Study Group Problems

Case study of Manyeleti Nature Reserve, Mariepskop Nature Reserve, Bushbuckridge Nature Reserve and Injaka Dam

Industry: Tourism Sector

Industry Representative: Dr Lombuso Precious Shabalala, University of South Africa 

Moderator:

Problem Statement:

The continuing tourism growth will eventually result in increased visitation to some destinations / tourist attractions. Certain tourist attractions are limiting the number of visitors they welcome each day. The main reasons are to protect sensitive environments and provide a more enjoyable visitor experience by lessening the crowd.  It must be noted that tourism caps have been around for decades and the pandemic travel patterns have encouraged new restrictions to take effect.   It is perceived that visitation caps make for an inherently less flexible travel experience but as well as minimizing crowd and putting less strain on staff (which continue to be in short supply), limiting the number of visitors also helps to preserve and conserve natural resources.

It is vital for natural attractions to sustain the physical or ecological impact of visitors. The issue for managers surrounds the number of visitors that can be accommodated before the experience provided by the attraction is compromised. This challenge can be resolved through determining the attraction's social carrying capacity (SCC) taking social comfort level (SCL) into account.

 The challenge of managing tourism sustainably for residents, tourists and day visitors has been recognised.  Hence, there is a radical change in the perceptions of local people to tourism, and in many destinations a tipping point has been reached and mass tourism has become a local political issue. Mass-tourism carries the same desription as Overtourism. Goodwin (2017)  views overtourism as a new term that describes “ destinations where hosts or guests, locals or visitors, feel that there are too many visitors and that the quality of life in the area or the quality of the experience has deteriorated unacceptably” .  Mass-tourism and Overtorism are  the opposite of Responsible Tourism which is about using tourism to make better places to live in and better places to visit.  The  lack of responsible tourism practice often results in visitors and guests experiencing the deterioration concurrently and rebel against it (Goodwin, 2017).

The problem to investigate:

• Develop a viable mathematical model to determine the social carrying capacity of a tourist attraction.  The capacity will assist management to determine the number of visitors that they can welcome each day.  A decision should take into account the available infrastructure, activities, natural resources (biodiversity), visitors (day visitors versus overnight guests), accommodation available in the attraction which talks to the number of beds available versus occupie, and other key unique social comfort level variables. 
• In addition, recalculate the visitor numbers that Manyeleti Nature Reserve should welcome per day.  It is understood that only overnight visitor’s numbers are capped based on available accommodation on the site.
• Lastly, establish the limit visitor numbers per day for Mariepskop Nature Reserve, Bushbuckridge Nature Reserve and Injaka Dam.

References

Goodwin, H., 2017. The challenge of overtourism. Responsible tourism partnership, 4, pp.1-19.

Morgan, D. and Lok, L., 1999. Social Comfort Within Natural Tourist Attractions: A Case Study of Visitors to Hanging Rock, Victoria.

Supporting Material

MISG2023 Problem 1 Supporting Material - Tourism Sector - Attraction Industry

Presentation

Study Group Problem 1 Presentation: Tourist attractions capping visitor numbers

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Tourist attractions capping visitor numbers Report-back presentation

Industry: Sugar Cane Processing 

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

Moderator:

Problem Statement:

A sugar factory can be considered as a series of unit operations interspersed with buffer tanks and storage. The process needs to be controlled so that the buffers neither run empty nor overflow. The sugar cane that is processed is made up of fibre (insoluble solids), brix (soluble solids) and water. The exact amount of each of the components depends on the time of year, the variety of cane and the growing conditions. The throughput of each unit operation is limited by at least one of these components. In some units, a minimum throughput is required to maintain performance. At different times of the year, the bottlenecks in the factory will depend on the composition of the cane. Under optimum conditions, the unit operation that is the bottleneck at the time will run at or near capacity. The other operations will be controlled to keep the levels in the buffers from running dry or overflowing. Some processes ( for example, clarification) are sensitive to rate of change of throughput rather than the throughput itself.

Figure 1 shows a simplified list of steps in the manufacture of sugar together with an indicator of the limiting factor.

• The orange blocks show steps where there is designed storage capacity.
• Green indicates operations that are dominated by fibre content. This is typically experienced in the extraction plant.
• This is typically experienced in the boiling house. The centrifuges can only handle a fixed amount of impurities (non-sucrose). Sugar driers can handle a maximum amount of sugar without compromising the moisture of the output.

After the cane is cut, it is transported to the factory. The unloading rate of the hilos and tractors together with the use of the cane yard provides some buffering before the cane enters the preparation process. When the cane enters the process, it is prepared in a shredder followed by extraction which may be by milling or diffusion. The capacity of the extraction process is limited by the fibre loading. The juice which is extracted is weighed using an automatic batch weigher and stored in the mixed juice tank. The juice is drawn from the mixed juice tank and clarified in a settling clarifier where all the insoluble solids are removed before storage in the clear juice tank. The evaporator station draws juice from the clear juice tank and increases its soluble solids (brix) concentration from about 12% to about 60% by mass before transferring it to the syrup tank. The pans draw syrup from the syrup tank and boil it further under vacuum while introducing seed crystals to produce the sugar crystal containing massecuite which is centrifuged to separate the sugar crystals from the molasses. The boiling process is a three-stage process where some of the material is recycled to increase the amount of sugar recovered. The raw sugar is dried and stored in a silo before transfer out of the factory or to the refinery.

If the bottleneck process will run out of the material (brix, fibre, or water), the ideal approach will be to increase the production rate of the preceding operations to increase stock levels otherwise, the production rate will need to be decreased at the bottleneck. This may ripple back to operations before that. Controls need to be in place to make sure that the preceding buffers do not overflow or run empty. A unit operation could demand brix from a fibre limited predecessor.

Each of the operations can be characterised as a transfer function based on production, or residence time, limited by capacity. The processes are linked with buffers of finite capacity. The control system and size of buffer tanks need to provide for system disturbances such as varying cane quality, batch operations in the processing chain and varying capacity due to stopping of parallel (or series) operations (e.g. stopping a centrifuge, part of the evaporator train or half the diffuser ).

Although greater flexibility can be achieved by increasing the size of the buffer tanks ( for example, the mixed juice tank or the syrup tank), there is a penalty in terms of product degradation ( for example, sucrose inversion and colour formation) over time and capital cost.

The questions are:

• Can the buffer tank theory be applied to the more complex multicomponent streams in sugar factories where the bottlenecking component changes along the process?
• How do we minimise the size of the buffer tanks (and hence the potential degradation) required to accommodate the normal fluctuations in operation?
• When is increasing the size of buffer tanks an economic alternative in terms of the value of through-put versus losses?

Presentation

Study Group Problem 2 Presentation: Sugar factory control strategy

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2023 Study Group Problem 2 Report-back Presentation

Industry: Water treatment plants

Industry Representatives:  David Albert, Alba Cabrera-Codony and Hector Monocles, LEQUIA, Institute of the Environment, University of Girona, Spain

Moderator:

Student Moderator:

Problem Statement:

Water treatment and distribution is one of the most energy consuming processes of all in the world. As an example, the percentage of energy usage in water treatment and distribution in Spain is 7% of all the energy consumed in Spain (Hardy et al., 2010). This elevated energy consumption is the reason why optimizing energy in water distribution is a priority for water distribution networks managers.

The Barcelona water distribution network supplies water to more than 100 municipalities that have more than 4.5 million inhabitants. In order to supply water to all of this population more than 1000 km of pipes and 65 water storage tanks are used. This water distribution network has a tariff in which the energy costs vary with three different prices based on three different time slots.

Tank operation

The management of the water tanks of this network is done based on the assignment of three level set-points for each one of the three different time slots. These set-points define the level at which the water pumps that supply water to the tank have to stop. The tank water demand decreases the tank water level until it reaches the hysteresis level. This value defines the minimum water level at which the water pump starts working again. The operation of these tanks is shown in Figure 1, 2 and 3.

Figure 1: Energy price (c€/kWh) during the day.

Figure 2: Time slots defined by the energy prices.

Figure 3: Example of tank setpoint and hysteresis levels.

Hypothesis

The hypothesis defined to optimize energy management of this water distribution network is that water storage tanks can be used to reduce pumping energy costs. In order to do so, tank level set-points and hysteresis can be optimized.

Assumptions

1. Pumping the maximum possible water during the cheap energy hours can be useful to reduce the energy costs
   1. The formation of toxic trihalomethanes, which are chemical disinfection byproduct compounds, is directly correlated with the hydraulic retention time of treated water in the storage tanks. Thus, a maximum tank level is defined in order to avoid their formation.
2. Pumping the minimum possible amount of water during the expensive energy hours to reduce energy costs
   1. Each tank must maintain a minimum volume in order to supply water in emergency cases. This means that the volume saved in the tanks must have the autonomy to be able to provide water for 20h to their delivery points.
   2. The autonomy of the tanks for emergency cases can be calculated considering a set of interconnected tanks. ( This means that, as an example, if  Tank 1 supplies water to  Tank 2 and Tank 2 supplies water to a delivery point, the autonomy/minimum volume of  Tank 2 can be calculated using the retained water in Tank 1).

Study case

The study case corresponds the Granollers water distribution branch (NE Barcelona). In this distribution network, there are 12 water distribution tanks and 11 delivery points. For this study case, there is flow data for each one of the flow meters shown in Figure 4.

The water distribution managers want to find a methodology to optimize the water set-point levels assigned for each one of the tanks to reduce energy costs.

Figure 4: Granollers water distribution branch

Presentation

2023 Study Group Problem 3 Presentation

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2023 Study Group Problem 3 Report Back Presentation

Industry: Climate change, Carbon capture

Industry Representative: Alba Cabrera-Codony* & Tim Myers^

 *LEQUIA, Institute of the Environment, Universitat de Girona, Spain

^Centre de Recerca Matemàtica, Campus de Bellaterra, Edifici C, Barcelona, Spain

Moderator:

Problem Statement:

Perhaps the greatest danger currently facing mankind concerns environmental challenges and climate change. In the most recent IPCC (Intergovernmental Panel on Climate Change) report [IPCC2021] on climate change it is stated that “It is unequivocal that human influence has warmed the atmosphere, ocean and land. [...] Observed increases in well-mixed greenhouse gas concentrations since around 1750 are unequivocally caused by human activities”. The link between climate change and human activity has been apparent for many years, it is therefore all the more tragic that first world countries could easily reduce emissions and achieve green energy targets. The well-known goal of maintaining the global temperature rise between 1.5-2°C can now only be achieved through drastic emission cuts combined with the active removal of greenhouse gases. Similarly the UN Sustainable Goal of a “toxic free environment” requires the removal of a multitude of ubiquitous pollutants.

One practical method of removing fluid based environmental contaminants is column sorption, either through absorption or adsorption. Column sorption involves passing a fluid through a tube filled with a material capable of capturing certain components of the fluid. The process is depicted in Figure 1 where a fluid enters at the inlet and contaminant components attach to the adsorbate. A standard laboratory experiment would involve a column of the order 20cm long and radius 5mm with a steady flow and contaminant escaping after around 15 minutes. Industrial columns are of the order 5m tall and may run continuously for months with a constantly varying fluid intake.

Figure 1: Adsorption process, whereby contaminant molecules attach to a solid adsorbent material.

Current adsorption models focus on the removal of a single contaminant, in which case the process is defined by an advection-diffusion equation linked to a sink model, typically an ODE, determined by the chemistry. The majority of studies involve numerical solutions. Mathematical analysis of single contaminant models is largely based on asymptotic reductions and travelling wave solutions [Myer20 ,Myer23].

Adsorption is particularly effective at the source of pollution, for example at a chimney outlet or exhaust, where concentrations are high, see Figure 2. Exhaust gases are usually composed of multiple components.

Figure 2: A rather unpleasant chimney emission, taken from https://www.tradeindia.com/products/stack-chimney-emission-and-flue-gas-treatment-from-aeolus-c4994396.html

Processes where more than one pollutant is removed require multiple concentration equations and moving boundaries. Some pollutants may adsorb and then desorb due to competition with other components. In a study sponsored by the Ford Motor Company [Tef14] the simultaneous adsorption (and desorption) of eight volatile organic compounds is studied. COMSOL was used to solve their system of approximately 50 equations. In a reduced case, where only two components are adsorbed (n-decane and n-heptane), their numerical results show that heptane is first adsorbed but subsequently displaced by decane, leading to three moving fronts: decane occupies , heptane occupies , with . The position  indicates an overlap region where both components simultaneously occupy the adsorbing material.

The goal of this study group problem is to develop and analyse models for the adsorption of a multiple contaminant fluid.

References

[Myer20] T.G. Myers, F. Font Martinez. Mass transfer from a fluid flowing through a porous media. Int. J. Heat Mass Trans., 2020.

[Myer23] T.G. Myers, A.  Cabrera-Codony, A. Valverde. On the development of a consistent mathematical model for adsorption in a packed column (and why standard models fail). Int. J. Heat Mass Trans., 2023.

[Tef14] D.T. Tefera. Modeling competitive adsorption of mixtures of volatile organic... Env. Science & Technology, 2014.

Supporting material

Presentation

Problem 4 Presentation: Adsorption of multiple contaminants from a fluid stream

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Problem 4 Report-back Presentation

Industry: Robotics

Industry Representative: Branden Ingram, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg

Moderator:

Student Moderators:

Problem Statement

The WITS RoboCup Team was founded in July 2019 and is affiliated with the RAIL Lab from the School of Computer Science and Applied Mathematics at the University of the Witwatersrand. The goal of the group is to develop asustainable and competitive team that competes in the annual international RoboCup robotics competition. https://www.robocup.org/. Here the objective is to develop teams which compete against each other in different leagues revolving around the game of Soccer. Robot Soccer has served as an excellent platform for testing learning scenarios in which multiple skills, decisions, and controls have to be learned by a single agent, and agents themselves have to cooperate or compete.

Problem 1 - Kicking

To field a competitive team, the development of quick and powerful kicks is necessary to score goals and defend effectively. Currently, there exists a parameterised policy which executes a basic kicking behaviour within a fixed time window. Can we optimise the values of these parameters to maximise the distance travelled?

Example of a fixed series of poses that make up a kicking motion.

Given

• A pre-defined parameterised kicking policy.
• A set of 52 hyper-parameters which are used to form the basic kicking policy.
• A simulator which allows you to sample the kicking distance for a given set of parameters.
• The type of robot as well as its physical properties.

Constraints

• Each robot has 22 degrees of freedom: six in each leg, four in each arm, and two in the neck.
• Each joint must obey certain physical properties (https://simspark.sourceforge.net/wiki/index.php/Models).
• The ball is located near the player.
• The position of the ball is known throughout.
• There are no other objects on the field.

Simulated Nao Model

Objective

To optimise a set of parameters which dictate the performance of a kicking policy to maximise the distance a ball is kicked.

Problem 2 - Formation

Soccer is a multi-agent dynamic environment which requires cooperation between teammates to succeed. This involves maintaining a balance between minimising the space opponent players have while also allowing your players to occupy free space. Given the set of all player positions (teammate and opponent) as well as the ball position, can we optimise our player positions to minimise defensive threats and maximise counterattack opportunities?

Given

• A set of teammate positions.
• A set of opponent positions.
• The ball position.

Constraints

• Each player should remain within the bounds of the field.
• No more than 3 players are allowed within the goal box at one time.
• Optimisation should be computationally efficient to be used during a live game.
• Players walk at a fixed speed.
• The opponent players may be faster.
• Turning around is costly in terms of speed.

Field Constraints

Objective

To model, a set of positions deemed useful for players to occupy as well as to optimise which players should occupy those locations efficiently. A Naive solution to the second part of matching players with positions has been achieved whereby the overall distance walked is minimised. This approach, however, can be ineffective in some situations where certain players should prioritise certain positions.

Example Naive Solution - Minimise global distance walked

Supporting Material

• https://courses.ms.wits.ac.za/~branden/RoboCup/index.html 
• https://www.robocup.org/ 
• https://gitlab.com/robocup-sim/SimSpark/-/wikis/home

Presentation

Study Group Problem 5 Presentation: RoboCup

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2023 Study Group Problem 5 Report-back Presentation

Industry: Platinum Processing

Industry Representative: John Atherfold, Opti-Num Solutions, Hyde Park, Johannesburg

Moderator:

Problem Statement:

Introduction

Pyrometallurgy deals with chemical reactions occurring at high temperatures. The purpose of the Conversion Process in Pyrometallurgy is to convert raw ore into matte and slag. Slag is molten rock, and for the purposes of the process is a waste product that’s discarded. Matte is a mixture of metal sulphides, and is the final product of the conversion process. The matte is an intermediary product in the separation of metals from impurities. Conversion is used in the copper and lead industries, as well as platinum group metals. Figure 1 illustrates the molten slag and matte in the furnace. The slag is less dense than the matte, and hence floats on top of the bath.

Figure 1: Full Bath Illustration

Physical Representation

Figure 2 shows a more detailed representation of the furnace. Process feed is fed into the top of the bath. In addition to this, a lance that feeds fuel coal, oxygen, and other streams necessary for the reaction is submerged in the slag bath. After a certain amount of time has passed, the matte and slag are tapped out of their respective tap holes. Ideally this is a continuous process, with constant feed and conversion, and batch tappings.

All the exothermic chemical reactions occur in the slag bath. Matte droplets form in the slag bath as a result of the chemical reactions. Due to their higher density, these matte droplets drop out of the slag bath into the matte bath. The slag bath is hotter than the matte bath, and the slag bath is the source that adds heat to the matte bath through various mechanisms. Heat is lost through the sides of the furnace through indirect contact heat exchangers. The offgas from the chemical reactions also carries some heat with it as it moves out the top of the furnace on to the next stage of the process. The temperature of the furnace needs to be carefully controlled in order to maintain product quality as well as for safety considerations.

Figure 2: Detailed Physical Representation of Furnace

Requirements

The Study Group is required to model the temperature in the furnace as a function of both temporal and spacial dimensions, i.e. 

Presentation

Study Group Problem 6 Presentation: Temperature modelling in a furnace

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2023 Study Group Problem 6 Report-back Presentation