Corresponding reciprocal rate (post-fracture production-Constant Bottomhole flowing conditions)


\(q_{D}\): Dimensionless Reciprocal Rate from Match Point (1/q_d) (dimensionless)

\(B_{g}\): Gas Formation Volume Factor \((\mathrm{RB} / \mathrm{MSCF})\)

\(p_{a i}\): initial Adjusted Pressure (psi)

\(p_{\text {awf }}\) Adjusted Well Flowing Pressure (psi)

\(\phi\) : Porosity (dimensionless)

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

\(\mu\) : Viscosity (cP)

\(\mathrm{h}\) : Formation Thickness ( \(\mathrm{ft}\) )

\(C_{r D}\) : Dimensionless Fracture Conductivity (dimensionless)

\(L_{f}\): Fracture Length \((\mathrm{ft})\)

\(t_{L f D}\) : Ending of Linear Part or Starting Time of Pseudo Radial Flow from Plot (dimensionless)

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

\(\Delta t\): Time Difference from Data (h)


\(\left(\frac{1}{q}\right)_{M P}\): Reciprocal Rate from Match Point (1/q)_(mp) (Days/MSCF)

\(L_{f M P}\): Length of Fracture from Match Point Analysis \((\mathrm{ft})\)

\(w_{f k_{f}}\) : Fracture Conductivity from Dimensionless Fracture Conductivity \((\mathrm{mD} \mathrm{ft})\)


\[ \begin{gathered} \left(\frac{1}{q}\right)_{M P}=\left(141.2 * B_{g} * \frac{\mu}{k * h *\left(p_{a i}-p_{a w f}\right)}\right) *\left(\frac{1}{q_{D}}\right) \\ L_{f M P}=\left(\left(\frac{0.0002637 * k}{\phi * \mu * c_{t}}\right) *\left(\frac{\Delta t}{t_{L f D}}\right)\right) \frac{1}{2} \\ w_{f k_{f}}=\pi * k * C_{r D} * L_{f} \end{gathered} \]


Lee, J., Rollins, J. B., & Spivey, J. P. (2003). Pressure Transient Testing (Vol. 9). Richardson, Texas: Society of Petroleum Engineers, Page: 126.

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