Simulation Of Hydraulic Fracturing Research Articles

An implicit level set algorithm for hydraulic fracturing with a stress-layer asymptote

The capability to simulate a hydraulic fracturing process is an essential tool that can be used to optimize treatment design and increase the efficiency of field operations. In most practical cases, hydraulic fractures propagate in a multi-layered rock formation. As a result, there is a need to incorporate the effect of such heterogeneities in fracturing models to achieve an accurate prediction. To capture the layered structure of rocks, a hydraulic fracture simulator typically requires a fine mesh, which leads to a drastic reduction in computational performance. An alternative is to use more sophisticated models that are capable of providing reasonably accurate predictions even on a relatively coarse mesh. In the case of fracture growth modeling, the pivotal component of the simulation is a fracture front tracking algorithm that accounts for the layered structure of the formation. Consequently, this paper aims to extend the established Implicit Level Set Algorithm (ILSA) to account for the effect of multiple stress layers within the tip asymptote. The enhanced front tracking algorithm involves the stress-corrected asymptote that incorporates the influence of stress layers within the near-tip region. To further increase the validity region of the stress-corrected asymptote, the stress relaxation factor is introduced, and its accuracy is examined. The numerical algorithm is validated against the reference semi-analytical solutions as well as experimental observations. In addition, we investigate the sensitivity of the fracture geometry to mesh size to demonstrate that the front tracking algorithm based on the stress-corrected asymptote retains its accuracy on a coarse mesh.

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.

Using fracture-based continuum modeling of coupled geomechanical-hydrological processes for numerical simulation of hydraulic fracturing

This paper describes numerical simulation of hydraulic fracturing using fracture-based continuum modeling (FBCM) of coupled geomechanical-hydrological processes to evaluate a technique for high-density fracturing and fracture caging. The simulations are innovative because of modeling discrete fractures explicitly in continuum analysis. A key advantage of FBCM is that fracture initiation and propagation are modeled explicitly without changing the domain grid (i.e. no re-meshing). Further, multiple realizations of a preexisting fracture distribution can be analyzed using the same domain grid. The simulated hydraulic fracturing technique consists of pressurizing multiple wells simultaneously: initially without permeating fluids into the rock, to seed fractures uniformly and at high density in the wall rock of the wells; followed by fluid injection to propagate the seeded fracture density hydraulically. FBCM combines the ease of continuum modeling with the potential accuracy of modeling discrete fractures and fracturing explicitly. Fractures are modeled as piecewise planar based on intersections with domain elements; fracture geometry stored as continuum properties is used to calculate parameters needed to model individual fractures; and rock behavior is modeled through tensorial aggregation of the behavior of discrete fractures and unfractured rock. Simulations are presented for previously unfractured rock and for rock with preexisting fractures of horizontal, shallow-dipping, steeply dipping, or vertical orientation. Simulations of a single-well model are used to determine the pattern and spacing for a multiple-well design. The results illustrate high-density fracturing and fracture caging through simultaneous fluid injection in multiple wells: for previously unfractured rock or rock with preexisting shallow-dipping or horizontal fractures, and in situ vertical compressive stress greater than horizontal. If preexisting fractures are steeply dipping or vertical, and considering the same in situ stress condition, well pressurization without fluid permeation appears to be the only practical way to induce new fractures and contain fracturing within the target domain.

Study of Permian Basin Provides Insight Into Parent-/Child-Well Interactions

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 211899, “Results From a Collaborative Parent/Child Industry Study: Permian Basin,” by Mark McClure, SPE, ResFrac; Magdalene Albrecht, SM Energy; and Carl Bernet, Ovintiv, et al. The paper has not been peer reviewed. _ The complete paper summarizes results from a collaborative industry study involving seven operators and 10 pad-scale data sets across four different shale plays. The paper specifically focuses on a subset of the data sets from the Midland and Delaware Basins. The project had three main objectives: compare and contrast observations between data sets and basins, develop general insights into parent- and child-well interactions, and provide customized economic optimization recommendations for each individual operator and data set. The simulations reveal that economic performance can be optimized with customized selection of well spacing, job size, and landing depth based on each company’s objectives and price deck. Methods Modeling Approach. The simulations were performed with a fully integrated hydraulic fracturing, wellbore, geomechanics, and reservoir simulator. The entire life cycle of the wells is captured in a single continuous simulation. The fractures are meshed as true cracks, with apertures on the order of microns to millimeters. Constitutive relations are used to capture transitions from being mechanically open to mechanically closed and vice versa. The simulations are fully 3D, and the equations are solved with a fully coupled scheme. For efficiency, the simulations include only one or a few stages along the wells. Fracture geometry is assumed to be planar, with no more than one dominant hydraulic fracture strand propagating per cluster. The modeling approach is based on the industry’s emerging recognition that hydraulic fractures in shale are planar at large scale, while being rough and complex at small scale. In the simulator, constitutive relations are used to account for the effect of small-scale complexity on processes such as proppant transport, fluid leakoff, and fracture propagation. Modeling Work Flow. For each data set, the modeling process consisted of the following steps: 1. Gather and organize data. 2. Create an initial model based on this data. 3. Create a list of key observations from the data set that constitute the objectives for the history-matching process. 4. Present the initial model and the list of key observations to stakeholders to obtain feedback and check communication. 5. Vary simulation input parameters to match the key observations while frequently communicating with stakeholders. 6. After finalizing the history match, perform a set of sensitivity analysis simulations, varying parameters such as well spacing and parent-well age. 7. Set up an economics model and perform a quantitative optimization of net present value (NPV)/section or discounted return on investment [DROI; defined as time-discounted revenue minus time-discounted operating expense divided by time-discounted capital expenditure (CAPEX)]. The steps of this work flow are detailed in the complete paper.

A phase‐field model for hydraulic fracture nucleation and propagation in porous media

AbstractMany geo‐engineering applications, for example, enhanced geothermal systems, rely on hydraulic fracturing to enhance the permeability of natural formations and allow for sufficient fluid circulation. Over the past few decades, the phase‐field method has grown in popularity as a valid approach to modeling hydraulic fracturing because of the ease of handling complex fracture propagation geometries. However, existing phase‐field methods cannot appropriately capture nucleation of hydraulic fractures because their formulations are solely energy‐based and do not explicitly take into account the strength of the material. Thus, in this work, we propose a novel phase‐field formulation for hydraulic fracturing with the main goal of modeling fracture nucleation in porous media, for example, rocks. Built on the variational formulation of previous phase‐field methods, the proposed model incorporates the material strength envelope for hydraulic fracture nucleation through two important steps: (i) an external driving force term, included in the damage evolution equation, that accounts for the material strength; (ii) a properly designed damage function that defines the fluid pressure contribution on the crack driving force. The comparison of numerical results for two‐dimensional test cases with existing analytical solutions demonstrates that the proposed phase‐field model can accurately model both nucleation and propagation of hydraulic fractures. Additionally, we present the simulation of hydraulic fracturing in a three‐dimensional domain with various stress conditions to demonstrate the applicability of the method to realistic scenarios.

EXPRESS 3D GEOMECHANICAL MODELING FOR INPUT TO HYDRAULIC FRACTURING ON CARBONATE OILFIELDS OF BASHKORTOSTAN REPUBLIC

The work describes a method of real-time 3D modeling of mechanical properties over the entire field area for the purposes of hydraulic fracturing. The uniqueness of this modeling approach is associated with the prompt acquisition of mechanical properties along the well paths of the field, which is especially important in conditions of insufficient geomechanics data.
 Traditional three-dimensional geomechanical modeling is a time-consuming and resource-intensive process. The data often describe the mechanical properties and stress-strain state of the rocks within the current drilling or development sector of the field and do not take into account the interwell space, especially in poorly drilled areas of the field. The method of real-time 3D geomechanical modeling makes it possible to quantify values of minimum horizontal stress used in hydraulic fracturing simulators, as well as static and dynamic Young's modulus and Poisson's ratio over the entire field area using the optimal amount of resources and in a shorter time.
 Based on the built three-dimensional cubes of elastic properties and stresses, correct data were obtained in the inter-well space, their vertical and lateral changes were analyzed, and frac design data were obtained at any well drilled through the simulated targets of the field.
 This paper covers the Arlanskoye, Znamenskoye and Yugomashevskoye fields (Bashneft PJSC). The target targets are carbonate deposits: Kashira and Podolsk strata of the Arlanskoye field, Tournaisian strata of the Znamensky field and Bashkir-Vereisky strata of the Yugomashevsky field.
 For the carbonate rocks of the target targets, laboratory core studies were carried out to determine elastic properties, and stable regional core-core relationships were obtained in the intervals of lower and middle Carboniferous carbonate deposits.
 1D geomechanical models were built in RN-SIGMA software 84 wells at the intervals of the study targets. In current 3D geological models are introduced and distributed values of Young's modulus, Poisson's coefficient and minimum horizontal stress gradient is calculated. Analysis of changes in geomechanical properties by area, for each study object was carried out and data were obtained to create frac designs for 15,000 wells.

Post-frac evaluation of deep shale gas wells based on a new geology-engineering integrated workflow

The development of shale gas reservoir is now shifting focus from mid-shallow reservoirs to deep reservoirs in the southern Sichuan Basin. For such reservoirs with high temperature, pressure, and stress difference, along with multiple folds, faults, and complex fracture networks, improving the stimulation performance of shale gas wells is the ultimate challenge. This study presents a new geology-engineering integrated workflow coupling hydraulic fracture simulation and reservoir simulation together with artificial intelligence to perform post-frac evaluations. A two-step calibration workflow of fracturing and reservoir simulations generated an ensemble of representative models, and a confidence interval of estimated ultimate recovery forecast were obtained. Four deep shale gas wells with two different completion versions (version 1.0 and version 2.0) in Y101 study area were evaluated. Some of the key learnings include: (1) the ratio of stimulated rock volume and drained rock volume is quantified to 8%–25% for the four characterized deep shale gas wells; (2) the version 2.0 completion design is able to stimulate the near-well region more effectively than version 1.0; (3) this novel geology-engineering integrated workflow performed the first reliable, robust and quantifiable post-frac evaluation in the southern Sichuan Basin deep shale reservoir.

Optimization of integrated geological-engineering design of volume fracturing with fan-shaped well pattern

According to the variable toe-to-heel well spacing, combined with the dislocation theory, discrete lattice method, and finite-element-method (FEM) based fluid-solid coupling, an integrated geological-engineering method of volume fracturing for fan-shaped well pattern is proposed considering the geomechanical modeling, induced stress calculation, hydraulic fracturing simulation, and post-frac productivity evaluation. Besides, we propose the differential fracturing design for the conventional productivity-area and the potential production area for fan-shaped horizontal wells. After the fracturing of the conventional production area for H1 fan-shaped well platform, the research shows that the maximum reduction of the horizontal principal stress difference in the potential productivity-area is 0.2 MPa, which cannot cause the stress reversal, but this reduction is still conducive to the lateral propagation of hydraulic fractures. According to the optimized fracturing design, in zone-I of the potential production area, only Well 2 is fractured, with a cluster spacing of 30 m and an injection rate of 12 m3/min per stage; in zone-II, Well 2 is fractured before Well 3, with a cluster spacing of 30 m and an injection rate of 12 m3/min per stage. The swept area of the pore pressure drop in the potential production area is small, showing that the reservoir is not well developed. The hydraulic fracturing in the toe area can be improved by, for example, properly densifying the fractures and adjusting the fracture distribution, in order to enhance the swept volume and increase the reservoir utilization.

A consistent linearization scheme for KGD problems using fracture tip asymptotic solutions

AbstractRecently, a fluid volume enrichment strategy based on the asymptotic solutions near the crack tip was proposed for fluid‐driven fracture propagation problems. Despite its successes in various benchmark and field‐scale problems of hydraulic fracturing simulations, the aforementioned enrichment strategy has the following limitations. First, the tightly coupled solid‐fluid nonlinear system cannot be consistently linearized due to the fast marching method applied to solve the Eikonal equation for fracture tracking. As a result, an approximated Jacobian had to be deployed for the Newton‐Raphson iterations. This is particularly troublesome when the fracture front propagates into newly fractured cells, since a large number of nonlinear iterations are required for convergence because of the inconsistent linearization. Second, the existing method only focused on the viscosity‐dominated fracture propagation regime. Even though the extension of the method to the toughness‐dominated regime could be relatively straightforward, it is not immediately clear how to apply the enrichment technique to the transition regime. This work is dedicated to address the above two limitations. Specifically, a unified fracture propagation criterion is proposed, which not only works for the viscosity‐dominated regime, but also for the toughness‐dominated regime and the transition regime in between. The techniques to consistently linearize the coupled solid‐fluid system and properly initialize the primary unknowns are demonstrated, which result in the significant reduction of required number of nonlinear iterations for convergence. The proposed technique is demonstrated in the context of the Khristianovic‐Geertsma‐de Klerk (KGD) problems due to its relative simplicity.

Research on the evolution law of hot spots in the field of coal seam hydraulic fracturing based on bibliometric analysis: review from a new scientific perspective.

As an unconventional natural gas, the calorific value of coal seam gas (CSG) is equivalent to that of natural gas. It is a high-quality, clean, and efficient green low-carbon energy source. Coal seam hydraulic fracturing is an important permeability enhancement measure in the process of CSG drainage. In order to further understand the overall research progress in the field of coal seam hydraulic fracturing, the Web of Science (WOS) database is used as a sample source, and the bibliometric analysis of the literature is carried out by CiteSpace software. The visual knowledge maps of the number of publications, the research countries, institutions, and keyword clustering are drawn. The research shows that it has gone through two stages of slow development and rapid growth in terms of time distribution. In terms of cooperation networks, the main active countries include China, the USA, Australia, Russia, and Canada, composed of China University of Mining and Technology, Chongqing University, Henan Polytechnic University, and China University of Petroleum as the core research institutions. Taking keywords as the theme, the coal seam hydraulic fracturing research field mainly involves high-frequency keywords such as hydraulic fracturing, permeability, model, and numerical simulation. The hotspot evolution law and frontier development trend of keywords with time are analyzed and obtained. On this basis, from a new perspective, the "scientific research landscape map" in the field of coal seam hydraulic fracturing is outlined, in order to provide a scientific reference for the research in this field.

Triaxial Deformation of the Goldwyer Gas Shale at In Situ Stress Conditions—Part II: Viscoelastic Creep/Relaxation and Frictional Failure

To understand the geomechanical implications of long-term creep (time-dependent deformation) response of gas shale, short-duration creep was recorded from laboratory triaxial tests on ten Goldwyer gas shale samples in the onshore Canning Basin at in situ stress conditions under constant differential axial stress. A simple power-law function captures primary creep behaviour involving elastic compliance constant B and time-dependent factor n. Experimental creep data revealed larger axial creep strain in clay and organic-rich rocks, than those dominated by carbonates. Anisotropic nature of creep was observed depending upon the direction of constant axial stress application (perpendicular or parallel to the bedding plane). Upon the application of linear viscoelastic theory on laboratory creep fitting coefficients, differential horizontal stress accumulation over a geological time scale was estimated from the viscoelastic stress relaxation concept. Further, this model was used to derive lithology-dependent least principal stress (Shmin) magnitude at depth for two vertical wells intersecting the Goldwyer gas shale formations. This newly proposed Shmin model was found to have a profound influence on designing hydraulic fracture simulation. Further, pore size distribution and specific surface area value SN2 were derived from low-pressure gas adsorption experiments. These physical properties along with weak mineral components were linked with creep constitutive parameters to understand the physical mechanisms of creep. A strong correlation was noted between SN2 and creep parameters n and B. Finally, an attempt was made to investigate how gas shale composition and failure frictional properties can influence shear fracturing.

Phase-Field Simulation of Hydraulic Fracturing by CO2 and Water with Consideration of Thermoporoelasticity

Phase-Field Simulation of Hydraulic Fracturing by CO2 and Water with Consideration of Thermoporoelasticity

Adaptive discretization refinement for discrete models of coupled mechanics and mass transport in concrete

An adaptive discretization refinement strategy for steady state discrete mesoscale models of coupled mechanics and mass transport in concrete is presented. Coupling is provided by two phenomena: the Biot’s theory of poromechanics and an effect of cracks on material permeability coefficient. The model kinematics is derived from rigid body motion of Voronoi cells obtained by tessellation of the domain. Starting with a coarse discretization, the density of Voronoi generator points is adaptively increased on the fly in regions where the maximum principal stress exceeds a chosen threshold. Purely elastic behavior is assumed in the coarse discretization, therefore no transfer of history/state variables is needed. Examples showing (i) computational time savings achieved via the adaptive technique and (ii) an agreement of the outputs from the fine and adaptive models during simulations of hydraulic fracturing and three-point bending combined with a fluid pressure loading are presented.

Simulation of fracture propagation law in fractured shale gas reservoirs under temporary plugging and diversion fracturing

Natural fractures (NFs) are developed in shale gas reservoirs, which can easily cause frac hits during hydraulic fracturing and reduce the productivity of infill wells and parent wells. Temporary plugging diverting fracturing (TPDF) can hinder the single forward extension of fracture transition and avoid the communication of hydraulic fractures (HFs) or NFs adjacent to wells. In order to explore the fracture propagation law of TPDF in fractured shale gas reservoirs, this study systematically evaluates the main factors such as stress difference, displacement, and fracturing fluid viscosity on the fracture temporary plugging diversion (TPD) law by means of true triaxial hydraulic fracturing simulation device and cohesive element model in ABAQUS. The findings reveal that (1) the law of fracture initiation and propagation at the engineering scale is similar to that in indoor experiments. Upon the primary fracturing (PF), the smaller the horizontal stress difference, the larger the pumping displacement, and the smaller the viscosity of the fracturing fluid is, the greater the corresponding fracture breakdown pressure and the stronger the rock compression resistance. (2) After TPD secondary fracturing, a small horizontal stress difference and a large pumping displacement facilitate the formation of a vertical complex fracture network structure on the primary fracture. Because of the small size of the indoor rock, viscosity has little effect on the fracture propagation of the TPDF, but the numerical simulation results reveal that the higher the viscosity, the greater the width of the new fracture. In addition, (3) the smaller the angle between the new fracture opened after PF and TPDF, the better the propagation effect of the new fracture. Meanwhile, the farther the temporary plugging zone is from the fracture front end, the wider the new fracture opened after TPDF. The field construction results reveal that the TPDF technology can avoid the effect of HFs, thus preventing frac hits during shale gas reservoir reconstruction. This study not only posits a physical and numerical simulation method for simulating the fracture propagation law of TPDF in fractured shale gas reservoirs but also provides theoretical guidance for applying TPDF to field construction.

Effects of different fracture parameters on microseisms induced by hydraulic fracturing

The microseism induced by hydraulic fracturing is of great significance to the development of geothermal reservoirs and the site selection of geothermal systems. In this study, taking geothermal field data from Qiabuqia as a geological reference, several models are developed for hydraulic fracturing simulations based on the models included in the commercial FracMan™ software suit. A series of numerical simulations are carried out to explore the effects of different fracture parameters, including the existence of faults, in-situ stress state, fracture occurrence, and fracture distribution near faults, on the induced microseisms. The results show that during hydraulic fracturing, the existence of faults does affect the propagation direction of the newly generated fractures, causing the fractures to extend toward the fault. The faults also increase the magnitude of microseismic events and make the distribution of microseismic events farther. Under three different in-situ stress states, the magnitudes of induced microseisms and the distance between microseismic events and injection wells are different, mainly due to the different forms of energy release. The total energy of induced microseisms under the reverse faulting stress state (RF) is the largest. Under the normal faulting stress state (NF), the number of microseismic events is the least, with only 28, and these microseismic events are concentrated near the well, with the farthest distribution distance of only 150 m. The fracture occurrence has a significant effect on induced microseisms, mainly affecting the number and distribution range of induced microseisms. With the same number of fractures, as the fracture concentration to the fault increases, both the maximum magnitude and the farthest distribution distance of the induced microseisms increase.

Numerical simulation of hydraulic fracturing and associated seismicity in lab-scale coal samples: A new insight into the stress and aperture evolution

Hydraulic fracturing and its associated seismic behaviour are increasingly important in the resource sector. In this paper, hydraulic fracturing and induced seismicity by both the constant flow rate and constant pressure injection was successfully simulated in lab-scale coal samples based on the discrete element method (DEM). Using the self-developed code in particle flow code (PFC), numerical simulations of fluid injection, fluid transport and seismic response are achieved simultaneously. The code has been applied to simulate water injection into an intact coal sample as well as coal samples with one pre-existing fracture. Model results follow observations from field practices and laboratory experiments, which demonstrate the reliability of the self-developed code. Induced seismicity by two injection methods shows that hydraulic fractures on the side of the sample with a pre-existing fracture present different cracking propagation patterns compared to the other side with no pre-existing fracture. Meanwhile, more peaks of extension-to-compression ratios calculated from the moment tensors of AE events are observed, which can be used to imply differential stress as well as reveal the impact of the pre-existing fracture on the aperture evolution of hydraulic fractures.

Phase field method to model hydraulic fracturing in saturated porous reservoir with natural fractures

In the present work, phase field model has been implemented for simulating hydraulic fracturing in porous reservoir which consists of several poorly connected natural fractures. We have used the finite element method (FEM) for solving the poro-elastic deformation and phase field equation, while the finite volume method (FVM) has been considered for solving the flow field. The validations of the numerical model with existing analytical and numerical solutions of fracture propagation are presented for an elastic medium subjected to incremental external loads and a poro-elastic medium undergoes hydraulic fracturing due to the increase of fluid injection pressure. The simulation results in this study show the ability of the phase field method based hydraulic fracturing (HF) model to obtain complex fracture propagation patterns including crack branching, merging, curving, and interacting with pre-existing natural fractures. Numerical simulation results suggest that for high injection pressure it is possible to get crack branching which is a desirable in the context of hydraulic fracture to create multiple high permeable flow paths with improved connectivity among the natural fractures for fluid circulation among injection and production wells. In the present study the values of aperture along the newly created hydraulic fracture and pre-existing fracture are determined from the displacement and phase fields at the end of hydraulic fracture simulations. The enhancement of effective transmissivity of the reservoir after hydraulic fracturing is compared for different network of pre-existing natural fracture. These results may be very insightful for industrial applications of hydraulic fracturing.

Hydraulic fracturing modelling of glutenite formations using an improved form of SPH method

Due to the low permeability and high heterogeneity properties of glutenite formations, the hydraulic fracture morphologies are extremely distorted during hydraulic fracturing operations, which is difficult to predict by traditional numerical method. Based on the existing limitations (i.e., the mesh re-division problems in FEM, complex parameter calibrations in DEM), an improved Smoothed Particle Hydrodynamics (SPH) method for modelling the hydraulic fracturing of glutenite formations was proposed. The interaction modes between the liquid and solid particles were first defined and the transformation algorithms of liquid, particles and damaged particles were also proposed. Then, the fracture mark ξ was introduced and the traditional kernel function in SPH was improved to simulate the hydraulic fracturing process. The “random gravel generation” algorithm combined with the “searching radius method” were proposed to well reproduce the meso-structures of glutenite. After that, the SPH model of glutenite was established, based on which, the influence of factors such as gravel size, content, strength as well as confining pressure were investigated. Results show that the crack patterns mainly include: 1) Propagating through the gravel; 2) Propagating around the gravel; 3) Stopping inside the gravel; 4) Crack bifurcation. The research results can provide some references for the comprehensive understandings of the internal mechanisms of glutenite hydraulic fracturing processes as well as the applications of SPH method into the simulations of glutenite hydraulic fracturing.

Comparative study on hydraulic fracturing using different discrete fracture network modeling: Insight from homogeneous to heterogeneity reservoirs

Conventional discrete fracture network (DFN) modeling is used to simulate hydraulic fracture propagation in fractured low permeability reservoirs. However, natural fractures have a certain degree of roughness, and reservoir rocks have significant heterogeneity characteristics. Therefore, it is necessary to compare the differences in hydraulic fracturing simulation of homogeneous and heterogeneous reservoirs caused by conventional and rough DFN modeling methods. Herein, new-generation algorithms for different DFNs are proposed. Combined the combined finite-discrete element method and different DFNs, four different simulation models are established, covering hydraulic fracturing models from relatively homogeneous to heterogeneous reservoirs. Then, the differences from different DFN modeling methods are compared and discussed. The results show that the relatively homogeneous and heterogeneous models established by conventional DFN may underestimate the bending propagation characteristics and fracturing time and overestimate the proportion of tensile failure. Meanwhile, when the nonuniform distribution of the mechanical parameters of rock blocks is considered, the bending propagation becomes more marked; thus, the fracturing time and the proportion of shear failure are further increased. The above results imply that to accurately predict the hydraulic fracture propagation in a real reservoir, it is vital to consider the roughness of real natural fractures and the nonuniform distribution of mechanical parameters in reservoir hydraulic fracturing modeling.

Integrated simulation of three-dimensional hydraulic fracture propagation and Lagrangian proppant transport in multilayered reservoirs

The numerical simulation of hydraulic fractures is a critical yet challenging computational problem due to its multi-physics nature. This paper develops an integrated hydraulic fracturing simulator by coupling a planar three-dimensional (PL3D) fracture propagation model with an efficient Eulerian–Lagrangian (E–L) proppant transport model. The fracture propagation model uses the finite volume method (FVM) and displacement discontinuity method (DDM) to solve the fluid flow and rock deformation, respectively. For proppant transport, we develop a pseudo-3D multiphase particle-in-cell (P3D MP-PIC) model, in which the fluid flow is addressed by FVM as a continuum, but the particles are tracked in a Lagrangian fashion as discrete phases. In contrast to Eulerian–Eulerian (E–E) proppant transport models, the P3D MP-PIC can efficiently deal with multi-modal particle simulations (i.e., particles of different sizes or materials) and avoid the problem of numerical diffusion. The fracture propagation and proppant transport models are validated by analytical solutions and laboratory experiments. We adopt a one-way coupling strategy to consider the effect of complex fracture propagation and fluid leak-off on slurry transport, in which the dynamic fracture geometry and fluid leak-off is first computed via the fracture propagation model, followed by the fully coupled fluid–particle simulation using the P3D MP-PIC. The integrated model can simulate the fracturing treatments in multilayered reservoirs with varying confining stresses at an industrial field scale. The simulation results can improve the prediction of effective/propped fracture geometries and better the fracturing designs.