Volumetric calculations

q_O = q_{Oo} + q_{Og}

q_G = q_{Gg} + q_{Go}

q_W = q_{Ww}

Following the definition of Solution GOR (Rs) and Vaporized Oil Ratio (Rv) :

R_s = q_{Go}/q_{Oo}

R_v = q_{Og}/q_{Gg}

so that:

q_O = q_{Oo} + R_v \, q_{Gg}

q_G = q_{Gg} + R_s \, q_{Oo}

q_W = q_{Ww}

Following the definition of Oil formation volume factor (Bo) , Gas formation volume factor (Bg) and Water formation volume factor (Bw):

q_{Oo}= \frac{q_o}{B_o}

q_{Gg} = \frac{q_g}{B_g}

q_{Ww} = \frac{q_w}{B_w}

so that:

q_O = \frac{q_o}{B_o} + R_v \,\frac{q_g}{B_g}

q_G = \frac{q_g}{B_g} + R_s \, \frac{q_o}{B_o}

q_W = \frac{q_w}{B_w}

and solving the above system of equations leads to:

q_o = \frac{B_o \cdot (q_O - R_v \, q_G)}{1- R_v \, R_s}

q_g = \frac{B_g \cdot (q_G - R_s \, q_O)}{1- R_v \, R_s}

q_w = B_w \cdot q_w

Mass calculations

The oil phase includes oil component and gas component so that the oil phase mass flux is:

m_o = m_{Oo} + m_{Go}

The gas phase includes gas component and oil component so that the gas phase mass flux is:

m_g = m_{Gg} + m_{Og}

The water phase includes water component only so that the water phase mass flux is:

m_w = m_{Ww}

→

m_o = \rho_O \cdot q_{Oo} + \rho_G \cdot q_{Go}

m_g = \rho_G \cdot q_{Gg} + \rho_O \cdot q_{Og}

m_w = \rho_W \cdot q_{Ww}

→

m_o = \rho_O \cdot q_{Oo} + \rho_G \cdot R_s \, q_{Oo}

m_g = \rho_G \cdot q_{Gg} + \rho_O \cdot R_v \, q_{Gg}

m_w = \rho_W \cdot q_{Ww}

→

m_o = (\rho_O + \rho_G \cdot R_s) \cdot q_{Oo}

m_g = (\rho_G + \rho_O \cdot R_v) \cdot q_{Gg}

m_w = \rho_W \cdot q_{Ww}

→

m_o = (\rho_O + \rho_G \cdot R_s) \cdot \frac{q_o}{B_o}

m_g = (\rho_G + \rho_O \cdot R_v) \cdot \frac{q_g}{B_g}

m_w = \rho_W \cdot \frac{q_w}{B_w}

→

\rho_o = \frac{\rho_O + \rho_G \cdot R_s}{B_o}

\rho_g = \frac{\rho_G + \rho_O \cdot R_v}{B_g}

\rho_w = \frac{\rho_W}{B_w}

The total mass flow of all phases:

\dot m = \dot m_o + \dot m_g + \dot m_w =  (\rho_O + \rho_G \cdot R_s) \cdot \frac{q_o}{B_o} + (\rho_G + \rho_O \cdot R_v) \cdot \frac{q_g}{B_g} + \rho_W \cdot \frac{q_w}{B_w}

→

\dot m = (\rho_O + \rho_G \cdot R_s) \cdot \frac{q_O - R_v \, q_G}{1-R_v \, R_s} + (\rho_G + \rho_O \cdot R_v) \cdot \frac{q_G - R_s \, q_O}{1- R_v \, R_s} + \rho_W \cdot q_W

→

\dot m = \frac{ (\rho_O + \rho_G \cdot R_s)\cdot (q_O - R_v \, q_G) +  (\rho_G + \rho_O \cdot R_v) \cdot (q_G - R_s \, q_O) }{1-R_v \, R_s} + \rho_W \cdot \frac{q_w}{B_w}

→

\dot m = \frac{ \rho_O \, q_O \, (1- R_v \, R_s) +  \rho_G \, q_G  \, (1- R_v \, R_s) }{1-R_v \, R_s} + \rho_W \cdot q_W

→

\dot m = \rho_O \cdot q_O +  \rho_G \cdot q_G  + \rho_W \cdot q_W = \dot m_O  + \dot m_G + \dot m_W

→

\dot m = \dot m_o + \dot m_g + \dot m_w = \dot m_O + \dot m_G + \dot m_W

which means that total mass flux of all fluid phases is equal to the total mass flux of all fluid components.

As volatile oil model does not assume water-component exchange between phases the equality can be broken down into two equalities:

\dot m_{HC} = \dot m_o + \dot m_g = \dot m_O + \dot m_G

 \dot m_w = \dot m_W

The total fluid density of Volatile Oil fluid @model is given by following equation (see Multiphase fluid for derivation):

\rho = s_o \, \rho_o + s_g \, \rho_g + s_w \, \rho_w

The total fluid compressibility of multiphase fluid is given by following equation (see Multiphase fluid for derivation):

c = s_o \, c_o + s_g \, c_g + s_w \, c_w

Volumetric calculations

Mass calculations

See Also