Various binary mixtures of carbon dioxide and hydrocarbons, especially propane or ethane, as alternative natural refrigerants to Chlorofluorocarbons (CFCs) or Hydro fluorocarbons (HFCs) are presented in this paper. Their environmental performance is friendly, with an ozone depletion potential (ODP) of zero and Global-warming potential (GWP) smaller than 20. The capillary tube performance for the alternative refrigerant HFC HCand mixed refrigerants have been widely studied. However, studies that discuss the performance of the capillary tube to a mixture of natural refrigerants, in particular a mixture of azeotrope carbon dioxide and ethane is still undeveloped. A method of empirical correlation to determine the mass flow rate and pipe length has an important role in the design of the capillary tube for industrial refrigeration. Based on the variables that effect the rate of mass flow of refrigerant in the capillary tube, the Buckingham Pi theorem formulated eight non-dimensional parameters to be developed into an empirical equations correlation. Furthermore, non-linear regression analysis used to determine the co-efficiency and exponent of this empirical correlation based on experimental verification of the results database.