adequate experimental data to cover the
range of conditions over which the model will be used. Sometimes this occurs
because prebuilt submodels are utilized
from within commercial simulation
packages without thoroughly investigating the data and assumptions that went
into the model. Other times, this occurs
because it is difficult to measure the
properties under those conditions. Ultimately, this can be a critical oversight
causing the overall model to perform
poorly if the submodel is extrapolating
well beyond the range of conditions under which it was developed.
To overcome these issues, CCSI has
developed a comprehensive, hierarchical
model calibration and validation framework, which utilizes Bayesian statistics
and other principles of uncertainty quantification, to provide stochastic model
predictions that result in a complete probability distribution of expected behavior.
This is especially important when using
models to help predict scale-up performance since it enables confidence bounds
to be placed on simulation results. Furthermore, the sensitivity of the model
predictions to uncertainty in specific
submodels and parameters can be determined. This allows technology developers to focus additional resources on those
aspects of their process that have the biggest influence on uncertainty, which is
closely related to technical risk.
Two examples of this framework are
described below. The first is the application of the framework to a high-fidelity
computational fluid dynamics (CFD)
model of bubbling fluidized bed (BFB)
adsorber for capturing CO2 on a chemically reactive solid sorbent. The second is
the application of the framework to a sol-vent-based CO2 capture system consisting of a packed bed absorber and packed
processes by using optimization tech-
niques to focus development on the
best overall process conditions and
by using detailed device-scale models
to better understand and improve the
internal behavior of complex equip-
ment, and ( 3) provides quantitative
predictions of device and process per-
formance during scale-up based on
rigorously validated smaller scale sim-
ulations that take into account model
and parameter uncertainty. This article
focuses on essential elements related
to the development and validation of
multi-scale models in order to help
minimize risk and maximize learning
as new technologies progress from pi-
lot to demonstration scale.
Models that predict device and process
behavior are actually a series of models
that are linked together. These submodels represent physical properties, thermodynamics, chemical reactivity, heat
transfer, hydrodynamics, mass transfer,
and other aspects of the device/process.
Oftentimes, these submodels can be
hidden from the user of a macroscopic
model (such as a model for an absorber); however, the reliability of the overall
model is highly dependent on the predictive capability of all the submodels.
Thus, it is essential to rigorously calibrate and validate both the underlying
submodels as well as the overall model
to ensure that it can accurately represent
the physical system.
Parameters for submodels are typically
calibrated deterministically for each submodel, which causes a number of issues.
First, both models and experimental data
are imperfect. Thus, given experimental
error, a number of sets of parameters can
represent experimental data equally well.
By taking only the “best fit” set of parameters, the submodel may not be able to
represent the “true” behavior. When combining multiple submodels together into
an aggregate model of a process or device,
these errors can multiply, resulting in
poor predictive capability.
A second issue arises from the fact that
submodels are often coupled with one another. Thus, if the parameters of one submodel are determined in isolation from
the related submodels, the regressed value
of the parameters of the second submodel
may be far from the “true” values.
A third issue that can arise is the lack of
SaskPower’s Boundary Dam Integrated Carbon Capture and
Storage Project is the world’s first commercial-scale CCS
project. Initiatives such as this hope to preserve the viability
of the coal-fired power industry. Photo courtesy: SaskPower