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 .