system. In addition, rapid chemical reaction coupled with mass transfer makes it
challenging to distinguish reaction rates
from mass transfer rates in actual operating contactors. Thus, it is essential to utilize a rigorous framework to determine
submodels for the hydrodynamic, mass
transfer, heat transfer, and kinetic and
physical properties of solvent systems.
The CCSI Technical Team recently
published a systematic approach for determining model parameters with due
consideration of uncertainty in the experimental data via a Bayesian approach.
As in the above example, this approach
ultimately yields a posterior distribution
of all the parameters in the model, which
can then be propagated through the process model to obtain the bounded confidence on the model’s predictions.
Following the calibration of the parameters in the submodels, the model of the
entire process (i.e., process model) consisting of the absorber and stripper can be
validated against experimental data from
a laboratory-scale system or a pilot plant.
Validation with data from a pilot plant
provides additional information due to
change in the scale. Both steady state and
dynamic models of the process should
be validated so that sufficient trust in the
models can be built before advancing to
the next level of scale-up.
CFD models have many parameters
that must be calibrated (i.e., regressed)
from the experimental data collected
through the unit problems. The CFD
model for the first two unit problems has
six model parameters relating to sorbent
particle properties that were thought to
be important and relevant. The reaction
equations in the fully coupled model add
another 13 such model parameters. Definitions of all 19 parameters in the fully
coupled model are provided. In each unit
problem the relevant parameters of the
CFD model were calibrated.
Uncertainty quantification is explicitly
built into each step via sensitivity analysis and a Bayesian calibration approach.
Bayesian model calibration requires that
a prior distribution first be placed on the
unknown parameters to represent the
scientists’ subjective belief about what
reasonable values of the parameters
might be. The prior distribution can be
as simple as a uniform range of values, to
a more complex parametric distribution
with dependencies among parameters.
The Bayesian model calibration of unit
problem 1:32D Cold Flow results in a posterior distribution to describe the remaining uncertainty in the model parameters
. This posterior distribution of is then
used as the prior distribution for for
the Bayesian calibration in unit problem
2:32D Hot Flow. This results in a more refined posterior distribution for , which
can then be used as a prior distribution
for the final calibration of unit problem
3:32D Reacting Flow. The end result of
the hierarchical calibration is a posterior
distribution for the model parameters
that has been refined at each layer of the
hierarchy. Each subsequent calibration results in a reduction in the variance of .
The Bayesian calibration framework also
provides an assessment for model validation via an estimate of model lack of fit in
each unit problem along the way. Overall,
the CFD modeling results demonstrated
that the multi-phase reactive flow models
can be used to accurately capture the bed
pressure drop, bed temperature, and CO2
breakthrough curves of the C2U.
The final posterior distribution at the
end of unit problem 3 characterizes the
state of knowledge (or uncertainty) in the
form of a probability distribution. This
uncertainty distribution is then finally
used to predict quantities of interest, such
as percent CO2 capture, at a larger ( 1 MW)
scale with uncertainty bounds. The posterior distribution from unit problem 3 was
used to predict the percent CO2 capture
and bed height.
This hierarchical calibration and validation framework is broadly applicable
and can be used to calibrate any complex
model of a physical process where multiple relevant experimental data sources
can be obtained.
VALIDATION OF PROCESS
MODELS FOR SOLVENT-
BASED CO2 CAPTURE
Chemical solvents are among the most
promising approaches for post-combus-tion CO2 capture systems. These systems
are highly non-ideal due to long-range
ion-ion and short-range ion-molecule and
molecule-molecule interactions. Thus, the
properties of CO2 loaded solvents change
nonlinearly with a number of variables
such as temperature, solvent concentration, extent of CO2 capture, and presence
of other species such as H2S or SO2 in the
CO2 Capture Fraction and Bed Height Prediction
Distributions for a 1-MW system
CO2 Capture Fraction Bed Height (m)
0.80 0.85 0.90 0.95 1.00 5. 36 5. 38 5. 40 5. 42 5. 44 5. 46 5. 48 5. 50