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The main objective of this work is to predict the mixing of two different miscible oils in a very long channel. The background to this problem relates to the mixing of heavy and light oil in a pipeline. As a first step, a 2D channel with an aspect ratio of 250 is considered. The batch-mixing of two miscible crude oils with different viscosities and densities is modeled using an unsteady laminar model and unsteady RANS model available in the commercial CFD solver ANSYSFluent. For a comparison, a LES model was used for a 3D version of the 2D channel. The distinguishing feature of this work is the Lagrangian coordinate system utilized to set no-slip wall boundary conditions. The global CFD model has been validated against classical analytical solutions. Excellent agreement has been achieved. Simulations were carried out for a Reynolds number of 6300 (calculated using light oil properties) and a Schmidt number of 104. The results show that, in contrast to the unsteady RANS model, the LES and unsteady laminar models produce comparable mixing dynamics for two oils in the channel. Analysis of simulations also shows that, for a channel length of 100 m and a height of 0.4 m, the complete mixing of two oils across the channel has not been achieved. We showed that the mixing zone consists of the three different mixing sub-zones, which have been identified using the averaged mass fraction of the heavy oil along the flow direction. The first sub-zone corresponds to the main front propagation area with a length of several heights of the channel. The second and third sub-zones are characterized by so-called shear-flow-driven mixing due to the Kelvin– Helmholtz vortices occurring between oils in the axial direction. It was observed that the third sub-zone has a steeper mass fraction gradient of the heavy oil in the axial direction in comparison with the second sub-zone, which corresponds to the flow-averaged mass fraction of 0.5 for the heavy oil.