Equation-oriented modelling comes of age

Next-generation process modelling power creates new value

It has long been agreed that the equation-oriented (EO) modelling approach has significant advantages over the current generation of sequential-modular (SM) simulators in terms of robustness, speed and power.

However, the challenges in obtaining an initial solution have limited the practical application of EO modelling environments, with projects requiring specialist modellers and long development times.

Recent breakthroughs mean that a new generation of process simulators, led by PSE’s gPROMS Process®, is now paving the way for a range of advanced, high-value applications that enable chemical & petrochemicals organisations to create new value and competitive advantage.

What is the difference?

The difference in the approaches is shown schematically below, along with their respective advantages and disadvantages.

Sequential-modular approach

Process units are solved in sequence, starting with the feed streams.


  • Easy to use, and quick for simple calculations
  • Failure is rare, and clear diagnostics are issued
  • User interfaces and special solution methods can be hand-coded for each module.


  • In-built directionality from inlets to outlets make ‘downstream’ specifications (e.g. product specs) difficult
  • Recycles may be (very) slow to converge, or fail to converge
  • Poor handling of multiple or complex recycles
  • Difficult to add new custom models; the user needs to code the solution method as well as model physics and chemistry
  • Optimization capability is very limited
  • Many other limitations for more complex problems.

Generally limited ability to create value beyond basic heat-and-material balance accounting.

Equation-oriented approach

The process flowsheet is treated as a set of equations to be solved simultaneously.


  • No inherent directionality of computation – can be solved with any valid degree-of-freedom specification
  • Multiple recycles do not slow down convergence – they are simply treated as any other equation
  • Powerful optimization, including integer decisions
  • Powerful custom modelling, with no need to program the mathematical solution
  • Repeat solution is much faster, making it possible to deploy large, complex models in demanding situations such as online real-time optimization.


  • Numerical solvers may fail to find an initial solution unless good initial guesses are provided for all key variables
  • It is often difficult to provide meaningful diagnostics on failure, making debugging difficult.

Generally capable of providing much more value but disadvantages have limited use to only the most experienced modellers.

A new and disruptive technology for the process industries

PSE’s many years of pioneering R&D into model and flowsheet initialization techniques have changed this picture.


Unit models can now be written in such a way that they capture the model writer’s experience within built-in Model Initialisation Procedures (MIPs), which help the unit to initialize without the need to preset variables.

At a flowsheet level, automatic flowsheet initialization procedures determine the most robust solution approach, and use homotopy-continuation techniques to ensure that even the most complex flowsheets can be solved rapidly with relative ease.

These techniques are embedded in all PSE’s gPROMS Process library models, which makes solution as or more robust than in the equivalent SM environments.

The combination of the power of the gPROMS equation-oriented approach with the ease-of-use of traditional flowsheeting tools represents a new and disruptive technology for the Chemicals & Petrochemicals industry and other sectors where process flowsheeting tools are in widespread use.

What is now possible?

By combining the ease of use of traditional flowsheeting packages with the modelling and solution power of the equation-oriented approach, gPROMS Process provides many new ways to create value and competitive advantage:

High-fidelity reactor modelling

It is now possible to include high-fidelity, multi-scale reactor models within process flowsheets and solve these rapidly to optimize process designs taking all relevant interactions into account.

Handle multiple recycles easily

Because equation-oriented solvers treat recycles as “just another equation”, it is now possible to simulate complex processes – for example, air separation flowsheets – in seconds rather than hours. This makes possible advanced applications such as sensitivity analysis or whole-plant optimization.

Design complex dynamic processes

Equation-oriented solvers handle highly dynamic processes such as periodic separations – for example, pressure-swing adsorption – robustly and with relatively rapid solution, making optimization a practical reality.

Include equipment configuration

The state-of-the-art optimization capabilities available with the equation-oriented approach make it possible to include equipment configuration decisions – such as the number of trays in a distillation column – in the optimization.

Easy creation of custom models

Powerful custom modelling capabilities allow companies easily to capture corporate knowledge in models and deploy these across the organisation to create competitive advantage.

Powerful data processing

Advanced parameter estimation capabilities allow processing of multiple steady-state and dynamic experiments to fit multiple parameters simultanously – enabling experimental data to be used to provide a greater predictive capability.

… and going further …

The speed and robustness advantages mean that it is now possible to:

Whole plant optimization

… perform whole-plant economic optimization involving many tens of continuous and integer (discrete) decision variables on large-scale plants.

Multi-site optimization

… perform optimization of multi-site or regional operation considering many decision variables simultaneously to ensure optimal asset utilisation.

Sensitivity analyses

… perform perform sensitivity analyses using Global System Analysis techniques to explore the decision space rapidly and effectively.

Online applications

… apply high-fidelity applications online for monitoring and operational optimization using high-fidelity models.