Developing models to better predict hydraulic fracture growth in Australian coal seams

Transcription

1 ENERGY Developing models to better predict hydraulic fracture growth in Australian coal seams National assessment of chemicals associated with coal seam gas extraction in Australia Technical report number 16: Hydraulic fracture growth in Australian coal basins Robert G Jeffrey, Xi Zhang, Zuorong Chen, Bisheng Wu, James Kear and Dane Kasperczyk CSIRO Manuscript Number: EP October 2016 This initiative was funded by the Department of the Environment The National assessment of chemicals associated with coal seam gas extraction in Australia was commissioned by the Department of the Environment and Energy and prepared in collaboration with NICNAS and CSIRO

2 Citation Jeffrey R, Zhang X, Chen Z, Wu B, Kear J & Kasperczyk D 2016 Hydraulic fracture growth in Australian coal basins, report prepared by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) as part of the National Assessment of Chemicals Associated with Coal Seam Gas Extraction in Australia, Commonwealth of Australia, Canberra. Copyright Commonwealth Scientific and Industrial Research Organisation To the extent permitted by law, all rights are reserved and no part of this publication covered by copyright may be reproduced or copied in any form or by any means except with the written permission of CSIRO. Important disclaimer CSIRO advises that the information contained in this publication comprises general statements based on scientific research. The reader is advised and needs to be aware that such information may be incomplete or unable to be used in any specific situation. No reliance or actions must therefore be made on that information without seeking prior expert professional, scientific and technical advice. To the extent permitted by law, CSIRO (including its employees and consultants) excludes all liability to any person for any consequences, including but not limited to all losses, damages, costs, expenses and any other compensation, arising directly or indirectly from using this publication (in part or in whole) and any information or material contained in it. CSIRO is committed to providing web accessible content wherever possible. If you are having difficulties with accessing this document please contact csiroenquiries@csiro.au. Page ii

3 Reports in this series The full set of technical reports in this series and the partner agency responsible for each is listed below. Technical report number Title Authoring agency Reviewing existing literature 1 Literature review: Summary report NICNAS 2 Literature review: Human health implications NICNAS 3 Literature review: Environmental risks posed by chemicals used coal seam gas operation 4 Literature review: Hydraulic fracture growth and well integrity 5 Literature review: Geogenic contaminants associated with coal seam gas operations 6 Literature review: Identification of potential pathways to shallow groundwater of fluids associated with hydraulic fracturing Department of the Environment and Energy CSIRO CSIRO CSIRO Identifying chemicals used in coal seam gas extraction 7 Identification of chemicals associated with coal seam gas extraction in Australia NICNAS Modelling how people and the environment could come into contact with chemicals during coal seam gas extraction 8 Human and environmental exposure conceptualisation: Soil to shallow groundwater pathways 9 Environmental exposure conceptualisation: Surface to surface water pathways 10 Human and environmental exposure assessment: Soil to shallow groundwater pathways A study of predicted environmental concentrations CSIRO Department of the Environment and Energy CSIRO Assessing risks to workers and the public 11 Chemicals of low concern for human health based on an initial assessment of hazards 12 Human health hazards of chemicals associated with coal seam gas extraction in Australia NICNAS NICNAS Page iii

4 Technical report number Title Authoring agency 13 Human health risks associated with surface handling of chemicals used in coal seam gas extraction Assessing risks to the environment 14 Environmental risks associated with surface handling of chemicals used in coal seam gas extraction Deeper groundwater research 15 Release of geogenic contaminants into Australian coal seams: Experimental studies NICNAS Department of the Environment and Energy CSIRO 16 Hydraulic fracture growth in Australian coal basins CSIRO 17 Simulation of hydraulic fracture fluid loss into an aquifer CSIRO Page iv

5 Acknowledgments This report is one in a series prepared under the National Assessment of Chemicals Associated with Coal Seam Gas Extraction in Australia. The project was commissioned by the Department of the Environment on advice from the Independent Expert Scientific Committee on Coal Seam Gas and Large Coal Mining Development (IESC). This report, entitled Hydraulic fracture growth in Australian coal basins, was prepared by Dr Rob Jeffrey, Dr Xi Zhang, Dr Zuorong Chen, Dr Bisheng Wu, Mr James Kear and Mr Dane Kasperczyk of the Commonwealth Scientific and Industrial Research Organisation (CSIRO). The report s authors gratefully acknowledge input from the Project Steering Committee, which comprised representatives from the National Industrial Chemicals Notification and Assessment Scheme (NICNAS), the Department of the Environment, the CSIRO, Geoscience Australia (GA), and an independent scientific member, Dr David Jones of DR Jones Environmental Excellence. This report was subject to internal review and independent, external peer review processes during its development. Page v

6 Contents Reports in this series... iii Acknowledgments...v Summary... ix Abbreviations... xi Glossary... xii 1 Introduction Hydraulic fracture growth into coal basins Hydraulic fracture growth Measurement of hydraulic fracture geometry Multi layer systems and vertical fracture growth General description of the 2D numerical method Fracture containment mechanisms Numerical results Summary T shaped fracture growth Cohesive zone model of hydraulic fracture Cohesive finite element model A three layer model and T shaped growth Finite element model Case study for a T shaped fracture Conclusions References Page vi

7 Figures Figure 1.2 Equivalent permeability for flow through a system of parallel cleats in coal... 7 Figure 1.3 A hydraulic fracture with an inflated hydraulic width of 10 to 30 mm also opens cleat fractures, but typically to a few 10s of microns in aperture... 8 Figure 2.1 Height growth of a vertical fracture can be analysed by modelling a two dimensional (2D) section through the fracture provided the fracture varies in height slowly along its length10 Figure 2.2 Variations of (a) Young s modulus and (b) Horizontal Confining Stress (HCS) with depth Figure 2.3 Fracture opening at a particular time (=39.2 s) under constant injection pressure (=17 MPa) Figure 2.4 Fracture growth (solid line) and fluid flux (dashed line) change over time, depicted for a low stress case Figure 2.5 Height growth and proppant distribution (shaded) predicted by P3D design model using the modulus and stress profiles associated with given boundary layer depth Figure 2.6 Fracture profile at the end of injection predicted by P3D design model, using the modulus and stress profiles associated with given boundary layer depth Figure 2.7 Fracture growth curve (time versus length) and fluid flux evolution for a particular minimum horizontal stress profile Figure 2.8 Fracture growth curve (solid line) and fluid flux evolution (dashed line) for a particular minimum horizontal stress profile Figure 2.9 (a) Young s modulus and (b) Horizontal Confining Stress variations with depth Figure 2.10 Fracture opening at a particular time (7.88 seconds) for a constant injection pressure (=20 MPa) Figure 2.11 Fracture growth curve and fluid flux evolution for the case shown in Fig Figure 2.12 Fracture flux evolution and growth curves for the upward going fracture at two different layer widths Figure 2.13 (a) Young s modulus (blue line) and 13(b) Horizontal Confining Stress (HCS) variations (red line) with depth Figure 2.14 Fracture trace for specific stress conditions, as given in Figure Figure 2.15 Fracture path for specific stress conditions, as given in Figure Figure 3.1 The process of hydraulic fracturing as depicted by a cohesive hydraulic fracture model Figure 3.2 The bilinear cohesive law used in this modelling generates tractions that depend on the path of the separation process at the tip, as illustrated in this diagram Figure 3.3 A depiction of the normal and tangential flow paths of fracturing fluid within a fracture Page vii

8 Figure 3.4 A three layer rock formation with pre defined fracture surfaces Figure 3.5 Finite element model mesh, with pre defined fracture planes indicating the pathways along which different T and H shaped fractures are grown Figure 3.6 Opening profile of the T shaped hydraulic fracture at 7 minutes Figure 3.7 The finite element model predicted injection pressure. A minimum and maximum in the pressure curve are indicted Figure 3.8 Fracture size and opening profile in an impermeable coal seam at 6 s and 43 s, respectively Figure 3.9 Opening profile of the T shaped hydraulic fracture within a permeable coal layer at 30 minutes Figure 3.10 The predicted injection pressure for the permeable case, indicating a decrease in pressure over time as the fluid leaks into the coal Figure 3.11 Pore pressure distribution in a permeable coal layer at 10 minutes Figure 3.12 Plan view of the hydraulic fracture mapped at Central Colliery in well ECC Figure 3.13 Two vertical cross sections through the fracture shown in Figure Figure 3.14 The change in surface injection pressure over time during the hydraulic fracture treatment of well ECC Tables Table 1.1 Properties affecting hydraulic fracture growth... 2 Table 1.2 Parameters describing hydraulic fractures mapped in various coal seams in Australia 5 Table 2.1 Mechanical property and stress layering used in the P3D hydraulic fracturing model Table 2.2 Confining Stress Profile Data Described By five Layers as used in the P3D hydraulic fracturing model Table 2.3 Rock Mechanics Parameters applied to coal and used for Cases 1 and Table 2.4 Reservoir data used for cases 1 and Table 2.5 Pumping Schedule; Identical for Cases 1 and Table 2.6 Proppant parameters, Identical for Cases 1 and Table 3.1 Physical properties of rock and coal Table 3.2 Treatment parameters used in the simulation Page viii

9 Summary In June 2012 the Australian Government commissioned the National Assessment of Chemicals Associated with Coal Seam Gas Extraction. The final assessment comprised a suite of 14 technical reports that identify risks to human health and the environment from surface handling of 113 chemicals used in drilling and hydraulic fracturing for coal seam gas in Australian between 2010 and This report was commissioned at the same time to provide further information about the development of numerical modelling for predicting fracture growth within coal seams in Australia. It supplements the National Assessment of Chemicals Associated with Coal Seam Gas Extraction. This report documents the development of numerical modelling for predicting fracture growth within coal seams in Australia. Predicting hydraulic fracture growth is fundamental to the design and optimisation of hydraulic fracture treatments with respect to hydrocarbon production. In addition, developing an understanding about the factors that control the hydraulic fracture growth process increases confidence in the accuracy of models used and can improve processes for assessing the risk of fracture growth into adjacent aquifers. In a coal basin, the adjacent aquifers may lie above or below the coal in a higher or lower stratigraphic sequence. For this reason, height growth of vertically oriented hydraulic fractures needs to be predicted for vertical or horizontal wells. However, any growth in height will directly affect the lateral or length growth of the fracture and vice versa. Therefore, it is equally important to be able to accurately predict growth of hydraulic fractures in both length (lateral growth) and height (vertical growth). A review of hydraulic fracture growth in coal is included in this report and concludes that the available evidence from instrumented fracture experiments and mineback experiments indicates that the hydraulic fractures consist of a main propped fracture channel rather than a branched network of finer propped fractures. Joints, natural fractures, and cleats in the coal are opened during the hydraulic fracturing process as a result of increased pore pressure from leak off but their aperture size is not sufficient to allow proppant to enter. Therefore, the propped fracture network consists of a main propped channel with some branches and offsets. This fracture geometry can be modelled using a planar fracture model, if that model accounts for non linear leak off effects. Such models are still not able to predict the higher treating pressures and slower fracture growth that result from the interaction with natural fractures and formation of offsets, but some effects of this process can be simulated using a higher fracture toughness tip effect. Development of more complete models that include offsetting, non linear leak off, modulus contrasts, and T shaped fracture growth is needed if prediction accuracy is to be improved. Results are presented from a modelling study of hydraulic fracture vertical height growth, through a layered sequence of rock with varying elastic stiffness and horizontal confining stress. A twodimensional (2D) model that can consider multiple strata (rock layers) was used to illustrate the importance of: rock layer thickness rock layer modulus (elastic stiffness) Page ix

10 the stress magnitude acting in each layer in controlling the amount of fracture height growth. Arrest of the hydraulic fracture was observed to occur when the fracture grew into thin softer layers that were overlain by a thicker stiffer and more highly stressed layer. Arrest or reorientation into horizontal growth also occurred when the hydraulic fracture penetrated a thick higher stress layer. In order to provide a more accurate assessment of fracture height growth, a pseudo 3D (P3D) fracture model was used to analyse a case with fewer layers. Because this model allows the fracture to grow both vertically through rock layers and laterally within the layers, the P3D fracture model predicted significantly reduced height growth (through rock layers) when compared with the results of the 2D fracture growth model. These current 2D and P3D fracture models provide an upper limit on the extent of height growth since they do not account for interactions with weaker bedding planes (which will act to slow or arrest vertical hydraulic fracture growth). One of the conclusions from this work is that further research into height growth in layered rock systems is required to develop methods that better account for the effect of weak bedding planes and the potential development of offsets as the fracture crosses these features. Evidence suggests that T shaped hydraulic fractures, consisting of a vertical branch in the coal seam and a large horizontal fracture at the coal roof rock interface, are commonly generated by coal seam gas hydraulic fracture treatments, perhaps forming during approximately half the treatments. This T shaped growth effectively limits the fracture to be contained to the coal seam, reducing the risk of fracture growth into overlying rock layers (such as aquifers). Modelling the growth of T shaped fractures requires a 3D model that can propagate fractures with out of plane components. Results from a 3D finite element model are presented. The numerical modelling approach used in the 3D finite element model requires significant computational effort with each simulation taking between 4 to 6 hours to run. The formation of the T shaped fracture mapped in well ECC90 in the Bowen Basin was analysed using this numerical model. The overall shape and pressure response obtained were similar between the model and the measured data; however, fine details of the fracture were not accurately reproduced because the model did not include offsets and sub branches in the fracture geometry. This qualitative agreement provides evidence suggesting that further development and refinement of the approach is warranted, so that T shaped fracture growth can be better understood and predicted, and incorporated into fracture designs and environmental impact and risk assessment processes. Page x

11 Abbreviations General abbreviations CSIRO CSG DoE GA HCS IESC NICNAS P3D SI US Description Commonwealth Scientific and Industrial Research Organisation Coal seam gas Department of the Environment Geoscience Australia Horizontal confining stress Independent Expert Scientific Committee on Coal Seam Gas and Large Coal Mining Development National Industrial Chemicals Notification and Assessment Scheme Pseudo 3D fracture model International System of Units United States of America Page xi

12 Glossary Term Annulus Borehole Casing Coal seam gas (CSG) Fracture toughness Green s function Height growth Hydraulic fracturing In situ stress Leak off Leak off test (LOT) Liner Mineback Description The gap between tubing and casing or between two casing strings or between the casing and the wellbore. The annulus between the tubing and casing is the primary path for normal producing gas from coal seam gas wells A hole drilled for purposes other than injection or production of oil, gas or water (e.g. a mineral exploration borehole) Steel or fibreglass pipe used to line a well and support the rock around it. Casing extends to the surface and is sealed by a cement sheath between the casing and the rock A form of natural gas (generally 95 to 97% pure methane, CH 4 ) typically extracted from permeable coal seams at depths of 300 to 1000 m. Also called coal seam methane (CSM) or coalbed methane (CBM). A material property that represents the resistance of a rock to fracture extension for calculations based on linear elastic fracture mechanics (see Error! Reference source not found. in report body for additional details) In elasticity, a Green s function is an exact solution to a simple load or displacement problem, such as a point force applied to a surface of a body or a point displacement applied in the material Vertical growth (upwards or downwards) of a vertical hydraulic fracture Also known as fracking, fraccing or fracture simulation, is one process by which hydrocarbon (oil and gas) bearing geological formations are stimulated to enhance the flow of hydrocarbons and other fluids towards the well. The process involves the injection of fluids, gas, proppant and other additives under high pressure into a geological formation to create a conductive fracture. The fracture extends from the well into the coal reservoir, creating a large surface area through which gas and water are produced and then transported to the well via the conductive propped fracture channel The stress acting in the rock The process that results in fluid lost during a hydraulic fracture treatment by diffusion from the fracture into the surrounding rock. A test performed during drilling to measure the pressure at which a hydraulic fracture will initiate from the wellbore Steel or fibreglass pipe used to line a well and support the rock. Liners are essentially the same as casing, but do not extend to the surface Mining through a hydraulic fracture, most commonly in an underground mine. The fracture geometry is mapped during and after the mine openings Page xii

13 Term Minimum principal stress Non linear leakoff Poisson s ratio Proppant Rheology Tubing Water frac Wellbore integrity Wellbore Well Young s modulus Description are excavated The state of stress in the earth is completely described by three mutually perpendicular normal stresses. Typically, one of the principal stresses is the vertical stress ( vert) and the other two are perpendicular horizontal stresses, the least compressive horizontal stress ( hmin) and the most compressive horizontal stress ( Hmax). Hydraulic fractures orient themselves as a plane perpendicular to the minimum principal stress, which at depth is often hmin. As such, a hydraulic fracture would be expected to be a vertical plane. At shallow depth or in regions subject to tectonic compression such as much of the east coast of Australia, the vertical stress is the minimum principal stress, and hydraulic fractures will grow as horizontal fractures Enhanced leak off caused by pore pressure increase interacting with natural fracture permeability in the coal reservoir around the hydraulic fracture. An elastic parameter that is defined as minus the ratio of lateral strain to axial strain under conditions of uniaxial stress. It is proportional to the lateral deformation produced by axial compression A component of the hydraulic fracturing fluid system comprised of sand, ceramics or other granular material that prop open fractures to prevent them from closing when the injection is stopped As used here, the study of shear and flow of fluids Steel pipe that is hung inside the casing. The tubing string may have a pump installed at its lower end and, for pumped wells, is a primary path for producing water from coal seam gas wells A hydraulic fracture treatment where the fluid pumped is almost entirely water. A biocide and a friction reducer are usually added to the water In contrast, gel fracs contain an additional viscosifier and therefore form a gel. A measure of whether a well is mechanically and hydrologically sound. A measure of the ability of the well and wellbore system to allow access to the reservoir while controlling fluid movement along the well or from the well into or out of the surrounding rock The hole produced by drilling, with the final intended purpose being for production of oil, gas, or water As used in this report: a completed wellbore, typically including casing and tubing strings and possibly a pump. A well is intended for injection or production of fluids An elastic modulus that describes the stiffness of the rock and is defined as the ratio of axial stress to axial strain under conditions of uniaxial stress Page xiii

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15 1 Introduction 1.1 Hydraulic fracture growth into coal basins In June 2012 the Australian Government commissioned the National Assessment of Chemicals Associated with Coal Seam Gas Extraction in Australia. The Assessment comprised a suite of 14 technical reports that identify risks to human health and the environment from surface handling of 113 chemicals used in drilling and hydraulic fracturing for coal seam gas in Australian between 2010 and This report was commissioned at the same time to provide further information about the development of numerical modelling for predicting fracture growth within coal seams in Australia. It supplements the National Assessment of Chemicals Associated with Coal Seam Gas Extraction in Australia. This report documents the development of numerical modelling for predicting fracture growth within coal seams in Australia. Predicting hydraulic fracture growth is fundamental to designing and optimising fracture treatments. In addition, developing an understanding about the factors that control the hydraulic fracture growth process increases confidence in the accuracy of models used and can improve processes for assessing the risk of fracture growth into adjacent agricultural and drinking water aquifers. In a coal basin, the adjacent aquifers may lie above or below the coal in a higher or lower stratigraphic sequence. For this reason, both upward and downward height growth of the hydraulic fracture needs to be predicted. However, any growth in height will directly affect the lateral or length growth of the fracture and vice versa. Therefore, it is equally important to be able to accurately predict growth of hydraulic fractures in both length (lateral growth) and height (vertical growth). A comprehensive literature review of hydraulic fracture growth in coal, with an emphasis on height growth (or vertical growth) was previously compiled by Jeffrey et al. (2017) This current project builds on the literature review cited above by providing some model generated examples that illustrate fracture growth and height growth for conditions existing in Australian east coast coal basins with the intention of illustrating the mechanisms and risk associated with a hydraulic fracture growing into an aquifer. Fracture growth into an aquifer results in some volume of fracturing fluid being injected from the fracture into the aquifer. These results may then be applied, through groundwater modelling exercises, to predict the further movement and ultimate fate of the fracturing fluid. To provide context, a short review of the types of hydraulic fracture growth is presented first in this report, with data coming from a number of mineback mapping projects (e.g. Jeffrey et al and other papers as cited in Table 1.2). Data was also obtained from offset well pressure measurements (Jeffrey and Settari 1998), and published tiltmeter and microseismic results (Johnson et al. 2010). Next, two generic coal basins are considered, one representing conditions in the Surat (sedimentary) Basin, Queensland and the other in the southern Sydney Basin near Wollongong, New South Wales. Generic mechanical earth models were constructed for each of these basins. For each one, hydraulic fracture height growth was considered in more detail, using research models and detailed vertical cross sections, and more simplified vertical sections for use with fracture design Page 1

16 models. Finally, this report presents evidence for (and growth modelling of) T shaped hydraulic fractures, which requires full 3 dimensional hydraulic fracture modelling. This modelling illustrates the parameters that most strongly affect fracture height growth, which in turn feeds into predictions to assess the risk of hydraulic fracture growth into overlying or underlying aquifers. 1.2 Hydraulic fracture growth Growth of hydraulic fractures in coal is strongly affected by the highly layered nature of coal and adjacent rocks. Table 1.1 summarises a number of factors that affect hydraulic fracture growth. Some of these factors, such as strong contrasts in rock stresses or rock properties, are more likely to come into effect for height growth because the coal seams that are stimulated by hydraulic fracturing exist in a generally horizontal layered sedimentary environment. Layering exists even in the coal itself with stony layers and dull and bright coal layers existing throughout the thickness of each coal seam. Table 1.1 Properties affecting hydraulic fracture growth Property or factor Stress contrasts Fracture toughness Rock elastic stiffness Fluid pressure gradient Effect on fracture growth Higher values of the minimum principal in situ stress in bounding layers slows or arrests fracture growth into that layer. Lower stress in a bounding layer results in faster growth into that layer. Lateral stress variation is usually assumed to not be significant, but may be present and affect the fracture growth at faults and dykes. Fracture toughness is a strength property of the rock. The pressure inside a hydraulic fracture opens it and increases the tensile stress at the leading edge (or tip) of the fracture. In linear elastic fracture mechanics, the magnitude of the near tip stress field is represented by the stress intensity factor. The fracture will extend when the stress intensity factor becomes equal to the rock fracture toughness. Different rock layers will have somewhat different fracture toughness. A bounding layer with higher fracture toughness will act to slow fracture growth or even arrest the fracture. A volcanic dyke that cuts the seam will have a fracture toughness that is higher than the toughness of the coal, potentially arresting lateral growth. Rock layers that are higher in elastic stiffness generally act to limit fracture growth. The fracture width is reduced in the stiffer layer, leading to more viscous fluid friction which reduces the fracture growth rate. In addition, the stress intensity at the tip of the hydraulic fracture is reduced as it approaches a stiff layer and, conversely, increased as it approaches a soft layer. Also, horizontal tectonic shortening in the basin will induce higher horizontal stress in the stiffer rock layers, producing stress contrasts that favour containment of the hydraulic fracture as discussed above. Fluid gradients (pressure change with position) inside the hydraulic fracture are generated primarily by flow of the viscous fracturing fluid through the hydraulic fracture channel. High gradients can exist where fluid is forced through an offset or tortuous pathway. Fracture growth is slowed by high fluid pressure gradients along the flow path. An obstruction in the fracture channel, such as Page 2

17 Property or factor Permeability Interfaces Effect on fracture growth provided by proppant plugging the fracture, can arrest fracture growth. Buoyant proppants have been developed to limit upward vertical growth of hydraulic fractures. Normal proppant that settles to the base of a vertical fracture acts to limit downward growth by the same mechanism. Permeability, which is measured in millidarcies (md) in the coal seam gas industry, is a measure of the flow capacity of the rock. Higher permeability can increase leak off but also improve production rates. The rock layers above and below the seam can vary significantly in permeability, but in the coal measures the shales and sandstones typically have very low permeability. Hydraulic fracture growth occurs more rapidly through a rock with a lower permeability because less of the injected fluid is lost into the surrounding rock. High permeability layers or zones act to slow or blunt fracture growth. A coal seam with a permeability of less than 10 md may require stimulation by hydraulic fracturing to yield economic flow rates, but higher permeability seams are also often fractured because a higher rate of gas production can then be achieved. Interfaces include natural fractures, faults, shear zones, and bedding interfaces. Interfaces are often weak in both tension and shear and may have an initial permeability that allows the fracturing fluid to more easily penetrate into them. As the hydraulic fracture interacts with such interfaces, offsets and branches may form which retard fracture growth. The interface between the coal and the rock is often a feature into which the initially vertical hydraulic fracture is diverted, resulting either in an offset in the vertical fracture which acts to slow the vertical growth or in a T shaped fracture geometry, which acts to contain the fracture to the seam. Source: Jeffrey et al. (2017) Hydraulic fractures that are designed to stimulate a coal seam must have a sufficient size and propped width to achieve that objective. Proppants, which are typically a round and sieved sand, are introduced to the fracturing fluid after the hydraulic fracture has been extended and opened sufficiently. The proppant is carried into the fracture by the moving fluid and is left there when the fracture closes at the end of the injection. The proppant then acts to keep the fracture open and its permeability provides the conductive flow path for producing fluids back to the well. The surface area of the fracture is the area through which the water and gas contained in the permeable coal seam is ultimately produced. A longer fracture will have a larger surface area than a shorter fracture and, provided it is propped well enough, will provide a larger stimulation effect. The propped width creates the permeability in the hydraulic fracture channel and this defines the flow capacity of the fracture. The surface area of the fracture combined with the coal seam permeability defines the flow capacity of the coal, which is its ability to deliver water and gas into the fracture. A longer fracture must be propped wide enough to take advantage of the additional production potential that exists because of the large fracture surface area in the permeable coal seam. A typical fracture treatment in a coal seam, which is designed to create and prop a fracture that is 150 to 300 m long requires an average propped width of 10 to 20 mm to provide sufficient Page 3

18 permeability to carry the water and gas back to the wellbore. Fractures mapped by mineback have been found to have propped widths that vary from near zero in some sections to over 100 mm in others. Fracture height growth is usually not desirable because it reduces the fracture length in the coal and places the fracture surface area next to siltstone and shale rock layers that contain little or no gas. The design process attempts to limit height growth to occur only across zones that contain coal seams and that can then be produced. The next section provides information about how hydraulic fracture geometry is measured and how these measurements can be used to improve the fracturing process. 1.3 Measurement of hydraulic fracture geometry The geometry of a hydraulic fracture, which includes its orientation, height, length, width and branching can be measured or inferred by a number of methods including: mapping the fracture after mining (mineback) image logging along the wellbore monitoring by microseismic event location tiltmeter mapping tracer studies analysis of pressure recorded at the injection well and in offset wells with which the fracture interacts. Mapping the propped fracture after mining (mineback) provides a direct measure of the exposed fracture orientation, propped width and amount of branching. Mineback may not reveal the entire extent of the fracture because the full height and length of the fracture may not be excavated. However, mineback data have proven to be essential in providing detail of hydraulic fracture growth mechanics, including the presence and frequency of offsets and branches along the main fracture, which result from interactions of the hydraulic fracture with natural fractures, faults, shear zones and bedding planes. The mineback studies that are available in the literature cover a wide range of injection rates, injected volumes and fluids. In Australia, the low injection rate research fracture treatments that were mined and mapped included both water only fluids and cross linked guar gel fluids. One commercial sized fracture treatment, which used cross linked gel, is included in this data set. Fracture geometry data from these mineback studies are consistent with each other over the range of injection rates and fluid types used, and with the United States (US) coal mineback data. These studies all involved commercial scale fracture treatments. The fracture geometry mapped in all of these cases consists of a primary propped fracture channel that contains some branches and offsets, but does not consist of a propped fracture network. This finding is discussed further later in this report. Nine hydraulic fractures placed into coal seams have been mapped after mining in Australia. Table 1.2 lists these mineback data sets. In addition, more than 30 documented mined fractures (see Diamond and Oyler 1987; Steidl 1991) and thousands of poorly documented fractures have been mined in US coals. This section will briefly summarise the main features of the fractures mapped in these studies. Page 4

19 Table 1.2 Parameters describing hydraulic fractures mapped in various coal seams in Australia Well Seam Basin Fluid Injection rate (L/min) Geometry References ECC90 ECC87 German Creek German Creek Bowen Cross linked 4760 T shaped Jeffrey et al. (1992) Bowen Cross linked 108 Vertical Jeffrey et al. (1993) DDH189 German Creek DDH190 German Creek Bowen Cross linked 93 Vertical Jeffrey et al. (1993) Bowen Cross linked 149 Vertical Jeffrey et al. (1993) PHKM 1 PHKM 2 PHKM 3 Great Northern Great Northern Great Northern Sydney Cross linked 246 T shaped Jeffrey et al. (1994) Sydney Water 291 T shaped Jeffrey et al. (1994) Sydney Cross linked 250 T shaped Jeffrey et al. (1998) DDH53 Bulli Sydney Water 350 X shaped Jeffrey et al. (1998) DDH139 Megaseam Sydney Water 420 Vertical Jeffrey et al. (1998) Of the nine fractures mapped in Australia, the propped geometry of each consisted of a main fracture channel or of two main channels in the case of T shaped fractures. T shaped fractures are discussed in detail below. None of these treatments formed fine networks of propped, multibranched fractures in the coal. However, opening of natural fractures in the coal around the hydraulic fracture is believed to have occurred during the injection part of the treatment, based on fracture growth data and fluid loss calculations (Jeffrey and Settari 1998). The lack of proppant mapped in these cross cutting natural fractures establishes a limit on the aperture attained by this inflated network of natural fractures. The finest sand proppant pumped in any of the treatments listed in Table 1.2 was 70 mesh (212 microns in diameter) implying that cross cutting natural fractures were opened to less than 400 microns, as significant amounts of proppant would have otherwise entered them. Three of the research treatments included stages containing 90 to 150 micron glass beads and this finer proppant was also not found to enter crosscutting natural fractures or cleats along the main hydraulic fracture. For comparison, the sand propped width of the main hydraulic fracture channel ranged from 1 mm up to 200 mm, with the smaller research treatments averaging 3 to 5 mm in width and the commercial treatment (ECC90) producing a fracture averaging 10 to 15 mm in propped width. The 200 mm width resulted from pumping into a near wellbore screenout, with an initial blockage of the fracture by sand located approximately 10 m from the well, producing very high pressures that opened the Page 5

20 fracture and packed it with sand proppant. The hydraulic width of the fracture during the injection phase of the treatment is significantly wider than these average propped widths. These conclusions are consistent with the findings of the mineback mapping studies of commercial size fractures done in US coals (Diamond and Oyler 1987). However, even small changes in aperture of the natural fractures produce large increases in fracture hydraulic conductivity because the conductivity of a fracture increases with the cube of the aperture. Fluid flow in a single fracture is often modelled as flow between parallel plates and the permeability of such a fracture is given by Equation 1 which shows the permeability depends on the square of the fracture width (Snow 1969; Zimmerman and Bodvarsson 1996): Where: k = the intrinsic permeability in SI units of metres squared (m 2 ) w = the aperture of the fracture in metres (m). [Equation 1] k The equivalent permeability,, of a rock layer that contains parallel fractures all of aperture, w, spaced at a distance S (m) from one another is given in Equation 2: [Equation 1] Fluid loss from a hydraulic fracture growing through a naturally fractured rock will depend on this equivalent permeability, which is proportional to the natural fracture width cubed and varies inversely with the natural fracture spacing. Figure 1.2 contains a graph of equivalent permeability as a function of fracture aperture and number of cleats per inch in a coal (the number of cleats per inch is the inverse of the fracture spacing in inches, N=1/S). The range of permeability where hydraulic fracturing in vertical wells might be applied is shown by the region between the two vertical dashed lines. If a cleat density of 1 cleat per inch (1 cleat per 25.4 mm) is assumed, cleat apertures between 5 and 20 microns will produce the permeability range indicated. Page 6

21 Source: Laubach et al. (1998)1. The dashed lines indicate on the x axis the range of coal permeability that is to be stimulated using hydraulic fracturing. The dashed horizontal line at 1 cleat per inch (1 cleat per 25.4 mm) intersects the vertical dashed lines to define a range of cleat apertures, varying from 5 to 20 microns that would result in this permeability range. Figure 1.2 Equivalent permeability for flow through a system of parallel cleats in coal Small changes in aperture width, w (measured in microns in Figure 1.2), will result in relatively large changes in equivalent permeability, provided other parameters remain unchanged. The aperture width is sensitive to the effective normal stress acting across the fracture. As the effective normal stress decreases, usually because of an increase in pore pressure, the fracture aperture increases. If the pore pressure exceeds the normal stress acting across a natural fracture, the fracture will be opened hydraulically. This is the process that results in non linear or pressuredependent leak off in hydraulic fractures as they grow through naturally fractured reservoirs. A history match of hydraulic fracture treatment data at a site where fracture growth rate was directly measured was achieved by increasing the coal permeability by a factor of 10 over its initial value (Jeffrey and Settari 1998). Such an increase in permeability is consistent with an increase in fracture aperture by a factor of 3.2, which based on the data in Figure 1.2, suggests the wider cleats would still be less than 100 microns in aperture. This line of reasoning provides an order of magnitude estimate for cleat aperture, around a growing hydraulic fracture, that supports the idea that they are in the order of 100 microns, which is too narrow to allow typical proppant grains to enter. Mineback of hydraulic fractures in coal, as mentioned above, has also shown that proppant does not often enter into the cross cutting cleat or fracture system. Therefore, the network of inflated fractures around a hydraulic fracture consists of fractures that are opened to a few 10s of microns in aperture, perhaps as much as 100 to 200 microns, with most being opened to less than this amount. The main hydraulic fracture channel, which is propped by the treatment, is opened during the injection to 20 to 30 mm in width, a factor of 100 to 300 times larger than the widest inflated cleat fractures. Thus, it is reasonable and consistent to model the hydraulic fracture Page 7

22 growth using a planar fracture model, but with the provision that non linear leak off should be accounted for by some means. Figure 1.3 contains a sketch of what such a fracture might look like. Note. The location of the wellbore is marked by the black dot at the centre of the propped hydraulic fracture pathway. The propped fracture channel is indicated by the thicker line extending NE SW from the wellbore with surrounding cleat fractures that were inflated during the fracturing operation shown in grey. Figure 1.3 A hydraulic fracture with an inflated hydraulic width of 10 to 30 mm also opens cleat fractures, but typically to a few 10s of microns in aperture Page 8

23 2 Multi layer systems and vertical fracture growth The fracture shown in Figure 1.3 in the previous section is reproduced in Figure 2.1 in two dimensions (2D), with the out of page geometry not included. However, a hydraulic fracture is a three dimensional (3D) feature with dimensions of length, opening or width, and vertical extent or height. A fracture contained to the coal seam will extend vertically in the coal and will usually have a height equal to the seam thickness. An earlier report (Jeffrey et al. 2017) reviewed the literature on hydraulic fracture height growth and factors that affect fracture height growth (listed in Table 1.1 in section 1.3 of this report). Whether a hydraulic fracture grows into and through the rock layers above and below the seam depends on the physical properties of those layers and their bedding interfaces and on the pressure distribution within the fracture and size of the hydraulic fracture. In this section the specific issue of the effect of rock layering and associated variation of elastic properties and stress between layers is studied using a two dimensional hydraulic fracturing research model and a pseudo 3D (P3D) hydraulic fracturing design model. The rock layering and stress conditions modelled are selected to represent average conditions in two Australian coal basins: Surat sedimentary basin southern Sydney sedimentary basin. 2.1 General description of the 2D numerical method The calculation for height growth presented here is based on a plane strain boundary element numerical hydraulic fracturing research model that uses a finite difference method to solve for fluid flow in the fracture channel (Zhang, et al. 2009). It has recently been extended to cope with fracture growth through multiple rock layers. Such a 2D model can be applied to a vertical section through a hydraulic fracture, as shown in Figure 2.1, to study details of the height growth problem that are not considered by more general 3D or P3D design models. For example, the P3D model used here is restricted to considering three elastic layers and five stress layers in its height growth calculation. Page 9

24 Source: Settari and Cleary (1986) Figure 2.1 Height growth of a vertical fracture can be analysed by modelling a two dimensional (2D) section through the fracture provided the fracture varies in height slowly along its length To enable the 2D model to calculate fracture opening in such a layered rock system, the Green s functions used in the model and the solution method have both been modified using an image method so that multiple layer effects are included in the elasticity problem. In elasticity, a Green s function is an exact solution to a simple load or displacement problem, such as a point force applied to a surface of a body or a point displacement applied in the material. By using superposition, a solution to other problems that cannot be solved directly, can be obtained. For example, integrating point dislocation dipoles (e.g. opening displacement at a point in a material) along a line in 2D provides a way to obtain the opening of a 2D fracture and the stress and stress intensity factors associated with this open fracture. The method used here is based on the analytical solution that gives the elastic deformation produced by a unit strength dislocation dipole in an infinite medium. This is then coupled with the image method for a dislocation dipole located in one layer of a two layer rock with the interface between perfectly bonded layers (Aderogba 1977; Zhang and Jeffrey 2006). Constructing the multi layer Green s function in this way involves an infinite series of images, but using a small number of the terms in the infinite series is found to give good accuracy. In particular, a cell containing a maximum of seven layers (at most three upper layers above the current element and three lower layers below the element) is used to construct, by the method of images, the multi layer Green s function for elastic deformation. The solutions for all sources and images within this cell are then determined and combined together to obtain the approximate multi layer Green s function for a given point on the fracture. Using this method, Green s functions are generated for each element, which take account of the local layering above and below the element. The coupled pressure, fracture opening, and fracture growth are then solved for using these Green s functions. This approach is implemented because there is no exact Green s Page 10

25 function for any problem with more than two layers and this method proves accurate when tested against some existing published numerical results (Zhang and Jeffrey 2006). The advantages of this method are: an accurate stress intensity factor is obtained when the tip is close to the layer interface the hydraulic fracture does not have to be orthogonal to the rock layers and an inclined fracture can be analysed. In a system of rock layers, the elastic properties of the layers affect how the applied far field stress is distributed among the layers. The vertical, compressive stress increases slowly with depth since it is generated by the weight of the overlying rock. However, the vertical compressive stress does not increase or decrease with local elastic property changes. The horizontal stress, however, is sensitive to the layer elastic properties. One component of the horizontal stress is generated by the far field tectonic stress acting across all of the layers. If this tectonic horizontal stress acts to compress or shorten the rock layers, then the layers with a higher stiffness (or higher Young s modulus) will carry a proportionally higher horizontal stress and the softer layers, such as the coal seams, will carry a proportionally lower horizontal stress. A tectonic shortening stress state is active in the Sydney Basin and results in a minimum horizontal stress in the rock layers that exceeds the vertical stress in magnitude. The Surat Basin is subject to less compression, which produces a minimum horizontal stress in the rock layers that is about equal to or slightly lower than the vertical stress magnitude. The contrast in the minimum principal horizontal stress between layers is one important factor that limits or promotes vertical hydraulic fracture height growth. The method of treatment in the 2D model for specifying in situ stresses acting in a multiple layered system is detailed below. The stress is taken as positive if it is compressive. Given that the model does not allow shear displacement to occur across bedding planes, the horizontal confining stresses on both sides of the layer interface must meet the strain continuity condition (see Rice and Sih 1965), which for the case of a non zero vertical stress,, acting across the interface, requires that Equation 3 be satisfied: [Equation 2] Where: = the plane strain Young s modulus for layer 1 = the plane strain Poisson s ratio for layer 1 = horizontal stresses acting in layer one = the horizontal stresses acting in layer two Within each layer, the confining stress is assumed to be constant with the depth (layer thickness). The stress in all the layers is calculated using the above equation, starting at the bottom layer stress and working up while considering two layers at a time. The real stresses for any site of interest must be measured in the well at that site. Page 11

26 The vertical stress across the interface is based on the cumulative weight of the overlying rock acting on a unit cross sectional area. A small additional stress, arising from the atmospheric pressure of 0.1 MPa acting on the ground surface, has been added to the vertical stress. In some published numerical calculations, the applied stresses are proportional to the modulus ratio (e.g. Helgeson and Aydin 1991) and this results in constant and equal strain in each layer, provided the vertical stress is zero. If a vertical stress is applied to such a system, strain compatibility is not satisfied at the bedding interfaces. If strain compatibility is not enforced, the bedding planes must be allowed to slip in shear, which in the model used here requires that each interface be discretised, increasing the computational effort and limiting the number of layers that can be considered to, at most, three or four. Therefore, strain compatibility is enforced by using Equation 3. For the modelling, it has been assumed that Young s modulus is constant within each layer, but varies from layer to layer. The maximum modulus contrast between two neighbouring layers is 25/8, which is a limit imposed by requiring this variation to be within the range used for verification of the numerical method. The Poisson s ratio is always 0.25 for all layers and the fracture toughness is also the same for all layers with a value of 1.0 MPa m,, where MPa is pressure in megapascals and m is length in metres. The fluid viscosity is equal to 0.01 Pa s for the fracturing fluids where Pa is pressure in Pascals and s is time in seconds. All results are obtained by specifying a constant injection pressure condition at the given injection location in the vertical fracture, which represents a vertical cross section through a 3D hydraulic fracture (see Figure 2.1). Normally, this pressure is found as part of the solution when using a 3D or a P3D model. The P3D model couples each vertical section of the fracture to the adjacent ones via the lateral growth and fluid flow algorithm (Settari 1988). In the 2D research model used here, the pressure at the coal seam that is being stimulated is specified as a percentage above the minimum principal stress acting in that seam. This pressure is then maintained constant by the model and the vertical fluid flux rate is adjusted to satisfy this specified pressure boundary condition. Thus, the fracture can arrest at a high stress layer or grow rapidly if low stress layers are encountered. However, the fluid flux calculated and the fracture growth rate may both become large when the layering and stresses favour height growth. In a hydraulic fracture, the pressure at a vertical cross section depends on the lateral and vertical growth. In addition, rapid vertical growth can occur, but only for a limited time if the vertical fluid flow exceeds the rate that fluid is injected into the well. Typically, the total maximum injection rate used in a treatment is less than 0.3 m3 per second and is usually less than half of this. Therefore, any local height growth that approaches or exceeds this rate will soon deplete the fluid volume being supplied, which limits the rate of height growth and can cause the fracture to locally close. The calculations presented below partly account for these restrictions by imposing an upper bound limit on the injection rate so that the unrealistic fast height growth does not occur. Page 12

27 2.2 Fracture containment mechanisms Several factors need to be considered to undertake a fracture containment analysis. Helgeson and Aydin (1991) listed a few such factors as: strength of interface Young s moduli and fracture toughness of the layers (Poisson s ratio should be included) thickness of the layers loading conditions. Additionally, the fluid pressure boundary condition that drives the fracture height growth must also be considered. In practice, this fluid pressure is a function of injection rate and fluid viscosity and is obtained by solving the coupled lateral and vertical fracture growth problem. For an interface that does not allow shear slip to develop during build up of the vertical stress, the stress conditions around the interface are given by Equation 3. For the case of a fracture growing from a lower stress layer (the coal) into a bounding higher stress layer (higher modulus siltstones), the larger horizontal stress in the bounding layer acts as a stress barrier to vertical growth. The difference between the hydraulic fracture pressure and the least compressive stress, which is called the excess pressure, is one important factor in calculating the stress intensity factor used for checking the onset of fracture growth. However, it is not the sole factor as this excess pressure varies with layers, as does the layer thickness. If the layer thickness is small, the excess pressure in the fracture below the layer can provide sufficient driving force for the hydraulic fracture to penetrate a thin stress barrier. Because the stress intensity at the fracture tip is generated by the excess pressure distribution along the entire fracture, the thickness of the layer must also be considered. This type of problem involves strong non local effects and to accurately account for these effects the 2D model was modified to include multiple layers. Although the importance of stress contrasts in affecting growth has been emphasised by many researchers, such as Helgeson and Aydin (1991) and Gudmundsson and Brenner (2001), additional research is needed into hydraulic fracture growth through layered rock systems to improve prediction of height growth. The growth of fractures through thin layers is postulated to result in the formation of offsets along the bedding planes (Helgeson and Aydin 1991). In addition, soft thin layers have been proposed as more efficient in arresting a hydraulic fracture (Charlez 1997; Yew 1997). It is still not clear why a soft thin layer can result in offset fractures in layered rocks. This type of interaction is revisited in section Page 13

28 2.3 Numerical results Effects of horizontal stresses in 2D modelling Based on mechanical earth models representative of coal basins on the east coast of Australia, two cases with different Young s modulus and in situ stress profiles with depth were considered (Figure 2.2). The Young s modulus varies between layers from a low of 8500 MPa which represents a coal layer, to a high of MPa which represents a stiff sandstone or siltstone. Three different in situ stress profiles are considered, as shown in Figure 2.2(b). The upper bound on the injection rate is set at 0.5 m2 per second if not otherwise specified. This is still a large injection rate equivalent to 188 barrels per minute or 30 m3 per minute for a one metre fracture lateral length. Only the upward going fracture growth is considered in this subsection. The fluid is injected into the fracture at a depth of 665 m for all cases considered in this section. For these modulus and stress conditions, Figure 2.3 and Figure 2.4 show the opening profile along the fracture at a given time. The injection pressure of 17 MPa is larger than the horizontal stress in every layer, by at least a relatively large amount of 1.3 MPa. Generally, speaking, this injection pressure provides a sufficient driving force to guarantee the fracture will continually propagate upwards to a large distance. This trend is clearly demonstrated in Figure 2.3 and Figure 2.4 where the fracture height growth has reached 200 m. Fracture opening or width (Figure 2.3) varies significantly from layer to layer because of the modulus and stress variation. The peak opening of m occurs in the low modulus, low stress layer at ~510 m depth, and the minimum opening of m (disregarding the fracture tip zones) occurs in the high stress, high modulus layer at ~610 m depth. Fracture growth rate can be divided into three phases. Initially the fracture grows quickly in height until it reaches the higher stress zones at ~610 m. Propagation through this zone and the high stress zone at 570 m proceeds relatively slowly. However, once the last and highest stress layer is breached, the fracture proceeds to maximum flux rate (0.5 m2/s). This computed rapid growth rate would be tempered in a true 3D model because of the drop in net pressure that normally accompanies rapid height growth in 3D models (which is representative of field conditions) but that is not incorporated into the 2D model when using a constant pressure condition at the injection point. As such, the 2D model is a worst case scenario for rapid height growth. Page 14

29 Depth (m) Young's Modulus (MPa) HCS (MPa) Note. The black line in (a) is for Young s modulus and in (b) the black, red, and blue lines are for different distributions of minimum horizontal stress. The horizontal confining stress is constant within each layer. An injection pressure of 17 MPa was used and the black line then corresponds to the lower stress case where the injection pressure is larger than the horizontal stress across every layer, and the red and blue lines represent the high stress cases where, in some layers, the injection pressure is lower than the horizontal stress. The dot on the y axis shows the injection point at 665 m and some key layers are labelled for reference. Figure 2.2 Variations of (a) Young s modulus and (b) Horizontal Confining Stress (HCS) with depth Time = 39.2 s Depth (m) Opening (m) Note. The constant injection pressure (=17 MPa) is larger than the any of the horizontal stresses (maximum of 15.7 MPa) with the horizontal stress distribution along a specific depth profile, as depicted by the black line in Figure 2 2. The single sided fracture propagates upwards from within the second layer located at 665 m and fracture length is measured from that depth. The injection point is indicated by the black dot. Figure 2.3 Fracture opening at a particular time (=39.2 s) under constant injection pressure (=17 MPa) Page 15

30 Height Growth Extent (m) Crack Length Injection Rate Time (s) Injection Rate (m 3 /s per m of fracture thickness) Note. Depicted for a low stress event, as shown in Figure 2.2 by the black line. The crack growth rate is reduced to 0.17 m/s after a fast growth stage ending at 27.8 s. The fracture inflates in width during this slow growth period and at a time after 40 s the fluid flux is reduced to zero as the pressure becomes uniform. Figure 2.4 Fracture growth (solid line) and fluid flux (dashed line) change over time, depicted for a low stress case Because this 2D modelling does not consider lateral growth as part of the solution, it predicts significantly more height growth than if lateral growth were included and provides an extreme upper limit for height growth. A simplified stress and modulus profile must be used in the P3D design model SIMFRAC (Duke Engineering and Services 1999) because the model can consider only three elastic layers and five stress layers in a problem. Therefore, the layering considered in the 2D modelling was simplified before being used in the P3D model. The P3D model assumes planar fracture growth but accounts for loss of fluid into the seam and couples lateral and height growth during the simulation. Stress and modulus parameters used are listed in Table 2.1, Table 2.2 and Table 2.3. The model was run for a water only fracture treatment pumped at a nominal rate of 60 barrels per minute (9.5 m3 per minute) through an open hole section across the 10 m thick coal seam. Other details of the reservoir and treatment parameters used in the P3D model are listed in Table 2.4, Table 2.5 and Table 2.6. Page 16

31 Table 2.1 Mechanical property and stress layering used in the P3D hydraulic fracturing model Layer Layer boundary depths (m) Modulus E (GPa) Poisson s Ratio Kc (kpa m 1/2 ) Top Bottom Overburden Reservoir Underburden Note: kpa is kilopascal, which is the pressure unit used in the model (1 MPa = 1000 kpa). Table 2.2 Confining Stress Profile Data Described By five Layers as used in the P3D hydraulic fracturing model Layer Layer boundary depths (m) Stress difference (kpa) Confining stress (kpa) Top Bottom 2 nd Top Layer st Top Layer Reservoir st Bottom Layer nd Bottom Layer Note: kpa is kilopascal, which is the pressure unit used in the model (1 MPa = 1000 kpa). Table 2.3 Rock Mechanics Parameters applied to coal and used for Cases 1 and 2 Property Case 1 Case 2 Vertical stress (kpa) (kpa) Horizontal stress (kpa) (kpa) Young s modulus (kpa) (kpa) Poisson s ratio Biot s constant Crit. Stress Intensity factor, Kc (kpa m) (kpa m) Calculated spec. surface energy (kpa m) (kpa m) Page 17

32 Table 2.4 Reservoir data used for cases 1 and 2 Property Avg. pressure In situ horizontal permeability Reservoir Layer (kpa) 3.0 (md) In situ porosity 0.02 Res. fluid viscosity Total in situ compressibility 0.85 (cp) (1/kPa) Initial reservoir temperature 31.0 (deg C) Layer thickness 10 (m) Table 2.5 Pumping Schedule; Identical for Cases 1 and 2 Step Volume (m 3 ) Rate (m 3 /min) Conc. (kg/m 3 ) Fluid type (number) Stage type (number) Shut in (days) Temp. (deg C) Table 2.6 Proppant parameters, Identical for Cases 1 and 2 Proppant no. Proppant (sieve size) Proppant diameter (mm) Porosity Density (kg/m 3 ) Permeability (md) sand sand The fracture produced by the P3D model for case 1 is shown in Figure 2.5. The figure shows a vertical fracture formed by the hydraulic fracture treatment in profile (side view). One half of the fracture is shown with the other half lying to the left of the y axis in this plot. The length of the fracture shown is, therefore, referred to as the fracture half length and is the horizontal distance from the well at the centre of the fracture to the most distant fracture leading edge. Height growth upwards was effectively limited by the first 15 m thick higher modulus layer above the seam, which did not arrest the fracture in the 2D modelling case shown in Figure 2.4. The P3D model predicts a vertical fracture extending laterally to 475 m and vertically to 6 m above and Page 18

33 below the seam near the wellbore (total height of 22 m at the wellbore). In reality, the fracture may be arrested at the coal rock interface because of interface effects not included in the design model and this would result in a fracture extending vertically only across the coal seam itself. An example of such a case is the mined fracture treatment carried out in ECC90, in the Bowen Basin of Queensland (Jeffrey et al. 1992), which is described in section of this report. Note. Boundary layer depth is as described in Table 2.1 and Table 2.2. Other parameters incorporated include layer thickness, viscosity, injection rate, vertical stress and others, as described in Case 1 listed in Table 2.3 to Table 2.6. Figure 2.5 Height growth and proppant distribution (shaded) predicted by P3D design model using the modulus and stress profiles associated with given boundary layer depth However, height growth from the coal seam into the surrounding layers does occur in coal seam gas treatments and if the lateral growth in the model were to be made more difficult for example, by using a higher apparent fracture toughness for the coal then more height growth would be predicted. To illustrate this effect, the coal fracture toughness was increased by a factor of two. This increase in toughness is used here to represent resistance to lateral fracture growth through the coal, caused by the fracture growing through offsets and as sub parallel segments developed as a result of interactions with natural fractures. Figure 2.6 contains the profile plot for the fracture at the end of the injection for this higher toughness case. The fracture is predicted to grow to a total height of 48 m and to a half length of 200 m, less than half the extent laterally and more than twice the extent vertically compared to the fracture case in Figure 2.5. The fracture is still limited to a relatively small amount of height growth, with more upward than downward growth occurring. In order to determine which of these two cases, or other growth cases, is closer to an actual geometry from a treatment, the actual treatment data obtained during an hydraulic fracturing operation would be analysed and compared to previously prepared modelling data. By adjusting the model parameters within limits constrained by the measurement variability, the pressure measured during the treatment can be matched by the model. If other data is available, such as Page 19

34 microseismic or tiltmeter monitoring data, it can be used to constrain the model results further. The calibrated model is then tested against other treatments and adjusted further. It can be used to design fracture treatments and predict fracture growth in nearby wells in the same field. The process of comparing and matching results from the model to measured data is continuous at a site during hydraulic fracturing operations. Note. Boundary layer depth is as described in the case shown in Figure 2.5, but with the fracture toughness of the coal increased by a factor of two. This increase in toughness causes the fracture to grow more slowly in the lateral direction and increases the pressure required to grow the fracture. Thus, the fracture then grows more in height. Figure 2.6 Fracture profile at the end of injection predicted by P3D design model, using the modulus and stress profiles associated with given boundary layer depth The 2D model overestimates the fracture height growth, primarily because the fracture is being strongly driven in height by a prescribed pressure at the depth of the injection point. Because the fluid does not have the freedom to move in the lateral direction, it is all directed into inflating the fracture and extending it in height. Fluid flux is increased to maintain the prescribed pressure constant and, when height growth is favoured by the stress and modulus layering, the fluid flux and growth rate increase dramatically and excessive height growth is predicted. The advantage of the 2D model lies in its ability to accurately model multiple layers and their effect on the fracture opening and growth, but not in predicting ultimate vertical extent. To obtain realistic height growth estimates a model that couples the lateral and vertical growth, such as the P3D model, must be used Larger confining stress in a layer For the stress case shown by the blue line in Figure 2.2(b), a stiffer layer with a larger horizontal stress (around 18 MPa which is greater than the injection pressure of 17 MPa) is located immediately above the coal seam layer. As shown in Figure 2.7, the fluid flux is much smaller than the upper limit rate and the fracture height growth only extends to around 12 m above the injection point. Page 20

35 The fracture tip is located in and arrested at the stiffer layer. The excess pressure is not large enough to extend the fracture further. The only way for the fracture to overcome this stress barrier is for an increase in the injection pressure to occur. Height Growth Extent (m) Crack Length Injection Rate Time (s) Injection Rate (m 2 /s per m of fracture thickness) Note. Minimum horizontal stress profile as per that shown in Figure 2.2(b) by the blue line. Figure 2.7 Fracture growth curve (time versus length) and fluid flux evolution for a particular minimum horizontal stress profile Limited injection rate In Figure 2.4, the results show that the fluid flux increases rapidly at a time of about 22 seconds. Thus, the injection rate associated with growing this fracture is unrealistically high since it far exceeds the capacity of current pumping systems available. As discussed in Zhang et al. (2008), opening of the fracture in the lower modulus, softer layer results in a larger fracture volume and this, in turn, results in a delay or arrest in fracture growth, if the fluid flux is limited. This mechanism directly contributes to fracture arrest as shown in Figure 2.4 after 28 seconds. In this case, the fracture tip is located in a stiffer layer and any increase in fluid pressure will result in a larger fracture volume increase in the layers below this stiffer layer. If the pressure was increased sufficiently, additional height growth of the fracture would occur. The fluid flux has been limited to its upper value of 0.5 m3/s per m of fracture thickness after 24.6 seconds of injection time (Figure 2.4). The flux is being stored in the fracture during this period by increased fracture width Softer layers A thick stiff layer in a compressional stress regime can act as a stronger stress barrier for height growth because it carries higher horizontal stresses distributed across a significant thickness. Page 21

36 However, there are inevitably many softer layers in layered coal basin rock sequences and these affect height growth. There are two factors that allow softer layers to arrest height growth of a hydraulic fracture. First, if the fracture tip is located within a softer layer, which is below a very stiff layer, and the excess pressure (pressure above the local horizontal stress) is too low to propagate the fracture towards the interface, the fracture will be arrested. The fracture arrest is consistent with linear elastic fracture analysis, in that the fracture tip stresses are reduced when the tip approaches the interface from the soft layer side. To put it another way, the stress intensity factor decreases when a fracture tip approaches the soft to stiff interface (Simonson et al. 1978; He and Hutchinson 1989). This mechanism may explain how hydraulic fractures are sometimes confined in the coal seam being stimulated. However, field cases and laboratory experiments have shown that it is possible for a hydraulic fracture to grow from a soft layer into a stiff layer, despite the elastic fracture theory predicting that this should not be possible. Second, if the fracture tip is located within a stiffer layer above a thin softer layer that carries lower in situ stress, the larger excess pressure acting in the thin layer that acts to assist in fracture penetration across the stiffer layers is limited in its effectiveness because of the limited thickness of the soft layer. However, in a 3D fracture the lower horizontal stress in the soft layer will allow the fracture to grow in length along it in preference to growing in height, especially if the soft layer is thicker. Therefore, the layer thickness is an important factor. If the thickness of the softer layer below a stiffer layer is small, the portion of the fracture subject to this higher excess pressure is therefore reduced. This limits the driving force for the fracture to continue to grow compared to a case with a thicker soft layer. But lateral growth is favoured in a thicker soft layer. This argument applies to all layers penetrated by the fracture. The weighted total of the excess pressure acting on the thickness of each layer along the fracture must produce a stress intensity factor at the fracture tip that equals the rock fracture toughness of the layer that the tip is located in or fracture arrest occurs. It should be noted that this arrest mechanism may only act for a short time, depending on the injection pressure, as shown in Figure 2.4. But in some cases, fracture arrest is permanent, as shown in Figure 2.8, which depicts the stress profile given by the red line shown in Figure 2.2(b). In this case, the fracture tip is still far away from a layer with the maximum confining stress, but the fracture has arrested in a layer with a confining stress of 16.2 MPa. Even though the confining stress is less than the injection pressure (17 MPa), the fracture criterion used by the model to determine when to extend the fracture further, is not met when the entire fracture is uniformly pressurised by the injection pressure. Therefore, the fracture can propagate further only if the injection pressure is increased. Page 22

37 Height Growth Extent (m) Crack Length Injection Rate Time (s) Injection Rate (m 3 /s per m of fracture thickness) Note. Minimum horizontal stress profile as shown by the red line in Figure 2.2(b) was used. The late increase in fluid flux is associated with volume needed to open the portions of the fracture next to low modulus layers. Figure 2.8 Fracture growth curve (solid line) and fluid flux evolution (dashed line) for a particular minimum horizontal stress profile Effects of the thickness of the softer layer Fracture growth is controlled by the non local effect of the net pressure distribution. A local zone with negative net pressure, even though close to the tip, is not by itself sufficient to stop fracture growth. The pressure loading along the entire fracture must be accounted for to determine if the fracture will continue to grow or not. This is the reason why a large fracture is more difficult to arrest than a small one. This feature becomes important for height growth, mainly because of the existence of low and high stress zones along the fracture trace, where the excess pressure varies. In other words, the layer thickness and stiffness define the range of excess pressure and its effect on fracture growth, and are thus important factors. The viscous fluid flow in the fracture is the other important factor that results in the excess pressure distribution driving fracture growth. When arrest occurs, the pressure in the fracture becomes uniform as fluid flow in vertical sections stops and viscous effects disappear. If the uniform pressure is not sufficient to restart height growth, then the fracture is arrested unless the injection pressure is increased. In this sub section, layering contrasts are more typical of Sydney sedimentary basin coals in the Wollongong area in south eastern Australia. The fractures are allowed to propagate upwards and downwards for these cases Effect of a thin soft layer Figure 2.9 shows the modulus and stress contrasts existing in the rock layers. The layer with the injection point has a lower modulus compared to its neighbours, since it is assumed to be located Page 23

38 in a coal seam. Note that for this case a thin layer (1 m) is located at a depth between 692 and 693 m and the injection point is at 743 m in depth. A constant pressure of 20 MPa is prescribed at the injection point. Upward growth occurs and the fracture extends into the fifth layer. However, the growth into the sixth thinner and softer layer results in a slower rate of growth. The blunt nature of the fracture tip can be seen in Figure 2.10 and the fracture tip is just above the thin softer layer. Note. The blue line is for Young s modulus and the red line for confining stress constant within each layer. The constant injection pressure is 20 MPa, which is larger than the confining stress for the layers immediately above the injection point. A thin soft layer (1 m thick) is located at a depth between 692 and 693 m. The dot on the y axis shows the injection point at 743 m and some key layers are labelled for reference. Figure 2.9 (a) Young s modulus and (b) Horizontal Confining Stress (HCS) variations with depth Page 24

39 Time = 7.88 s Depth (m) Opening (m) Note. Constant injection pressure (=20 MPa) is larger than the horizontal confining stress 16.7 MPa for the layers immediately above the injection point. The fracture propagates upwards and downwards from the injection point within the fourth layer at 743 m. Figure 2.10 Fracture opening at a particular time (7.88 seconds) for a constant injection pressure (=20 MPa) The downward growth is arrested by the higher confining stress of the third layer. The opening at the middle of the lower part of the third layer becomes zero, implying the fracture is closed on itself in this region. Why a thin softer layer is efficient in stopping hydraulic fracture growth as seen in this example, and as has been experimentally observed by Charlez (1997) and Yew (1997), requires further investigation, both numerically and experimentally, since the roughness of the interfaces, plasticity of the thin layer, the strength of the layer, and the distribution of flaw sizes and confining stresses may all affect the conclusion. However, the arrest observed in this numerical case results only from elastic layering and associated horizontal stress contrasts. The fracture in Figure 2.10 arrests after penetrating 0.25 m into the higher stressed and thicker layer above the thin soft layer. This fracture arrest situation is not completely consistent with the analyses by He and Hutchinson (1989) and Simonson et al. (1978). Their analyses suggest that a fracture in a softer layer should not be able to penetrate into the stiff layer (although He and Hutchinson (1989) did not consider the effects of layer thickness). In this case, further fracture growth into the above stiffer layer has stopped but the fracture has crossed the interface. For other cases when the softer layer thickness is increased or in the absence of this thin softer layer, there was no difficulty in driving additional fracture growth. Page 25

40 The fracture growth curves and injection rate changes for the upward and downward extending fractures are shown in Figure It is found that the fluid flux into both fracture wings eventually decreases to zero, which then leads to the arrest of each fracture wing. The flux continues to be non zero for some time after fracture arrest and this period is associated with changing pressure and width in the fracture as the pressure becomes more uniform and viscous flow pressure effects disappear. Height Growth Extent (m) Crack Length (upward) Crack length (downward) Injection Rate (upward) Injection rate (downward) Time (s) Injection rate (m 3 /s per m of fracture thickness) Note. The blue line is for upward going fracture and the red line for downward going fracture. Figure 2.11 Fracture growth curve and fluid flux evolution for the case shown in Figure 2.9 From these results it is noted that the selection of the new fracture size as it penetrates into each layer needs to be considered in more detail. This size can control whether further growth is possible or not. Here, 0.25 m is used for element sizes and this is also the smallest fracture size to apply to a new fracture crossing an interface. The dependence of the numerical results on this size requires further investigation Increased layer thickness Next, a different layer thickness for the softer layer was selected. The soft layer depth range is changed from between 693 and 692 m to 717 and 692 m. The thickness of the softer layer is therefore increased from 1 m to 25 m. Apart from this, the confining stress and the modulus for each layer are the same as those used in producing the results shown in Figure 2.10 and Figure Figure 2.12 shows the fracture growth curve for the upward fracture growth after increasing the bottom location of the softer thin layer from 693 to 717 m. The fracture now penetrates the stiff layer above 692 m, which contains higher horizontal stress. This further illustrates the non local Page 26

41 effect on crack growth and how an increase in excess pressure and the distribution of this excess pressure influences vertical fracture growth through the layered rock sequence. However, the fracture growth is eventually arrested by a stiffer layer, whose base is at 681 m, for this case. The softer layer below this stiffer layer is only 3 m in thickness. Again, this thin softer layer affects the fracture growth as described above, leading to arrest of the vertical fracture height growth. Height Growth Extent (m) Time (s) Injection Rate (m 3 /s per m of fracture thickness) Note. The period during which the flux exceeds 0.5 m3/s is caused by the reverse flow from the downward going fracture. Figure 2.12 Fracture flux evolution and growth curves for the upward going fracture at two different layer widths In laboratory experiments and in mineback investigations of full size fractures, hydraulic fractures are documented to enter into bedding planes and extend along them for some distance. Such growth into interfaces results in diversion of the fracture direction or restrictions in fracture opening that then act to slow or arrest fracture vertical growth. The case of growth into interfaces is not considered in this set of numerical results because the direction of fracture has been restricted so far to only be vertical. When the fracture tip passes through the interface, a high stress gradient is generated along the interface, and this may lead to initiation of a new fracture at some point near the tip but along the interface. This situation has been studied in detail for nonfluid driven fractures by researchers working on composite structures and materials (He and Hutchinson 1989) and for fluid driven fractures (Zhang et al. 2008). In addition, the fracture can also deflect and become horizontal if the stress condition in a layer is such that the vertical stress is the minimum principal stress. This case will be studied below. Page 27

42 2.3.6 Fracture deflection to horizontal In an unfractured rock, hydraulic fractures will orient to grow and open against the smallest principal stress. This orientation minimises the energy required to extend the fracture further. If a vertical hydraulic fracture grows into a rock that contains high horizontal stress, the vertical stress may become the minimum principal stress. In response to this change in stress, the fracture may reorient to extend horizontally. Next we consider such a case, as shown in Figure 2.13, where the horizontal stress in some layers is higher than the vertical stress in magnitude. Fluid pressure is prescribed at the injection point located at a depth of 743 m in this layered sequence and a constant injection pressure of 20 MPa is used. Only the upward growing fracture is considered. The maximum injection rate is still controlled as 0.5 m2/s per m of fracture thickness. Within the fifth layer, which is one layer above the injection point, the vertical stress is less than the horizontal stress in this thick layer, and this stress state is expected to cause the upwards growing fracture to reorient to become horizontal. Figure 2.14 and Figure 2.15 show results produced when using the modulus and stress state shown in Figure Two cases are shown, one without and one with a small change in the initial fracture angle so the fracture was not perfectly vertical. A perturbation of the fracture s orientation is required to break the perfect symmetry in the numerical model and allow the fracture to reorient to become horizontal. Without such a perturbation to fracture direction, the modelled fracture does not deflect. In nature, a rock mass will contain many flaws and bedding features that will cause the fracture to be deflected from a perfectly straight path Depth (m) Young's Modulus (MPa) HCS (MPa) Note. The green dashed line is the variation of the vertical stress induced by gravity, and it is nearly linear with depth. Note that the sixth layer that is 1 m thick is replaced by a stiffer rock with a higher horizontal stress. The dot shows the injection point at 743 m and some key layers are labelled for reference (1, 5, 8 and 12). Figure 2.13 (a) Young s modulus (blue line) and 13(b) Horizontal Confining Stress (HCS) variations (red line) with depth Page 28

43 Time = 12 s 700 Depth (m) layer Horizontal Distance (m) Note. The fracture propagates vertically. The upward growing fracture penetrates two thin, stiffer layers. There is no sign that the fracture growth is arrested and in this case its direction is not affected by the large horizontal stresses in some layers. Figure 2.14 Fracture trace for specific stress conditions, as given in Figure 2.13 Page 29

44 Time = 3.5 s 700 Depth (m) layer Horizontal Distance (m) Note. The y axis is depth, increasing downwards. The fracture is initially 5 degrees miss aligned to vertical (y direction). The upward growing fracture reorients to align with the lower horizontal in situ stress first, but it continues to turn away from the stiffer upper layer as it extends further in the x direction. Figure 2.15 Fracture path for specific stress conditions, as given in Figure 2.13 In general, if a fracture propagates into a thick layer with horizontal stress larger than the vertical stress, the vertical stress becomes the minimum principal stress. If the vertical stress is the minimum principal stress the fracture growth direction will become horizontal with vertical growth not then a concern. 2.4 Summary An in situ horizontal stress acting across the plane of a vertical fracture, with a magnitude larger than the fluid pressure inside the hydraulic fracture, acts to impede fracture height growth. However, due to the non local effect that the pressure inside the fracture has on fracture growth, fracture growth can occur even if this horizontal stress in a particular rock layer is larger than the injection pressure. Modulus contrast is also an important factor in determining fracture growth through layers. Softer layers result in a locally wider fracture segment. This effect can reduce fracture growth rate if the injection rate is constrained, although it does not stop fracture growth by itself. But when driven by constant pressure, the growth rate may not slow when growing though these soft layers. Page 30

45 Fracture containment, assuming a basin shortening stress environment, is more likely in the situations detailed below, although some conditions are chosen arbitrarily for illustrative purposes. For a softer thin layer, the associated zone of low stress provides additional excess pressure to open the fracture, but this pressure is limited to act only on the part of the fracture in the thin layer. Two numerical cases are provided in the body of the report where a thin soft layer located below a thicker stiff layer resulted in fracture arrest. Additional study is required to define and verify the process leading to this model result. For a stiffer thick layer, the high horizontal stress acting in that layer which exists across the entire thickness of the layer will retard or arrest fracture growth. Arrest may occur when there is a very stiff and high stress layer immediately above the fracture zone. Fracture growth can either be arrested within this stiffer layer as fracture nucleation becomes difficult, or the fracture may reorient to become horizontal if the vertical stress is the minimum stress. The duration and strength of the injection should be taken into account for fracture height growth analyses. Design models couple the height and length growth processes and provide more realistic estimate of fracture height growth overall. Additional details of the layering and of the mechanics of a fracture growing through multiple layers, not captured in design models, can be considered using 2D research models. Interface strength can affect fracture growth. Shear slip on bedding planes is a mechanism that can blunt vertical fracture growth or lead to an offset in the fracture path, both factors that act to arrest or retard fracture growth. These factors have been studied previously and results are in the literature cited in Section 2.2. When a design model that couples lateral and vertical growth was used, height growth was reduced dramatically. The stress and modulus profiles used in this P3D design model are simplified compared to the detailed layering used in the 2D research model, but the main effect of reduced height growth in the P3D model is likely to be a result of the model allowing the fracture to grow laterally. The mechanics of height growth obtained from the 2D model provide valuable research data, but the injection conditions used result in large height growth because the fluid flux is directed into a fracture that can only grow in the vertical direction with no possible diversion of fluid into lateral growth. Page 31

46 3 T shaped fracture growth T shaped hydraulic fractures have been mapped by mineback at a number of sites in the US. Diamond and Oyler (1987) document 22 mined hydraulic fractures and found that approximately 50% of them were T shaped. In Australia, of the nine hydraulic fractures that have been mapped after mining, four of these were found to be T shaped. An example of a T shaped fracture, including mineback drawings and data, is included at the end of this section of this report (Figures 3.8, 3.12 and 3.13). In addition, horizontal fracture growth has been determined to occur, by remote monitoring using tiltmeters, as a result of several commercial coal seam gas hydraulic fracture treatments in Australia (Johnson et al. 2010). In this section, a 3D numerical model is described and used to study T shaped hydraulic fracture growth. Preliminary results presented here are a first attempt to more completely model the T shaped mode of fracture growth, using the commercial finite element package ABAQUS (ABAQUS 2012) and cohesive finite elements to discretise the fracture path (Chen 2012). The cohesive finite element method has its origin in the concepts of a cohesive zone model for fracture growth and was originally introduced by Dugdale (1960) and Barenblatt (1962). It has been extensively used to simulate damage and fracture processes in concrete, rock, ceramics, metals, polymers, and composites. Classic linear elastic fracture mechanics approaches use an elastic fracture tip region, resulting in a predicted infinite stress at the fracture tip. The cohesive zone model assumes the existence of a simplified fracture process zone characterised by a traction separation law. In this way, the cohesive zone model avoids the singularity in the fracture tip stress field that is present in classic fracture mechanics. In addition, the cohesive zone model fits naturally into the conventional finite element method, and thus can be easily implemented. The cohesive finite element method therefore provides a computationally tractable alternative approach for quantitative analysis of fracture behaviour through the explicit simulation of the fracture development process. Compared to the conventional fracture mechanics method, the cohesive element method has the following advantages in modelling hydraulic fracturing. First, the cohesive zone model effectively avoids the singularity at the fracture tip region, which poses considerable challenges for numerical modelling in classic fracture mechanics. The lubrication equation, governing the flow of viscous fluid in the fracture, involves a degenerate non linear partial differential equation (Peirce and Detournay 2008). The coefficients (permeability) in the principal part of this equation vanish as a power of the unknown fracture width (opening). The fracture opening tends to zero near the tip of an elastic fracture as described by classic fracture mechanics. This non linear degeneracy poses a considerable challenge for numerical modelling. In contrast, the fracture opening is not zero but finite at the cohesive fracture tip, which naturally avoids the non linear degeneracy problem associated with the singularity in fluid pressure that otherwise must be handled at the fracture tip. Secondly, the hydraulic fracture propagation is a moving boundary value problem in which the unknown footprint of the fracture and its encompassing boundary need to be found while satisfying an additional fracture propagation criterion when using the classic fracture mechanics method. Also, in the cohesive zone finite element model the location of the fracture tip is not an input parameter but a natural, direct outcome of the solution, which improves the computation Page 32

47 efficiency. In addition, the cohesive zone model has the capability of modelling the microstructural damage that is inherently present in hydraulic fracturing initiation conditions (usually caused by drilling operations, perforation or from an interface). The cohesive element method has been applied to modelling hydraulic fracture propagation by several researchers (Chen et al. 2009; Sarris and Papanastasiou 2011; Chen 2012). 3.1 Cohesive zone model of hydraulic fracture As illustrated in Figure 3.1, a fracture that is hydraulically driven with the injection of a fluid from the wellbore into the fracture channel is considered. A horizontal fracture growing from a vertical wellbore is shown in Figure 3.1 and vertical fractures are treated in a similar manner. In the cohesive zone hydraulic fracture model, a pre defined surface (fracture path) made up of cohesive elements that support the cohesive traction separation calculation is embedded in the finite element model and the hydraulic fracture grows along and within this pre defined surface. The fracture process zone (that is, the unbroken cohesive zone) is defined within the separating surfaces where the surface tractions are non zero. The fracture is fully filled with fluid in the broken part of the cohesive zone where no traction from rock fracture exists, but where fluid pressure is acting on the open fracture faces. The definition of the fracture tip, as used in Shet and Chandra (2002), is adopted here: The mathematical fracture tip refers to the point which is yet to separate The cohesive fracture tip corresponds to the damage initiation point where the traction reaches the cohesive strength and the separation reaches the critical value The material fracture tip is the complete failure point where the separation reaches the critical value and the traction or cohesive strength acting across the surfaces are equal to zero. Source: Chen (2012) Figure 3.1 The process of hydraulic fracturing as depicted by a cohesive hydraulic fracture model Page 33

48 3.1.1 The cohesive law A cohesive traction separation law is a fundamental aspect of using the cohesive fracture model. The traction separation law defines the relationship between the traction tensor and the separation (displacement jump) δ across a pair of cohesive surfaces. A cohesive potential function is defined so that the traction is given by Equation 4: [Equation 3] Various types of traction separation relations (potential functions) for cohesive surfaces have been proposed to simulate the fracture process in different types of material systems. The irreversible bilinear cohesive traction separation law, as shown in Error! Reference source not found., is used here. This law assumes that the cohesive surfaces are initially intact without any relative displacement, and exhibit reversible linear elastic behaviour until the traction reaches the cohesive strength or equivalently the separation exceeds. Beyond, the traction reduces linearly to zero up to and any unloading takes place irreversibly. T T 0 Traction K G c δ 0 Separation δ f δ Figure 3.2 The bilinear cohesive law used in this modelling generates tractions that depend on the path of the separation process at the tip, as illustrated in this diagram The irreversible bilinear cohesive traction separation constitutive relation is given by Equation 5: when 0 [Equation 4] when This bilinear law is a special case of the trapezoidal model. It can also be regarded as a generalised version of the initial rigid, linear decaying irreversible cohesive law. The bilinear law has been widely used to simulate fracture or fragmentation processes in brittle materials, like rocks. Use of a cohesive separation law, such as the irreversible bilinear law in Equation 5, applies at the tip of the propagating hydraulic fracture and replaces the fracture toughness and stress intensity factors used in linear elastic fracture mechanics treatment of fracture growth. Page 34

49 3.1.2 Fluid flow within fracture The flow pattern of the fluid within the fracture is shown in schematically in Figure 3.3. The fluid is assumed to be incompressible and to display Newtonian rheology. A fluid with Newtonian rheology, such as water, displays a shear rate that is proportional to the applied shear stress with the constant of proportionality being the fluid viscosity. The fluid flow along the fracture is governed by the lubrication equation (Batchelor 1967), which is formulated from Poiseuille's law (Equation 6): [Equation 5] and the continuity equation of mass conservation (Equation 7): [Equation 6] Where:, = fluid flux of the tangential flow, = fluid pressure gradient along the cohesive zone, = fracture opening = fluid viscosity = injection rate., and,, are the normal flow rates into the top and bottom surfaces of the cohesive elements, respectively, which reflect the leak off through the fracture surfaces into the adjacent porous material. For an impermeable fracture, there is no leak off and,, 0. The normal flows are defined by Equation 8: [Equation 7] Where: and = pore pressures in the adjacent poroelastic material on the top and bottom surfaces of the fracture, respectively and = the corresponding fluid leak off coefficients Here the leak off coefficients with the unit of m/pa.s are input as constants or functions of field variables by the user and can be interpreted as the effective permeability of a finite layer of permeable material on the cohesive element surfaces. The leak off coefficients allow the fluid pressure to act through the otherwise impermeable cohesive element on the surrounding permeable material in the main finite element model (ABAQUS 2012). Page 35

50 Normal flow Crack Opening Tangential flow Figure 3.3 A depiction of the normal and tangential flow paths of fracturing fluid within a fracture The normal flow can significantly change the fluid mass balance or fluid loss within the fracture, and as a result the fracture opening and propagation are changed. It is necessary to note that the leak off model defined by Equation 8 is different from the Carter leak off model (Economides and Nolte 2000). Carter leak off is given by Equation 9: Where:, [Equation 9] = the Carter leak off coefficient whose magnitude characterises the permeability of the porous medium = the time that the fracturing fluid reached the point for the first time. The Carter leak off model is a simplified, one dimensional decoupled model, which predicts the leak off intensity as an explicit function of the time elapsed since the fluid first reached the point. The mechanical properties of the fluid and porous medium are taken into account indirectly by specification of the leak off coefficient (Howard and Fast 1970). Leak off into a permeable material in the ABAQUS model is treated as a 2D or 3D diffusion problem in the same manner as pressure and flow is solved for in a 2D or 3D reservoir simulator (ABAQUS 2012). Substituting Equation 6 into Equation 7 results in the Reynolds lubrication equation (Equation 10): [Equation 10] The fluid pressure is considered as traction acting on the open surfaces of the fracture. As complete failure eventually occurs within the cohesive zone, there will be no contribution from the cohesive traction in the open part of the fracture channel. The fluid pressure, which acts to open the hydraulic fracture, is balanced by the far field stress acting across the entire fracture including the cohesive zone and by the cohesive tractions acting across the fracture surfaces in the cohesive zone. A coupled fluid pressure traction separation relationship exists between the cohesive zone defined by the traction separation law and the pressurised fracture as found from solving the lubrication equation (Equation 10) with the constraint that all tractions acting on the entire fracture and cohesive zone must be in equilibrium. Page 36

51 3.2 Cohesive finite element model The cohesive finite element model is applied here to model the 3D T (or H ) shaped hydraulic fracture by using the commercial finite element package ABAQUS (2012). A Fortran program has been written to generate the mesh and boundary conditions for the finite element model. The program can automatically generate the finite element meshes with given finite element model parameters such as number of elements, element aspect ratio, and overall dimensions (size) of the model. It can also assign different material parameters for the surrounding rock, for the coal layer, and define the cohesive traction separation law for different branches of the T (or H ) shaped hydraulic fracture. Different initial stresses and boundary conditions can also be applied to the model by the program. The generated analysis input file can be directly run by submitting it to ABAQUS. The current Fortran code can generate half (symmetrical) or full hydraulic fracture models. 3.3 A three layer model and T shaped growth As illustrated in Figure 3.4, a three layer formation with pre defined surfaces is modelled in the finite element model. The three layer formation consists of upper and lower (e.g. roof and floor rock layers), and a middle layer (e.g. coal layer). Each layer can have a different thickness and mechanical properties. To model T (or H ) shaped hydraulic fracture propagation, two horizontal surfaces (as shown denoted by blue planes in Figure 3.4) between the layers and one vertical surface (as denoted by the red plane in Figure 3.4) within the middle layer are pre defined so that the fracture may grow along them. Pre defined horizontal fracture surface (Top) Pre defined vertical fracture surface (red) Pre defined horizontal fracture surface (Bottom) Note. A three layer rock formation consisting of upper and lower (e.g. roof and floor rock layers), and middle (e.g. coal layer) layer is considered in the finite element model. Two horizontal surfaces (blue planes) between the layers and one vertical surface (red plane) within the middle layer are pre defined, to simplify the numerical modelling problem, so that the fracture may propagate along them to model the T (or H ) Shaped hydraulic fracture growth. Figure 3.4 A three layer rock formation with pre defined fracture surfaces Page 37

52 3.4 Finite element model In the finite element model, different mesh densities with variable or constant mesh sizes can be assigned to different parts of the finite element model. For example, coarse meshes and fine meshes can be generated for modelling the far field and the hydraulic fracture, respectively. An example of the finite element mesh is shown in Figure 3.5. The 8 node 3D linear brick elements (named C3D8 elements in ABAQUS) are used to model the impermeable upper, lower and middle layers. When modelling fracture growth in permeable formations, the 8 node 3D tri linear displacement and pore pressure elements (C3D8P) are used. The 12 node displacement and pore pressure three dimensional cohesive elements (COH3D8P) are used to model both the vertical and horizontal branches of the T (or H ) shaped hydraulic fracture. A surface based tie constraint has been used to connect the different layers and/or parts that have different mesh densities at the interface boundaries in the finite element model. Fixed displacement boundary conditions in the x, y, and z directions are applied to the left, front, and bottom surfaces of the model, respectively. Tractions (far field confining stress) in the x, y, and z directions are applied to the right, back, and top surfaces, respectively. Different initial stresses are imposed to different formation layers so as to model the in situ stress variations. The injection point can be assigned to any pressure node in the cohesive fracture surfaces. In the current finite element model, the injection point is located at the vertical fracture surface in the middle (coal) layer. A constant or time varying injection rate is applied at the injection point. Page 38

53 Figure 3.5 Finite element model mesh, with pre defined fracture planes indicating the pathways along which different T and H shaped fractures are grown 3.5 Case study for a T shaped fracture In this example, site conditions and fracturing parameters are used from a hydraulic fracture treatment that was carried out in well ECC90, which penetrated the German Creek coal seam at Central Colliery located in the Bowen Basin of east central Queensland. The hydraulic fracture Page 39

54 treatment has been described elsewhere in detail (Jeffrey et al. 1992; Jeffrey et al. 1995). This fracture was mapped as it was mined and thus both injection data and propped fracture geometry data are available for the comparison. The properties of the rock and coal layers used in the simulation, which are taken from the literature (Jeffrey et al. 1992), are listed in Table 3.1. Table 3.2 lists the treatment parameters used in the finite element simulation. In Table 3.1, k is the permeability of the coal, E is the Young s modulus of the coal and rock, is the Poisson s ratio of the rock, and G c is the critical energy release rate which is used in determining when the fracture will propagate. A symmetrical model with respect to the plane y = 0 is used in this study, and a constant injection rate of 0.04 m3/s is used in the simulation, allowing for the half fracture symmetry. Table 3.1 Physical properties of rock and coal Description k (md) E (GPa) G c (Pa m) Roof rock Coal Floor rock Table 3.2 Treatment parameters used in the simulation Property Value Injection rate (m 3 /s) 0.08 Fluid apparent viscosity (Pa s) 1.0 Horizontal stress in coal σ h (MPa) 4.4 Vertical stress σ v (MPa) Coal layer thickness (m) 2.6 Roof layer thickness (m) 30.0 Floor layer thickness (m) 30.0 Dimension in x direction (m) Dimension in y direction (m) Impermeable coal case In this first analysis of T shaped hydraulic fracture growth, the permeability of the coal (and the roof and floor rock layers) is set to zero so that all of the injected fluid is stored in the fracture itself and acts to extend the fracture. This simulation thus provides an upper limit on fracture growth for the injection rate and fluid type and volume used and is somewhat faster computationally because fluid pressure in the surrounding rock is not calculated as part of the Page 40

55 solution. The treatment carried out in ECC90 at Central Colliery used a borate cross linked fluid, which is a thick gel that acts to limit leak off. This fluid was modelled by a 1 Pa.s fluid with Newtonian rheology although such gels actually have shear thinning or visco elastic rheological properties, this more complicated rheology was not used because the element library in ABAQUS currently only supports Newtonian rheology. Results for fracture dimensions, including fracture opening width distributions are shown in Figure 3.6. The vertical fracture branch is seen to grow faster than the horizontal branch. Figure 3.7 contains a plot of model predicted injection pressure at the wellbore with time. The injection pressure reaches a maximum point, after 43 seconds from the start of injection, which is associated with the initiation of the horizontal fracture branch. After this maximum is reached, the pressure then decreases slowly for the rest of the treatment. Note. The rock layers are impermeable in this case. The maximum fracture opening is about 11 mm. The vertical fracture grows faster than the horizontal wings of the T shaped fracture. The fracture is about 80 m wide (tip to tip) in x direction and 130 m long (tip to tip) in y direction. The fracture is symmetric with respect to the plane y=0. Half of the fracture is shown in this figure. Figure 3.6 Opening profile of the T shaped hydraulic fracture at 7 minutes Page 41

56 Figure 3.7 The finite element model predicted injection pressure. A minimum and maximum in the pressure curve are indicted Two snap shots of the fracture growth and opening are shown in Figure 3.8, corresponding to the minimum in the pressure curve at 6 seconds (s) and the maximum at 43 s (Figure 3.7). The vertical branch is open and extending by the time the minimum pressure is reached. At this time the vertical branch has extended across the full height of the seam and the pressure starts to increase with time. Because the opened horizontal fracture cannot support shear stress, shear displacement progressively develops along the coal roof rock interface, causing the vertical branch to assume an open blunted shape there. By the later time shown, the horizontal branch has developed further and a well developed T shaped geometry is present with an extent of about 12 m in the x direction and opened to 8 mm near its centre. Because no fluid loss into the coal or rock is allowed in the impermeable case, fracture growth occurs rapidly. The alternative case of fracture growth in a permeable coal seam is considered in the next section. Page 42

57 Figure 3.8 Fracture size and opening profile in an impermeable coal seam at 6 s and 43 s, respectively Permeable case The permeable T shaped fracture growth case includes loss of fracturing fluid from the fracture into the coal, which is assigned a permeability of 5 md in this case. As fluid is lost from the fracture into the coal, the fracture growth is slowed. Figure 3.9 shows the geometry and fracture opening after 30 minutes of injection. The vertical fracture extends beyond the horizontal fracture in the y direction. Figure 3.10 shows the injection pressure with time. For the permeable case the injection pressure shows a smooth and continuous decrease with time, rather than the local minimums and maximums that were seen in the impermeable case. Finally, Figure 3.11 shows contours of pore pressure in the coal seam arising from the pressurisation of the coal by the fluid leaking into it from the horizontal and vertical fracture branches. The parameters used in the finite element model were selected to represent conditions for the hydraulic fracture treatment carried out in well ECC90 in This fracture was later mined and mapped and the propped extents of the horizontal and vertical branches are shown in the plan Page 43

58 view in Figure Two vertical sections through the fracture are shown in Figure 3.13, revealing the overall T shaped geometry. These vertical sections show the propped vertical fracture in detail but show only a small portion of the horizontal branch. Figure 3.14 contains the pressure recorded during the treatment and a few data points from the T shaped model pressure for the permeable case. The pressure in the field was measured at the well head. The bottom hole pressure, which is what the model calculates, was not measured directly. The bottom hole pressure has to be estimated after correcting for fluid friction, fluid density and the elevation difference between the well head and the coal seam. This is a difficult and not very accurate process and has not been done for this data. The bottom hole pressure from the model calculation shows a similar trend with time to the measured surface pressure and is somewhat higher throughout, which seems reasonable. The pressure response of the permeable model case is quite different from the impermeable case response. The impermeable case produced a pressure that remained at approximately 8 MPa during the T shaped growth while the permeable case predicts that the pressure will continuously decline during fracture growth. This trend is seen in the measured pressure data presented in Figure Note. The vertical fracture grows faster than the horizontal wings of the T shaped fracture. The horizontal wing of the T shaped fracture is about 90 m wide in x direction, extending 45 m to either side of the vertical fracture and 50 m long Page 44

59 in y direction. The vertical branch extends 70 m in y direction from the well. The fracture is symmetric with respect to the plane y=0 with half of the fracture shown in this figure Figure 3.9 Opening profile of the T shaped hydraulic fracture within a permeable coal layer at 30 minutes Figure 3.10 The predicted injection pressure for the permeable case, indicating a decrease in pressure over time as the fluid leaks into the coal Page 45

60 Figure 3.11 Pore pressure distribution in a permeable coal layer at 10 minutes Source: Jeffrey et al. (1992) Figure 3.12 Plan view of the hydraulic fracture mapped at Central Colliery in well ECC 90 Page 46

61 Source: Jeffrey et al. (1992); Note. (a) The cross section is located just to the south west of the well (ECC90), (b) the cross section is located approximately 5 m north east of the well. Figure 3.13 Two vertical cross sections through the fracture shown in Figure 3.12 Source: Jeffrey et al. (1992); Pressure data predicted by the ABAQUS T shaped model are also shown indicating a similar reduction in pressure over time as seen in the observed data. Figure 3.14 The change in surface injection pressure over time during the hydraulic fracture treatment of well ECC90 Page 47