Student Number : 9611112G - PhD thesis - School of Chemical and Metallurgical Engineering - Faculty of Engineering and the Built Environment / Attainable Region analysis is a chemical process synthesis technique that enables a design engineer to find process unit configurations that can be used to identify all possible outputs, by considering only the given feed specifications and permitted fundamental processes. The mathematical complexity of the attainable regions theory has so far been a major drawback in the implementation of this powerful technique into standard process design tools. In the past five years researchers focused on developing systematic methods to automate the procedure of identifying the set of all possible outputs termed the Attainable Regions. This work contributes to the development of systematic numerical formulations for attainable region analysis. By considering combinations of fundamental processes of chemical reaction, bulk mixing and heat transfer, two numerical formulations are proposed as systematic techniques for automation of identifying optimal process units networks using the attainable region analysis. The first formulation named the recursive convex control policy (RCC) algorithm uses the necessary requirement for convexity to approximate optimal combinations of fundamental processes that outline the shape of the boundary of the attainable regions. The recursive convex control policy forms the major content of this work and several case studies including those of industrial significance are used to demonstrate the efficiency of this technique. The ease of application and fast computational run-time are shown by assembling the RCC into a user interfaced computer application contained in a compact disk accompanying this thesis. The RCC algorithm enables identifying solutions for higher dimensional and complex industrial case studies that were previously perceived impractical to solve. The second numerical formulation uses singular optimal control techniques to identify optimal combinations of fundamental processes. This formulation also serves as a guarantee that the attainable region analysis conforms to Pontryagin’s maximum principle. This was shown by the solutions obtained using the RCC algorithm being consistent with those obtained by singular optimal control techniques.

The availability of kinetic data for the oxidative dehydrogenation (ODH) of n-butane from Téllez et al. (1999a and 1999b) and Assabumrungrat et al. (2002) presented an opportunity to submit a chemical process of industrial significance to Attainable Region (AR) analysis. The process thermodynamics for the ODH of n-butane and 1-butene have been reviewed. The addition of oxygen in less than the stoichiometric ratios was found to be essential to prevent deep oxidation of hydrocarbon products {Milne et al. (2004 and 2006c)}. The AR concept has been used to determine the maximum product yields from the ODH of n-butane and 1-butene under two control régimes, one where the partial pressure of oxygen along the length of the reactor was maintained at a constant level and the second where the oxygen partial pressure was allowed to wane. Theoretical maxima under the first régime were associated with very large and impractical residence times. The Recursive Convex Control policy {Seodigeng (2006)} and the second régime were applied to confirm these maxima {Milne et al. (2008)}. Lower and more practical residence times ensued. A differential side-stream reactor was the preferred reactor configuration as was postulated by Feinberg (2000a). Abstract A.D. Milne Page 4 of 430 The maximum yield of hydrocarbon product, the associated residence time and the required reactor configuration as functions of oxygen partial pressure were investigated for the series combinations of an inert porous membrane reactor and a fixed-bed reactor. The range of oxygen partial pressures was from 85 kPa to 0.25 kPa. The geometric profile for hydrocarbon reactant and product influences the residence times for the series reactors. The concept of a residence time ratio is introduced to identify the operating circumstances under which it becomes advantageous to select an inert membrane reactor in preference to a continuously stirred tank reactor and vice versa from the perspective of minimising the overall residence time for a reaction {Milne et al. (2006b)}. A two-dimensional graphical analytical technique is advocated to examine and balance the interplay between feed conditions, required product yields and residence times in the design of a reactor {Milne et al. (2006a)}.. A simple graphical technique is demonstrated to identify the point in a reaction at which the selectivity of the feed relative to a product is a maximum {Milne et al. (2006a)}. Literature Cited Assabumrungrat, S. Rienchalanusarn, T. Praserthdam, P. and Goto, S. (2002) Theoretical study of the application of porous membrane reactor to Abstract A.D. Milne Page 5 of 430 oxidative dehydrogenation of n-butane, Chemical Engineering Journal, vol. 85, pp. 69-79. Feinberg, M. (2000a) Optimal reactor design from a geometric viewpoint – Part II. Critical side stream reactors, Chemical Engineering Science, vol. 55, pp. 2455-2479. Milne, D., Glasser, D., Hildebrandt, D., Hausberger, B., (2004), Application of the Attainable Region Concept to the Oxidative Dehydrogenation of 1- Butene in Inert Porous Membrane Reactors, Industrial and. Engineering Chemistry Research, vol. 43, pp. 1827-1831 with corrections subsequently published in Industrial and Engineering Chemistry Research, vol. 43, p. 7208. Milne, D., Glasser, D., Hildebrandt, D., Hausberger, B., (2006a), Graphical Technique for Assessing a Reactor’s Characteristics, Chemical Engineering Progress, vol. 102, no. 3, pp. 46-51. Milne, D., Glasser, D., Hildebrandt, D., Hausberger, B., (2006b), Reactor Selection : Plug Flow or Continuously Stirred Tank?, Chemical Engineering Progress. vol. 102, no. 4, pp. 34-37. Milne, D., Glasser, D., Hildebrandt, D., Hausberger, B., (2006c), The Oxidative Dehydrogenation of n-Butane in a Fixed Bed Reactor and in an Inert Porous Membrane Reactor - Maximising the Production of Butenes and Butadiene, Industrial and Engineering Chemistry Research vol. 45, pp. 2661-2671. Abstract A.D. Milne Page 6 of 430 Milne, D., Seodigeng, T., Glasser, D., Hildebrandt, D., Hausberger, B., (2008), The Application of the Recursive Convex Control (RCC) policy to the Oxidative Dehydrogenation of n-Butane and 1-Butene, Industrial and Engineering Chemistry Research, (submitted for publication). Seodigeng, T.G. (2006), Numerical Formulations for Attainable Region Analysis, Ph.D. thesis, University of the Witwatersrand, Johannesburg, South Africa. Téllez, C. Menéndez, M. Santamaría, J. (1999a) Kinetic study of the oxidative dehydrogenation of butane on V/MgO catalysts, Journal of Catalysis, vol. 183, pp. 210-221. Téllez, C. Menéndez, M. Santamaría, J. (1999b) Simulation of an inert membrane reactor for the oxidative dehydrogenation of butane, Chemical Engineering Science, vol. 54, pp. 2917-2925. __________________________________

ABSTRACT This work applies the concepts of the attainable region for process synthesis in comminution. The attainable region analysis has been successfully applied for process synthesis of reactor networks. The Attainable Region is defined as the set of all possible output states for a constrained or unconstrained system of fundamental processes (Horn, 1964). A basic procedure for constructing the attainable region for the fundamental processes of reaction and mixing has been postulated in reaction engineering (Glasser et al., 1987). This procedure has been followed in this work to construct the candidate attainable region for size reduction processes as found in a size reduction environment. A population balance model has been used to characterise the evolution of particle size distributions from a comminution event. Herbst and Fuerstenau (1973) postulated the dependency of grinding on the specific energy. A specific energy dependent population balance model was used for the theoretical simulations and for the fitting of experimental data. A new method of presenting particle size distributions as points in the Euclidian space was postulated in place of the traditional cumulative distribution. This allows successive product particle size distributions to be connected forming a trajectory over which the objective function can be evaluated. The curve connects products from successive batch grinding stages forming a pseudo-continuous process. Breakage, mixing and classification were identified as the fundamental processes of interest for comminution. Agglomeration was not considered in any of the examples. Mathematical models were used to describe each fundamental process, i.e. breakage, mixing and classification, and an The application of the attainable region analysis in comminution Abstract algorithm developed that could calculate the evolution of product particle size distributions. A convex candidate attainable region was found from which process synthesis and optimisation solutions could be drawn in two dimensional Euclidian space. As required from Attainable Region Theory, the interior of the bounded region is filled by trajectories of higher energy requirements or mixing between two boundary optimal points. Experimental validation of the proposed application of the attainable region analysis results in comminution was performed. Mono-sized feed particles were broken in a laboratory ball mill and the products were successfully fitted using a population balance model. It was shown that the breakage process trajectories were convex and they follow first order grinding kinetics at long grind times. The candidate attainable region was determined for an objective function to maximise the mass fraction in the median size class 2. It was proved that the same specific energy input produces identical products. The kinematic and loading conditions are supposed to be chosen as a subsequent event after the required specific energy is identified. Finally the fundamental process of classification was added to the system of breakage and mixing. The attainable regions analysis affords the opportunity to quantify exactly the reduction in energy consumption due to classification in a comminution circuit, thus giving optimal targets. Classification showed the potential to extend the candidate attainable region for a fixed specific energy input. The boundary of the attainable region is interpreted as pieces of equipment and optimum process conditions. This solves both the original process synthesis and successive optimisation problems.

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The objective of this study was to improve the operation of the classical semiautogenous and ball milling circuit also known as the SABC circuit. In order to achieve this goal, the challenges around this circuit were identified as the formation of critical sized material in a SAG mill. The size class considered for the critical sized material also known as pebbles was -100+23 mm. The attainable region (AR) method was used as an optimisation technique for the generated results using a computer simulation programme. MODSIM® demo version 3.6.22 is ore processing simulator that was used. The research was divided into two sections, the first being the variation of feed flow rate ranging from 50 – 150 tph and ore feed size ranging between 100 and 600 mm. The second section compared the variation of the operating parameters of the SAG mill, which were mill filling, ball filling, ball size and mill speed. The AR technique graphically presented the results which indicated the best operating conditions to minimise pebble formation. The effects of mill filling on a SAG mill indicate that a higher filling produces lower pebbles. Lower pebble generation also was observed at a higher ball filling. The influence of ball size indicated that the larger ball size was more effective in the reduction of pebbles. For mill speed the media displayed two common mode operations namely cascading at a low speed of 65% and cataracting at higher speed of 75%. The higher speed generated the least pebbles. / College of Engineering, Science and Technology / M. Tech. (Chemical Engineering)

This study investigated the influence of the attainable region technique to ball milling as applied in reactor technology. Flow rate, ball filling, mill speed, ball size and mill density were varied. When each was varied, the rest of the parameters were kept constant in-order to determine the influence of each parameter on the process of milling. Selection function and breakage function parameters were selected for the mill model. These were kept constant for all four circuit configurations: open milling circuit, normal closed circuit, reverse closed circuit, and combined closed circuit. Flow rate was varied from 10 tph to 150 tph. It was observed that in all circuit configurations the optimum results were obtained from 90 tph upwards. When ball filling was varied, the optimum results were obtained between 30 % and 40 % of ball filling. At this range the mill is neither experiencing under-filling nor over-filling. When the mill speed was varied, at 60 – 80 % of critical speed the product specification was achieved and for grinding balls, sizes of between 60 mm and 90 mm yielded the optimum results. Varying the mill density resulted in insignificant changes. From the results, the combined closed circuit produced more of the product specification. / School of Engineering / M. Tech. (Engineering: Chemical)

Kansanshi mine sulphide ore circuit did not achieve target flotation recovery in 2016, hence it was deemed necessary to carry out a research aimed at optimizing this circuit. The objective of the research was to optimise the Kansanshi milling and flotation circuit processing a copper sulphide ore. In line with this, samples were obtained around the circuit and processed in the laboratory for moisture content, slurry concentration, particle size distribution, and flotation response. This information was then used to build a computer-based model of the Kansanshi milling and flotation circuit. This was done in MODSIM®, a software package specialising in the design and simulation of mineral processing operations. After careful appraisal, appropriate models were selected for the semi autogenous grinding (SAG) and ball mills, SAG mill discharge screen, hydrocyclones, pebble crusher, and the flotation cells. The calibrated model was then used to simulate the effects of key operating parameters on flotation recovery. Analysis using the attainable region technique revealed that the SAG mill feed-rate should be adjusted from 1719 tph to 2090 tph. This would lead to a better utilisation of the pebble crusher that can process 358 tph of pebbles from the current 198 tph. From the simulation work, it was established that rougher flotation recovery can be improved from the current 80.0 % to 82.3 %. The technoeconomic benefits of the proposition are yet to be investigated. Findings from the research concluded that the milling circuit optimum operating parameter; which generated a final product falling predominantly in the range - 150 +38 μm were SAG and ball mills conditions of ball sizes 200 and 40mm respectively, ball mill ball filling 32% and rotational speed between 75 and 80% for both SAG and ball mills. The optimum hydrocyclone feed slurry concentration was found to be 62% solids. Additionally, the SAG mill discharge screen aperture size of 6 mm was the optimum. It must be noted that slurry concentration did not show any impact on both the SAG and ball mills performance. The SAG mill ball filling did not show any significant improvement on performance. / College of Engineering, Science and Technology / M. Tech. (Chemical Engineering)