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\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} |
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\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 |
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\dot m = \rho_O \, q_O + \rho_G \, q_G + \rho_W \cdot q_W = \dot m_O + \dot m_G + \dot m_W |
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\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.
