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\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}) }

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where


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



water density, oil density and gas density


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M_{rw}(s, p, T) = \frac{k_{rw}(s)}{\mu_w(p, T)}, \quad M_{ro}(s,p, T) = \frac{k_{ro}(s)}{\mu_o(p, T)}, \quad M_{rg}(s,p, T) = \frac{k_{rg}(s)}{\mu_g(p, T)}



relative phase mobilitiesas functions of reservoir saturation

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at reservoir location
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and reservoir

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R_{sn}(p, T) = \frac{R_s B_g}{B_o} \ , \quad R_{vn}(p, T) = \frac{R_v B_o}{B_g}


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This concept gives more wightweight 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.