(92d) Data Clustering Based Dimensional Analysis for Uncertainty Quantification in Modeling of Pipeline Erosion

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 rates 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 talk presents a framework capable of quantifying prediction uncertainty for erosion models under a wide range of input conditions, especially focusing on regions where experimental data is scarce or not available. We applied dimensional analysis in conjunction with Gaussian Process Modeling (GPM, Rasmussen and Williams, 2006) to quantify the model uncertainties in the erosion process. Dimensional analysis is a method for grouping and reducing the number of independent variables which affect a given physical phenomenon (White, 2010). It can suggest the representation of a process using dimensionless numbers, and most importantly, provide insight into the form of the physical relationship between the response and independent variables. In the estimation of erosion-rate-prediction uncertainty in percentage, the dimensionless numbers instead of the dimensional variables are used as the inputs to the GPM. The dimensionless output is the ratio of model discrepancy to the erosion model prediction, where the model discrepancy is defined as the difference between experimentally measured erosion rates and the erosion-rate predictions from the erosion model. The GPM approach is preferred due to its capability in estimating the model discrepancy together with prediction uncertainties.

To develop GPM for the estimation of model uncertainty in erosion-rate prediction, a comprehensive database of erosion-rate measurements, consisting of measurement approaches, flow regimes and configuration details is assembled. The database covers a wide range of input conditions resulting in significantly different erosion rates. To make prediction for a new input condition with unknown erosion rate and find the most influential dimensionless numbers, a four-step approach is developed: (1) Identify all possible dimensionless groups that are relevant to erosion phenomena using Buckingham Pi theorem. (2) Cluster the dimensionless groups and select the cluster closest to the new input condition. (3) Use the selected cluster’s corresponding dimensionless numbers as the inputs to GPM. (4) Obtain the erosion prediction with uncertainty for the new input condition from GPM. A leave-one-out cross validation technique is used to validate the approach. The dimensionless groups identified in each flow regime has been shown as the most influential variables in the quantification of erosion-rate model discrepancy in percentage as the GPM adjusted erosion model predictions are comparable to the experimental data. Our preliminary analysis using model discrepancy as the output also indicates that using dimensionless numbers as inputs to GPM improves the uncertainty quantification of erosion-rate modeling, and results in a 40% reduction in the total prediction uncertainties when compared to GPM developed using dimensional inputs.

Reference

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

White, F., 2010, Fluid Mechanics. McGraw-Hill Education; 7 edition, p 277