# 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.