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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
C = \{ W, O, G \}:
existing in three possible phases
\alpha = \{ w, o, g \}:
The volumetric phase-balance equations is:
where
| share of total fluid volume
V occupied by water phase
V_w |
| share of total fluid volume
V occupied by oil phase
V_o |
| share of total fluid volume
V occupied by gas phase
V_g |
The accountable cross-phase exchanges are illustrated in the table below:
Volatile oil fluid model is widely used to model Volatile Oil Reservoir and Pipe Flow Simulations.
The relations between in-situ and surface (usually SPE Standard Conditions (STP) ) flow properties are given by following equations (see Derivation):
(2) |
q_O = \frac{q_o}{B_o} + \frac{R_v \, q_g}{B_g} |
|
(3) |
q_G =\frac{q_g}{B_g} + \frac{R_s \, q_o}{B_o} |
|
(4) |
q_W = \frac{q_w}{B_w} |
|
(5) |
q_o = B_o \cdot ( q_O - R_v \, q_G) |
|
(6) |
q_g = B_g \cdot ( q_G - R_s \, q_O) |
| |
(8) |
\rho_o = \frac{
\dot m_o}{q_o}= \frac{\rho_O + \rho_G \, R_s}{B_o} |
|
(9) |
\rho_g = \frac{\dot m_g}{q_g}= \frac{\rho_G + \rho_O \, R_v}{B_g} |
|
(10) |
\rho_w =\frac{\dot m_w}{q_w}= \frac{\rho_W}{B_w} |
|
(11) |
\dot m_O = \rho_O \cdot q_O
|
|
(12) |
\dot m_G = \rho_G \cdot q_G
|
|
(13) |
\dot m_W = \rho_W \cdot q_W
|
|
(14) |
\dot m_o = \rho_o \cdot q_o = (\rho_O + \rho_G \, R_s) \cdot \frac{ q_o}{B_o}
|
|
(15) |
\dot m_g = \rho_g \cdot q_g = (\rho_G + \rho_O \, R_v) \cdot \frac{q_g }{B_g} |
|
(16) |
\dot m_w = \rho_w \cdot q_w |
|
(17) |
\dot m_o =
\frac{(\rho_O + \rho_G \, R_s) \cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s}
|
|
(18) |
\dot m_g =
\frac{ (\rho_G + \rho_O \, R_v) \cdot ( q_O - R_v \, q_G) }{1- R_v \, R_s} |
|
(19) |
\dot m_w = \rho_W \cdot \frac{q_w}{B_w} = \rho_W \cdot q_W |
|
(20) |
\dot m = \dot m_o + \dot m_g + \dot m_w = \dot m_O + \dot m_G + \dot m_G |
|
(21) |
q_t = q_o + q_g + q_w |
|
(22) |
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 |
|
(23) |
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}
|
|
(24) |
\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}
} |
|
In-situ oil-cut:
(25) |
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 } |
|
In-situ gas-cut:
(26) |
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 } |
|
In-situ water-cut:
(27) |
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 } |
|
The total fluid density:
(28) |
\rho = s_o \, \rho_o + s_g \, \rho_g + s_w \, \rho_w |
|
The total fluid compressibility:
(29) |
c = s_o \, c_o + s_g \, c_g + s_w \, c_w |
|
See Also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Fluid (PVT) Analysis / Fluid @model
[ Volatile Oil ][ Volatile Oil Reservoir ]