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Study Group Problems

Study Group Problems 2018

Problem 1: DIFFUSER TRACER TEST INTERPRETATION

Industry: Sugar Cane Processing

Industrial Representatives: Bryan Barker and Mathew Starzak, Sugar Milling Research Institute, University of KwaZulu-Natal

Moderator:
Student Moderator:

Problem Statement
A cane diffuser uses a counter-current process for extracting sugar from sugar cane. A typical layout of a cane diffuser is shown in Figure 1

Study Group Problem 1 Figure 1 Schematic diagram of a diffuser (Rein 1995, SASTA)

Figure 1 Schematic diagram of a diffuser (Rein 1995, SASTA)

Cane, rich in sugar, enters the diffuser and is drawn to the exit usually by means of a chain conveyor, moving floor or walking floor. Hot water is poured onto the cane bed near the cane discharge end. The water percolates through the cane bed and is collected in a tray below the bed from where it is pumped forward to the top of the bed in a position so that it will move on to the next stage. It once again percolates through the bed increasing in sugar concentration as it goes. It reaches maximum concentration when it reaches the stage at the cane feed end from where it is taken to further processing and crystallisation steps (draft juice). This is how the counter current effect is achieved. The cane moves in one direction and the juice in the counter current direction.

There is some dispersion as the water flows through the cane. Some of it reaches the correct tray, some of it returns to the tray from which it originated and is recycled to the same place and some reaches the tray in front of where it was aimed and bypasses the stage.

Mass transfer of sugar between the cane and the water depends on the amount of water flowing in the cane. A certain amount of recycle of the water is desirable to ensure adequate wetting of the cane without overloading the bed with water to the point where flooding occurs and water flows over the top of the bed.

The position of the spray relative to the trays below the diffuser determines the amount of recycle that occurs. This adjustment is used to set the amount of recycle achieved and is set according to parameters that need to be measured.

Sodium chloride (salt) is used as a tracer to determine the flow characteristics of the cane bed. Fifty kilograms of salt dissolved in 200 litres of hot water is injected into the suction side of a stage pump. The concentration of salt is measured at sample points on the stage pump line of the tray where the juice is expected to leave the bottom of the bed as well as two trays either side. The five traces, similar to those shown in Error! Reference source not found., are used for analysis.

Study Group Problem 1 Figure 2 Typical tracer result

Figure 2 Typical tracer result

The high peak between 12 and 18 minutes indicates the time at which the tracer is added. The curves indicate the arrival of the tracer at the respective trays. The effect of the background conductivity of the cane juice has already been subtracted from the data. The system is calibrated using normal cane juice and cane juice with salt added to the concentration of 1 g/L. This gives the output in g/L.

One technique used for estimating the degree of recycle uses the bed height, mean residence time and chain speed to give the distance between the point where the tracer was added and the point where it leaves the cane bed. The simplified theory used relies on the tracer injection being able to be modelled as a pulse applied at a line across the width of the diffuser. As can be seen in Error! Reference source 

not found., this is not always the case and corrections have to be made by modelling the system as an upward step response followed by a downward step. Another method (Love 1980, ISSCT) uses a dispersion model to estimate the percolation velocities and tracer distribution characteristics. This model accommodates the width of the spray but still needs a narrow pulse width.

Both these methods for determining the amount of recycle require the estimation of a reference distance between the point of addition and the positions of the trays. It is often difficult to

determine the exact position where the spray enters the cane bed because the only visual access is through narrow sight glasses which could be some distance away from the point of interest.

We are looking for a single method to process the data to give degree of recycle. The method must:

  • Be able to give results for short as well as long tracer injection times
  • Accommodate line as well as wide juice sprays
  • Not rely on accurate determination of the point of entry of tracer from the spray into the cane bed
  • Be immune to some noise in the data

In addition to this it may be useful to confirm that the reported value of 32% recycle will indeed give ideal condition where near maximum wetting is achieved without flooding occurring. Is there a simple relationship between imbibition rate and target recycle rate?

Problem 2: STOCHASTIC BLOCK ECONOMIC VALUE MODELLING FOR GENERATING PROBABILITY STOPES

Industry: Mining

Industry representative: Tinashe Tholana, School of Mining Engineering, University of the Witwatersrand

Moderator: Montaz Ali, University of the Witvatersrand

Student Moderator:

Background Information
Irrespective of the mining method, either underground or surface, mining starts with prospecting and exploring for mineral resources of economic interest. From the exploration data a model of the orebody is created called a geological block model which is a spatial representation of the distribution of mineralised rocks below the earth’s surface. It is an orebody model in 3D that is divided into regular blocks Bijk as shown in Figure 1 which shows a simplified schematic representation of a geological block model, the basis for subsequent mine design and planning processes.

Problem 2 Figure 1 A 3D block model view

Figure 1: A 3D block model view

Depending on the size of the deposit and the mining method, these blocks can be in the magnitude of thousands, hundreds of thousands or millions of blocks as shown in Figure 2 which shows an actual geological block model with 187,465 blocks.

Figure 2 An actual geological block model

Figure 2: An actual geological block model

Each of the regular blocks within the geological block model contains its specific characteristic data; most importantly grade, volume and density. These parameters are used to calculate block economic values (BEVs) that identify each block within the geological block model. The block economic value for a block Bijk is the revenue derived from mining, processing and

selling block Bijk less the cost of mining and processing block Bijk. The basic BEV calculation formula for a 2D block model is as expressed by Equation 1.

BEV calculation formula for a 2D block model Equation 1 

Block revenue is a function of metal contained in the block and the unit price of the metal. Furthermore, the metal content is a function of block tonnage, block grade, mining and plant recovery. On the other hand, costs can be divided into mining and processing costs where mining costs are those costs associated with mining a particular block and transporting it to the processing plant. Processing costs are those costs associated with recovering the metal content from the block. Therefore, Equation 1 can be re-written as shown by Equation 2.

BEV calculation formula for a 2D block model Equation 2

For each set of cost and revenue parameters applied, the BEVs distinguish economically and uneconomically mineable ore blocks. A block will be economic to mine if the revenue from mining is greater than the cost of mining and processing, that is, if the block economic value is positive. Figure 3 shows a simplified result in 2D. For example, blocks B11 and B12 have BEVs of 3 and -2, respectively.

Figure 3 A 2D deterministic BEV calculation model

Figure 3 A 2D deterministic BEV calculation model

Problem statement
The current BEV calculation model is deterministic in nature; fixed values of geological (grade), technical (recovery) and economic (price and costs) parameters are used in the BEV calculation. The assumption with this deterministic approach is that geological and economic parameters and the resulting block economic values are known with certainty. However, this assumption ignores the known fact that realistically, these input parameters are variable hence are uncertain but, the traditional deterministic modelling technique does not incorporate that uncertainty. This has several implications to mine planning including underestimating or overestimating mineable resources which compromises the success of optimisation efforts of subsequent mine design and planning processes. This makes mines fail to obtain optimum value from their finite mineral resources and may result in modification of mine designs later in the life of mine, ultimately destroying value. Figure 4 shows a simplified example of a deterministic BEV cal- culation model.

Figure 4 A deterministic BEV calculation model

Figure 4: A deterministic BEV calculation model

 

To minimise all these shortcomings and ensure mine plans incorporate uncertainty in geological, economic and technical parameters there is a need for a paradigm shift from deterministic to stochastic BEV calculation, where these parameters are modelled appropriately to incorporate their variability in the BEV calculation process. Probabilistic BEV calculation will result in accurate orebody models that accurately represent the quantity and quality of mineral resources thereby improving confidence levels in mine designs and subsequently in production schedules. Efforts have been made to develop stochastic models for orebody evaluation, but their limitations are that most of the models only address grade uncertainty and a few incorporate economic uncertainty, albeit in a fragmented manner. Therefore, the main question for this research is:

Can geological and economic uncertainty be simultaneously incorporated into a single stochastic BEV calculation model? 

In other words the question is can Equation 2 be turned into a stochastic model?

The aim of the research study is to develop a stochastic model that integrates uncertainty in key parameters used in calculating block economic values. The stochastic model will appreciate that each of the parameters in BEV calculation has a different probability distribution and incorporate the various probability distributions into a single BEV calculation model as shown in Figure 5

Figure 5 A stochastic BEV calculation model

Figure 5: A stochastic BEV calculation model

 

Problem 3: AN ALGORITHM FOR STOPE BOUNDARY OPTIMISATION FOR UNDERGROUND MINES

Industry: Mining

Industry Representative: Sihesenkosi Nhleko, School of Mining Engineering, University of the Witwatersrand

Moderator: 

Student Moderator:

Background

After the exploration phase, data collected is analysed and interpreted using geostatistical modelling techniques to produce an orebody model. The orebody model is delineated into thousands of mining blocks in 3D space with assigned grade per tonne values. The geological information will inform the type of mining to be adopted whether surface or underground mining. Consequently, the appropriate mining method is selected. It is at this juncture that mine planners can commence with the generation of an optimal stope layout. A stope is an underground production area where ore is extracted from the surrounding rock mass using underground mining methods. A stope comprises of a certain number of the individual economic blocks. Figure 1 depicts the layout of the sublevel stoping mining method.

Figure 1 mining layout for a primary/secondary longhole stoping sublevel.

Figure 1: mining layout for a primary/secondary longhole stoping sublevel.

 

After selecting the mining method, the mineable part of the orebody has to be identified subject to technical and economic constraints. Technical constraints are development and infrastructure location, equipment size, stope size and geometry constraints. Whereas economic constraints are grade (g/t); cost of mining; processing cost; refining cost and metal price.

The geological block model has to be converted to an economic block model taking into account the economic block values (see Figure 2) by using Equation 1.

Figure 2 Geological block model converted into an economic block model.

Figure 2: Geological block model converted into an economic block model.

After generating the economic model, the applied algorithm needs to generate stope size in terms of the number of blocks in the x, y, & z axes, and produce a set of possible stopes. The defined stope size is floated along the x, y and z axes to identify all possible stopes in the economic model that should be included in the final stope layout. Figure 3 shows an example of how the Maximum Value Neighbourhood algorithm works when applied to a one dimensional block model. This example consists of a row of seven blocks assigned with block economic values labelled a-g for reference. MVNs comprising of blocks b, c, d, e and f. This stope layout solution is not practical for mining purposes. For instance, if solution i in step 2 was selected, mining of block b would not be impossible as it violates the minimum stope size constraint. Similarly, if solution ii in step 3 was selected, mining of block f would have been impossible considering the minimum stope size constraint.

In order to ensure that the generated stope layout is optimum, the algorithm has to factor in the periphery of the orebody which might not comply with the set stope dimension, thus variable stope sizes have to be used. These variable stope sizes should not violate any of the constraints.

There are numerous techniques that have been developed for optimisation of underground stope layout, however, none of these techniques generates a guaranteed optimum stope layout. This study has identified Dynamic Programming and Particle Swarm Optimisation techniques as suitable to address the challenge of stope layout optimisation.

 

Figure 3 Example illustrating an optimisation process in 1D.

Figure 3: Example illustrating an optimisation process in 1D.

Dynamic Programming Algorithm

Dynamic Programming Algorithm (DP) has been applied to the optimisation of the underground mining limit for designing a layout for block caving mine. The DP recursive formula for optimisation of a block caving mine is shown in Equation 2:

Dynamic Programming Algorithm

Particle Swarm Optimisation Algorithm

Particle Swarm Optimisation Algorithm has not been applied to underground mining to optimise stope layout. In PSO, each particle modifies its position according to its current position, its current velocity, the distance between its current position and personal best (pbest), and the distance between its current position and global best (gbest). Therefore, the PSO can be used to solve the optimisation problem in 3D. The PSO can be used to optimise NPV in the long-term (gbest) whilst optimising the profit in the short-term (pbest) for a mining project. Mathematically, particles in the swarm are manipulated based on Equations 3 and 4:

 

Particle Swarm Optimisation Algorithm

Particle Swarm Optimisation Algorithm

Problem statement

In order to address the generation of optimum stope layout, there is a need for the applied algorithm to be iterative given the nature of the constraints. The combination of Dynamic Programming and Particle Swarm Optimisation algorithms is the most appropriate to determine the optimum stope layout. The challenge is how one can develop an algorithm based on the principles of DP and PSO without violating the mining constraints. This algorithm has to generate unique non-overlapping stope sets to be included in the final stope layout.

Problem 4: MATHEMATICAL MODELLING OF METHANE GAS EXTRACTION FROM LAKE KIVU

Industry: Energy

Industry Representative: Denis Ndanguza, University of Rwanda, Rwanda

Moderator:

Student Moderator:

Problem Statement

Lake Kivu, located on the border of Rwanda and the Democratic Republic of Congo is one of the world's most unique lakes, and at the same time, potentially one of the most dangerous.  The uniqueness and the danger of Lake Kivu arise from the large amount of carbon dioxide (CO2) and methane (CH4) gases dissolved in the deep waters of the lake.  Most of the methane is stored in the deep part of the lake, indicated as the Resource Zone in the length of 500 m. These gases are a natural hazard, as they could potentially lead to a gas eruption from the lake if their concentrations increase further. The best approach to eliminate any risk for a gas eruption would be to completely remove all the gases from Lake Kivu immediately.  Currently, the dissolved CH4 is being extracted from the lake and used for power production. In order to support environmental scientists in finding a sustainable solution, we will develop an adequate model of the gas extraction process.  The model will provide the development of all variables relevant for the study, i.e. the gas content (CO2 and CH4), the temperature and the nutrient fluxes (PO4 and NH4).  Once the model is found, we will perform simulations using different models, we will assess the identifiably and estimate the values of model parameters (using measured data), and  estimate prediction uncertainty.  We will also study the stability analysis of the system since by removing the methane the extraction will reduce the potential risk of gas eruption in the lake and maximize the energy gain. On the other hand, maintain permanent stratification and avoid nutrients increase in the biozone.

Supporting documents

Lake Kivu Gas Extraction Report

Schmid The volcanic risk Kivu

Schmid etal 2005 G3 Weak Mixing Lake Kivu

Schmid Comment Extraction Methane Kivu 2012

 

Problem 5: APPLICATION OF AIRBORNE THERMAL IMAGING TO WILDLIFE MANAGEMENT

Industry: Wildlife management

Industry Representative: Barend Erasmus, Director, Global Change Institute, University of the Witwatersrand, Johannesburg

Moderator:

Student Moderator:

Problem statement

The development of airborne thermal imaging systems for security applications opens up many possibilities for other applications. Even though commercial and industrial applications of thermal sensors in the 8 – 12 ?m range is quite common, these sensors are not suitable for long range, high resolution detection application due to lower sensitivity, small swath width and low pixel count. With the advent of commercial unmanned aerial vehicles (UAVs) some of these challenges can be overcome. However, the extent to which any airborne thermal imaging system and associated data processing chain can be used to map and count large mammals in a repeatable manner, with an accuracy that exceeds conventional aerial counts and at a lower operating cost than conventional aerial counts, remains unknown. Here is a list of capabilities required for such a system. I suggest selecting one of these as a problem.

  • Locate all warm-blooded animals above the minimum detectable size from an airborne platform

  • Count all these warm-blooded animals

  • Record the position of each warm-blooded animal

  • Record an image of a representative animal in each group with enough pixels to allow for species identification, using shape (from thermal information) or colour (RGB information)

  • Ability to track a chosen animal while circling

  • Post processing: Produce a map in a GIS with the location and species of each animal observed.

Supporting Documents

http://www.owyheeair.com/wildlife

Adapting astronomical source detection software to help detect animals in therma

Problem 6: ALGORITHM TO COUNT MODERN HOUSES FROM LIDAR DATA SETS OVER RURAL AREAS IN MPUMALANGA

Industry: Environmental monitoring

Industry Representative: Barend Erasmus, Director, Global Change Institute, University of the Witwatersrand, Johannesburg

Moderator:

Student Moderator:

Problem statement

Air-born light image detection and ranging (lidar) systems provide a high resolution, 3D picture of any landscape. The picture is generated by tracking the time-to-return of individual laser pulses that bounce off objects on the ground. The time-to-return is used to measure height and combined with highly accurate GPS systems, generates a 3D point cloud, with each point representing a point where a laser pulse hit an object. Modern lidar systems create point clouds with up to 20 points per square meter, over potentially thousands of hectares, resulting in very large data sets of x-y-z data. Off-the-shelf processing tools are very good at extracting features of interest (e.g. power lines, trees, roads, roofs etc.) from this data set, but these are typically designed for European urban environments. Through a large research collaboration, we have acquired extensive lidar data sets over rural areas in Mpumalanga, and we need an algorithm to count modern houses. By modern, we refer to brick structures, with angled and tiled roofs, constructed with pre-fab wooden trusses. By counting the change in the number of such tiled roofs, we could develop a measure of economic welfare that covers much larger areas than would be possible through conventional survey techniques. The challenge is to extract a clustered collection of connected, small angled planar surfaces, that would represent the roof of a new house, from a large 3D point cloud of millions of points.

Problem 7: SPONTANEOUS COMBUSTION OF STOCK-PILED COAL

Industry: Coal Industry Representative:

Moderator: Student Moderator:

Problem statement

Spontaneous combustion of stock-pilled coal is a well-known problem in the coal mining industry. The effects of individual causal factors are known, but typically for a specific location, or conditions at a location. The interaction between causal effects and how their relative importance varies with environmental conditions, are not well understood. The height and shape of a stockpile, the variation in grain size, the degree of compaction, oxygen availability, moisture content and the chemical composition of the coal are all known contributing factors to the probability of spontaneous combustion in coal.

Supporting Documents

http://coalspot.com/technical/file/SPONTANEOUS%20COMBUSTION%20IN%20COAL.pdf

http://www.fossilfuel.co.za/conferences/2014/SponCombustion130214/ManagingSpontaneousCombustion-JdK.pdf

A Simplified Model for Spontaneous Combustion in Coal Stockpiles

 

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