Article by Rob Barrett CEng MIChemE

Rob Barrett explains how dynamic simulators can be emulated using a series of steady-state models

PROCESS simulation software has become almost universal in the chemical engineering sector, and many students have access to at least one commercial process modelling software package at university. Industry professionals are increasingly using software to model their processes. However, dynamic modelling (that accounts for time-dependent changes in the state of a system) is still, for many, an unknown quantity within the chemical engineering sector, and is more expensive than steady-state modelling.

The basic software that most engineers are familiar with (HYSYS, UniSim, CHEMCAD etc) tends to be based on steady-state systems; that is, the assumption that there is no accumulation of mass in the system – mass flow rate and composition do not change over time. In reality, there is no such thing as steady state, and constant change is taking place. However, this is often at such a negligible rate that a steady-state process is a convenient and sound assumption for many processes within the operating envelope.

There are many instances for which a plant cannot be assumed to be at a steady state, with the rate of change in the system too significant to ignore. For example, what is happening at plant startup? The mass flow rate is changing over time as the process is ramped up, and temperature and pressure are changing due to unit processes coming on-line, as well as the dependent properties that are affected by these changes.

Once a continuous-flow plant is operating at normal conditions, there are still limitations to what a steady-state model can show. Say you have a steady-state model, for example, a vessel with a heat duty. If the heat duty is in kilojoules per hour (kJ/h), then the steady state model will show the physical properties of the fluid at the end of that hour. But what if you prefer to know what happens in that vessel over the course of this hour? One answer involves dynamically modelling the process.

## Dynamic modelling

Based on fundamental engineering principles, dynamic modelling software uses mathematical functions to describe the behaviour of a process over a specified amount of time. Unlike steady-state models, dynamic models calculate the rate of accumulation of mass and energy in a system in a given time, allowing greater scrutiny of the process and a more in-depth analysis of the pathway from initial to final state.

An accurate dynamic model can help to predict plant behaviour by changing any number of variables, such as change in ambient temperature, inadvertent valve closure, loss of utilities etc. It can also provide a basis for process control philosophies. If a process is modelled with sufficient rigor, the use of dynamic modelling software can be greatly beneficial to a process engineer.

If a process is modelled with sufficient rigor, the use of dynamic modelling software can be greatly beneficial to a process engineer... however, what if you don’t have the means to dynamically model a process?

However, a question may then arise: What if you don’t have the means to dynamically model a process? The software, despite being provided for free at universities, can often be very expensive in industry, and the requirement for additional tokens or licences to run the software in dynamics mode may not always be seen as the most cost-effective use of company resources. Models with any degree of complexity may prove time-consuming to build. Often, training is required even for users with extensive knowledge of the software in steady-state mode.

Although the trend for dynamic modelling will almost inevitably increase in the future, it is often seen as an unnecessary luxury as we become more reliant on technology.

## Pseudo-dynamic modelling

One solution is to adapt a steady state model into a ‘pseudo-dynamic’ model. A pseudo-dynamic model is an approximation of a dynamic model using a series of steady-state models to represent time steps. The steady state or equilibrium conditions at the end of each time step represent the state of the system at that point in a manner which, if modelled rigorously, can closely match that of a dynamic model.

There are some limitations when using pseudo-dynamic models. For example, they are not a good fit for processes that involve chemical reactions

In many cases (but not all) this method can provide sufficient accuracy so as to negate the need for dynamic modelling of a dynamic problem. However, as discussed later in the article, the model builder must be aware of certain limitations.

Let’s discuss an example of how to pseudo-dynamically model a multicomponent relief event for a fire case.

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