ResInsight/3d-main-window/derivedresultsgeomech/index.html

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        Cell Results

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        Result Color Legend

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        Contour Maps

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        Flow Results

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        Tensor Results

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        Surfaces

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        Allan Diagram

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        Faults

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         Zonations/Formations

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        Grid Property Calculator

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        Grid Statistics Dialog

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        Grid Case Groups and Statistics

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        Linked Views

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        Measurement

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      <li data-nav-id="/3d-main-window/annotations/" title="Annotations" class="dd-item ">
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        Annotations

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        Derived Results - Eclipse

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      <li data-nav-id="/3d-main-window/derivedresultsgeomech/" title="Derived Results - Geomechanical" class="dd-item active">
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        Derived Results - Geomechanical

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          Plot Main Window

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        Summary Plots

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        Data Sources

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        Summary Plot Manager

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        Summary Plot Source Stepping

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        Summary Plot Editor

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        Summary Cross Plot

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        Summary Plot Template

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      <li data-nav-id="/plot-window/multiplots/" title="Multi Plots" class="dd-item ">
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        Multi Plots

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      <li data-nav-id="/plot-window/ensembleplotting/" title="Ensemble Plotting" class="dd-item ">
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        Ensemble Plotting

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      <li data-nav-id="/plot-window/objectivefunctions/" title="Objective Functions" class="dd-item ">
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        Objective Functions

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        Analysis Plots

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        Grid Statistics Plots

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        Correlation Plots

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        Curve Calculator

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        Well Log Plots

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      <li data-nav-id="/plot-window/wellborestabilityplots/" title="Well Bore Stability Plots" class="dd-item ">
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        Well Bore Stability Plots

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      <li data-nav-id="/plot-window/rftplot/" title="RFT Plot" class="dd-item ">
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        RFT Plot

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      <li data-nav-id="/plot-window/rftsegmentplot/" title="RFT Segment Plot" class="dd-item ">
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        RFT Segment Plot

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      <li data-nav-id="/plot-window/ensemblerftplot/" title="Ensemble RFT Plot" class="dd-item ">
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        Ensemble RFT Plot

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        PLT Plot

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        VFP Plot

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        Flow Diagnostics Plots

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        Grid Cross Plots

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        Saturation Pressure Plots

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        ">
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          Workflows

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      <li data-nav-id="/workflows/biotcoefficient/" title="Biot Coefficient" class="dd-item ">
        <a href="/workflows/biotcoefficient/">
        Biot Coefficient

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      <li data-nav-id="/workflows/ensemblesurface/" title="Ensemble Surface" class="dd-item ">
        <a href="/workflows/ensemblesurface/">
        Ensemble Surface

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      <li data-nav-id="/workflows/ensemblewelllog/" title="Ensemble Well Log" class="dd-item ">
        <a href="/workflows/ensemblewelllog/">
        Ensemble Well Log

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        </ul>

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    <li data-nav-id="/wells-and-completions/" title="Wells and Completions" class="dd-item


        ">
      <a href="/wells-and-completions/">
          Wells and Completions

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        <ul>


      <li data-nav-id="/wells-and-completions/simulationwells/" title="Simulation Wells" class="dd-item ">
        <a href="/wells-and-completions/simulationwells/">
        Simulation Wells

        </a>
    </li>


      <li data-nav-id="/wells-and-completions/wellpaths/" title="Well Paths" class="dd-item ">
        <a href="/wells-and-completions/wellpaths/">
        Well Paths

        </a>
    </li>


      <li data-nav-id="/wells-and-completions/createnewwellpaths/" title="Create Well Paths" class="dd-item ">
        <a href="/wells-and-completions/createnewwellpaths/">
        Create Well Paths

        </a>
    </li>


      <li data-nav-id="/wells-and-completions/createmultilateralwellpaths/" title="Create Multilaterals Well Paths" class="dd-item ">
        <a href="/wells-and-completions/createmultilateralwellpaths/">
        Create Multilaterals Well Paths

        </a>
    </li>


      <li data-nav-id="/wells-and-completions/3dwelllogcurves/" title="3D Well Log Plots" class="dd-item ">
        <a href="/wells-and-completions/3dwelllogcurves/">
        3D Well Log Plots

        </a>
    </li>


      <li data-nav-id="/wells-and-completions/completions/" title="Completions" class="dd-item ">
        <a href="/wells-and-completions/completions/">
        Completions

        </a>
    </li>


      <li data-nav-id="/wells-and-completions/ensemblefracturestatistics/" title="Ensemble Fracture Statistics" class="dd-item ">
        <a href="/wells-and-completions/ensemblefracturestatistics/">
        Ensemble Fracture Statistics

        </a>
    </li>


      <li data-nav-id="/wells-and-completions/completionslgr/" title="Completions LGR" class="dd-item ">
        <a href="/wells-and-completions/completionslgr/">
        Completions LGR

        </a>
    </li>


      <li data-nav-id="/wells-and-completions/wellmeasurements/" title="Well Measurements" class="dd-item ">
        <a href="/wells-and-completions/wellmeasurements/">
        Well Measurements

        </a>
    </li>


        </ul>

    </li>


    <li data-nav-id="/import/" title="Import" class="dd-item


        ">
      <a href="/import/">
          Import

      </a>


        <ul>


      <li data-nav-id="/import/eclipsecases/" title="Eclipse Cases" class="dd-item ">
        <a href="/import/eclipsecases/">
        Eclipse Cases

        </a>
    </li>


      <li data-nav-id="/import/eclipsesummarydata/" title="Eclipse Summary Data" class="dd-item ">
        <a href="/import/eclipsesummarydata/">
        Eclipse Summary Data

        </a>
    </li>


      <li data-nav-id="/import/ensemblefiledialog/" title="Ensemble File Dialog" class="dd-item ">
        <a href="/import/ensemblefiledialog/">
        Ensemble File Dialog

        </a>
    </li>


      <li data-nav-id="/import/lasfile/" title="Log ASCII Standard File" class="dd-item ">
        <a href="/import/lasfile/">
        Log ASCII Standard File

        </a>
    </li>


      <li data-nav-id="/import/geomechanicaldata/" title="Geomechanical Data" class="dd-item ">
        <a href="/import/geomechanicaldata/">
        Geomechanical Data

        </a>
    </li>


      <li data-nav-id="/import/soursimrlresults/" title="SourSimRL Results" class="dd-item ">
        <a href="/import/soursimrlresults/">
        SourSimRL Results

        </a>
    </li>


      <li data-nav-id="/import/elementpropertytable/" title="Element Property Table" class="dd-item ">
        <a href="/import/elementpropertytable/">
        Element Property Table

        </a>
    </li>


      <li data-nav-id="/import/observeddata/" title="Observed Time History Data" class="dd-item ">
        <a href="/import/observeddata/">
        Observed Time History Data

        </a>
    </li>


      <li data-nav-id="/import/pasteexceltimedata/" title="Paste Excel Time History Data" class="dd-item ">
        <a href="/import/pasteexceltimedata/">
        Paste Excel Time History Data

        </a>
    </li>


        </ul>

    </li>


    <li data-nav-id="/export/" title="Export" class="dd-item


        ">
      <a href="/export/">
          Export

      </a>


        <ul>


      <li data-nav-id="/export/snapshots/" title="Snapshots" class="dd-item ">
        <a href="/export/snapshots/">
        Snapshots

        </a>
    </li>


      <li data-nav-id="/export/eclipseproperties/" title="Eclipse Properties" class="dd-item ">
        <a href="/export/eclipseproperties/">
        Eclipse Properties

        </a>
    </li>


      <li data-nav-id="/export/fluxnummultnum/" title="FLUXNUM/MULTNUM" class="dd-item ">
        <a href="/export/fluxnummultnum/">
        FLUXNUM/MULTNUM

        </a>
    </li>


      <li data-nav-id="/export/completionexport/" title="Completions" class="dd-item ">
        <a href="/export/completionexport/">
        Completions

        </a>
    </li>


      <li data-nav-id="/export/exportwellpaths/" title="Well Paths" class="dd-item ">
        <a href="/export/exportwellpaths/">
        Well Paths

        </a>
    </li>


      <li data-nav-id="/export/sectormodel/" title="Sector Model" class="dd-item ">
        <a href="/export/sectormodel/">
        Sector Model

        </a>
    </li>


      <li data-nav-id="/export/contourmapexport/" title="Contour Map Export" class="dd-item ">
        <a href="/export/contourmapexport/">
        Contour Map Export

        </a>
    </li>


        </ul>

    </li>


    <li data-nav-id="/scripting/" title="Scripting" class="dd-item


        ">
      <a href="/scripting/">
          Scripting

      </a>


        <ul>


      <li data-nav-id="/scripting/pythoninterface/" title="Python interface" class="dd-item ">
        <a href="/scripting/pythoninterface/">
        Python interface

        </a>
    </li>


      <li data-nav-id="/scripting/commandlineinterface/" title="Command Line Interface" class="dd-item ">
        <a href="/scripting/commandlineinterface/">
        Command Line Interface

        </a>
    </li>


      <li data-nav-id="/scripting/commandfile/" title="Command File" class="dd-item ">
        <a href="/scripting/commandfile/">
        Command File

        </a>
    </li>


      <li data-nav-id="/scripting/octaveinterface/" title="Octave Interface" class="dd-item ">
        <a href="/scripting/octaveinterface/">
        Octave Interface

        </a>
    </li>


      <li data-nav-id="/scripting/octaveinterfacereference/" title="Octave Interface Reference" class="dd-item ">
        <a href="/scripting/octaveinterfacereference/">
        Octave Interface Reference

        </a>
    </li>


        </ul>

    </li>


    <li data-nav-id="/misc/" title="Miscellaneous" class="dd-item


        ">
      <a href="/misc/">
          Miscellaneous

      </a>


        <ul>


      <li data-nav-id="/misc/preferences/" title="Preferences" class="dd-item ">
        <a href="/misc/preferences/">
        Preferences

        </a>
    </li>


      <li data-nav-id="/misc/projectfile/" title="Project File and Caching" class="dd-item ">
        <a href="/misc/projectfile/">
        Project File and Caching

        </a>
    </li>


      <li data-nav-id="/misc/memorymanagement/" title="Memory Management" class="dd-item ">
        <a href="/misc/memorymanagement/">
        Memory Management

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  <ul>
    <li>
      <ul>
        <li><a href="#derived-geomechanical-results">Derived Geomechanical results</a>
          <ul>
            <li><a href="#relative-results-time-lapse-results">Relative Results (Time Lapse Results)</a></li>
            <li><a href="#derived-result-fields">Derived Result Fields</a></li>
            <li><a href="#definitions-of-derived-results">Definitions of Derived Results</a></li>
            <li><a href="#case-constants">Case Constants</a></li>
            <li><a href="#compaction">COMPACTION</a></li>
            <li><a href="#st---total-stress">ST - Total Stress</a></li>
            <li><a href="#stm---total-mean-stress">STM - Total Mean Stress</a></li>
            <li><a href="#q---deviatoric-stress">Q - Deviatoric Stress</a></li>
            <li><a href="#dpn---shear-slip-indicator">DPN - Shear Slip Indicator</a></li>
            <li><a href="#gamma---stress-path">Gamma - Stress Path</a></li>
            <li><a href="#se---effective-stress">SE - Effective Stress</a></li>
            <li><a href="#sem---effective-mean-stress">SEM - Effective Mean Stress</a></li>
            <li><a href="#sa---stress-anisotropy">SA - Stress Anisotropy</a></li>
            <li><a href="#sfi">SFI</a></li>
            <li><a href="#dsm">DSM</a></li>
            <li><a href="#fos">FOS</a></li>
            <li><a href="#e---strain">E - Strain</a></li>
            <li><a href="#ev---volumetric-strain">EV - Volumetric Strain</a></li>
            <li><a href="#ed---deviatoric-strain">ED - Deviatoric Strain</a></li>
            <li><a href="#element-nodal-on-face">Element Nodal On Face</a></li>
            <li><a href="#sn---stress-component-normal-to-face">SN - Stress component Normal to face</a></li>
            <li><a href="#tph---horizontal-in-plane-shear-component">TPH - Horizontal in-plane shear component</a></li>
            <li><a href="#tnqv---horizontal-in-plane-shear-component">TNQV - Horizontal in-plane shear component</a></li>
            <li><a href="#tp---total-in-plane-shear">TP - Total in-plane shear</a></li>
            <li><a href="#tpinc---direction-of-tp">TPinc - Direction of TP</a></li>
            <li><a href="#pinc-and-pazi---face-inclination-and-azimuth">Pinc and Pazi - Face Inclination and Azimuth</a></li>
            <li><a href="#pore-compressibility">Pore Compressibility</a></li>
            <li><a href="#porosity-and-permeability">Porosity and Permeability</a></li>
            <li><a href="#mud-weight-window">Mud Weight Window</a></li>
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            <h1>

              Derived Results - Geomechanical
            </h1>


<p>ResInsight computes several derived results. In this section we will explain what they are, and briefly how they are calculated.</p>
<h2 id="derived-geomechanical-results">Derived Geomechanical results</h2>
<p>ResInsight calculates several of the presented geomechanical results based on the native results present in the odb-files.</p>
<h3 id="relative-results-time-lapse-results">Relative Results (Time Lapse Results)</h3>
<p>ResInsight can calculate and display relative results, sometimes also referred to as Time Lapse results.
When enabled, every result variable is calculated as:</p>
<p>$Value_{[t-b]} = Value_{[t]} - Value_{[b]}$</p>
<p>where:</p>
<ul>
<li>$b$ is the base time step,</li>
<li>$t$ is the current time step</li>
</ul>
<p>Select the appropriate <strong>Base Time Step</strong> option in the <strong>Difference Options</strong> group to enable the time lapse result.</p>
<p><img src="/images/appendix/DerivedRelativeResults.png" alt=""></p>
<p>Note: Relative Results calculated based on Gamma values and Stress Anisotropy are calculated slightly differently:</p>
<p>Gamma:</p>
<p>$Gamma_{i[t-b]} = \frac{ST_{i[t]} - ST_{i[b]}}{ POR_{[t]} - POR_{[b]}  }$</p>
<p>Stress Anisotropy:</p>
<p>$SA_{ij[t-b]} = 2 * \frac{(ST_{i[t]} - ST_{i[b]}) - (ST_{j[t]} - ST_{j[b]})}{(ST_{i[t]} - ST_{i[b]}) + (ST_{j[t]} - ST_{j[b]})}$</p>
<h3 id="derived-result-fields">Derived Result Fields</h3>
<p>The calculated result fields are:</p>
<ul>
<li>Nodal
<ul>
<li>COMPACTION (Magnitude of compression)</li>
</ul>
</li>
<li>Element Nodal and Integration Points
<ul>
<li>ST (Total Stress)
<ul>
<li>All tensor components</li>
<li>Principals, with directions ($S_iinc, S_iazi$)</li>
<li>STM (Mean total stress)</li>
<li>Q (Deviatoric stress)</li>
</ul>
</li>
<li>Gamma (Stress path)</li>
<li>SE (Effective Stress)
<ul>
<li>All tensor components</li>
<li>Principals, with directions</li>
<li>SEM (Mean effective stress)</li>
<li>SFI</li>
<li>FOS</li>
<li>DSM</li>
</ul>
</li>
<li>E (Strain)
<ul>
<li>All tensor components</li>
<li>EV (Volumetric strain)</li>
<li>ED (Deviatoric strain)</li>
</ul>
</li>
</ul>
</li>
<li>Element Nodal On Face
<ul>
<li>Plane
<ul>
<li>Pinc (Face inclination angle)</li>
<li>Pazi (Face azimuth angle)</li>
</ul>
</li>
<li>Transformed Total and Effective Stress
<ul>
<li>SN (Stress component normal to face)</li>
<li>TP (Total in-plane shear)</li>
<li>TPinc (Direction of TP)</li>
<li>TPH ( Horizontal in-plane shear component )</li>
<li>TPQV ( Quasi vertical in-plane shear component )</li>
<li>FAULTMOB</li>
<li>PCRIT</li>
</ul>
</li>
</ul>
</li>
</ul>
<h3 id="definitions-of-derived-results">Definitions of Derived Results</h3>
<p>In this text the label Sa and Ea will be used to denote the unchanged stress and strain tensor respectively from the odb file.</p>
<p>Components with one subscript denotes the principal values 1, 2, and 3 which refers to the maximum, middle, and minimum principals respectively.</p>
<p>Components with two subscripts however, refers to the global directions 1, 2, and 3 which corresponds to  X, Y, and Z and thus also easting, northing, and depth.</p>
<ul>
<li>Inclination is measured from the downwards direction</li>
<li>Azimuth is measured from the Northing (Y) Axis in Clockwise direction looking down.</li>
</ul>
<h3 id="case-constants">Case Constants</h3>
<p>Two constants can be assigned to a Geomechanical case:</p>
<ul>
<li>Cohesion</li>
<li>Friction angle</li>
</ul>
<p>In the following they are denoted s0 and fa respectively. Some of the derived results use these constants, that can be changed in the property panel of the Case.</p>
<p><img src="/images/appendix/GeoMechCasePropertyPanel.png" alt=""></p>
<h3 id="compaction">COMPACTION</h3>
<p>Compaction is the difference in vertical displacement (U3) between a grid node and a specified reference K layer.
The reference K layer is specified in the property editor.</p>
<p>For each node <i>n</i> in the grid, a node <i>nref</i> in the reference K layer is found by vertical intersection from the node <i>n</i>.</p>
<p>$ If (Depth_n &lt;= Depth_{nref}) $</p>
<p>$ \space \space COMPACTION_n = -(U3_n - U3_{nref})$</p>
<p>$ else $</p>
<p>$\space \space COMPACTION_n = -(U3_{nref} - U3_n )$</p>
<h3 id="st---total-stress">ST - Total Stress</h3>
<p>$ST_{ii} = -Sa_{ii} + POR (i= 1,2,3)$</p>
<p>We use a value of $POR=0.0$ where it is not defined.</p>
<p>$ST_{ij} = -Sa_{ij} (i,j = 1,2,3 \text{ and i $\ne$ j})$</p>
<p>$Sa_{ii}$ and $Sa_{ij}$ are the stresses calculated by Abaqus.</p>
<p>$ST_i = \text{Principal value i of ST}$</p>
<h3 id="stm---total-mean-stress">STM - Total Mean Stress</h3>
<p>$STM = \frac{ST_{11} + ST_{22} + ST_{33}}{3} $</p>
<h3 id="q---deviatoric-stress">Q - Deviatoric Stress</h3>
<p>$Q = \sqrt {\frac{3}{2} * ((ST_1 - STM)^2 + (ST_2 - STM)^2 + (ST_3 - STM)^2 }$</p>
<h3 id="dpn---shear-slip-indicator">DPN - Shear Slip Indicator</h3>
<p>Excess pore pressure parameter is defined as</p>
<p>$DPN = \frac{P_p - P_0} { \sigma_v - P_0  }$</p>
<p>Where:</p>
<ul>
<li>$P_0$ is hydrostatic pore pressure,</li>
<li>$P_p$ is pore pressure (at the time of the incident) and</li>
<li>$\sigma_v$ total vertical stress ($ ST_{33} $).</li>
</ul>
<p>Hydrostatic pore pressure is</p>
<p>$ P_0 = \rho_w * TVDMSL * g $</p>
<p>Where:</p>
<ul>
<li>$\rho_w$ is (average) density of formation water (default = 1.03),</li>
<li>TVDMSL is true vertical depth mean sea level and</li>
<li>$g$ is gravity.</li>
</ul>
<h3 id="gamma---stress-path">Gamma - Stress Path</h3>
<p>$Gamma_{ii} = \frac{ST_{ii}} {POR} (i= 1,2,3) $</p>
<p>$Gamma_{i} = \frac{ST_{i}} {POR}  $</p>
<p>In these calculations we set Gamma to <em>undefined</em> if abs(POR) &gt; 0.01 MPa.</p>
<h3 id="se---effective-stress">SE - Effective Stress</h3>
<p>$SE_{ij} = -Sa_{ij} (i,j = 1,2,3 \text{ where POR is defined})$</p>
<p>where $Sa_{ij}$ is the stress calculated by Abaqus.</p>
<p>$SE_i = \text{Principal value i of SE} $</p>
<h3 id="sem---effective-mean-stress">SEM - Effective Mean Stress</h3>
<p>$SEM = \frac{SE_{11} + SE_{22} + SE_{33}} {3}  $</p>
<h3 id="sa---stress-anisotropy">SA - Stress Anisotropy</h3>
<p>$SA_{ij} = 2 \frac{ST_{i} - ST_{j}}{ ST_{i} + ST_{j}} (i,j = 1,2,3 \text{ and i $\lt$ j})$</p>
<p>The same expressions are available for effective stresses (where SE replaces ST in the equation above).</p>
<h3 id="sfi">SFI</h3>
<p>$$SFI = \frac{\frac{S0}{tan(fa)} + 0.5 * (SE_1 + SE_3) * sin(fa)} {0.5*(SE_1-SE_3)}  $$</p>
<h3 id="dsm">DSM</h3>
<p>$DSM = \frac{tan(\rho)} {tan(fa)} $</p>
<p>where</p>
<p>$$ \rho = 2 * (arctan (\sqrt \frac{ SE_1 + a} {SE_3 + a}) \space – \frac {\pi} {4}) $$
$$ a = \frac {s0} {tan(fa)} $$</p>
<h3 id="fos">FOS</h3>
<p>$FOS = \frac{1}{DSM}$</p>
<h3 id="e---strain">E - Strain</h3>
<p>$E_{ij} = -Ea_{ij}$</p>
<h3 id="ev---volumetric-strain">EV - Volumetric Strain</h3>
<p>$EV = E_{11} + E_{22} + E_{33} $</p>
<h3 id="ed---deviatoric-strain">ED - Deviatoric Strain</h3>
<p>$ED = 2*\frac {E1-E3} {3}  $</p>
<h3 id="element-nodal-on-face">Element Nodal On Face</h3>
<p>For each face displayed, (might be an element face or an intersection/intersection box face),
a coordinate system is established such that:</p>
<ul>
<li>Ez is normal to the face, named N - Normal</li>
<li>Ex is horizontal and in the plane of the face, named H - Horizontal</li>
<li>Ey is in the plane pointing upwards, named QV - Quasi Vertical</li>
</ul>
<p>The stress tensors in that particular face are then transformed to that coordinate system.  The following quantities are derived from the transformed tensor named TS in the following:</p>
<h3 id="sn---stress-component-normal-to-face">SN - Stress component Normal to face</h3>
<p>$SN = TS_{33}$</p>
<h3 id="tph---horizontal-in-plane-shear-component">TPH - Horizontal in-plane shear component</h3>
<p>$TPH = TS_{31} = TS_{ZX} $</p>
<h3 id="tnqv---horizontal-in-plane-shear-component">TNQV - Horizontal in-plane shear component</h3>
<p>$TPQV = TS_{32} = TS_{ZY}$</p>
<h3 id="tp---total-in-plane-shear">TP - Total in-plane shear</h3>
<p>$TP = \sqrt {(TPH^2 + TPQV^2)} $</p>
<h3 id="tpinc---direction-of-tp">TPinc - Direction of TP</h3>
<p>Angle of the total in-plane shear relative to the Quasi Vertical direction</p>
<p>$TPinc = acos (\frac {TPQV} {TP}) $</p>
<h3 id="pinc-and-pazi---face-inclination-and-azimuth">Pinc and Pazi - Face Inclination and Azimuth</h3>
<p>These are the directional angles of the face-normal itself.</p>
<h3 id="pore-compressibility">Pore Compressibility</h3>
<h4 id="pore-compressibility-1">Pore Compressibility</h4>
<p>Pore compressibility between a reference state and the current stress state is defined as:</p>
<p>$ C_{p} = -\frac{ \alpha \Delta\epsilon_{vol}}{ \Delta P_p \phi_0} + \frac{1}{K_s} ( \frac{ \alpha } { \phi_0 } - 1) $</p>
<p>Where:</p>
<ul>
<li>$ \alpha $ is the Biot coefficient,</li>
<li>$ \Delta\epsilon_{vol} $ is volumetric strain change (EV in ResInsight) between curret state and reference state,</li>
<li>$ \phi_0 $ is porosity on the Geostatic step,</li>
<li>$ \Delta P_p $ is change in pore pressure between current state and reference state,</li>
<li>$ K_s $ bulk modulus for the solid material (grain).</li>
</ul>
<p>The Biot porelastic coefficient ($\alpha$) defines the compressibility of sand grains: $\alpha = 1.0$ for incompressible grains,
and $\alpha &lt; 1.0$ for compressible grains. $\alpha$ is not used for the initial (Geostatic) time step. The default value is 1.0, but values
per element can be imported as an <a href="/import/elementpropertytable/">element property table</a>.</p>
<p>The bulk modulus for solid material is defined as:</p>
<p>$ K_s = \frac{ K_{fr} }{ 1 - \alpha}, K_{fr} = \frac{ E }{ 3(1-2\nu)} $</p>
<p>Where:</p>
<ul>
<li>$ E $ is the elastic modulus (Young&rsquo;s modulus) from element property table <a href="/import/elementpropertytable/">MODULUS</a>.</li>
<li>$ \nu $ is Poisson&rsquo;s ratio imported from element property table <a href="/import/elementpropertytable/">RATIO</a>.</li>
</ul>
<h4 id="vertical-compressibility">Vertical Compressibility</h4>
<p>$ C_{v} = - \frac{ \Delta\epsilon_{\nu}}{ \alpha \Delta P_p } $</p>
<p>$ \Delta\epsilon_\nu $ is the vertical strain change between current state and reference state (E33 in ResInsight).</p>
<h4 id="vertical-compressibility-ratio">Vertical Compressibility Ratio</h4>
<p>$ C_{vr} = \frac{ C_v E(1-\nu) } { (1+\nu) ( 1 - 2\nu) } $</p>
<p>Vertical Compression Ratio is the ratio between the real vertical compression and the compression in a uniaxial strain case.
All parameters are described above.</p>
<h3 id="porosity-and-permeability">Porosity and Permeability</h3>
<h4 id="porosity">Porosity</h4>
<p>Porosity change is defined as either total change in porosity between initial (geostatic) state and current state,
or change in porosity between a reference state and the current state $ \Delta\phi $. The latter is given as</p>
<p>$ \Delta\phi = \phi_0(C_p \Delta P_p + \Delta\epsilon_{vol}) $</p>
<p>Here, $\Delta\phi_0$ is found from this equation with the reference state being the initial state (geostatic).
The current porosity is then given as</p>
<p>$ \phi = \phi_0 + \Delta\phi_0 $</p>
<p>with $ \phi_0 $ being the porosity at the initial state, $\Delta\phi_0$ is porosity change between initial (geostatic)
state current, $C_p$ is pore compressibility (between reference and current state), $\Delta P_p$ is change in pore pressure
and $\Delta\epsilon_{vol}$ is volumetric strain change.</p>
<h4 id="initial-porosity">Initial Porosity</h4>
<p>Porosity at the initial state:</p>
<p>$ \phi_0 = \frac{VOIDR} {1 + VOIDR} $</p>
<p>Where:</p>
<ul>
<li>VOIDR is void ratio from Abaqus.</li>
</ul>
<h4 id="permeability">Permeability</h4>
<p>An expression for permeability is taken from Petunin (2011).</p>
<p>$ k = k_0( \frac{\phi}{\phi_0} )^A $</p>
<p>Where:</p>
<ul>
<li>$k_0$ is the permeability at the initial state (unit: mD),</li>
<li>$\phi$ is porosity at current state,</li>
<li>$\phi_0$ is initial porosity,</li>
<li>$A$ is a constant</li>
</ul>
<h3 id="mud-weight-window">Mud Weight Window</h3>
<p>Mud Weight Window (MWW) represents the difference between the minimum and the maximum possible
mud weight between specific formation layers representing top and base of a fictitious well section.</p>
<p>To find MWW a two step procedure is needed:</p>
<ul>
<li>first find the limits per element,</li>
<li>determine the MWW for each element based on the vertical column.</li>
</ul>
<h4 id="finding-upper-and-lower-mud-weight-limit">Finding Upper and Lower Mud Weight Limit</h4>
<p>The upper mud weight limit (UMWL) and lower mud weight limit (LMWL) is found for each element intersected by the fictitious well.
The UMWL is either the fracture gradient (FG) or minimum horizontal stress (SHmin) for both sand and shale.
The LMWL is defined as the maximum of shear fracture gradient (SFG) and/or pore pressure in shale, and as pore pressure in sand.</p>
<p>The calculations for fracture gradient and shear fracture gradient, and the needed input, are described in detail
in <a href="/plot-window/wellborestabilityplots/">Well Bore Stability Plots</a>.</p>
<h4 id="mud-weight-window-1">Mud Weight Window</h4>
<p>Thereafter, the combined use of mud weight limits for all elements between the top and base (for a given IJ)
determines the MWW parameters as will be further described below.</p>
<p>A reference element index ($K_{ref}$) represents the base or the top of the fictitious well. Then for a set
of elements with i = I, j = J and k = K to $K_{ref}$ the maximum LWML and the minimum UWML must be found from
these element values. Then the difference between the two defines the MWW parameter.</p>
<p>Thus for a vertical stack of elements $element_{ijk} = K \to K_{ref}$, $MWW_{ijk}$ is given as</p>
<p>$ MWW_{ijk} = maximum(LMWL) - minimum(UMWL) (k = K \to K_{ref}) $</p>
<p>Similar calculations are made below the reference layer, but then with the reference layer as the top layer.</p>
<p>In addition to the MWW parameter, the mud weight representing the middle of the drilling window (MWM) is calculated if MWW &gt; 0.
Otherwise, MWM should is undefined.</p>


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