| (1) | \phi \cdot c_t \cdot \mu \cdot \partial_t \Psi - \nabla \cdot \left( k \cdot \vec \nabla \Psi \right) = 0 |
where
p(t, {\bf r}) | reservoir pressure | t | time |
\rho({\bf r},p) | fluid density | {\bf r } | position vector |
\phi({\bf r}, p) | effective porosity | {\bf r }_k | position vector of the k-th source |
c_t({\bf r},p) | total compressibility | \delta ( \bf r ) | Dirac delta function |
q_k(t) | sandface flowrates of the k-th source | \nabla | gradient operator |
M = k / \mu | phase mobility | { \bf g } | gravity vector |
k | formation permeability to a given fluid | { \bf u } | fluid velocity under Darcy flow |
\mu(p) | dynamic viscosity of a given fluid | ||
Z(p) | fluid compressibility factor | ||
\displaystyle \Psi(p) =2 \, \int_0^p \frac{p \, dp}{\mu(p) \, Z(p)} | Pseudo-Pressure | ||
See also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Pressure Diffusion / Pressure Diffusion @model