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

$\begin{array}{l}W\end{array}$	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 two possible phases $\begin{array}{l}\alpha = \{ w, o \}\end{array}$ :

$\begin{array}{l}w\end{array}$	water phase, consisting of water component only
$\begin{array}{l}o\end{array}$	oil phase, consisting of dead oil pseudo-component and dissolved natural gas pseudo-component (called solution gas)

The phase volume balance equations is:

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

where

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

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

It's a typical case for undersaturated reservoir.

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