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In this case a pressure drop and well flowrate can be roughly related to each other by means of a simple analytical homogeneous reservoir flow model with wellbore and boundary effects neglected.

Since the well radius is neglected the well is modeled as a vertical 0-thickness line sourcing the fluid from a reservoir, giving a model a specific name Line Source Solution.

Inputs & Outputs

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p(t,r) = p_i - \frac{q_t}{4 \pi \sigma} \left[  
\gamma + \ln \left(\frac{r^2}{4 \chi t} \right) \right] 

= p_i - \frac{q_t}{4 \pi \sigma} \ln \left(\frac{2.24585 \, t}{r^2} \right)

Plots

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See also

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Physics / Fluid Dynamics / Radial fluid flow / Line Source Solution

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