GLOSSARY

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



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-\frac{k}{\mu} \, \int_{\Sigma} \, \nabla p \, d {\bf A\Sigma} = q(t)



where

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

reservoir pressure

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bodyt

time

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body--uriencoded--\phi(%7B\bf r%7D)

effective porosity 

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body--uriencoded--%7B\bf r %7D

position vector


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bodyc_t(p)
total compressibility 

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body\nabla

gradient operator


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bodyk
formation permeability to a given fluid

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body--uriencoded--d %7B\bf A%7D\Sigma%7D

normal surface element of well-reservoir contact


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body\mu(p)

dynamic viscosity of a given  fluid

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

Pseudo-Pressure


LaTeX Math Inline
bodyZ(p)
fluid compressibility factor

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body--uriencoded--\displaystyle \tau(t) = \int_0%5et \frac%7Bdt%7D%7B\mu(p) \, c_t(p)%7D

Pseudo-Time



LaTeX Math Inline
bodyq(t)

sandface flowrates to/from the well-reservoir contact

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