Derivation of Linear pressure diffusion @model

We start with (Single-phase pressure diffusion @model:1):

(1)	$\begin{array}{l}\displaystyle \phi \cdot c_t \cdot \partial_t p + \nabla {\bf u} + c \cdot ( {\bf u} \, \nabla p) = \sum_k q_k(t) \cdot \delta({\bf r}-{\bf r}_k)\end{array}$

(2)	$\begin{array}{l}\displaystyle {\bf u} = - M \cdot ( \nabla p - \rho \, {\bf g})\end{array}$

and neglect the non-linear term $\begin{array}{l}c \cdot ( {\bf u} \, \nabla p)\end{array}$ for low compressibility fluid $\begin{array}{l}c \sim 0\end{array}$ .

Page tree

Derivation of Linear pressure diffusion @model