#### Quantifying Uncertainty in Computer Model Predictions

The U.S. Department of Energy has great interest in technologies that will lead to reducing the CO_{2} emissions of fossil-fuel-burning power plants. Advanced energy technologies such as Integrated Gasification Combined Cycle (IGCC) and Carbon Capture and Storage (CCS) can potentially lead to the clean and efficient use of fossil fuels to power our nation. The development of new energy technologies, however, takes a long time, as the technologies need to be tested at multiple scales, progressing from lab scale to pilot scale to demonstration scale before widespread deployment. In addition to developing new energy technologies, NETL’s research is working to reduce the cost and time of technology development.

Advanced modeling and simulation capabilities can significantly reduce the time and cost of the development and deployment of energy technologies. In particular, modeling and simulation can be used to increase the confidence as technologies are scaled up, such as, for example, when designing a 285 MWe gasifier based on data generated from a 13 MWth pilot-scale gasifier. This allows the rapid scale-up of technologies, reducing or even avoiding costly intermediate-scale testing. New designs can be tested with the help of simulations to ensure reliable operation under a variety of operating conditions. However, before simulation results can be used with confidence for scale-up, the reliability of the predictions must be established. Therefore, in 2011, NETL initiated work on the verification, validation and uncertainty quantification of multiphase computational fluid dynamics (CFD) models that underpin the simulation of several advanced energy technologies, adapting methods developed for other applications such as the stewardship of the nuclear stockpile. This involves exploring “how to make models as useful as possible by quantifying how wrong they are” as stated in a National Academies report, the basic idea being quantifying the uncertainty in the predictions.

Multiphase CFD models, for example, have the ability to predict the performance of scaled-up fluidized bed reactors, but they must be validated with data from small, pilot-scale units. The validation studies usually report the ability of the model to agree with measured values in qualitative terms (e.g. , “good” agreement). Because various sources of uncertainty unavoidably get introduced by the time a numerical solution is computed, even though multiphase CFD models are based on a set of deterministic mathematical equations, the ideal of a “perfect” agreement between model and experiment is practically unachievable.

NETL’s objective is to demonstrate how a comprehensive uncertainty quantification method can be adopted for describing the validity of multiphase CFD models. A gasifier simulation, for example, uses a set of input parameters taken from the design (e.g. , geometry specifications, gas/solid flow rates, and composition) and laboratory measurements (e.g. , chemical reaction rates) and predicts the quantity of interest (e.g. , carbon conversion, pressure drop). There exist a number of challenges when applying uncertainty quantification techniques. In multiphase flows, for example, many uncertain parameters exist. Another challenge may be the computational cost, requiring a compromise in terms of the grid resolution used. Since the governing physics in multiphase flows is more complex than in single phase flow simulations, the computational cost increase plays a key role in the determination of adequate sampling technique and number of samples.

Using a framework established by earlier researchers in this field, NETL researchers apply the following steps to describe the validity of the models they use and the differences observed in predicted vs. observed phenomena: (1) identify and characterize the sources of uncertainty as being uncertainty due to inherent variation in a quantity (aleatory) or uncertainty due to information missing on the part of modelers or experimenters (epistemic); (2) understand the propagation of uncertainties using quasi-Monte Carlo, Latin hypercube, orthogonal arrays, etc. calculations; (3) estimate uncertainties due to numerical approximations (e.g. , discretization errors); (4) estimate uncertainty in experimental data; and (5) estimate model form uncertainty.

Some preliminary results of this research were published in two 2013 papers titled “Validation and Uncertainty Quantification of a Multiphase Computational Fluid Dynamics Model” and “Applying Uncertainty Quantification to Multiphase Flow Computational Fluid Dynamics,” that were published in *Industrial & Engineering Chemistry Research* journal and in *Powder Technology* journal, respectively.

**Contact: **Mehrdad Shahnam, 304-285-4546 and Madhava Syamlal, 304-285-4685