To clean highly viscous fluids from pipework, flushing processes are used. The cleaning time for a pair of fluids, one being flushed and one used for flushing the other out, is typically estimated by using expensive experiments or costly fully resolved numerical simulations. In this work the authors propose a new approach to determine an accurate approximation of the cleaning time for a flushing process at substantially lower cost. This is done through a simplification of the cleaning process. The process is composed of two phases: core removal and layer removal. Sub-models for each phase are developed and then combined yielding the cleaning model. Subsequently, this model is validated using highly resolved CFD data of a cleaning process. The cleaning model is able to predict the cleaned radius over time with an error of less than 8% during core removal and less than 2% during layer removal compared to the CFD data. The computing time is negligible which makes the model highly suitable for practical application.