# Pseudo-steady state productivity of horizontal Wells - Method 1

## Input(s)

A: Drainage Area $$\left(\mathrm{ft}^{2}\right)$$

s: Skin Factor (dimensionless)

D: Turbulence Coefficient (1/BOPD for oil and 1/MSCFD for gas)

C: Shape Factor Conversion Constant $$=1.386$$ (dimensionless)

$$s_{C A h}$$: Shape-Related Skin Factor (dimensionless)

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

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

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

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

q: Flow Rate (BOPD for oil and MSCFD for gas)

L: Fracture Length $$(\mathrm{ft})$$

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

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

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

## Output(s)

$$r_{e}$$: Effective Radius of Drainage Area (ft)

$$s_{m}$$: Mechanical Skin Factor (dimensionless)

$$s_{f}$$: Skin Factor of an Infinite-conductivity, Fully Penetrating Fracture of Length L (dimensionless)

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

## Formula(s)

$\begin{gathered} r_{e}=\left(\frac{A}{\pi}\right)^{0.5} \\ s_{m}=s * \frac{h}{L} *\left(\frac{k_{h}}{k_{v}}\right)^{0.5} \\ s_{f}=-\ln \left(\frac{L}{4 * r_{w}}\right) \\ J_{h}=\frac{0.007078 * k * \frac{h}{\mu_{o} * B_{o}}}{\ln \left(\frac{r_{e}}{r_{w}}\right)-A+s_{f}+s_{m}+s_{C A h}-C+D * q} \end{gathered}$

## Reference(s)

Joshi, S. D. 1991, Horizontal Well Technology. Tulsa, Oklahoma: PennWell Publishing Company. Chapter: 7, Page: 221.

## Related

### Depth of a washout - Method 1

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