# Pseudo-steady state productivity of horizontal Wells - Method 2

## Input(s)

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

$$B_{o}$$: Oil Formation Volume $$(\mathrm{RB} / \mathrm{STB})$$

$$A_{t}$$: Horizontal Well Drainage Area in the Vertical Plane $$=2$$ y_eh $$\left(\mathrm{ft}^{2}\right)$$

$$s_{R}$$: Skin Factor Due to Partial Penetration of Horizontal Well (dimensionless)

$$x_{e}$$: Half Length of the Short Side of the Rectangular Drainage Area (ft)

$$y_{e}$$: Half Length of the Long Side of the Rectangular Drainage Area (ft)

$$y_{w}$$: Distance from the Horizontal Well to the Closest Boundary in Y Direction (ft)

$$\mathrm{h}$$: Thickness of Reservoir (ft)

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

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

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

$$z_{w}$$: Vertical Distance between Horizontal Well and Bottom Boundary of Reservoir (ft)

## Output(s)

$$\operatorname{InC}_{h}$$: A Constant Related to the Natural Logarithm of Shape Factor (dimensionless)

$$J_{h}$$: Pseudo-steady State Productivity of Horizontal Wells (bbl/day/psi)

## Formula(s)

\begin{aligned} & \operatorname{InC} C_{h}=6.28 *\left(2 * \frac{y_{e}}{h}\right) *\left(\frac{k_{v}}{k_{y}}\right)^{0.5} *\left(\frac{1}{3}-\frac{y_{w}}{2 * y_{e}}+\left(\frac{y_{w}}{2 * y_{e}}\right)^{2}\right)-\ln \left(\sin \left(180 * \frac{z_{w}}{h}\right)\right)-0.5 * \ln \left(\left(2 * \frac{y_{e}}{h}\right) *\left(\frac{k_{v}}{k_{y}}\right)^{0.5}\right) \\ & -1.088 \\ & J_{h}=0.007078 * 2 * x_{e} * \frac{\frac{\left(k_{y}{ }^{*} k_{v}\right)^{0.5}}{\mu_{o} * B_{o}}}{\ln \left(\frac{\left(A_{t}\right)^{0.5}}{r_{w}}\right)+\operatorname{In} C_{h}-0.75+s_{R}} \end{aligned}

## Reference(s)

Joshi, S. D. 1991, Horizontal Well Technology. Tulsa, Oklahoma: PennWell Publishing Company. Chapter: 7, Page: 22 .

## Related

### Depth of a washout - Method 2

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