Mathematical foundations for play-agnostic thermo-poro-hydro-mechanical modeling of hydraulic fracture initiations from perforated wells: Towards a predictive tool

Refracturing technology has become an important means for the regeneration of old wells reconstruction. It is of great significance to understand the formation mechanism of hydraulic fracturing fracture for the design of hydraulic fracturing. In order to accurately evaluate and improve fracturing volume after refracturing, it is necessary to understand the mechanism of refracturing fracture in shale formation. In this paper, a true triaxial refracturing test method was established. A series of large-scale true triaxial fracturing experiments were carried out to characterize the refracturing fracture initiation and propagation. The results show that for shale reservoirs with weak bedding planes and natural fractures, hydraulic fracturing can not only form the main fracturing fracture, which is perpendicular to horizontal minimum principal stress, but it can also open weak bedding plane or natural fractures. The characteristics of fracturing pump curve indicated that the evolution of fracturing fractures, including initiation and propagation and communication of multiple fractures. The violent fluctuation of fracturing pump pressure curve indicates that the sample has undergone multiple fracturing fractures. The result of refracturing shows that initial fracturing fracture channels can be effectively closed by temporary plugging. The refracturing breakdown pressure is generally slightly higher than that of initial fracturing. After temporary plugging, under the influence of stress induced by the initial fracturing fracture, the propagation path of the refracturing fracture is deviated. When the new fracturing fracture communicates with the initial fracturing fracture, the original fracturing fracture can continue to expand and extend, increasing the range of the fracturing modifications. The refracturing test results was shown that for shale reservoir with simple initial fracturing fractures, the complexity fracturing fracture can be increased by refracturing after temporary plugging initial fractures. The effect of refracturing is not obvious for the reservoir with complex initial fracturing fractures. This research results can provide a reliable basis for optimizing refracturing design in shale gas reservoir.

ABSTRACT: Hydraulic fracture trajectory near the wellbore directly influences the efficiency of fluid flow into and out of the well. Modeling the near-wellbore hydraulic fracture behaviors has been challenging due to the combined impacts of wellbore perforation placement, stress concentration around the wellbore and perforation tunnels, in-situ stress conditions, as well as pre-existing fractures in the subsurface that interact with hydraulic fractures. In this paper, we have built numerical models to take into account the aforementioned factors and investigate near-wellbore fracture growth and fluid pressure characteristics. The numerical models use a distinct element method (DEM) approach that explicitly represents the well casing, cement sheath, and perforation tunnels, with natural fractures represented by Smooth Joint Model. The results show that natural fractures intersecting the perforation tunnels at a favorable angle with respect to in-situ stress directions can facilitate fracture initiation in hard rocks. Multiple initiation points may occur, while one fracture becomes dominant at a later time in the simulated case. In addition, the simulation results show the termination of hydraulic fracture growth in the highly fractured zone, as well as hydraulic fractures crossing natural fractures that have small effective sizes at the interaction location. This study also demonstrates the efficacy of the near-wellbore model to represent detailed wellbore elements, consider complex discrete fracture networks, and capture the fundamental mechanisms that influence near-wellbore hydraulic fracture behaviors. 1. INTRODUCTION The trajectory of hydraulic fractures near the wellbore directly influences the efficiency of fluid flow into and out of the well, making it a crucial factor that can impact several critical aspects in unconventional reservoirs and enhanced geothermal systems, such as reservoir connectivity, fluid circulation, proppant transportation, and energy production efficiency. Modeling near-wellbore fracture initiation and propagation has been challenging due to complex influencing factors that need to be considered, including the casing-cement sheath-perforation tunnel-rock structure, stress concentrations resulting from the wellbore and perforation tunnels, interference, competition, and merging of hydraulic fractures, interactions within the hydraulic discrete fracture network, and in-situ stress conditions. A model must span multiple scales to accurately capture different fracture behaviors, from fracture initiation along perforation tunnels at a millimeter scale to fracture propagation near the wellbore at a meter scale. In this study, a numerical model was established to investigate hydraulic fracture behaviors in the near-wellbore region. Utilizing a distinct element method (DEM) lattice approach, we analyzed hydraulic fracture initiation and propagation behaviors under the combined impacts of wellbore perforation and discrete fracture network (DFN). The model is based on hydraulic fracturing tests conducted at the Utah FORGE Site. Well casing, cement sheath, and perforation tunnels were explicitly represented in the simulation, and fluid pressure characteristics and corresponding fracture behaviors are discussed in detail.

ABSTRACT: Analysis of the stress field around the wellbore is a prerequisite for predicting the formation breakdown pressure. With the development of hot dry rock and deep oil and gas reservoirs, thermoelastic stress has become one of the significant factors in the analysis of the stress field around the wellbore. Based on linear elastic theory and heat transfer theory, this paper analyzed the effect mechanism of thermoelastic stress around the wellbore by establishing a two-dimensional wellbore physical model. Through the finite difference method, this paper simulated the thermoelastic stress field around the wellbore under quasi-static and transient conditions. Numerical simulation results show that the calculation results of the finite difference scheme established in this paper are consistent with the analytical solutions under quasi-static conditions. The finite difference scheme established in this paper can accurately calculate the thermoelastic stress field around the wellbore. When the cold liquid injected from the wellbore acts on the hot rock, the circumferential tensile stress is generated around the wellbore. With the increase of Young’s modulus, Poisson’s ratio, and the linear expansion coefficient of the rock, the thermoelastic circumferential stress value around the wellbore increases significantly. The faster the cooling rate of the wellbore, the greater the thermoelastic circumferential stress generated around the wellbore. The finite difference solution of the thermoelastic stress field established in this paper can provide theoretical guidance for the design of hot dry rock hydraulic fracturing and drilling fluids. INTRODUCTION Hydraulic fracturing is a significant development technology for unconventional reservoir exploitation (Wang et al., 2021). With the increase of reservoir mining depth and the development of hot dry rock, the influence of thermal stress during hydraulic fracturing becomes more and more important (Zhou et al., 2020). The heat exchange between the fracturing fluid and the reservoir causes the rock temperature to change, which in turn generates thermal stress. Thermal stress will directly change the effective stress field of the reservoir and affect the failure of the wellbore and the propagation of fractures (Wang and Papamichos, 1994). Chen and Ewy (2005) found that heating the wellbore increases collapse and fracturing mud weight, destabilizing the near-wellbore area. Ghassemi et al. (2009) established a coupled thermoelastic model of a chemically-active rock, which showed that cooling high-salinity mud would increase the possibility of tensile failure. Zhou et al. studied the stress field formed by the seepage force around the wellbore and analyzed the effect of poroelastic stress on the initiation of fractures (Zhou et al., 2021; Wang et al., 2021). Zhou and Ghassemi (2009) developed a finite element model that couples linear and nonlinear chemistry-pore-thermoelasticity, which can be used to analyze the wellbore stability of shale reservoirs. Roy et al. (2018) studied the effect of thermal stress on the integrity of the wellbore during the CO2 injection process, and the results show that the existence of effective in-situ horizontal stress reduces the negative impact of the thermal stress around the wellbore. Wang et al. (2019) developed a new non-isothermal wellbore strengthening model, which showed that mud loss aggravated the redistribution of thermal stress near the wellbore. The above studies have shown that during fluid injection, thermal stress has a significant impact on wellbore stability. It is necessary to study the thermoelastic stress generated by the cooling effect of the fracturing fluid during the hydraulic fracturing process to analyze the initiation of the hydraulic fracturing fracture.

Response characteristics of coal subjected to hydraulic fracturing: An evaluation based on real-time monitoring of borehole strain and acoustic emission

A series of laboratory hydraulic fracture experiments was conducted on synthetic rock samples to investigate the mechanism of hydraulic fracture initiation and propagation of a pressurised wellbore in non-fractured and fractured reservoirs. To achieve this goal, the influence of pre-existing fracture (both on and far from the wellbore wall) and horizontal differential stress was investigated on the fracture initiation and propagation in different stress regimes. In reservoirs with no fracture due to the high stress concentration in surrounding rock of the well, the fracture initiation and propagation pressure are increased. In fractured reservoirs, the presence of pre-existing fracture on the wellbore wall reduced the effect of the original stress concentration around the wellbore, which led to a drastic decrease in the fracture initiation and propagation pressure. In the far-wellbore region by increasing dip and strike of the pre-fracture, the fracture propagation pressure was decreased when it intersected the pre-fracture and arrest behaviour of the fracture was also decreased. In-situ horizontal differential stress, () played an important role on the fracture propagation behaviour and the fracture initiation and propagation pressure both in non-fractured and fractured reservoirs. Unlike low differential stress, at high differential stress due to decreasing the interaction between hydraulic and pre-existing fractures, the dominant behaviour of fracture propagation was changed from arrest to crossing mode. In addition, at high differential stress because of decreasing the stress state concentration around the wellbore, initiation and propagation pressure of the hydraulic fracture were decreased.

Numerical models of hydraulic fracturing and the interpretation of syntectonic veins

The flow of fracturing fluid through rock pores generates a seepage force (SF) that disrupts the existing stress equilibrium and significantly affects rock deformation and failure. Despite its impact, the effect of SF on hydraulic fracture (HF) initiation has yet to be fully understood. In this study, a mechanistic model of SF's impact on fracture initiation was established through analysis of the force balance on a microscopic element. Using the finite difference method, a transient hydro‐mechanical model was developed to simulate fluid seepage‐induced stress distribution and pore pressure variation around a wellbore. Model results were validated through comparison with an analytical solution of pore pressure. The influence of SF on fracture initiation was investigated by conducting simulations with various wellbore pressurization rates and fracturing fluid viscosities. The results showed that fluid viscosity and pressurization rate have a significant impact on fracture initiation pressure (FIP) and SF‐induced circumferential stress. A larger SF‐induced circumferential stress and a lower FIP were observed when the viscosity and pressurization rate were smaller. A higher Biot coefficient results in stronger SF and reduced FIP. The theoretical mechanical model of seepage force established in this paper can provide crucial theoretical support for understanding the mechanism of fracture initiation and propagation, as well as for optimizing the effectiveness of hydraulic fracturing construction.

Understanding the effect of natural fractures on the propagation of a hydraulic fracture has challenged the fracturing community for a very long time. Nearly all previous investigations address the problem with the assumption that the natural and hydraulic fractures are all vertical and basically two-dimensional. While it is realistic to assume that the hydraulic fractures are vertical, the natural fractures have random orientations, and many of them are not in a vertical plane. This paper offers a first look at the 3D interactions between a vertical hydraulic fracture and randomly oriented natural fractures. It computes the stresses acting on the natural fractures induced by the three in-situ principal stresses plus an actively growing hydraulic fracture. It shows that as the inclination of the natural fracture with respect to the vertical plane increases, the chances of its activation by a hydraulic fracture diminishes, with a horizontal natural fracture having a very low chance of activation. Natural fractures are divided into three general groups; open, closed unbonded, and closed bonded. Activation of each of these general groups are reviewed separately and factors that control the process are identified and discussed. Paper shows that when an advancing hydraulic fracture intersects an open natural fracture, the initial result is local fracture arrest. Next, the hydraulic fracture grows three-dimensionally around the natural fracture and joins it from the opposite side. Continuous three-dimensional growth of the hydraulic fracture increases the fluid pressure inside the open natural fracture and can cause initiation of a branch fracture from one or more of its extremities. The net result is creation of a main fracture together with a set of smaller and very narrow offset branch fractures. An unbonded closed natural fracture has no tensile strength and can open when exposed to a tensile normal stress acting on its face. Intersection of these types of natural fractures by a hydraulic fracture can have one or more of three different consequences; crossing through, limited natural fracture opening in mixed mode (tensile plus shear) and extension, or creation of offset parallel branches. The conditions leading to each of these are identified and discussed. Bonded closed natural fractures can activate if the magnitude of the tensile stress induced on its face by the advancing hydraulic fracture causes the normal stress on its face to exceed its bond strength. In this situation the activation of the natural fracture will be in mixed more (tensile plus shear). However, under most actual situations hydraulic fractures are more likely to cross through them. The important parameters controlling activation of natural fractures are their inclination angle with respect to the hydraulic fracture and the three in-situ principal stresses, the magnitude of fluid pressure inside the fracture relative to the difference between the two horizontal principal stresses, and their size and location.

In this work we study the effect of fluid viscosity on hydraulic fracturing initiation and near-wellbore propagation on block samples of tight shales subjected to representative effective in-situ stress conditions. Combined analysis of acoustic emission, ultrasonic transmission and volumetric deformation indicates that the viscosity of the injected fluid had a strong influence on hydraulic fracturing initiation, fracture propagation and fracture geometry. Injection of high viscosity fluid into the stressed tight shale resulted in fracture initiation at a bore pressure higher than the overburden stress and occurred significantly earlier than the borehole breakdown pressure. After initiation, the hydraulic fracture propagated symmetrically from the borehole in the direction parallel to the maximal horizontal stress, causing significant volumetric deformation of the rock. In the case of injecting a low viscosity fluid into the stressed block, fracture initiation occurred at a borehole pressure significantly lower than it was required with the higher viscosity fluid, and occurred almost simultaneously with the bore pressure breakdown. AE measurements during hydraulic fracturing allowed us to estimate that the average speed of hydraulic fracture propagation was approximately thousand times faster for the low viscosity fluid than for the high viscosity fluid.

Hydraulic fracturing is recognized as a successful stimulation technique for enhanced hydrocarbon recovery from unconventional tight reservoirs. Technological advancement in directional drilling has led the petroleum industry to drill arbitrarily oriented wellbores for exploitation of reservoirs, which otherwise could not be economically produced. Prediction of fracture initiation from such wellbores is therefore essential for petroleum industries to undertake efficient hydraulic fracturing stimulation tasks. In a hydraulic fracturing process, fluid is injected under pressure through the wellbore in order to overcome native stresses and to cause failure of rocks, thus creating fractures in a reservoir. These fractures create a passage through which hydrocarbon flows into the well from the shale formation. Based on the superposition principle and elasticity theory, a total stress field mathematical model while staged fracturing for horizontal well is abstractly presented in this paper, considering systematically influencing factors such as wellbore pressure, in-situ stress distribution, seepage effect of fracturing fluid, and induced stress produced by hydraulic fracture. The law of initial and subsequent fractures initiation is studied. The results show that the initial fracture initiation is affected by the wellbore azimuth angle, and it is easy for transverse fractures to form when the minimum in-situ horizontal stress along the wellbore direction. The stress distribution around wellbore is influenced by induced stress field, and when the initial fracture height is constant, the effect decreases gradually along wellbore direction until the combined stress field tends to the in-situ stress field. In a certain position from the initial fracture, the bigger the fracture height, the greater the induced stress, and in particular, the influence on induced stress along the wellbore direction is more obvious. Induced stress can increase subsequent fractures initiation pressure, whose level will reach 30% and increase as the fracture height increases. When fracture height is constant, the increase level of initiation pressure decreases rapidly with the increase of fracture spacing. There is well coincidence between computational solution and measured result. Results from the analytical and numerical models used in this study are interpreted with a particular effort to enlighten the causes of abnormally high treating pressures during hydraulic fracture treatments, as well as engineers study recovery techniques.

In order to investigate the effect of different perforation angles (the angle between the perforation direction and the maximum horizontal principal stress which is also called the preferred fracture plane (PFP)) on the fracture initiation and propagation during the hydraulic fracturing of highly deviated well, laboratory experiments of the hydraulic fracturing of the BZ25-1 oilfield had been carried out on the basis of non-dimensional similar criteria by using 400mm3 cement cubes. We built the geometric model of the hydraulic fracturing fractures which considered the influences of the wellbore azimuth (the angle between the wellbore axis and the PFP), the perforation angle and the well deviation. The results showed that: the perforations in the PFP produce plane fracture; the fractures initiate from the perforations at the upper side of the well hole and then turn to the PFP when the perforation angle is 45°; when the well deviation angle and the perforation angle are both larger than 45°, the fracture initiates difficultly from the perforations at the lower side of the well hole, and multi-fractures easily initiate; when the perforation angle is 90°, multi-fractures initiate, such as twisting fracture, plane fracture, horizontal fracture and T-shape fracture, in addition, the fracture cannot initiate from the perforation tunnels; the larger the well deviation angle is, the easier is the multi-fractures initiation. Moreover, it is easier to result in micro-annulus which makes the fractures more complicated during the hydraulic fracturing of highly deviated well when the perforation angle is not along with the PFP. Oriented perforating technology should be applied in highly deviated well to obtain the big single plane fracture.

According to the theory of plane mechanics involving the interaction of hydraulic and natural fractures, the law of hydraulic fracture propagation under the influence of natural fractures is verified using theoretical analysis and RFPA2D-Flow numerical simulation approaches. The shear and tensile failure mechanisms of rock are simultaneously considered. Furthermore, the effects of the approach angle, principal stress difference, tensile strength and length of the natural fracture, and elastic modulus and Poisson’s ratio of the reservoir on the propagation law of a hydraulic fracture are investigated. The following results are obtained: (1) The numerical results agree with the experimental data, indicating that the RFPA2D-Flow software can be used to examine the hydraulic fracture propagation process under the action of natural fractures. (2) In the case of a low principal stress difference and low approach angle, the hydraulic fracture likely causes shear failure along the tip of the natural fracture. However, under a high stress difference and high approach angle, the hydraulic fracture spreads directly through the natural fracture along the original direction. (3) When natural fractures with a low tensile strength encounter hydraulic fractures, the hydraulic fractures likely deviate and expand along the natural fractures. However, in the case of natural fractures with a high tensile strength, the natural fracture surface is closed, and the hydraulic fracture directly passes through the natural fracture, propagating along the direction of the maximum principal stress. (4) Under the same principal stress difference, a longer natural fracture corresponds to the easier initiation and expansion of a hydraulic fracture from the tip of the natural fracture. However, when the size of the natural fracture is small, the hydraulic fracture tends to propagate directly through the natural fracture. (5) A smaller elastic modulus and larger Poisson’s ratio of the reservoir result in a larger fracture initiation pressure. The presented findings can provide theoretical guidance regarding the hydraulic fracturing of reservoirs with natural fractures.

Hydraulic fracturing is an important and prevalent process both in the natural environment and industrial applications. At the same time, field hydraulic fracturing tests data provide valuable information regarding the mechanical and hydraulic behaviours of the reservoir formation. By history-matching the field bottom-hole-pressure versus time curve from hydraulic fracturing tests, a set of field-validated geomechanical models can be obtained, which is an important asset for any further works on utilizing geomechanics to enhance the injection and production performance. This paper presents a 3-dimensinal finite element model for history matching the complete bottomhole- pressure versus time curve generated during hydraulic fracturing tests considering the injection rate as input. To stimulate the hydraulic fracturing process in unconsolidated sands formation, a poro-elasto-plastic constitutive model together with a strain-induced anisotropic fill permeability model are formulated and implemented into a 3D finite element geomechanical simulator. Unlike the conventional simulation of hydraulic fracturing in hard rock, hydraulic fracture in unconsolidated sands reservoir is stimulated as a large area of dilation zone or a net or micro-cracks, inside which the effective stresses are low and hydraulic conductivities are high. It is shown the proposed numerical model can successfully capture the hydraulic fracture initiation and propagation in unconsolidated sands formation and matches the field pressure versus time curve very well. Introduction Hydraulic fracturing can be broadly defined as a process by which a fracture initiates and propagates due to hydraulic loading (i.e., pressure) applied by a fluid inside the fracture(1). Fractures in the earth's crust are desired for a variety of reasons, including enhanced oil and gas recovery, re-injection of drilling or other environmentally sensitive wastes, measurement of in situ stresses, geothermal energy recovery, and enhanced well water production(2). Although hydraulic fracturing in hard rock has been comprehensively studied both experimentally and numerically, some fundamental mechanisms of hydraulic fracturing in unconsolidated sands have not been well understood. Experimental data clearly show that fracturing in unconsolidated sands is significantly different than those encountered in hard rock. Unconsolidated sands do not exhibit elastic-brittle behavior. In addition, unconsolidated sands have very low tensile and shear strengths at low effective stresses as well as relatively large fluid leak-off(3–5). Based on other researchers' work(3–7) on the fundamental mechanisms of hydraulic fracturing in unconsolidated sands, this paper presents the constitutive modeling and numerical simulation of hydraulic fracturing in unconsolidated sands within the framework of continuum mechanics. Numerical experiments show that this approach has special advantages in numerical modeling of large scale field problems, such as the disposal of waste cutting fluid, and micro/mini fracture tests in unconsolidated sands formation. Even in its most basic form, hydraulic fracturing in unconsolidated sands is a complex process to model, as it involves the coupling of at least three processes:the solid matrix deformation and failure induced by the pore fluid pressure;the flow of fluid within the fracture and solid matrix; andthe fracture initiation and propagation after the failure of formation.

Fracture behaviour and seismic response of naturally fractured coal subjected to true triaxial stresses and hydraulic fracturing

SummaryIntegrated modeling of refracturing is a comprehensive and complex task for engineers involved in field development, especially in previously developed mature fields. The modeling process requires consideration of numerous factors to accurately predict fracture propagation patterns during refracturing and production. During the initial fracturing process, hydraulic fractures generate an altered induced stress field. Later, during the post-fracturing production process, hydrocarbon extraction causes formation pore pressure depletion, leading to further alterations in the stress field. However, due to the complexity of these phenomena, most existing workflows simplify the coupled simulation problems of stresses at different stages in the modeling process. Consequently, this often results in questionable hydraulic fracture geometries during refracturing and suboptimal refracturing designs. The goal of this study is to develop a novel integrated workflow for refracturing, specifically tailored for complex fracture networks in tight oil reservoirs. This model incorporates the hydraulic fracture propagation process during the initial fracturing and dynamic stress changes during the initial production process. It employs artificial intelligence algorithms to calibrate the wellhead treating pressure using a physics-based model, enabling a better understanding of the initial fracturing fracture geometries. The production history match is then conducted based on the initially calibrated hydraulic fracture geometries, preserving the precision of the original fracture geometry. In addition, geomechanics modeling is conducted to obtain dynamic stress changes during the initial production process. For the refracturing design, the fracture propagation model for the refracturing process is later conducted on the depleted stress field. Following a 240-day period after refracturing, the production history is matched using an artificial intelligence–assisted reservoir simulator. Our results indicate that, due to prolonged production, significant changes occur in the stress field during the initial development period, with an average horizontal stress deviation angle of approximately 35° in the near-well zone. With the combined influence of the changing stress field and natural fractures, refracturing results in longer and more complex hydraulic fracture geometries, ultimately increasing individual well production.