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.