can anybody help on proving equality of those two expressions? Actually, those are different forms of Gassmann equation, the first one is considered to be the main form.
$$K_{sat}=K_{dr}+\frac{K_f\alpha^2}{\Phi +\frac{K_f}{K_m}(\alpha-\Phi)}$$ and
$$\frac{K_{sat}}{K_m-K_{sat}}=\frac{K_{dr}}{K_m-K_{dr}}+\frac{K_{m}}{\Phi(K_m-K_{f})} $$ ,where $$\alpha=1-\frac{K_{dr}}{K_m}$$