\phi \cdot \partial_\tau \Psi -   
 \nabla \cdot \left( k \cdot   \vec \nabla \Psi   \right) 
  = 0

where

reservoir pressure

time

fluid density 

position vector

effective porosity 

position vector of the -th source

total compressibility 

gradient operator

sandface flowrates of the -th source

Pseudo-Pressure

formation permeability to a given fluid

Pseudo-Time

dynamic viscosity of a given  fluid



fluid compressibility factor




Derivation of pseudo-linear pressure diffusion @model



See also


Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Pressure Diffusion / Pressure Diffusion @model