Article

In-Situ Stresses: The Predominant Influence on Hydraulic Fracture Containment

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Abstract

In-situ experiments, which are accessible by mineback, have been conducted to determine the parameters that control hydraulic fracture containment. These experiments demonstrate that a stress contrast between the pay zone and a bounding layer is the most important factor controlling fracture height. Material property interfaces are shown to have little effect. Introduction Hydraulic fracturing has been used extensively for more than 30 years to stimulate the production of natural gas from many different reservoir rocks. Most treatments were small since their primary, purpose was to link the wellbore to the undamaged reservoir rock, and fracture lengths greater than a few hundred feet seldom were required. With increasing depletion of conventional natural gas reserves, attention has been focused on producing gas from unconventional gas resources such as tight gas sands and Devonian shales. Presently, stimulation of these formations is being attempted by massive hydraulic fracturing, a scale-up of at least an order of magnitude over conventional fracturing treatments. It is proposed that fractures longer than 4,000 ft (1200 m) be propagated in the low-permeability, gas-bearing formations to provide a high-conductivity path for the gas to reach the wellbore. Unlike small conventional treatments in which the fractures are propagated only a short distance, it is imperative that the large and massive hydraulic fractures be contained largely within the pay zone. Obviously, if only a small portion of the fracture surface is in contact with the reservoir rock, the result may well be an uneconomic well in a reservoir that has sufficient resources if stimulated correctly. Detrimental results will occur should the fracture break into a water-bearing zone. When referring to massive hydraulic fracturing in the tight gas sands, containment may referto confinement of the fracture to specified intervals comprising both gas-bearing sandstones lenses and surrounding shale zones orto the usual concept of confinement within a single reservoir zone. In either case, the study of the containment of hydraulic fractures is directed toward determining the parameters and the conditions that will limit the height of a fracture and control its direction of propagation so that the necessary fracture lengths will be obtained. Implicit in these studies is the presumption that sufficient understanding of these conditions will allow operators to alter treatment parameters to help control containment, at least in those formations where there is already some propensity for containing the fractures. If this is not possible, it still may be possible to define a priori those zones that most likely will provide economic production as a result of favorable fracture growth (or containment) conditions. Background The parameters that are considered to have some effect on the containment of hydraulic fractures have been detailed previously in the literature. A difference in elastic modulus between the reservoir rock and the barrier rock usually is singled out as the primary mechanism controlling containment. In their work on composite materials, Cook and Erdogan calculated the stress intensity factor for the two-dimensional crack approaching an interface between two materials with different clastic moduli. Simonson et al. and Rogers et al. applied these results to hydraulic fracturing and observed that since the stress intensity factor K at the tip approaches zero as a fracture in a lower-modulus material propagates toward a higher-modulus material, the fracture will tend to be arrested. JPT P. 653

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... Usually, microseismic monitoring of actual fracking operations show limited vertical extents of the fractures, however, these data are proprietary and methodological descriptions are scarce (Fisher and Warpinski, 2012). Experimental fracturing data is of little help as volumes injected are typically below or close to our volumetric limit, with injected volumes of 2 to 20 m 3 (Warpinski, Schmidt, and Northrop, 1982;Pandurangan, Chen, and Jeffrey, 2016). ...
... Isotropic rock mass and fracture arrest: Fluid-filled fractures pass through interfaces separating elastics of different stiffness as these travel. Observations of this exist in both natural and industrial settings (Warpinski, Schmidt, and Northrop, 1982;Rivalta et al., 2015). Experimental data of this process is also abundant, showing how the aperture and shape of fractures change as these approach such interfaces (Rivalta and Dahm, 2006;Urbani, Acocella, and Rivalta, 2018). ...
... An additional process is that of a freely slipping interface (Weertman, 1980). This causes fractures to arrest as their leading tip advances towards the interface (Warpinski, Schmidt, and Northrop, 1982). How frictional effects on this 'freely slipping' interface change this result have been explored, showing they only arrest under certain conditions (Renshaw and Pollard, 1995). ...
Thesis
Fluids in the Earth's crust can move by creating and flowing through fractures, in a process called `hydraulic fracturing’. The tip-line of such fluid-filled fractures grows at locations where stress is larger than the strength of the rock. Where the tip stress vanishes, the fracture closes and the fluid-front retreats. If stress gradients exist on the fracture's walls, induced by fluid/rock density contrasts or topographic stresses, this results in an asymmetric shape and growth of the fracture, allowing for the contained batch of fluid to propagate through the crust. The state-of-the-art analytical and numerical methods to simulate fluid-filled fracture propagation are two-dimensional (2D). In this work I extend these to three dimensions (3D). In my analytical method, I approximate the propagating 3D fracture as a penny-shaped crack that is influenced by both an internal pressure and stress gradients. In addition, I develop a numerical method to model propagation where curved fractures can be simulated as a mesh of triangular dislocations, with the displacement of faces computed using the displacement discontinuity method. I devise a rapid technique to approximate stress intensity and use this to calculate the advance of the tip-line. My 3D models can be applied to arbitrary stresses, topographic and crack shapes, whilst retaining short computation times. I cross-validate my analytical and numerical methods and apply them to various natural and man-made settings, to gain additional insights into the movements of hydraulic fractures such as magmatic dikes and fluid injections in rock. In particular, I calculate the `volumetric tipping point’, which once exceeded allows a fluid-filled fracture to propagate in a `self-sustaining’ manner. I discuss implications this has for hydro-fracturing in industrial operations. I also present two studies combining physical models that define fluid-filled fracture trajectories and Bayesian statistical techniques. In these studies I show that the stress history of the volcanic edifice defines the location of eruptive vents at volcanoes. Retrieval of the ratio between topographic to remote stresses allows for forecasting of probable future vent locations. Finally, I address the mechanics of 3D propagating dykes and sills in volcanic regions. I focus on Sierra Negra volcano in the Gal\'apagos islands, where in 2018, a large sill propagated with an extremely curved trajectory. Using a 3D analysis, I find that shallow horizontal intrusions are highly sensitive to topographic and buoyancy stress gradients, as well as the effects of the free surface.
... Therefore, it is critical for the industry to understand the key parameters for restricting the growth of hydraulic fractures. Previous studies indicate that several parameters affect vertical fracture propagation and have potential for massive fracture containment in layered rock, including the minimum horizontal in-situ stress, which is referred to as a stress barrier (Fisher and Warpinski 2012;Simonson et al. 1978;Warpinski et al. 1982;Yu et al. 2014), and materiel properties, such as Young's modulus, on either side of the interface, which are referred to as materiel barriers (Carrier and Granet 2012;Gu and Siebrits 2006;Zhang et al. 2010). To thoroughly investigate the effects of factors on hydraulic fracture containment in layered formations, first we determinate the rock parameters with logging data, and obtain the in situ geostress field by inversion analysis based on hydraulic fracturing test, a conceptual model is derived from the rock parameters and in situ geostress field to encompass the typical process of hydraulic fracturing operation in layered formations. ...
... Early attempts to resolve hydraulic fracture height containment problems have shown that the stress barrier is the predominant influence on containment (Fisher and Warpinski 2012), whereas the material properties, including intrinsic properties, such as the Young's modulus (E 0 ), Poisson's ratio ( v 0 ), and initial permeability ( K 0 ), were generally concluded to be less important for the direct control of fracture propagation (Warpinski et al. 1982). To thoroughly investigate the effects of key factors in determining fracture height containment, the eight tested parameters presented in Table 3 were varied at three levels, namely, low (90%), medium (100%) and high (110%). ...
... Early research has shown that fractures can be arrested wherever there are discontinuities or sufficiently large minimum in-situ stress gradients (Warpinski et al. 1982). Our statistical results highlight that the minimum horizontal stress ratios in the sandstone (SRc) and mudstone layers (SRm) are highly statistically significant for fracture height containment (Fig. 10). ...
Article
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Hydraulic fracturing is widely accepted as a geotechnical application that can be used to enhance productivity in unconventional reservoirs. However, if the hydraulic fracture is not contained within a single stratigraphic interval, the fracture treatment could harm the integrity of the caprock, and even threaten underground drinking water. Thus, for the purpose of effectively and economically recovering oil/gas from reservoirs, it is critical for the industry to understand the key parameters needed to restrict the vertical growth of massive hydraulic fractures. To this end, we introduce a comparative hydro-mechanical coupling finite element model to describe the initiation and propagation of a hydraulic fracture. The material properties and the stress field of the model are determined by the field logging data and field hydraulic fracture test. The significance of key parameters to fracture height were concluded from a statistical perspective, to thoroughly investigate the effects of key factors in determining fracture height containment, we present an uncertainty analysis of the in situ stress and intrinsic properties of the target sandstone layer and overlying mudstone. The results show that the minimum horizontal in-situ stress contrast at the caprock/reservoir interface, referred to as a stress barrier, is the most important factor for hydraulic fracture containment. A larger stress barrier hinders the fracture height elongation and increases the fracture width. Under the same stress contrast conditions, the effect of a material barrier on fracture containment is dominated by the contrast of Poisson's ratio at the caprock/reservoir interface, once the fracture tip penetrates the interface, the caprock a with lower Poisson's ratio would effectively hinder fracture propagation, the Young’s modulus contrasts are probably not an important parameter in terms of directly controlling the fracture height, whereas a higher Young’s modulus in both the caprock and reservoir would generally enhances the fracture height.
... presence of natural fractures, we first present a comprehensive workflow to model hydraulic fracturing by 17 accounting for interactions with numerous natural fractures. This model is a coupled fluid flow and 18 deformation finite element model with adaptive insertion of three-dimensional cohesive elements to 19 simulate fracture propagation through the rock matrix and a network of intersecting natural fractures. ...
... This process adopts cyclic injection treatments by shutting the pump in the 14 middle of the job or even allowing it to flow back during hesitation intervals, and then resuming the initiate through weak interfaces along the fracture. Kiel was believing that cyclic injection treatments could 19 generate large enough pressure disturbances in the rock to expand fracture network and further enhance 20 production in naturally fractured formations as well as soft formations with no detectable natural fractures. ...
... Additionally, mechanical properties of the digenetic cement 18 inside natural fractures can also be incorporated into the model. In CZM, the constitutive model for the 19 crack tip is characterized by the traction-separation law intended for bonded interfaces whose thickness is 20 small. Using this method, rock mechanical behavior during fracturing can be described in two parts: a linear 21 elastic deformation prior to the damage; and progressive degradation of stiffness driven by the damage 22 process during initiation and propagation of the fracture. ...
Article
Full-text available
Microseismic data and post-fracturing production analysis have confirmed a positive correlation between fracture complexity and production enhancement in fractured wells. While operators are looking for modifications in their pumping schedules such as adding pumping hesitations to enhance fracture complexity, the physics behind the effectiveness of these trial and error efforts is not fully understood. In this paper, we try to investigate different scenarios that may enhance fracture complexity by introducing changes in the pumping schedule. Since field evidence shows effectiveness of these techniques more in the presence of natural fractures, we first present a comprehensive workflow to model hydraulic fracturing by accounting for interactions with numerous natural fractures. This model is a coupled fluid flow and deformation finite element model with adaptive insertion of three-dimensional cohesive elements to simulate fracture propagation through the rock matrix and a network of intersecting natural fractures. Simulations have been implemented for different natural fracture patterns. Our analyses have shown that in addition to the differential stress and fractures’ intersection angle, pumping rate and its breaks can play a significant role in fracture branching and its diversion into natural fractures. For continuously crosscutting natural fractures, higher injection rates are found to have a positive effect in overcoming the resistance of natural fractures in different directions. While in the case of discontinuously hierarchical natural fractures, this improvement can be very limited, while adding a hesitation in the middle of the pumping period can force the fractures to divert into other directions, which is effective to develop more complex fractures for different natural fracture patterns.
... This situation causes significant contrasts of the four "natural" variables between layers, especially between the pay zone and the adjacent layers. In the early stages of fracturing studies, Warpinski [12,13], conducted experiments to determine which of the two parameters (stiffness contrast and in situ stress contrast) is predominant for controlling hydraulic fracture containment. Experiments demonstrated that the in situ stress contrast is the most important factor controlling fracture height, while the stiffness contrast has little effect. ...
... This conclusion is consistent with numerical and semi-analytical results in the paper [14]. In contrast to conclusions in [12][13][14], papers [6,15] gave quantitative descriptions of the effects of formation stiffness (Young's modulus and Poisson's ratio) contrast on hydraulic fracture propagation. In [16,17], pseudo-3D models were presented for hydraulic fracture growth in a layered formation with contrasts in both stiffness and in situ stress. ...
... Thirdly, the obtained numerical values of w i,j,k+1 are inversely substituted into Equation (12) for the solutions of p i,j,k+1 . At last, the calculation enters into the next time step t = t k+2 , and solutions w i,j,k+1 and p i,j,k+1 are regarded as the solutions of the previous time step. ...
Article
Full-text available
The effectiveness of the hydraulic fracturing procedure is crucially dependent on the stage of fracture planning and design. Forecasting fracture behavior in rock formations characterized by non-uniform toughness is a serious challenge. In the present paper, a planar-3D model considering the rock’s non-uniform fracture toughness has been developed for the uneven propagation of a hydraulic fracture. The series of numerical experiments were designed to study the effect of inhomogenous fracture toughness. The results show that the fracture toughness contract significantly controls the overall direction of fracture propagation, and a combination of toughness contrast and the proportion between the pay zone and barrier zone determine the fracture profile: from almost circular with or without a pair of narrow wedges when the proportion is small to almost rectangular otherwise. This paper also discusses the process of cleaning a fracture from hydraulic fracturing fluid by oil. Using numerical modeling on the basis of the constructed mathematical model, a relationship is established between the quality of hydraulic fracture cleaning and the geometrical parameters of the fracture and the region filled with the hydraulic fracturing fluid. The results of numerical experiments show that while fracturing fluid is more viscous than oil, the length of the fracture has a greater influence on the cleaning process than the viscosity of the fracturing fluid.
... Moreover, many studies have shown that the dominant factor affecting fracture height growth during hydraulic fracturing is the stress difference between the pay layer and the barrier layer (Jeffrey and Bunger, 2009;Li et al., 2017;Warpinski et al., 1982b;Wasantha et al., 2019). Some other authors have observed that material stiffness contrast at the interface can also serve as a barrier to fracture propagation (Gao and Ghassemi, 2020;Gu and Siebrits, 2008;Salimzadeh et al., 2019;Wu et al., 2008Wu et al., , 2004Yue et al., 2019). ...
... In contrast, when a fracture propagates from a soft layer to a stiffer layer, it can be arrested and other fracture mechanisms such as the formation of secondary fractures across the interface (again leading to fracture branching), delamination along the interface, or crack kinking resulting in fracture containment, are also possible (Wu et al., 2008(Wu et al., , 2004. However, several authors have shown the opposite experimental results that demonstrate that a hydraulic fracture crosses an interface if it propagates from a low stiffness to a high stiffness layer (Casas et al., 2006;Warpinski et al., 1982b;Zhang et al., 2017b). The authors concluded that the stiffness contrast by itself is insufficient to arrest a fracture at an interface and other parameters, such as stress contrasts, can be more important. ...
Article
A propagating fluid driven fracture in a rock mass is expected to interact with geological interfaces on a wide variety of length scales. The vertical growth of hydraulic fractures in layered rocks is of pivotal importance for the successful stimulation in reservoir development. In this study, 2D discrete element modeling is used to investigate the influence of the stiffness and toughness ratio, as well as stress contrast between layers on the hydraulic fracture height growth. In particular, the ultimate goal is to better understand mechanisms of the fracture height containment by contrasts of different rock properties and to quantitatively determine which parameters provide a stronger influence. In addition, the analysis is performed in the context of hydraulic fracture regimes, whereby the dominant dissipation mechanism in the system can either be associated with fracture toughness or viscous fluid flow. As a starting point, we investigated the propagation of a plane strain hydraulic fracture from a low stiffness layer to a high stiffness layer and vice versa, while keeping the stress constant. The influence of stress on hydraulic fracture propagation in layered rocks is investigated afterwards. The numerical results demonstrate that the hydraulic fracture can either directly pass through the geological interface, be arrested at the interface, or stop before reaching the interface. The interface itself is assumed to be perfectly bonded, therefore no slippage is considered. Ability of the hydraulic fracture to approach the interface is first determined by the elastic modulus ratio of the two adjacent layers. Once reached the interface, the further growth is then affected by the toughness ratio between the layers. After that, if the fracture crosses the interface, then it is affected by the stress contrast. The propagation regime has an important influence on the fracture propagation in layered rocks. If the propagation regime is closer to the viscosity dominated, the hydraulic fracture is likely to cross the interface. In contrast, it is more difficult for a fracture to cross the barrier if the propagation regime is near the toughness dominated. A map of fracture crossing behavior versus propagation regime and contrast in properties has been constructed, that can be used to quantify strength of mechanical barriers and to deduce hydraulic fracture height growth behavior for various scenarios.
... Contrasts in the in-situ stresses impose the biggest influence on fracture growth (Simonson et al., 1978;Warpinski et al., 1982;Voegele et al., 1983;Palmer and Luiskutty, 1985;Warpinski, 2016). Fracture height growth is constrained if the layers above and below a growing fracture are under higher stress than the layer the fracture is propagating in. ...
... Presence of weak layer interfaces can blunt fracture growth (Perkins and Kern, 1961;Nierode, 1985;Warpinski, 2016) as noted in laboratory (Anderson, 1981;Teufel and Clark, 1984) and mineback studies (Warpinski et al., 1982;Warpinski and Teufel, 1987;Jeffrey et al., 1992;Zhang et al., 2007). This blunting effect is most important in shallow depths at low values, which minimizes friction effects. ...
Thesis
Full-text available
Fluid-driven fracture initiation from oil and gas wells is examined in detail. The dissertation covers three subtopics: drilling, completion (stimulations), and post-blowout capping-induced fracture initiation. Drilling-induced tensile fractures (DITFs) are located in an azimuth orthogonal to wellbore breakouts and are observed from image logs obtained during drilling operations. Fully analytical criteria for the orientation of DITFs initiating from wells in porous, permeable media are derived considering fluid infiltration from a pressurized wellbore. DITF orientation (longitudinal or transverse-to-the-wellbore) is used to constrain the magnitude of the local maximum horizontal principal stress. The range of the possible stress states is indicated on dimensionless plots vis-à-vis a given DITF orientation and in-situ stress regime. Completion-induced hydraulic fractures (CIHFs) are initiated from perforated wells during stimulation practices, aimed at improving the permeability in the near-wellbore region. For application in low permeability formations, such as shale reservoirs, transverse fractures are more desired from a productivity perspective. A horizontal well with multiple transverse fractures outperforms the same horizontal well with a gigantic longitudinal fracture. Closed-form analytical approximations from the literature for the longitudinal and transverse fracturing stresses are modified to incorporate pore pressure effects and then used to develop a criterion for the orientation of fractures initiating from perforated wells. The validity of this criterion is numerically assessed and found to overestimate transverse fracture initiation, which occurs under a narrow range of conditions; when (i) the formation tensile strength is below a critical value, and (ii) the breakdown pressure within a “window.” At a known breakdown pressure, the fracture initiation pressure can be determined semi-analytically. Following blowouts after mismanaged loss of well control situations, tensile fractures can initiate during capping stack shut-in. Upward propagation of these fractures can provide a broaching pathway for reservoir fluids towards the seafloor leading to an ecological disaster. Being able to predict fracture initiation, a-priori to post-blowout capping, thus preventing broaching from taking place is of considerable importance. Capping stack shut-in procedures can be optimized using the post-blowout discharge flowrates. A deepwater Gulf of Mexico case study is performed, extended to a comprehensive stability analysis of the casing-cement sheath-rock formation system.
... Several authors investigated the factors influencing the hydraulic fracturing process, including the characteristics of the pre-existing joints, the in-situ stress state, the fracturing fluid viscosity and injection rate, and the anisotropy and heterogeneity of the rock mass [8][9][10]. Blanton [8] and Warpinski et al. [9] argued that the differences in the in-situ stress and the approach angle (i.e., the angle between the propagating HF and the joint) are the key factors determining HF propagation behavior in fractured formation. ...
... Several authors investigated the factors influencing the hydraulic fracturing process, including the characteristics of the pre-existing joints, the in-situ stress state, the fracturing fluid viscosity and injection rate, and the anisotropy and heterogeneity of the rock mass [8][9][10]. Blanton [8] and Warpinski et al. [9] argued that the differences in the in-situ stress and the approach angle (i.e., the angle between the propagating HF and the joint) are the key factors determining HF propagation behavior in fractured formation. HF tend to cross pre-existing joints under high horizontal/vertical stress difference and high approach angle. ...
... Contrasts in the in-situ stresses impose the biggest influence on fracture growth (Simonson et al., 1978;Warpinski et al., 1982;Voegele et al., 1983;Palmer and Luiskutty, 1985;Warpinski, 2016). Fracture height growth is constrained if the layers above and below a growing fracture are under a higher stress than the layer the fracture is propagating in. ...
... Layer Interfaces. Presence of weak layer interfaces can blunt fracture growth (Perkins and Kern, 1961;Nierode, 1985;Warpinski, 2016) as noted in laboratory (Anderson, 1981;Teufel and Clark, 1984) and mineback studies (Warpinski et al., 1982;Warpinski and Teufel, 1987;Jeffrey et al., 1992;Zhang et al., 2007). This blunting effect is most important in shallow depths at low S v values, which minimizes friction effects. ...
Conference Paper
During loss of well control events, fracture initiation occurring during the post-blowout capping stage following uncontrolled discharge, can lead to reservoir fluids broaching to the seafloor. A classic example is Union Oil's 1969 oil spill in Santa Barbara channel, where fracture initiation at various locations caused thousands of gallons per hour to broach in the ocean floor over a period of a month before it could be controlled (Mullineaux, 1970; Easton, 1972). The impacts on California's oil industry are still felt strongly today. Disasters as such could be prevented if the effects of the post-blowout loss of well control stages (uncontrolled discharge and capping) are incorporated into the shut-n procedures and the wellbore architecture. Analytical models are used to simulate the loads on the wellbore in the different stages during loss of control and predict capping pressure build-up during the shut-in to indicate fracture initiation during the capping stage. Using these models, critical capping pressure and subsequently critical discharge flowrates is calculated for a well below which fracture initiation would occur. A hypothetical case study with typical deepwater Gulf of Mexico parameters is performed demonstrating the likelihood of fracture initiation during different discharge flowrates, discharge periods and shut-in methods (abrupt/"hard" or multi-stage/"soft"). Further discussion addresses reservoir depletion during the discharge stage preceding the capping, as well as the conditions necessary for upward propagation of these fractures towards the seafloor. Through these fractures fluids from the reservoir ultimately broach into the seawater. The ability to model these fracture failures will enhance the understanding of wellbore integrity problems induced during loss of control situations and create workflows for predicting possible broaching happening during the post-blowout capping stage early on. Dimensionless plots are used to present fracture initiation for different scenarios useful for drilling and wellbore integrity engineers when making contingency plans for dealing with loss of well control situations.
... Both laboratory investigation [16][17][18][19][20][21][22][23][24][25] and numerical simulations on the influence mechanism for fracture vertical propagation had been widely investigated. In the aspect of experiments, Simonson et al. [16] and Chudnovsky et al. [17] concluded that fracture height containment was mainly determined by the mechanical property difference between layers. ...
... However, some scholars [18][19][20] argued that the difference in elastic modulus between layers was not the main factor for controlling fracture containment. Warpinski et al. [21] and Teufel and Clark [22] found that the interfacial shear strength and interlayer stress difference were the most important parameters to control the fracture height. It was enough to restrain the HF propagation when the interlayer stress difference was 2-3 MPa. ...
Article
The transition zone was defined as an interface with certain thickness, strong heterogeneity and anisotropy in the vertical profile for layered formations, which had great effect on hydraulic fracture (HF) height propagation. In this paper, a numerical model for transversely isotropic layered shale with transition zone was established by utilizing the extended finite element method (XFEM) based on cohesive zone model (CZM). The effects of in-situ stress, dip angle, anisotropy and tensile strength of transition zone, and anisotropy of shale matrix, and injection rate on fracture vertical propagation behavior were investigated. Dimensionless fracture offset distance in transition zone (DFODT) and dimensionless fracture height (DFH) were defined to quantitatively evaluated the results of hydraulic fracture vertical propagation. Numerical results showed that the transition zone could induce the HF to turn and distort within and between layers, significantly improving the degree of fracture tortuosity. Also, the greater the DFODT, the smaller the DFH. The anisotropy of transition zone and coefficient of effective vertical stress difference had the greatest influence on DFODT; anisotropy of shale rock and injection rate had the greatest influence on DFH; while tensile strength of transition zone had a relatively weaker influence on both DFODT and DFH.
... (1) fluid-driven fractures are well confined within the rock layer with a constant height H, due to the stress/stiffness contrast between rock layers acting as a height growth barrier (Bunger & Lecampion, 2017;Gudmundsson, 2005;Rivalta et al., 2015;Warpinski et al., 1982). Additionally, based on the stability analysis of fracture geometry (Rice, 1985), these fluid-driven fractures can be idealized to have a flat edge in their length direction. ...
Article
Full-text available
Multistage multicluster hydraulic fracturing is currently the most effective method to stimulate low‐permeability hydrocarbon reservoirs. The desired result of this stimulation technique is highly uniform growth of multiple closely spaced hydraulic fractures. In order to deepen our understanding on the competitive growth of these fractures, we have investigated the growth behaviors of multiple hydraulic fractures under different conditions. A fully coupled model with a 3‐D influence coefficient is presented for fracture growth in a rock layer, based on a combination of boundary element method and finite volume method. It is validated against classic solutions and lab experiments. The parametric analyses of dimensionless arguments to quantify the uniformity of fracture growth are performed, with varying fracture geometries and geotechnical conditions including preexisting natural fractures. The results demonstrate that fracture competition is controlled by the dimensionless toughness, the initial fracture geometric settings, and the ratio of fracture spacing to height. A higher fluid viscosity, a smaller initial length offset, and a larger spacing benefit simultaneous fracture growth for conventional bi‐wing hydraulic fractures. By contrast, single wing ones exhibit a remarkably better performance in long‐time simultaneous fracture growth at a small separation, especially at low dimensionless toughness. Under certain conditions, the closely spaced single‐wing fractures are prone to grow simultaneously and uniformly in less energy consumption. The simultaneous growth is found to be insensitive to the interference from small‐scale natural fractures. The uniform single‐wing fracture growth from the perspective of geomechanics will provide a new insight for both reservoir stimulation and formation of vein and dike swarms.
... Common applications include the study of safe drilling pressure windows, the analysis of hazards when drilling nearby geological faults or the assessment of trapping mechanism during hydrocarbon migration. Estimating the in-situ stress is also important in hydraulic fracturing since high stress concentration in thin layers can act as a barrier for the vertical propagation of the fractures (Warpinski et al. 1982;Garcia et al. 2013). The horizontal propagation of the fractures is also influenced by stress heterogeneity but at a scale in the order of hundreds of meters. ...
Preprint
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This paper proposes a methodology to estimate stress in the subsurface by a hybrid method combining finite element modeling and neural networks. This methodology exploits the idea of obtaining a multi-frequency solution in the numerical modeling of systems whose behavior involves a wide span of length scales. One low-frequency solution is obtained via inexpensive finite element modeling at a coarse scale. The second solution provides the fine-grained details introduced by the heterogeneity of the free parameters at the fine scale. This high-frequency solution is estimated via neural networks -trained with partial solutions obtained in high-resolution finite-element models. When the coarse finite element solutions are combined with the neural network estimates, the results are within a 2\% error of the results that would be computed with high-resolution finite element models. This paper discusses the benefits and drawbacks of the method and illustrates their applicability via a worked example.
... As the hydraulic fracture grows in the vertical direction, it might encounter layers or distinct lithofacies (Donovan et al., 2016;McGarity, 2013;Workman, 2013) with different geomechanical properties. If the layers are stiff, the fracture's vertical penetration will be temporarily limited as its lateral dimension increases (Warpinski et al., 1982;Maxwell, 2014). Layers with a higher Poisson's ratio can also be associated with this phenomenon because of the greater lateral expansion that results from lithostatic loading (Maxwell, 2014). ...
Article
Industry needs techniques for expediting understanding on shale reservoir deliverability and spatial drainage. Horizontal wells are currently the option of choice for these investigations but their early adoption is costly and time consuming. Stimulated and flow tested vertical exploration wells could address this challenge. Multi-domain data from one of the initial Eagle Ford stimulated vertical wells in DeWitt County, Texas was used to illustrate the viability of this approach. Completion and short duration flow data were used to predict induced fracture geometry, incorporate natural fractures, and interpret reservoir flow regimes. Solving analytical relations for the latter provided an estimate of system and representative matrix permeability. The latter was in picoDarcy range after inclusion of natural fractures and other preexisting discontinuities. The aforementioned results were used to build reservoir deliverability and drainage models. Subsequently, scaling of these models predicted performance and drainage of horizontal wells. For verification, the systematic scaling of forecasted flow from an early vertical well predicted the long-term performance of offset multi-stage fractured horizontal wells. A scaled single horizontal well profile also matched the total production from DeWitt County which had almost two thousand wells by the time of this study. The latter required accounting for cross-well interference-driven productivity loss as a result of suboptimal well spacing. The derived PicoDarcy permeability was validated by correcting for in situ stress and use of a representative Biot coefficient. For optimal recovery, a set of theoretical optimal stimulations (TOSs) with their associated spatial drainage were derived for immediate field trials in Eagle Ford and its analogues. Contrary to the current philosophy, exploration phase data including stimulation and flow details of a vertical well provided reliable predictions of parameters critical for field development. It was posited that costly, time-consuming, and trial and error shale derisking approaches can be optimized.
... Frictional discontinuities (FDs) are a common geological structure in sandstone, laminated shale or coal bed (Jaeger et al. 2007 hydraulic fracture (HF) geometry may be influenced by them as HFs may cross, bend into, or be arrested by FDs (Warpinski et al. 1982;Jeffrey et al. 2009;Guo et al. 2021). Microseismic events and HF height are also closely related to HF-FD interaction (Daneshy 2009;Wasantha et al. 2014;Tang et al. 2019;Zhang et al. 2019;Tan et al. 2022). ...
Article
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Understanding the mechanical responses of frictional discontinuities (FDs) with hydraulic fractures (HFs) is essential to interpret microseismic events and fracture propagation for geomechanics and geophysics. However, the mechanical analysis is not clearly studied using a robust numerical method because of its complexity with nonlinear constraints. In the study, we present a 2D boundary element model with a complementarity algorithm to investigate this nonlinear contact problem in HF–FD interaction. The new model enforces appropriate contact boundary conditions of the FD through a complementarity algorithm. All the contact modes of the FD, including sticking, opening, and slipping, can be precisely described and efficiently determined. The new model avoids the drawbacks of using trial calculations or fracture stiffness as in previous studies to prevent the interpenetration of fracture surfaces. The model has been validated against analytical solutions of frictional inclined fractures and previously published numerical solutions of HF–FD interaction. Parametric studies show that the FD’s opening or slipping responses generally exist in the HF–FD contact position neighborhood. FD slippage is the dominant mechanical response induced by the approaching pressurized HF. Such slippage can be reduced by increasing in its friction coefficient or friction strength, whereas FD opening can be increased under higher friction coefficient and strength. The higher the fluid pressure in the HF, the more likely the HF crosses the FD; thus, using viscous fluid or high pumping rate is conducive to HF crossing FDs. HFs tend to cross FDs with a slight shift, especially in formations with variable friction coefficients or cohesions along the FD. This is a new mechanism used to interpret fracture offset observed in geomechanics and geophysics. The study provides a systematical analysis of the mechanism for HF–FD interaction and can help investigate the mechanism of microseismic events and complex HF propagation. Article highlights A 2D boundary element model with a complementarity algorithm for HF–FD interaction is proposed. Three contact modes of fracture discontinuity including sticking, slipping, and opening are efficiently described and systematically analyzed. Mechanical heterogeneity of the FD is a new and essential mechanism for fracture offset.
... The second category is focused mainly on the propagation of hydraulic fracturing when the fracture tip approaches the material interfaces in layered formations or interlayers. In early studies, the capability of material interfaces to contain or deflect fractures was usually analyzed by comparing the ratio of the energy release rates or material toughness (He and Hutchinson, 1989), and stress contrasts were regarded as the predominant influence on hydraulic fracture containment (Warpinski et al., 1982), while material contrasts did not directly control fracture height (Smith et al., 2001). Cleary described a generalpurpose numerical scheme to analyze the conditions and possibilities for fractional interfacial slippage leading to interface separation (Cleary, 1978). ...
Article
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Understanding the hydromechanical responses of faults during supercritical CO2 fracturing is important for reservoir management and the design of energy extraction systems. Reservoirs of thin sand and mudstone interbedding are developed in Chang 7 member of the Yanchang Formation, Ordos Basin, China, supercritical CO2 fracturing operation has the potential to reactive the undetected small faults and leads to unfavorable fracking fluid migrate. In this work, we examined the role of fault slippage and permeability evolution along a small fault connecting the pay zone and the confining formation during the whole process of fracturing and production. A coupled hydromechanical model conceptualized from actual engineering results was introduced to address the main concerns of this work, including (1) whether the existence of a undetected small fault would effectively constrain the hydraulic fracture height evolution, (2) what the magnitude of the induced microseismic events would be and (3) whether the permeability change along the fault plane would affect the vertical conductivity of the confining formation and thus increase the risk for the fracturing fluid to leak. Our results have shown that the initial hydrofracture formed at the perforation and propagated upward, once it merged with the fault surface, the existence of an undetected small fault would effectively constrain the hydraulic fracture height evolution. The tensile stress in front of the hydrofracture tip resulted in a concentration of fault slippage at the fracture-fault intersection; the permeability-enhanced zone was also concentrated there and mainly localized on the high-permeability fault portion in the pay zone. As fracturing continued, further slippage spread from the permeability increase zone of high permeability to shallower levels, and the extent of this zone was dependent on the magnitude of the fault slippage. At the end of extraction, the slip velocity decreases gradually to zero and the fault slippage finally reaches stabilization. In general, the induced microseismic events ranging from Mw=-1.8 to -2.6 could be considered as the sources of acoustic emission events detected while monitoring the fracturing fluid front, and due to the limited fault slippage and lower initial permeability, the change in conductivity within the upper portion of the fault in the confining formation was relatively insignificant, the vertical conductivity of the confining formation was almost unaffected.
... Fault refraction is namely due to different types of failure (extension 368 vs. shear) of layers(Schöpfer et al., 2006). Studies on fluid-driven fractures suggest that the in-369 situ stress contrast between layers is the most important factor controlling fracture containment 370(Nolte and Smith, 1979;Warpinski et al., 1981Warpinski et al., , 1982; Teufel and Clark, in-situ stress distribution, hence the variation in fracture dip, is controlled by, 374 among others, contrasting rock mechanical properties (e.g., Strength, Young's modulus, 375Poisson's ratio) of adjacent layers (e.g.,Peacock and Sanderson, 1992; Ferrill and Morris, 2003; 376 van Gent et al., 2010; Kettermann and Urai, 2015). During deformation, the weak layer elongates 377 more than the strong layer, causing an additional extensional force in the strongest layer (Bourne, 378 2003) (Figure 7). ...
Article
Open natural fractures allow fluids to flow, which is necessary for the production of low-permeable geothermal and petroleum reservoirs. These reservoirs often consist of lithological layers with significant variation in rock strength, which makes it difficult to predict fracture containment within the rock succession. In this paper, fractures are classified as contained, when they do not cross the layer interface of the adjacent layer, so that formation and growth are inhibited in the adjacent layer. This study concerns the impact of the differences in rock strength (i.e., mechanical contrast) between two adjacent brittle layers on the fracture containment in finely-layered rocks. Laboratory deformation tests and 2D finite element modelling were performed on three-layered samples with varying mechanical contrasts to examine the behaviour of fractures at different stress conditions. Fractures initiate as shear fractures in weak layers, and propagate with a steeper angle (tensile fracture) through the adjacent stronger layer. The mechanical contrast within a layered rock does not always act as a containment barrier, meaning that fractures do not cross the layer interface of the adjacent layer. This is due to differences in differential stress between the weakest layer and strongest layer. The mechanical contrast combined with the magnitude of the confining pressure has a significant influence on fracture containment. An increase in mechanical contrast and confining pressure prevents fractures from propagating into stronger layers. The results contribute to predict natural fracture containment in brittle sequences at shallow depth in the subsurface.
... Mineback tests under in-situ conditions showed that hydraulic-fracture containment in the target layer is predominantly controlled by the contrast in the minimum principal in-situ stress between the target layer and the bounding layers (Warpinski et al. 1982). Hydraulic fractures were observed to propagate across interfaces with materials that have a higher Young's modulus by factors as high as 15, but were arrested at interfaces with layers under a higher minimum principal stress by a factor of two (Teufel and Warpinski 1983). ...
Article
Hydraulic-fracture initiation and propagation in the presence of multiple layers with different mechanical and flow properties are investigated experimentally using a novel fracturing cell. Mixtures of plaster, clay, and hydrostone are used to cast sheet-like and porous test specimens in layers with different configurations and properties. The layered specimens are hydraulically fractured under varying far-field differential stress. Fracture growth is recorded using a high-resolution digital camera. Key frames are subsequently analyzed using digital image correlation (DIC) to reveal microcracks, measure strains, and show other features such as shear-failure events that are difficult to detect with the naked eye. The problem of a hydraulic fracture induced in a soft layer bounded by harder layers is considered. We demonstrate numerous laboratory experiments that reveal a clear tendency for induced fractures to avoid harder bounding layers. This is seen as fracture deflection or kinking away from the harder layers, fracture curving between the harder bounding layers, and fracture tilt from the maximum far-field stress direction. These observations appear to be more pronounced as the contrast in Young's modulus and fracture toughness between the layers increases and/or the far-field differential stress decreases. Moreover, when a fracture is induced in a relatively thin layer, the fracture avoids the harder bounding layers by starting and propagating parallel to the bounding interfaces. Fracture propagation parallel to the bounding layers is also observed in relatively wide layers when the far-field stress is isotropic or very low. A fracture approaching a dipping, harder layer tends to curve away from the hard layer by kinking toward the high side of the interface. Nonplanar fracture trajectories are observed even in homogeneous materials when the far-field differential stress is relatively low. Furthermore, various other fracture behaviors in layered specimens are demonstrated and discussed, such as fracture offsetting at material interfaces, fracture branching and complex fracture trajectories, and shear failure of weakly bonded interfaces.
... Interconnected hydraulically conductive fractures enable significantly higher flow rates than the surrounding rock matrix, which in some cases may otherwise be effectively impermeable. This is important for a variety of applications including hydraulic fracturing (Bunger et al., 2013;Warpinski et al., 1982), geothermal energy (Tester et al., 2006), aquifer contaminant transport (Berkowitz, 2002), caprock seal integrity, (Benson et al., 2005;Nicholson & Wesson, 1951), and nuclear waste disposal (Bastiaens et al., 2007). For all of these applications, prediction of in situ fracture flow is of the utmost importance but it is also highly uncertain because of its sensitivity and dependence on in situ parameters that are difficult or impossible to measure with the accuracy and precision needed for prediction. ...
Article
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Shear fractures can facilitate fluid conductivity through rock. Aperture and roughness are controlling characteristics for a fracture's fluid conductivity. Inspired by en echelon fractures, we develop a shear “fracturelet” model that predicts anisotropic aperture with respect to the direction of shearing, rougher (nonplanar) rather than smoother (planar) fractures, and the bounds of this roughness for a coalesced fracture. This tendency for rougher fracture creation is validated by in situ X-ray images and fluid conductivity measurements from triaxial direct shear experiments on anhydrite and shale. These experiments were conducted at confining stresses from 4 to 30 MPa and shear displacement magnitudes from 0 to 2 mm on initially intact rock specimens. Hydraulic, dilatational, and local fracture apertures were measured in the experiments. Apertures exhibited strong anisotropy with more conductive flow paths forming perpendicular to the direction of shearing. Local and dilatational aperture were found to be positively correlated with increasing shear displacement but hydraulic aperture was found to vary significantly, always having values smaller than the other aperture measures at factors ranging from 0.6 to 0.0. An implication of these results is that shear fractures have a mechanism for simultaneously exhibiting very low fluid conductivity and high fluid storage volume.
... In the context of hydraulic fracturing, which is performed to enhance the recovery of unconventional hydrocarbons, several indicators are important for defining the effective penetration and propagation inside the source rocks. These factors include the interface property, the vertical compressive stress difference, the mechanical properties of the producing formation and interlayers, and the horizontal stress difference (e.g., Anderson, 1981;Biot et al., 1983;Warpinski et al., 1980Warpinski et al., , 1982Warpinski & Teufel, 1987;Gu et al., 2008;Huang & Liu., 2018;Zhang et al., 2008). The mechanical properties of gas-bearing shales in the Polish part of the BB have not yet been studied with such interdisciplinary magnetic and sedimentary methods. ...
Article
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Analysis of anisotropy of magnetic susceptibility (AMS) and anhysteretic remanent magnetization (AARM) was conducted on unconventional gas-bearing Silurian shale rocks from northern Poland. Samples of these rocks were collected from depths greater than 3500 m from two drill cores. The aim was to investigate magnetic fabrics to verify current models of depositional conditions, current direction, and/or tectonic evolution. To obtain an in-depth interpretation, rock magnetic studies, microscopic analyses, and graptolite orientation measurements were performed. The results indicate that the magnetic susceptibility is mainly governed by paramagnetic minerals (phyllosilicates) with a small contribution of ferromagnetic minerals, mostly magnetite. Typically, in the studied mudstones, the AMS and AARM fabrics are characterized by strong bedding-parallel foliation, resulting mostly from compaction. The foliation is much weaker in the associated early-diagenetic calcareous concretions. Although the mudstones are almost isotropic in the bedding plane, there is a slight tendency for grouping of magnetic lineation axes with an orientation of approximately NNW-SSE. The corresponding orientation of the AMS lineation is preserved in the concretions, and the same trend also prevails in the preferred orientation of graptolites. Thus, we interpret this orientation to be related to paleocurrents. The observed directions show that during the Wenlock (Silurian) in the studied part of the Baltic Basin, the dominant currents had an orientation of circa NNW-SSE along the margin of Baltica. Our results confirm that even in such fine-grained sediments, in which there are no other unequivocal directional sedimentary indicators, paleocurrent directions can be determined by applying AMS and AARM methodology.
... The rock tensile strength is generally determined using a Brazilian-test setup (Yu et al. 2009). To investigate the fracture development and mechanical behavior of rocks, many researchers have conducted experimental work on the strength and failure of different formations (Warpinski et al. 1982;Zhao et al. 1999;Zhou and Zhao 2011;Olson et al. 2012;Suarez-Rivera et al. 2013;Mokhtari et al. 2014a;Frash et al. 2015;Li et al. 2016;. Anisotropy and layer orientation also greatly influence rock strength (Mokhtari et al. 2014;Tavallali and Vervoort 2010;. ...
Article
Understanding the mechanical behavior (compression, shear, or tension) of rocks plays an important role in wellbore-stability design and hydraulic-fracturing optimization. Among rock mechanical properties, strain is a critical parameter describing rock deformation under stress with respect to its original condition, yet conventional methods for strain measurement have several deficiencies. In this paper, we analyze the application of the optical method digital-image correlation (DIC) to provide detailed information regarding fracture patterns and dynamic strain development under Brazilian testing conditions. The effects of porosity, rock type, lamination, and saturation (freshwater and brine) on indirect tensile strength are also discussed. To examine the effect of rock type, 60 samples of sandstone (Parker, Nugget, and Berea) and carbonate rocks (Winterset Limestone, Silurian Dolomite, Edwards Brown Carbonate, and Austin Chalk) were tested under dry and saturated conditions with regard to lamination angle in laminated samples. A photogrammetry system was used to monitor the samples in a noncontact manner while conducting the indirect tensile experiment. DIC depends on the photogrammetry system, which helps to visualize and examine rock-fracture patterns from the recorded images of the rock before and after deformation by assessing the strain development in samples. The experimental results show the following. Average tensile strength declines with increasing porosity for homogeneous, laminated, and heterogeneous rock specimens. Lower tensile strengths are observed in carbonate-rock samples compared with sandstones, except for Silurian Dolomite. Saturation reduces rock strength; for homogeneous samples, the highest strength decline (28%) was observed in Berea Sandstone, whereas the largest decrease (65%) for heterogeneous samples was observed in fully heterogeneous Edwards Brown Carbonate samples. Increase of lamination angle (from 0 to 90°) affects the tensile strength. Average tensile strength observed for the Parker and Nugget Sandstones was greater in the direction perpendicular to the lamination direction (θ = 90°) compared with that of the parallel direction (θ = 0°). Fracture patterns examined for homogeneous rocks are nearly centrally propagated and relatively linear. Three different fracture patterns (central fracture, layer activation, and noncentral or mixed mode) were investigated for laminated and heterogeneous samples. Finally, DIC results illustrated the fracture creation and propagation with consistent strain mapping. The homogeneous samples produced a uniform fracture strain until the diametrical split, where the laminated samples were influenced by planes of weakness and fully heterogeneous anisotropic rocks produced winding and erratic fractures.
... Suppose 'f' is a rectangular fracture with height H (parallel to the vertical principal stress V or axis Z) and length L (parallel to the maximum horizontal principal stress H or axis X). It is assumed that the height of the fracture 'f' is contained to the reservoir layer thickness, H, due to higher stress barriers acting in the outer layers 46,47 and the fracture propagation is dominant only along its length. Under this scenario, when L/H 1, it is appropriate to consider plane Z-Y in the state of plane strain. ...
Article
Using a newly developed 2D numerical model based on the displacement discontinuity method (DDM) and the fictitious stress method (FSM), hydraulic fracture propagation near and away from a horizontal wellbore in anisotropic mudstones is studied. In addition to elastic anisotropy, the effect of fracture toughness anisotropy on hydraulic fracture propagation is included and fluid flow in fractures is fully coupled with rock deformation. Simulations show wellbore failure pressure, fracture trajectory, and near wellbore fracture apertures are significantly affected by elastic and fracture toughness anisotropy. A simple plane strain analytical solution might indicate that near wellbore fracture opening is enhanced in vertically transversely isotropic (VTI) rock. However, near wellbore fracture turning in a rock with high fracture toughness anisotropy results in severe constriction of fracture apertures. This effect becomes more severe with increase in fracture toughness anisotropy and perforation misalignment angle. Simulations of multiple hydraulic fractures from horizontal wellbores suggest that fracture lengths and apertures are affected by their orientation with respect to the directions of elastic symmetry. The spatial extent of the induced normal stresses perpendicular to the fracture surface increases when the fracture is aligned with the direction of least Young's modulus. The larger spatial extent of induced stresses in anisotropic rock leads to early termination of the fractures emanating from the inner perforation clusters, resulting in fracture networks with dominant outer fractures. In the presence of fracture toughness anisotropy, the fractures deviate towards the plane of least fracture toughness under low differential stress conditions.
... References Griffith, 1921Sneddon, 1946Harrison et al., 1954Irwin, 1957Hubbert and Willis, 1957Perkins and Kern, 1961Settari and Cleary, 1984De Pater et al., 1994Wang et al., 1994Yew, 1997Economides, 2000Zhang et al., 2005Economides et al., 2007Wu et al., 2007Bjerrum et al., 1972 Dusseault, 1988Atkinson et al., 1994Soga et al., 2006Shin and Santamarina, 2010Holtzman et al., 2012Lamont and Jessen, 1963Daneshy, 1974Zoback et al., 1977Warpinski et al., 1982Lam and Cleary, 1984Teufel and Clark, 1984Blanton, 1986Blair et al., 1990Heuze et al., 1990Renshaw and Pollard, 1995 Potluri et al., 2005Adachi et al., 2007Zhou et al., 2008Akulich and Zvyagin, 2008Zhang et al., 2009Rahman et al., 2010Chuprakov et al., 2011Batchelor and Pine, 1984Warpinski and Teufel, 1987 Dusseault, 1988Harper and Last, 1990Last and Harper, 1990Britt et al., 1994Kohl and Hopkirk, 1995Bhasin and Hoeg, 1998 Beugelsdijk et al., 2000Chen et al., 2000Kulatilake et al., 2001Rutqvist and Stephansson, 2003 De Pater and Beugelsdijk, 2005Jeffrey et al., 2010Dusseault, 2011 Notation. d: grain size. ...
Thesis
Energy related geo-systems involve a wide range of engineering solutions from energy piles to energy geo-storage facilities and waste repositories (CO2, nuclear). The analysis and design of these systems require proper understanding of geo-materials, their properties and their response to extreme temperature and high stress excitations, the implications of mixed-fluid conditions when contrasting fluid viscosities and densities are involved, the effect of static and cyclic coupled hydro-thermo-chemo-mechanical excitations, and rate effects on the response of long design-life facilities. This study places emphasis on thermal geo-systems and associated physical properties. Uncemented soils and rocks are considered. The research approach involves data compilation, experimental studies and analytical methods. Emphasis is also placed to engineer geomaterials in order to attain enhanced performance in energy geo-systems. The thermal conductivity and stiffness of most geomaterials decrease as temperature increases but increase with effective stress. This macroscale response is intimately related to contact-scale conduction and deformation processes at interparticle contacts. Pore-filling liquids play a critical role in heat conduction as liquids provide efficient conduction paths that can diminish the effects of thermal contact resistance. Conversely, grains and fluids can be selected to attain very low thermal conductivity in order to create mechanically sound thermal barriers. In the case of rock masses, heat (and gas) recovery can be enhanced by injecting fluids at high pressure to cause hydraulic fractures. Scaled experiments reveal the physical meaning of hydraulic fractures in pre-structured rocks (e.g., shale) and highlight the extensive self-propped dilational distortion the medium experiences. This result explains the higher production rate from shale gas and fractured geothermal reservoirs that is observed in the field, contrary to theoretical predictions.
... The value of induced stress field would increase with the increase in vertical stress. This conclusion was also verified by field test (Warpinski et al. 1982b;Fisher and Warpinski 2011). Rabaa (1987) studied the law of fracture height propagation of layered formation considering the stress difference between layers. ...
Article
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The fracture vertical stretching distance and fracture morphologies have great impact on the stimulated reservoir volume and well production in layered formation reservoirs. However, the prediction of fracture height shows large biases with the actual height in field operation. Fracture vertical propagation behavior and multi-field coupling mechanism are still unclear. In this paper, the fracture geometry patterns in conventional and unconventional layered formation are discussed, and multiple factors on hydraulic fracture height propagation are analyzed. We summarized advantages and disadvantages for present studies on fracture height growth and gave prospects for further research.
... In aspects of laboratory research, Anderson (1981) and Hanson et al. (1981) studied the effect of interfacial friction on fracture height growth and found that the lower the friction coefficient, the greater the normal stress required for hydraulic fracture to cross the interface. Based on laboratory experiments and field tests, Warpinski et al. (1982), Teufel and Warpinski (1983) and Teufel and Clark (1984) revealed that mechanical property differences between layers were not sufficient to prevent the propagation of hydraulic fractures at the interface, whereas the minimum in situ stress difference was critical for the fracture propagation path. Roundtree and Miskimins (2011) performed experiments combined with acoustic emission monitoring to analyze hydraulic fracture propagation patterns in layered media. ...
Article
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Whether hydraulic fractures could connect multiple gas zones in the vertical plane is the key to fracturing treatment to jointly exploit coalbed methane and tight sandstone gas through integrative hydraulic fracturing in tight sandstone-coal interbedded formations. Laboratory true triaxial hydraulic fracturing experiments were conducted on layered specimens with different combination types of natural sandstone and coal to simulate the propagation behavior of hydraulic fractures. The effects of the fracture initiation position, fracturing fluid viscosity and injection rate were discussed. The results showed that different fracture morphologies could be found. When initiating from coal seams, three patterns of fracture initiation and propagation were obtained: (1) The main hydraulic fracture initiated and propagated along the natural fractures and then diverged due to the effects of in situ stress and formed secondary fractures. (2) The hydraulic fracture initiated and propagated in the direction of the maximum horizontal stress. (3) Multiple fractures initiated and propagated at the same time. With the same fracturing fluid viscosity and injection rate, the hydraulic fractures initiating in sandstones had greater chances than those in coal seams to penetrate interfaces and enter neighboring layers. Excessively small or large fracturing fluid viscosity and injection rate would do harm to the vertical extension height of the induced fracture and improvement of the stimulated reservoir volume. Compared with operation parameters (fracturing fluid viscosity and injection rate), the natural weak planes in coals were considered to be the key factor that affected the fracture propagation path. The experimental results would make some contributions to the development of tight sandstone-coal interbedded reservoirs.
... The occurrence (orientation and length/width/height) of hydraulic fracture is related to the stress state of reservoir and surrounding rock [16][17][18][19], pumping parameters and working fluid viscosity [20,21]. The most ideal form of hydraulic fractures is to make fractures in the reservoir, that is, the length reaches the preset requirements, and the fractures are confined to the reservoir as far as possible in the longitudinal direction. ...
... The minimum horizontal stress profile and hydraulic fracture growth and termination plotted based on hydraulic fracture mined-back measurements ([10] with modification). ...
Article
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Methods for determining in situ stresses are reviewed, and a new approach is proposed for a better prediction of the in situ stresses. For theoretically calculating horizontal stresses, horizontal strains are needed; however, these strains are very difficult to be obtained. Alternative methods are presented in this paper to allow an easier way for determining horizontal stresses. The uniaxial strain method is oversimplified for the minimum horizontal stress determination; however, it is the lower bound minimum horizontal stress. Based on this concept, a modified stress polygon method is proposed to obtain the minimum and maximum horizontal stresses. This new stress polygon is easier to implement and is more accurate to determine in situ stresses by narrowing the area of the conventional stress polygon when drilling-induced tensile fracture and wellbore breakout data are available. Using the generalized Hooke’s law and coupling pore pressure and in situ stresses, a new method for estimating the maximum horizontal stress is proposed. Combined it to the stress polygon method, a reliable in situ stress estimation can be obtained. The field measurement method, such as minifrac test, is also analyzed in different stress regimes to determine horizontal stress magnitudes and calibrate the proposed theoretical method. The proposed workflow combined theoretical methods to field measurements provides an integrated approach for horizontal stress estimation.
... Often in the petroleum engineering and dynamics of fluids in porous media literature, the Linear Hydraulic Diffusivity Equation (LHDE) is solved through Laplace and Fourier transform or Boltzmann transformation, (Everdingen & Hurst 1949, Peres et al. 1989. Warpinski, Northrop, Schmidt, Vollendorf & Finley (1981), Warpinski, Tyler, Vollendorf & Northrop (1981), Warpinski, Fnley, Vollendorf, O'Brien & Eshom (1982), Warpinski, Schmidt & Northrop (1982), Warpinski et al. (1985) carried out a series of field experiments to research the in situ stresses and geological discontinuities influence in the hydraulic fractures growth. Warpinski et al. (1993Warpinski et al. ( , 1998 analyzed a cored hydraulic fracture in a gas well in two different intervals to investigate the abnormal fracturing pressuring occurrences, fracture height growth and proppant transport. ...
Conference Paper
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Analytical solutions for nonlinear oil and real gas flow through pressure-sensitive reservoirs constitute the state of the art of the reservoir engineering and formation evaluation literature. This work develops an analytical model to evaluate the formation mechanical damage caused by the effective permeability loss as a function of the pore pressure and oil flow rates in a fractured vertical well fully penetrating a pressure-sensitive reservoir with source. The nonlinear hydraulic diffusivity equation (NHDE) is solved through an integro-differential approach coupled to Green's function (GF) related to a semi-infinite source plan that represents a hydraulic fracture (HF). This paper also shows that the general solution is expressed by the sum of the linear solution plus a corrective term given by the complementary error function erfc(y D , t D). The proposed model is implemented in Matlab ® software and the calibration is performed through a porous media numerical oil flow simulator, widely used in the petroleum industry and scientific works, which showed high convergence. The permeability curves are obtained experimentally through two case studies that constitute two reservoir layers in the same vertical well with permeabilities in initial pressure values k(p i) of 170 mD and 340 mD.
... In layered rock strata, the hydraulic fracture morphology has unique characteristics and complexity [33][34][35][36][37]. Previous hydrofracturing experiments generally install a group of artificial fractures in the poured homogeneous test block to study the influence of weak surface. ...
Article
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Hydraulic fracturing is a rock structure transformation method that significantly weakens the mechanical properties of the hard roof strata. Considering the poor hydraulic fracturing effect of special structure such as composite layered rock, this paper carries out hydraulic fracturing numerical simulation experiments and compares the hydraulic fracture morphology and bedding plane interaction mode under different injection rate and injection modes. The experimental results show that the bedding plane can change the trajectory and propagation direction of hydraulic fracture. Under the low injection rate, hydraulic fracturing is conducive to open the bedding plane, but the expansion length of the main hydraulic fracture is easy to be limited. Under the high injection rate, the hydraulic fracture can extend for a long distance. But the fracture morphology tends to be slender and single, which is not conducive to the formation of fracture network. Compared with conventional hydraulic fracturing, stepped variable injection rate hydraulic fracturing can activate more bedding planes, so as to improve the effect of rock strata transformation. The experimental results are instructive in achieving effective control of composite layered rock.
... More specially, the weak hor-izontal plane distributing ahead of the fracture tip significantly reduces the HF height [6]. The HF geometries are determined by the in situ stress difference between production layer and interlayer [7][8][9], elastic parameter difference [10][11][12], fracture toughness difference [13][14][15], interface strength [15], the distribution of fluid-injection pressure inside the fracture, and rheological and viscous characteristics of fracturing fluid [16][17][18][19]. ...
Article
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Hydraulic fracturing can improve the permeability of composite thin coal seam. Recently, characterizing hydraulic fracture (HF) propagation inside the coal seam and evaluating the permeability enhancement with HF extension remain challenging and crucial. In this work, based on the geological characteristics of the coal seam in a coal mine of the southwest China, the RFPA2D-Flow software is employed to simulate the HF propagation and its permeability-increasing effect in the composite thin coal seam, and a couple of outcomes were obtained. (1) Continuous propagation of the hydraulic microcrack-band is the prominent characteristic of HF propagation. With the increment of the injection-water pressure, HF generation in the composite thin coal seam can be divided into three stages: stress accumulation, stable fracture propagation, and unstable fracture propagation. (2) The hydraulic microcrack-band propagates continuously driven by the fluid-injection pressure. The microcrack-band not only cracks the coal seam but also fractures the gangue sandwiched between the coal seams. (3) The permeability in the composite thin coal seam increases significantly with the propagation of hydraulic microcrack-band. The permeability increases by 1~2 magnitudes after hydraulic fracturing. This study provides references to the field applications of hydraulic fracturing in the composite thin coal seam, such as optimizing hydraulic fracturing parameters, improving gas drainage, and safe-efficient mining.
... Although the number of samples in our HF test is small, all three samples exhibit the formation of the main fracture framework during the first pumping, which indicates that the initial HF operation would likely has a large impact on field reservoir construction. And high confining pressure will cause the fracture modification to be concentrated near the borehole, but lower confining pressure help to the main fractures to extend longer (Warpinski et al., 1982). This suggests that HF at shallow depths (low confining pressure) may result in greater reservoir space, while the deeper depths (high confining pressure) is likely to create smaller reservoir space, but with more adequate reservoir construction effect. ...
Article
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Hydraulic fracturing (HF) technology is crucial to form connected fracture network within the low-permeability geothermal reservoir. However, the HF process and failure mechanism in this process are only partly understood. A series of true triaxial hydraulic fracturing tests on large-scale natural granite samples were conducted under different confining conditions, combining with acoustic emission monitoring to evaluate the initiation and propagation of hydraulic fractures. Results show that a main hydro-fracture was formed in three samples during the first fracturing process. Many AE events occurred during the first pump period. The proportion of tensile fractures during the hydraulic fracturing accounted for more than 85% of all fractures. The test results could provide a new understanding of the effect of HF under different stress conditions. And implied that field engineering should pay attention to the initial HF, which may determine the main fracture framework of the field at the first pump procedure.
... The model developed was based on point-source as part of a more general theory of GF's to solve difficult flow problems. Warpinski, Northrop, Schmidt, Vollendorf & Finley (1981), Warpinski, Tyler, Vollendorf & Northrop (1981), Warpinski, Fnley, Vollendorf, O'Brien & Eshom (1982), Warpinski, Schmidt & Northrop (1982), Warpinski et al. (1985) carried out a series of field experiments to research the in situ stresses and geological discontinuities influence in the hydraulic fractures growth. Nolte & Smith (1981) presented a work about the pressure interpretation to identify periods of confined-height extension, uncontrolled height growth and critical pressure during the hydraulic fractures manufacturing. ...
Conference Paper
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This work presents a new analytical model to evaluate the effective permeability response during the oil’s production through a fractured vertical well fully penetrating a pressure-sensitive reservoir. The nonlinear hydraulic diffusivity equation (NHDE) is solved analytically through an integro-differential model coupled to Green’s function (GF) related to a semi-infinite oil source plan that represents a hydraulic fracture. The NHDE is perturbed using a first-order asymptotic series expansion method and the solution is derived in terms of a new effective permeability pseudo-pressure function, considering the matrix and fracture permeability roles. A new hydraulic diffusivity deviator factor is also derived to represent the effective permeability loss as a function of the pore pressure throughout the well-reservoir life-cycle. For this modeling, the general solution is expressed by the sum of the linear solution (constant permeability) plus a corrective term given by the combination of the exponential function and the complementary error function erfc(yD,tD). The model calibration is performed through a porous media numerical oil flow simulator, named IMEX® and the results presented high accuracy.
... Several factors govern hydraulic fracture patterns. In-situ stress anisotropy plays the forefront role in controlling fracture geometry (Warpinski et al., 1982), but when stresses are more isotropic, hydraulic fractures can branch into multiple directions (Kresse et al., 2013). Furthermore, weak geological discontinuities, such as pre-existing natural fractures, can promote hydraulic fracture branching (Olson et al., 2012;Zoback et al., 1977). ...
Article
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Plain Language Summary Hydraulic fracturing involves injecting fluid under high pressure into wells to create fractures. This is a key technique that enables economic hydrocarbon production from tight petroleum‐bearing formations whose ability to produce is otherwise too low. The same technique has also been researched for geothermal energy exploitation. Previous studies demonstrate that hydraulic fractures can either grow as planar or bifurcate into multiple branches. Branched fractures provide a larger surface area which is beneficial for increasing gas production from wells. Except for a 2019 incomplete theoretical study by the authors, the conditions that cause branching were until now experimentally unverified, and so one had to rely on intuitive guessing how to achieve it and optimize it. To address this problem, we conducted laboratory hydraulic fracturing experiments to quantify the injection rates and fluid viscosities that will cause branching. Our results indicate that fractures can transition from a single planar crack to branched cracks when the fluid viscosity is in an optimum range for a given injection rate. We also propose a theory to predict our experimental results and apply our results to field applications. This provides a useful new capability to improve the control of hydraulic fracturing.
... In recent years, relevant scholars have carried out many experiments on the interaction mechanism between hydraulic fractures and rock bedding planes [6][7][8][9]. The research results show that under the condition of different bedding plane strength [10], in situ geo stress coefficient [11], the material difference [12,13], injection pressure, and rheological and viscous characteristics of fracturing fluid [14][15][16], hydraulic fractures will form three modes: (1) expanding along the bedding plane, (2) expanding along the bedding plane and crossing the bedding plane, and (3) crossing the bedding plane. These three kinds of propagation modes can be observed in relevant hydraulic fracturing tests and reservoir microseismic monitorization [17]. ...
Article
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The stress disturbance effect will significantly affect the propagation path of hydraulic fractures in the composite rock reservoir. To reveal the influence mechanism of stress disturbance effect on the hydraulic fracture propagation, several groups of laboratory tests and simulation tests were carried out. The test results showed that the hydraulic fracture tip formed a disturbing stress field because of the pore water pressure. Before the hydraulic fracture was extended to the bedding plane, the bedding plane had been damaged under stress disturbance, and the disturbed fracture zone was formed. The propagation mode of hydraulic fracture at the bedding plane was highly sensitive to the formation of the disturbed fracture zone. The sensitivity is mainly reflected from two aspects. (1) Under the action of the hydraulic fracture tip disturbance stress, many microfractures are generated and penetrated into the disturbance fracture zone on the bedding plane. This behavior is accompanied by energy dissipation causing the bedding plane material to be significantly softened, and the energy required for hydraulic fracture propagation is reduced dramatically. (2) The formation of the disturbed fracture zone improves the degree of fragmentation of the bedding plane, and the permeability of the local area increases significantly, forming the dominant circulation path. The higher the development of the disturbed fracture zone, the greater the hydraulic fracture propagation tendency along the bedding plane. According to the formation characteristics of the bedding plane disturbed fracture zone, the author proposed a nonlinear fracture model of the bedding plane disturbed fracture zone and established the hydraulic fracture propagation path criterion. This paper further analyzed the influencing factors of the disturbed fracture zone’s formation conditions and found that the bedding plane’s cementation strength was the main factor affecting the development degree of the disturbed fracture zone. 1. Introduction The reservoir rock mass of oil, natural gas, and unconventional natural gas reservoirs comprises various rock materials, discontinuous structural planes, and microfractures. When hydraulic fracturing is applied to a composite rock reservoir, the existence of a weak bedding plane will significantly affect the extension path of hydraulic fractures [1]. How to control the propagation of hydraulic fractures in such reservoirs is a critical problem in a hydraulic fracturing design [2–5]. In recent years, relevant scholars have carried out many experiments on the interaction mechanism between hydraulic fractures and rock bedding planes [6–9]. The research results show that under the condition of different bedding plane strength [10], in situ geo stress coefficient [11], the material difference [12, 13], injection pressure, and rheological and viscous characteristics of fracturing fluid [14–16], hydraulic fractures will form three modes: (1) expanding along the bedding plane, (2) expanding along the bedding plane and crossing the bedding plane, and (3) crossing the bedding plane. These three kinds of propagation modes can be observed in relevant hydraulic fracturing tests and reservoir microseismic monitorization [17]. With the research deepening, some scholars carried out experiments on microcrack propagation mechanism and found that [18–20]; when the fracture approached the bedding plane, the disturbing stress field at the fracture tip would lead to the early failure of the bedding plane and form the microfracture zone, which was called Cooke-Garden cracking effect [21]. This early bedding plane fracture zone has a significant trapping effect on fracture propagation [22, 23]. However, at present, the research on this effect mainly focuses on surface crack propagation under a single stress state. By contrast, the research on fracture propagation under complex stress of fluid-solid coupling is rare, and it is helpful to reveal the mechanical mechanism of hydraulic fracture propagation at the bedding plane of composite rock material and is an effective means to solve the problem of reservoir reconstruction. At present, the mechanical mechanism of the development of hydraulic fracture at the composite rock bedding plane is mainly divided into the following two aspects: firstly, based on the linear elastic mechanic’s theory, taking the two-dimensional plane fracture as the research object and assuming a constant static pressure in the hydraulic fracture ignore the induced stress in the direction of perpendicular to the fracture [24]. The Mohr-Coulomb failure criterion is used to analyze the tensile failure caused by tensile stress acting on the fracture [25], and the shear slip failure caused by the shear stress acting on the fracture is considered through the linear friction theory [26]. Secondly, based on the linear elastic fracture mechanics, the analytical model of induced stress distribution at the fracture tip is established to provide the basis for judging whether the hydraulic fracture initiated or expanded [27]. The above research provides a useful reference for revealing the hydraulic fracture propagation mode and propagation path at the bedding plane, but there are still some deficiencies as follows: (1) both analytical criteria are based on the assumption that the rock bedding plane is completely cemented and ignored the change of stress field distribution and damage to materials caused by disturbed stress of hydraulic fracture. (2) Relevant scholars have revealed the morphological characteristics of actual hydraulic fractures by drilling cores [28]. Many microfractures or secondary fractures formed at the tip of actual hydraulic fractures reflect the morphological characteristics of complex clusters of small-sized fractures, which is inconsistent with the conventional understanding of wing hydraulic fractures. Therefore, the traditional hydraulic fracturing theory [29] based on elastic-plastic mechanics and linear elastic fracture parameters can not adequately describe the hydraulic fracture morphology and propagation law. At present, it is necessary to establish a nonlinear fracture model as the theoretical basis of the new hydraulic fracturing model to understand the hydraulic fracture extension mode comprehensively. Most of the hydraulic fracturing experiments are also realized by direct observation of the internal hydraulic fracture morphology of the text block by the naked eye and microscope. Due to the closed confining pressure loading environment in the hydraulic fracturing test, it is difficult to observe the bedding fracture zone and the dynamic hydraulic fracture propagation process under the existing technology. Although the formation process of the fracture zone can be monitored by associated acoustic emission equipment (AE) [30–33], there is a significant disadvantage of determining the dynamic propagation process of hydraulic fracture only by the distribution range of acoustic emission events because the damage process of bedding plane is a quasistatic process with low energy release rate and long formation time, which is difficult to monitor. Moreover, it is difficult to distinguish whether the bedding fracture zone’s formation is caused by stress induction or direct invasion of fracturing fluid. Thus, the distribution of the stress field in the test block can not be obtained. So, many studies in this part only focus on the macrophenomenon but the lack of research on the mesomechanism of the event restricts the understanding of the hydraulic fracture propagation mechanism and the formation mechanism of the hydraulic fracture network. Therefore, the particle flow calculation method proposed by Dr. Cundall based on the discrete element theory is used to tackle this problem [34, 35], whose modelled failure process is very consistent with the real failure of rock compared with other methods. It can monitor the dynamic fracture propagation process [36, 37]. It has been widely used in many geotechnical engineering research fields, such as rock mechanics tests, underground space excavation, slope engineering, and mining engineering. The fluid-structure coupling model established by PFC software can genuinely reproduce the hydraulic fracturing process and benefit from observing the hydraulic fracture morphology, which is an effective method to study the interaction between hydraulic fracture and bedding plane [38]. To sum up, this paper described the formation characteristics of bedding fracture zone under stress disturbance effect and the interaction mechanism between hydraulic fracture and bedding microfracture zone. A nonlinear fracture model of a disturbed fracture zone was proposed. The judgment criterion of the propagation path at the hydraulic fracture bedding plane considering the stress disturbance effect was improved. The sensitivity analysis of the influencing factors of the disturbance effect was carried out. 2. Particle Flow Method Relevant research results have proved that the parallel bond model can simulate the fracture initiation and propagation of rock under different stress conditions, and it is in good agreement with the results of laboratory tests and theoretical analysis [35]. Besides, the channel formed between broken rigid bodies can be used to simulate fluid flow in pipes. Based on the fluid-solid coupling algorithm proposed by Cundall in 2000, after continuous improvement by relevant scholars, the fluid-solid coupling problem can be better simulated and calculated [39–45]. 2.1. Parallel Bond Model The particle discrete element method is based on Newton’s second law and force-displacement rule to determine the motion of particles and the force on the contact surface. Its core is the contact characteristics of particles, that is, the constitutive contract law. The constitutive contact model is described by a mesomodel and parameters which characterize the stiffness, damping, and friction (Figure 1). A parallel bonding model is similar to a group of springs, which are evenly arranged on the adjacent area of two contact particles. It has not only standard stiffness and tangential stiffness but also normal tensile strength and shear strength, which can transfer the force and moment between particles. If maximum stresses exceed the corresponding bond strength [46], the parallel bond will break, and the bond material and its associated forces, moments, and stiffness will be removed from the model, and only the linear model will be available. The failure criterion is closer to the real rock failure condition [38–40]. (a)
... show that the injection rate, in situ stress coefficient, bedding plane bonding strength, and fracturing fluid viscosity have an obvious influence on the interaction mode of hydraulic fractures at the bedding plane [13][14][15][16][17][18][19][20]. The above experiments provide good references for related mechanistic research. ...
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Hydraulic fracturing applications have shown a stress disturbance effect during hydraulic fracture propagation, which is often ignored. Using laboratory and discrete element numerical simulation tests, hydraulic fracture propagation under this stress disturbance is systematically studied. The results show that during hydraulic fracturing, the bedding plane is damaged by the stress disturbance, forming a bedding fracture zone (BFZ). The nonlinear fracture characteristics of the formation process of the disturbed fracture zone are revealed, and two indexes (the number of fractures in the disturbed fracture zone and the size of the disturbed fracture zone) are proposed to evaluate the fracturing effect of the stress disturbance. Based on these indexes, multifactor sensitivity tests are conducted under different geological conditions and operational factors. When the principal stress () difference is large, the number of hydraulic fractures gradually decreases from many to one, and the direction of the hydraulic fractures gradually approaches the vertical direction of , but the change in the in situ stress condition has no obvious effect on the stress disturbance effect. The weaker the bonding strength of the bedding plane, the more significant the stress disturbance effect is, and the easier it is for the fractures to expand along the bedding plane. With increasing injection rate, the stress disturbance effect first increases and then decreases, and the hydraulic fracture propagates from along the bedding plane to cross the bedding plane. With increasing relative distance between the injection hole and bedding plane, the stress disturbance effect presents a linearly increasing trend, and the hydraulic fractures along the bedding planes extend. Based on the experimental results, the relationship between the fracturing effect of the stress disturbance and the extension mode of the hydraulic fracture is determined, and an optimization method for hydraulic fracturing in composite rock reservoirs is given. The research results can provide a theoretical basis for controlling the formation of complex fracture networks in composite rock reservoirs. 1. Introduction Since its successful application in Kansas in 1947, hydraulic fracturing has been widely used in oil-gas field development, mine roof control, and other related fields and has achieved good application results [1–4]. The key to hydraulic fracturing design is the morphology of hydraulic fractures [5]. Due to long-term geological movement, most rock masses in nature (including tight oil-gas reservoirs and deep coal rock masses) contain a large number of structural planes of different sizes, such as bedding planes, joints, and natural fractures [6, 7]. When hydraulic fracturing is carried out on reservoirs with bedding planes, hydraulic fractures extending to bedding planes will exhibit behaviours such as penetration, steering, capture, and bifurcation [8]. The existence of bedding planes significantly affects the extension mode and expansion morphology of hydraulic fractures [9–11], which directly determines the final hydraulic fracturing effect of the reservoir [12]. Therefore, the key to improving the permeability of low permeability reservoirs and enhancing the weakening effect of hard roofs above coal seams is to study the propagation mechanism of the hydraulic fracture in composite rock materials with bedding planes. In recent years, relevant scholars have carried out a large number of experiments on the interaction mechanism between hydraulic fractures and bedding planes. The results show that the injection rate, in situ stress coefficient, bedding plane bonding strength, and fracturing fluid viscosity have an obvious influence on the interaction mode of hydraulic fractures at the bedding plane [13–20]. The above experiments provide good references for related mechanistic research. However, the above research focuses on the overall propagation response characteristics of the hydraulic fracture under different hydraulic macrofracturing conditions, ignoring the influence of the fracturing effect induced by the disturbing stress of hydrofracturing on the propagation path of the hydraulic fracture at the bedding plane, and the relationship between them is not clear. Therefore, there are limitations in the understanding of the hydraulic fracture propagation law of composite rock materials, which cannot overall describe the real hydraulic fracture propagation in the bedding plane. Related theories of rock fracture mechanics have shown that the disturbance stress produced in the process of crack propagation will lead to a continuous change in the surrounding rock stress field and then to a change in the rock mechanical properties. With the deepening of research studies, some scholars have carried out experiments on microcrack propagation mechanisms and found that [21, 22], when the fracture approaches the bedding plane, the disturbing stress field at the fracture tip will lead to the early failure of the bedding plane and form a microfracture zone on the bedding plane, which is referred to as the fracturing effect induced by the disturbing stress [23, 24]. The bedding plane fracture zone induced by the disturbance stress has a significant trapping effect on the fracture propagation. However, to date, research on this effect has been mainly focused on surface fracture propagation under a single stress loading state. In contrast, research on fracture propagation under the complex stress of hydraulic fracturing fluid-solid coupling has been minimal. Due to the “black box” environment of hydraulic fracturing experiments [25], this effect is difficult to monitor in hydraulic fracturing wells and laboratories, which explains why most studies ignore the influence of the fracturing effect induced by the disturbing stress on hydraulic fracture propagation. At present, the stress disturbance effect of hydraulic fracturing is still in the theoretical stage, and there is no systematic research on this influencing factor through relevant experiments or numerical simulations. With the continuous progress of computer technology and numerical simulation algorithms, the combination of experimental research and numerical simulations provides a feasible solution to solve this problem [12, 26–29]. At present, there are four popular numerical simulation methods used to research hydraulic fracturing [30–32]: the finite element method (FEM), extended finite element method (XFEM), boundary element method (BEM), and discrete element method (DEM). The basic idea of the FEM is to discretize the elastic body into an equivalent system of small elements [33]. In this method, the crack boundary coincides with the mesh nodes, and a mesh reconstruction method is used to simulate the crack propagation. The hydraulic fracturing model established by this method requires less calculation and has a high efficiency. However, the hydraulic fracture can only extend along a preset path, and the FEM cannot simulate the deflection of hydraulic fractures or the formation process of a complex fracture network [34, 35]. The XFEM is based on the FEM and introduces a shape function to represent the discontinuity of the displacement field [36–38], so the description of the discontinuous displacement field is completely independent of the mesh boundary. This method can simulate the fracture propagation along any path without grid reconstruction. This is advantageous in the analysis and calculation of fracture problems and greatly improves the calculation efficiency. The disadvantage of the XFEM is that the hydraulic fracturing simulation of a natural fractured reservoir needs further development. The BEM is a numerical method that divides the elements along the boundary of the domain and approximates the boundary conditions with functions satisfying the governing equations by interpolating at the boundary elements. Because the number of elements needed in the calculation model is small and the data preparation is simple, the solution efficiency and accuracy of the BEM are high. However, this method requires a known analytical solution to solve the problem, so it is only suitable for solving linear and homogeneous problems [39–42]. The main idea of the DEM is to use an explicit algorithm to calculate the motion of particles or blocks: that is, update the motion and contact state of particles in each calculation [43, 44]. When the contact force exceeds its bearing limit, the material will demonstrate shear dislocation, compression shear failure, tensile failure, and other rock fracture phenomena [45, 46]. The channel formed between particles can be used to simulate the fluid flow in a pipe. Because the DEM does not need to satisfy the continuity condition, it has significant advantages in dealing with discontinuous structures such as bedding planes and natural fractures. In addition, the DEM is very suitable for simulating the initiation and propagation of microcracks in rock. Considering that this paper mainly focuses on the micromechanism of the stress disturbance effect on the bedding plane damage in the process of hydraulic fracture propagation, the discrete element simulation method is more suitable. According to the laboratory experimental results, a discrete element numerical simulation program is debugged and validated, to verify the validity of the numerical model, to truly reproduce the whole process of the dynamic propagation of hydraulic fractures, and to observe the stress field distribution inside the test block and the bedding plane fracture zone formed by the disturbance effect, which is an effective way to study the hydraulic fracture propagation law of composite rock materials considering the stress disturbance effect. In conclusion, experimental research and a DEM numerical simulation using particle flow code (PFC) are combined in this paper, focusing on the stress disturbance fracturing effect of hydraulic fracturing and describing the formation characteristics of the bedding disturbance microfracture zone. The interaction mechanism between the hydraulic fracture and bedding disturbance fracture zone is studied, and a sensitivity analysis of geological conditions and hydraulic fracturing conditions affecting the fracturing effect of stress disturbance is carried out. The research results can provide a theoretical basis for controlling the formation of a complex fracture network of composite rock materials. 2. Particle Flow Method 2.1. Parallel Bond Model The linear parallel bond model used in this paper is appropriate for simulating the micromechanical properties of composite rock material. The parallel bonding model (BPM) is similar to a group of springs, which are evenly arranged on the adjacent area of two contact particles centered on the contact point and consist of a linear element and a parallel bond element [47] (Figure 1). Among them, linear element can transmit elastic interactions between particles. Parallel bond element provides a bonded effect that can transfer forces and moments between particles [48]. If maximum stresses exceed the corresponding bond strength [49], the parallel bond will break. The bond material and its associated forces, moments, and stiffness will be removed from the model, and only the linear model will be available.
... They outlined that HF would be contained if the stiffness of the pay zone was less than that of the adjacent caprock layers; otherwise, fracture penetration would occur. However, some scholars claimed that the fracture containment was ascribed not only to stiffness between layers but also to interface properties and interlayer stress differences (Warpinski et al., 1982;Teufel and Clark, 1984;Smith et al., 2001;Gu and Siebrits, 2005;Daneshy, 2007;Zhou et al., 2017). In addition, the interfacial shear strength and the angle of approach between the HF and natural interface may play an important role in HF containment. ...
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Geothermal energy has been widely proposed as a potential renewable energy to replace traditional fossil fuel energy. Hot dry rock (HDR) reservoir which contains abundant geothermal energy widely distributes in China. The Gonghe Basin in Northwest China is chosen to develop the Chinese first HDR field operation project. HDR is a low-permeability, high temperature and hard granite without fluid. Developing HDR requires water cyclically flowing between injection and production wells to extract heat energy. Hydraulic fracturing, as a key reservoir stimulation technology, can create the path of fluid cyclically flowing. However, few studies have investigated hydraulic induced artificial fractures in HDR geothermal formations. This paper investigated HDR geothermal reservoir stimulation characteristics and fracture patterns during hydraulic fracturing. Reservoir stimulation was conducted with a true triaxial hydraulic fracturing apparatus which could establish a real HDR formation environment in the laboratory. The factors affecting breakdown pressure and fracture creation were investigated via experiments and numerical simulations. This study could be used to evaluate and design reservoir stimulation in field HDR geothermal operation.
Article
Fracture-filling hydrates were recovered above the gas chimneys originating from the Songnan Low Uplift in the northern Qiongdongnan Basin, South China Sea. The variable distributions of gas hydrate and free gas at different drilling sites indicate that fluid flows varied significantly in space. The ambiguous and indistinct migrations of gas-bearing fluid and associated flows are potential geohazards, but limited data hampered the evaluation of the fluid flow before drilling. Nearly no study focused on the typical characteristics of heterogeneous fluid flows in the study area yet. Several wells were mainly drilled through the seepage pathways on three gas chimneys where the fluid flows exhibited three different levels from weak to strong. Fractures in these seepage pathways are the direct evidences of up-going fluid flow. To quantify these fractures, we established a new rock-physics model for unconsolidated and anisotropic hydrate-bearing sediments based on the experimental tests and pressure cores, where high-angle fractures developed within the unconsolidated deposits. The model parameters unrelated to the fractures were optimized using a reference well without gas or hydrate occurrence. Then, the fracture parameters including the fracture density and the aspect ratio of the fracture, were obtained through the Monte Carlo inversion. We found that the evolution of the fracture characterized the heterogeneous fluid flows. Weak flows only made few fractures in the sediments, but sufficient gas supply and long-term seepage produced more fractures. They gradually changed the shape of the fractures in the sediments with fewer fractures, where the isolated fractures merged to form longer fractures, and provided fracture-induced porosity similar to that of sediments with more fractures when the fractures were almost completely filled with hydrates, and nearly all of the free gas beneath the bottom simulating reflectors had been released at this time. These insights are consistent with the drilling. We analyzed the related seismic attributes, submarine geomorphology, and geochemical index, which significantly supported the proposed model. The model provides a direct and quantitative insight of the fracture-filling hydrates and explains the variations distribution of underlying free gas.
Conference Paper
Microseismic data and post-fracturing production have confirmed the positive role of fracture complexity on production enhancement in fractured wells. While operators are looking for different fluids and pumping schedules to enhance fracture complexity, the mechanisms ruling the process is not fully understood. This paper provides a comprehensive workflow to model the fracture pattern development by accounting for interactions with numerous natural fractures. We present a robust finite element model with adaptive insertion of three-dimensional cohesive elements for fracture propagation through the intact rock as well as the network of intersecting natural fractures. Cohesive elements are coupled with general Darcy's flow to incorporate fluid flow as well as elastic and plastic deformations of rock during initiation, propagation and closure of hydraulic fractures. Hydraulic fracturing treatment has been simulated for different natural fracture patterns. Fluid injection pressure fluctuations are observed while reopening natural fractures. The impact of operation schedules on network complexity such as hesitation time is investigated. The complexity of fracture network is characterized by the ratio of total fracture length to its effective radius from the wellbore. Our analysis has shown that in addition to the differential stress and the fracture intersection angle which are already determined by the nature, pumping injection rate and hesitation time can play a significant role in fracture branching and its diversion to different natural fracture sets. Higher injection rate is found to have a positive effect to overcome the resistance of natural fractures in different directions, and hesitation in the middle of pumping can force the fracture to divert into other directions, both of which help develop a more complex fracture pattern.
Article
The widely accepted formulation for the crack tip plastic zone in metals is reviewed. Observations on how rock fracture differs from metal fracture motivates a change from the Von Mises yield condition to a maximum normal stress criterion. This results in a crack tip microcrack zone description that is consistent with observed fracture toughness behavior for rock. The model is extended to include the application of confining stresses. This includes anisotropic in situ stress states as well as hydrostatic compression, Verification of this model rests on its ability to explain observed fracture behavior. A suggestion is made for improving hydraulic fracture containment models based on average crack-tip stresses rather than the stress intensity factor. Refs.
Article
American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract For many years hydraulic fracturing has been used as a stimulation tool for oil and gas reservoirs. Hydraulic fracturing has also been developed as a method to measure in situ stresses. The correspondence between the measured fluid pressures and the in situ stresses has been studied and is fairly well understood. The characteristics of the fractures created by hydraulic fracturing are not understood. Information about the fractures at the wellbore can be obtained by a number of techniques but knowledge of the fractures behavior away from the well is very limited. The fracture behavior may determine either the stress direction for a stress measurement or the difference between a good or bad stimulation job. To better understand the hydraulic fracture technique, experiments were performed in a tuff formation in Rainier Mesa performed in a tuff formation in Rainier Mesa at the Nevada Test Site. The purpose of the experiments was to determine the stresses in the mesa; and, to examine the fracture behavior produced by the hydraulic fracture technique. Hydraulic fracturing was performed in both vertical and horizontal performed in both vertical and horizontal boreholes with a maximum overburden of 1490 ft. All experiments were done in the vicinity of an existing tunnel complex but sufficiently remote to avoid unwanted boundary effects. The stresses were determined from the hydraulic fracture data using the theory of Fairhurst and Haimson. The maximum horizontal, vertical and minimum horizontal principal stresses for 1365 ft. of overburden principal stresses for 1365 ft. of overburden were 1788 psi, 1183 psi, and 1015 Psi, respectively. A number of the fractures produced during the tests were mapped by produced during the tests were mapped by mining from the tunnel complex and physically examining the fractured formation. physically examining the fractured formation. Dyed water was used for all the holes drilled in the tunnel complex. Dyed cement grouts were used to tag the fractures formed in a 1365 ft. deep hole from the top of the mesa. Two fracture jobs were performed at two locations in the vertical hole using yellow and red grouts. These fractures were essentially vertical and parallel.
Article
In situ experiments, which are accessible for direct observation by mineback, were conducted to determine the effect that material-property interfaces and in situ stress differences have on hydraulic fracture propagation and the resultant overall geometry. These experiments show conclusively that a difference in elastic modulus at a geologic interface has little or no effect on crack growth and, therefore, is not a feature which would promote containment of fractures within a specified reservoir zone. However, differences in the in situ stress between adjacent layers is shown to have a considerable influence on fracture propagation. Experiments were conducted in a low modulus ash-fall tuff which contained two layers of high minimum principal in situ stress and which was overlain by a formation with at least a factor of 5 increase in elastic modulus. Fractures were observed to terminate in regions of high minimum principal in situ stress in nearly every case.
Article
Two theoretical models that simulate, respectively, the local and distance effects of the hydraulic fracturing process were formulated. Application and analysis have indicated that for a penetrating fluid the stress intensity factor tends to decrease as the pore pressure increases. Laboratory fracturing experiments the hydraulic fluid pressure necessary to initiate a crack is relatively insensitive to the applied load on the block. The sensitivity of the principal stress magnitudes on the fracture orientation was also tested. A rock geometry and mechanics study of the Western tight gas sands was also completed. Bibtex entry for this abstract Preferred format for this abstract (see Preferences) Find Similar Abstracts: Use: Authors Title Keywords (in text query field) Abstract Text Return: Query Results Return items starting with number Query Form Database: Astronomy Physics arXiv e-prints
Article
Hydraulic fracture containment is discussed in relationship to linear elastic fracture mechanics. Three cases are analyzed,the effect of different material properties for the pay zone and the barrier formation,the characteristics of fracture propagation into regions of varying in-situ stress, propagation into regions of varying in-situ stress, andthe effect of hydrostatic pressure gradients on fracture propagation into overlying or underlying barrier formations. Analysis shows the importance of the elastic properties, the in-situ stresses, and the pressure gradients on fracture containment. Introduction Application of massive hydraulic fracture (MHF) techniques to the Rocky Mountain gas fields has been uneven, with some successes and some failures. The primary thrust of rock mechanics research in this area is to understand those factors that contribute to the success of MHF techniques and those conditions that lead to failures. There are many possible reasons why MHF techniques fail, including migration of the fracture into overlying or underlying barrier formations, degradation of permeability caused by application of hydraulic permeability caused by application of hydraulic fracturing fluid, loss of fracturing fluid into preexisting cracks or fissures, or extreme errors in preexisting cracks or fissures, or extreme errors in estimating the quantity of in-place gas. Also, a poor estimate of the in-situ permeability can result in failures that may "appear" to be caused by the hydraulic fracture process. Previous research showed that in-situ permeabilities can be one order of magnitude or more lower than permeabilities measured at near atmospheric conditions. Moreover, studies have investigated the degradation in both fracture permeability and formation permeability caused by the application of hydraulic fracture fluids. Further discussion of this subject is beyond the scope of this paper. This study will deal mainly with the containment of hydraulic fractures to the pay zone. In general, the lithology of the Rocky Mountain region is composed of oil- and gas-bearing sandstone layers interspaced with shales (Fig. 1). However, some sandstone layers may be water aquifers and penetration of the hydraulic fracture into these penetration of the hydraulic fracture into these aquifer layers is undesirable. Also, the shale layers can separate producible oil- and gas-bearing zones from nonproducible ones. Shale layers between the pay zone and other zones can be vital in increasing successful stimulation. If the shale layers act as barrier layers, the hydraulic fracture can be contained within the pay zone. The in-situ stresses and the stiffness, as characterized by the shear modulus of the zones, play significant roles in the containment of a play significant roles in the containment of a hydraulic fracture. The in-situ stresses result from forces in the earth's crust and constitute the compressive far-field stresses that act to close the hydraulic fracture. Fig. 2 shows a schematic representation of in-situ stresses acting on a vertical hydraulic fracture. Horizontal components of in-situ stresses may vary from layer to layer (Fig. 2). For example, direct measurements of in-situ stresses in shales has shown the minimum horizontal principal stress is nearly equal to the overburden principal stress is nearly equal to the overburden stress. SPEJ P. 27
Article
This paper reports theoretical and experimental developments involving propagation of hydraulic fractures in layered formations. Unobstructed fractures are shown experimentally to propagate with a decreasing fracturing fluid pressure. This general trend is in agreement with pressure. This general trend is in agreement with theoretical predictions. Restrictions in fracture propagation result in an increase in fluid pressure. propagation result in an increase in fluid pressure. The relative fracturability of rocks can be determined by a direct experiment, the results of which are clear, easy to interpret, and include all pertinent parameters, such as physical and pertinent parameters, such as physical and mechanical properties of rocks, as well as the reactions between formation and fracturing fluid (for example, leak-off). Fracturing experiments with layered samples show that with strong bonding between rocks it is difficult to contain a fracture in a formation totally. The strength of the interface between adjacent formations is shown theoretically to be an important factor in fracture containment. With a weak bonding, fracture containment is possible and is associated with slippage at the interface. The pattern of propagation then will depend on the relative propagation then will depend on the relative mechanical properties of fractured formations. Introduction Most industrial hydraulic fractures are created in layered formations. During propagation, these fractures encounter various formations with different physical and mechanical properties. This paper physical and mechanical properties. This paper discusses the effect of those properties on propagation of the fracture. propagation of the fracture.Most of the theoretical studies on fracture propagation have been extensions of Griffith's propagation have been extensions of Griffith's work. Based on an energy criterion, Griffith developed a relationship among fracture shape, material properties, and the external force needed for fracture propagation. The energy source in hydraulic fracturing is the fluid pressure inside the fracture. The relationship between this pressure and material properties is (1) (2) in which L = fracture extent (length of a two-dimensionalfracture or radius of a penny-shapedfracture) E = Young's modulus of material mu = Poisson's ratio of material gamma = effective fracture surface energy of material sigma = least in-situ principal stress A similar equation for a three-dimensional fracture is derived in Appendix A in the form of (3) in which hf = fracture height E(k) = complete elliptic integral of the secondkind K(k) = complete elliptic integral of the first kind k = parameter of the elliptic integrals Eqs. 1 through 3 show p to decrease with increasing L (Fig. 1) As the fracture becomes larger, it needs less pressure for propagation. In deriving these equations, no allowance has been made for fluid leak-off into the formation. SPEJ P. 33
Article
The well-fracturing operation is modeled by a band of uniform pressure and two bands of uniform shear stress acting in a cylindrical cavity in an infinite body. Two interesting regions of induced stress are: either end of the pressurized interval where the tan- gential stress is zero (the vertical stress is approximately 95 per cent of the pressure) and the center of the packed-off interval where the tangential stress equals the pressure (the vertical stress is zero). The tectonic stresses are the overburden load and two unknown principal horizontal stresses that cause easily determined stress concentrations at the well bore. All calculated stresses are modified to account for the interstitial pore-fluid pressure. It is found that three situations are of interest: (1) the induced vertical stress is less than the overburden pressure; (2) the induced vertical stress and the instantaneous shut-in pressure are greater than the overburden pressure; (3) the induced vertical stress is greater than the overburden pressure but the instantaneous shut-in pressure is less than the overburden pressure. In (1) the fracture is vertical and the stresses are determinable. In (2) the fracture is horizontal and the stresses are indeterminate. In (3) the fracture is initially horizontal but becomes vertical as it propagates away from the well, the vertical and minimum horizontM compressions are determinable, and the other principal stress is bounded by a set of inequalities. Several exam- ples are presented in which the tectonic stress states appear to be relaxed--approximately equivalent to the 'hydrostatic' pressure.
Article
Two hydraulic fractures were created, one above and one below an ash-fall tuff-welded tuff formation interface. These formations have significant differences in their Young`s moduli, Poisson`s ratios and porosities. Sufficient cement was injected into each zone to create vertical fractures of 600 ft total length if the height was restricted to 50 ft; 256 and 117 bbls were injected at 6 bbl/min into the ash-fall tuff and welded tuff zones. Mineback along the interface has revealed a total fracture length of 150 ft; coring has shown that the heights of the fractures are about 100 ft for the fracture in the ash-fall tuff and 200 ft for the welded tuff fracture. The fracture which was initiated in the low modulus ash-fall tubb propagated upwards into the higher modulus welded tuff. No containment was observed. The results from the fracture subsequently initiated in the welded tuff are obscured because it propagated alongside the lower fracture and thus provided no definitive information on behavior at the interface. Widths in both the ash-fall and welded tuffs are consistent with design calculations. The in-situ stresses were found to have the greatest effect on fracture behavior and geometry. Variations in the minimum principal in situ stresses controlled the direction of fracture propagation and the final height of the fracture. The low stress measured in the welded tuff probably aided the propagation of the fracture into that region. Natural fractures in the welded tuff caused significant offsets in the induced fractures and resulted in filling of some of the natural fractures with grout and severe fluid Leakoff. These experiments show that material property interfaces should not, in general, be considered containment features. A more likely factor in controlling fracture height is in situ stress differences.
Article
An experiement has been conducted in which a sand-propped hydraulic fracture is created and then mined back to observe fracture behavior and proppant distribution. Three stages of different colored, different concentration sand transported by a water-based gel were injected into a volcanic ash fall tuff formation at a depth of 1400 ft near an existing tunnel complex. The resultant fracture was subsequently mined back for direct observation and photographed and mapped. This particular region was highly faulted and exhibited significant changes in in situ stress magnitudes across the faults; it is felt that this stress distribution resulted in very complex fracture behavior and growth processes. The fracture was bounded on one wing by a fault which was only a few feet from the wellbore. The fracture terminated on top at an unbonded bedding plane. Most of the injected volume of sand and fluid was forced downward, considerably below the elevation where the fracture was initiated. The different colors of sand were randomly distributed, although they were usually found in distinct layers, but this may have been due to the complex growth process. At different locations the fracture was found to have considerable variations in width; from several sand grains wide (1 cm) to devoid of sand altogether (2 to 3 mm average).
Conference Paper
The process of fracture initiation and propagation, from a pressurized borehole into a fluid-saturated stratified formation, is examined toward better understanding of the implications from pressure records (e.g., toward bounding of in situ stresses under minifrac conditions) and to assist in better designs of pumping sequences, especially for containment in pay zones. The work addresses 2 major groups of problems. First, some simple estimates of rupture pressures are made, allowing for frac fluid penetration, material variability and pre-existing flaws (or strength anisotropy) in borehole walls, which exhibit a wide range of deducible tectonic conditions for any particular rate and pressure required to cause break-down (unstable crack propagation) from the well bore. Second, dominant mechanisms of crack growth stabilization (due to pore-fluid effects) are rationalized: required driving stresses show a monotonic dependence on growth speed which reveals one possible source for inhibition of spreading into adjacent shale strata (as against lateral propagation into more permeable sandstones). 41 references.
Article
The plane problem of two bonded elastic half planes containing a finite crack perpendicular to and going through the interface is considered. The problem is formulated as a system of singular integral equations with generalized Cauchy kernels. Even though the system has three irregular points, it is shown that the unknown functions are algebraically related at the irregular point on the interface and the integral equations can be solved by a method developed previously. The system of integral equations is shown to yield the same characteristic equation as that for two bonded quarter planes in the general case of the through crack, and the characteristic equation for a crack tip terminating at the interface in the special case. The numerical results given in the paper include the stress intensity factors at the crack tips, the normal and shear components of the stress intensity factors at the singular point on the interface, and the crack surface displacements.
Article
The problem of two elastic bonded half planes containing a crack perpendicular to the interface is considered. First the solution for the semi-infinite crack under concentrated wedge loading is given. Then the problem of a finite crack fully imbedded in one of the half planes of terminating at the interface is considered. The Mellin transform in conjunction with the dislocations is used to formulate the problem and to derive the integral equation. The integral equation is solved; the stress intensity factors, the crack surface displacement, and the stresses around the crack tip terminating at the interface are obtained. Noting that the power of the singularity for the interface tip of the crack is not -1/2, a tentative fracture criterion dealing with the initiation of fracture propagation is proposed.
Massive Hydraulic Fracture Containment Analysis Utiliz-ing Rock Mechanics Considerations
  • L A Rogers
  • E R Simonson
  • A S Sayed
  • A H Jones
Rogers, L.A., Simonson, E.R., Abou-Sayed, A.S., and Jones, A.H.: "Massive Hydraulic Fracture Containment Analysis Utiliz-ing Rock Mechanics Considerations," Proc., Massive Hydraulic Fracturing Symposium, U. of Oklahoma, Norman (1977).
Hydraulic Fracture Propagation in Layered Rock: Experimental Studies of Fracture Contain-ment," paper SPE 9878 presented at the 1981 SPEIDOE Low Permeability Symposium
  • L W Teufel
  • J A Clark
Teufel, L.W. and Clark, J.A.: "Hydraulic Fracture Propagation in Layered Rock: Experimental Studies of Fracture Contain-ment," paper SPE 9878 presented at the 1981 SPEIDOE Low Permeability Symposium, Denver, May 27-29.
Theoretical and Experimental Research on Hydraulic Fracturing
  • M E Hanson
  • G D Anderson
  • R J Shaffer
  • D O Emerson
  • H C Heard
  • B C Haimson
Hanson, M.E., Anderson, G.D, Shaffer, R.J., Emerson, D.O., Heard, H.C., and Haimson, B.C.: " Theoretical and Experimental Research on Hydraulic Fracturing," Proc., DOE Fourth Annual Symposium on Enhanced Oil and Gas Recovery and Improved Drilling Methods, Tulsa (1978).
Fracture Containment Analysis Conducted on the Benson Pay Zone in Col-umbia Well 20538-T
  • C E Brechtel
  • D S Abou-Sayed
  • A H Jones
Brechtel, C.E., Abou-Sayed, D.S., and Jones, A.H.: "Fracture Containment Analysis Conducted on the Benson Pay Zone in Col-umbia Well 20538-T," Proc., U.S. DOE Morgantown Energy Technology Center Second Eastern Gas Shales Symposium, Morgantown, WV, Oct. 16-18, 1978.
Rock Mechanics Aspects of MHF Design in Eastern Devonian Shale Gas Reservoirs
  • A H Jones
  • A S Sayed
  • L A And Rogers
Jones, A.H., Abou-Sayed, A.S., and Rogers, L.A.: "Rock Mechanics Aspects of MHF Design in Eastern Devonian Shale Gas Reservoirs," Proc., ERDA Third Symposium on Enhanced Oil and Gas Recovery and Improved Drilling Methods, Tulsa (1977).
Analyses of an Elmworth Hydraulic Fracture in Alberta Paper accepted for publication Sept. 1 1. 1981. Revised manuscript received Feb. 1. 1982. Paper (SPE 8932) first presented at the SPEIDOE Unconventional Gas Recovery Symposium held in Pittsburgh
  • R E Wyman
  • S A Holditch
  • P L Randolph
Wyman, R.E., Holditch, S.A., and Randolph, P.L.: "Analyses of an Elmworth Hydraulic Fracture in Alberta," 1. Pet. Tech. (Sept. 1980) 1621-1630. 1980. Paper accepted for publication Sept. 1 1. 1981. Revised manuscript received Feb. 1. 1982. Paper (SPE 8932) first presented at the SPEIDOE Unconventional Gas Recovery Symposium held in Pittsburgh. May 18-21. 1980.