# Summary

Due to their large capital expense, pipelines are often utilized for the transfer of multiple products. During operation of these multi-product pipelines, the interface between two adjacent products extends (referred to as interface mixing), resulting in the contamination of each product. This interface is typically sent to slops collection for reprocessing or disposal at additional cost to the operator. Therefore the economics of a pipeline can often be improved through a study of product interfaces under various operational conditions to aide in the minimization of interface mixing. This article presents several empirical methods by which interface mixing can be quantified.

# Definitions

: | Reynolds number | |

: | Inner diameter of the pipeline | |

: | Length of the pipeline | |

: | Fluid density | |

: | The Darcy friction factor of the pipe line. |

# Calculation Inputs

## Reynolds Number

The methodologies presented in this article require the calculation of the Reynolds number. The Reynolds number should be calculated using the viscosity of the interface mixture rather than that of an individual product. Due to the complexity in estimating the composition of the interface, it is generally assumed that the interface is a 50:50 mix of the leading and trailing products.

## Friction Factor

Some methods for calculating interface lengths (such as Udoetok), account for the effect of pipeline friction on interface mixing using the Darcy friction factor. It is generally recommended that the Darcy friction factor is calculated using the Serghides equation.

# Methods for Estimating Interface Length

Several methods have been developed for calculating the length of the interface between two products in a pipeline. Due to the complex nature of modelling interface mixing, solutions from these methods lie in a wide range (this will be further explored in subsequent sections). A selection of these methods, commonly cited for quantification of interface mixing are listed below.

## Jablonski (1946)

## Birge (1947)

For a gasoline-gasoline interface:

For a gasoline-kerosene interface:

## Smith & Schulze (1948)

## Taylor (1954)

## Sjenitzer (1958)

## Austin & Palfrey (1964)

For :

For :

## Udoetok & Nguyen (2009)

The Udoetok and Nguyen model is perhaps the most recently published correlation for quantifying interface mixing. This method utilizes a parameter *n* to account for the effect of pipe roughness on interface spread at the walls and which may be calculated as follows:

The interface length can subsequently be calculated using the *n* and an experimental constant *w* as follows:

Udoetok & Nguyen suggest based on field data they used to develop the model, however if the opportunity exists one should calibrate this model to pipeline specific measurements.

# Interface Volume

The interface volume can be easily calculated using the interface length and the cross sectional area of the pipeline as shown below.

# Comparison of Methods

## Interface Length vs Pipeline length

The graphs below display the change in the predicted interface length with an increasing pipeline length for a selection of Reynolds numbers. Here it is interesting to note the behaviour of each method as the Reynolds number increases, particularly the Austin & Palfrey method which proves to be the most conservative method for lower Reynolds numbers but provides average results for higher Reynolds numbers.

## Interface Length vs. Reynolds Number

The figure below displays the behaviour of each of the prediction methods as a function of Reynolds number for a 100 km, DN300 line.

# Further Reading

- Udoetok, E.S and Nguyen, A.N.,
*A disc pig model for estimating the mixing volumes between product batches in multi-product pipelines**, Journal of Pipeline Engineering, 2009, 8 (3): p. 195-204* - Vincent-Genod, J.,
*Fundamentals of Pipeline Engineering*, 1984, Editions Technip - Kennedy, J. L.,
*Oil and Gas Pipeline Fundamentals*, 2nd Edition, 1993, Pennwell Books.

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