First-principles theory + validation = predictive power
Advanced process models are constructed in such a way that they predict operation accurately over a wide range of process configurations and conditions, allowing rapid exploration of the design or operating space.
Their predictive power derives principally from the combination of first-principles theory and real-life data.
What is Advanced Process Modelling?
Advanced process modelling is a combination of three elements:
- mathematical models based on chemical engineering first-priciples theory
- experimental data – laboratory, pilot or operating plant – used to fit the empirical parameters in the model (or 'validate' the model)
At this stage the model may be used for simple steady-state or dynamic simulation. However typically the investment in the advanced process model is leveraged using
- advanced solution techniques – for example, optimisation – to exploit the rich information in the model to its full extent.
This differs significantly from the application of the 'black-box' models typically found in traditional process flowsheeting simulators.
The three elements are explained in more detail below.
1. First-principles models
First-principles chemical engineering models typically comprise heat and mass transfer, equilibrium (or rate-based models based on multicomponent diffusion), reaction kinetics, hydraulics and geometry relationships.
Models can be lumped-parameter or distributed in a number of dimensions, including, for example, particle size distributions.
Where do first-principles models come from?
Theoretical models can come from a variety of sources:
- PSE provides an extensive set of first-principles models with its various products
- Others, such as specialist reactor configurations, can be supplied or tailor-made on request
- For people who want to construct their own models, research literature is an excellent source. Many papers are published containing models in equation form.
gPROMS advanced process modelling power
PSE's gPROMS® is specifically designed to allow easy transcription of mathematics from paper to model. The process is shown in schematic form in the following diagram:
Once a model has been constructed and the equations have been verified, it is possible to add an icon, port specifications and user interface elements such as specification dialogs and reports.
The model can then be added to a library and used in flowsheets just like any other library model.
Steady-state vs. dynamic
Note that until now there has been no distinction made between steady-state and dynamic model applications. Advanced process models should be fit-for-purpose; if heat and material holdups are not important, they can be steady-state; if transients are to be studied, they will be dynamic. gPROMS caters equally for steady-state and dynamic models.
Advanced process models are usually dynamic, in order to reap the full range of benefits of creating the model. However some of the most impressive applications have been performed using only steady-state models.
Dealing with detailed hydrodynamics
Detailed hydrodynamics are not usually addressed, as these are much better dealt with by Computational Fluid Dynamics (CFD) applications. PSE has relationships with CFD providers and has developed a number of gPROMS-CFD interfaces to handle coupled hydrodynamic and chemical phenomena.
2. Model validation
Advanced process models typically (though not always) combine first-principles theoretical models with observed – experimental, pilot plant or operating – data.
The process is known as model validation and it typically involves fitting the empirical elements of the first-principles relationships – for example, the reaction kinetic parameters, heat transfer coefficients and so on – to experimental data using parameter estimation techniques.
Validation is most important in the case of kinetic relationships – for example, reaction kinetics or crystal growth kinetics – where the kinetic parameters need to be estimated from well-defined (typically small-scale) experiments.
It is the combination of first-principles theory and real-life data than provides the powerful predictive capability of such models.
3. Advanced solutions
Once a predictive model has been constructed it can simply be used for steady-state or dynamic simulation. However the real power in advanced process modelling lies in the ability to exploit the rich information in the model to optimise the design or operation, using an arbitrary objective function and constraints.
gPROMS is supplied with state-of-the-art optimisation techniques:
- continuous steady-state and dynamic optimisation (example: "determine the grade-change sequence that minimises off-spec production")
- mixed integer optimisation, for making integer or discrete decisions (example: "find the optimal distillation feed tray location").
A large number of decision variables can be manipulated simultaneously. For example, the Repsol whole-plant economic optimisation mentioned above varied 49 variables that included reactor geometry, distillation column size, operating conditions and product specifcations, distillation feed tray locations, and process routing decisions, among others, to determine the economic optimum.
The following are typical applications that leverage the power of advanced process modelling:
- optimising a batch crystallization recipe
- minimising the amount of platinum catalyst used in a fuel cell, taking performance requirements into account
- optimising the design of a gas-to-liquids process (simultaneously optimising the catalyst size)
- determining the optimal safe start-up of a shut-in oil well.