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.