One of the most important aspects when transporting multiple different liquid products within the same pipeline, is being able to know where the head and tail of each batch is at any given time based on the current operation to provide an accurate Estimated Time of Arrival (ETA) at upcoming stations. With this information, pipeline operators can be ready to execute valve swings at intermediate delivery and injecting stations helping minimize product contamination.

It is relatively simple to track these batches and their interfaces when the pipeline has a uniform and gradual elevation profile. However, when pipelines travel through mountainous regions with high and drastic elevation changes, the ability to track the head and tail of these batches become far more complex due to the presence of slack. When slack is present, the common assumption that the volume of liquid equals the physical volume of the pipe is no longer valid. The fraction of the pipe filled with liquid, called the "liquid holdup", has a large impact on the position of the batch head and tail. As a result, the accuracy of the volume contained within the region and the corresponding Estimated Times of Arrival at upcoming stations are directly affected.

An empirical approach using volume accumulation at a pipeline injections and deliveries has been successfully implemented with an end user to account for the liquid volume within a specific region known to have slack during normal operations. However, this approach does not provide an accurate solution for the exact location of where the slack occurs, nor the size of the slack itself, which has a direct effect on the location estimate for when the head or tail is passing through the area.

With the current empirical approach, Estimated and Actual Times of Arrival are within a 15-minute time window after a batch has traveled a total distance of 1,200 km (746 mile) with a drastic slack region along the route.

This paper provides an analysis on the current empirical approach used in the daily operation by the existing end user, and how the results compared to a full scientific approach running a slack model based on the field instrumentation, and the physical properties of the pipeline.

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