Hydrofracture Propagation Research Articles

Height Effect on Interactions between the Hydraulic Fracture and Natural Fractures

Since natural fractures have shorter heights, it is necessary to incorporate the height difference in the mechanical behavior of hydraulic fracture crossing cemented natural fractures at different angles. However, the impact of fracture height growth on the mechanical behavior of intersection of natural fracture and hydraulic fracture is not yet fully understood at present. In this study, we use adaptive cohesive zone methods to investigate the impact of fracture height on the mechanical behaviors of a propagating hydrofracture crossing natural fractures at different intersection angles. The fracture patterns and mechanical mechanisms for crack propagation crossing with cemented natural fractures are discussed. The increase of fracture height could restrain the crack propagation along the southwest orientation of the natural fracture, but it hardly affects the propagation along the northeast orientation of the natural fracture. A lot of bands appear at a relatively larger formation thickness. The stress shadow between adjacent cohesive layers increases as the formation height increases, which could promote crack initiation and propagation between the adjacent joints or natural fractures. The cracking zone is related to the position of the natural fracture or joint sets with respect to the advancing hydrofracture. Key factors, including the formation height, tensile strength of cemented natural fractures, and their intersection angle with the growing hydrofracture propagation, are investigated in details. In addition, the pressure fluctuation frequency increases as the fracture height increases due to the strong hydraulic and natural fracture interaction. This study provides a new perspective for the development of complex fracture network patterns in cemented formations.

Numerical Simulation on Hydrofracture Propagation in Fractured-Vuggy Unconventional Reservoirs

The unconventional reservoirs such as carbonate formation develops complex and diverse storage space structures, and it is composed of large-scale cavity, dissolved vug, and fractures. The carbonate reservoir is highly heterogeneous. Acid fracturing of carbonate reservoir is completed through the complex mechanical mechanism of interaction between vug and hydraulic fracture (HF). We use the equivalent method of reducing the rock strength by acid etching and serious fluid leakoff during interaction of HF and vug to establish a finite element (FE) model of HF propagation during acid fracturing in the fractured-vuggy carbonate reservoir. The model considers the effect of serious fluid leakoff during interaction between HF and vug, mechanism of interaction between HFs and the fracture-vug system, and change in acid etching intensity. Then, we carry out numerical simulation on impacts of injection rate, fluid viscosity, leakoff behavior in fractures and vugs, and natural fracture (NF) approaching angle on HF propagation in acid fracturing and compare the characteristics of injection pressure, fracture pressure, and HF size. It is suggested that the acid fracturing treatment should be operated by increasing the acid solution viscosity to reduce fluid leakoff, injecting fracturing fluid and acid fluid alternatively, increasing injection rate, and injecting fibers and ceramics when small pressure drop occurs during the HF interacts with the fracture-vug. When a large pressure drop occurs, it is suggested that the middle-low viscosity acid be injected at a low rate to etch the carbonate rock and enhance the fracture conductivity. HF propagates under higher pressure when the NF approaching angle is smaller.

Experimental study on hydrofracture propagation through perforated wellbore in naturally fractured Guanyinqiao calcareous mudstone under true triaxial stress

Hydraulic fracturing technology has become successful in enhancing the permeability of unconventional gas reservoirs. However, due to the geological complexity, considerable challenges remain in understanding hydraulic fracturing of calcareous mudstone. In the main production area of shale gas reservoirs in South China, the tight interlayer of Guanyinqiao calcareous mudstone widely spreads in Wufeng-Longmaxi shale, which could heighten the risk of stimulation treatments and hinder fracturing stimulation efficiency. To investigate the characteristics of hydrofracture propagation in naturally fractured Guanyinqiao calcareous mudstone, we conducted a series of fracturing tests through perforated wellbore under true triaxial stresses. The features of fracturing treatment pressure curves, effect of stress difference and natural fracture on hydrofracture geometry, perforations breakdown modes, and the distinction between calcareous mudstone fracturing and shale fracturing were analyzed. It revealed that the breakdown pressure of perforated fracturing was lower than that of the open hole fracturing, and a smaller perforation phase angle and higher horizontal stress difference could facilitate the hydraulic fracture initiation. The natural fractures mainly developed along the bedding plane, which could cause step-over or diversion of hydrofracture at weakly cemented bedding interfaces. When horizontal stress difference increased from 4 MPa to 8 MPa, the propagation orientation of the dominant hydrofracture would change from oblique mode to transverse mode. The rock brittleness and anisotropy significantly influenced fracture geometry. The hydrofracturing in less brittle and anisotropic calcareous mudstone would produce a single dominant vertical hydrofracture, by contrast, multiple hydrofractures were prone to initiate from the perforations at a lower injection pressure in brittle shale. The understanding of hydrofracture propagation through perforated wellbore in calcareous mudstone may provide some basic data for gas reservoir fracturing engineering and academic application.

Interaction between Crustal-Scale Darcy and Hydrofracture Fluid Transport: A Numerical Study

Crustal-scale fluid flow can be regarded as a bimodal transport mechanism. At low hydraulic head gradients, fluid flow through rock porosity is slow and can be described as diffusional. Structures such as hydraulic breccias and hydrothermal veins both form when fluid velocities and pressures are high, which can be achieved by localized fluid transport in space and time, via hydrofractures. Hydrofracture propagation and simultaneous fluid flow can be regarded as a “ballistic” transport mechanism, which is activated when transport by diffusion alone is insufficient to release the local fluid overpressure. The activation of a ballistic system locally reduces the driving force, through allowing the escape of fluid. We use a numerical model to investigate the properties of the two transport modes in general and the transition between them in particular. We developed a numerical model in order to study patterns that result from bimodal transport. When hydrofractures are activated due to low permeability relative to fluid flux, many hydrofractures form that do not extend through the whole system. These abundant hydrofractures follow a power-law size distribution. A Hurst factor of ~0.9 indicates that the system self-organizes. The abundant small-scale hydrofractures organize the formation of large-scale hydrofractures that ascend through the whole system and drain fluids in large bursts. As the relative contribution of porous flow increases, escaping fluid bursts become less frequent, but more regular in time and larger in volume. We propose that metamorphic rocks with abundant veins, such as in the Kodiak accretionary prism (Alaska) and Otago schists (New Zealand), represent regions with abundant hydrofractures near the fluid source, while hydrothermal breccias are formed by the large fluid bursts that can ascend the crust to shallower levels.

The Method to Model Microseismic Events during Hydrofracture Propagation

The physical-and-mathematical model is presented for generation of microseismic events during hydrofracture propagation. Defects (discontinuities) are described using the ESC-model. The formulas are given for the jumps of discontinuities, characteristics of seismic and aseismic events, as well as the seismic moment and seismic magnitude. The algorithm is developed to model microseismic events during hydrofracture propagation by the known geometry and physical properties of the medium as the input data. The calculations are performed for the pseudo-3D and planar models of hydrofracture propagation. It is shown that a majority of events take place at the front of the growing hydrofracture, which agrees with the observations.

Study on microseismic mechanism of hydro-fracture propagation in shale

Microseismic monitoring technology is widely used to evaluate the results of hydraulic fracturing. It is difficult to get unified theoretical understanding because of the complex mechanism of microseismic release. Based on the theory of seismology, the physical simulation experiment and the numerical analysis method are used to study microseismic mechanism from the shale hydro-fracture expanding in this paper. In theory, crack propagation is dependent on the stress distribution of the hydraulic crack tip. The characteristic equation of moment tensor and its eigenvalue are obtained by the inverse method, and the destruction mechanism of the focal point is determined. The basic rule of crack propagation is obtained by the true triaxial water fracturing physical test and Acoustic Emission experiment. The dominant frequency characteristics and the initial motions of AE signal are used to determine the ratio of tensile and shear damage at the focal points. The microseismic wave of focal points is studied by means of horizontal well fracturing numerical simulation. The frequent and energy characteristics of microseismic wave in different positions, different plane, and different direction are obtained. The distribution of microseismic wave is verified by numerical analysis, and the focal mechanism released under hydraulic fracturing is verified. The research results are of great practical significance for the study of shale performance, evaluation of the reconstruction of shale gas reservoir, optimizing the parameters of fracturing and improving the recovery rate.

On the Propagation Path of Magma‐Filled Dikes and Hydrofractures: The Competition Between External Stress, Internal Pressure, and Crack Length

AbstractMixed‐mode fluid‐filled cracks represent a common means of fluid transport within the Earth's crust. They often show complex propagation paths which may be due to interaction with crustal heterogeneities or heterogeneous crustal stress. Previous experimental and numerical studies focus on the interplay between fluid overpressure and external stress but neglect the effect of other crack parameters. In this study, we address the role of crack length on the propagation paths in the presence of an external heterogeneous stress field. We make use of numerical simulations of magmatic dike and hydrofracture propagation, carried out using a two‐dimensional boundary element model, and analogue experiments of air‐filled crack propagation into a transparent gelatin block. We use a 3‐D finite element model to compute the stress field acting within the gelatin block and perform a quantitative comparison between 2‐D numerical simulations and experiments. We show that, given the same ratio between external stress and fluid pressure, longer fluid‐filled cracks are less sensitive to the background stress, and we quantify this effect on fluid‐filled crack paths. Combining the magnitude of the external stress, the fluid pressure, and the crack length, we define a new parameter, which characterizes two end member scenarios for the propagation path of a fluid‐filled fracture. Our results have important implications for volcanological studies which aim to address the problem of complex trajectories of magmatic dikes (i.e., to forecast scenarios of new vents opening at volcanoes) but also have implications for studies that address the growth and propagation of natural and induced hydrofractures.

Experiment and Simulation for Controlling Propagation Direction of Hydrofracture By Multi-Boreholes Hydraulic Fracturing

Hydraulic fracturing has been applied to enhance CBM production and prevent gas dynamical hazard in underground coal mines in China. However, affected by in situ stress orientation, hydrofracture can hardly continuously propagate within coal seam but may easily extend to the adjacent roof-floor strata, causing ineffective permeability enhancement in coal seam and increasing the risk of gas transfinite during mining coal. Thus, it is very necessary to artificially control the propagation direction of hydrofracture and make it well-aligned in large scale in coal seam. In this study, a method for controlling propagation direction of hydrofracture by multi-boreholes is investigated by theoretical analysis, laboratory experiment and numerical simulation. And this is followed by an on-site test in an underground coal mine to verify this method. Firstly, stress intensity factor at the hydrofracture tip is analyzed where pore pressure is taken into consideration. Results show that the pore pressure is able to increase the stress intensity factor and reduce hydrofracture propagation pressure. Based on this, a method of hydraulic fracturing using multi-boreholes to control hydrofracture direction is proposed. Afterwards, laboratory experiments are conducted to explore the impact of pore pressure on hydrofracture propagation. The experimental results agree with the theoretical analysis very well. Later on, a series of numerical simulations are performed to examine the influence of principal stress difference, the angle between assistance drillholes and the maximum principal stress, and the fluid pressure of the assistance drillholes on hydrofracture propagation. Finally, an on-site test in an underground coalmine is practiced where this proposed method is used to enhance the CBM production. Results show the scope of the hydro-fracture resulting from the multi-boreholes hydraulic fracturing method increases 2.7 times compared with that of conventional hydraulic fracturing. And gas production rate also increases 4.1 times compared with that of conventional hydraulic fracturing and 12.3 times compared with direct borehole extraction without fracturing.

A Hybrid Finite Volume and Extended Finite Element Method for Hydraulic Fracturing with Cohesive Crack Propagation in Quasi-Brittle Materials.

High-pressure hydraulic fractures are often reported in real engineering applications, which occur due to the existence of discontinuities such as cracks, faults, or shear bands. In this paper, a hybrid finite volume and extended finite element method (FVM-XFEM) is developed for simulating hydro-fracture propagation in quasi-brittle materials, in which the coupling between fluids and deformation is considered. Flow within the fracture is modelled using lubrication theory for a one-dimensional laminar flow that obeys the cubic law. The solid deformation is governed by the linear momentum balance equation under quasi-static conditions. The cohesive crack model is used to analyze the non-linear fracture process zone ahead of the crack tip. The discretization of the pressure field is implemented by employing the FVM, while the discretization of the displacement field is accomplished through the use of the XFEM. The final governing equations of a fully coupled hydro-mechanical problem is solved using the Picard iteration method. Finally, the validity of the proposed method is demonstrated through three examples. Moreover, the fluid pressure distribution along the fracture, the fracture mouth width, and the pattern of the fracture are investigated. It is shown that the numerical results correlated well with the theoretical solutions and experimental results.

Numerical analysis of the hydrofracturing behaviours and mechanisms of heterogeneous reservoir rock using the continuum-based discrete element method considering pre-existing fractures

The continuum-based discrete element method was applied to probe 3D hydrofracturing behaviours. The interaction between hydrofracturing cracks and pre-existing fractures was modelled. Glutenite, a typical heterogeneous rock, was numerically reconstructed using physical parameter tests, computed tomography and imaging processing methods. The effect of pre-existing fractures on hydrofracture propagation was characterized, and the effects of material heterogeneity and horizontal in situ stress differences on fracturing were characterised using fractal theory. Investigation of hydraulic fracture (HF) propagation in heterogeneous rock, and of the mechanism by which complex hydrofracturing crack networks form through numerical simulation, revealed four typical influencing factors. These four, namely mineral particles, in situ stress difference, natural fracture (NF) density, and NF aperture inside the glutenite, were analysed to determine their effect on the HF propagation pattern, and the mechanism of complex fracture network formation in glutenite was determined. A 3D fractal dimension was proposed to characterize the spatial distribution of complex fracture networks. With increasing aperture and density of NFs, the hydrofracturing crack network becomes more complex. Mineral particles hinder the propagation of HFs; analogously, the higher the volume percentage of mineral particles is; the more complex is the hydrofracturing crack network that forms. The HFs generate and propagate near the bilateral tips of the NFs. The HFs will propagate along the direction of maximum horizontal in situ stress, and they are prone to turn into a single crack with greater in situ stress difference. The 3D fractal dimensions were computed and quantitatively reflected the above phenomena.

The role of rock strength heterogeneities in complex hydraulic fracture formation – Numerical simulation approach for the comparison to the effects of brittleness –

It is imperative to develop deep understanding of the behavior of hydro fracture propagation, in which numerous rock-physics factors could be involved, to manage or control fracturing to form a network of interconnected fluid pathways. Since it is known that the strength heterogeneities of rock mass are one of the factors, we conduct numerical experiments using the discrete element method to estimate how the formation of fractures are quantitatively influenced by the strength heterogeneities in the process of fracture network formation. We first justify the validity to introduce the heterogeneities in the numerical models under an assumption that the microscopic strengths of our numerical models conform to the Weibull distribution, and then the simulation of hydraulic fracturing is conducted. In our heterogeneous models, a complex fracture network growth is induced by branching of micro cracks around the tip of main fracture and pores depending on the uniformness of the surrounding stress field. It is revealed that the complication caused by the strength heterogeneities is quite different from that introduced by the brittleness, although the complication factor is thought directly related to the brittleness in practice in the field. Our results indicate that the effect of the strength heterogeneities of rock should be considered as a key factor of the complication of fracture networks, and the evaluation accuracy could be improved by taking into account the strength heterogeneities of rock.

Speeded simulation of seismicity accompanying mining and hydrofracture

PurposeAt present numerical simulation of seismicity, used in mining and hydraulic fracturing practice, is quite time expensive what hampers its combined employing with observed seismicity in real time. The purpose of this paper is to suggest a mean for drastic speeding up numerical modeling seismic and aseismic events.Design/methodology/approachThe authors propose the means to radically decrease the time expense for the bottleneck stage of simulation: calculations of stresses, induced by a large group of already activated flaws (sources of events), at locations of flaws of another large group, which may be activated by the stresses. This is achieved by building a hierarchical tree and properly accounting for the sizes of activated flaws, excluding check of their influence on flaws, which are beyond strictly defined near-regions of strong interaction.FindingsComparative simulations of seismicity by conventional and improved methods demonstrate high efficiency of the means developed. When applied to practical mining and hydrofracturing problems, it requires some two orders less time to obtain practically the same output results as those of conventional methods.Originality/valueThe proposed improvement provides a means for simulation of seismicity in real time of mining steps and hydrofracture propagation. It can be also used in other applications involving seismic and aseismic events and acoustic emission.

Geometric Heterogeneity of Continental Shale in the Yanchang Formation, Southern Ordos Basin, China

Favorable prospects for the exploration of shale gas have been demonstrated in the Ordos Basin, China. Outcrop and core observations indicate that there are abundant laminas in the shale strata, which exert a great influence on hydro-fracture propagation, gas storage and fluid flow. In this study, the continental shale of the Chang 72 Member, collected from the south of Ordos Basin, was investigated to characterize the geometric heterogeneity. Laminas at multiple scales were observed and measured using conventional logging, borehole TV, core analysis, scanning electron microscopy, and the Particle and Crack Analysis System. These measurement tools correspond to the meter scale, decimeter scale, centimeter scale, millimeter scale and ten-micrometer scale, respectively, with measured thicknesses of 2.26 m, 2.09 dm, 1.70 cm, 1.48 mm and 11.70 μm, respectively. Fractal theory was used to analyze the power exponent distribution of the lamina thickness, with a resulting fractal dimension of 1.06. Finally, a geometric heterogeneity model was proposed for the Upper Triassic Yanchang Formation in the study area and verified by a modeled thickness of 26.30 m for the Chang 72 Member at the 10-m scale. The model facilitates cross-scale analysis and provides parameter guidance for heterogeneity characterization in the numerical simulation and model test of the shale gas reservoir.

Study on the Propagation Laws of Hydrofractures Meeting a Faulted Structure in the Coal Seam

Hydraulic fracturing is an important technique for increasing coal seam permeability and productivity of CBM (coalbed methane). As a common type of faulted structure in the coal seam, the fault has a direct impact on the direction and scope of hydrofracture propagation, weakening fracturing effects. To study the propagation laws of a hydrofracture meeting a fault in the coal seam, based on a two-dimensional model of a hydrofracture meeting a fault, the combined elastic mechanics and fracture mechanics, the propagation mode, critical internal water pressure, and influencing factors were analyzed. A numerical simulation on the propagation laws of hydrofracture meeting a fault was conducted by using the coupling system of flow and solid in the rock failure process analysis (RFPA2D-Flow). The results show that the horizontal crustal stress difference, the intersection angle between hydrofracture and fault plane, and the physical mechanics characteristics of coal-rock bed are the main factors influencing fracture propagation. With a decrease of horizontal crustal stress differences, intersection angle and an increase of roof elasticity modulus, it is easier for the footwall hydrofracture to enter the hanging wall along the bedding plane, forming an effective fracture. When the stress difference is large and the dip angle of fault plane surpasses 45°, the hydrofracture is easy to propagate towards the coal roof and floor by going through the fault plane. At this time, the coal seams of the footwall and the hanging wall should be fractured respectively to ensure fracturing effects, and the support of the roof and floor should be strengthened. The field experiment, theoretical analysis and numerical simulation were consistent in their results, which will contribute to the optimization of hydraulic fracturing and the prediction of hydrofracture in the coal seams containing faults.

Mechanism of Hydrofracture Propagation Control by Non-uniform Pore Pressure Field

Mechanism of Hydrofracture Propagation Control by Non-uniform Pore Pressure Field

A method for hydrofracture propagation control based on non-uniform pore pressure field

Hydraulic fracturing technology, a technique for increasing productivity applicable in low-permeability oil-gas reservoir, has been used in the extraction of coal seam methane in underground coal mines. However, because of the more complex structure of coal seam compared with that of oil-gas reservoir, the hydrofracture propagation can easily extend to roof-floor rocks, limiting the range of permeability and making damages of roof-floor rocks in subsequent coal mining and support difficulty. How to control the hydrofracture propagation well-aligned in a large area of coal seam has become the key to long-time highly effective extraction of coal seam methane. Firstly, it starts with the perspective of stress field of crack tip, by means of thermal elasticity fracture mechanics theory, to get the stress intensity factor of hydrofracture tip while taking pore pressure into consideration. Next, a laboratory fracturing experiment using sandstone specimens was conducted to study the impact of non-uniform pore pressure on the direction of hydrofracture propagation. Lastly, a numerical simulation software RFPA2D-Flow is adopted to further verify the theoretical and experimental results. The study shows that pore pressure can effectively increase the stress intensity factor of the crack tip, the more pressure of pore, the smaller the needed fluid pressure for hydrofracture propagation. In a large area, affected by the direction and distribution of pore pressure gradient, the hydrofracture will propagate along higher pore pressure area. A method is put forward for controlling hydrofracture propagation in underground coal mines accordingly. Meanwhile, the matching relationship between the space between boreholes and the water injection maintaining pressure and maintaining time are studied together, with methods and steps for calculating key fracture parameters established.

The Behaviour of Fracture Growth in Sedimentary Rocks: A Numerical Study Based on Hydraulic Fracturing Processes

To capture the hydraulic fractures in heterogeneous and layered rocks, a numerical code that can consider the coupled effects of fluid flow, damage, and stress field in rocks is presented. Based on the characteristics of a typical thin and inter-bedded sedimentary reservoir, China, a series of simulations on the hydraulic fracturing are performed. In the simulations, three points, i.e., (1) confining stresses, representing the effect of in situ stresses, (2) strength of the interfaces, and (3) material properties of the layers on either side of the interface, are crucial in fracturing across interfaces between two adjacent rock layers. Numerical results show that the hydrofracture propagation within a layered sequence of sedimentary rocks is controlled by changing in situ stresses, interface properties, and lithologies. The path of the hydraulic fracture is characterized by numerous deflections, branchings, and terminations. Four types of potential interaction, i.e., penetration, arrest, T-shaped branching, and offset, between a hydrofracture and an interface within the layered rocks are formed. Discontinuous composite fracture segments resulting from out-of-plane growth of fractures provide a less permeable path for fluids, gas, and oil than a continuous planar composite fracture, which are one of the sources of the high treating pressures and reduced fracture volume.

Effects of mechanical layering on hydrofracture emplacement and fluid transport in reservoirs

Fractures generated by internal fluid pressure, for example, dykes, mineral veins, many joints and man-made hydraulic fractures, are referred to as hydrofractures. Together with shear fractures, they contribute significantly to the permeability of fluid reservoirs such as those of petroleum, geothermal water, and groundwater. Analytical and numerical models show that – in homogeneous host rocks – any significant overpressure in hydrofractures theoretically generates very high crack tip tensile stresses. Consequently, overpressured hydrofractures should propagate and help to form interconnected fracture systems that would then contribute to the permeability of fluid reservoirs. Field observations, however, show that in heterogeneous and anisotropic, e.g., layered, rocks many hydrofractures become arrested or offset at layer contacts and do not form vertically interconnected networks. The most important factors that contribute to hydrofracture arrest are discontinuities (including contacts), stiffness changes between layers, and stress barriers, where the local stress field is unfavourable to hydrofracture propagation. A necessary condition for a hydrofracture to propagate to the surface is that the stress field along its potential path is everywhere favourable to extension-fracture formation so that the probability of hydrofracture arrest is minimised. Mechanical layering and the resulting heterogeneous stress field largely control whether evolving hydrofractures become confined to single layers (strata¬bound frac¬tures) or not (non-stratabound fractures) and, there¬fore, if a vertically intercon¬nec¬ted fracture system forms. Non-stratabound hydrofractures may propagate through many layers and generate interconnected fracture systems. Such systems commonly reach the percolation threshold and largely control the overall permeability of the fluid reservoirs within which they develop.

Relationship Between the Hydraulic Fracture and Observed Microseismicity in the Bossier Sands of Texas

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 137936, ’Relationship Between the Hydraulic Fracture and Observed Microseismicity in the Bossier Sands, Texas,’ by A. Guest, SPE, and A. Settari, SPE, University of Calgary, prepared for the 2010 Canadian Unconventional Resources & International Petroleum Conference, Calgary, 19-21 October. The paper has not been peer reviewed. There is an increased effort to improve our understanding of hydrofracturing by use of microseismic monitoring and analysis. A numerical method was developed to predict microseismicity occurring during hydrofracturing and the influence of fracturing on the permeability of the reservoir. The core of this technique is a representative pre-fractured volume of the reservoir that deforms locally and allows the coalescence of deformation as the stress re-equilibrates. Introduction Hydraulic fracturing is used to increase the effective permeability of a producing formation and, thus, increase the production of hydrocarbons. Even though microseismicity provides a reasonable estimate of fracture parameters, our understanding of the relationship between microseismic events and the induced hydraulic fracture is not complete. Hydrofracturing of the Bossier sandstone in east Texas was studied. Early on, hydrofracturing was modeled assuming a single fracture propagating from the treatment well, with geomechanical permeability changes determined from changes of fluid pressure or stress. Reservoir properties were matched to fit the bottomhole pressure for the hydrofracturing and production for an 80-day period such that the permeability used in this model reasonably represents the permeability of the reservoir. A technique was developed to simulate the occurrence of microseismic events during hydrofracturing by numerical modeling of fracture self-localization. This technique forms fractures the size of the grid cell and allows coalescence of neighboring fractures, depending on the evolution of stress in the reservoir. The analysis of the deformation modes (seismic-moment tensors) of such fractures showed that such deformation, even though locally and temporally variable, reflects the overall macroscopic deformation that would be caused by classical hydrofracture propagation. Technique To solve for the deformation associated with hydrofracturing, mechanical equations and equations for fluid motion in porous media must be solved. The equations are coupled through pressure and permeability. In this paper, because the calculation of permeability for this technique is still not fully resolved, the mechanical and fluid-flow solutions are coupled in only one way—by treating the pressure function, generated by the flow model with pressure-dependent permeability and a hydraulic fracture, as input into the mechanical equations. Then, the local 2D geomechanical solution is based on the constitutive and geometrical equations, and mechanical equilibrium equations, which are detailed in the full-length paper. The fracture formation is solved by use of damage theory. The damage initiates when the Mohr-Coulomb or tensile-failure criteria are satisfied locally. The heterogeneity of the material can be introduced through a random function following the Weibull distribution. The heterogeneity is input for strength of the material and Young’s modulus.

Linking of fractures in layered rocks: Implications for permeability

The permeability of many rocks, including many reservoirs, is mostly attributable to fractures that form interconnected clusters. Here we present the results of field studies and numerical models on the linkage of fractures, using primarily fractures in carbonate rocks from the UK. The numerical models focus on two fracture configurations: five offset fractures in a 5-layer model, and a single hydrofracture in a 3-layer model. In some of the 3-layer models, a weak, open contact is added between the two topmost layers. In the 5-layer models loading is by 5 MPa tensile stress, whereas the 3-layer models the only loading is the internal fluid overpressure of 6 MPa in the hydrofracture itself, located in the lowermost of the three layers. For the 5-layer models, tensile stresses occur between the nearby tips of the offset fracture pairs, but these stresses are generally too low in the soft shale layers to initiate fractures. The tensile stresses, however, commonly concentrate at the contacts between the shale and limestone layers and may therefore result in delamination (debonding), that is, opening of the contacts. By contrast, the shear stresses between the nearby tips of the fracture pairs are often high enough to generate shear or mixed-mode fractures that connect the nearby tips of the original offset fractures, resulting in clusters that can conduct fluids. For the 3-layer models, the fracture-induced tensile stresses in the uppermost layer are suppressed by a comparatively thick compliant (shale) layer and/or the weak, open contact. Thus, no fracture formation is possible in that layer but at their contacts with the compliant layer the hydrofracture apertures increase. Thus, a compliant layer may arrest the vertical hydrofracture propagation from its stiff host layer but, at the same time, increase its maximum aperture and encourage lateral fluid transport at the layer contact between the layers.