# 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 .

An unhandled error has occurred. Reload 🗙