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Study Group Problem 1 : The Batch Pan Scheduling Problem in a white sugar refinery
Industry: Sugar
Industry Representative: Dr Richard Loubser, Sugar Milling Research Institute, University of KwaZulu-Natal, Durban
Moderator: Professor Montaz Ali, University of the Witwatersrand, Johannesburg
Student Moderator:
Problem Statement
In a typical white sugar refinery, the sugar is crystalised in batch “Vacuum Pans”. These are evaporative crystallisers where evaporation and crystallisation takes place simultaneously under vacuum (to be able to operate at a reduced pressure where the boiling temperature is reduced and there is thus less thermal degradation of sucrose). At the end of each batch pan cycle the pan will contain a mixture of crystals and mother liquor with 50% of the sugar (typically) being in crystal form.
The crystallisation is followed by centrifugation to separate the crystal sugar from the mother liquor. There is some water addition at this stage to wash the sugar and dissolve small crystals that can pass into the separated mother liquor (normally called jet). The crystallisation is done in multiple stages with the impurities, predominantly “colour”, remaining in the mother liquor.
The flow scheme for a typical refinery multiple stage crystallisation process is shown in the diagram below:
The pieces of process equipment used in this flow scheme are:
The crystallisation takes place in a batch pan where water is removed from the liquor fed to the pan, using heating steam to drive the evaporation. When each batch is complete, the contents of the batch pan are discharged into a “strike receiver” which will have a capacity of 1.5 times the size of the batch. This means that the “strike receiver” does not have to be completely empty before a batch pan is discharged into it.
The mixture of crystals and mother liquor (called massecuite) will be processed in centrifugals to separate the crystals. Although this is a batch process, it can be considered as continuous for this exercise as the centrifugal batch sizes are small relative to the pan batch sizes.
The impurities concentrate up across each crystallisation cycle. Of particular interest is “colour” – an analytical result that can be treated as if it is concentration (expressed as parts per million on solids).
The colour in the sugar is dependant on the colour remaining in the mother liquor. With 50% of the sucrose being removed from the liquor in each stage of crystallisation the mother liquor colour and the sugar colour doubles for each stage. At the same time the quantity of sugar produced in each stage halves. Typical sugar colours would be :
- First sugar : 20
- Second sugar: 40
- Third sugar: 80
- Fourth sugar: 160.
These four sugars will be mixed together to give an average final sugar colour of :
(1 * 20) + (0.5 * 40 ) + (0.25 * 80) + (0.125 * 160) / (1 + 0.5 + 0.25 + 0.125) = 70.7
It is important that the rate of production of sugars is maintained in this ratio so that the average sugar colour (of the mixed sugar) does not deviate from the long term average value.
The length of the batch cycles becomes longer for the later crystallisation stages as a result of the concentrating impurities slowing down the crystallisation rate.
In terms of steam demand, a typical batch pan cycle can be approximated as follows.
Typical values for a batch pan of a standard design that is able to produce 75 tons of massecuite in each batch pan cycle would be as follows:
The following performance data for pans of this design can be assumed:
As a first approximation, assume that the demand for liquor to a pan is spread evenly over the batch cycle.
The task is to develop a scheduling program that allocates pans appropriately to be able to process a specified quantity of fine liquor (say 100 tons/hr with a concentration of 76% - thus 76 tons of dissolved sugar) with the following constraints:
- Achieve the smoothest possible total steam demand from all pans
- Add waiting times between batches to achieve the required scheduling
- Do not start a batch pan unless there is sufficient liquor/jet in the feed tank to complete the batch
- There must be sufficient space in the strike receiver to accommodate the contents of a batch pan at the end of its cycle
- Processing of sugar through the centrifugals must match the requirements for correct proportional mixing of sugars of different grades (so as to maintain the required average sugar colour)
- Determine the minimum number of pans necessary to meet the requirements.
References
Supporting Material
Presentation
MISG 2024 Study Group Problem 1 Presentation - Scheduling
Report-back Presentation
MISG 2024 Study Group Problem 1 Report-back presentation Batch_Pan_Scheduling
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Study Group Problem 3: Modelling a gas chromatograph
Industry: Agriculture, food and beverage, pharmaceutical
Industry Representative: Dr Alba Cabrera-Codony, Laboratory of Chemical and Environmental Engineering, University of Girona, Spain
Moderator: Professor Tim Myers, Centre de Recerca Matemática, Barcelona, Spain
Student Moderator:
Problem Statement
Gas chromatography (GC) is a widely used technique for separating and analysing volatile compounds in gas mixtures. GC has a broad range of applications, for example in detecting and quantifying pollutants, pesticides and environmental contaminants in air, water and soil samples. In food and beverage analysis, it can be used to determine the presence and concentrations of flavour compounds or additives. In the pharmaceutical industry, it permits the analysis of drugs, including purity and quantifications of active ingredients. In forensic analysis it plays a crucial role in toxicology and arson investigations. Additionally, in clinical and medical laboratories, GC is used for analysing blood, urine and other biological samples.
Here's a brief overview of how gas chromatography works:
- A small amount of the sample containing different compounds is injected into the chromatograph.
- A carrier gas, usually helium or nitrogen, carries the vaporized sample through the chromatographic column. The column is a long, thin tube: there are two types of column, i) Packed Columns, which contain a solid support material coated with a liquid stationary phase, and ii) Capillary Columns, which are narrower and contain a thin film of stationary phase on the inner wall.
- Adsorption: This causes separation, based on the different interactions of the compounds, with the stationary phase.
- Separation: As the sample travels through the column, different compounds interact differently with the stationary phase. The extent of interaction depends on factors such as molecular size, polarity, and volatility. Compounds that interact strongly with the stationary phase will spend more time in the column, leading to a slower movement through the column. Conversely, compounds that interact weakly will move faster.
- Detection: As each separated compound exits the column, it passes through a detector. The detector responds to the presence of compounds and generates signals proportional to the concentration. Common detectors include flame ionization detectors (FID), electron capture detectors (ECD), and mass spectrometers (MS).
- The signals from the detector are recorded and analysed to produce a chromatogram, which is a graphical representation of the separation of compounds over time that permits the data analysis.
Figure 1: Schematic of a gas chromatography system: a sample is added to the carrier gas flow. This passes through the column and concentrations are measured at the outlet and the data passed to a computer.
Adsorption and desorption are fundamental processes that occur in GC, contributing to the separation of compounds as they move through the chromatographic column. Adsorption refers to the adhesion of molecules to the surface of a solid. In gas chromatography, the stationary phase, which is typically a solid support or a liquid film on the column wall, acts as the adsorbent. The compounds in the vaporized sample interact with the stationary phase and the strength of this interaction depends on the chemical nature of both the stationary phase and the sample compounds.
Compounds that strongly adsorb to the stationary phase spend more time in the column, resulting in longer retention times. The degree of adsorption is influenced by factors such as the temperature, type of stationary phase, and the nature of the sample compounds.
Desorption is the process of releasing adsorbed molecules from the surface of the stationary phase. As the carrier gas (mobile phase) transports the sample through the column, the temperature of the column is typically controlled.
GC analyses use oven temperature programming, where the column temperature is increased gradually during the analysis. Increasing temperature speeds up the desorption of compounds by progressively reducing their affinity for the stationary phase. This allows for efficient separation of different compounds based on their boiling points and affinities for the stationary phase.
The final outcome is the chromatogram, a graphical representation illustrating the compounds analysed by the detector over time. In Figure 2 we present a typical example.
Figure 2: The chromatogram demonstrates the separation of 4 volatile organic compounds using a Flame Ionization Detector (FID): The x-axis represents time. Each peak corresponds to a specific compound and is related its retention time, i.e. the time it takes to travel through the chromatographic column and reach the detector. The y-axis represents the signal obtained with the FID. The chromatogram shows how the signal intensity changes over the course of the analysis, providing information about the concentration of the sample.
References
Supporting Material
Presentation
MISG 2024 Study Group Problem 3 Presentation - Gas chromatograph
Report-back Presentation
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Study Group Problem 4: Axial strain evaluation without the use of strain gauges
Industry: Mining
Industry Representative: Dr Halil Yilmaz, Rock Mechanics Laboratory, CC CSIR, Melville, Johannesburg
Moderator:
Student Moderator:
Problem statement
Uniaxial compressive strain testing with the use of axial and lateral strain gauges is one of the most common tests required by the mining industry. Strain gauges are used for the calculation of the Young’s modulus and the Poisson ratio. Young’s modulus is generated from the axial stress versus actual strain data and the Poisson ratio is calculated using the lateral strain versus axial strain data. Most universal testing machines are capable of measuring the force and the machine displacement as a crosshead movement in the direction of the applied force. The machines unfortunately cannot measure the deformation of the specimen in the same direction.
Is it possible to infer the axial deformation taking place on the rock specimen without using a strain gauge by using the data generated by the machine.
A strain gauge can be used only once and is expensive. The materials remain elastic throughout the deformation and linear elasticity described by the generalised Hooke’s law applies.
Shown below are:
- A universal testing machine with a rock specimen
- A rock specimen before and after testing with axial and lateral strain gauges
- Graphs of stress plotted against strain and load plotted against machine crosshead movement
Universal testing machine with rock specimen
A rock specimen before and after testing with axial and lateral (radial) strain gauges.
Example: Stress vs Strain curves
Example: Load vs Machine Crosshead Movement
References
Supporting Material
Presentation
MISG 2024 Study Group Problem 4 Presentation - Axial Strain
Report-back Presentation
MISG 2024 Study Group Problem 4 Report-back Presentation - Axial strain
