Crystallization

Simulation and modelling challenges

Wrong size crystals?

The gPROMS Advanced Model Library for Solution Crystallisation represents the state-of-the-art in crystallisation modelling

Mass transfer and surface integration growth kinetics

Typical growth kinetic equations (implicit in L and T)

Hybrid Multizonal schematic – click to see more

Hybrid Multizonal links gPROMS zone models to CFD

Parameter estimation showing confidence interval

Crystal size vs. time at startup – click to see more

Dynamic simulation: crystal size vs. mass density and time during startup

Although crystallisation is one of the older unit operations in the chemical industry, the design and operation of crystallisation processes still pose many problems.

These are mainly related to product quality and process reliability, and lead to reduced production, lower commercial value of products and operating problems with downstream solids operations such as filtration.

Decision support based on accurate quantitative information from rigorous process and product models is considered key to achieving optimal crystalliser design and operation.

However, until recently, there have been few tools capable of providing the required capabilities. This is because modelling of crystallisation processes poses a number of challenges.

The challenges

The key challenge is representing the inherent physical and chemical complexity of crystallisation phenomena mathematically, and validating the resulting mathematical model against experimental data.

Some of the key challenges, and the way that these are addressed by PSE's products and services, are listed below.

Challenge: Population balance modelling

Population balance modelling is required in order to represent the crystal (particle) size distribution (CSD or PSD) accurately under all circumstances.

Various means, such as the use of moments, have traditionally been used to circumvent this problem, but these typically provide a poor representation of the size distribution.

The situation is further complicated by the fact that in order to accurately represent certain crystallisations, multiple population balances are required.

All the models in the gPROMS Advanced Model Library for Solution Crystallisation (AML:SC) use a population balance approach. If necessary, models can be readily tailored to represent multiple population balances.

Challenge: Representation of kinetics of fundamental crystallisation phenomena

Within the population balance framework, it is possible to represent the key phenomena affecting crystal development: nucleation, growth, agglomeration and attrition.

This involves complex, often implicit sets of equations that need to be solved for and often over each element of the population balance.

Moreover, the accurate representation of kinetics requires accurate determination of the kinetic rate constants (see model validation below).

In gPROMS, these phenomena are described simply by writing relationships such as the ones on the right in gPROMS language. gPROMS is designed to solve large numbers of implicit equations.

Challenge: Hydrodynamic effects

Crystallisation and in particular nucleation is significantly influenced by the hydrodynamics of the system. For example, secondary nucleation by means of attrition is a result of crystal-impeller or crystal-wall collisions and the nucleation rate is thus related to local velocities around impellers, inlet nozzles, etc.

Crystal growth rates, in particular when the growth process is diffusion-controlled, also depend on local hydrodynamic conditions as these determine the thickness of the boundary layer surrounding the crystal through which the solute molecules or ions need to diffuse.

Finally, segregation or classification of crystals in systems where there is a significant density difference between the solid and liquid phase is a direct result of the solid and liquid phase hydrodynamics.

Hydrodynamic effects are a particularly important consideration during scale-up, where the hydrodynamics in different parts of the target production vessel can differ significantly from the original laboratory equipment.

The Hybrid gPROMS–CFD Multizonal interface allows connection between gPROMS well-mixed zone models – representing the crystallisation process – and Computational Fluid Dynamic (CFD) models – representing the detailed hydrodynamics of the system. This provides an unprecedented degree of accuracy for scale-up.

Challenge: Model validation, using parameter estimation

Investment in experimental analysis techniques is a crucial step towards better process understanding. Model validation techniques allow the most efficient extraction of the information contained in experiments.

Even though the fundamental crystallisation phenomena may be well represented using first-principles relationships, in order for these to represent the observed behaviour accurately it is necessary to provide accurate values for parameters such as the growth kinetic rate constants.

These values are typically derived from experimental or pilot plant data using parameter estimation techniques in a process called model validation.

To do this effectively requires estimation techniques that are capable of extracting the maximum amount of information from experimental data, including dynamic experiments which usually contain much more information than steady-state ones.

gPROMS has technology-leading model validation capabilities, built on the foundation of state-of-the-art parameter estimation and experiment design techniques.

gPROMS' parameter estimation facilities work with both dynamic and steady-state experimental data (simultaneously if required). Results include a full statistical significance analysis of the quality of estimates.

Challenge: Gathering the required experimental data

Frequently the information necessary to provide the required parameter accuracy is not available from the available experimental data.

This means that further experiments are required to fill in the missing information. The question is, which experiments?

gPROMS' model-based experiment design capability – part of our Model-Based Innovation service – uses models of the experimental setup to design the optimal next experiments. This maximises the information content of the experimental data with respect to the parameters being fitted.

The approach ensures that the maximum amount of information is extracted from the minimum number of experiments, reducing experimentation time and cost.

Challenge: Dynamics

Many crystallisation processes are batch processes, and are thus inherently dynamic. In order to represent them accurately, it is necessary to use dynamic simulation models.

gPROMS is a dynamic simulation tool, specifically designed to be able to simulate and optimise batch processes. AML:SC models – as with most models built in gPROMS – include full dynamics. If required, models can be written for steady-state only, or dynamic models can be solved for steady state.

A major advantage of gPROMS is the ability to apply dynamic optimisation to, for example, determine optimal batch recipes.

Challenge: Optimisation

Almost all simulation is about optimisation of a particular aspect of design or operation.

Currently most "optimisation" is done manually by performing repeated simulation runs. This is not an efficient approach, nor will it ever find the optimum in a complex case such as optimisation of a batch recipe.

gPROMS' rigorous mathematical optimisation allows you to establish optimal designs of crystallisers and their control systems by posing the objectives and constraints directly. It can also be used to derive optimal steady-state and/or dynamic operating procedures while satisfying all important constraints on product quality and throughput.

Integer (or discrete) decision capability means that you can also determine the optimal number of stages – or, for example, the optimal seeding stages – for a multi-stage operation.

Challenge: Flowsheeting capability

In most cases it is not enough to just represent the crystalliser vessel; the associated heat exchangers, pumps, centrifuges and pipework are also important, particularly when it comes to continuous crystallisation systems including mother liquor recycles.

gPROMS is a complete graphical flowsheeting system. In addition it has many capabilities that assist in the creation of flowsheets for crystallisation processes, such as an open-source Process Model Library of typical processing equipment, and fully-configurable stream types.

Challenge: Modelling effort required

Until recently there have been very few models available capable of describing crystallisation phenomena to any degree of accuracy.

Standard flowsheeting tools have ignored the area, and most of the viable standalone models have been written in FORTRAN, C++ or Delphi, requiring significant programming effort for both the physical model description and numerical solution techniques.

Most of the latter are 'black box' models that allow only limited user configuration or require programming to change, and lack flowsheeting or model validation capabilities.

The gPROMS Advanced Model Library for Solution Crystallisation (AML:SC) contains largely open-source fully-configured state-of-the-art population balance models. The default kinetics and thermodynamics can be customised as required.

If preferred, users can build models from scratch using gPROMS' powerful modelling and solution capabilities. Only the fundamental physical and chemical relationships need to be described; all mathematical solution is taken care of automatically by gPROMS and no programming is required.

Most customers' preferred solution is to use PSE's ModelCare services to work closely with their modelling, R&D and Engineering personnel. This ensures rapid project delivery and transfers modelling know-how to the internal teams.