Isothermal oil compressibility below bubblepoint pressure

At pressures below the bubblepoint, oil compressibility is defined as

1. McCain et al (1988)
$$\ln (c_o)=a_1+a_2\ln (p)+a_3\ln (P_b)+a_4\ln (T)+a_5\ln ({\gamma }_{API})+a_6\ln (R_{sb})$$ $$\overline{)\begin{array}{cc}\text{Coefficient}& \text{Original}\\ a_1& -7.573\\ a_2& -1.450\\ a_3& -0.383\\ a_4& 1.402\\ a_5& 0.256\\ a_6& 0.449\end{array}}$$




2. Al-Marhoun (2009)
$$\ln c_{op}=\ln c_{ob}+a_2(\frac{1}{{\gamma }_{op}}-\frac{1}{{\gamma }_{ob}})$$

where

$${\gamma }_{op}=({\gamma }_o+2.18x{10}^{-4}{R}_s{\gamma }_g)/B_{ob}$$ $$a_2=2.7314$$