The industrial applications of common pipelines to simultaneously deliver multiple types of gases or liquids widely occur in petroleum and natural gas industries. Therein, the pipelines compose of significant horizontal and vertical sections can range from several meters to several km in length. The longitudinal dispersion of matter is an important aspect of such flows in safety and reliability. This paper sets out an analytic simulation model on the basis of the profiles of velocity and turbulent viscosity via steady numerical solutions by computational fluid dynamics (CFD) method. The mixing length and the wasting lengths of the original and latter fluids were applied as the key parameter to describe the extent of axial mixing in the pipe. In both turbulent and laminar pipe flows, the relative errors in the present model were reduced to 5% or less, which is 5%–15% lower than those in previous models. Moreover, the accuracy of the present model was nearly not less than that of unsteady numerical solutions in the same meshing density, whereas the computational load of the present model was far less than that of unsteady numerical solutions. Further, through investigating effects of buoyancy on axial mixing, it is found that the wasting length of the lighter fluid was higher than that of the heavier fluid.

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