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The alternative form is to write down equations
| LaTeX Math Block Reference |
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and
| LaTeX Math Block Reference |
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in reservoir volume outside wellbore and match the solution to the fluid flux through the
well-reservoir contact:
| LaTeX Math Block |
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| \phi \cdot c_t \cdot \partial_t p + \nabla {\bf u}
+ c \cdot ( {\bf u} \, \nabla p)
= 0 |
| | LaTeX Math Block |
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| {\bf u} = - M \cdot ( \nabla p - \rho \, {\bf g}) |
|
| LaTeX Math Block |
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| \int_{\Sigma_k} \, {\bf u} \, d {\bf \Sigma} = q_k(t) |
| | LaTeX Math Block |
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| anchor | qGamma |
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| alignment | left |
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| \int_{\Gamma} \, {\bf u} \, d {\bf \Sigma} = q_\Gamma(t) |
|
where
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| |
| LaTeX Math Inline |
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| body | --uriencoded--d %7B\bf \Sigma%7D |
|---|
|
| normal vector of differential area on the well-reservoir contact, pointing inside wellbore |
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