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InputsOutputs

LaTeX Math Inline
bodyq_t

total sandface rate

LaTeX Math Inline
bodyp(t,x)

reservoir pressure

LaTeX Math Inline
bodyp_i

initial formation pressure

LaTeX Math Inline
bodyp_{wf}(t)

well bottomhole pressure

LaTeX Math Inline
bodyd

reservoir channel width



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}




Expand
titleDetailing


LaTeX Math Inline
body

\mudynamic fluid viscosity

LaTeX Math Inline
bodyk

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}mu

dynamic fluid viscosityporosity

LaTeX Math Inline
bodyc

fluid compressibility

LaTeX Math Inline
body{\phi}

porosity




Physical Model

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Linear fluid flowHomogenous reservoirInfinite boundarySlightly compressible fluid flowConstant rate production

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

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

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

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

LaTeX Math Inline
bodyx \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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