Motivation
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In many practical cases the reservoir flow created by well or group of wells is getting aligned with a specific linear direction away from well.
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This type of flow is called linear fluid flow and a type library model provides a reference for linear fluid flow diagnostics.
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Physical Model
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Mathematical Model
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| Expand |
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| \frac{\partial p}{\partial t} = \chi \, \frac{d^2 p}{dx^2} |
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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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| p(t,x) = p_i - \frac{q_t}{\sigma \, d} \bigg[ \sqrt{\frac{4 \chi t}{\pi}} \exp \bigg( -\frac{x^2}{4 \chi t} \bigg) - x \, \bigg[ 1- {\rm erf} \bigg(\frac{x}{\sqrt{4 \, \chi \, t}} \bigg) \bigg] \bigg] |
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| p_{wf}(t) = p(t,x=0)= p_i - \frac{q_t}{\sigma \, d} \, \sqrt{\frac{4 \chi t}{\pi}} |
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Scope of Applicability
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See also
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Physics / Fluid Dynamics / Linear fluid flow
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