(255g) Machine Learning Based Uncertainty Quantification of Erosion in Pipeline Transportation

The transport of solids in multiphase flows is common practice in energy industries because of the unavoidable extraction of solids from oil and gas bearing reservoirs. For safe and efficient operation, reliable estimates of the erosion that occurred inside the pipelines is required. However, the phenomenon that leads to erosion, especially in multiphase flow systems, is very complex and depends on many factors. Consequently, the developed erosion-rate prediction models cannot exactly capture this complicated process. In some cases, there are considerable model uncertainties in the erosion-rate predictions.

The uncertainty in model predictions can stem from three sources in general: (1) uncertainty in experimental measurements of input conditions, (2) model form uncertainty (i.e., incomplete presentation of the actual system due to lack of knowledge or imprecise experimental observations), and (3) model parameter uncertainty. The experimental data uncertainty consists of measurement errors due to both instrumental and human errors. The reliability of the models largely depends on the ability of model form to capture the details of erosion process in enough granularity. The uncertainty in the model parameters results from an inability to accurately quantify the parameters of a model (Shrestha, 2009).

In previous studies, we introduced a systematic framework to quantify erosion-rate prediction uncertainty for operating conditions where experimental data are not available (Dai and Cremaschi, 2016). The framework incorporates the impacts of model form and parameter uncertainties to estimate prediction uncertainties, and combines data clustering and Gaussian Process Modeling (GPM) (Rasmussen and Williams, 2006) approaches with Monte Carlo Simulation. The results of these previous studies revealed that our systematic framework reduced estimated prediction uncertainties by 30% when compared to applying GPM alone. Despite this reduction, the estimated prediction uncertainties remain relatively large, because the training data - erosion-model prediction discrepancy – span over six orders of magnitude. In our previous studies, the training data was normalized to [0.1, 1] to reduce its large range. Although this reduced the range of the training data, it also masked some data features, especially in regions around origin, i.e., where erosion-model prediction discrepancies were small. There were significant inconsistencies in GPM predictions in these regions, and, GPM failed to estimate the correct sign of the model-discrepancy resulting in contradicting conclusions on whether the model under or over-predicted the erosion rate. The differentiation of model over- or under- predictions has significant engineering consequences for erosion applications. Higher orders of over-predictions may result in unnecessary overdesign, increase capital costs, and limit the production efficiency. On the other hand, under-estimated erosion rates may cause facility integrity issues, and, may result in considerable downtime for unexpected repairs.

This talk will discuss a novel approach developed for overcoming these challenges. The approach distributes the data into a finer grid, yet still resolves the challenges associated with large data ranges, and hence, it enhances differentiability of data when constructing GPM. The developed approach combines GPM classification and log transformation, and introduces them to our previously developed systematic framework for model-uncertainty quantification. The training data that is used to construct GPM (erosion-model prediction discrepancy) is the difference between the erosion-model predictions and the experimental measurements for a large set of experimental and field conditions. In the developed approach, GPM-based classification (Rasmussen and Nickisch, 2010) is applied to estimate the sign of the discrepancy, while GPM regression (Shi and Choi, 2011) trained using log-transformed absolute values of the discrepancy data is employed to estimate the magnitude of the discrepancy. The approach, using our systematic framework, is employed to estimate prediction uncertainty of a well-known erosion model (Mazumder et al., 2005), which is routinely used by upstream oil and gas industry. Our analysis indicates that using the log-transformed data as inputs improves the uncertainty quantification of erosion-rate modeling, and resulted in an additional 20% reduction in prediction uncertainties when compared to the previous approach.

Acknowledgements

This work is supported by the Chevron Energy Technology Company. Discussions and comments from the Haijing Gao and Janakiram Hariprasad of Chevron and Brenton McLaury, Siamack Shirazi of E/CRC at the University of Tulsa were highly acknowledged.

Reference

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

Mazumder, Q., Shirazi, S.A., McLaury, B., Rybicki, E., and Shadley, J., 2005, Development and Validation of a Mechanistic Model to Predict Solid Particle Erosion in Multiphase Flow, International Journal of Wear.

Rasmussen, C.E. and Nickisch, H., 2010, Gaussian processes for machine learning (GPML) toolbox. J Mach Learn Res 11:3011–3015.

Rasmussen, C.E. and Williams, C.K. I., 2006, Gaussian Processes for Machine Learning, The MIT Press.

Shi, J. and Choi, T., 2011, Gaussian Process Regression Analysis for Functional Data, U.K., London:Chapman & Hall.

Shrestha, D.L., 2009, Uncertainty Analysis in Rainfall-Runoff Modelling: Application of Machine Learning Techniques, PhD. Dissertation, UNESCO-IHE, the Netherlands.