Uncertainty quantification for multiphase flow

Abstract

The purview of this thesis is insight into, and development of, methods for uncertainty quantification in multiphase flow. The work is directed towards commercial simulators for transport of gas and liquid in pipelines and the primary quantities of interest are pressure drop and liquid holdup. In science and engineering, processes are frequently described by mathematical models, which generally include several uncertain components. The specification of model structure may be associated to simplifications or lack of knowledge. Uncertainty also arise when the state of the system is gauged. In practice, the models are implemented on computers, and are also referred to as simulators. The simulator representations of variables and operations are prone to errors as well. Also multiphase flow simulators include several layers of uncertain quantities and closure laws. Consequently, predictions are not exactly equal to the outcomes of the experiment or operation they represent. Investigations and development of methods to quantify three sources of uncertainty are described in this thesis. The focus of the first paper was uncertainty in input variables of a steady-state simulator. Uncertainty propagation with a Monte Carlo method was faster and more robust than polynomial chaos expansions. Further, the coverage of prediction intervals was satisfactory for liquid holdup but rather low for pressure drop. In the second paper, the focus is shifted to uncertainty in model formulation. Closure laws are modeled as stochastic components of the simulator, and two methods to quantify uncertainty were developed. The aim was to tune closure law uncertainty such that simulator prediction intervals were adequate with respect to observations. The two methods yielded similar estimates for closure law uncertainties. Variability is the topic of the third paper, and refers to uncertainty about the state of the process due to excluded variables or fundamental stochastic phenomena. Repeatability, which is closely related to variability, was quantified based on novel replicated experiments. The relative deviations in pressure drop and volume flow rates were found to be much less than one percent for nearly all replicates, and express a high degree of repeatability. The collection of papers constitute a comprehensive overview of uncertainty in multiphase pipe flow, in terms of variable uncertainty, model uncertainty and variability. Accessible methods are developed to quantify uncertainty to make improved predictions and more effectively plan and make decisions for multiphase pipe flow operations.