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            <a href='/'>ResInsight</a> > <a href='/plot-window/'>Plot Main Window</a> > Well Bore Stability Plots


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        <li><a href="#create-well-bore-stability-plots">Create Well Bore Stability plots</a></li>
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        <li><a href="#equations-and-calculations">Equations and calculations</a>
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            <li><a href="#stresses-at-the-borehole-wall---kirsch-equations">Stresses at the borehole wall - Kirsch equations</a></li>
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            <h1>

              Well Bore Stability Plots
            </h1>


<p><img src="/images/plot-window/WellBoreStability.png" alt=""></p>
<p>ResInsight can create <strong>Well Bore Stability</strong> plots for Geomechanical cases. These plots are specialized <a href="/plot-window/welllogsandplots/">Well Log Plots</a> to visualize <a href="/3d-main-window/formations/">Formations</a>, <a href="/wells-and-completions/wellmeasurements/">Well Measurements</a>, <a href="/wells-and-completions/wellpaths/#well-path-attributes">Well Path Attributes</a> as well as a set of well path derived curves in different tracks.</p>
<p>In the figure above, the first track contains <a href="/3d-main-window/formations/">Formations</a> and an indication of sea level.</p>
<table>
<thead>
<tr>
<th>Sea Level</th>
<th>Formations</th>
</tr>
</thead>
<tbody>
<tr>
<td><img src="/images/plot-window/WaterLevel.png" alt=""></td>
<td><img src="/images/plot-window/FormationLevels.png" alt=""></td>
</tr>
</tbody>
</table>
<p>The second track contains a visualisation of the well, with well attributes of <a href="/wells-and-completions/wellpaths/#casing-design">Casing Design</a> as well <a href="/wells-and-completions/completions/">Completions</a></p>
<p>The third track, which is disabled by default, contains the input parameters of the plot as described in the <a href="#input-requirements">Input Requirements</a> section.</p>
<p>The fourth track (third visible by default) shows the following stability gradients (all normalized by mud weight):</p>
<ul>
<li><strong>FG</strong>: Fracture Gradient in sands based on Kirsch and in shale based on the K0_FG parameter or proportional to SHMIN.</li>
<li><strong>OBG</strong>: Overburden stress gradient: Stress component S_33.</li>
<li><strong>PP</strong>: Pore pressure.</li>
<li><strong>SFG</strong>: Shear Failure Gradient for shale based on Stassi-d&rsquo;Alia.</li>
<li><strong>SHMIN</strong>: Minimum horizontal stress from grid.</li>
<li><strong>SH_MK</strong>: Minimum horizontal stress from Matthews &amp; Kelly.</li>
</ul>
<p>The fifth track contains curves showing the angular orientation of the well path as azimuth (deviation from vertical) and inclination (deviation from x-axis) in degrees.</p>
<p>If any <a href="/wells-and-completions/wellmeasurements/">Well Measurements</a> are present, they will be visible as symbols in the track <strong>Stability Curves</strong>.</p>
<h2 id="create-well-bore-stability-plots">Create Well Bore Stability plots</h2>
<p>Well Bore Stability plots can be created from the right-click menu for a well path in <strong>Project Tree</strong> or from the the right-click menu of the Well Log Plots entry in <strong>Plot Project Tree</strong>. In the former case, the well bore stability plot will be created for the selected <strong>Well Path</strong>. In the latter case, it will be created for the first well path in the well path list and the well path for the entire plot can be changed with the <a href="/plot-window/welllogsandplots/#change-data-source-for-plots-and-curves">Change Data Source Feature</a>.</p>
<p><img src="/images/plot-window/WellBoreStabilityCreation.png" alt="">
<img src="/images/plot-window/WellBoreStabilityCreation2.png" alt=""></p>
<h2 id="input-requirements">Input requirements</h2>
<p>In order to calculate <strong>PP</strong>, <strong>FG</strong>, <strong>SFG</strong> and <strong>SH_MK</strong>, the following input parameters are required:</p>
<table>
<thead>
<tr>
<th>Curve</th>
<th>Required Parameters</th>
</tr>
</thead>
<tbody>
<tr>
<td>PP</td>
<td>Pore Pressure in reservoir (PP Reservoir) and outside the reservoir (PP Non-Reservoir)</td>
</tr>
<tr>
<td>FG</td>
<td>Pore Pressure (PP Reservoir), Poissons&rsquo; Ratio in Sand, FG Shale in shale</td>
</tr>
<tr>
<td>SFG</td>
<td>Uniaxial Compressive Strength (UCS)</td>
</tr>
<tr>
<td>SH_MK</td>
<td>K0_SH, Overburden Gradient at initial time (OBG0) and the Depletion Factor (DF)</td>
</tr>
</tbody>
</table>
<p>For parameters with multiple available sources, the sources will be tried in numbered order for each curve point (where well path intersects with grid). However, the options for <strong>FG Shale</strong> are mutually exclusive and will apply to the whole domain.</p>
<table>
<thead>
<tr>
<th>Parameter</th>
<th>Default</th>
<th>Sources</th>
</tr>
</thead>
<tbody>
<tr>
<td>Density of Sea Water</td>
<td>$1.03 g/cm^3$</td>
<td>User setting in GUI</td>
</tr>
<tr>
<td>PP Reservoir</td>
<td>Grid Nodal Values (POR)</td>
<td>1. Grid (Grid units), 2. LAS-file as equivalent mud-weight (Variable: &ldquo;PP_INP&rdquo; or &ldquo;PP_RES_INP&rdquo;, Units: SG_EMW), 3. Element Property Table (Variable: &ldquo;POR_INP&rdquo; with Units: Pascal or Variable: &ldquo;PP_INP&rdquo; with Units: SG_EMW)</td>
</tr>
<tr>
<td>PP Non-Reservoir</td>
<td>Hydrostatic PP (from TVDRKB, Density of Sea Water and gravity)</td>
<td>1. LAS-file as equivalent mud-weight (Variable: &ldquo;PP_NONRES_INP&rdquo;, Units: SG_EMW), 3. Element Property Table (Variable: &ldquo;POR_NONRES_INP&rdquo; with Units: Pascal or Variable: &ldquo;PP_NONRES_INP&rdquo; with Units: SG_EMW), 4. Hydrostatic Pressure</td>
</tr>
<tr>
<td>Poissons&rsquo; Ratio</td>
<td>0.35</td>
<td>1. LAS-file (Variable: &ldquo;POISSON_RATIO_INP&rdquo;), 2. Element Property Table (Variable: &ldquo;POISSON_RATIO_INP&rdquo;)</td>
</tr>
<tr>
<td>UCS</td>
<td>100 bar</td>
<td>1. LAS-file (Variable: &ldquo;UCS_INP&rdquo;, Units: bar), 2. Element Property Table (Variable: &ldquo;UCS_INP&rdquo;, Units: Pascal)</td>
</tr>
<tr>
<td>Initial Overburden Gradient (OBG0)</td>
<td>OBG at initial time step</td>
<td>1. Grid (Grid units), 2. LAS-file (Variable: &ldquo;OBG0_INP&rdquo;, Units: Bar)</td>
</tr>
<tr>
<td>DF</td>
<td>0.7</td>
<td>1. LAS-file (Variable: &ldquo;DF_INP&rdquo;, No Units), 2. Element Property Table (Variable: &ldquo;DF_INP&rdquo;, No units), 3 User Defined</td>
</tr>
<tr>
<td>K0_SH</td>
<td>0.65</td>
<td>1. LAS-file (Variable: &ldquo;K0_SH_INP&rdquo;, No Units ), 2. Element Property Table(&ldquo;Variable: &ldquo;K0_SH_INP&rdquo;, No Units), 3. User Defined</td>
</tr>
<tr>
<td>FG Shale</td>
<td>Derived from K0_FG</td>
<td>Derived from K0_FG and PP Non-Reservoir, Proportional to SH or LAS-file (Variable: &ldquo;FG_SHALE_INP&rdquo;, Units: SG_EMW)</td>
</tr>
<tr>
<td>K0_FG</td>
<td>0.75</td>
<td>1. LAS-file (Variable: &ldquo;K0_FG_INP&rdquo;, No Units ), 2. Element Property Table(&ldquo;Variable: &ldquo;K0_FG_INP&rdquo;, No Units), 3. User Defined</td>
</tr>
</tbody>
</table>
<p>In addition to the units above, it LAS-files it is possible to supply PP in Bar and UCS in Pascal or MPa. Conversion will be handled automatically.</p>
<p><img src="/images/plot-window/WellBoreStabilityParameters.png" alt=""></p>
<h2 id="equations-and-calculations">Equations and calculations</h2>
<h3 id="stresses-at-the-borehole-wall---kirsch-equations">Stresses at the borehole wall - Kirsch equations</h3>
<p>The basic input to wellbore stability models is the stresses at the borehole wall given by the Kirsch equations in cylindrical coordinates:</p>
<p><img src="/images/plot-window/WellBoreStabilityKirschEquations.png" alt=""></p>
<p>The transformation of stresses from cartesian coordinate system to x&rsquo;, y&rsquo;, z&rsquo; is performed by pre- and transposed postmultiplication of the stress tensor with a 3x3 transformation matrix <strong>M</strong>, i.e.
<img src="https://resinsight.org/images/plot-window/WellBoreStabilityStressTransformation.png" style="display:inline; vertical-align:middle; margin:0">
.</p>
<h3 id="fracture-gradient-calculations-based-on-kirsch-in-sand">Fracture gradient calculations based on Kirsch in sand</h3>
<p>To estimate the fracture gradient <em>FG</em>, first step is to find the principal effective stresses at the borehole wall:</p>
<p>$$\sigma&rsquo;_1 = \sigma&rsquo;_1 (\theta)= \sigma&rsquo;_r = p_w - p_0$$</p>
<p>$$\sigma&rsquo;_2 = \sigma&rsquo;_2 (\theta) = \sigma_{t \max} = \frac{1}{2} \left( (\sigma_z + \sigma_\theta) + \sqrt{(\sigma_z + \sigma_\theta)^2 + 4\tau_{\theta z}^2} \right) - p_0$$</p>
<p>$$\sigma&rsquo;_2 = \sigma&rsquo;_3 (\theta) = \sigma_{t \min} = \frac{1}{2} \left( (\sigma_z + \sigma_\theta) - \sqrt{(\sigma_z + \sigma_\theta)^2 + 4\tau_{\theta z}^2} \right) - p_0$$</p>
<p>Next step is to solve for the value of $\theta \in [0 - 180]$ that yields $\sigma&rsquo;_3 (\theta) = 0$ which in turn gives us $\sigma_\theta$ which can be used to solve for $P_w$ in the Kirsch equations.</p>
<p>Then calculate <em>FG</em> in equivalent mud weight units as
$$ FG = \frac{P_w}{TVD_{RKB} \: g  \: \rho}$$ where $TVD_{RKB} = TVD_{MSL} + AirGap$, the gravity acceleration $g = 9.81 m/s^2$ and  the density of sea water $\rho$ in $kg/m^3$ (thus 1000 x the UI input in $g/cm^3$).</p>
<h3 id="fracture-gradient-in-shale">Fracture gradient in shale</h3>
<p>$$FG_{shale} = K0_{FG} \times (OBG0 - PP0) + PP0$$</p>
<h3 id="sh-from-matthews--kelly">SH from Matthews &amp; Kelly</h3>
<p>$$SH_{MK} = K0_{SH} \times (OBG0 - PP0) + PP0 + DF \times (PP-PP0)$$</p>
<h3 id="stassi-dalia-failure-criterion-in-shale">Stassi-d&rsquo;Alia failure criterion in shale</h3>
<p>Stassi-d&rsquo;Alia failure criterion in shale is calculated by finding the well pressure $P_w$ that satisfies the following equation
for  $\theta \in [0 - 180]$:</p>
<p><img src="/images/plot-window/WellBoreStabilityStassiEquations.png" alt=""></p>
<p>where <img src="https://resinsight.org/images/plot-window/WellBoreStabilityPrincipalStresses.png" style="display:inline; vertical-align:middle; margin:0">
 are the effective principal stresses from the Fracture Gradient calculation.
and <em>UCS</em> is the <em>uniaxial compressive strength</em>.</p>
<p>The Shear Failure Gradient is then given as</p>
<p>$$SFG = \frac{P_w}{TVD_{RKB} \: g \: \rho}$$</p>
<h2 id="python-interface">Python Interface</h2>
<p>The <a href="https://api.resinsight.org">ResInsight Python API</a> offers functionality for creating Well Bore Stability Plots from Python.
For an example of use, see <a href="https://api.resinsight.org">ResInsight Python API</a>, and the <em>Create WBS Plot</em> script listed
under <em>Python Examples</em>.</p>


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