Payne method for intercompartmental flow in tight gas reservoirs

Input(s)

k: Permeability $(\mathrm{mD})$

$\mathrm{T}$: Temperature $\left({ }^{\circ} \mathrm{R}\right)$

A: Cross-Sectional Area $\left(\mathrm{ft}^{2}\right)$

L: Distance between the Center of the Two Compartments (ft)

$\mathrm{m}\left(\mathrm{P}_{1}\right)$: Gas Pseudo pressure in Compartment (Tank) $1\left(\mathrm{psi}^{2} / \mathrm{cP}\right)$

$\mathrm{m}\left(\mathrm{P}_{2}\right)$: Gas Pseudo pressure in Compartment (Tank) $\left(\mathrm{psi}^{2} / \mathrm{cP}\right)$

Output(s)

$\mathrm{Q}_{12}$: Flow Rate between the Two Compartments (SCF/day)

Formula(s)

$$ \mathrm{Q}_{12}=\left(\frac{0.111924 * \mathrm{k} * \mathrm{~A}}{\mathrm{~T} * \mathrm{~L}}\right) *\left(\mathrm{~m}\left(\mathrm{P}_{1}\right)-\mathrm{m}\left(\mathrm{P}_{2}\right)\right) $$

Reference(s)

Ahmed, T., McKinney, P.D. 2005. Advanced Reservoir Engineering, Gulf Publishing of Elsevier, Chapter: 3, Page: 234, 235.