ABSTRACT: In computational simulations of drilling mud flow in fractured formations, consideration of interactions between the fracture networks and the porous rock requires an appropriate coupling procedure from the local fractures to the scale of typical finite elements in poromechanics problems. A hydro-mechanically coupled model is developed in this paper to characterize drilling mud flow in naturally fractured formations. Especially, the mud leak-off from fractures into the matrix is described by a new method. The finite element equations are derived for the model and integrated over time. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The resulting discrete equations are non-linear due to the non-linearity of the leak-off effect, and the Newton–Raphson method is used to solve the nonlinear equations. Simulation results show that the fracture deformation and leak-off effect both have significant impacts on mud loss volume, especially the expansion of the fracture network due to mud invasion can further increase the cumulative mud loss volume. The presented model improves the accuracy of the mud loss prediction, and thereby results in a more realistic characterization of naturally fractured reservoirs.

ABSTRACT: In Brazil, the discovery of carbonate reservoirs in the pre-salt fields has raised several engineering challenges, particularly in the oil production forecasting. Carbonate reservoirs are much stiffer than conventional reservoirs. Consequently, under certain levels of deformation, fractures can develop, reactivate and/or propagate, forming complex fracture networks. Indeed, the enhanced permeability found in pre-salt reservoirs has been directly associated with the presence of hydraulically active fractures, providing those fields with high production capacity. However, the pressure changes induced during the production phase can affect the geomechanical and hydraulic behavior of such fractures. From a geomechanical point of view, the stresses induced on the fracture surfaces can trigger processes such as opening and closure of the fractures. In turn, changes in fracture apertures can alter the flow process along and across fractures. In order to predict those phenomena, this work presents a numerical model of oil production in a naturally fractured reservoir. For such, we have implemented a methodology based on zero-thickness interface elements for explicit fracture representation in an in-house finite element simulator. In order to represent the geomechanical behavior of the fractures, Mohr-Coulomb criterion is adopted together with a traction-separation law based on the model proposed by Bandis. Parallel plate law describes the longitudinal fluid flow along the fracture. According to the results, the stress changes that develop particularly around wells can affect significantly the oil production during the lifecycle of a naturally fractured reservoir. Furthermore, these results may contribute to a better understanding of the fracture behavior and can help to optimize reservoir production and well performance.

ABSTRACT: This work presents a numerical technique capable of handling evolving fractures in rocks that allows extending, in a simple manner, standard finite element programs developed for geological (continuum) media to deal with the presence of discontinuities. The proposed mesh fragmentation technique consists in introducing especial (high-aspect ratio finite elements) in- between the regular (bulk) finite elements. This methodology has been successfully used to model both, drying cracks in soils and fractures in concrete structures. The proposed approach is fully coupled and has been implemented in the finite element program CODE_BRIGHT, which was especially developed to tackle coupled thermo-hydro-mechanical problems in geological media. The paper presents the main components of the proposed approach and its implementations in CODE_BRIGHT. It also discusses the main advantages and shortcomings associated with this technique. The proposed method is verified and validated using available analytical and numerical solutions associated with the problem of hydraulic fracturing in rocks. The technique is also applied to solve engineering problems involving the formation and propagation of discontinuities in geo-materials. A very satisfactory performance of the proposed method is observed in all the analyzed cases.

ABSTRACT: In CO 2 storage reservoirs with poor-to-marginal permeability, it could be beneficial to stimulate the reservoir by generating hydraulic fractures to improve injectivity. Compared with injection from a traditional line source in an unstimulated reservoir, injection through a fracture can substantially increase the contact area with the reservoir. However, the poroelastic effect, namely the loss of effective compressive stress as pore pressure propagates into the rock from the fracture, could make the fracture close over time, thereby either demanding continuously increasing injection pressure or rendering the injectivity enhancement short-lived. In this work, we develop a fully coupled thermo-hydro-mechanical (THM) model that couples multiphase flow of supercritical CO 2 and reservoir brine, rock and fracture deformation, and thermal contraction. We use this model to study the parameters affecting the poroelastic sustainability of a hydraulic fracture within the CO 2 storage reservoir rock. The results show that the rock's Biot coefficient has a remarkable effect on the outcomes.

ABSTRACT: Experimental studies on fracture flow processes are vital to understand the dependence of fracture permeability on various complex processes. A key parameter in such experiments is the fracture aperture, which can be determined using light transmission techniques when using transparent fracture models. For this, scientific-grade monochrome cameras are used to record light intensity under different conditions. The output data of scientific cameras is linearly related to the radiance scene, which allows one to do quantitative analysis using such data. On the contrary, consumer-grade digital (CGD) cameras usually output nonlinear color images (e.g. JPG or TIFF files), which are not suitable for most scientific uses. In this paper, we outline an image analysis procedure to use CGD cameras for light intensity measurements. We demonstrate that the direct use of raw data from such cameras is adequate for scientific quantification and prevents the introduction of artefacts from further image processing that usually occurs within the built-in software of most cameras.

ABSTRACT: In this paper, we present a new parameterization of the hydraulic fracturing modeling which allows the use of a coupled flow/geomechanics reservoir simulator to predict fracture propagation. To do this we used our in-house reservoir simulator (OpenSim) which implements a fully coupled flow/geomechanics formulation, where the fluid-flow is modeled following conventional black-oil model. To simulate the hydraulic fracturing process, we define a critical strain to allow the fracture to propagate which can be conceptually related to the stress intensity factor. The permeability of fractured blocks is related to its strain assuming that the deformation is associated with the presence of a local fracture. Once a given block reaches the critical conditions, both its mechanical properties and permeability/strain behavior are modified to mimic that of a fractured block. Leak-off is naturally included in our model as the fluid transfer between fractures and matrix is ruled by the usual flow parameters (permeability, pressure, and saturation). Proppant transport is not considered explicitly, however, the water saturation distribution can be used to build a proxy for the proppant distribution. We present results for realistic models and run sensitivities to the different model parameters.

ABSTRACT: Geothermal energy from naturally or hydraulically fractured reservoirs is extracted by cold water injection and circulation using injection and production wells. Well spacing, well pattern, and injection-extraction rate schedule are among the most important factors that control the efficiency of heat extraction. Aside from the heat transfer aspect of the process, the hydromechanics of the circulation and fracture stability also needs be considered. Previous work and analysis has been mostly restricted, assuming stationary fractures without the possibility of fracture propagation during the circulation period. This paper addresses these issues by focusing on the hydro-mechanical aspect of the circulation and the possibility of natural fracture propagation in geothermal systems with reference to the planned “EGS Collab” project’s circulation experiment. A fully coupled 3-dimensional model is developed for this study using the displacement discontinuity method along with a finite difference scheme. Fracture propagation is incorporated into the model by enforcing the critical stress intensity condition at the fracture boundary. Simulation results indicate that natural fracture propagation is likely to occur during circulation. Furthermore, fracture opening variation by propagation, in turn, controls the hydro-mechanics of the circulation as it affects the fracture conductivity and the production rate.

ABSTRACT: The cleat or natural fracture system is a dominant factor controlling the permeability of coal seams. Since coal permeability is sensitive to stress, fundamental understanding of gas flow in coal fracture networks and permeability change with varying effective stress is necessary in the processes of CBM production. Considering the fracture aperture, roughness and density, coal fracture networks are reconstructed on the basis of the Voronoi tessellations. Based on the rock elastic theory, the stress-strain model of reconstructed coal fracture networks under stress condition is established. Then the lattice Boltzmann method (LBM) is applied to simulate fracture flows and to predict the associated permeability. For comparison purposes, gas permeability and porosity of coal samples with artificially generated fractures are measured under varying effective stress. Based on the experimental results and the Walsh model, fracture width and roughness are estimated. The predicted stress-dependent permeability in a single coal fracture by LBM simulation is in acceptable agreement with laboratory measurement. Furthermore, the stress-dependent permeability in fracture networks is investigated. The present study provides a promising approach to predict the associated permeability and transport characteristics in coal fracture networks.

ABSTRACT: The hydraulic and mechanical behaviors of a rough fracture largely depended on the fracture geometries formed between two rough surfaces, especially for deformable fractures under the normal stress. To investigate the variations of fracture geometric characteristics with normal stresses, a total of six fractured rock specimens, including cubic cement and cylindrical sandstone specimens with different grain sizes, were chosen to conduct the normal compression tests. The 3D scanner was used to capture the surface characteristics of the rough fracture, and the point-cloud data matching method was adopted to calculate the fracture apertures distribution variation with increasing normal stress. Then, the geometric characteristics of the fracture, including the areas of distributions of the contact and interconnected void, and the size of apertures of the interconnected voids, were determined. Test results shows that the required normal stress to achieve the maximum facture closure are different for various specimens, which are largely related to the joint compression strength and the matching degree between two surfaces. Besides, the distribution of the void and contact regions shows heterogeneous under different normal stress, and the frequency of apertures variation approximately follows a normal distribution function. With the increase of the normal stress, the contact area ratio shows a rapid increase at low stress and then tend to stable at higher level, while the variation of the interconnected void area ratio is just the opposite. Meanwhile, both the effective mechanical and mechanical aperture show rapid decrease at low stress and then tend to stable at high stress,. The gap between these two apertures are larger for high normal stress than for low normal stress, mainly due to the rapid increase of the isolated void spaces at high stresses. The test results is helpful to the knowledge of the hydro-mechanical behavior of the rough fracture.

ABSTRACT: In this study, an improved version of the Simplified 3D Displacement Discontinuity Method (S3D DDM) is introduced which can be used to simulate single and multiple fracture problems in a layered formation. The developed model is then used to predict the geometry of hydraulic fractures, and to characterize the stress shadowing effect between fractures with variable heights and vertical offsets. Similar to the original S3D DDM, 3D correction factors are used to calculate the normal and shear displacements along the fracture length. For this improved version, the original 3D correction factors are modified to account for fractures with nonuniform height along the length direction. A stress correction factor is employed to calculate the influence of stress contrast between layers on fracture opening. Static simulation results from the improved model compare favorably with reference analytical solutions for penny-shaped fractures and with fully 3D numerical solutions. While the fully 3D model requires discretization in both lateral and vertical directions, the simplified model requires only a single row of elements in height, resulting in considerably lower computation time and memory utilization without a loss of accuracy.

ABSTRACT: Laboratory tests were conducted in this study in order to examine the changes in aperture of an open single fracture in a granite core over time, under confining pressures of 1-3 MPa and temperatures of 20°C and 60°C. During the experiment, the fracture aperture was monitored with X-ray CT. For a quantitative evaluation of the fracture aperture, the CT images were processed with image co-registration by the Scale-Invariant Feature Transform (SIFT) method and fracture surface extraction using the Canny edge detection algorithm. Based on the fracture surface geometry data extracted from the CT images, the aperture and contact ratio were calculated and compared. The effect of the confining pressure and temperature on the aperture and contact ratio was not clear from the results. However, the trend of the fluctuation in the aperture and contact ratio over time was found to be consistent with the trend of the fluctuation in permeability.

ABSTRACT: Recently, water injectivity index was found to be huge different between process of hydraulic fracturing and long-term water injection during enhanced geothermal energy development. This discrepancy is due to improving the conductivity of natural fractures in geothermal reservoirs is essentially different from traditional hydraulic fracturing in conventional oil and gas reservoirs. The effective conductivity aperture of natural fractures becomes an important parameter to characterize fracture conductivity in geothermal reservoirs, which is affected by initial fracture roughness, shear-induced dilation, thermoelasticity as well as chemistry of hot dry rocks. A coupled thermal-hydro-mechanical-chemistry model was developed to analyze the composition of the total hydraulic aperture and primary role in different fracture section. The result shows that thermal effect plays a major role in increasing the conductive aperture in the near borehole area, which is also an effective way to reduce the surface pumping pressure at the hydraulic fracturing site. However, relative to thermal induced aperture, shear dilation remains stable along the fracture and increases with the injection pressure. The effect of chemical dissolution/precipitation of short-term hydraulic fracturing on fracture aperture is too small to be negligible. Therefore, Long term high pressure injection is the best way to enhance the conductivity of several hundred meters of underground water circulation and heat exchange fracture network.

ABSTRACT: In measuring rock fracture apertures from X-ray CT images, a binarization method has generally been used to separate the air void parts (fractures) from the rock parts. However, reasonable thresholding is often an essential problem in this method, especially for heterogeneous rock materials. This paper suggests a new method for detecting fracture surfaces from CT images using an edge detection algorithm that is known well in the field of image processing as Canny edge detection. Applying this edge detection method to the CT images of a single granite fracture, 15 mm in diameter and 30 mm in length, this study successfully measures the fracture surface geometry, the aperture distribution, and the contact ratio.

ABSTRACT: We improved our thermal-hydraulic-mechanical-chemical (THMC) simulator to predict the long-term permeability change of the fractured rocks. The model evaluates the influence of the geochemical reaction on the evolution of the permeability in fractured rocks by considering pressure solution in detail. Pressure solution that occurs at both grain contacts and contacting asperities within fractures was incorporated in the model. By using the developed THMC numerical model, long-term prediction of rock permeability was conducted by replicating the subsurface environment near the radioactive waste repository. As a result of the analyses, the permeability decrease by two orders of magnitude smaller than the initial value occurs due to pressure solution at contacting asperities within fractures in the EDZ area. In carrying out radioactive waste disposal, it is apparent that pressure solution within the fractures has significant impact on minimizing the increase of the permeability in EDZ area. 1. INTRODUCTION

ABSTRACT: In fluid driven fractures, energy is dissipated by creating new fracture surfaces and overcoming viscous resistance to fluid flow. It is known that when fluid driven fractures propagate in a rock with a finite amount of resistance to fracture, the toughness (? 1/2 ) and viscosity (? 2/3 ) solutions for the fracture aperture co-exist near the fracture tip. Depending on the ratio of viscous dissipation and fracture resistance, the region for the validity of each tip asymptote varies. In this paper, we developed a 2D displacement discontinuity based hydraulic fracture propagation model for multiple large-scale hydraulic fracture propagation while taking into account the multi-scale nature of the fracture tip. The numerical model is capable of distinguishing between viscosity and toughness dominated propagation regimes, and takes into account their corresponding solutions as boundary conditions near the fracture tips. We provide numerical examples of large-scale multiple fracture propagation in a rock with finite fracture toughness using injection fluid viscosities range from 1-1000 cP. The results include fracture geometry, aperture distribution and regime of fracture propagation. To study the effect of fracture tip asymptote on the resulting fracture cluster, we approximated multi-scale fracture tip asymptotes with toughness asymptote showing that for a rock with finite toughness and for the range of fluid viscosities considered, the toughness solution provides sufficiently accurate results irrespective of the regime of fracture propagation.

ABSTRACT: Rock fractures in the subsurface have the potential to act as fluid flow pathways but the permeability of existing, new, or future in-situ rock fractures is difficult to characterize. We perform triaxial direct shear experiments to evaluate the permeability potential of freshly created fractures as a function of stress/depth using specimens of carbonate-rich Marcellus Shale. Applied confining stress ranged from 2 to 30 MPa, specimens were 25 mm diameter and 25 mm length, shearing displacement of at least 2 mm was imposed, and measured permeability ranged between 10 -3 and 10 4 mD as dependent on stress and fracture conditions. Simultaneous X-ray video and computed tomography were used to directly measure fracture displacement and apertures. Results show that the stress at which fractures form is likely the most significant factor controlling fracture permeability, with higher stresses causing significant 2 to 4 orders of magnitude permeability reduction. The effect of creating fractures at high stress on permeability reduction was significantly stronger than the effect of increasing the confining stress on an existing fracture. Results included analysis of transient fracture permeability following renewed shear displacement, a process which resulted in rapid permeability enhancement followed by a slower decay in permeability.

ABSTRACT: Water-based fracking fluids are currently used to enhance the gas production from unconventional gas reservoirs, while the formation damage due to the interaction between rock matrix and residual water significantly reduce the pore space available for gas movement. In this paper, the effect of different fracturing fluids on fracture permeability is investigated using the same fractured siltstone sample in five rounds of cycling test (CO 2 -CO 2 -CO 2 -water-CO 2 ). The experimental results reveal that the maximum confining pressure dominated fracture permeability. The fracture permeability for CO 2 at 10MPa confining pressure decreased by around 75% after applying 40MPa confining pressure. After water flooding in the fourth round, the fracture permeability for CO 2 was considerably reduced by around 70-85% compared with that in the second cycling test, and the influence of water flooding was much stronger at lower CO 2 injection pressure. The experimental results showed that the fracture permeability for gas reduced significantly after water flooding due to formation damage. Thus, liquid CO 2 is much more suitable than water as fracturing fluid for clay-abundant unconventional gas reservoirs.

Abstract: This study presents three dimensional (3D) analyses of a fracture network in an Enhanced Geothermal System (EGS) with special emphasis on the role of hydraulic fracture/natural mechanical interactions and coupled thermo-poromechanical processes. The behavior of the system is modeled by coupling a thermo-poroelastic displacement discontinuity (DD) method (for fracture opening and shear, fluid and heat diffusion in the reservoir matrix) with a finite element method (for fluid flow and heat transport inside the fractures). The nonlinear characteristics of fracture opening and shear deformation are taken into account. The resulting method is then used to simulate an injection/production processes into/from a synthetic fracture network consisting of a major fracture intersected by a set of smaller natural fractures. Injection/production into/from the fracture network results in gradual shearing of the fractures that impacts the thermo-hydro-mechanical characteristics of the fracture system. It is also shown that the early micro-seismic events can be associated with fracture slip on smaller connected fractures due to thermal perturbation. Continued injection leads to stress intensity conditions favorable for fracture propagation in shear and tensile modes , which could increase the reservoir surface area and further contribute to seismicity. Introduction Design and management of enhanced geothermal system (EGS) and hydrothermal reservoirs can benefit from simulation of coupled fracture deformation and fluid flow - since interactions among fluid and heat flow, and the mechanical response of the fracture and matrix impact reservoir permeability variations and occurrence of seismicity. The coupling between these processes during injection/extraction can be taken into account using linear theory of thermo-poroelasticity. Often, heat transport in a reservoir is dominated by advection. However, when the rock matrix permeability is low (Delaney, 1982) and fluid flows mainly within deformable fractures or a fault, conductive transport in the rock matrix leads to important phenomena related to coupling between temperature, pore pressure, and stress that may result in delayed rock matrix and/or natural fracture failure, potentially producing delayed seismicity. Although the thermo-poroelastic constitutive equations are linear, analytical solutions can be found only for relatively simple geometries and processes (e.g., Tao and Ghassemi, 2010; Ghassemi et al. 2008; Li et al. 1998; Kurashige, 1989) and the solution of problems such as injection /extraction into a deformable fracture network requires numerical modeling even in two dimensions.

Abstract: A three-dimensional finite-element model for hydraulic fracturing has been developed that accounts for local thermal non-equilibrium between the injected fluid and host rock. The model also accounts for fluid flow and heat transfer within the fracture, heat conduction through the solid rock, deformation of the rock, and propagation of the fracture. Fluid flow through the fractures is modeled using the lubrication equation, and is fully coupled to the thermoelastic mechanical model through the pressure exerted by the fluid on the fracture walls, as well as by ensuring compatibility of fracture volumetric strains. Fractures are discretely modeled using triangular surfaces in an unstructured three-dimensional mesh. The growth of fractures is modeled using linear elastic fracture mechanics (LEFM), with the onset and direction of growth based on stress intensity factors that are computed for unstructured triangle-tetrahedral meshes. The model has been verified against analytical solutions available in the literature for penny-shaped (3D) fractures. A radial hydraulic fracture from a horizontal well is simulated to investigate the effects of the thermal non-equilibrium between the fracturing fluid and the host rock. For the case of very low matrix rock permeability, results show very little influence of thermal effects on the creation of hydraulic fractures. Introduction In hydraulic fracturing, the fracturing fluid is commonly not in thermal equilibrium with the solid medium, leading to heat transfer between the fluid inside the fracture and the host rock, through the fractures surfaces. Natural and man-made examples are the creation of several-kilometers-long magma-driven dikes (Spence and Turcotte, 1985) and hydraulic fracturing of gas shale (Tran et al., 2013), respectively. Hydraulic fracturing has attracted a great deal of attention over the past decades. Many analytical and semi-analytical solutions have been developed to quantify hydraulic fracturing variables of interest, such as injection pressure, fracture aperture and fracture length (cf. Adachi et al., 2007). These semi-analytical solutions provide the foundation for hydraulic fracturing design (e.g. Cleary, 1980; Cleary et al., 1988). These solutions are constructed by combining the equations for laminar flow through the fracture with elastic deformation of the adjacent rock. Fluid flow through the fracture is commonly modelled using lubrication theory (Batchelor, 1967) for an incompressible Newtonian fluid obeying the cubic law, while fracture aperture is calculated using linear elasticity in conjunction with Linear Elastic Fracture Mechanics (LEFM) for the computation of the mode I stress intensity factor at the fracture tip (Geertsma and de Klerk, 1969; Spence and Sharp, 1985). The lubrication equation is derivable from the general Navier-Stokes equation for the flow between two parallel plates (Zimmerman and Bodvarsson, 1996). Heat conduction between the fluid inside fracture and surrounding rock solid has been of particular interest in many cases including magma-driven fractures (Spence and Turcotte, 1985), hydraulic fracturing of wells (Wang and Papamichos, 1999), and hydraulic fracturing of gas shale (Tran et al., 2013; Enayatpour and Patzek, 2013). Rock temperature at the surfaces of the hydraulic fracture is often considered constant and equal to the temperature of the injected fluid (Tran et al., 2013; Abousleiman et al., 2014). However, such an assumption does not satisfy conservation of energy, and does not account the fact that heat exchange between the fracturing fluid and the rock gradually causes the fracturing fluid to thermally equilibrate with the matrix rock. Consequently, an unrealistically large effect due to thermal non-equilibrium is predicted by such approaches.

Abstract: The paper presents three-dimensional coupled poroelastic analysis of multiple fracture propagation from horizontal wells. A 3D numerical model is developed using a combination of displacement discontinuity method for the hydro-mechanical response of porous rocks and finite element method for the fracture fluid flow simulation. The fracture propagation is analyzed based on the linear elastic fracture mechanics approach. The reservoir rock mass is assumed homogenous and isotropic with constant poroelastic physical properties and the fracturing fluid is assumed incompressible and shows Newtonian behavior. Numerical examples of multiple fracture propagation from the horizontal wells are presented. The results show that along with reservoir rock properties and in-situ stress state, the spacing among fractures has a strong influence on the evolution of multiple fracture propagation. Finally, simulation of refracturing of un-depleted zones between closely-spaced horizontal wells is presented. The results demonstrate the change of stresses and pore pressure due to reservoir depletion mainly depends on the stress anisotropy, reservoir poroelastic properties, and the timing of infill well stimulation or production duration. Introduction Horizontal well stimulation usually involves creating cluster of multiple fractures in stages along the wellbore using different well completion techniques. These multiple fractures stages generate large contact surface area with the reservoir which results in increase of permeability and hence, increases the oil and gas production, and the heat energy production in case of the geothermal systems. The multistage fracturing of a single or multiple horizontal wells is usually carried out either in simultaneous or sequential manner. The multiple fracturing creation process is controlled by the mechanical interaction or “stress shadowing” among multiple fractures, in-situ stress anisotropy, and the net applied fluid pressure. The term stress shadow represents variation of stresses in the region surrounding a pressurized fracture, which is a function of applied fluid pressure. The spacing between the fractures and the horizontal wells, and the in-situ stress contrast play an important role in the mechanical interaction (Sesetty and Ghassemi, 2015 & 2016). Several numerical models have been developed to simulate hydraulic fracturing process in the oil and gas reservoirs based on the elastic rock mass assumptions. The poroelastic effects on the hydraulic fracturing process are generally ignored. The rational is that the hydraulic fracture simulation time-scale is such that these effects have not time to develop or the magnitude of these effects are small enough to be neglected. However, in case of low permeability reservoirs (e.g., tight oil and shale gas reservoir), where hydraulic fracturing is carried out using relatively low viscosity fluids and high injection rates, the coupled poroelastic phenomenon such as changes in the rock deformation due to diffusion of the pore pressure and pressure induced by mechanical deformation of the solid rock need to be incorporated for better understanding of the fracturing mechanism which often involves rock failure and/or reactivation of natural fractures. These poroelastic effects on the hydraulic fracturing process are included using the back-stress and back-pressure concept (Cheng and Detournay, 1988; Vandamme et al., 1989; Vandamme and Roegiers, 1990; Clifton and Wang, 1991; Ghassemi and Roegiers, 1996).