Processes, Volume 4, Issue 1 (March 2016) – 7 articles

This work presents a methodology to represent logical decisions in differential algebraic equation simulation and constrained optimization problems using a set of continuous algebraic equations. The formulations may be used when state variables trigger a change in process dynamics, and introduces a pseudo-binary decision variable, which is continuous, but should only have valid solutions at values of either zero or one within a finite time horizon. This formulation enables dynamic optimization problems with logical disjunctions to be solved by simultaneous solution methods without using methods such as mixed integer programming. Several case studies are given to illustrate the value of this methodology including nonlinear model predictive control of a chemical reactor using a surge tank with overflow to buffer disturbances in feed flow rate. Although this work contains novel methodologies for solving dynamic algebraic equation (DAE) constrained problems where the system may experience an abrupt change in dynamics that may otherwise require a conditional statement, there remain substantial limitations to this methodology, including a limited domain where problems may converge and the possibility for ill-conditioning. Although the problems presented use only continuous algebraic equations, the formulation has inherent non-smoothness. Hence, these problems must be solved with care and only in select circumstances, such as in simulation or situations when the solution is expected to be near the solver’s initial point. Full article

Chemical processes with complex reaction mechanisms generally lead to dynamic models which, while beneficial for predicting and capturing the detailed process behavior, are not readily amenable for direct use in online applications related to process operation, optimisation, control, and troubleshooting. Surrogate models can help overcome this problem. In this research article, the first part focuses on obtaining surrogate models for emulsion copolymerization of nitrile butadiene rubber (NBR), which is usually produced in a train of continuous stirred tank reactors. The predictions and/or profiles for several performance characteristics such as conversion, number of polymer particles, copolymer composition, and weight-average molecular weight, obtained using surrogate models are compared with those obtained using the detailed mechanistic model. In the second part of this article, optimal flow profiles based on dynamic optimisation using the surrogate models are obtained for the production of NBR emulsions with the objective of minimising the off-specification product generated during grade transitions. Full article

This paper discusses the initial steps towards the formulation and implementation of a generic and flexible model centric framework for integrated simulation, estimation, optimization and feedback control of polymerization processes. For the first time it combines the powerful capabilities of the automatic continuous on-line monitoring of polymerization system (ACOMP), with a modern simulation, estimation and optimization software environment towards an integrated scheme for the optimal operation of polymeric processes. An initial validation of the framework was performed for modelling and optimization using literature data, illustrating the flexibility of the method to apply under different systems and conditions. Subsequently, off-line capabilities of the system were fully tested experimentally for model validations, parameter estimation and process optimization using ACOMP data. Experimental results are provided for free radical solution polymerization of methyl methacrylate. Full article

A nonlinear reduced-order state observer is applied to estimate the degree of polymerization in a series of polycondensation reactors. The finishing stage of polyethylene terephthalate synthesis is considered in this work. This process has a special structure of lower block triangular form, which is properly utilized to facilitate the calculation of the state-dependent gain in the observer design. There are two possible on-line measurements in each reactor. One is continuous, and the other is slow-sampled with dead time. For the slow-sampled titration measurement, inter-sample behavior is estimated from an inter-sample output predictor, which is essential in providing continuous corrections on the observer. Dead time compensation is carried out in the same spirit as the Smith predictor to reduce the effect of delay in the measurement outputs. By integrating the continuous-time reduced-order observer, the inter-sample predictor and the dead time compensator together, the degree of polymerization is accurately estimated in all reactors. The observer performance is demonstrated by numerical simulations. In addition, a pre-filtering technique is used in the presence of sensor noise. Full article

This study aimed to develop optimal microwave assisted extraction conditions for recovery of phenolic compounds and antioxidant properties from the macadamia skin, an abundant waste source from the macadamia industry. Water, a safe, accessible, and inexpensive solvent, was used as the extraction solvent and Response Surface Methodology (RSM) was applied to design and analyse the conditions for microwave-assisted extraction (MAE). The results showed that RSM models were reliable for the prediction of extraction of phenolic compounds and antioxidant properties. Within the tested ranges, MAE radiation time and power, as well as the sample-to-solvent ratio, affected the extraction efficiency of phenolic compounds, flavonoids, proanthocyanidins, and antioxidant properties of the macadamia skin; however, the impact of these variables was varied. The optimal MAE conditions for maximum recovery of TPC, flavonoids, proanthocyanidins and antioxidant properties from the macadamia skin were MAE time of 4.5 min, power of 30% (360 W) and sample-to-water ratio of 5 g/100 mL. Under these conditions, an extract could be prepared with TPC of 45 mg/g, flavonoids of 29 mg RUE/g of dried macadamia skin. Full article

Kinetic modeling of the bulk copolymerization of d-limonene (Lim) and n-butyl acrylate (BA) at 80 °C was performed using PREDICI^®. Model predictions of conversion, copolymer composition and average molecular weights are compared to experimental data at five different feed compositions (BA mol fraction = 0.5 to 0.9). The model illustrates the significant effects of degradative chain transfer due to the allylic structure of Lim as well as the intramolecular chain transfer mechanism due to BA. Full article