The characterization of uncertainty for steady state multiphase flow models in pipelines

Steady state multiphase flow models are used for the design and operation of pipelines that are used in the oil and gas industry. The predictions obtained with these models contain uncertainties, which arise from model assumptions and simplifications, and from uncertainties in the input parameters. In this thesis we investigate the effect of uncertainties in the input parameters (such as the wall roughness or the superficial velocities) on two main quantities of interest in steady state multiphase flow in pipelines: the liquid holdup and the pressure drop. The approach that we take is to describe the uncertain input parameters by probability density functions (PDFs), propagate these through the steady state models, and obtain a PDF for the quantities of interest. We use two methodologies from the field of Uncertainty Quantification (UQ) to perform the propagation step: Monte Carlo sampling, the current standard in the literature, and Polynomial Chaos Expansion (PCE), our proposed approach. Furthermore, we use Sobol indices to perform a sensitivity analysis that ranks the input parameters depending on their contribution to the output. Our proposed UQ methodology is applied on two commonly used multiphase flow models in the oil and gas industry: a 0-D model, the Shell Flow Correlations (SFC), and a 1-D model, PIPESIM. First, application to the SFC reveals that PCE is much more efficient than Monte Carlo sampling, and an improvement of several orders of magnitude is achieved in terms of the number of samples required for a given accuracy, while the evaluation of a single sample requires the same computation time for the two methods. Furthermore, with UQ the flow pattern maps commonly used in industry can now be displayed in a probabilistic way. This allows the quantification of the probability that a flow regime (e.g. slug, stratified) occurs under given conditions. These are significant improvements compared to existing work that handles uncertainties in multiphase flow models. Second, application of PCE to a multiphase pipeline, known as Goldeneye, modelled in PIPESIM revealed that several uncertain variables, namely the wall roughness, the ambient temperature and the outlet pressure, play a role in determining the liquid holdup and the pressure drop. This is in contrast to what was assumed in an earlier benchmarking study. Furthermore, our probabilistic approach allows us to make predictions under uncertainty. For instance, we can now predict that the liquid holdup of the Goldeneye pipeline will have a 65% probability to be lower than the value of 1496 m3, the value obtained when using a deterministic setting.