Quantification and Reduction of Uncertainties for Solids Transport Velocity Predictions at Low Concentrations in Near-Horizontal Flow
Authors: Cremaschi Selen , Sarica Cem , Subramani Hariprasad Janakiram , Soepyan Frits Byron , Kouba Gene Edward 
Published: May 2013

Abstract
This paper presents a systematic methodology of quantifying the fluid velocity needed to transport solid particles in a conduit for a given field operating condition. The methodology uses data clustering and model parameter fine-tuning approaches, statistical analysis, and an uncertainty propagation method. Publicly-available experimental data on solids transport and solids transport models were gathered through an extensive literature review. The data clustering algorithm selects the representative experimental data points that lie closest to the operating condition. Then, the parameters of the solids transport models are fine-tuned using unconstrained optimization with the representative experimental data. The fine-tuned models are compared using statistical analysis to identify the ones that provide the most accurate velocity predictions for the operating condition. The uncertainties in the experimental data are incorporated into the methodology using the Monte Carlo simulation method to quantify the bounds of the models' velocity predictions to within a predetermined confidence level. To demonstrate the performance of the methodology, the solids transport velocity predictions and their bounds are quantified for an experimental datum point, removed from the database, used as an operating condition. When the uncertainties in the experimental data are ignored, the velocity predictions of the higher-ranked models fall to within the same order of magnitude. And when the uncertainties of the experimental data are incorporated into the methodology, the mean velocity predictions produced by the higher-ranked models not only fall to within the same order of magnitude, but they are nearly equal to each other, which means that these velocity predictions can be accepted with higher confidence. In addition, the mean velocity predictions and the 97.5th percentile velocity predictions are nearly equal to each other, which means that these velocity predictions can be accepted at the 95% confidence level. It was found that for the case study, the solids transport velocity predictions produced by the proposed methodology are sufficient to transport the solid particles in the pipe, and these velocity predictions fall to within +30% of the experimental velocity.

Introduction
To prevent the accumulation of solid particles in pipelines, the velocity of the fluid in the pipe needs to exceed the critical velocity (i.e., the minimum fluid velocity required for transporting the solid particles).1,2 To predict the critical velocity, solids transport models are used. However, many solids transport models have been developed over the years, and these models can produce velocity predictions that vary by orders of magnitude for the same operating condition.3 Moreover, these models only report single values for the critical velocity prediction. Thus, in using a model's velocity prediction, there will be questions regarding whether or not operating at such velocity is sufficient to transport the solid particles. Therefore, it is important that one identifies the appropriate models for a given operating condition, and quantify the uncertainties in the models' velocity predictions to ensure a safe and efficient operation.
A methodology was developed by Soepyan et al.3 to identify the appropriate models for a given operating condition. The methodology consists of a data clustering component, a model parameter fine-tuning module, and a model ranking protocol. The data clustering component selects the experimental data from the database that are most similar to the operating condition, which would best represent the operating condition. The model parameter fine-tuning module uses the selected experimental data to adjust the parameters of the models in order for the models to produce the most accurate velocity predictions possible for the selected data. The model ranking protocol uses statistical analysis to determine the models that provide the most accurate velocity predictions for the operating condition. For a given operating condition, the methodology was capable of generating velocity predictions that fall to within the same order of magnitude.