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titleDetailing


{c_r

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

transmissibility

LaTeX Math Inline
body\mu

dynamic fluid viscosity

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

pressure diffusivity

LaTeX Math Inline
body{t}

time

LaTeX Math Inline
bodyk

absolute permeability

LaTeX Math Inline
body{r}

radial direction

LaTeX Math Inline
body{\phi}

porosity

LaTeX Math Inline
body{c_t

= c_r + c,
LaTeX Math Inline
body
}

, mathinline

bodyc
total , pore and fluid compressibility



Physical Model

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Radial fluid flowHomogenous reservoirInfinite boundarySlightly compressible fluid flowConstant rate production

LaTeX Math Inline
bodyp(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(p) = c_r +c = \rm const

LaTeX Math Inline
bodyq_t = \rm const

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