonically with an increase in hole size. The influence of crack length on f varies depending on hole sizes. Under different bedding orientations, significant anisotropy in f was observed. In addition, the degree of anisotropy in Young's modulus has a major impact on f, which is related to the bedding orientation of the specimen. The apparent shear modulus ratio has relatively little influence on f. As the hole size and crack length increase, the influence of the anisotropy of elastic parameters on f increases. Based on numerical calculations, hydraulic fracturing experiments were conducted on HDWS specimens of Longmaxi shale with three bedding orientations, and the results showed that the peak pressure and fracture toughness of the samples in the ST direction were the lowest, while those in the A direction were the highest.

Development of fracture diagnostic methods for fluid distribution based on quantitative interpretation of distributed acoustic sensing and distributed temperature sensing

Multistage hydraulic fracturing design on horizontal wells has significantly evolved with larger fluid volume, more fracturing stages, and tighter perforation cluster spacing to efficiently stimulate unconventional reservoirs. From the published field observations, the recent fracturing design results in complex fracture networks or swarm of fractures. Fracture treatment evaluation is extremely challenging in such a case because of the large amount of variables in well completion and stimulation design. Combined measurements from different technologies can help in fracture diagnosis. Fluid distribution, either during fracture injection or during production, directly relates to the stimulation efficiency at the cluster level and at the stage level. Because it is unlikely in the real world to distribute the injected fluid uniformly among all the clusters, we need diagnostic techniques to generate the flow profile along a lateral. Fiber-optic measurements, such as distributed acoustic sensing (DAS) and distributed temperature sensing (DTS), are currently used to diagnose downhole flow conditions. This technology allows us to qualitatively confirm the fluid flow profile and other issues occurring downhole during fracturing such as leakage through plugs. For optimizing a fracturing design, we also need to understand how the design parameters are correlated with the stimulation efficiency. In this study, we combine two sets of models of DAS and DTS data interpretation for injected fluid volume distribution. The DAS is interpreted based on an empirical correlation between fluid flow rates and frequency band energy from the acoustic signals. The DTS is interpreted by performing temperature history match-based thermal energy conservation. Because of the completely different physics behind the interpretations, the confirmation of two interpretations provides confidence in fluid distribution.

Significant Influence of Sand Production on the Well's Drainage Area

The exploration of unconventional oil and gas reservoirs is a prominent global trend today. Achieving cost-effective and efficient hydrocarbon production from these reservoirs necessitates advanced technologies. One such technology that has been employed in the oil and gas industry for many decades is hydraulic fracturing. It is used to create highly conductive channels within formations characterized by extremely low permeability values. The successful implementation of hydraulic fracturing hinges on the development of an effective fracturing design. This design is crucial to achieving the anticipated production outcomes from unconventional reservoirs, including tight gas, shale gas, coal bed methane, and reservoirs with very low permeability. Key parameters for the success of hydraulic fracturing operations include the determination of the optimal fracturing rate, fracture height, and the selection of propping agents. These factors collectively contribute to the efficiency and productivity of hydraulic fracturing activities in unconventional reservoirs.

Research on Fracturing Technology for Low Production and Low Efficiency Casing Damaged Wells

With the further development of Daqing Oilfield, the proportion of casing damaged wells is increasing day by day, because the casing damage location is mostly located in the upper part of the reservoir, the conventional technology can not carry out targeted fracturing construction,the low-yield and low-efficiency wells which limits the efficient development of the oil field. In order to satisfy the needs of subdivision and large-scale fracturing construction of low-yield and low-efficiency wells with casing damage, this paper studied the fracturing design principles, determined the optimal design theory of different types of wells, and can make effective fracturing schemes for different reservoirs and well conditions. At the same time, a kind of small diameter segmented fracturing tools have been developed, which can meet the fracturing operation of wells with diameter above 104mm, so that the number of fracturing segments and the scale of reconstruction are greatly higher than those of conventional technology. 30 wells have been tested in the field, and the effect of increasing oil and injection is obvious. The results show that this process can effectively improve the production status of casing damage, low production and low efficiency wells and increase the productivity of single wells.

Influence of Horizontal Multi-Bedding on Hydraulic Fracture Propagation in Shale Reservoirs

Artificial fractures can easily occur and propagate in shale reservoir bedding. Their height restricts the volume of fracturing modification. A physical simulation of true triaxial hydraulic fracturing was used to analyze the characteristics of fracture morphology and the fracturing curve, as well as explore the influence of horizontal multi-bedding on the hydraulic fracture propagation of shale reservoirs. The results showed that a weaker bedding strength increased bedding fracture activation and reduced the fracture height. A higher bedding density increased the fracture complexity and reduced the main fracture height. A high injection flow can easily cause morphologically complex multi-bedding fractures. A higher injected fracturing-fluid viscosity increased the layer-penetration ability of the main hydraulic fracture when it expanded and reduced the opening degree of the bedding plane. This study provides technical support for the hydraulic fracturing design of shale reservoirs.

Numerical simulation of proppant transportation and placement in several complex structure fractures of a shale reservoir using a CFD approach

In the experimental simulation of proppant transportation in the complex fractures of shale reservoirs, the influence of many factors such as partial fracture parameters are often ignored, which cannot fully reflect the proppant transportation in the real situation. The Euler model and turbulence model were performed to numerically investigate proppant transportation and placement using the computational fluid dynamics (CFD) method, and was verified with experimental results. The formation process of proppant banks in branched, staggered, and different types of combined fractures was analyzed. The effects of the position, width, included angle of the secondary fracture, and fracture structure type on proppant transportation and placement were discussed. The simulations indicate that the proppant bank formation in the primary fracture is considered to occur in four stages and different from three stages in the secondary fractures. The proppant bank located at the node between the primary and the secondary fractures possesses good continuity, and the propagation of the proppant bank in the secondary fracture is closely related to the proppant bank state at the node in the primary fracture. The equilibrium time of the proppant bank in the secondary fracture and the primary fracture is related to the position of the secondary fracture. The total placement rate and settlement volume of proppant in the symmetrical oblique fracture is the highest for the same oblique angles, and the proppant bank morphology in the orthogonal fracture has good symmetry, improving the reliability of the fracturing design and the post-fracturing evaluation in shale reservoirs.

Investigation of Natural Weak Interface Properties and Their Impact on Fracture Propagation in Shale Reservoirs

Horizontal well multi-cluster fracturing technology is crucial for the economic development of fractured shale reservoirs. The abundance of natural fractures in shale reservoirs significantly influences the propagation path of hydraulic fractures and determines the formation of complex fracture networks. To investigate the impact of natural weak planes on the geometric parameters of fractures in shale reservoirs, we first conducted tests on the mechanical characteristics of core samples from outcropping shale in the Weiyuan area using the indoor three-point bending method and digital image correlation (DIC) technology, providing data validation for subsequent numerical models. Secondly, considering the interaction between hydraulic and natural weak planes in three-dimensional space, we established a three-dimensional numerical model for horizontal well fracturing to simulate the synchronous competition and expansion of fractures in multi-cluster fracturing. Based on this foundation, we analyzed the influence of formation parameters and engineering parameters on the formation patterns of complex fracture networks. The results indicate that the difference in in situ stress is a significant factor affecting the selection of fracture propagation paths. As the in situ stress difference increases, it becomes more challenging to open natural fractures, leading to a reduced probability of activation of natural weak interfaces. When the cohesive strength of natural fractures is smaller, they are more likely to open and capture hydraulic fractures, thereby increasing shear slip length and fracture network area. Each fracturing stage has an optimal perforation density combination, where a higher density of perforations leads to reduced perforation pressure drop and weaker ability to mitigate inter-cluster stress interference. To achieve a comprehensive and balanced development of multi-clusters, the inter-cluster stress interference can be alleviated by increasing the perforation pressure drop. For dense perforation clusters, higher injection rates and viscosity can be employed to ensure the uniform development of multiple perforation clusters. This study provides new insights into predicting the formation of complex fracture networks in shale reservoirs and offers valuable guidance for optimizing hydraulic fracturing designs.

The non-plane initiation and propagation mechanism of multiple hydraulic fractures in tight reservoirs considering stress shadow effects

Multi-cluster fracturing in horizontal wells is an important stimulation technology for unconventional tight reservoirs. The interference among multiple simultaneously growing hydraulic fractures results in a non-uniform fluid distribution into fractures and non-planar fracture geometries. In this paper, the competition mechanism between perforations under the stress shadow, the formation mechanism of complex non-plane fractures near the wellbore, and the initiation and propagation mechanism of multiple hydraulic fractures are investigated by using the 3D lattice method. Also, the effects of fracture geometry, fracture spacing and rock mechanics parameters on the stress interaction among fractures are analyzed by the dislocation theory. The results showed the complexity of fracture initiation near the wellbore and the low efficiency of the perforation initiation in the case of spiral perforation, due to a strong interaction between perforations. However, these initial micro-cracks will eventually coalesce to be a macroscopical fracture which perpendicular to the direction of minimum principal stress. The study indicated that stress interaction and fracture propagation is significantly affected by inclined well orientation. The hydraulic fracture is more likely to deflect and propagate non-uniformly with the increasing width of hydraulic fracture, the decreasing spacing between perforation clusters and the increasing rock modulus. When the horizontal principal stress difference is small, it is obvious to cause a large deflection angle and sometimes furcation of fractures. This study can provide a theoretical basis and technical guidance for hydraulic fracturing design in tight reservoirs.

Bone crack inspired pair of Griffith crack opened by forces at crack faces

The mathematical theory of elasticity helps in the study of physical quantities in the problem of structures. The structures face the problem of crack’s presence, which makes the problem difficult but not impossible to deal. Integral equations are useful in a variety of problems. Integral equations are used to solve problems like fracture mechanics or fracture design. The physical interest in the fracture design criterion is due to stress and crack opening displacement components. We have an accurate form of stress and displacement components for a pair of longitudinal crack propagations in the bone fracture of the human body at the interface of an isotropic and orthotropic half-space that are bounded together in the proposed study. The expression was calculated using the Fourier transform approach near the crack tips, but these components were evaluated using Fredholm integral equations and subsequently reduced to coupled Fredholm integral equations. We employ the Lowengrub and Sneddon problem in this research and reduce it to triple integral equations. The Srivastava and Lowengrub method reduces the solution of these equations to a coupled Fredholm integral equation. The problem is further reduced to a decoupled Fredholm integral equation of the second kind. Triple integral equations are solved, and the problem is reduced to a coupled Fredholm integral equation. The Fredholm integral equation is solved and reduced to a decoupled Fredholm integral equation of the second kind. Stress and crack opening displacement components drive physical interest in fracture design criteria. Finally, the stress and displacement components may be simply calculated in their exact form.

Test Shows Fracturing Can Also Create Underground Water Heating Systems

Fervo Energy has shown that fracturing can be used to build a geothermal heating system in hot, hard rock. During a 37-day test at its Project Red test site, the Houston company produced as much as 63 L/s (998 gal/min) of water heated to 336°F. By pumping water from an injection well through fractured hot rock to a producing well, it heated enough water to generate up to 3.5 MW of power, according to a company release. In a world where demand is commonly measured in gigawatts, that’s not much, but it is more than double the highest flow rate from tests going back decades. And unlike those earlier tests, the company has a clear path to heating higher volumes and lowering the cost. “I think this is just a big moment for both our company, but also the industry at large, to finally have this proof point where we can deliver commercial levels of permeability and flow rates for these wells,” said Jack Norbeck, co-founder and chief technical officer for Fervo. The idea of injecting water through hot rock has been around for decades as a way to create enhanced geothermal systems (EGS), but this is the first time someone has achieved this level of flow and is moving next to create a group of geothermal wells for commercial generation. Fervo has taken methods developed to extract oil and gas from ultratight rock and shown they can be used to do something quite different. “Overall, there’s nothing really surprising here—they used a pretty standard shale frac design and observed pretty similar performance from what you would see in a shale play. Or at least, what you’d expect if you used a shale well as a long-term water injector and circulated fluid over to a neighboring production well,” said Mark McClure, chief executive of ResFrac, a reservoir modeling and consulting firm, in a blog post. This fracturing-based option poses a challenge to EGS researchers who live in countries where completions using oil industry fracturing techniques are not an option. “The EGS community has conventionally been focused on ‘stimulating natural fractures,’ and this has led them to use fracture designs that would be considered suboptimal, from the perspective of oil and gas field experience,” McClure said. What Fervo has done is show that fracturing can be used to get past a barrier blocking EGS development using current fracturing technology. “The breakthrough is that someone actually had the guts and organization to go out and do it,” McClure said. Those at Fervo, though, have little time to celebrate the milestone as they focus on improving those methods to economically produce geothermal energy. “In successfully completing this project, we have demonstrated that no major technical barriers exist to deploying horizontal EGS in similar meta-sedimentary or igneous formations to temperatures of approximately 400°F,” according to a Fervo paper. That feat was recognized by a leader at the FORGE test site, which is also doing EGS research and development with substantial financial support from the US Department of Energy.

A Volume Fracturing Percolation Model for Tight Reservoir Vertical Wells

Based on the non-linear seepage characteristics of tight reservoirs and the reconstruction mode of vertical wells with actual volume fracturing, a seven-area percolation model for volume fracturing vertical wells in tight reservoirs is established. Laplace transform and Pedrosa transform are applied to obtain analytical solutions of bottom hole pressure and vertical well production under a constant production regime. After verifying the correctness of the model, the influence of the fracture network parameters on the pressure and production is studied. The research results indicate that as the permeability modulus increases, the production of volume fracturing vertical wells decreases. The penetration ratio of the main crack and the half-length of the main crack have a small impact on production, while the diversion capacity of the main crack has a significant impact on the initial production, but it is ultimately limited by the effective volume of the transformation. Under constant pressure conditions, the greater the width and permeability of the ESRV region, the higher the vertical well production rate is. The smaller the aspect ratio of the ESRV region, the higher the mid-term yield and the faster the yield decrease. The research results show guiding significance for the design of vertical well volume fracturing in tight reservoirs.