Oil viscosity above bubblepoint pressure

Oil viscosity above bubblepoint pressure measures the oil’s resistance to flow and it is defined as the ratio of shear stress to shear rate induced in the oil by the stress. Four methods for estimating oil viscosity above bubblepoint pressure are presented.

1. Beal (1946)
$${\mu }_o={\mu }_{ob}+\left(p-p_b\right)\left({\text{a}}_1{\mu }_{\text{ob}}^{{\text{a}}_{\text{2}}}+a_3{\mu }_{ob}^{a_4}\right)$$ $$\overline{)\begin{array}{cc}\text{Coefficient}& \text{Original}\\ a_1& 24x{10}^{-6}\\ a_2& 1.60\\ a_3& 38x{10}^{-6}\\ a_4& 0.56\end{array}}$$




2. Vasquez and Beggs (1980)
$${\mu }_o={\mu }_{\text{ob}}{\left(p/p_{\text{b}}\right)}^m$$

where

$$\ln m=a_1+a_{2}p+a_3\ln p$$ $$\overline{)\begin{array}{cc}\text{Coefficient}& \text{Original}\\ a_1& -10.55749\\ a_2& -89.80x{10}^{-6}\\ a_3& 1.187\end{array}}$$




3. Labedi (1992)
$${\mu }_{\text{a}}={\mu }_{\text{ob}}+m(p-p_b)$$ $$\ln m=a_{\text{1}}+a_{\text{2}}{\gamma }_{API}+a_{\text{3}}\ln {\mu }_{\text{od}}+a_{\text{4 }}\ln p_{\text{b}}$$ $$\overline{)\begin{array}{cc}\text{Coefficient}& \text{Original}\\ a_1& -5.728832\\ a_2& -45.360926x{10}^{-3}\\ a_3& 0.9036\\ a_4& -0.3849\end{array}}$$




4. Al-Marhoun (2004)
$$\ln {\mu }_o=\ln {\mu }_{\text{ob}}+a_1{\gamma }_{ob}{}^2\left(p-p_{\text{b}}\right)$$

where

$$a_1=0.151292x{10}^{-3}$$