gPROMS v3.3

Model initialisation

Initialising flowsheets of complex units with recycles has been a challenge in the past

Most models of practical interest – for example detailed reactor models in conjunction with separation sections – are very large in terms of numbers of equations, and often highly nonlinear.

Conventional numerical solution methods for such models often have difficulty in establishing initial solutions, even if given good starting guesses for unknown variables.

gPROMS v3.3 includes a revolutionary toolbox of initialisation techniques – embodying many years' fundamental R&D – that have been developed specifically to address this challenge.

Background and purpose

This exciting new development allows users to combine the modelling power of the gPROMS equation-oriented environment with the robustness of initialisation that has traditionally been exhibited by sequential modular simulators.

Dr Pablo Rolandi, Head of gPROMS Software Development

In the past, an advantage of sequential-modular simulators was the ease of obtaining an initial solution.

This was tempered by the fact that it was often difficult to converge systems with recycles, the solution approach limited the complexity of process that could be simulated, and it was not practical to perform optimisation with more than a few optimisation variables.

While the advantages of equation-oriented environments such as gPROMS for rapid solution of large-scale real-world systems have been well known for many years, obtaining an initial solution for such systems has remained a challenge until now.

This ground-breaking development from PSE combines the initialisation robustness of sequential-modular simulators with the power of the gPROMS equation-oriented environment by capturing the knowledge of experienced modellers in the form of initialisation procedures implemented within the model.

Details

See the gPROMS v3.3 release notes for further detail

Standard initialisation techniques use initial guesses for the values of unknown variables to attempt the solution of the equation set for unknown values. This works well for systems in which there is not a high degree of non-linearity.

Most processes that involve reaction or phase equilibrium are described by highly non-linear equations. Initial guesses that work for some scenarios will not necessarily work for others; in any case it is impractical to expect users to provide large numbers of initial guesses. This severely limits the ability to provide general models that are robust over a large envelope of operating conditions.

gPROMS's new Initialisation Procedures provides a set of techniques to establish of a nominal feasible point from poor initial guesses, and then progress in a rubust fashion from that nominal point to the actual solution.

How it works

An Initialisation Procedure uses model-specific knowledge to assist the solution process by providing a number of intermediate 'solution' steps along the path to the final desired solution.

Consider the following examples:

Example 1: initialising a 3D fixed-bed reactor model:

Set the reaction rate constant to zero and solve the non-reacting problem. This provides an initial consistent mass and energy balance.
Now switch the reaction on, but specify the temperature profile. This provides a solution with approximately correct product compositions.
Now let the energy balance determine the temperature profile. This provides the final desired solution.

Example 2: initialising a rate-based distillation column model with a purity specification

Ignore the purity specification for the time being – specify the reflux ratio instead.
Now set the inter-phase mass transfer to zero, and solve the column model. This provides an initial converged solution for the column (which doesn't do any separation at this point …)
Now switch the separation on by allowing calculation of the inter-phase mass transfer. This will provide a solution for the real distillation column, but with a reflux ratio specification
Now unspecify the reflux ratio and get the purity to reach the required specification. This provides the required solution

Initialising a single distillation column

gPROMS language showing different equations used in normal and simplified mode

The steps in these examples simply echo the approach that any experienced modeller would take to achieve an initial solution. The major advance of gPROMS v3.3. is that it is now possible to embed these procedures within the gPROMS model so that they can be automatically invoked when the model is used as part of any other model, for example in a flowsheet.

gPROMS v3.3 contains a set of language additions for Initialisation Procedures, which can be seen in more detail in the gPROMS v3.3 release notes.

Example

Simple equilibrium distillation

Dialogs and gPROMS language for a simple steady-state equilibrium distillation column are shown above right (click to enlarge).

The gPROMS model contains different sets of equations for simplified and normal mode of calculation. The normal calculation uses that results of the converged simplified calculation as its starting point.

Interlinked distillation columns with heat intagration and recycles

Consider the more complex steady-state distillation problem on the right. This is a representation of an air separation unit (ASU) which separates air into three product streams.

Typically each of these columns presents solution difficulties in its own right, and the combined system of interlinked columns (with its heat integration of reactant and product streams, reboilers and condensers) is difficult to converge.

Approach

Two-step procedure for initialising a complex distillation flowsheet

Flowsheet state after step 1

Achieving the initial solution follows a two-step approach:

Step 1: Each of the columns is converged individually, with the recycles broken, using an approach similar to that used for the rate-based distillation above. This takes a few minutes. In the example the indicators on the columns turn from red (unconverged) to amber (converged but not connected).
Step 2: Then the columns are connected and converged as a whole. Again, this takes a few minutes. The indicators on the columns turn from amber to green (connected flowsheet converged).

Once initialised, the system will iterate rapidly to a solution, despite the numerous recycles. This means that altering specifications and rapidly recalculating results can be done efficiently and robustly.

Because – once initialised – the system solves rapidly, it is possible to add optimisation calculations that seek the optimal values of decision variables directly, rather than by trial-and-error iteration as is traditionally the case. Optimisation can be used to determine the optimal location of feed trays, number of stages, reflux ratio and many other quantities of interest.

PSE acknowledges the support of the London Development Agency for the fundamental R&D involved in this development.

Like to know more?

Request a WebEx or on-site update