A method to average the multi-phase fluid density depending on relative phase mobilities:

\rho(p, T) = \frac{ M_{rw} \rho_w + M_{ro}  (1 + R_{sn}) \rho_o  + M_{rg}  (1+R_{vn}) \rho_g }{ M_{rw}  + M_{ro}  (1 + R_{sn})  + M_{rg}  (1+R_{vn}) }

where


\rho_w(p, T), \; \rho_o(p, T), \; \rho_g(p, T)



water density, oil density and gas density as functions of reservoir pressure and temperature 


M_{rw}(s, p, T) , \; M_{ro}(s,p, T), \; M_{rg}(s,p, T)



relative phase mobilities as functions of reservoir saturation at reservoir location and reservoir pressure and temperature 


R_{sn}(p, T) , \;   R_{vn}(p, T)



normalized cross-phase exchange ratios as functions of reservoir pressure and temperature


This concept gives more weight to phases with higher relative phase mobilities.

This normally finds application in multi-phase pressure diffusion where more agile phase contributes more to average phase pressure variation.