Pseudo-steady state productivity of horizontal Wells - Method 2


\(\mu_{o}\): 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)


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

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


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


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


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