McGuinness, Mark

Whiten, Bill

English

Mathematics in Industry Information Service Eprints Archive

 Page 21 of 25 
SUSTAINABLE WATER MANAGEMENT IN THE MINERALS INDUSTRY 
                          (Centre for Water in the Minerals Industry) 
 
Industry representative:  
Mr Horatio Davis, Centre for Water in the Minerals Industry, Queensland, 
 Australia 
 
Moderators:  
Professor Bill Whiten, University of Queensland, Australia 
Assoc. Professor Mark McGuinness, Victoria University of Wellington, NZ 
 
Student Moderator  
Mr Sayed Hoseini, University of Wollongong, NSW, Australia 
 
 
The MISG was asked to examine the problem of water storage at 
Queensland coal mines. The water dams (or reservoirs) at the coal mines 
need to hold sufficient water to maintain a supply to the mine and need to 
be large enough to avoid overflow of water that does not meet 
environmental specifications. The water supply comes from rain and a 
pipeline from a public water source. The water is used for washing coal, 
and for dust suppression on roads and in underground mines. There is 
also an amount of water lost to evaporation and seepage. 
 
Two major questions were of interest: What size does the dam need to be 
to reduce the probability of running empty and of overflowing to 
acceptable levels, and how should the use of pipeline water be scheduled. 
An additional question on the control of salt content in the dam was of 
interest. 
 
Variation in the rain fall provides the major variation in the water balance. 
Rain falls in summer and in winter there is typically a net loss of water 
due to evaporation. The amount of summer rain varies considerably from 
year to year. Forty years of monthly rainfall data was available. 
 
A Fourier analysis of the rainfall data showed, as expected, a strong 
annual period and also a six monthly period. There was no sign of longer 
periods. The total summer rain was found to closely follow a log normal 
distribution. 
 
The problem was found to be similar to inventory problems that have 
been studied extensively. These included dam capacity problems. 
However, it was found that these used unrealistic rainfall assumptions and 
neglected the problem of dam overflow. 
 
Order of magnitude estimates were made for the major flows for a typical 
mine. There clearly was a need for more accurate data for these 
estimates, and in the absence of these the subsequent work used 
assumed values that could be updated when more accurate data came 
available. 
 
 Page 22 of 25 
It was realised that to avoid overflow and emptying of the dam, feedback 
control is needed. Without feedback from the dam level, if the net mean 
flow into the dam is above zero the dam will eventually overflow, and if it 
is below zero the dam eventually empties. Even when the net mean flow 
is exactly zero, the dam level behaves as a random walk eventually 
emptying at times and also at other times overflowing. 
 
The level in the dam could be approximated by a Wiener process and thus 
a Fokker-Planck equation. This however resulted in zero probabilities for 
the dam being empty or full. A definition of empty as being below a given 
level is needed for this type of formulation. Some care is needed in 
interpreting the probability that the dam is eventually emptied or 
overflows, or in finding the expectation of the time for the dam to empty. 
 
A discrete formulation based on monthly steps gave greater flexibility for 
using different rainfall assumptions and adding feedback control. Using 
this formulation an optimal control problem can be formulated as per 
Bellman. 
 
Simulations using bootstrap data for 1000 years were run to test and 
evaluate different control policies. As the appropriate weighting between 
overflow and emptying was not known a Pareto diagram which plotted 
overflow probability verses underflow probability was used to evaluate the 
policies. Each control policy was run 100 times to determine the expected 
variation in performance. It was found that a control policy of using 
pipeline water only when the dam level is below a set level gave good 
results. 
 
A simplified simulation that divided the year into wet and dry parts was 
used to determine the size of dam required to reduce probability of 
overflow and empty conditions below given maximum values. Parametric 
bootstrap data based on a log normal distribution for the summer rain was 
used for this simulation. 
 
For the case of a fresh water dam and a separate used-water (i.e. 
recycled 
water) dam, a simple simulation of the salt content was undertaken. It 
was found that the salt concentration in the used-water dam would build 
up to some natural mean level consistent with the concentration of the 
recycled water, if there were no control actions taken to reduce the salt 
content. 
 
The project has provided the methods that could be used to determine 
dam size and evaluate feedback control for the maintenance of dam 
levels. There remain several extensions that could be implemented using 
the techniques demonstrated. The first area that needs attention is to 
determine typical values of flows into and out of the dam. Investigating 
the benefits of extending the control policies to be season dependent as 
well as using feedback from the dam level is an obvious next step. 
Incorporating the feedback control effects into the determination of dam 
size would also be useful. 
 
******************** 


Sustainable Water Management in the Minerals Industry

Abstract

Similar works

Full text

Available Versions

Mathematics in Industry Information Service Eprints Archive