Fracture Propagation Model Research Articles

Stochastic modeling of fracture initiation and propagation during fluid flow in carbonate reservoir

Fracture initiation and propagation in fractured carbonate reservoirs or shale ones during the production phase of the reservoir goes without paying particular attention because of the complex model that represents in itself the propagation of fracture. It goes without saying how important an assessment of this phenomenon, propagation, would be in quantitative terms for reservoir engineering in reservoir simulators. This fact becomes even more interesting when our data are stochastic, such as boundary conditions, pressure, viscosity, and other targeting functions. Exactly in this paper, we will address such a problem, i.e., the configurations of the crack network as propagating them in time when the inputs are random starting directly with stochastic optimal control Brinkman model in fractured rocks, which is known to be a problem that includes areas where the Darcy flow predominates and areas where the Stokes flow predominates. We will then develop our flow model in fractured rocks under the effects of geomechanical processes by undergoing energy minimization processes. Our method is robust, although at the moment, it requires a bit of calculation time. In the future, the “reduction” of this handicap would pave the way for the implementation of this model on a large Darcy scale.

Classification and Localization of Fracture-Hit Events in Low-Frequency Distributed Acoustic Sensing Strain Rate with Convolutional Neural Networks

Summary Distributed acoustic sensing (DAS) has been used in the oil and gas industry as an advanced technology for surveillance and diagnostics. Operators use DAS to monitor hydraulic fracturing activities, examine well stimulation efficacy, and estimate complex fracture system geometries. Particularly, low-frequency DAS can detect geomechanical events such as fracture hits because hydraulic fractures propagate and create strain rate variations in the rock. Analysis of DAS data today is mostly done post-job and subject to interpretation methods. However, the continuous and dense data stream generated live by DAS poses the opportunity for more efficient and accurate real-time data-driven analysis. The objective of this study is to develop a machine learning-based workflow that can identify and locate fracture-hit events in simulated strain rate responses correlated with low-frequency DAS data. In this paper, “fracture hit” refers to a hydraulic fracture originating from a stimulated well intersecting an offset well. We start with building a single fracture propagation model to produce strain rate patterns observed at a hypothetical monitoring well. This model is used to generate two sets of strain rate responses with one set containing fracture-hit events. The labeled synthetic data are then used to train a custom convolutional neural network (CNN) model for identifying the presence of fracture-hit events. The same model is trained again for locating the event with the output layer of the model replaced with linear units. We achieved near-perfect predictions for both event classification and localization. These promising results prove the feasibility of using CNN for real-time event detection from fiber-optic sensing data. Additionally, we use edge detection techniques to recognize fracture-hit event patterns in strain rate images. The fracture-hit location can be identified using recognized pixels in the image. The accuracy of edge detection-based location identification is also plausible, but edge detection is dependent on the assumption of pattern shape and image quality, hence it is less robust compared to CNN models. This comparison further supports the need for CNN applications in image-based real-time fiber-optic sensing event detection.

Numerical simulation of planar hydraulic fracture propagation with consideration to transition from turbulence to laminar flow regime

Turbulent flow in fluid-driven fractures exerts important effects on the hydraulic fracture extension, fracture geometry, and proppant transport. Based on linear elastic fracture mechanics, the implicit level set algorithm, laminar flow theory, and turbulent flow theory, this study established planar fracture propagation models of permeable and impermeable reservoirs with consideration the flow regime transition from turbulent to laminar flow when the Reynolds number is larger than the critical Reynolds number. Additionally, the frictional behavior of the fluid in the turbulent flow regime was approximated based on the MDR asymptote and Blasius correlation. The influence of the turbulent flow effect on the hydraulic fracture propagation was theoretically and numerically analyzed. The results reveal that the turbulent flow regime exerts a significant effect within the first few minutes of fracture propagation. Compared with the fully-laminar-flow model, the turbulent-laminar flow model predicted a shorter fracture radius, larger maximum fracture width, and fluid net pressure. This indicates that the fracturing process requires greater pumping power than that predicted by the laminar flow models under the influence of turbulent flow to achieve the desired design parameters. Compared with impermeable rock, the turbulent flow in the fracture is enhanced by fluid leak-off. Slickwater can transition from turbulent to laminar flow at a lower critical Reynolds number compared with pure water. The normalized fracture parameters indicate that the fracture radius corresponding to pure water is smaller, and the maximum width of fracture and maximum net pressure are larger than those of slickwater. The threshold time of turbulent flow for different fracture parameters varies depending on the injected fluid properties and reservoir parameters. Our study contributes toward a deeper understanding of the real physical behavior of hydraulic fracture propagation at large injection rates.

Numerical study on the law of fracture propagation in supercritical carbon dioxide fracturing

Compared with conventional hydrofracturing fluid, SC-CO2 has the merits of no water sensitivity and effective carbon dioxide storage. At present, the research on the fracture initiation mechanism of SC-CO2 fracturing is still at the exploring phase. This paper conducts a detailed study on the fracture initiation mechanism of SC-CO2 fracturing, and establishes a fracture initiation and propagation model of flow-stress-damage coupling according to damage mechanics. A series of numerical simulation studies have been carried out on the rock physical parameters, fracturing construction parameters, natural fracture distribution and other factors that affect the fracture propagation of the reservoir to provide a reference for the SC-CO2 fracturing construction design. The findings suggest: the lower formation permeability, the less SC-CO2 filtration loss, and the larger total fracture length and width; SC-CO2 is easier to improve the reservoir continuity and result in a complex fracture network; The lower the viscosity of SC-CO2, the larger total length of fractures, and the more complex the fracture network; As the delivery of pump increases, the width of fracture continues to increase, and the total fracture length decreases; SC-CO2 has a better effect on communicating natural fractures and porous media, and the fracture network is more complex.

Numerical simulation of the non‐Newtonian fracturing fluid influences on the fracture propagation

AbstractHydraulic fracturing fracture propagation is the main factor affecting the fracturing effect. In view of the more diversified selection of fracturing fluid, the problem of fracture propagation in non‐Newtonian fluid fracturing is often encountered in fracturing. In this paper, the influencing factors of fracture propagation of non‐Newtonian fluid fracturing fluid are analyzed. Based on PKN model, a three‐dimensional fracture propagation model considering the rheology and filtration of fracturing fluid is established, the better fracture shape simulation results are given, and the effects of fluid properties, rock physical properties, and injection parameters on fracture propagation are analyzed in detail. The research shows that (1) in the process of fracture propagation, the fracture length and width gradually increase, and the corresponding pressure in the fracture also increases. The overall increase trend is that the growth is rapid in the initial stage of fracturing and gradually slows down in the later stage. (2) The greater the consistency coefficient and rheological index, the greater the fracture width and pressure in the fracture, and the easier it is to form wide fracture. The larger the filtration coefficient is, the weaker the fracture forming ability is, and the fracture width, length, and pressure in the fracture are reduced. (3) Rock physical properties have a certain influence on fracture propagation, Young's modulus has a great influence on fracture propagation, while Poisson's ratio has little influence on it. However, the larger the Young's modulus, the more difficult the fracture is to expand, and the smaller the corresponding fracture width. (4) The larger the pump injection rate, the larger the fracture size and the higher the pressure in the fracture. The model can provide a theoretical basis for fracturing design and fracture shape prediction.

Hydro-mechanical modelling of gas transport in clayey host rocks for nuclear waste repositories

Host rocks, as the final impediment to waste migration, play a significant role in the nuclear waste repositories. Modelling of gas migration in saturated host rocks as well as its coupled hydro-mechanical (HM) behaviors is of importance to the assessment of geological disposal facilities. A comprehensive literature review is carried out on the models for simulating gas migration in saturated rock materials. Several aspects have been provided and discussed, including the material properties and experimental interpretations, governing equations, constitutive models for hydraulic and mechanical processes, fracture propagation models. Specifically, these models are discussed in detail with respect to their performance in describing the recorded experimental behaviors. It is found that the visco-capillary two phase flow model with enriched intrinsic permeability is commonly used to describe the advective gas transport in saturated host rocks. The embedded fracture model (EFM) or enriched EFM seems to be the most favored model as it accounts for the fracturing mechanism which is more representative to implicitly simulate the preferential gas pathways. To describe the mechanical behavior of rocks during the gas migration process, linear/nonlinear elastic, elastoplastic and damage models have been included in the mechanical processes. The HM models incorporating plasticity or damage may not be applicable in most experimental studies, which are not competent to simulate the key experimental behavior associated with the development of gas preferential pathways. Current models that can explicitly describe the gas induced micro-fracturing are seldomly reported, the existed ones are not able to represent all the key experimental behaviors related to preferential gas flow. Advanced approaches, i.e., phase field (PF) method, extended finite element method (XFEM), discrete element method (DEM), hybrid finite discrete element method (FDEM) can be integrated with cohesive zone model (CZM) to provide some promising aspects in representing the development of preferential gas pathways. Lastly, the conclusions and recommendations for future modelling are given.

A configurational force-based material point method for crack propagation modelling in 2D

The modelling of fracture initiation and propagation is a nontrivial problem in computational mechanics. However, it is an area that is extremely important in engineering applications, requiring accurate and robust numerical methods that can be applied to a variety of materials. This paper presents the development of a new numerical modelling approach, which combines material, or configurational, forces and the material point method (MPM), for finite deformation crack modelling of linear elastic solids in two dimensions. The combination of these numerical methods offers a number of advantages relating to the flexibility of the MPM in terms of decoupling the material deformation from the computational grid and the general nature of configurational force theory in terms of being applicable across different material behaviour. In the method presented in this paper, the MPM forms the basis of the mechanical response of the underlying material, while the configurational force theory provides a fracture criterion for crack modelling through a post-processing procedure. The developed modelling framework is applied to a number of benchmark problems for linear elastic solids in 2D. All simulations show good agreement with the results in the literature, which demonstrates that the combined configuration force-material point framework is a promising numerical tool for fracture modelling.

Implementation of planar 3D hydraulic fracture model in rock with layered compressive stress

Plane 3D model of hydraulic fracture propagation is implemented. Fluid flow inside the fracture, leak-of, rock deformation and breaking are taken into account. Asymptotic solution for tip of semi-infinite plane fracture is used to set boundary conditions for fluid flow problem and to calculate fracture front propagation velocity. Elastic and fluid flow equations are united in one system of nonlinear equations and solved simultaneously by Newton method with analytically calculated Jacoby matrix. The implemented model may be used as a start point for testing various methods of solution of “hydrodynamic-elasticity” problem and improving their convergence speed. Also model can be used for developed hydraulic fracture simulation.

Optimization of perforation parameters for horizontal wells in shale reservoir

Volume fracturing of horizontal wells is the key technology for efficient development of shale reservoirs, and perforation is the basic condition of hydraulic fracturing. In this paper, based on the basic equation of fluid–structure coupling and the cohesive fracture model, a three-dimensional numerical model of spiral perforation hydraulic fracture propagation in near well bore horizontal wells was established. The pipe flow elements were introduced to characterize the automatic distribution of fluid and the pressure drop caused by friction. The results show that the vertical perforation initiation pressure is lower than the horizontal perforation, the vertical perforation is easier to release energy after initiation, the fracturing fluid is easier to flow into the vertical perforation, and eventually form 1–2 major fractures. The common rule among different pore densities is that the fracture distribution at both ends of the cluster is more, and the fracture distribution in the middle is less, and the gap between the two increases with the increase of injection. When the hole density is higher than 8 P/m, the uneven development of fractures is significant. If the hole density is 4 P/m, the number of effective fractures around the wellbore decreases. Therefore, it is suggested that the optimal hole density is 8 P/m. With the increase of perforation depth, the effective area of liquid pressure on the hole wall increases, and the initiation pressure decreases. With the increase of the diameter of the hole, the initiation pressure is lower and the initiation and extension of the fracture are easier. Compared with pore diameter, the effect of pore depth on fracture propagation is greater than that of pore diameter. Under the calculation conditions, it is recommended that 8 P/m, hole depth is 0.8 m, and aperture is 20 mm.

Real-time analysis and forecasting of the microseismic cloud size: Physics-based models versus machine learning

The spatiotemporal distribution of hydraulic fracturing microseismicity is complicated and depends on various mechanical and diffusional parameters. Hydraulic fracture modeling can aid in understanding fracture propagation and microseismicity. Nevertheless, the complex spatial and temporal interaction of several processes occurring within and around the fracture represents a challenge for developing real-time tools for microseismic prediction. Two approaches are developed to forecast the microseismic cloud size in real time. The first approach uses fracture propagation models to derive the cloud size directly from the microseismic observations. The second approach is based on a convolutional neural network (CNN) trained with the engineering parameters and past microseismic cloud size values. A rolling forecasting strategy is used to train consecutive CNN models in real time to make predictions at a specified time lag. A data augmentation technique known as double noise injection is used to ensure that the amount of training examples available to the machine-learning models at each time step is similar to or larger than the number of free parameters. The results indicate that the CNN outperforms the quality of predictions of the physics-based models but with a reduced prediction capability. The physics-based approach can predict growth at any time but ignores the engineering parameters. Conversely, physics-based methods lead to real-time insights into the fracturing regime, revealing whether microseismicity is most likely generated due to a leak-off-dominated or a storage-dominated regime. The CNN model can forecast the cloud size only at a single future time lag while using the engineering parameters and past cloud growth as input. However, this approach does not provide a physical interpretation of the fracture propagation regime. The prediction accuracy of both methodologies varies depending on the microseismic behavior. We postulate that CNN forecasts could be improved by including more physical constraints into the predictive model.

Experimental Study of Hydraulic Fracture Propagation Behavior during Multistage Fracturing in a Directional Well

Due to the limited space of offshore platform, it is unable to implement large-scale multistage hydraulic fracturing for the horizontal well in Lufeng offshore oilfield. Thus, multistage hydraulic fracturing technology in directional well was researched essentially to solve this problem. Modeling of fracture propagation during multistage fracturing in the directional and horizontal wells in artificial cores was carried out based on a true triaxial hydraulic fracturing simulation experiment system. The effects of horizontal stress difference, stage spacing, perforation depth, and well deviation angle on multifracture propagation were investigated in detail. Through the comparative analysis of the characteristics of postfrac rock and pressure curves, the following conclusions were obtained: (1) multistage fracturing in horizontal wells is conducive to create multiple transverse fractures. Under relatively high horizontal stress difference coefficient (1.0) and small stage spacing conditions, fractures tend to deflect and merge due to the strong stress interference among multiple stages. As a consequence, the initiation pressure for the subsequent stages increases by more than 8%, whereas in large stage spacing conditions, the interference is relatively lower, resulting in the relatively straight fractures. (2) Deepening perforation holes can reduce the initiation pressure and reduce the stress interference among stages. (3) When the projection trace of directional wellbore on horizontal plane is consistent with the direction of the minimum horizontal principal stress, fractures intersecting the wellbore obliquely are easily formed by multistage fracturing. With the decrease of well deviation angle, the angle between fracture surface and wellbore axis decreases, which is not conducive to the uniform distribution of multiple fractures. (4) When there is a certain angle between the projection trace of directional wellbore on horizontal plane and the direction of minimum horizontal principal stress, the growth of multiple fractures is extremely ununiform and the fracture paths are obviously tortuous.

Influence of heterogeneity, natural fracture, and bedding plane on fracture propagation in the vicinity of a borehole

The majority of lost circulation events during drilling include drilling fluid losses through natural or drilling-induced fractures, but this problem can be prevented by understanding fracture propagation behavior. However, studies have mostly focused on the influence of natural fracture and bedding planes on hydraulic fracture propagation, and few studies have explored the fracture propagation in the vicinity of a borehole. Therefore, the present paper intends to simulate the fracture propagation in the vicinity of a borehole under the joint impact of heterogeneity, natural fracture, bedding planes, and borehole. The theoretical model of flow-rock failure process analysis2D was introduced, and the uniaxial compressive testing results of Longmaxi shale were obtained to verify the present model. Then, fracture propagation models in the vicinity of a borehole were proposed by considering heterogeneity, bedding planes, and natural fracture. Numerical findings were analyzed and discussed. Results indicated that heterogeneity, bedding planes, and natural fracture significantly influenced fracture propagation in the vicinity of the borehole. As such, this influence should be considered in the analysis and treatment of lost circulation. This study could help elucidate how lost circulation could be prevented during drilling in fractured formations.

Analytical model of fracture propagation in carbonate reservoirs

The fracture propagation length and propagation angle can be calculated quickly using the fracture propagation analytical model. But for fractured-vuggy carbonate reservoirs, the addition of a discontinuous medium in the analytical model makes it difficult to obtain accurate results via calculation. In this paper, an analytical solution model for fracture propagation in carbonate reservoirs is established. On the premise of ensuring calculation accuracy, the discontinuous displacement algorithm is used to introduce the fracture and hole characteristics into the calculation. The model comprehensively considers the interference of in-situ stress, fracture tip stress, and stress field of fractures and holes on fracture propagation. The calculation accuracy of the model in a fractured-vuggy carbonate reservoir is verified by a true triaxial fracturing physical simulation experiment. The model can be used for subsequent research on the fracture propagation law of carbonate reservoirs containing discontinuous bodies, such as fractures and caves.

Phase field modeling of multi-cluster hydraulic fracturing in horizontal wellbore with inconsistent direction to minimum principal stress

Zhongjiang gas field is a typical narrow channel tight sandstone gas reservoir. In order to obtain enough horizontal section length in high-quality reservoir, horizontal wellbore azimuth is basically consistent with direction of narrow channel sand body, resulting in a certain included angle θ between wellbore azimuth and in-situ minimum principal stress orientation. In this study, a seepage-stress-damage coupled dynamic fracture propagation model is established through phase field method to investigate the effect of angle θ on multi-cluster fracture simultaneous propagation based on geological engineering data of JS-X well. Propagation of hydraulic fracture is automatically tracked through phase field evolution without additional criteria or grid direction limitation. Simulation results show that: (1) Fracture tip of each cluster would approach to stress diversion zone created by adjacent clusters. Simultaneous propagating fractures of each cluster are prone to deflect, interconnect with each other and form one single fracture eventually. (2) Increasing cluster number or decreasing cluster spacing in the same fracturing stage would further promote diverting of each cluster fracture and accelerates fractures merging into one single fracture. We suggest that azimuth of horizontal wellbore in tight gas reservoir should be consistent with in-situ minimum principal stress orientation to reduce the effect of angle θ.

Simulation and evaluation for acid fracturing of carbonate reservoirs based on embedded discrete fracture model

Acid fracturing is an important means of reservoir stimulation, whose purpose is to form an incompletely closed acid-etched fracture as the flow channel for oil and gas during production. The length and conductivity of acid-etched fractures can be used to evaluate acid fracturing and directly impact production. To study their influence on the stimulation effect and final production, an acid fracturing coupling model including a fracture propagation model coupled with reservoir flow and temperature field models is established for the first time in this study based on an embedded discrete fracture model (EDFM), which can realize the coupling of fracture propagation and reservoir flow and simplify the solution of fracture and reservoir temperatures. The simulation results of the acid fracturing coupling model are introduced into the productivity model, which is also based on the EDFM to analyze and evaluate well productivity. The results show that: (1) the EDFM can easily couple fracture propagation and reservoir flow and can be used to rapidly solve the temperature fields in the fracture and reservoir successfully for the first time. (2) Reservoir flow impacts the propagation of fractures by increasing or decreasing the leak-off velocity of the working fluid. (3) Temperature diffusion is much weaker than pressure diffusion during acid fracturing and is limited near the acid fracture. The reaction between the acid and rock increases the local temperature around the acid fracture, and may even exceed the initial formation temperature. (4) Raising the injection rate reasonably enhances H+ diffusion, increases the effective length of acid-etched fractures, enlarges the drainage area of oil and gas, and benefits long-term well production.

A hybrid potential of mean force approach for simulation of fracture in heterogeneous media

Material heterogeneity at small scales is a key driver of material’s effective macroscopic properties and fracture response. We present a hybrid energy-based approach based on a potential of mean force formulation of lattice element method for reliable and efficient modeling of fracture and crack propagation in heterogeneous materials. The proposed framework rests on direct application of the Griffith fracture criteria and removes material points to create fracture surfaces in energetically favorable directions. Computational efficiency is achieved through a probing of high energy bonds and quasi-static relaxation leading to near global imposition of the energy-based criteria for crack path resolution. We validate the proposed hybrid approach against results in literature and use it to examine fracture response of defective and layered materials. For layered materials with fracture energy heterogeneity, the effective toughness is shown to be the maximum of fracture energies of layers irrespective of their volume fraction and the direction of crack propagation. For layered materials with elastic modulus heterogeneity, the maximum energy release rate occurs when the crack approaches the compliant-stiff interface from within the compliant phase. We examine the scaling of fracture toughness with modulus contrast, the link to volume fraction of the layers and the relationship between toughness anisotropy and the gradient of elastic modulus heterogeneity, offering insights with potential to inform the design of materials for fracture.

Numerical Study of the Effect of Perforation Friction and Engineering Parameters on Multicluster Fracturing in Horizontal Wells

Simultaneous multiple-fracture treatments in horizontal wellbores have become one of the key methods for economically and efficiently developing oil and gas resources in unconventional reservoirs. However, field data show that some perforation clusters have difficulty propagating fractures due to the internal mechanism of competing initiation and propagation among the fractures. In this paper, the physical mechanisms that influence simultaneous multiple-fracture initiation and propagation are investigated, and the effects of engineering parameters and in situ conditions on the nonuniform development of multiple fractures are discussed. A 3D fracture propagation model was established with ABAQUS to show the influence of the stress shadow effects and dynamic partitioning of the flow rate by simulating the propagation of multiple competing fractures generated in the perforation clusters. Based on the results of these simulations, simultaneous flow in multiple fractures can propagate evenly. Through adjusting the number of perforations in each cluster or the perforation diameter, the effect of the stress shadow can be significantly reduced by increasing the perforation friction, and the factors that affect the development of multiple fractures are changed, from the stress shadow effect to the dynamic partitioning of the flow rate. When the stress shadow effect is dominant, increasing the fracturing fluid viscosity promotes the uniform development of multiple fractures and increases the fracture width. When the dynamic partitioning of the flow rate is dominant, increasing the injection rate greatly affects the uniform development of multiple fractures.

Numerical Simulation for Fracture Propagation in Elastoplastic Formations

Current hydraulic fracture models are mainly based on elastic theories, which fail to give accurate prediction of fracture parameters in plasticity formation. This paper proposes a fluid–solid coupling model for fracture propagation in elastoplastic formations. The rock plastic deformation in the model satisfies the Mohr-Coulomb yield criterion and plastic strain increment theory. The extended finite-element method (XFEM) combined with the cohesive zone method (CZM) is used to solve the coupled model. The accuracy of the model is validated against existing models. The effects of stress difference, friction angle, and dilation angle on fracture shape (length, width), injection pressure, plastic deformation, induced stress, and pore pressure are investigated through the model. The results indicate that compared with elastic formation, fracture propagation in elastoplastic formation is more difficult, the breakdown pressure and extending pressure are greater, and fracture shape is wider and shorter. The plastic deformation causes the fracture tip to become blunt. Under the condition of high stress difference or low friction angle formation, it is prone to occur large plastic deformation zones and form wide and short fracture. Compared with friction angle, dilation angle is less sensitive to plastic deformation, fracture parameters, and fracture geometry. For the formation with high stress difference and friction angle, the effect of plasticity deformation on fracture propagation should not be ignored.

Study on CO2 foam fracturing model and fracture propagation simulation

CO2 foam fracturing fluid has the advantages of water saving and environmental protection, which has been widely used in unconventional oil and gas reservoir. However, there are still many technical difficulties in fracture propagation model and numerical calculation method of CO2 foam fracturing. In this paper, a CO2 foam fracturing fracture propagation model with temperature-pressure-phase coupling is established. Physical parameters of CO2 are calculated by Span-Wagner method, and the finite difference and displacement discontinuity methods are used to solve the model. Moreover, we compare the results of this model with the field measured data, KGD model and EFRAC-3D model to verify the model. The computation results show that in the process of fracturing, improving the CO2 foam quality can significantly enhance the fracturing effect. When the quality increased from 0.5 to 0.8, the fracture width raised by more than 2 times. In addition, the fracture propagation is significantly affected by injection temperature. With the increase of injection temperature, fracture width decreases continuously, and if the CO2 foam is supercritical phase state, it is not conducive to increase the fracture width.

Phase field model for hydraulic fracture propagation in porous medium and numerical simulation analysis of hydraulic fracture propagation in a layered reservoir

Phase field model for hydraulic fracture propagation in porous medium and numerical simulation analysis of hydraulic fracture propagation in a layered reservoir