Analysis of a post-fracture - Constant-rate flow test with boundary effects

Input(s)

$\mathrm{q}_{\mathrm{g}}$: Gas Flow Rate (MSCF/day)

$\mathrm{B}_{\mathrm{g}}$: Gas formation Volume Factor $(\mathrm{RB} / \mathrm{MSCF})$

$\mathrm{m}$: Slope from Curve (psi/cycle)

$\mathrm{m}_{\mathrm{L}}$: Slope from linear Region of Curve (psi/cycle)

$\mathrm{p}_{\mathrm{ai}}$: Initial Adjusted Well Pressure (psi)

$\mathrm{p}_{\mathrm{ahr}}$: Adjusted Well pressure at $t=1 \mathrm{~h}(\mathrm{psi})$

$\mathrm{p}_{\mathrm{D}}$: Dimensionless Pressure (dimensionless)

Ø: Porosity (dimensionless)

$\mathrm{c}_{\mathrm{t}}$: Compressibility (1/psi)

$\mathrm{r}_{\mathrm{w}}$: Radius of Wellbore $(\mathrm{ft})$

$\mu$: Viscosity $(\mathrm{cP})$

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

$t_{L f D}$: Time of end of Linear or Pseudo Radial flow from Plot (dimensionless)

$\Delta \mathrm{t}_{\mathrm{a}}$: Adjusted Delta Time from Derivative Curve (h)

Output(s)

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

$\mathrm{L}_{\mathrm{fPR}}$: Length of Fracture for Pseudo Radial Flow (ft)

$\mathrm{L}_{\mathrm{fL}}$: Length of Fracture for Linear Flow (ft)

$\mathrm{L}_{\mathrm{fMP}}$: Length of Fracture from Match Point Analysis $(\mathrm{ft})$

$\mathrm{s}$: Skin Factor (dimensionless)

$\Delta \mathrm{P}_{\mathrm{a}_{\mathrm{MP}}}$: Adjusted Pressure Difference at Match Point from Plot (psi)

Formula(s)

$$ \begin{gathered} \mathrm{k}=162.6 * \mathrm{q}_{\mathrm{g}} * \mathrm{~B}_{\mathrm{g}} * \frac{\mu}{\mathrm{m} * \mathrm{~h}} \\ \mathrm{~L}_{\mathrm{fPR}}=1.151 *\left(\left(\frac{\mathrm{p}_{\mathrm{ai}}-\mathrm{p}_{\mathrm{ahr}}}{\mathrm{m}}\right)-\log \left(\frac{\mathrm{k}}{\emptyset * \mu * \mathrm{c}_{\mathrm{t}} * \mathrm{r}_{\mathrm{w}}^{2}}\right)+3.23\right) \\ \mathrm{L}_{\mathrm{fL}}=2 * \mathrm{r}_{\mathrm{w}} * 2.71^{-\mathrm{s}} \\ \mathrm{L}_{\mathrm{fMP}}=4.064 * \mathrm{q}_{\mathrm{g}} * \frac{\mathrm{B}_{\mathrm{g}}}{\mathrm{m}_{\mathrm{L}} * \mathrm{~h} * \mathrm{k}^{0.5}} *\left(\left(\frac{\mu}{\varnothing} * \mathrm{c}_{\mathrm{t}}\right)^{\frac{1}{2}}\right) \\ \mathrm{s}=\left(141.2 * \mathrm{q}_{\mathrm{g}} * \mathrm{~B}_{\mathrm{g}} * \frac{\mu}{\mathrm{k}} * \mathrm{~h}\right) *\left(\mathrm{p}_{\mathrm{D}}\right) \\ \Delta \mathrm{P}_{\mathrm{a}_{\mathrm{MP}}}=\left(\left(\frac{0.0002637 * \mathrm{k}}{\varnothing * \mu * \mathrm{c}_{\mathrm{t}}}\right) *\left(\frac{\Delta \mathrm{t}_{\mathrm{a}}}{\mathrm{t}_{\mathrm{LfD}}}\right)\right)^{\frac{1}{2}} \end{gathered} $$

Reference(s)

Lee, J., Rollins J.B., and Spivey J.P. 2003, Pressure Transient Testing, Vol. 9, SPE Textbook Series, Vol. 9, Henry L. Doherty Memorial Fund of AIME, Richardson, Texas, SPE, Chapter: 6, Page: 121.