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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.
Inputs & Outputs
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Physical Model
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Mathematical Model
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| LaTeX Math Block |
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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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Pressure Testing
| Pressure Drop |
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| \delta p = p_i - p_{wf}(t) \sim t^{1/2} |
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| Log derivative |
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| t \frac{d (\delta p)}{dt} \sim t^{1/2} |
| Fig. 2. PTA Diagnostic plot for LFS |
See also
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Physics / Fluid Dynamics / Linear fluid flow
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