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Applications
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title | Line Source Solution |
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In simplest case of infinite homogeneous reservoir, produced by a vertical well the function has an exact analytical formula, given by exponential integral LaTeX Math Inline |
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body | F(z) = {\rm Ei}_1 (z) |
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| (see Line Source Solution (LSS) @model). |
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Isobar equation for a constant-rate production: LaTeX Math Block |
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| p(t,r) = p_i + \frac{q_t}{4 \pi \sigma} \, F \bigg( - \frac{r^2}{4 \chi t} \bigg) = {\rm const} \quad \rightarrow \quad \frac{r^2}{4 \chi t}= {\rm const} |
Since the pressure disturbance at moment was at well walls then the formula for constant-pressure front propagation becomes: LaTeX Math Block |
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| r(t) = r_w + 2 \sqrt{\chi t} |
This leads to estimation of isobar velocity: LaTeX Math Block |
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| u_p(t) = \sqrt{\frac{\chi}{t}}
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See also
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Physics / Fluid Dynamics / Radial fluid flow
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