Assessing Pillar Geometries in the Witbank and Highveld Coalfields Using Geostatistical Techniques
Gavin
H Lind
Department
of Mining Engineering
University
of the
Private
Bag X3, WITS, 2050
Isobel
Clark
Geostokos Limited
Alloa
Business Centre
Whins Road
Alloa,
Abstract
Research is currently
underway, as part of the Coaltech 2020 initiative, to investigate ways of
safely and economically extracting pillars in the Witbank and Highveld
Coalfields. As a portion of this
research, the widespread application of geostatistics is extended to the
estimation of coal pillar sizes and their distribution from sample pillar
geometries of pillars left as a result of the widespread use of bord and pillar
mining methods. Indicator Kriging (IK)
is used to identify areas that are mined and those areas that remain as solid
(in the form of coal pillars or unmined ground) in the area under
consideration. This exercise forms the
basis in attempting to simplify the estimation problem of the extent of the
pillars, the pillar geometries and thus provide parameters to consider for
pillar recovery.
Introduction
The Witbank coalfield has been
extensively mined for their favourable geology, relative ease of mining and
their economic value. However, the
tangible reserves have been identified as being less favourable in terms of
economic quantity than was expected. This
indicates that either new reserves have to be found (such as the Waterberg with
its difficult mining parameters and unfavourable geology), or consideration has
to be given to fully extracting what remains in the Witbank coalfield
area. Considering that partial
extraction was practiced over the majority of the coalfield, the remaining
amount lies dormant as stability pillars and also provides the potential for
complete extraction. These large areas
left in the form of pillars may themselves have weakened or caused the
overlying strata to weaken. Prevost
(1999) suggests that although stricter pollution controls are now in place, the
fact that mines and mine owners have become liable for any environmental impact
caused by their mines has made industry aware of more efficient mining and
processing methods. He further explains
that the intense past and present coal mining activity in the Witbank coalfield
has caused, as a result closed coal mines, the contamination of water, air and
ground, with the worse of these problems caused by relatively shallow,
underground, bord and pillar mines.
Methodology
In terms of designing a methodology to
conduct pillar extraction techniques, the extent of the workings needs to be
estimated. This could take the approach
of taking every available underground coal mine in the Witbank area and then counting
the number of pillars, or taking a novel approach to this onerous task. In attempting to assess an appropriate novel
method for estimating the extent of the remaining reserves, an application
using Indicator Kriging (IK) to estimate the extent of abandoned workings in
the
Indicator
Kriging
Indicator Kriging (IK) has been
traditionally applied to quantitative data (such as ore grade assays or seam
thickness). However, the data obtained
from a drilling programme designed to detect unknown or known areas of void and
pillar (like bord and pillar mining methods) is less quantitative. To analyse this type of data
geostatistically, the qualitative data is transformed into numerical data. IK utilises a binary indicator function to
perform the necessary transformations.
Clark & Harper (2000) suggest that the approach take the form of
specifying some selection criterion (usually a discriminator value in which you
are interested). They caution that this
should not be confused with an economic cut-off or some critical level, and
would probably be something which affects the depositional mechanism of the
variable we are measuring. This sort of
analysis of estimating the extent of previously mined areas on a regular
pattern of bord and pillar mining falls into this category.
The drilling pattern should fall into one
of two mutually exclusive classes:
1.
Those that indicate
mine void (the bords), and
2.
Those that do not (the
pillars or unmined ground).
The indicator function I(x) can be used to code in a binary
form the drilling patterns as follows:
I(x)
= 1, given all x Î C
I(x)
=0, given all x not Î C
Where C
represents all cases where one drill hole would intersect mine void (bord).
The task, of course, of actually
conducting a drilling programme on a regular pattern is expensive and onerous. Computing power does exist for IK
semivariograms and Kriging estimates to be produced with any univariate Kriging
software. For this paper, the
demonstration ECOSSE Software
supplied with the book Practical
Geostatistics 2000 is used with the indicator values substituted for sample
values as input data.
Data
Collection
To achieve the goal of estimating the
extent of underground reserves using the Indicator Kriging approach as
discussed in this paper a relevant sample is needed. It was decided that the best way to achieve
this would be to sample mine plan of a defunct operation in the Witbank
Coalfield. As these mine plans are at a
scale of 1:1,500 feet and extend over a large area, the actual extent of the maps
range from 7 metres to 12 metres in length.
To narrow the extent of the search, an A3 sample of some of these plans
was taken around the main adit of the mine, and these were felt to be
representative enough for the approach to test whether IK is a suitable tool to
estimate underground mine workings. Mine
A was chosen as a suitable sample, shown in Figure 1.
This sample was chosen for its various
mining directions and the mixed regular and irregular mining layout. It is a typical bord and pillar type mining
operation of the No. 2 Seam in the Witbank Coalfield. It has a depth below surface of approximately
90 metres and is roughly horizontal. The
seam thickness and mining height in the area is 3 metres. The mine ceased operation in the late 1960s.
Figure 1. Sample A3 plan of Mine A around
the main adit (not to scale)
The sample as shown in Figure 1 was
unsuitable for use in Geostatistical analysis, as clear areas of binary coding
[1,0] needed to be identified. To this
end, it was decided to colour all areas of void black and all areas of unmined
ground white. The binary coding took the
convention as described above of [1] for intersecting mine void (i.e. black)
and [0] for intersecting solid (i.e. white).
The result is shown in Figure 2, which represents the area in the Paint
application as a Bitmap file.
Data
Analysis
For the development of the argument that
Geostatistical analyses can be used to estimate the extent of underground
workings, a portion of the area under consideration was chosen on which
extensive analyses could be done. The
portion shown in Figure 3 was decided upon it was not regular in its direction
(not north-south or east-west in orientation), has varied pillar and bord width
sizes and consists of both regular and irregular mining layouts. This area is approximately 270 metres in the
north-south direction and approximately 230 metres in the east-west direction.
Figure 2. Mine A coded for binary coding
analysis (not to scale)
Figure 3. Portion of Mine A used for
Geostatistical analyses (not to scale)
A tool, called Bitmap Decoder was developed to enable the above map to be decoded
into a form that any Geostatistical package would understand so that analyses
of the area could be conducted. It
enables the image to be read in on a pixel grid spacing of one’s choice with
the closer the spacing the more detailed the analysis. These images were scanned at 100pixels per
inch (roughly 3,94 pixels per millimeter).
The above image was thus represents a size of 724 x 648 pixels. An iterative drilling pattern based on this
information can thus be designed. It was
decided to decode the image in Figure 3 using the Bitmap Decoder on a sampling gird spacing of 25 x 25 pixels
(starting in both directions from the first pixel), 10 x 10 pixels, 5 x 5
pixels and 2 x 2 pixels.
The 25 x 25 sampling grid proved to be
too sparse for any valuable analyses to be conducted and was excluded from any
further analyses. The remaining three
samples appeared to be adequate for the analyses as they show definite signs of
spatial correlation (confirmed by the semivariograms shown later), and the post
plots for these are shown in Figures 4, 5 and 6. It is observed that the denser the gird
spacing, the more true the pattern of the sample.
Looking closer at the 5 x 5 and the 2 x 2
post plots, little difference in the quality of the sample is given and for the
purposes of this paper, the less sampled 10 x 10 and the more detailed 5 x 5
sample will be further analysed..
The corresponding data files were then
inputted in the ECOSSE programme to
produce the following corresponding experimental semivariograms. The input parameters for all three examples
specified a search radius of 100 pixels (approximately 4 pillars off the plan)
and calculated the experimental semivariograms looking at the main point son
the compass (north, east, south, west).
So, for example, for the 5 x 5 grid spacing, the interval between the
points on the graph was 5, and the number of intervals was 20 to give a search
radius of 100 pixels. These experimental
semivariograms are shown in Figures 7 and 8.
Models were then fitted to these
experimental semivariograms. The
Paddington Mix model was chosen to be the most suitable, with the results of
fitting the same inputs into both the 10 x 10 and the 5 x 5 experimental
semivariograms being the same. They
consisted of 2 components with a nugget effect of 0.04. The cycle period was 30, the decay parameter
was 100 and the sill for the cycle was 0.03.
These fitted models are depicted in Figures 9 and 10.
If we take the 5x 5 scenario further and
fit a Paddington Mix model on all possible pairs in all direction, one gets the
result shown in Figure 11. What one sees
happening is an increase in the damping of the cycles when one goes from 10 x
10 to 5 x 5. Obviously the spherical
parameters were refined to achieve this as the cycles started to interfere with
one another. What this modelling shows
is that if the pillars were exactly the same size and exactly equidistant apart
that the cycle parameter would be the same.
Taking the process a step further and
conducting Kriging analysis on the 5 x 5 grid gives a probability estimate and
also calculates the variance associated with each estimation. This variance provides a measure of reliability
with respect to the probability map. In
areas where the estimation is relatively high the reliability of the estimated
probability is low. Figure 11 shows the
Kriging estimate of the area and shows that the area can be roughly reproduced
on the 5 x 5 sampling grid.
Figure 12 shows the map of standard
errors (variance). This map shows a
regular pattern of areas where the highest estimation errors exist. Not surprisingly these areas occur between
points on the regular 5 x 5 grid spacing.
This map will in the real world identify areas where additional
information may be gathered to reduce the uncertainty associated with this
analysis.
Conclusion
The work conducted by Ovanic &
Cawlfield (1990) an exponential model to fit the experimental
semivariogram. What has been shown in
this paper is that a better model to fit the experimental semivariogram has
been used to better estimate the extent of the underground workings.
This paper has shown that Indicator
Kriging (IK) has application in the estimation of underground reserves. It is a useful tool that directly yields
values for the estimation variance associated with the probability
estimates. The results obtained thus far
show promise that the IK approach can be used as a practical tool for
estimation of underground workings when either one only has a sample of the
area or one needs a quick way to get around the size of the legal plans kept at
the Department of Minerals and Energy.
It must be accepted that this is work in
progress and that the refining of the technique is still being conducted. The future objective of furthering this
technique will be to determine the optimal balance between defining the cycles
(which will then give the size of the voids and unmined ground) and refining
the full model especially as regards the nugget effect and short range
component.
References
Clark, I. & Harper, W. V. Practical Geostatistics 2000, Greyden
Press, Columbus, Ohio, USA, 2000, pp. 329-333.
Journel, A. G. The indicator approach to
estimation of spatial distributions, 17th APCOM,
Ovanic, J & Cawlfield, J.D. The use
of Indicator Kriging to estimate the extent of abandoned underground workings, AEG Subsidence Symposium, 1990, pp.
51-59.
Prevost, X.M. Unpublished report,
Department of Minerals and Energy,