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<!DOCTYPE HTML>
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<TITLE>Introduction to Energy Geomechanics</TITLE>
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<B> Next:</B> <A
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<H1 class="CENTER">Introduction to Energy Geomechanics</H1>
<P class="CENTER"><STRONG>D. Nicolas Espinoza</STRONG>
<BR><I>Department of Petroleum and Geosystems Engineering
<BR>
The University of Texas at Austin
<BR>--
<BR>
Copyright 2019 by DN Espinoza
<BR><a href="mailto:espinoza@austin.utexas.edu">espinoza@austin.utexas.edu</a></I>
</P>
<BR><P class="CENTER"><B>Date:</B> March 17, 2020</P>
<HR>
<BR><HR>
<!--Table of Child-Links-->
<A ID="CHILD_LINKS"></A>
<UL CLASS="ChildLinks">
<LI><A ID="tex2html231"
HREF="node1.html">Contents</A>
<LI><A ID="tex2html232"
HREF="node2.html"><SPAN CLASS="arabic">1</SPAN>. Introduction</A>
<UL>
<LI><A ID="tex2html233"
HREF="node3.html"><SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">1</SPAN> Structural Geology</A>
<LI><A ID="tex2html234"
HREF="node4.html"><SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN> Geomechanics in the Energy Industry</A>
<UL>
<LI><A ID="tex2html235"
HREF="node4.html#SECTION00221000000000000000"><SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN> Drilling and wellbore stability</A>
<LI><A ID="tex2html236"
HREF="node4.html#SECTION00222000000000000000"><SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN> Wellbore completion</A>
<LI><A ID="tex2html237"
HREF="node4.html#SECTION00223000000000000000"><SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN> Reservoir geomechanics</A>
</UL>
<LI><A ID="tex2html238"
HREF="node5.html"><SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">3</SPAN> Problems</A>
</UL>
<BR>
<LI><A ID="tex2html239"
HREF="node6.html"><SPAN CLASS="arabic">2</SPAN>. Subsurface Stresses and Pore Pressure</A>
<UL>
<LI><A ID="tex2html240"
HREF="node7.html"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN> Lithostatic gradient</A>
<UL>
<LI><A ID="tex2html241"
HREF="node7.html#SECTION00311000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">1</SPAN> Stress concept and equilibrium 1D</A>
<LI><A ID="tex2html242"
HREF="node7.html#SECTION00312000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN> Rock vertical stress gradient</A>
<UL>
<LI><A ID="tex2html243"
HREF="node7.html#SECTION00312100000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN> Onshore total vertical stress</A>
<LI><A ID="tex2html244"
HREF="node7.html#SECTION00312200000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN> Offshore total vertical stress</A>
<LI><A ID="tex2html245"
HREF="node7.html#SECTION00312300000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN> General calculation of total vertical stress</A>
</UL>
</UL>
<LI><A ID="tex2html246"
HREF="node8.html"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN> Non-hydrostatic pore pressure</A>
<UL>
<LI><A ID="tex2html247"
HREF="node8.html#SECTION00321000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN> Mechanisms of overpressure</A>
<LI><A ID="tex2html248"
HREF="node8.html#SECTION00322000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN> Disequilibrium compaction and excess pore pressure</A>
<LI><A ID="tex2html249"
HREF="node8.html#SECTION00323000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN> Reservoir depletion</A>
</UL>
<LI><A ID="tex2html250"
HREF="node9.html"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN> Horizontal stresses</A>
<UL>
<LI><A ID="tex2html251"
HREF="node9.html#SECTION00331000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN> Background</A>
<LI><A ID="tex2html252"
HREF="node9.html#SECTION00332000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN> Geological indicators</A>
<LI><A ID="tex2html253"
HREF="node9.html#SECTION00333000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN> In-situ measurement</A>
<LI><A ID="tex2html254"
HREF="node9.html#SECTION00334000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">4</SPAN> Stress Regimes</A>
<UL>
<LI><A ID="tex2html255"
HREF="node9.html#SECTION00334100000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">1</SPAN> Normal faulting stress regime</A>
<LI><A ID="tex2html256"
HREF="node9.html#SECTION00334200000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">2</SPAN> Strike slip faulting stress regime</A>
<LI><A ID="tex2html257"
HREF="node9.html#SECTION00334300000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">3</SPAN> Reverse faulting stress regime</A>
</UL>
<LI><A ID="tex2html258"
HREF="node9.html#SECTION00335000000000000000"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">5</SPAN> Ideal orientation of open-mode fractures</A>
</UL>
<LI><A ID="tex2html259"
HREF="node10.html"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">4</SPAN> Problems</A>
<LI><A ID="tex2html260"
HREF="node11.html"><SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">5</SPAN> Further reading and references</A>
</UL>
<BR>
<LI><A ID="tex2html261"
HREF="node12.html"><SPAN CLASS="arabic">3</SPAN>. Fundamentals of Linear elastic Continuum Mechanics</A>
<UL>
<LI><A ID="tex2html262"
HREF="node13.html"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN> Stress tensor</A>
<UL>
<LI><A ID="tex2html263"
HREF="node13.html#SECTION00411000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">1</SPAN> Cauchy's equations of stress equilibrium</A>
<LI><A ID="tex2html264"
HREF="node13.html#SECTION00412000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN> Application of Cauchy's equations for total vertical stress calculation</A>
<LI><A ID="tex2html265"
HREF="node13.html#SECTION00413000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">3</SPAN> Continuum mechanics solution of an arbitrary problem</A>
</UL>
<LI><A ID="tex2html266"
HREF="node14.html"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN> Kinematic equations: displacements and strains</A>
<LI><A ID="tex2html267"
HREF="node15.html"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN> Constitutive equation: stress-strain relationships</A>
<UL>
<LI><A ID="tex2html268"
HREF="node15.html#SECTION00431000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN> Linear isotropic elasticity</A>
<LI><A ID="tex2html269"
HREF="node15.html#SECTION00432000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN> The isotropic solid in Voigt notation</A>
<LI><A ID="tex2html270"
HREF="node15.html#SECTION00433000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN> Effective stress and elasticity</A>
<LI><A ID="tex2html271"
HREF="node15.html#SECTION00434000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">4</SPAN> Calculation of horizontal stress according to linear elasticity</A>
<LI><A ID="tex2html272"
HREF="node15.html#SECTION00435000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">5</SPAN> Calculation of reservoir compressibility with linear elasticity</A>
<LI><A ID="tex2html273"
HREF="node15.html#SECTION00436000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">6</SPAN> Generalized linear elasticity problem</A>
</UL>
<LI><A ID="tex2html274"
HREF="node16.html"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">4</SPAN> Elastic anisotropy</A>
<LI><A ID="tex2html275"
HREF="node17.html"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">5</SPAN> Permanent deformation: Elasto-plasticity</A>
<LI><A ID="tex2html276"
HREF="node18.html"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">6</SPAN> Time-dependent deformation: Visco-elasticity</A>
<LI><A ID="tex2html277"
HREF="node19.html"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">7</SPAN> Multiphysics problems</A>
<UL>
<LI><A ID="tex2html278"
HREF="node19.html#SECTION00471000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">1</SPAN> Poro-elasticity</A>
<LI><A ID="tex2html279"
HREF="node19.html#SECTION00472000000000000000"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">2</SPAN> Thermo-elasticity</A>
</UL>
<LI><A ID="tex2html280"
HREF="node20.html"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">8</SPAN> Problems</A>
<LI><A ID="tex2html281"
HREF="node21.html"><SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">9</SPAN> Further reading and references</A>
</UL>
<BR>
<LI><A ID="tex2html282"
HREF="node22.html"><SPAN CLASS="arabic">4</SPAN>. Rock Yield and Failure</A>
<UL>
<LI><A ID="tex2html283"
HREF="node23.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">1</SPAN> Preliminary concepts</A>
<UL>
<LI><A ID="tex2html284"
HREF="node23.html#SECTION00511000000000000000"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">1</SPAN> Microstructure of geologic materials</A>
<LI><A ID="tex2html285"
HREF="node23.html#SECTION00512000000000000000"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN> Length scales v.s. process zone size</A>
<LI><A ID="tex2html286"
HREF="node23.html#SECTION00513000000000000000"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">3</SPAN> Overview of types of rock failure</A>
</UL>
<LI><A ID="tex2html287"
HREF="node24.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">2</SPAN> Tensile failure</A>
<UL>
<LI><A ID="tex2html288"
HREF="node24.html#SECTION00521000000000000000"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN> Direct tension</A>
<LI><A ID="tex2html289"
HREF="node24.html#SECTION00522000000000000000"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN> The Brazilian test</A>
</UL>
<LI><A ID="tex2html290"
HREF="node25.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">3</SPAN> Shear failure</A>
<UL>
<LI><A ID="tex2html291"
HREF="node25.html#SECTION00531000000000000000"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN> Frictional Strength</A>
<LI><A ID="tex2html292"
HREF="node25.html#SECTION00532000000000000000"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN> Unconfined compression strength</A>
<LI><A ID="tex2html293"
HREF="node25.html#SECTION00533000000000000000"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN> Confined strength: the triaxial test</A>
<LI><A ID="tex2html294"
HREF="node25.html#SECTION00534000000000000000"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">4</SPAN> Triaxial tests of fluid saturated rocks and sediments</A>
</UL>
<LI><A ID="tex2html295"
HREF="node26.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">4</SPAN> Compression failure: Pore collapse</A>
<LI><A ID="tex2html296"
HREF="node27.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">5</SPAN> Yield/failure locus</A>
<LI><A ID="tex2html297"
HREF="node28.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">6</SPAN> Strength anisotropy</A>
<LI><A ID="tex2html298"
HREF="node29.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">7</SPAN> Deformation beyond the elastic limit</A>
<LI><A ID="tex2html299"
HREF="node30.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">8</SPAN> Rock damage and failure revisited</A>
<LI><A ID="tex2html300"
HREF="node31.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">9</SPAN> Problems</A>
<LI><A ID="tex2html301"
HREF="node32.html"><SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">10</SPAN> Further reading and references</A>
</UL>
<BR>
<LI><A ID="tex2html302"
HREF="node33.html"><SPAN CLASS="arabic">5</SPAN>. Stresses on Faults and Fractures</A>
<UL>
<LI><A ID="tex2html303"
HREF="node34.html"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">1</SPAN> Introduction</A>
<LI><A ID="tex2html304"
HREF="node35.html"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">2</SPAN> Mapping of faults and fractures</A>
<UL>
<LI><A ID="tex2html305"
HREF="node35.html#SECTION00621000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN> Orientation of planes with respect to the geographical coordinate system</A>
<LI><A ID="tex2html306"
HREF="node35.html#SECTION00622000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN> Stereonets for plotting fault orientation</A>
<LI><A ID="tex2html307"
HREF="node35.html#SECTION00623000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN> Faults in geological maps</A>
</UL>
<LI><A ID="tex2html308"
HREF="node36.html"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">3</SPAN> Frictional strength of faults and fault types</A>
<UL>
<LI><A ID="tex2html309"
HREF="node36.html#SECTION00631000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN> Fault strength</A>
<LI><A ID="tex2html310"
HREF="node36.html#SECTION00632000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN> Normal faults</A>
<LI><A ID="tex2html311"
HREF="node36.html#SECTION00633000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN> Thrust and reverse faults</A>
<LI><A ID="tex2html312"
HREF="node36.html#SECTION00634000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">4</SPAN> Strike-slip faults</A>
<LI><A ID="tex2html313"
HREF="node36.html#SECTION00635000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">5</SPAN> Stress and faulting regimes</A>
<LI><A ID="tex2html314"
HREF="node36.html#SECTION00636000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">6</SPAN> Ideal orientation of faults</A>
</UL>
<LI><A ID="tex2html315"
HREF="node37.html"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">4</SPAN> Determination of normal and shear stresses on the fault plane</A>
<UL>
<LI><A ID="tex2html316"
HREF="node37.html#SECTION00641000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">1</SPAN> Mohr's circle method</A>
<LI><A ID="tex2html317"
HREF="node37.html#SECTION00642000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">2</SPAN> Tensor method</A>
</UL>
<LI><A ID="tex2html318"
HREF="node38.html"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">5</SPAN> Applications</A>
<UL>
<LI><A ID="tex2html319"
HREF="node38.html#SECTION00651000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">1</SPAN> Critically stressed fractures and permeability</A>
<LI><A ID="tex2html320"
HREF="node38.html#SECTION00652000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">2</SPAN> Determination of horizontal stresses assuming limit equilibrium</A>
<LI><A ID="tex2html321"
HREF="node38.html#SECTION00653000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">3</SPAN> Determination of stress regime and horizontal stress direction from fault orientation</A>
<LI><A ID="tex2html322"
HREF="node38.html#SECTION00654000000000000000"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">4</SPAN> Fault reactivation</A>
</UL>
<LI><A ID="tex2html323"
HREF="node39.html"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">6</SPAN> Problems</A>
<LI><A ID="tex2html324"
HREF="node40.html"><SPAN CLASS="arabic">5</SPAN>.<SPAN CLASS="arabic">7</SPAN> Further reading and references</A>
</UL>
<BR>
<LI><A ID="tex2html325"
HREF="node41.html"><SPAN CLASS="arabic">6</SPAN>. Wellbore Stability</A>
<UL>
<LI><A ID="tex2html326"
HREF="node42.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">1</SPAN> The wellbore environment</A>
<LI><A ID="tex2html327"
HREF="node43.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">2</SPAN> Kirsch solution for stresses around a cylindrical cavity</A>
<UL>
<LI><A ID="tex2html328"
HREF="node43.html#SECTION00721000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN> Cylindrical coordinate system</A>
<LI><A ID="tex2html329"
HREF="node43.html#SECTION00722000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN> Kirsch solution components</A>
<LI><A ID="tex2html330"
HREF="node43.html#SECTION00723000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN> Complete Kirsch solution</A>
</UL>
<LI><A ID="tex2html331"
HREF="node44.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">3</SPAN> Shear failure and wellbore breakouts</A>
<UL>
<LI><A ID="tex2html332"
HREF="node44.html#SECTION00731000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN> Breakout angle determination</A>
<LI><A ID="tex2html333"
HREF="node44.html#SECTION00732000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN> Breakout measurement</A>
<LI><A ID="tex2html334"
HREF="node44.html#SECTION00733000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN> Maximum horizontal stress determination from breakout angle</A>
</UL>
<LI><A ID="tex2html335"
HREF="node45.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">4</SPAN> Tensile fractures and wellbore breakdown</A>
<UL>
<LI><A ID="tex2html336"
HREF="node45.html#SECTION00741000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">1</SPAN> Identification of tensile fractures in wellbores</A>
</UL>
<LI><A ID="tex2html337"
HREF="node46.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">5</SPAN> The mud window</A>
<LI><A ID="tex2html338"
HREF="node47.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">6</SPAN> Mechanical stability of deviated wellbores</A>
<UL>
<LI><A ID="tex2html339"
HREF="node47.html#SECTION00761000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">1</SPAN> Wellbore orientation</A>
<LI><A ID="tex2html340"
HREF="node47.html#SECTION00762000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">2</SPAN> Calculation of stresses on deviated wellbores</A>
<LI><A ID="tex2html341"
HREF="node47.html#SECTION00763000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">3</SPAN> Breakout analysis for deviated wellbores</A>
<LI><A ID="tex2html342"
HREF="node47.html#SECTION00764000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">4</SPAN> Tensile fractures analysis for deviated wellbores</A>
</UL>
<LI><A ID="tex2html343"
HREF="node48.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">7</SPAN> Thermal, chemical, and leak-off effects on wellbore stability</A>
<UL>
<LI><A ID="tex2html344"
HREF="node48.html#SECTION00771000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">1</SPAN> Thermal effects</A>
<LI><A ID="tex2html345"
HREF="node48.html#SECTION00772000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">2</SPAN> Chemo-electrical effects</A>
<LI><A ID="tex2html346"
HREF="node48.html#SECTION00773000000000000000"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN> Leak-off effects</A>
</UL>
<LI><A ID="tex2html347"
HREF="node49.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">8</SPAN> Strength anisotropy</A>
<LI><A ID="tex2html348"
HREF="node50.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">9</SPAN> Problems</A>
<LI><A ID="tex2html349"
HREF="node51.html"><SPAN CLASS="arabic">6</SPAN>.<SPAN CLASS="arabic">10</SPAN> Further reading and references</A>
</UL>
<BR>
<LI><A ID="tex2html350"
HREF="node52.html"><SPAN CLASS="arabic">7</SPAN>. Hydraulic fracturing</A>
<UL>
<LI><A ID="tex2html351"
HREF="node53.html"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">1</SPAN> Fluid-driven fractures in nature</A>
<LI><A ID="tex2html352"
HREF="node54.html"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">2</SPAN> Hydraulic fractures in well testing</A>
<UL>
<LI><A ID="tex2html353"
HREF="node54.html#SECTION00821000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN> Leak-off test</A>
<UL>
<LI><A ID="tex2html354"
HREF="node54.html#SECTION00821100000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">1</SPAN> Determination of the instantaneous shut-in pressure (ISIP)</A>
<LI><A ID="tex2html355"
HREF="node54.html#SECTION00821200000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN> Determination of the fracture closure pressure (FCP)</A>
</UL>
<LI><A ID="tex2html356"
HREF="node54.html#SECTION00822000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN> Diagnostic fracture initiation test (DFIT)</A>
<LI><A ID="tex2html357"
HREF="node54.html#SECTION00823000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN> Step-rate test</A>
</UL>
<LI><A ID="tex2html358"
HREF="node55.html"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN> Hydraulic fracture design: Single fracture completion</A>
<UL>
<LI><A ID="tex2html359"
HREF="node55.html#SECTION00831000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN> Improvement of reservoir access and wellbore-reservoir surface area</A>
<LI><A ID="tex2html360"
HREF="node55.html#SECTION00832000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN> The coupled fluid-driven fracture propagation problem</A>
<UL>
<LI><A ID="tex2html361"
HREF="node55.html#SECTION00832100000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">1</SPAN> Mechanics: The pressurized linear crack problem</A>
<LI><A ID="tex2html362"
HREF="node55.html#SECTION00832200000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">2</SPAN> Mechanics: stress intensity factor and fracture toughness</A>
<LI><A ID="tex2html363"
HREF="node55.html#SECTION00832300000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">3</SPAN> Transport: leak-off</A>
<LI><A ID="tex2html364"
HREF="node55.html#SECTION00832400000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN>.<SPAN CLASS="arabic">4</SPAN> Transport: fluid flow through fracture</A>
</UL>
<LI><A ID="tex2html365"
HREF="node55.html#SECTION00833000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN> Fracture design: Single planar models</A>
<UL>
<LI><A ID="tex2html366"
HREF="node55.html#SECTION00833100000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">1</SPAN> The PKN model</A>
<LI><A ID="tex2html367"
HREF="node55.html#SECTION00833200000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">2</SPAN> The KGD model</A>
</UL>
<LI><A ID="tex2html368"
HREF="node55.html#SECTION00834000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">3</SPAN>.<SPAN CLASS="arabic">4</SPAN> Stress logs and implications on hydraulic fracture height</A>
</UL>
<LI><A ID="tex2html369"
HREF="node56.html"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">4</SPAN> Multistage stage hydraulic fracturing</A>
<UL>
<LI><A ID="tex2html370"
HREF="node56.html#SECTION00841000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">1</SPAN> Increased surface area with multiple fractures</A>
<LI><A ID="tex2html371"
HREF="node56.html#SECTION00842000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">2</SPAN> Fracture interference and fracture hit</A>
<LI><A ID="tex2html372"
HREF="node56.html#SECTION00843000000000000000"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">4</SPAN>.<SPAN CLASS="arabic">3</SPAN> Fracture reactivation and microseismicity</A>
</UL>
<LI><A ID="tex2html373"
HREF="node57.html"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">5</SPAN> Practical aspects of hydraulic fracturing</A>
<LI><A ID="tex2html374"
HREF="node58.html"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">6</SPAN> Problems</A>
<LI><A ID="tex2html375"
HREF="node59.html"><SPAN CLASS="arabic">7</SPAN>.<SPAN CLASS="arabic">7</SPAN> Suggested Reading</A>
</UL>
<BR>
<LI><A ID="tex2html376"
HREF="node60.html"><SPAN CLASS="arabic">8</SPAN>. Reservoir depletion and injection</A>
<UL>
<LI><A ID="tex2html377"
HREF="node61.html"><SPAN CLASS="arabic">8</SPAN>.<SPAN CLASS="arabic">1</SPAN> Changes of stress in the reservoir rock</A>
<UL>
<LI><A ID="tex2html378"
HREF="node61.html#SECTION00911000000000000000"><SPAN CLASS="arabic">8</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">1</SPAN> Rock compressibility and permeability</A>
<LI><A ID="tex2html379"
HREF="node61.html#SECTION00912000000000000000"><SPAN CLASS="arabic">8</SPAN>.<SPAN CLASS="arabic">1</SPAN>.<SPAN CLASS="arabic">2</SPAN> Linear poroelasticity solution</A>
</UL>
<LI><A ID="tex2html380"
HREF="node62.html"><SPAN CLASS="arabic">8</SPAN>.<SPAN CLASS="arabic">2</SPAN> Changes of stress in the vicinity of the reservoir</A>
<LI><A ID="tex2html381"
HREF="node63.html"><SPAN CLASS="arabic">8</SPAN>.<SPAN CLASS="arabic">3</SPAN> Fluid injection</A>
<LI><A ID="tex2html382"
HREF="node64.html"><SPAN CLASS="arabic">8</SPAN>.<SPAN CLASS="arabic">4</SPAN> Fault stability</A>
<LI><A ID="tex2html383"
HREF="node65.html"><SPAN CLASS="arabic">8</SPAN>.<SPAN CLASS="arabic">5</SPAN> Suggested Reading</A>
</UL>
<BR>
<LI><A ID="tex2html384"
HREF="node66.html">About this document ...</A>
</UL>
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