Effective prediction of downhole mixing and channeling at an interface between two or more wellbore fluids may prevent the unnecessary consumption of resources at a well site and enhance the performance of wellbore operations, including drilling operations, completion operations, and reservoir management. A model for a length and a volume of the interface between two wellbore fluids may be used to characterize the amount of mixing and channeling. The model may use known properties of the wellbore fluids before mixing and channeling occurs. The model may account for eccentricity in an annulus of the wellbore by partitioning a three dimensional flow profile in the wellbore into a plurality of segments for separate analysis. Outputs from the model may be used to determine one or more locations of the interface at one or more intervals of time as the wellbore fluids circulate through the wellbore. One or more compositions may be determined and recorded for one or more wellbore fluids at one or more depths of the wellbore during one or more intervals of time. To improve operational decision making at a well site, operators or automated processes may modify a wellbore operation based, at least in part, on the one or more compositions and the one dimensional model for mixing and channeling.