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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\chi

pressure diffusivity



absolute permeability
Expand
titleDetailing


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

k

c_t = c_r + c

total compressibility

LaTeX Math Inline
body

\phi

k

porositydynamic fluid viscosity LaTeX Math Inlinebodyc_t =
absolute permeability

LaTeX Math Inline
body

\mu

{c_r

+ c

}

total
pore compressibility

LaTeX Math Inline
body

c_rpore compressibility

{\phi}

porosity

LaTeX Math Inline
bodyc

fluid compressibility




Physical Model

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Constant rate production

LaTeX Math Inline
bodyq_t = \rm const

Linear fluid flow

LaTeX Math Inline
bodyp(t, x)

Slightly compressible fluid flow

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

Homogeneous reservoir

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

Infinite boundary

LaTeX Math Inline
bodyx \rightarrow \infty

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