# 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.

## Related

### Slope of pseudo-steady state flow in pressure buildup test

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