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Numerical Formulations For Attainable Region AnalysisSeodigeng, Tumisang Gerald 14 November 2006 (has links)
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.
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The application of the attainable region concept to the oxidative dehyrogenation of N-butanes in inert porous membrane reactorsMilne, Alan David 02 April 2009 (has links)
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.
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The application of the attainable region analysis in comminution.Khumalo, Ngangezwe 09 June 2008 (has links)
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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Kinetic bounds on attainability in the reactor synthesis problemAbraham, Thomas Kannankara 07 October 2005 (has links)
No description available.
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Optimisation of the classical semi-autogenous and ball milling circuit using the attainable region techniqueBashe, Luzuko 10 1900 (has links)
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)
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Construction of the attainable region candidates for ball milling operations under downstream size constraintsDlamini, Mlandvo Brian Thembinkosi 09 1900 (has links)
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)
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An integrated model of milling and flotation for the optimal recovery of sulphide ores at the Kansanshi mineLusambo, Martin 11 1900 (has links)
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)
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