1. INTRODUCTION

The transport of different petroleum products or different grades of a same product through a single pipeline is known as batch transfer and is a very common practice in the pipeline industry. Unless mechanical separators are used such as scrapers, there will be a certain amount of mixing between the products' interface which is called mixing volume. To ensure the quality of the products being transported, the mixing volume should be accurately predicted and/or continuously monitored so that the contaminant can be isolated without harming the products' specifications. The mixing zone which develops at 1 the batches' boundary increases in extension as the batches travels along the pipe. Such a phenomenon is driven by dispersion of matter and is currently evaluated by a number of classical models (Aunicky, 1970; Austin and Palfrey, 1964; Levenspiel, 1958; Ovffadi and Torok, 1977; Sjenitzer, 1958; Smith and Schulze, 1948a; Netchval et al., 1972) which assume, as a basic hypothesis, continuous pumping during the transfer. However, in many practical situations, the pumping must be interrupted either by voluntary or unintentional operational events. In such cases pipeline flow rate experiences significant variations and so does the dispersion coefficient. So, a question arises as to the suitability of the classical models in predicting mixing volumes under these conditions. On the other hand, it has been pointed out by some specialists that the act of stopping the line during a batch transfer could be one of the factors responsible for the increase in the mixing volume. Since the occurrence of mixing zones implies in additional costs associated to shipping the mixture back to refinery for later reprocessing, it becomes evident the reason for investigating the influence of pumping shut-down on the mixing volume. A new model capable to evaluate mixing volumes under pump shut-down and start-up events is presented in this paper. The model is formed by a set of differential equations that describes the momentum conservation and concentration distribution for the fluids, which are considered as incompressible. By assuming that the concentration distribution does not affect substantially the momentum variation, the time-dependent flow rate in the line is firstly computed by solving the momentum equation and then used as an input in the solution of the dispersion equation. Numerical simulations carried out for a specific batch have shown that if the pumping shut-down operation is repeated several times during the transfer it may induce a significant growth in mixing volume.

2. THEORETICAL DEVELOPMENT

To manage different products in the line, product pipelines conveying batches are commonly susceptible to pump-shut down operational conditions. In such a event, the hydraulic gradient line is severely reduced causing the fluids to de accelerate and even to stop in the entire pipeline extension. The flow, which is in general highly turbulent in batch transfers, becomes laminar until the fluid comes to rest.

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