Mobility-weighted fluid density

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

$\begin{array}{l}\displaystyle \rho(p, T) = \frac{ M_{rw} \rho_w + M_{ro} (1 + R_{sn}) \rho_o + M_{rg} (1+R_{vn}) \rho_g }{ M_{rw} + M_{ro} (1 + R_{sn}) + M_{rg} (1+R_{vn}) }\end{array}$

where

(1)	$\begin{array}{l}\displaystyle \rho_w(p, T), \ \rho_o(p, T), \ \rho_g(p, T)\end{array}$

water density, oil density and gas density

(2)	$\begin{array}{l}\displaystyle M_{rw}(s, p, T) = \frac{k_{rw}(s)}{\mu_w(p, T)}, \quad M_{ro}(s,p, T) = \frac{k_{ro}(s)}{\mu_o(p, T)}, \quad M_{rg}(s,p, T) = \frac{k_{rg}(s)}{\mu_g(p, T)}\end{array}$

relative phase mobilities as functions of reservoir saturation $\begin{array}{l}s({\rm \bf r})\end{array}$ at reservoir location $\begin{array}{l}\bf r\end{array}$ and reservoir pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$

(3)	$\begin{array}{l}\displaystyle R_{sn}(p, T) = \frac{R_s B_g}{B_o} \ , \quad R_{vn}(p, T) = \frac{R_v B_o}{B_g}\end{array}$

normalized cross-phase exchange ratios as functions of reservoir pressure $\begin{array}{l}p\end{array}$ and temperature $\begin{array}{l}T\end{array}$

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.

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Mobility-weighted fluid density