Critical rate for horizontal Wells in edge-water drive reservoirs

Input(s)

e1: Constant for $\mathrm{C} 1$ Equals +0.023 or -0.023 (dimensionless)

$e 2$: Constant for $\mathrm{C} 2$ equals +0.0013 or -0.0013 (dimensionless)

e3: Constant for $\mathrm{C} 3$ equals +0.022 or -0.022 (dimensionless)

e4: Constant for $\mathrm{C} 4$ equals +0.0013 or -0.0013 (dimensionless)

$\Delta_{\rho}$: Density Difference between water and oil or, oil and gas $(\mathrm{gm} / \mathrm{cc})$ h: Pay Zone Thickness (ft)

L: Length of Well (ft)

$x_{e}$: Distance between Horizontal Well and Constant Pressure Boundary (ft)

$\mu_{o}$: Oil Viscosity $(\mathrm{cP})$

$k_{h}$: Vertical Permeability $(\mathrm{mD})$

$k_{v}$: Horizontal Permeability $(\mathrm{mD})$

Output(s)

$c_{1}$: Dimensionless Constant for calculation (dimensionless)

$c_{2}$: Dimensionless Constant for calculation (dimensionless)

$c_{3}$: Dimensionless Constant for calculation (dimensionless)

$c_{4}$: Dimensionless Constant for calculation (dimensionless)

$q_{c}$: Dimensionless Critical Rate per Unit length (STB/day/ft)

$q_{o}$: Critical Rate (STB/day)

$z_{c}$: Critical Height Representing the Difference between the Apex of the Gas/Water Crest from the Well Elevation $(\mathrm{ft})$

Formula(s)

$$ \begin{gathered} c_{1}=1.4426+e 1 \\ c_{2}=-0.9439+e 2 \\ c_{3}=0.4812+e 3 \\ c_{4}=-0.9534+e 4 \\ q_{c}=c_{1} *\left(\frac{x_{e}}{h *\left(\frac{k_{h}}{k_{v}}\right)^{0.5}}\right)^{c_{2}} \\ q_{o}=\left(4.888 * 10^{-4}\right) * \Delta_{\rho} * h *\left(k_{h} * k_{v}\right)^{0.5} * L * \frac{q_{c}}{\mu_{o}} \\ z_{c}=c_{3} * h *\left(\frac{x_{e}}{h *\left(\frac{k_{h}}{k_{v}}\right)^{0.5}}\right)^{c_{4}} \end{gathered} $$

Reference(s)

Joshi, S.D. 1991, Horizontal Well Technology. Tulsa, Oklahoma: PennWell Publishing Company. Chapter: 7, Page: 309,310 .