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| LaTeX Math Block |
|---|
| anchor | rho_dif |
|---|
| alignment | left |
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| \frac{\partial (\rho \phi)}{\partial t} + \nabla \, ( \rho \, {\bf u}) = \sum_k m_k(t) \cdot \delta({\bf r}-{\bf r}_k) |
| | LaTeX Math Block |
|---|
| \int_{\Sigma_kGamma} \, \rho(p) \, {\bf u} \, d {\bf A} = m_k\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 |
| mass rate at -th well | LaTeX Math Inline |
|---|
| body | m_k(t) = \rho(p) \cdot q_k(t) |
|---|
|
|
| |
| |
...
| LaTeX Math Block |
|---|
| anchor | pre_filnal |
|---|
| alignment | left |
|---|
| \rho \, \phi \, c_t \cdot \frac{\partial p}{\partial t} + \nabla \, ( \rho \, {\bf u}) = \rho \, \sum_k q_k(t) \cdot \delta({\bf r}-{\bf r}_k) |
| | LaTeX Math Block |
|---|
| \int_{\Sigma_kGamma} \, {\bf u} \, d {\bf A} = q_k\Gamma(t) |
|
where
...
| LaTeX Math Block |
|---|
| anchor | pre_filnal |
|---|
| alignment | left |
|---|
| \phi \, c_t \cdot \frac{\partial p}{\partial t} + \nabla {\bf u}
+ c \cdot ( {\bf u} \, \nabla p) = \sum_k q_k(t) \cdot \delta({\bf r}-{\bf r}_k) |
| | LaTeX Math Block |
|---|
| \int_{\Sigma_kGamma} \, {\bf u} \, d {\bf A} = q_kGamma(t) |
|
See also
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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Pressure Diffusion / Pressure Diffusion @model / Single-phase pressure diffusion @model
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