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

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

Modified Black Oil fluid @model is widely used to model Volatile Oil Reservoir and Pipe Flow Simulations.

The relations between in-situ (at given temperature and pressure) and STP masses, volumes, densities and compressibilities are given by the following equations (see Derivation):

(2)	$\begin{array}{l}\displaystyle V_O = \frac{V_o}{B_o} + R_v \,\frac{V_g}{B_g}\end{array}$

(3)	$\begin{array}{l}\displaystyle V_G = \frac{V_g}{B_g} + R_s \, \frac{V_o}{B_o}\end{array}$

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

(5)	$\begin{array}{l}\displaystyle V_L = V_O + V_W\end{array}$

(6)	$\begin{array}{l}\displaystyle V_o = \frac{B_o \cdot (V_O - R_v \, V_G)}{1- R_v \, R_s}\end{array}$

(7)	$\begin{array}{l}\displaystyle V_g = \frac{B_g \cdot (V_G - R_s \, V_O)}{1- R_v \, R_s}\end{array}$

(8)	$\begin{array}{l}\displaystyle V_w = B_w \cdot V_W\end{array}$

(9)	$\begin{array}{l}\displaystyle V_t = V_o + V_g + V_w\end{array}$

In-situ oil-cut:

(10)	$\begin{array}{l}\displaystyle s_o = V_o/V_t\end{array}$

In-situ gas-cut:

(11)	$\begin{array}{l}\displaystyle s_g = V_g/V_t\end{array}$

In-situ water-cut:

(12)	$\begin{array}{l}\displaystyle s_w = V_w/V_t\end{array}$

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

Surface oil mass rate:

(14)	$\begin{array}{l}\displaystyle m_O = \rho_O V_O\end{array}$

Surface gas mass rate:

(15)	$\begin{array}{l}\displaystyle m_G = \rho_G V_G\end{array}$

Surface gas mass rate:

(16)	$\begin{array}{l}\displaystyle m_W = \rho_W V_W\end{array}$

Surface total fluid mass rate:

(17)	$\begin{array}{l}\displaystyle m = m_O + m_G + m_W\end{array}$

In-situ oil mass:

(18)	$\begin{array}{l}\displaystyle m_o = (\rho_O + \rho_G \cdot R_s) \cdot \frac{V_o}{B_o}\end{array}$

In-situ gas mass:

(19)	$\begin{array}{l}\displaystyle m_g = (\rho_G + \rho_O \cdot R_v) \cdot \frac{V_g}{B_g}\end{array}$

In-situ water mass:

(20)	$\begin{array}{l}\displaystyle m_w = \rho_W \cdot V_w/B_w\end{array}$

In-situ total fluid mass:

(21)	$\begin{array}{l}\displaystyle m = m_o + m_g + m_w\end{array}$

In-situ oil density:

(22)	$\begin{array}{l}\displaystyle \rho_o = \frac{\rho_O + \rho_G \cdot R_s}{B_o}\end{array}$

In-situ gas density:

(23)	$\begin{array}{l}\displaystyle \rho_g = \frac{\rho_G + \rho_O \cdot R_v}{B_g}\end{array}$

In-situ water density:

(24)	$\begin{array}{l}\displaystyle \rho_w = \frac{\rho_W}{B_w}\end{array}$

In-situ Total fluid density:

(25)	$\begin{array}{l}\displaystyle \rho_t = m/V_t = s_o \, \rho_o + s_g \, \rho_g + s_w \, \rho_w\end{array}$

In-situ total fluid compressibility:

(26)	$\begin{array}{l}\displaystyle c = \rho_t^{-1} \cdot ( s_o \, \rho_o \, c_o + s_g \, \rho_g \, c_g + s_w \, \rho_w \, c_w )\end{array}$

where $\begin{array}{l}B_o, \, B_g, \, B_w, \, R_s, \, R_v\end{array}$ are Dynamic fluid properties.

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