The pH neutralization process model

7.1.1 The pH neutralization process model

As explained above, the first primary objective of this research involved modelling a pH neutralization process for the pilot plant installed at UTP. The main feature of interest in this pilot plant is that it incorporates instrumentation and types of actuators that are currently being used in the process industries. It is believed that, from this point of view, the investigation has provided realistic solutions which may be of direct interest to industry.

The approach adopted for the modelling process is based on the use of physical and chemical principles and fundamental laws, using a conventional mathematical modelling process, coupled with information obtained from preliminary tests carried out on the pilot plant itself in order to obtain estimates of certain parameters which were not known a priori. This physico-chemical modelling approach is a rigorous and generally applicable method of deriving dynamic equations for a pH neutralization process using a type of representation based on the concept of a continuous stirred tank reactor (CSTR) model. This was the modelling approach introduced by McAvoy in 1972 for this type of process application.

The pH neutralization process model that was first developed provided a form of dynamic response which was in agreement with most published results in the literature, especially in terms of the simple titration curve experiments. During the model analysis stage, the developed model provided useful insight associated with the theoretical understanding of factors such as the influence of concentration and flowrate on the pH neutralization process. In terms of the initial model verification and validation process, the computer-based simulation results also demonstrated behaviour that is broadly similar to the dynamic characteristics found from tests carried out on the actual pilot plant. However, some important differences were found between responses of the model and system for particular test conditions.

Thus, it may be concluded that the first model is satisfactory, reliable and adequate for representation of the actual behaviour of the pH neutralization plant but has some important limitations. Although these results were encouraging and suggested that the developed model could be used to provide a model for the development of various types of intelligent controller, subseque nt enhancement of the data acquisition system and the associated user interface made more complex experiments possible. These allowed an improved simulation model to be developed which led to the possibility of further improvements in the performance of control systems implemented on the pilot plant.

Further investigation of the improved model at the formal model validation stage has also been performed successfully. Transients observed in computer-based simulation of the developed model were critically evaluated through comparison with experimental results. This more detailed investigation of the model was feasible using the new and improved system for distributed data collection and control system that was installed on the pilot plant mid-way through the current investigation. This new system offers much more flexibility in terms both of implementation of control schemes and dynamic testing of the system under open- loop conditions. It was observed that the model first developed showed some discrepancies when its responses were compared with the response from the pilot plant. Thus, based on these differences in behaviour and more detailed analysis of the model it was concluded that some assumptions made during development of the first model were unacceptable and needed to be revised.

In the re-evaluation of the pH model it has been established that two factors could be changed to ensure that the model provides dynamic responses more consistent with those observed on the plant itself. The first of these related to the values of the dissociation constants. Using the dynamic response from the pH neutralization pilot plant new dissociation constant values were determined from plant observations rather than from theory.

The modified dynamic model of the pilot plant has been compared in detail with the results of experiments on the pilot plant. Detailed investigations were carried out, during the model validation process, where the dynamic response from the pH model was tested and analysed in several ways. Based on graphical evaluation, the dynamic response from the improved model was very similar to the dynamic transient of the pilot plant. In terms of more detailed point by point evaluation within records and statistical analysis, it has been shown that the data from the computer-based simulation are very close to the experimental data. The final evaluation involved a comparison of experimental and model time series using Theil’s Inequality Coefficient (TIC). The outcome from the TIC analysis has successfully sho wn that there is a good agreement between the developed model and the actual transients in the measured responses from the actual plant.

Therefore, in general terms, it may be concluded that the developed pH model with a new set of dissociation constant s has successfully demonstrated dynamic performance which is adequate for control system design purposes when compared with the actual pH neutralization pilot plant. Thus the development of the nonlinear dynamic model for the pH plant has been successfully achieved. The simulation results from the computer-based simulation demonstrate behaviour that is very similar to the actual pilot plant, taking into account the uncertainties in measured quantities and model parameters.

The second significant factor related to imperfect mixing. Although representation of imperfect mixing was not incorporated in the final version of the pH model, investigations indicate it is a key factor that needs to be explored further. It was observed that the volume of the reactor tank in the pH neutralization pilot plant is larger than the volume of reactor tank used in most previous reported studies. Thus the initial assumptions in which the acid-base reaction process in the reactor tank is taken to be instantaneous and the tank is assumed perfectly mixed at all times were judged to be inappropriate. It is believed with an additional representation and more experimental work involving rigorous external validation and evaluation of models, a new pH model can be developed which will be able to represent the behaviour of the pilot plant even more accurately.

7.1.2 The implementation of the feedback/feedforward control scheme