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LaTeX Math Block
anchorrho_dif
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\frac{\partial (\rho \phi)}{\partial t} + \nabla \, ( \rho \, {\bf u}) = \sum_k \dot m_k(t) \cdot \delta({\bf r}-{\bf r}_k)
LaTeX Math Block
anchorqGamma
alignmentleft
{\rm F}_{\Gamma}(p, {\bf u}) = 0

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LaTeX Math Inline
body\Sigma_k

well-reservoir contact of the 

LaTeX Math Inline
bodyk
-th well

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

normal vector of differential area on the well-reservoir contact, pointing inside wellbore

LaTeX Math Inline
body \dot m_k(t)

mass rate flowrate at 

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bodyk
-th well 
LaTeX Math Inline
body\dot m_k(t) = \rho(p) \cdot q_k(t)

LaTeX Math Inline
bodyq_k(t)

sandface flowrate at 

LaTeX Math Inline
bodyk
-th well 

LaTeX Math Inline
body\rho(p)

fluid density as function of reservoir fluid pressure 

LaTeX Math Inline
bodyp

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