Simulation Of Hydraulic Fracturing Research Articles

Learnings Applied to Reservoir Simulation of Unconventional Plays

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 199164, “Applied Learnings in Reservoir Simulation of Unconventional Plays,” by Raphael Altman, SPE, Roberto Tineo, SPE, and Anup Viswanathan, SPE, Schlumberger, et al., prepared for the 2020 SPE Latin American and Caribbean Petroleum Engineering Conference, Bogota, Colombia, 17-19 March. The paper has not been peer reviewed. Reservoir simulation is valuable in understanding dynamics of unconventional reservoirs. Applications include estimating long-term production behavior, enhancing well-spacing and pad-modeling efficiency, optimizing completion and stimulation of horizontal wells, and understanding production drivers that cause differences in productivity between wells. In the complete paper, the authors revisit fundamental concepts of reservoir simulation in unconventional reservoirs and summarize several examples that form part of an archive of lessons learned. Reservoir Simulation Applications in Unconventionals Reservoir simulation plays an important role in many stages of unconventional reservoir field development. In the initial pilot phase, a calibrated reservoir simulation model can provide an indication of estimated ultimate recovery (EUR), which is advantageous given few wells with short production time. EUR evaluation with incorporated uncertainties is a key variable in asset evaluation and investment decisions. During the ramp and development phases, reservoir simulation aids completion optimization by providing a link between completion parameters, such as cluster spacing and stimulation pumping parameters, and a well’s production. Extending this idea further, the integrated nature of reservoir simulation enables identification of production drivers and understanding of why wells are producing differently. During the mature stages of unconventional reservoir development, well spacing and hydraulic fracture and pressure interference, together with refracturing, require advanced modeling techniques that can include a combination of hydraulic fracture simulation, 3D stress simulations, and advanced reservoir simulation. Reservoir Simulation Modeling in Unconventionals Unconventional reservoirs are heterogeneous across multiple scales and exhibit variations in production performance across wells. The production variation is influenced by a large variation in production drivers that simultaneously affect the production. Examples of these drivers include reservoir properties such as hydrocarbon-filled porosity, moveable hydrocarbons, matrix permeability, relative permeability and pressure/volume/temperature, completion properties such as stress-state and natural fractures, and stimulation (pumping) parameters. Reservoir simulation constitutes one of the best tools to understand the dominant production drivers because of the multidisciplinary data required to build simulation models for unconventional reservoirs. Because of the orders of magnitude of difference in matrix permeability between conventional and unconventional reservoirs, pressure gradients from the sandface to the formation (pressure drawdowns) are larger in unconventional reservoirs and drainage radii are more likely to be smaller. Therefore, in the case of shale reservoirs, single-well models usually suffice except for the case of multiwell pads. Very fine grid cells (on the order of inches to a few feet) are used close to, and immediately surrounding, the perforation clusters, whereas in conventional reservoirs, coarser grid cells are used, especially in full-field models, even with local grid refinements.

Fracture Toughness and Surface Energy Density of Kerogen by Molecular Dynamics Simulations in Tensile Failure

Fracture toughness and surface energy density are critical parameters in the simulation of hydraulic fracturing in shale formations. In this study, a microscopic insight into the mechanisms of tensile failure in kerogen is advanced by molecular dynamics simulations for the first time. The elastic properties, critical stress, surface energy density, and fracture toughness of kerogen are analyzed systematically. Our work reveals that kerogen is potentially a weak component in shale, which may serve as a region of fracture initiation and preferential fracture propagation path. The critical energy release rate Gc is higher than the doubled surface energy density γs (Gc ≥ 2γs), which indicates that there may be pronounced plastic deformation in kerogen in the tensile failure. This work sets the stage for the determination of various shale mechanical properties and surface energy density to examine fracturing effectiveness in shale media from the molecular scale.

Coupled Hydraulic Fracture and Proppant Transport Simulation

This paper focuses on the study of proppant transport mechanisms in fractures during frac-packing operation. A multi-module, numerical proppant, reservoir and geomechanics simulator has been developed, which improves the current numerical modeling techniques for proppant transport. The modules are linked together and tailored to capture the processes and mechanisms that are significant in frac-pack operations. The proposed approach takes advantage of a robust and sophisticated numerical smeared fracture simulator and incorporates an in-house proppant transport module to calculate propped fracture dimensions and concentration distribution. In the development of software capability, the propped fracture geometry and proppant concentration, which are the output of the proppant module, are imported to the hydraulic fracture simulator through mobility modification. Complex issues of proppant transport in fractures that are addressed in the literature and captured by the current model are: hindered settling velocity (terminal velocity of proppant in the injection fluid), the effect of fracture walls, proppant concentration and inertia on settling (due to extra drag forces applied on particles, compared to single-particle motion in Stokes regime in unbounded medium), possible propped fracture porosity and also mobility change due to the presence of proppant, and fracture closure or extension during proppant injection. A sensitivity analysis is conducted using realistic parameters to provide guidelines that allow more accurate predictions of the proppant concentration and fluid flow. The main objective of this study is to link a numerical hydraulic fracture model to a proppant transport model to study the fracturing response and proppant distribution and to investigate the effect of proppant injection on fracture propagation and fracture dimensions.

Optimization Scheme of Hydraulic Fracturing Simulation Experiments using Mixed-level Uniform Design Method Based on the PKN model

This paper aims at revealing the hydraulic fracturing effect of hydrodynamic influencing factors of fracturing fluid by laboratory experiments. The experimental design for huge number of hydrodynamic influencing factors with many levels, is oftentimes incorporated with the conventional methods, i.e. Based on the PKN model, injection rate, viscosity, and density (of the fracturing fluid) and their parameter values (levels) were considered for the construction of an optimal mixed-level design table U* 12(43×6), which constructed the optimization scheme. The experiments results were subjected to multiple regression analysis to establish optimal fitting formulas for the relationship of single factor or multi-factor with rock fracturing value. Compared with other experimental designs, experimental number of U* 12(43×6) yielded only half the number of experiments in the orthogonal design L24(43×6) and presented better distribution uniformity of experimental points than Ui2(43×6). This paper provides a fast and effective experimental scheme for the effect analysis, as well as a substantially accurate method for in-situ stress measurement.

Coupling of fracture model with reservoir simulation to simulate shale gas production with complex fractures and nanopores

A novel integrated approach that couples hydraulic fracturing and production simulation was proposed for Marcellus shale gas reservoir. A discrete element method based hydraulic fracturing simulator was utilized for multi-stage hydraulic fracturing simulation. Moving tip clustering (MTC) and linear regression clustering (LRC) algorithms were proposed to characterize the complex fracture geometry. Embedded discrete fracture model method was used to transfer the complex geometry of multiple fractures into a third-party reservoir simulator for history matching of shale gas production and production forecasting. It was observed that the LRC algorithm can generate smooth fracture geometries and detect overall fracture paths reasonably. The MTC algorithm, however, can capture more branches of microcracks and recover zig-zag fracture paths with larger apparent fracture lengths. The zig-zag fractures contribute to larger stimulated reservoir volume and result in an extra shale gas production of 5.2% compared to the smooth fractures. The gas slippage effect increases apparent matrix permeability to 4.6 times of intrinsic permeability. Reduction of fracture conductivity and matrix permeability due to decreasing bottomhole pressure leads to 9.25% and 9.28% decrease of gas production respectively in 30 years and should be taken into account for long-term production prediction.

Numerical investigation of complex fracture network creation by cyclic pumping

Horizontal well with multistage fracturing is an effective method to improve the development of shale gas reservoirs. However, it is challenging to create fracture network in the formation with high horizontal stress difference. On the basis of damage mechanics, a 2D fracture propagation model coupled seepage-stress-damage was established to study the influence of cyclic pumping on fracture network. In this model, the continuum variables were used to describe the cracks and joints that provide another means of modeling a joint rock mass. Subsequently, the Weibull distribution function was introduced to describe the heterogeneity of rock mechanics. Then, the maximum tensile stress criterion and the Mohr-Coulomb criterion were used as the threshold of the constitutive relation of the damage. Furthermore, when the unit’s stress state attain maximum tensile stress criterion or the Mohr-Coulomb criterion, then tensile or shear failure of the unit occurred. In current study, the finite element simulation of hydraulic fracturing was carried out with the size of 200×60 m2. The results showed that the cyclic pumping was an effective means to create complex fracture network, and the horizontal stress difference, the flow rate, and the frequency of cyclic pumping govern the fracture network generation and fracture morphology. When the horizontal stress difference was below 12 MPa, the total fracture length increased by 37.5% at least. Meanwhile, the total length of the fracture network increased with the increasing of flow rate. Compared of fracture length under four different pumping rate, it found that the total fracture length increased by 12.1% at least. The fracture network complexity increased with increasing number of loading cycles, and the cycle pumping with variable frequency was more effective to create fracture network. In the simulation, when the frequency of the cyclic pumping increased from 7 cycles to 10 cycles, the total fracture length increased by 10.2%. When the variable frequency applied in the model, the total fracture length increased by 14.8%. Based on the simulation, it indicated that the cyclic pumping was an effective way to create the complex fracture network, it also provided a means to create the complex fracture network in the formation with high horizontal stress difference.

Multi-Size Proppant Pumping Schedule of Hydraulic Fracturing: Application to a MP-PIC Model of Unconventional Reservoir for Enhanced Gas Production

Slickwater hydraulic fracturing is becoming a prevalent approach to economically recovering shale hydrocarbon. It is very important to understand the proppant’s transport behavior during slickwater hydraulic fracturing treatment for effective creation of a desired propped fracture geometry. The currently available models are either oversimplified or have been performed at limited length scales to avoid high computational requirements. Another limitation is that the currently available hydraulic fracturing simulators are developed using only single-sized proppant particles. Motivated by this, in this work, a computationally efficient, three-dimensional, multiphase particle-in-cell (MP-PIC) model was employed to simulate the multi-size proppant transport in a field-scale geometry using the Eulerian–Lagrangian framework. Instead of tracking each particle, groups of particles (called parcels) are tracked, which allows one to simulate the proppant transport in field-scale geometries at an affordable computational cost. Then, we found from our sensitivity study that pumping schedules significantly affect propped fracture surface area and average fracture conductivity, thereby influencing shale gas production. Motivated by these results, we propose an optimization framework using the MP-PIC model to design the multi-size proppant pumping schedule that maximizes shale gas production from unconventional reservoirs for given fracturing resources.

A Novel Approach for Direct Numerical Simulation of Hydraulic Fracture Problems

Hydraulic fracturing is a non-linear and multi-physics problem involving the break up of a solid medium due to the action of hydrodynamic forces. Fluid and solid mechanics are involved at the same time together with fracture mechanics. Despite its relevance in many scientific and engineering fields, the theoretical and numerical description of hydraulic fracturing remains a challenging matter and the capabilities of existing models for applications are still limited. In this context, we propose a novel numerical approach to the Direct Numerical Simulation of hydraulic fracturing based on the Navier–Stokes equations coupled with peridynamic theory of solid mechanics through a multi-direct Immersed Boundary Method. The main advantage of this approach consists in the reliable crack-detection and tracking capabilities of peridynamics together with the capability of the Immersed Boundary Method of managing no-slip and no-penetration boundary conditions on complex and time-evolving interfaces. A massive-parallel solver based on this model has been implemented. We present a detailed theoretical description of the proposed methodology as well as the results of an extensive validation campaign for the new solver. Different benchmarking tests are provided together with the qualitative results of a simulation reproducing the fracture of a solid structure in a laminar, unsteady flow.

Effect of rock brittleness on propagation of hydraulic fractures in shale reservoirs with bedding‐planes

AbstractHydraulic fracturing forms complex hydraulic fracture networks (HFNs) in shale reservoirs and significantly improves the permeability of shale reservoirs. Although rock brittleness is a major factor in determining whether a shale reservoir can be fractured, the relationship between HFNs and rock brittleness remains unclear. To investigate this relationship in a shale reservoir with bedding planes, this paper presents a series of hydraulic fracturing simulations based on a hydromechanically coupled discrete element model. In addition, we analyzed the sensitivity of the difference in rock brittleness to bedding‐plane angle and density. The parameters used in the model were verified by comparing the simulated results with experimental results and a theoretical equation. The results showed that breakdown pressure and injection pressure increased with increasing rock brittleness. The tensile hydraulic fracture of a shale reservoir (THFSR) was always the most abundant type of hydraulic fracture (HF)—almost 2.5 times the sum of the other three types of HFs. The distribution of areas with higher fluid pressure deviated from the direction of the maximum principal stress when the angle between the bedding plane and maximum principal stress directions was large. Upon increasing this bedding‐plane angle, the breakdown pressure and rock brittleness index first decreased and then increased. However, regardless of bedding angle, the relative proportions of the various types of HFs remained essentially constant, and the seepage area expanded in the direction of the maximum principal stress. Increased bedding‐plane density resulted in a gradual increase in the total number of HFs, with significantly fewer of the THFSR type, and the large seepage areas connected with each other. This study thus provides useful information for preparing strategies for hydraulic fracturing.

Shale structure implication in hydraulic fracturing production results: Case study in low resistivity low quality reservoir, offshore North West Java area

Low-resistivity & low-quality reservoir has been successfully developed in ONWJ area by using hydraulic fracturing stimulation method to optimize production gain due to low-permeability reservoir property. The purpose of this research is to understand implication of shale structure for increasing gain production after hydraulic fracturing stimulation. Implementation of hydraulic fracturing was first completed at BerylE-1 and the well could produce 455 BOPD at 560 psi in reservoir 33 and 35. This reservoir was found in Upper Cibulakan Formation that consists of various lithology’s such as very fine-grained sandstone, shale, siltstone & thin tight carbonate that deposited in shallow marine neritic to littoral environment. Production anomaly occurs after hydraulic fracturing stimulation. Some of well in this reservoir show good incremental production, but in the other well there was no significantly incremental production in this reservoir. There were three types of shale structure classification based on effective porosity distribution: laminated shale, structural shale and dispersed shale. Shale structure for each well has been defined based on Thomas Stieber plot and calibrated using petrographic analysis from 8 sample depth point. Based on this method, reservoir 33 is dominated by structural shale while reservoir 35 is dominated by laminar shale. Production data and shale type from each well has been compared and it shows that hydraulic fracturing simulation will increase effective porosity and will also increase effective permeability value. In BerylD-1 well hydraulic fracturing only completed in reservoir 35 and produced 340 BOPD with initial water cut 0 %. Laminar shale that dominates in reservoir 35 has high factor to increasing production gain after hydraulic fracturing was applied. Release of clay that caused by hydraulic fracturing will increase effective porosity and permeability.

Strongly coupled XFEM formulation for non-planar three-dimensional simulation of hydraulic fracturing with emphasis on concrete dams

This paper presents a novel and robust three-dimensional plain concrete cracking model applicable to the study of structural stability of large structures, such as dams, while considering the presence of pressurized water in propagating cracks. When leaving the elastic range, there is a transition from a continuum approach to a XFEM approach. This mechanical model is coupled with a poro-damage model where the permeability is increased as micro-cracks coalesce into macro-cracks. The crack opening computation during continuum damage is based on a local XFEM formulation without the need for a reference length in a strongly coupled hydro-mechanical formulation to update the uplift pressures. The 3D crack path computation is adapted from an analogy to the heat conduction problem to draw the envelope of the discontinuities’ tangent vector field. Six benchmark problems available from the literature, including a 96m-high arch dam, are considered and indicate the very good performance of the proposed model as well as its applicability to real industrial structures.

Phase-field simulation of hydraulic fracturing with a revised fluid model and hybrid solver

With an intrinsic advantage in describing complex fracture networks, the phase field method has demonstrated promising potential for the simulation of hydraulic fracturing processes in recent literatures. We critically examine the existing phase-field hydraulic fracturing models, and propose a hybrid solution scheme with a revised fluid model. Specifically, the formation deformation and phase field are solved using the finite element method (FEM), while the fluid flows are solved using the finite volume method (FVM). The proposed hybrid scheme is validated with the analytical solution for the toughness-dominated fracture propagation and is tested on the complex hydraulic fracturing process in a naturally fractured formation. Demonstrated by numerical examples, the proposed hybrid phase-field framework has several advantages: (1) it captures the effect of fluid pressure inside the fracture and reservoir more accurately than existing models; (2) it provides a sharper capture of formation fractures; (3) it avoids the nonphysical oscillation of fluid pressure when using a pure FEM solver; and (4) it has a superior performance in mesh and time step convergence.

Fully hydromechanical coupled hydraulic fracture simulation considering state transition of natural fracture

The natural fracture in the reservoir presents different properties in the inactivated and the activated state. To model the hydromechanical behaviors of the natural fractures in the two states, the element partition method(EPM) is employed. The EPM is a fracture simulation method, which allows a crack run across an element without introducing any extra degrees of freedom. For the element containing an inactivated fracture segment, it is treated as a potential partitioned element, but its permeability is related to the normal stress to the embedded fracture. A Mohr-Coulomb type of activation criterion is developed for the inactivated fracture. Once the fracture is activated, this potential element is transformed into a partitioned element. The constitutive relation with consideration of shear dilation and the fully hydromechanical coupled equation of a partitioned element are derived. Based on this method, the activation process of a fracture and its propagation are simulated. The simulation results suggest that the present method can capture the full hydromechanical properties of a natural fracture from its inactivated to activated state. Besides the natural fracture, the randomized cavities are another type of discontinuities in some reservoir. The effect of the cavity on hydraulic fracture(HF) is also considered. It is suggested that the cavity strongly repels the HF due to the surrounding stress concentration, but whether the HF can connect with the cavity depends. If there are some cracks adjunct to the cavity, the HF may connect with the cavity through these adjunct cracks. The simulation results suggest that the present method is a simple and efficient simulation method for the HF in the complex reservoir. It can comprehensively consider the behaviors of the natural fracture and cavity.

Numerical study of the effect of natural fractures on shale hydraulic fracturing based on the continuum approach

Because of the complexity of shale reservoirs and multiple physical coupling processes, numerical implementation remains a challenge in engineering applications. Unlike conventional reservoirs, shale reservoirs always contain two main discontinuities: bedding interface and natural fractures. The existence of these discontinuities is the key reason a fracture network is formed. Therefore, the numerical model should contain both bedding interface and natural fractures. In this paper, the fracturing propagation process is described based on continuum theory. In contrast to other research, an anisotropic strength criterion is adopted to consider the anisotropic properties of shale, including the failure of both shale matrix and discontinuities. The criterion is described by the Mohr-Coulomb model combined with tensile failure. When fractures are generated in the shale rock mass, the stiffness and permeability of the fractured rock are homogenized in an element, and volume fracturing is represented by the deformation of three orthogonal fractures in the rock element. Simultaneously, the anisotropic permeability is also enhanced. Hence, based on this continuum approach and finite element method, a three-dimensional model for shale hydraulic fracturing simulation is presented. This model fully considers the direct coupling of fluid flow and rock deformation during hydraulic fracturing. To verify the anisotropic strength criterion, a shale compression test is conducted. Through a comparison of the numerical and experimental results, the applied criterion can describe the shale compressive strength anisotropy. In addition, the KGD analytical model is also adopted to verify the performance of the developed model for hydraulic fracturing. Finally, several cases of shale hydraulic fracturing are simulated, and the results show the geometry of the fracture region under different conditions. Furthermore, the impacts of three factors on hydraulic fracturing geometry are considered, including natural fractures, spacing of perforations and differential in situ stress. The influence of these factors on the complexity and scale of the fracturing region is also discussed.

Simulation of Hydraulic Fracturing Using Different Mesh Types Based on Zero Thickness Cohesive Element

Hydraulic fracturing is a significant technique in petroleum engineering to enhance the production of shale gas or shale oil reservoir. The process of hydraulic fracturing is extremely complicated, referring to the deformation of solid formation, fluid flowing in the crack channel, and coupling the solid with fluid. Simulation of hydraulic fracturing and understanding the course of the mechanism is still a challenging task. In this study, two hydraulic fracturing models, including the Khristianovic–Geertsma–de Klerk (KGD) problem and the hydraulic fracture (HF) intersection with the natural fracture (NF), based on the zero thickness pore pressure cohesive zone (PPCZ) element with contact friction is established. The element can be embedded into the edges of other elements to simulate the fracture initiation and propagation. However, the mesh type of the elements near the PPCZ element has influences on the accuracy and propagation profile. Three common types of mesh, triangle mesh, quadrangle mesh, and deformed quadrangle mesh, are all investigated in this paper. In addition, the infinite boundary condition (IBC) is also discussed in these models. Simulation indicates that the results of pore pressure for zero toughness regime simulated by the triangle mesh are much lower than any others at the early injection time. Secondly, the problem of hydraulic fracturing should be better used with the infinite boundary element (IBE). Moreover, suggestions for crack intersection on the proper mesh type are also given. The conclusions included in this article can be beneficial to research further naturally fractured reservoirs.

Numerical performances of invariable and moving boundary methods during fluid penetration into anisotropic porous media

Fluid penetration has been observed to have significant impacts on the distributions of pore pressure and effective stress in hydraulic fracturing experiments. This fluid penetration is usually simulated by the invariable boundary method which neglects the impacts of fluid front motion and introduces significant errors in the simulation of hydraulic fracturing. This study proposed a moving boundary method to describe the fluid front motion and established an anisotropic fluid-solid-motion coupling model for fluid penetration into anisotropic porous media. The performances of invariable and moving boundary methods were numerically evaluated for the impacts of fluid front motion on the field variables (including pore pressure, principal stresses and permeability) and breakdown pressure. Simulation results showed that the penetration depth and pore pressure distribution obtained from the moving boundary method fit experimental observations better than those obtained from the invariable boundary method. Anisotropic fluid front motion forms a changing elliptical seepage zone. The pore pressure, principal stresses, hoop and radial permeability have significant changes within seepage zone. The fluid front is the dividing line between seepage zone and initial state zone. The moving boundary method can accurately simulate the hydraulic fracturing.

Lattice simulation of hydraulic fracture containment in the North Perth Basin

The results of numerical simulations of hydraulic fracturing based on the concept of lattice, a grain based method, are presented. Five cases of numerical simulations were conducted to analyze the effects of changing rock properties and in-situ stresses on hydraulic fracture propagation and its containment. The study was done based on the data from one of the shale gas wells in the North Perth Basin (NPB) in Western Australia and the hydraulic fracturing lab experimental data on a 50 mm cubical sample. The hydraulic fracturing initiates and propagates within Carynginia Formation surrounded by the Irwin River Coal Measures (IRCM) Formation from the top and Kockatea Formation at the base. The lab experiments were upscaled to both intermediate and field scales to simulate fracture propagation in the viscosity dominated regime. Penetration parameters, including the depth and area of the fracture crossing the interface, were proposed to characterize fracture containment capacity. It was observed that the fracture is contained by both IRCM and Kockatea Formations due to the large contrast between the minimum horizontal stresses in these layers and that of the Carynginia formation. However, as quantified by the penetration parameters, the fracture propagates more easily into the IRCM Formation with higher brittleness than Carynginia Formation. Kockatea Formation with lower brittleness than that of Carynginia Formation inhibits vertical migration of the fracture, i.e. results in more visible fracture containment. The results suggest that decrease in rock brittleness inhibits fracture propagation and lower minimum horizontal stress contrast leads to fracture containment.

Effects of nonuniform initial stress state on apparent fracture toughness

We analyze the nonuniform stress state in the vicinity of the fracture tip and its impact on apparent fracture toughness. It is shown that prescribing the boundary conditions at the deformed fracture faces allows one to take into account the effect of nonuniform tectonic stresses acting in the plane of the fracture. We conclude that the fracture may take an ellipsoidal form (aspect ratio departs from unity) as a result of interactions with anisotropic distribution of initial stresses, which leads to nonuniform growth in longitudinal and vertical directions. An expression for the effective stress intensity coefficient (fracture toughness) is obtained as a function of the nonuniform initial stress state. A simplified asymptotic approximation to the solution for the effective apparent fracture toughness is given, which may be further implemented into the near-tip asymptotics used in the form of a tip element in the numerical implementation of a Planar3D approach to hydraulic fracture simulation.

Mathematical modeling heat and mass transfer in a vertical hydraulic fracture crack during inflation and cleaning*

When designing hydraulic fracturing for high-temperature formations, it is important to know the temperature change in the fracture during the injection of fracturing fluid. The temperature profile in the hydraulic fracture is necessary to calculate the optimal composition of the fracturing fluid, which necessarily includes a crosslinker (crosslinker) and a breaker (breaker), the concentration of which is calculated by the temperature at the end of the crack. Currently, this concentration is calculated based on the maximum temperature of the formation, which can lead to a decrease in the efficiency of hydraulic fracturing, since a breaker will not completely destroy the crosslinked gel. Therefore, when a well is brought into operation after the stimulation, proppant removal may occur, reducing the effectiveness of stimulation to zero. In this regard, the optimization of the decision-making process in the design of hydraulic fracturing in terrigenous and carbonate reservoirs by calculating the optimal parameters of process fluids based on predicting heat and mass transfer processes occurring during processing is a very urgent task. A tool has been developed to improve the design efficiency of hydraulic fracturing based on mathematical modeling of temperature fields in a hydraulic fracture during its development and during the period of technological sludge. A mathematical model that describes the temperature dynamics in a hydraulic fracture taking into account fluid leakage into the formation represents the evolutionary equation of convective heat transfer with a source, which is defined as the density of the heat flux from the formation. To check the adequacy of the model of temperature dynamics in a hydraulic fracture, a model of temperature recovery in a fracture is presented with the subsequent adaptation of simulation results to actual data. Developed mathematical models can be used in hydraulic fracturing simulators.

Numerical investigation of single and multiple fractures propagation in naturally fractured reservoirs

The properties of natural fractures (NFs), including fracture size, aperture width, and mechanical properties, etc., cannot be neglected when developing a model of hydraulic fracturing. Without considering the geological characterisation of NF properties, hydraulic fracture simulations will give much less accurate prediction of complex fracture propagation pattern. In this research, a novel two-dimensional finite-discrete element method (FDEM) model has been developed to describe complex fracture propagation in unconventional formations. We developed a natural fracture network builder by considering natural fractures geological observations. Simulations have been conducted to investigate single fracture and complex fracture network propagation in naturally fractured reservoirs. In hydraulic fracturing treatments, opening of natural fractures is determined by geological properties of NFs. For multiple fractures propagation in naturally fractured reservoirs, stress shadowing effect plays a key role in fracture network evolution. This work provides a framework for more realistic prediction of complex fracture geometry in naturally fractured formations. [Received: December 11, 2017; Accepted: July 6, 2018]