Interporosity flow coefficient in pressure build-up test

Input(s)

ω\omega: Storativity of the Fractures (dimensionless)

ϕm\phi_{m}: Matrix Porosity (fraction)

hmh_{m}: Matrix Thickness (ft)(\mathrm{ft})

cmc_{m}: Matrix Compressibility (1/psi)

μ\mu: Viscosity (cP)(\mathrm{cP})

rwr_{w}: Wellbore Radius (ft)

kfk_{f}: Fracture Permeability (mD)(\mathrm{mD})

tpt_{p}: Production Time (day)

Δt\Delta \mathrm{t}: Shut-in Time (h)

Output(s)

λ\lambda: Interporosity Flow Coefficient (dimensionless)

Formula(s)

λ=(w1ω)(ϕmhmcmμrw21.781kftp)(tp+ΔtΔt)1\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

λ=(11ω)(ϕmhmcmμrw21.781kftp)(tp+ΔtΔt)2\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.


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