Interporosity flow coefficient in pressure build-up test
Input(s)
\(\omega\): Storativity of the Fractures (dimensionless)
\(\phi_{m}\): Matrix Porosity (fraction)
\(h_{m}\): Matrix Thickness \((\mathrm{ft})\)
\(c_{m}\): Matrix Compressibility (1/psi)
\(\mu\): Viscosity \((\mathrm{cP})\)
\(r_{w}\): Wellbore Radius (ft)
\(k_{f}\): Fracture Permeability \((\mathrm{mD})\)
\(t_{p}\): Production Time (day)
\(\Delta \mathrm{t}\): Shut-in Time (h)
Output(s)
\(\lambda\): Interporosity Flow Coefficient (dimensionless)
Formula(s)
\[
\lambda=\left(\frac{w}{1-\omega}\right) *\left(\frac{\phi_{m} * h_{m} * c_{m} * \mu * r_{w}^{2}}{1.781 * k_{f} * t_{p}}\right) *\left(\frac{t p+\Delta t}{\Delta t}\right)_{1}
\]
or
\[
\lambda=\left(\frac{1}{1-\omega}\right) *\left(\frac{\phi_{m} * h_{m} * c_{m} * \mu * r_{w}^{2}}{1.781 * k_{f} * t_{p}}\right) *\left(\frac{t p+\Delta t}{\Delta t}\right)_{2}
\]
Reference(s)
Ahmed, T., McKinney, P.D. 2005. Advanced Reservoir Engineering, Gulf Publishing of Elsevier, Chapter: 1, Page: 84.