Pseudo-steady state productivity of horizontal Wells - Method 2

Input(s)

μo\mu_{o}: Viscosity of Oil (cP)

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

AtA_{t}: Horizontal Well Drainage Area in the Vertical Plane =2=2 y_eh (ft2)\left(\mathrm{ft}^{2}\right)

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

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

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

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

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

kvk_{v}: Vertical Permeability (mD)(\mathrm{mD})

kyk_{y}: Horizontal Permeability (mD)(\mathrm{mD})

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

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

Output(s)

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

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

Formula(s)

InCCh=6.28(2yeh)(kvky)0.5(13yw2ye+(yw2ye)2)ln(sin(180zwh))0.5ln((2yeh)(kvky)0.5)1.088Jh=0.0070782xe(kykv)0.5μoBoln((At)0.5rw)+InCh0.75+sR\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 .


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