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InputsOutputs

LaTeX Math Inline
bodyq_t

total sandface rate

LaTeX Math Inline
bodyp(t,xr)

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

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Constant rate production

LaTeX Math Inline
bodyq_t = \rm const

Linear fluid flow

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

Slightly compressible fluid flow

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

Homogeneous reservoir

LaTeX Math Inline
bodyM(x{\bf r}, p)=M =\rm const

LaTeX Math Inline
body\phi(x{\bf r}, p)=\phi =\rm const

LaTeX Math Inline
bodyh(x{\bf r})=h =\rm const

Infinite boundary

LaTeX Math Inline
bodyx r \rightarrow \infty


Mathematical Model

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Expand
titleDefinition



LaTeX Math Block
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\frac{\partial p}{\partial t}  = \chi \, \frac{d^2laplace p}{dx^2}



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



LaTeX Math Block
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p(t, xr \rightarrow \infty ) = p_i



LaTeX Math Block
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\frac{\partial p(t, xr )}{\partial xr} \bigg|_{xr \rightarrow 0} = \frac{q_t}{\sigma \, d}



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