Non-linear dynamic porosity @model

Small deviations of ambient pressure  $//<![CDATA[ \begin{array}{l}p\end{array} //]]>$ from initial pressure formation  $//<![CDATA[ \begin{array}{l}p_0\end{array} //]]>$ lead to the exponential changes in porosity:

where  $//<![CDATA[ \begin{array}{l}c_r\end{array} //]]>$ is formation compressibility,  $//<![CDATA[ \begin{array}{l}\phi_0\end{array} //]]>$ is porosity at reference pressure  $//<![CDATA[ \begin{array}{l}p_0\end{array} //]]>$ (usually picked up at initial reservoir pressure  $//<![CDATA[ \begin{array}{l}p_0 = p_i\end{array} //]]>$ ).

The above correlation assumes constant formation compressibility which in most practical applications holds true in a wide range of pressure variations all the way down to porosity cut-off and all the way up to the fracture point.