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InputsOutputs

LaTeX Math Inline
bodyq_t

total sandface rate

LaTeX Math Inline
bodyp(t,r)

reservoir pressure

LaTeX Math Inline
body{p_i}

initial formation pressure

LaTeX Math Inline
body{p_{wf}(t)}

well bottomhole pressure

LaTeX Math Inline
body\sigma

transmissibility,

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



LaTeX Math Inline
body\chi

pressure diffusivity,

LaTeX Math Inline
body\chi = \frac{k}{\mu} \, \frac{1}{\phi \, c_t}



LaTeX Math Inline
bodyS

skin-factor

LaTeX Math Inline
bodyr_w

wellbore radius

LaTeX Math Inline
bodyr_e

drainage 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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Expand
titleDefinition



LaTeX Math Block
anchorP1
alignmentleft
r_{wf} < r \leq r_e



LaTeX Math Block
anchor52112
alignmentleft
\frac{\partial p}{\partial t}  = \chi \, \left( \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right)



LaTeX Math Block
anchor88AEG
alignmentleft
p(t = 0, {\bf r}) = p_i



LaTeX Math Block
anchor3MUX9
alignmentleft
\left[ a \cdot ( p(t, r \rightarrow r_e ) -= p_i)

or

LaTeX Math Block
anchor3MUX9
alignmentleft
\left[ + b \cdot \frac{\partial p}{\partial r} \right]_{r \rightarrow \infty=r_e} = 0



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
anchorPE
alignmentleft
p_{wf}(t)= p(t,r_w) - S \cdot r_w \, \frac{\partial p}{\partial r} \Bigg|_{r=r_w}



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