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

Input(s)

$q_{D}$: 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)

Output(s)

$\left(\frac{1}{q}\right)_{M P}$: 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 $(\mathrm{mD} \mathrm{ft})$

Formula(s)

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

Reference(s)

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