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.

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