Selection of the Optimal Critical Velocity for Sand Transport at Low Concentrations for Near-Horizontal Flow
Authors: Soepyan Byron F. , Cremaschi Selen , Sarica Cem , Subramani Hariprasad J. 
Published: April 2012

Abstract
This manuscript presents a systematic methodology to determine the optimalcritical velocity for sand transport on-the-fly for a given field operatingcondition. Using publicly-available experimental data on sand transport andsand transport models, the methodology combines data clustering andoptimization approaches with statistical analysis. The data clusteringalgorithm is used to select the representative data points that lie closest tothe operating condition, and then, the parameters of the sand transport modelsare fine-tuned using unconstrained optimization with the representative data. Using statistical analysis, the fine-tuned models are compared to identify theones that are most applicable and provide accurate velocity predictions for thegiven operating condition. Upon applying the methodology to a field operatingcondition, the sand transport velocity for the operating condition, assuggested by the methodology, are consistent.

Introduction
Sand transport models are used to predict the critical velocity, defined as therequired "fluid velocity for particle motion" [1], in order for the fluid to beable to transport the sand particles in the pipe. The transport of the sandparticle must take place in order to prevent the accumulation of sandparticles, which is of importance, as the accumulation of sand particles inpipes can have consequences, such as blockage in the pipeline [2], theprevention of corrosion inhibitors from reaching the bottom of the pipe [3], and erosion due to the decreased flow area in the pipe [4]. In industrialapplications, sand transport models are used to provide a reasonable estimatefor the operating velocity of existing pipelines to ensure that the sandparticles are transported. Due to the wide range of possible operatingconditions that exist, and the different possible mechanisms for particletransport, many sand transport models were developed by different authorsthroughout the years.
Fig. 1 shows the critical velocity predictions of 40 sand transport models fora field operating condition, which will be referred as the case study for theremainder of this manuscript. The case study corresponds to solid/liquid flowwith a particle concentration of 5 lbm/1000 bbl, a fluid density of 850 kg/m3,a fluid viscosity of 15 cp, a particle density of 2630 kg/m3, and a particlediameter of 60 µm, for flow in a horizontal pipe with a diameter of 8.25inches. As can be seen from Fig. 1, the values of the predicted sand transportvelocity vary over four orders of magniture. Therefore, out of these 40 models, it is necessary to identify the ones that will provide accurate and consistentvelocity predictions for the given operating condition.
This manuscript presents a mechodology, which, on-the-fly, determines the sandtransport models that provide accurate and consistent critical velocitypredictions for an operating condition. In what follows, the details of themethodology are summarized. Then, the methodology is used to determine the sandtransport velocity for the case study, and the results are discussed. Finally, the last section provides concluding remarks and the future directions of thecurrent study.

Methodology
Our database contains 478 sand transport data for gas/solid flow and 161 sandtransport data for liquid/solid flow, for a total of 639 data points, all ofwhich were obtained from open literature [1, 2, 5-19], where the authors whoconducted the studies were interested in quantifying the sand transportvelocity for different sets of operating conditions. In addition, for thevelocity predictions, 40 sand transport models were considered, and similar tothe sand transport data, the models are also publicly available from theliterature [1-4, 7, 9-11, 18, 20-47], and the models were developed to predictthe velocity required for transporting solids given an operating condition.