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Radial fluid flowHomogenous reservoirFinite reservoir flow boundarySlightly compressible fluid flowConstant rateConstant skin

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

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body{\bf r} \in ℝ^2 = \{ x, y\}

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bodyM(r, p)=M =\rm const

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body\phi(r, p)=\phi =\rm const

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bodyh(r)=h =\rm const

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bodyc_r(r)=c_r =\rm const

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bodyr_w \leq r \leq r_e < \infty

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bodyc_t(r,p) = \rm const

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bodyq_t = \rm const

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bodyS = \rm const


Mathematical Model

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titleDefinition



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r_{wf} < r \leq r_e


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p(t, r ) = p(r) \Leftrightarrow  \frac{\partial p}{\partial t}  =  0



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 \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} =0



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p(r_e ) = p_i



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\left[ r\frac{\partial p(r )}{\partial r} \right]_{r \rightarrow r_w} = \frac{q_t}{2 \pi \sigma}



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p_{wf}= p(r_w ) - S \cdot r_w \, \frac{\partial p}{\partial r} \Bigg|_{r=r_w}



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