Effective wellbore radius of a horizontal well - Method 1- Anisotropic reservoirs

Input(s)

L: Horizontal Well Length (ft)

h: Pay Zone Thickness (ft)

rw\mathrm{r}_{\mathrm{w}}: Wellbore Radius ( ft\mathrm{ft} )

kh\mathrm{k}_{\mathrm{h}}: Horizontal Permeability (mD)

kv\mathrm{k}_{\mathrm{v}}: Vertical Permeability (mD)(\mathrm{mD})

A: Drainage Area (acre)

Output(s)

reh\mathrm{r}_{\mathrm{eh}}: Effective Drainage Radius (ft)

a: Horizontal wellbore variable from Joshi (dimensionless)

3: Permeability Ratio constant (dimensionless)

rwd\mathrm{r}_{\mathrm{wd}}: Effective Wellbore Radius (ft)

Formula(s)

reh=sqrt(A435603.14)a=(L2)sqrt(.5+sqrt(0.25+2(rehL)4))β=sqrt(khkv)rwd=rehL2a((1+sqrt(1(L2a)2))(hβ2rw)βhL)\begin{gathered} r e h=\operatorname{sqrt}\left(A * \frac{43560}{3.14}\right) \\ a=\left(\frac{L}{2}\right) * \operatorname{sqrt}\left(.5+\operatorname{sqrt}\left(0.25+2 *\left(\frac{r e h}{L}\right)^{4}\right)\right) \\ \beta=\operatorname{sqrt}\left(\frac{k h}{k v}\right) \\ r w d=r e h * \frac{\frac{L}{2}}{a *\left(\left(1+\operatorname{sqrt}\left(1-\left(\frac{L}{2 * a}\right)^{2}\right)\right) *\left(h^{*} \frac{\beta}{2 * r w}\right)^{\beta * \frac{h}{L}}\right)} \end{gathered}

Reference(s)

Horizontal Well Technology, Joshi, Page: 90.


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