| LaTeX Math Block |
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| \phi \cdot \partial_\tau \Psifrac{\partial \Psi}{\partial \tau}
-
\nabla \cdot \left( k \cdot \vec \nabla \Psi \right)
= 0 |
| | LaTeX Math Block |
|---|
| -\frac{k}{\mu} \, \int_{\Sigma} \, \nabla p \, d {\bf A\Sigma} = q(t) |
|
where
...
| LaTeX Math Block |
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\phi \, c_t \, \mu \cdot \frac{\partial_t \Psi}{\partial \tau} -
\nabla \cdot \left( k \cdot \vec \nabla \Psi \right)
= 0 |
...
In case of the ideal gas equation of state, the Z-factor has a unit value:
and viscosity , viscosity does not depend on pressure
and total compressibility is fully defined by fluid compressibility | LaTeX Math Inline |
|---|
| body | --uriencoded--\displaystyle c_t = c_r + c \sim \frac%7B1%7D%7Bp%7D |
|---|
|
which simplifies the expression for
Pseudo-Pressure as and Pseudo-Time as to:
| LaTeX Math Block |
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| \Psi(p) = \frac{p^2}{\mu}
|
| | LaTeX Math Block |
|---|
| \tau(t) = \frac{1}{\mu} \int_0^t p_{BHP}(t) dt |
|
See also
...
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Pressure Diffusion / Pressure Diffusion @model
...
