Table Of ContentSPRINGER BRIEFS IN EARTH SCIENCES
Mark W. McClure · Roland N. Horne
Discrete Fracture
Network Modeling
of Hydraulic
Stimulation
Coupling Flow and
Geomechanics
SpringerBriefs in Earth Sciences
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Mark W. McClure Roland N. Horne
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Discrete Fracture Network
Modeling of Hydraulic
Stimulation
Coupling Flow and Geomechanics
123
MarkW.McClure Roland N.Horne
Petroleum and Geosystems Engineering Energy Resources Engineering
Universityof Texasat Austin Stanford University
Austin, TX Stanford,CA
USA USA
ISSN 2191-5369 ISSN 2191-5377 (electronic)
ISBN 978-3-319-00382-5 ISBN 978-3-319-00383-2 (eBook)
DOI 10.1007/978-3-319-00383-2
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Preface
Inthepastdecade,developmentofunconventionaloilandgasresourceshasbeen
perhaps the biggest new trend in the energy sector. It has become possible to
produce huge new resources that were previously considered uneconomic. Key
enabling technologies have been long horizontal wells and multiple fracturing
stages (King 2010).
Hydraulic fracturing in geothermal energy is typically referred to as Enhanced
Geothermal Systems, or EGS (Tester 2007). EGS researchers hope that improve-
mentsinstimulationdesignwillenablegeothermaltoonedayexperiencethesame
growth inproductionthat is now being seen inunconventional oil and gas.
Despite years of research and field experience, fundamental questions remain
unanswered. What is the relative importance of new and preexisting fractures in
stimulation?Whydothefracturenetworksgeneratedinunconventionaloilandgas
frequently appear to be so complex? What does a stimulated, unconventional
reservoir ‘‘look like?’’
Computational modeling has the potential to be very useful for stimulation
design,helpingengineersmakeroutinedesigndecisions,testnovelideas,perform
formation evaluation, and make decisions about data collection. A remarkable
diversity of models and modeling approaches exists. Unfortunately, progress is
hamperedbythenonuniquenesscausedbylimitedandincompletedata,resultingin
difficultyinconfirmingmodelassumptions.Therefore,whilestimulationmodeling
holdstremendouspromise,itremainsaworkinprogress.Atremendousamountof
work is beingdone inthis area, and progress is expected in the years ahead.
This book summarizes a hydraulic stimulation model developed especially for
unconventional applications in oil, natural gas, and geothermal. The model
described in this book remains incomplete. Several important physical processes
remainneglectedorincompletelydescribed.However,thestrengthofthismodelis
that it fully, efficiently, couples fluid flow and the stresses caused by deformation
in large, complex discrete fracture networks. We believe that realistically cap-
turing induced stresses will lead to better insight into stimulation processes. Fur-
thermore, we believe that the complexities of the reservoir—spatially variable
fracture density, orientation, stresses, and so on—have profound effects on the
stimulation process that cannot easily be simplified out of a numerical model
without obscuring important details.
v
vi Preface
Several novel techniques were developed for this work, and existing methods
were combined in novel ways. We hope that this work provides a useful contri-
bution to the field of stimulation modeling and lays the groundwork for future
research.
References
King, G.: Thirty years of gas shale fracturing: what have we learned? SPE 133456, paper
presented at the SPE annual technical conference and exhibition. Florence (2010). doi:
10.2118/133456-MS
Tester, J. (ed.): The Future of Geothermal Energy: Impact of Enhanced Geothermal Systems
(EGS)ontheUnitedStatesinthe21stCentury.MassachusettsInstituteofTechnology(2007).
http://geothermal.inel.gov/publications/future_of_geothermal_energy.pdf
Acknowledgments
This work was supported financially by the Precourt Institute for Energy at
StanfordUniversity.ThereweremanypeopleatStanfordandelsewherewhowere
very kind to share their expertise as this work was performed. We want to espe-
cially thank Drs. David Pollard and Andrew Bradley. Dr. Pollard provided the
code COMP2DD that was used to verify the accuracy of the model. Dr. Bradley
sharedhiscodeHmmvpthatisusedbyCFRACforefficientmatrixmultiplication.
Thank you to Jakob Alejandre, a Stanford undergraduate who helped with code
development as part of a summer research project.
vii
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Discrete Fracture Network Modeling. . . . . . . . . . . . . . . . . . . . 3
1.2 Review of Stimulation Models . . . . . . . . . . . . . . . . . . . . . . . . 4
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Governing and Constitutive Equations . . . . . . . . . . . . . . . . . . . 13
2.2 Initial Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Methods of Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Iterative Coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.2 Fracture Deformation: Displacement Discontinuity
Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.3 Stresses Induced by Normal Displacements
of Closed Fractures. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.4 Solution to the Fluid Flow and Normal Stress
Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.5 Solution to the Shear Stress Equations. . . . . . . . . . . . . . 24
2.3.6 Inequality Constraints on Fracture Deformations. . . . . . . 25
2.3.7 Changing Mechanical Boundary Conditions. . . . . . . . . . 27
2.3.8 Formation of New Tensile Fractures. . . . . . . . . . . . . . . 28
2.3.9 Adaptive Time Stepping . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.10 Wellbore Boundary Conditions. . . . . . . . . . . . . . . . . . . 30
2.4 Spatial Domain. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.1 Generation of the Discrete Fracture Network . . . . . . . . . 31
2.4.2 Spatial Discretization. . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5 Special Simulation Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5.1 Efficient Matrix Multiplication. . . . . . . . . . . . . . . . . . . 34
2.5.2 Crack Tip Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.5.3 Dynamic Friction Weakening. . . . . . . . . . . . . . . . . . . . 36
2.5.4 Alternative Method for Modeling Friction . . . . . . . . . . . 38
2.5.5 Adaptive Domain Adjustment. . . . . . . . . . . . . . . . . . . . 41
ix
x Contents
2.5.6 Strain Penalty Method. . . . . . . . . . . . . . . . . . . . . . . . . 42
2.5.7 Neglecting Stresses Induced by Deformation . . . . . . . . . 44
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1 Simulation and Discretization Details. . . . . . . . . . . . . . . . . . . . 49
3.2 Model A: Small Test Problem. . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2.1 Solving Directly for the Final Deformations. . . . . . . . . . 57
3.2.2 Testing the Effect of cstress. . . . . . . . . . . . . . . . . . . . . 57
3.3 Models B and C: Large Test Problems. . . . . . . . . . . . . . . . . . . 58
3.3.1 Model B: Large Test Problem of Shear Stimulation . . . . 59
3.3.2 Model C: Large Test Problem of Mixed-Mode
Stimulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.4 Model D: Testing the Strain Penalty Method . . . . . . . . . . . . . . 67
3.5 Hierarchical Matrix Decomposition. . . . . . . . . . . . . . . . . . . . . 69
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1 Model A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1.1 General Description of Results. . . . . . . . . . . . . . . . . . . 73
4.1.2 Effect of Spatial and Temporal Discretization . . . . . . . . 74
4.1.3 Solving Directly for Final Deformations . . . . . . . . . . . . 75
4.1.4 Effect of cstress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2 Model B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
4.2.1 General Description of Results. . . . . . . . . . . . . . . . . . . 77
4.2.2 Effect of Temporal Discretization Refinement . . . . . . . . 79
4.2.3 Effect of cstress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
4.2.4 Effect of Adaptive Domain Adjustment. . . . . . . . . . . . . 80
4.2.5 Dynamic Friction Weakening. . . . . . . . . . . . . . . . . . . . 81
4.2.6 Neglecting Stress Interaction . . . . . . . . . . . . . . . . . . . . 82
4.3 Model C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4 Model D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.5 Hierarchical Matrix Decomposition. . . . . . . . . . . . . . . . . . . . . 83
4.6 Extension of the Model to Three Dimensions. . . . . . . . . . . . . . 84
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
List of Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Chapter 1
Introduction
Computational modeling of hydraulic fracturing can be used for stimulation
optimization, long term production forecasting, basic research into fundamental
mechanisms, and investigation of novel techniques. However, modelers face
daunting challenges: a variety of complex physical processes, limited and
imperfect information, and a heterogeneous and discontinuous spatial domain.
Becauseofthesedifficulties,itisnecessarytomaketrade-offsbetweenefficiency,
spatial resolution, and inclusion of physical processes.
Theclassicalconceptualmodelofhydraulicfracturingisthatasingleopening-
mode fracture propagates away from the wellbore (Khristianovich and Zheltov
1959;PerkinsandKern1961;GeertsmaanddeKlerk1969;Nordgren1972).This
conceptual model is still used in hydraulic fracturing design and modeling in
conventional settings (Economides and Nolte 2000; Meyer and Associates 2011;
Adachietal.2007).However,insettingswithcomplexfracturenetworks,classical
hydraulic fracturing models may be overly simplified.
This book describes the development and testing of a two-dimensional
hydraulic stimulation model that has been developed specifically for simulating
hydraulic fracturing in settings with very low matrix permeability and where
preexisting fractures play an important role, such as Enhanced Geothermal Sys-
tems (EGS) or gas shale. The model simulates fluid flow in a discrete fracture
network (DFN), directly discretizing individual fractures (e.g., Karimi-Fard et al.
2004; Golder Associates 2009). The DFN approach is distinct from effective
continuum modeling, which averages fracture properties into effective properties
over volumetric grid blocks (Warren and Root 1963; Kazemi et al. 1976; Lem-
onnierandBourbiaux2010).Themodelcalculatesthestressesinducedbyopening
and sliding along individual fractures and couples opening and slip to fracture
transmissivity. The model couples deformation with flow using iterative coupling
(Kimetal.2011)andisefficientenoughtosimulateproblemsinvolvingthousands
of individual fractures in a few hours or days on a single processor. The model
assumesflowissingle-phaseandisothermal,matrixpermeabilityisnegligible,and
deformation issmall strain inan infinite, linearlyelastic medium. The model was
written using C++.
M.W.McClureandR.N.Horne,DiscreteFractureNetworkModeling 1
ofHydraulicStimulation,SpringerBriefsinEarthSciences,
DOI:10.1007/978-3-319-00383-2_1,(cid:2)TheAuthor(s)2013
