Study Group Problems

Industry: Sugar Cane Processing

Industry Representative: Richard Loubser, Sugar Milling Research Institute NPC, c/o University of KwaZulu-Natal, Durban.

Moderator:

Problem Statement:

Typical sugar cane consists of 70% water, 15% insoluble material referred to as fibre and 15% dissolved solids. What is reported as fibre is mostly made up of fibrous material from the cane stalk and leaves, but also includes small amounts of soil and other insoluble components.

The dissolved solids are mostly made up of sucrose with smaller amounts of other components such as monosaccharides and inorganic salts.

The dissolved solids are extracted from the plant and concentrated by boiling off water to produce a syrup. Crystal sugar is produced during additional concentration steps in a process called pan boiling.

Before sugar-bearing juice can be extracted from the cane, cane stalks are prepared by shredding with a hammer-mill shredder. This reduces the cane to short fibres where the sap or juice within the cells is exposed. This juice contains the sucrose. The extraction process involves washing the sugar-containing juice out of the shredded cane. The most common type of extraction unit in South Africa is a diffuser, which is a staged counter-current leaching process. Additional water, called imbibition, is added to facilitate washing. The extraction process has two mechanisms: free juice is washed off the prepared cane in each stage of the diffuser by the liquid that passes over the fibres, and diffusion of sucrose through the walls of unbroken cells within the cane fibre. The free juice is much easier to separate from the fibre and dominates the extraction process. These processes are driven by the difference in concentration of juice attached to the fibre and the juice percolating through the bed as well as the contact between the flowing juice and the fibre.

The capacity of the extraction plant is considered to be limited by fibre throughput. Consequently, the amount of imbibition added is calculated and reported as a percentage of the fibre.

Any water added to the process needs to be evaporated before the sugar can be crystallised. This evaporation requires energy that comes from burning fuel in a boiler. Much of the energy is supplied by burning the spent fibre after sucrose has been extracted, known as bagasse. If there is insufficient bagasse, the fuel has to be supplemented with coal. Burning of coal adds to the production cost so the trend has been to reduce the amount of imbibition used so as to control energy costs.

Common wisdom suggests that reduction in the amount of added imbibition water results in reduced sucrose recovery efficiency, reported as extraction. Figure 1 shows how the reduction of imbibition has been associated with reduced extraction. The question is whether this is the consequence of a fundamental dependence of extraction on imbibition rate, or whether changes to diffuser operational parameters or configuration could allow high extraction efficiency at reduced imbibition rates.

Figure 1: Sucrose-based Extraction, [1]Corrected Reduced Extraction (CRE) and Imbibition % Fibre in South Africa for ten seasons.

(https://sasta.co.za/download/6/2010-2020/625/2018-madho-s-et-al-refereed-paper-  ninety-third-annual-review-of-the-milling-season-in-southern-africa-2017-18-dm_cmb.pdf)

The diffuser is divided into around 14 stages with prepared cane moving from stage 1 to stage 14. Imbibition is applied by pouring water over the cane at the start of the last stage. Counter current flow is achieved by collecting juice in a tray below the prepared cane bed in each stage and pumping it to a spray above the bed in advance of where it was collected. The spray is positioned so that the majority of the juice will percolate through the bed and fall into the previous stage. Some of the juice, however, returns to the same tray. This is known as recycle. The effect of the recycle is to increase the amount of water held up in the stage, i.e. the mass of juice resident in that stage at a particular point in time. Greater juice hold-up results in increased juice percolation rates (volume of juice per area of cane bed), a property that has been experimentally shown to influence extraction efficiency. The recycle of juice, however, may increase the amount of dissolved sugar in the juice within a stage, relative to a condition with less recycle. This may compromise the efficiency of sucrose extraction from the cane. Achieving optimum extraction therefore depends on a balance between factors such as quantity of juice hold-up and sucrose concentrations in that juice.

We are looking for an indication whether reducing imbibition will inevitably result in a penalty in extraction efficiency, or whether adjustments can be made to parameters, such as spray position (or the bed speed/height relationship), that will compensate for the reduction in imbibition.

[1] Extraction value adjusted to remove effects of cane quality

Presentation

Study Group Problem 1 Diffuser optimisation Presentation

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Study Group Problem 1 Report-back Presentation

Industry: Airline (Tourism Sector)

Industry Representative:  Dr Lombuso Precious Shabalala, University of Mpumalanga

Moderator:

Problem Statement

According to Saayman (2013) Tourism is about movement of people from one place to another.  The need or desire to travel takes place for various reasons which includes business, leisure and visiting friends and relatives. Transport is used to effect the movement.  The movement takes place within the eight industries that form the tourism sector. The transport industry makes a vital contribution to the total tourism experience. Transport in tourism has three components:

1. Travel to the destination
2. Travel at the destination
3. Travel back to the place of residence.   

Transport is divided into four types namely: Air, Water, Rail and Road.

Government plays a role on ensuring that a good transport system is developed for a number of reasons: Increase accessibility; save time; make travel easier; contribute to safety in transport; enhance trade; increase travel; and increase wealth.

The problem focuses on air transport. Air transport comes in different sizes/ carrying capacity. Table 1 is based on the National Department of Tourism 2021 quarterly performance report by region on passenger arrival movement during July to September 2021 compared with July to September 2020.  It shows the total passenger arrivals at Airports Company South Africa (ACSA) airports. The results can be attributed to the lockdown restrictions that were eased to allow international travel as from 01 October 2020. Strict lockdown regulations were in place during July, August and September 2020.

Table 1: Tourism quarterly performance report by region on passenger arrival movement

Table 2 presents Year Percentage Change by month for departing passengers for year 2021 compared to year 2020.

Table 2: Year Percentage Change by month for departing passengers

The 1996 White Paper on the Development and Promotion of Tourism in South Africa provides for the promotion of domestic and international tourism. The National Development Plan identifies tourism as a labour©\intensive sector with the potential to stimulate economic growth and transformation.

 As part of the Tourism Sector Recovery Plan COVID-19 Response aiming to ignite the tourism sector, optimisation of profit through reduction in tax on available seats was suggested.  The example of a Domestic Air Ticket is given in Table 3.  It illustrates possible ways of achieving all available seats sold through tax reduction allowing the airline to make /maximise profit.  Questions that need to be answered are:

1. What changes need to be implemented?
2. How many seats need to be sold and the cost per seat taking note that due to COVID-19 regulations airlines are not permitted to carry a full capacity.

Table 3: Domestic Air Tickets cost breakdown example

Source: Travelstart (2021).

How can airlines find ways to increase their profit using the available seats under the given COVID-19 regulations and taking into account the new Omicron variant?

References

5. Department of Environmental Affairs and Tourism (1996). White Paper on the development and promotion of tourism in South Africa. Access date: 17 December 2021. Available from: https://www.tourism.gov.za/ÍøÒ×ÌåÓýNDT/Publications/Tourism%20White%20Paper.pdf  .  
6. National Department of Tourism (2021). Tourism Quarterly Performance Report, 3rd Edition: July-September 2021. Access date: 17 December 2021. Available from: https://www.tourism.gov.za/ÍøÒ×ÌåÓýNDT/Publications/Q3%20Tourism%20Performance%20Report%20-%20Jul-Sept%202021%20.pdf .
7. National Department of Tourism (2021). Tourism Sector Recovery Plan COVID-19 Response.   Access date: 17 December 2021.  Available from: https://www.tourism.gov.za/ÍøÒ×ÌåÓýNDT/Documents/Tourism%20Sector%20Recovery%20Plan.pdf .
8. Saayman, M. (2013). En Route with Tourism - An Introductory. ISBN: 13: 978-0-70219-754-3.
9. Travelstart (2021). Access date: 18 December 2021. Available from: https://www.travelstart.co.za/itinerary/traveller .

Supporting Material

1. National Department of Tourism (2021). COVID19 Tourism Relief Fund (TRF) demand continues. Access date: 17 December 2021. Available from: https://www.tourism.gov.za/ÍøÒ×ÌåÓýNDT/Publications/COVID19%20Tourism%20Relief%20Fund%20(TRF)%20demand%20continues.pdf

Presentation

Study Group Problem 2 Presentation Tourism problem MISG South Africa 2022

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Report-back Presentation for Problem 2

Industry:  Carbon Capture

Industry Representatives:

Alba Cabrera: Laboratori d'Enginyeria Química i Ambiental, Girona, Spain

Tim Myers: Centre de Recerca Matemàtica, Barcelona, Spain

Moderator:

Problem Statement

When developing new processes which are to be employed on a large scale it is much more cost effective to test on small scale devices and subsequently scale. However, simply scaling dimensions seldom leads to the same behaviour predicted by the test device. Consequently the process of scale-up is non-trivial and often contentious.

For this investigation we will focus on a specific configuration, where a fluid is passed through a cylindrical column containing a porous adsorbent material. Column adsorption is employed in a variety of areas including carbon capture and the removal of many environmental contaminants.

Fig. 1 Industrial adsorption columns (taken from https://www.aiche.org/academy/webinars /pressure-swing-adsorption-ubiquitous-gas-separation-technology)

Fig. 2 Laboratory scale experiments.

Figure 1 shows a typical set of industrial adsorption columns, with dimensions of the order metres. Figure 2 shows a typical laboratory test, where the tube diameter is around 1.5cm.

Industrial columns typical contain pellets of adsorbent material, in Figure 3 we show pellets of activated carbon with a diameter of 4mm. For experiments these are ground into a powder with micron dimensions, as shown in Fig. 4.

Fig. 3 Pellets of activated carbon, diameter 4mm.

Fig. 4 Ground up pellets, with diameter on the micron scale.

The mathematical model for column adsorption is relatively straightforward, involving an advection-diffusion equation coupled to a linear mass sink which represents the adsorption. The question for the study group will be to define parameters, such as flow regime, particle size, column dimensions, and examine wall effects, which will allow results from small scale tests to guide and understand the large scale process. Alternatively, how can the tests be related to the industrial set-up?

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Study Group Problem 3 Presentation Industrial Maths

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Study Group Problem 3 Report-back Presentation

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Industry: Generation of Electricity

Industry Representative: Professor Denis Ndanguza,  College of Science and Technology, University of Rwanda, Kigali, Rwanda.

Moderator: David Mason, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg.

Problem Statement

Lake Kivu is a fresh water lake and, along with Cameroonian Lake Nyos and Lake Monoun, is one of three that are known to undergo limnic eruptions. Around the lake, geologists have found evidence of massive local extinctions about every thousand years, presumably caused by out gassing events. The trigger for lake overturns in Lake Kivu is unknown, but volcanic activity is suspected. The gaseous chemical composition of exploding lakes is unique to each lake. In Lake Kivu's case, it includes methane  and carbon dioxide, as a result of lake water interaction with volcanic hot springs.

The amount of methane contained at the bottom of the lake is estimated to be 65 cubic kilometres. If burnt over one year, it would give an average power of about 100 gigawatts for the whole period. The lake also holds an estimated 256 cubic kilometres of carbon dioxide which, if released in an eruption event, could suffocate all of the inhabitants of the lakeshore. The methane is reported to be produced by microbial reduction of the volcanic carbon dioxide. A future overturn and gas release from the deep waters of Lake Kivu would result in a catastrophe, dwarfing the historically documented lake overturns at the much smaller Lakes Nyos and Monoun. The lives of the approximately two million people who live in the lake basin area would be threatened.

To overcome this threat, the government of Rwanda is reducing the methane gas by converting it into electrical power.  A tube is injected into the resource zone (Layer 4) and due to high pressure, bubbles are formed and their buoyancy drives the upward flow in the tube. We are interested to study the bubble formation, bubble growth and movement within the tube. ( Prior knowledge of its diameter is an added value). When the temperature is increased sufficiently such that the water becomes saturated with the dissolved gases, what determines where bubbles will first form? Will bubbles form near the glass, along the plastic, or randomly along the length? What determines the bubble size?

Bubbles that form in the tube will grow to a size inconsistent with the amount of dissolved gas initially present in the water in the tube. This is due to diffusion of air into the tube which adds to the volume of air that already is in the bubbles.

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Study Group Problem 4 Presentation

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Study Group Problem 4 Report-Back Presentation

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Industry:  Beverage

Industry Representative:  Professor Stephen Visagie, University of Stellenbosch, Stellenbosch.

Moderator:  Professor Montaz Ali, University of the Witwatersrand, Johannesburg.

Problem Statement

The drop shunting problem will only happen within cities or at least big densely populated areas. The company has truck and trailer combinations but it has more trailers than trucks. A trailer is loaded at the depot with the bottles of beverage for a number of clients.  A truck then takes it to the first drop off point and leaves it there for that client’s stock  to be offloaded and the empty bottles to be loaded. While that happens the truck moves to another trailer that is finished at another client and moves the trailer to its next client or takes an empty trailer back to the depot or collects another full trailer from the depot and takes it to a client. One thus has a pool of trucks shunting a pool of trailers around between clients and the depot.

                           How do we do this while travelling the least distance?

Of course the trucks have a fixed cost of higher and therefore it is cheaper to keep them moving and  shunting trailers around rather than just waiting at the depot or at each client while the trailers get loaded or unloaded. There are a whole number of questions here:

                           What is the right number of trucks and trailers?

                           How should the deliveries be structured to minimise total cost? 

One can assume a predetermined demand at each client. This problem also has a time component to it because the trailers must have spent different minimum times at each point before the next truck can come and take it to its next destination. This minimum time would be roughly proportional to the size of the loading/unloading. And of course it takes time for the trucks to move as well. Trailers cannot stand overnight at a client and therefore they must come back to the depot by close of day.

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Study Group Problem 5 Presentation Montaz Ali 

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Study Group Problem 5 Report-back presentation

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