GLOSSARY

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InputsOutputs

LaTeX Math Inline
bodyq_t

total sandface rate

LaTeX Math Inline
bodyp(r)

reservoir pressure

LaTeX Math Inline
body{p_i}

initial formation pressure

LaTeX Math Inline
bodyp_{wf}

well bottomhole pressure

LaTeX Math Inline
body\sigma

transmissibility,

LaTeX Math Inline
body\sigma = \frac{k \, h}{\mu}



LaTeX Math Inline
bodyS

skin-factor

LaTeX Math Inline
bodyr_w

wellbore radius


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titleDetailing


LaTeX Math Inline
bodyk

absolute permeability

LaTeX Math Inline
bodyc_t

total compressibility,

LaTeX Math Inline
bodyc_t = c_r + c

LaTeX Math Inline
bodyh

effective thickness

LaTeX Math Inline
body{c_r}

pore compressibility

LaTeX Math Inline
body\mu

dynamic fluid viscosity

LaTeX Math Inline
bodyc

fluid compressibility

LaTeX Math Inline
body{\phi}

porosity


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titleDefinition



LaTeX Math Block
anchor52112
alignmentleft
\frac{\partial p}{\partial t}  =  0 \Leftrightarrow \, \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} =0



LaTeX Math Block
anchor3MUX9
alignmentleft
p(t, r_e ) = p_i



LaTeX Math Block
anchorEM415
alignmentleft
\left[ r\frac{\partial p(t, r )}{\partial r} \right]_{r \rightarrow r_w} = \frac{q_t}{2 \pi \sigma}



LaTeX Math Block
anchor3MUX9
alignmentleft
p_{wf}= p(r_w ) - S \cdot r_w \, \frac{\partial p}{\partial r} \Bigg|_{r=r_w}




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titleSolution



LaTeX Math Block
anchorpwf
alignmentleft
p(r) = p_i - \frac{q_t}{2 \pi \sigma} \ln \frac{r}{r_w}




LaTeX Math Block
anchorpwf
alignmentleft
p_{wf} = p_i - \frac{q_t}{2 \pi \sigma} \, \bigg[ S + \ln \frac{r_e}{r_w} \bigg]



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