(126h) Dimensional Analysis Based Uncertainty Quantification: Modeling of Erosion in Pipeline Transportation

The transport of solids in multiphase flows is common practice in energy industries due to the unavoidable extraction of solids from oil and gas bearing reservoirs either from onshore or offshore sites. The safe and efficient operation requires reliable estimates of erosion happening in the pipelines. The phenomenon that leads to erosion, especially in multiphase flow systems, is very complex and depends on many factors including the fluid and solid characteristics, the pipeline material properties, and the geometry of the flow lines. Empirical and semi-mechanistic models have been developed to quantify the erosion rate within pipelines that transport solids in both single-phase and multiphase flows. However, due to the process complexity, the discrepancies between these models’ predictions and actual erosion rates can be very significant, e.g., several orders of magnitude for some operation conditions[1], and the uncertainty of model predictions is generally not provided.

For estimating uncertainty of erosion-rate prediction, particularly, the distribution of the model discrepancy, we successfully adopted Gaussian Process Modeling1,[2],[3] (GPM) in our previous studies. The model discrepancy is defined as the difference in erosion-rate between experimental measurement and model prediction. For erosion rate predictions, we employ a widely used erosion model[4]. The Gaussian Process Regression (GPR) model specified by a mean and a covariance function with optimized hyperparameters is used to estimate the distribution (mean and variance values) of model discrepancy2. The prediction of erosion model is then corrected by adding the mean value of the estimated model discrepancy. The estimated variance is used to calculate a confidence interval of the corrected erosion-rate prediction at a specified level. To assess the GPR model performance, Area Metric[5] (AM) is used, where a smaller AM value represents a more reliable prediction of the model discrepancy.

In this talk, we introduce dimensional analysis to extend the applicable range of operating conditions of the GPR model. The analysis starts by compiling all 11 physical variables (i.e. sand particle size and density, gas/liquid viscosity, density and flow rate, pipe diameter, gravity constant and surface tension) that influence the erosion process in a pipeline. Buckingham Pi analysis is employed to determine all 648 dimensionless numbers using 81 combinations of repeating variables. We then construct a set that contains the 366 unique dimensionless numbers. Considering the three fundamental dimensions (mass, length and time), from this set, the eight most relevant dimensionless numbers are identified using Automatic Relevance Determination[6] (ARD) approach, and these numbers are used to construct GPR models. The model discrepancy is normalized by the prediction from the erosion model to keep a consistent non-dimensional relationship between the inputs and output. Prior to training GPR models, the training data is clustered using an object-cluster similarity metric based iterative clustering learning approach[7] to capture different fundamental phenomena that governs erosion process in multi-phase flow. Seven clusters are obtained and for each cluster, a GPM is trained where the inputs are gas Galileo number, ratio of gas and liquid density, Reynolds number of gas, liquid and mixed flows, mixed Weber number, gas Froude number and gas Capillary number, and the output is normalized model discrepancy. A comparison with the uncertainty predictions developed using dimensional inputs in our previous study[8] reveals that the dimensional analysis based approach noticeably improve the prediction of model uncertainty with a 30% reduction in the overall AM value. The developed GPR models can also be extended to a wide range of operating conditions with the obtained dimensionless numbers and used as a suggestion for possible improvements in erosion process modeling and experimental design.

References

[1] Dai, W. and Cremaschi, S., Quantifying Model Uncertainty in Scarce Data Regions - A Case Study of Particle Erosion in Pipelines, 2015. doi:10.1016/B978-0-444-63577-8.50147-9.

[2] Dai, W., Cremaschi, S., A Data-Mining Framework for Uncertainty Analysis in Pipeline Erosion Modeling, 2016 AIChE Annual Meeting, November 13-18, 2016, San Francisco, CA, USA.

[3] Dai, W., Cremaschi, S., Machine Learning Based Uncertainty Quantification of Erosion in Pipeline Transportation, 2017 AIChE Annual Meeting, October 29-31, 2017, Minneapolis, MN, USA.

[4] Mazumder, Q.H., Shirazi, S.A., McLaury, B.S., Shadley, J.R., and Rybicki, E.F., Development and validation of a mechanistic model to predict solid particle erosion in multiphase flow, Wear, 259 (2005), 203–207.

[5] Ferson, S., Oberkampf, W.L., and Ginzburg, L., Comput. Methods Appl. Mech. Eng., 197 (2008), 2408–2430.

[6] Rasmussen, C. E. and Williams, C. K., Gaussian Process for Machine Learning, The MIT Press. 2006.

[7] Cheung, Y., and Jia, H., Categorical-and-numerical-attribute data clustering based on a unified similarity metric without knowing cluster number, Pattern Recognit. 46 (2013) 2228–2238.

[8] Dai, W., Cremaschi S, Subramani H.J., Gao H., Uncertainty Analysis in Multiphase Flow Prediction in Presence of Solids. In: Foundations of Computer-Aided Process Operations, 2017.