(301e) A Predictive Approximation Based on Squeeze Functional in Solving Large Scale Dynamic Simulation Problems

The performance requirement for large scale dynamic simulation of an industrial
process is especially important when used in an operator training simulator (OTS),
which is usually integrated with an emulator of a distributed control system (DCS).
While coupled with such a DCS system, the dynamic simulator must be able to respond
faster than real-time to process variations and upsets. Without this performance
requirement, model fidelity will suffer and the simulator may fail to predict dangerous
process conditions or warnings. In this paper, we address the performance issue by
introducing a predictive approximation of physical properties based on the concept of
a squeeze functional. Proof of accuracy and computational performance enhancement
are given by examples, including dynamic simulation of a polyethylene synthesis process
using the PC-SAFT model and an olefin metathesis process using NRTL model.

Industrial-scale steady-state and dynamic process simulations often involve large-scale nonlinear
equation solving problems. For example, typical refinery plant simulations may require
solving the nonlinear phase equilibrium equations for systems of hundreds of components or
pseudo-components. Such large-scale nonlinear equation solving problems may be computationally
expensive, yet for dynamic simulation, high computational performance is still
a requirement that must be satisfied. A well-defined dynamic simulator can help to make
decisions by providing a virtual representation of a real plant, from which digital feedback
of an operation (or a series of operations) can be obtained before the real feedback happens.
Such a simulator is often regarded as a digital twin of a real plant that can provide a glimpse
into what is happening, what can happen, and most importantly, what is going to happen
within the real plant. For the digital twin to provide such an efficient and reliable representation,
the underlying thermodynamic models must be chosen carefully. For example, typical
cubic equation of state models may not be sufficient to represent a polyethylene synthesis
process. Instead, modern thermodynamic models such as PC-SAFT[1] must be considered
to simulate phase equilibria that involve solvent, monomer and polymer molecules at high
temperature and pressure. The modeling accuracy from such modern thermodynamic models
comes at the cost of computational performance, as such models are significantly more
complicated than typical cubic equation of state models such as Soave-Redlish-Kwong[2] or
Peng-Robinson[3]. As a result, when simulating real-time operations, a virtual representation
using such modern thermodynamic models could fail to provide feedback faster than realtime.
Such performance issues could lead to failure in predicting warnings (or even disasters)
within the real plants.

To overcome such performance issues, different ways to approximate the digital feedback
have been developed and applied. One method to gain performance while retaining accuracy
under a certain tolerance is to apply linear approximation within a defined region where
operation conditions are not changing significantly. Such an approach is still based on the
underlying thermodynamic models, and thus can be considered a first-principles approach.
In recent years, machine learning (ML) has also been considered in the approximation of
the phase equilibrium result in order to gain performance[4,5]. While each of these approaches
may have its advantages, neither provides a guarantee on simulation accuracy, especially
under conditions involving critical variations such as start up and shut down of the real
plants. For the first-principles approach, the modeling accuracy may fail if the variations in
the real plant are outside of the predefined region of the property approximation, leading
to uncertain digital representations. For the ML approach, the training process must be
done a priori using previously collected plant data, which is commonly referred to as “big
data”. However, such “big data” may never be big enough to cover all possible scenarios.
Furthermore, to be able to cover a wider range of scenarios, a significant portion of the data
collection must come from failures, which is not likely to be affordable for a large refinery or
chemical plant.
In this paper, we enhance the first-principles approach by introducing a predictive approximation
of the underlying thermodynamic model with an automatic and rigorous update
procedure controlled by a bounding gap from a pair of squeeze functional equations. It is
worth emphasizing that this approach was motivated by the well-known squeeze theorem,
by which a function value can be tightly bounded (squeezed) by a pair of bounding functions
or functionals at some reference points or limiting values. Away from such a reference point,
this pair of functionals will diverge and provide a bounding gap, which may grow as distance
from the reference point increases. The size and growth rate of the bounding gap provided
by these squeeze functionals can be used to decide whether the current linear approximation
of a physical property is still valid, or whether the next rigorous property update is needed.
A numerical validation of the accuracy and the performance improvement of this approach
is given using examples involving both simple and real process-related test cases.

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Learning Based Approaches for Vapor–Liquid–Liquid Phase Equilibria in n-
Octane/Water, as a Naphtha–Water Surrogate in Water Blends. Processes 2021, 9,
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[5] Wang, K.; Luo, J.; Wei, Y.; Wu, K.; Li, J.; Chen, Z. Practical application of machine
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