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Linear fluid flowHomogenous reservoirInfinite boundary

Zero wellbore radius

Slightly 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


Mathematical Model

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titleDefinition



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



LaTeX Math Block
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p(t = 0, x) = p_i



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p(t, x \rightarrow \infty ) = p_i



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\frac{\partial p(t, x )}{\partial x} \bigg|_{x \rightarrow 0} = \frac{q_t}{\sigma \, d}



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