fluid dynamics - How do I calculate the Reynolds number in multiphase flows?

I am modeling a gas flowing through a liquid. How do I calculate the Reynolds number in multiphase flows? And, at what Reynolds number should I consider the flow to be turbulent?

The problem is of a typical drilled wellbore in the oil and gas industry. Fresh cement is poured into an annulus between the steel casing and the drilled formation. Before the cement is set it is vulnerable to formation gas over coming its pore pressure (or hydrostatic head) and flowing through the cement, often times forming channels for more gas to flow through in the future, rendering the cement sheath useless.

EDIT:

I am currently using a Bingham fluid to describe the viscosity of the cement slurry. The yield stress will be in the range of 300 to 700 kPa. The plastic viscosity will be in the order of 0.05-0.10 Pa.s.

It is hard for me to estimate gas velocity but in preliminary models I have seen velocities in the range of 5-10 mm/s in preliminary models.