Motivation
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In many practical cases the reservoir flow created by well is getting aligned with a radial direction towards or away from well.
This type of flow is called radial fluid flow and a type library model provides a reference for radial fluid flow diagnostics.
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Physical Model
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Mathematical Model
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| \frac{\partial p}{\partial t} = \chi \, \left( \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right) |
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| p(t = 0, {\bf r}) = p_i |
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| p(t, r \rightarrow \infty ) = p_i |
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| \frac{\partial p(t, r )}{\partial r} \bigg|_{r \rightarrow 0} = \frac{q_t}{\sigma \, d} |
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| p(t,r) = p_i + \frac{q_t}{4 \pi \sigma} \, {\rm Ei} \bigg( - \frac{r^2}{4 \chi t} \bigg) |
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| p_{wf}(t) = p_i + \frac{q_t}{4 \pi \sigma} \, \bigg[ - 2S + {\rm Ei} \bigg( - \frac{r_w^2}{4 \chi t} \bigg) \bigg] |
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Scope of Applicability
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See also
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Physics / Fluid Dynamics / Radial fluid flow
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