Multi-phase fluid model based on three pseudo-components $\begin{array}{l}C = \{ W, O, G \}\end{array}$ :

$\begin{array}{l}W\end{array}$	water pseudo-component, which may include minerals (assuming formation water and injection water composition is the same)
$\begin{array}{l}O\end{array}$	dead oil pseudo-component
$\begin{array}{l}G\end{array}$	dry gas pseudo-component

existing in three possible phases $\begin{array}{l}\alpha = \{ w, o, g \}\end{array}$ :

$\begin{array}{l}w\end{array}$	water phase, consisting of water component, dead oil pseudo-component and dry gas pseudo-component
$\begin{array}{l}o\end{array}$	oil phase, consisting of dead oil pseudo-component and dissolved dry gas pseudo-component (called Solution Gas) and water
$\begin{array}{l}g\end{array}$	gas phase, consisting of dry gas pseudo-component and vaporized dead oil pseudo-component (called Volatile Oil)

The volumetric phase-balance equations is:

(1)	$\begin{array}{l}\displaystyle s_w + s_o+s_g =1\end{array}$

where

$\begin{array}{l}s_w = \frac{V_w}{V}\end{array}$	share of total fluid volume $\begin{array}{l}V\end{array}$ occupied by water phase $\begin{array}{l}V_w\end{array}$
$\begin{array}{l}s_o = \frac{V_o}{V}\end{array}$	share of total fluid volume $\begin{array}{l}V\end{array}$ occupied by oil phase $\begin{array}{l}V_o\end{array}$
$\begin{array}{l}s_g = \frac{V_g}{V}\end{array}$	share of total fluid volume $\begin{array}{l}V\end{array}$ occupied by gas phase $\begin{array}{l}V_g\end{array}$

The accountable cross-phase exchanges are illustrated in the table below:

Injection water and production water are assumed to have the same dynamic fluid properties and not being discerned.

It's a typical case for saturated reservoir.

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