Synonym: Volatile Oil fluid @model = Modified Black Oil (MBO) fluid @model

Specific case of a 3-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 only
$\begin{array}{l}o\end{array}$	oil phase, consisting of dead Oil pseudo-component and dissolved dry Gas pseudo-component t (called Solution Gas)
$\begin{array}{l}g\end{array}$	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:

	$\begin{array}{l}w\end{array}$	$\begin{array}{l}o\end{array}$	$\begin{array}{l}g\end{array}$
$\begin{array}{l}W\end{array}$	x
$\begin{array}{l}O\end{array}$		x	x
$\begin{array}{l}G\end{array}$		x	x

Volatile oil fluid model is widely used to model Volatile Oil Reservoir and Pipe Flow Simulations.

The relations to STP flowrates $\begin{array}{l}\{ q_O, \, q_G, \, q_W \}\end{array}$ and mass flowrates $\begin{array}{l}\{ \dot m_O, \, \dot m_G, \, \dot m_W \}\end{array}$ are given by following equations (see Derivation):

(2)	$\begin{array}{l}\displaystyle q_O = \frac{q_o}{B_o} + \frac{R_v \, q_g}{B_g}\end{array}$

(3)	$\begin{array}{l}\displaystyle q_G =\frac{q_g}{B_g} + \frac{R_s \, q_o}{B_o}\end{array}$

(4)	$\begin{array}{l}\displaystyle q_W = \frac{q_w}{B_w}\end{array}$

(5)	$\begin{array}{l}\displaystyle q_o = \frac{ B_o \cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s}\end{array}$

(6)	$\begin{array}{l}\displaystyle q_g = \frac{ B_g \cdot ( q_G - R_s \, q_O)}{1- R_v \, R_s}\end{array}$

(7)	$\begin{array}{l}\displaystyle q_w = B_w \cdot q_W\end{array}$

(8)	$\begin{array}{l}\displaystyle \rho_o = \frac{ \dot m_o}{q_o}= \frac{\rho_O + \rho_G \, R_s}{B_o}\end{array}$

(9)	$\begin{array}{l}\displaystyle \rho_g = \frac{\dot m_g}{q_g}= \frac{\rho_G + \rho_O \, R_v}{B_g}\end{array}$

(10)	$\begin{array}{l}\displaystyle \rho_w =\frac{\dot m_w}{q_w}= \frac{\rho_W}{B_w}\end{array}$

(11)	$\begin{array}{l}\displaystyle \dot m_O = \rho_O \cdot q_O\end{array}$

(12)	$\begin{array}{l}\displaystyle \dot m_G = \rho_G \cdot q_G\end{array}$

(13)	$\begin{array}{l}\displaystyle \dot m_W = \rho_W \cdot q_W\end{array}$

(14)	$\begin{array}{l}\displaystyle \dot m_o = \rho_o \cdot q_o = (\rho_O + \rho_G \, R_s) \cdot \frac{ q_o}{B_o}\end{array}$

(15)	$\begin{array}{l}\displaystyle \dot m_g = \rho_g \cdot q_g = (\rho_G + \rho_O \, R_v) \cdot \frac{q_g }{B_g}\end{array}$

(16)	$\begin{array}{l}\displaystyle \dot m_w = \rho_w \cdot q_w\end{array}$

(17)	$\begin{array}{l}\displaystyle \dot m_o = \frac{(\rho_O + \rho_G \, R_s) \cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s}\end{array}$

(18)	$\begin{array}{l}\displaystyle \dot m_g = \frac{ (\rho_G + \rho_O \, R_v) \cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s}\end{array}$

(19)	$\begin{array}{l}\displaystyle \dot m_w = \rho_W \cdot \frac{q_w}{B_w} = \rho_W \cdot q_W\end{array}$

(20)	$\begin{array}{l}\displaystyle \dot m = \dot m_o + \dot m_g + \dot m_w = \dot m_O + \dot m_G + \dot m_G\end{array}$

(21)	$\begin{array}{l}\displaystyle q_t = q_o + q_g + q_w\end{array}$

(22)	$\begin{array}{l}\displaystyle q_t = \frac{B_o - B_g \, R_s}{1-R_v \, R_s} \cdot q_O +\frac{B_g - B_o \, R_v}{1-R_v \, R_s} \cdot q_G + B_w \cdot q_W\end{array}$

(23)	$\begin{array}{l}\displaystyle q_t = \frac{B_o - B_g \, R_s}{1-R_v \, R_s } \cdot \frac{\dot m_O }{\rho_O} +\frac{B_g - B_o \, R_v}{1-R_v \, R_s } \cdot \frac{\dot m_G }{\rho_G} + B_w\cdot \frac{\dot m_W}{\rho_W}\end{array}$

(24)	$\begin{array}{l}\displaystyle \rho = \frac{\dot m}{q_t} = \frac{\dot m_O + \dot m_G + \dot m_G}{ \frac{B_o - B_g \, R_s}{1-R_v \, R_s } \cdot \frac{\dot m_O }{\rho_O} +\frac{B_g - B_o \, R_v}{1-R_v \, R_s } \cdot \frac{\dot m_G }{\rho_G} + B_w\cdot \frac{\dot m_W}{\rho_W} }\end{array}$

In-situ oil-cut:

(25)	$\begin{array}{l}\displaystyle s_o = \frac{q_o}{q_t} = \frac{ B_o \, (q_O - R_v \, q_G)}{(B_o - B_g \, R_s) \, q_O + (Bg - B_o \, R_v) \, q_G + B_w \, (1- R_v \, R_s) \, q_W }\end{array}$

In-situ gas-cut:

(26)	$\begin{array}{l}\displaystyle s_g = \frac{q_g}{q_t} = \frac{ B_g \, (q_G - R_s \, q_O)}{(B_o - B_g \, R_s) \, q_O + (Bg - B_o \, R_v) \, q_G + B_w \, (1- R_v \, R_s) \, q_W }\end{array}$

In-situ water-cut:

(27)	$\begin{array}{l}\displaystyle s_w = \frac{q_w}{q_t} = \frac{ B_w \, (1- R_v \, R_s) \, q_W}{(B_o - B_g \, R_s) \, q_O + (Bg - B_o \, R_v) \, q_G + B_w \, (1- R_v \, R_s) \, q_W }\end{array}$

The total fluid density:

(28)	$\begin{array}{l}\displaystyle \rho = s_o \, \rho_o + s_g \, \rho_g + s_w \, \rho_w\end{array}$

The total fluid compressibility:

(29)	$\begin{array}{l}\displaystyle c = s_o \, c_o + s_g \, c_g + s_w \, c_w\end{array}$

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Volatile Oil Fluid @model

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