General

This assignment may be completed in groups of two, following you are enrolled for the same course. Both must declare and sign off that yourself and the other person contributed adequately towards the assignment. You therefore agree before submission that you are comfortable that both receive the same mark. Note that groupwork is not obliged, and it is your preference whether you want to work with someone else or not, provided there is someone who can and want to work with you.

Further note, plagiarism will not be tolerated between different submissions, and will be penalised that may include a disciplinary hearing.

Background to the problem

Underground mining requires air cooling to provide a save working environment for the workforce. As a result, central air cooling is typically available. However, due to the expansion of mining tunnels, over time, the outskirts of the mine are typically above safe working temperatures.

Additional or larger air chiller plants can be installed, but at great costs. As a result, the mining industry requires other means of providing cooled air in the warmer parts where the central cooling does not have the required effect. If cooled air cannot be provided, production time (and revenue) will be lost.

One solution is mobile air-cooling units. These units comprise refrigeration cycle, exactly as a typical home fridge. To cool the surrounding air, cooling water (also known as mine service water) is required for these units. The cooling water is used to transport the heat extracted from the air away from the immediate environment. If the heat cannot be extracted from the environment, then no air cooling is possible.

Water flows are, however, not constant. This can result in sub-optimal decision making when choosing which air-cooling units to invest in.

What further complicates the decision is that these units do not always operate at the same efficiency, to be discussed in the next section.

Scientific working principles

Before any modelling can commence, a basic working principle of these cooling systems must be grasped, which is the coefficient of performance or COP. The COP provides the ratio of air cooling in kilo Watts [kW] over electricity costs (compressor work) in kilo Watts [kW] that are required to operate the system. The COP is defined as: COP=����̇����������������̇������������������ ������������������

Where ����̇������������ is then the air-cooling rate [kW] at any time and ����̇������������������ ������������������ the electrical input (compressor work) [kW] required to deliver the air-cooling.

Air-cooling units under investigation

There are four air cooling units to choose from and the required information for the units are provided in the following tables. The first table provides the minimum and maximum compressor work required by each system, together with the water flow that will result in the compressor work. It can be assumed that there exists a strict linear correlation between the compressor work [kW] and water flows [kg/s] for when the unit is in operation. When a unit is not in operation, the compressor work is equal to zero, irrespective of the water flow.

Units

Minimum compressor work [kW]

Water flow required for minimum air-cooling rate [kg/s]

Maximum compressor work [kW]

Water flow required for maximum air-cooling rate [kg/s]

Unit I

32

2.0

50

6.0

Unit II

40

2.2

55

7.0

Unit III

26

2.0

64

7.0

Unit IV

33

2.5

69

8.0

The following tables provide the COP intervals in terms of water flow conditions for each unit.

Unit 1: water flows kg[s]

2.0 – 3.0

3.0 – 4.0

4.0 – 6.0

COP

2.5

3.0

4.0

Unit 2: water flows kg[s]

2.2 – 3.5

3.5 – 5.5

5.5 – 7.0

COP

2.5

3.0

4.0

Unit 3: water flows kg[s]

2.0 – 4.0

4.0 – 6.0

6.0 – 7.0

COP

2.3

2.5

3.3

Unit 4: water flows kg[s]

2.5 – 4.0

4.0 – 6.0

6.0 – 8.0

COP

2.4

3.0

3.5

Very important to note. No unit can be operational if water flows are below its minimum level. Take Unit 4; if the water flow rate is 1.95 [kg/s], then the unit will shut down and produce zero cooling for that interval. Further importance, the unit cannot utilise more than its maximum flow rate rating. If 10.0 [kg/s] water is available for Unit 4, it can only draw 69 [kW] electrical power for the compressor and provide 69×3.5 = 241.5 [kW] of air cooling.

What is provided

You will receive an Excel file with a six-hourly averaged water flow data set over a time period. The flows within the six-hour intervals may be assumed to be constant, i.e., no variance within any six-hour interval. The profiles is a typical representation of waterflows that can be expected during any time of the year when production occurs at the mine and labelled Data 1.

What is required

You are required to set up four LP models if you are enrolled for Optimisation 874, or only three models if you are enrolled for Optimisation 774. Models I to III (both 774 and 874) must be solved for and Model IV (only 874) only need