Fracture conductivity (bilinear-flow regime in gas wells)

Input(s)

q: Flow Rate $(\mathrm{bbl} / \mathrm{d})$

ø: Porosity (fraction)

$\mu$: Viscosity (cP)

B: Formation Volume Factor (BBL/STB) $m_{b}$: Slope of Pressure vs Fourth Root of Time (Bi-linear Flow Analysis) (psi/h ${ }^{0.25}$ )

$c_{t}$: Total Compressibility $(1 / \mathrm{psi})$

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

$\mathrm{h}$: Reservoir Thickness (ft)

Output(s)

$w_{f} . k_{f}$: Fracture Conductivity $(\mathrm{ft} \mathrm{mD})$

Formula(s)

$$ w_{f} \cdot k_{f}=\left(\frac{44.1 * q * \mu * B}{h * m_{b}}\right)^{2} *\left(\frac{1}{\phi * \mu * c_{t} * k}\right)^{0.5} $$

Reference(s)

Lee, J., Rollins, J. B., \& Spivey, J. P. (2003). Pressure Transient Testing (Vol. 9). Richardson, Texas: Society of Petroleum Engineers, Page: 117.