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.