Dear Vahid: Firstly you need to characterize thoroughly the phenomena under study and particularly the geometry and all the conditions of frontier. For example you need to know if you are in presence of a steady or unsteady flow, and, assuming a turbulent flow, the flow pattern and if you are interested in instantaneous values or average values for the variables.

Thanks Antonio. Because my field is not fluid mechanics, therefore I do not know the keywords for finding relevant papers. As you may know my phenomenon is one dimensional which is different from bubble dynamics. Here, I interested to unsteady but not turbulent behavior. 

I agree with Dr. Diogo. It is not clear the problem makes sense without flow, as gravity would cause the gas slug to rise to the top of the pipe. If there is flow, this would correspond to the "slugging" regime of two-phase flow, and you should search on line for references.