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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


Expand
titleDetailing


LaTeX Math Inline
body

\mudynamic fluid viscosity
LaTeX Math Inline
body

k

absolute permeability

LaTeX Math Inline
bodyc_t = c_r + c

total compressibility

LaTeX Math Inline
bodyh

effective thickness

LaTeX Math Inline
body{c_r}

pore compressibility

LaTeX Math Inline
body

{

\

phi}porosity

mu

dynamic fluid viscosity

LaTeX Math Inline
bodyc

fluid compressibility

LaTeX Math Inline
body{\phi}

porosity




Physical Model

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Radial fluid flowHomogenous reservoirInfinite boundary

Zero wellbore radius

Slightly compressible fluid flowConstant rateConstant skin

LaTeX Math Inline
bodyp(t, {\bf r}) \rightarrow p(t, r)

LaTeX Math Inline
bodyM(r, p)=M =\rm const

LaTeX Math Inline
body\phi(r, p)=\phi =\rm const

LaTeX Math Inline
bodyh(r)=h =\rm const

LaTeX Math Inline
bodyc_r(r)=c_r =\rm const

LaTeX Math Inline
bodyr \rightarrow \infty

LaTeX Math Inline
bodyr_w = 0

LaTeX Math Inline
bodyc_t(r,p) = \rm const

LaTeX Math Inline
bodyq_t = \rm const

LaTeX Math Inline
bodyS = \rm const

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