Volume 4, Issue 3 - Chemeca 2008

The papers in this issue of Chemical Product and Process Modeling are substantially those that arose from special sessions on “mathematical modeling" at the 36th Australasian Chemical Engineering Conference (held between 28th September to 1st October 2008, in Newcastle, Australia). The papers in this special issue are available at: www.bepress.com/cppm/vol4/iss3.

Accurate control of product properties through the manipulation of transfer agents can be of great benefit to industry in producing targeted polymeric materials. In this work we developed experimental protocols and mathematical models for understanding and characterising semi-batch emulsion polymerization in the presence of a xanthate-based transfer agent. Zero-one kinetics was employed with population balance equations to predict monomer conversion, molecular weight (MWD) and particle size (PSD) distributions in the presence of xanthate-based reversible addition-fragmentation chain transfer (RAFT) agents. The effects of the transfer agent (AR), surfactant, initiator (KPS) and temperature were investigated. Monomer feed rate was found to strongly affect conversion, MWD and PSD. The polymerization rate (Rp), number average molecular weight (Mn) and particle size () decreased with increasing AR. Rp increased with increase in SDS and KPS; while with increase in temperature, Mn decreased, Rp increased and increased. With semi-batch mode, Mn and increased with monomer flow rate.

The breakup of a laminar liquid jet is the underling phenomena used to generate emulsions in micro-scale devices. Jet breakup is induced by the most unstable disturbance growing on the jet surface, and linear instability analysis can be utilized to predict the resultant droplet size. Previously, instability analysis has been applied to stationary jets at intermediate Re only. This study investigates the influence of the jet velocity on the jet breakup at low Re number. The breakups of moving liquid jets were monitored using a high speed camera. The jet diameter, jet breakup length and resultant droplet sizes were strongly influenced by jet velocity. In addition to a simplified solution, a linear analysis for a moving jet was developed to determine the resultant droplet size. It was found that the full analysis is required to correctly predict the droplet size at low Re number.

Recently, the demand of the steel having superior chemical and physical properties has increased for which the content of carbon must be in ultra low range. There are many processes which can produce low carbon steel such as tank degasser and RH (Rheinstahl-Heraeus) processes. It has been claimed that using a new process, called REDA (Revolutionary Degassing Activator), one can achieve the carbon content below 10ppm in less time. REDA process, in terms of installment cost, is in between the tank degasser and RH processes. As such, REDA process has not been studied thoroughly. Fluid flow phenomena affect the decarburization rate the most besides the chemical reaction rate. Therefore, momentum balance equations along with k-? turbulent model have been solved for gas and liquid phases in two-dimension (2D) for REDA process. The fluid flow phenomena have been studied in details for this process by varying gas flow rate, depth of immersed snorkel in the steel, diameter of the snorkel and change in vacuum pressure. It is found that the design of the snorkel affects the melt circulation of the bath significantly.

Eight lanthanum- (La0.25H2.25[PMo12O40], La0.5H1.5[PMo12O40], La0.75H0.75[PMo12O40], La[PMo12O40]) and cerium- (Ce0.25H2.25[PMo12O40], Ce0.5H1.5[PMo12O40], Ce0.75H0.75[PMo 12O40], Ce[PMo12O40]) containing phosphomolybdate catalysts have been synthesized and analysed using a low pressure steady state technique. The products from isobutane oxidation using the catalysts were water, methacrolein, carbon dioxide and lactone. Methacrylic acid is not detected under the low-pressure molecular-flow conditions; lactone is postulated to be intermediary in methacrylic acid production. The methacrolein and lactone data were simulated using two different theoretical models in order to determine kinetic parameters. The activation barriers for methacrolein formation vary substantially throughout each lanthanum and cerium series, however the most active catalyst is determined to be Ce[PMo12O40]. Only three of the eight catalysts produced significant quantities of lactone (La0.75H0.75 [PMo12O40], La[PMo12O40] and Ce[PMo12O40]) and this activity is correlated with the most active catalysts for methacrolein formation. The trends in selective oxidation activity must be due to the acidity and redox properties, as well as the structural phases, but it is difficult to quantify in all cases.

It has been understood for decades that process operability does not depend entirely upon the control system but also on the inherent properties of the process itself. For example, the decision on the size of equipment or the use of a highly integrated process may have a significant impact on the overall operability. Ignoring operability during process design may lead to a very difficult to control process. In this paper, a dynamic operability analysis of a Methyl Tertiary Butyl Ether (MTBE) reactive distillation column is presented. The effects of two design parameters, i.e. the reboiler duty and the reflux ratio, on the operability of the reactive distillation system are studied. Process operability is defined as the ability of the process to return to the steady-state in spite of unknown but bounded disturbances. The nonlinearity of the process is represented using a Hammerstein model, which can be easily obtained during process design from the steady-state model combined with some limited information on the process dynamics. The recent operability analysis method proposed by Rojas et al. (2007) is extended such that it can be implemented conveniently as one extra step after the flowsheet simulation using a process simulator. Based on this approach, an optimal controller for this highly nonlinear process is determined by solving a linear matrix inequality (LMI) optimization problem.

Stiction in control valve is the most common and long standing problem in process industry, resulting in oscillations in process variables which subsequently lower product quality and productivity, accelerates equipment wear and tear, or leads to system instability. In this paper, we apply the Mixed-Integer Quadratic Programming (MIQP)–based Model Predictive Controller (MPC) that was originally developed for system with backlash, to the system with the control valve stiction. The objective is to investigate the robustness of the original MIQP-based MPC in the presence of control valve stiction nonlinearity. To have the real stiction model, we apply neural-network modelling from simulated data of real valve stiction and then use it to test the MIQP-based MPC control. Different scenarios of control valve stiction are considered. Simulation studies using an industrial case study of fluid catalytic cracking unit (FCCU) show that, if the approximate dead-band value is known a priori, the MIQP-based MPC can effectively improve the closed-loop performance in the presence of stiction through the reduction of oscillations in the process variables.

We investigate the thermal performance of protective clothing that has an embedded phase change layer. Heat absorption due to phase change within the material is used to limit the thermal penetration of heat into the material and hence to the firefighter. The distribution of temperature within the fabric and skin during the exposure to an extreme firefighting situation is determined. To determine the protective nature of the clothing, we also include a model of the skin as three layers with differing thermal properties namely the epidermis, dermis and the subcutaneous layer. In our model, we have also incorporated the air gap between the garment and the body. The mathematical model is used to predict the duration of fire exposure during which the garment is able to protect the firefighter from getting first and second degree burns.

In this paper we undertake a numerical investigation of travelling nonadiabatic combustion waves for the case of a two-step chain branching reaction mechanism. For simplicity we have assumed equal diffusivity of the reactant, radicals and heat. The speed of the combustion wave is analysed for different values of the heat loss parameter. We also determine how the extinction limit depends on the heat loss parameter as well as properties of the fuel.

A three-dimensional (3D) model of a methane-air counter-flow, non-premixed flame with a global reaction step for methane oxidation was developed using computational fluid dynamics (CFD) simulation. A specific computational domain, and relevant thermodynamic and transport data calculated by the chemical kinetic code CHEMKIN, were incorporated into the model. The model was validated by comparing predictions with the spontaneous Raman scattered profiles of major combustion species reported in the literature. The model was employed to carefully examine the self-similarity assumptions normally invoked in simulating counter-flow non-premixed flames. It was found that while most assumptions were strictly satisfied within the jet region for the case of plug flow boundary conditions (B.C.) along the central axis, for the quadratic boundary condition case (corresponding to uniform plug-flow), assumptions were only approximately valid within the jet region. Also, the influence of shroud gas was examined by setting the surrounding gas as air and increasing the shroud gas through widening the shroud gas gap while maintaining a constant shroud gas velocity. Calculations revealed that, the resulting flames for shroud gas gaps greater than half of the jet radius, were totally insulated from mixing with the ambient air. The effect of buoyancy on the flame structures was also studied by comparing contours of the combustion products, temperature and turbulent properties.

Two-dimensional numerical simulations for the ohmic heating of whole milk solutions in an annular geometry were performed using a general-purpose partial-differential equation solver, FlexPDE software. The flow, energy, and concentration equations were developed and solved for laminar flow. The reaction kinetics model for beta-lactoglobulin proposed by Toyoda and Fryer (1996) was adopted to solve for the native, denatured, and aggregated protein concentrations in the full-flow domain. The aim of this work is to investigate how the applied voltage and flow rate affect the temperature field, and the effects on the concentration profile of each protein type in the solution. Despite what is usually expected of the ohmic heating as a uniform heating method, temperature gradients were seen to be significant from the wall to the bulk solution. The results show that a higher voltage causes a faster disappearance of native protein concentration, especially near the wall. Depending upon the applied voltage, the denatured protein concentration initially increases along the axial distance, then starts to decrease at different axial locations. The aggregated protein concentration was found to be much higher at the wall then in the bulk. In addition to describing the protein concentration distributions in the heater, the fouling tendency of the milk components on the walls is also discussed in this paper.

This paper presents a systematic computational study of the inhibition of premixed flames of short chain hydrocarbons with CF3I, focusing on sensitivity analysis of the (normalized) burning velocity and reaction pathway analysis using the "iodine-flux" approach. A comprehensive kinetic mechanism was obtained by combining the GRI, hydrofluorocarbon and CF3I sub-mechanisms, and updating the rates of some of the elementary reactions. Calculations were performed using the PREMIX computer code in the CHEMKIN suite of computer codes. The updated mechanism yielded estimates of the normalized laminar burning velocities which concurs closely with published measurements. The sensitivity analysis resulted in a positive coefficient for CF3I + M ? CF3 + I + M, confirming the promoting effect of CF3I on the laminar flame velocity and is consistent with previous studies. Reaction pathways were drawn for stoichiometric, fuel-lean and fuel-rich flames doped with 1 and 2% of CF3I at atmospheric pressure. The reaction pathway analysis served to identify four major inhibition cycles, denoted as HI ? I ? HI, HI ? I ? I2 ? HI, HI ? I ? CH3I ? HI and HI ? I ? C2H5I ? HI. Furthermore, the paper developed a linear expression linking the normalized rate of heat release with the ratio of laminar burning velocities of mitigated and non-mitigated flames, and verified the efficacy of this expression for flames inhibited with CF3I.

A novel supervisory control system was developed for a boutique, walking beam-type, natural gas-fired industrial reheating furnace for steel slabs. The control system was developed to provide furnace temperature set points for the operators. The system development ideology was to utilise the considerable and inexpensive computing resources available today, to solve problems in real time in a discrete and digitised manner in place of complex analytical solutions. The control system utilises an entirely iterative regime to calculate the required furnace heating profiles to ensure that slab delivery temperatures are optimised. A two-dimensional slab conduction and radiation model was developed to fulfil the supervisory control function. The results are promising with estimated control performance at least as good as current manual achievement but with the benefit of additional information being provided to the expert human operator in the control loop.

We investigate the behavior of a reaction described by Michaelis-Menten kinetics in an immobilized enzyme reactor (IER). The IER is treated as a well stirred flow reactor, in which the immobilized bounded and unbounded enzyme species are constrained to remain within the reaction vessel. The product species leaves the IER in the reactor outflow. Before the substrate can react with the enzyme, the enzyme must first be activated by absorption of an activator. We use steady state analysis to identify the best operating conditions or the reactor. To this end, we show that the concentration of product is maximized at low residence time whereas the productivity of the reactor is maximized at high residence times.