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LaTeX Math Block
anchorXSQUE
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\phi \, c_t \, \mu \cdot \partial_t \Psi -   
 \nabla \cdot \left( k \cdot   \vec \nabla \Psi   \right) 
  = 0

where

LaTeX Math Inline
body--uriencoded--p(t, %7B\bf r%7D)

reservoir pressure

LaTeX Math Inline
bodyt

time

LaTeX Math Inline
body--uriencoded--\rho(%7B\bf r%7D,p)

fluid density 

LaTeX Math Inline
body--uriencoded--%7B\bf r %7D

position vector

LaTeX Math Inline
body--uriencoded--\phi(%7B\bf r%7D, p)

effective porosity 

LaTeX Math Inline
body--uriencoded--%7B\bf r %7D_k

position vector of the

LaTeX Math Inline
bodyk
-th source

LaTeX Math Inline
body--uriencoded--c_t(%7B\bf r%7D,p)

total compressibility 

LaTeX Math Inline
body\

delta ( \bf r )Dirac delta function

nabla

gradient operator

LaTeX Math Inline
bodyq_k(t)

sandface flowrates of the

LaTeX Math Inline
bodyk
-th source



LaTeX Math Inline
body

\nabla

gradient operator LaTeX Math InlinebodyM =

k

/ \mu

phase mobility

LaTeX Math Inline
body--uriencoded--%7B \bf g %7D

gravity vector

LaTeX Math Inline
bodyk

formation permeability to a given 
fluid

LaTeX Math Inline
body--uriencoded--%7B \bf u %7D

fluid
 velocity under Darcy flow 



LaTeX Math Inline
body\mu(p)

dynamic viscosity of a given  fluid



LaTeX Math Inline
bodyZ(p)

fluid compressibility factor

LaTeX Math Inline
body--uriencoded--\displaystyle \Psi(p) =2 \, \int_0%5ep \frac%7Bp \, dp%7D%7B\mu(p) \, Z(p)%7D

Pseudo-Pressure



Expand
titleDerivation


Panel
borderColorwheat
bgColormintcream
borderWidth7

Derivation of Single-phase pseudo-pressure diffusion @model


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