A model for coal depyritization

Resources, Conservation and Recycling, 5 ( 1991 ) 285-295 Elsevier Science Publishers B.V./Pergamon Press plc

285

A model for coal depyritization

Graham Andrews Biotechnology Unit, Idaho National Engineering Laboratory, P.O. Box 1625, Idaho Falls, ID 83415,

USA

(Received January 3, 1990; accepted after revision November 30, 1990)

ABSTRACT

Andrews, G., 1991. A model for coal depyritization. Resour. Conserv. Recycl., 5: 285-295.

A simplified geometric model for the coal/pyrite system is based on the assumption that pyritic inclusions are spherical with a log-normal size distribution. A computer program simulates grinding of a coal sample following rules that produce several types of particle including liberated inclusions ( unbroken by grinding), cubes of coal containing inclusions either submerged or protruding from one or more faces, and cubes of coal with spherical segments missing. It then examines each panicle and predicts as a function of particle size, the float/sink curve, the fraction of the pyrite liberated, the fraction that is exposed to bacterial attack and the exposed surface area of the pyrite. It is shown that a bacterial depyritization process should produce a given level of pyrite removal with a larger coal particle size and loss of heating value than a physical gravity separation. The coal "sample" size that can be examined is limited to that containing 1000 inclusions by computer time considerations.

I N T R O D U C T I O N

During the design and operation of processes to remove pyrite from coal, several questions arise that are related to the distribution of inclusion sizes in a particular coal. For example, many coals contain very many, very small (micron-size) pyritic inclusions, but exactly what fraction (if any) of this finely dispersed pyrite must be removed in order to achieve a given level of pyrite reduction? The operation of gravity-based physical processes depends strongly on the liberation of pyrite during coal grinding, but what is the optimum combination of coal grind and media density for a particular coal? A microbiological process can only degrade those pyrite inclusions that are exposed to attack by bacteria at the coal particle surface. This makes the fraction of the pyrite that can be removed by bacteria a complex function of the size distributions of the coal particles and the pyritic inclusions. What is the exact form of this function for a particular coal?

A particularly interesting question is how the physical and bacterial processes can best be combined to give very high pyrite removals with minimum coal grinding and wastage of heating value. The argument for this combina-

0921-3449/91/$03.50 © 1991 - - Elsevier Science Publishers B.V./Pergamon Press plc

286 G. ANDREWS

tion is that physical processes are separation processes that work best on large inclusions, while the bacterial process actually degrades the pyrite and thus works best on the finely dispersed pyrite. To illustrate the point, suppose that a 4% (w/w) pyrite coal could be ground into particles of exactly 100 mesh ( 150//m). Some particles would be pure, liberated pyrite. A piece of pyrite this size would have a settling velocity in water six times larger than that of a pure coal particle, so it would be easy to separate physically. However, an average 100 mesh particle would contain a single pyritic inclusion of 38 tim and have a settling velocity (in water) only 9% higher than a pure coal particle, making it difficult to separate physically. Grinding to approximately 50 ~m would be the only way to remove this pyrite physically without suffering a large loss of heating value. On the other hand, the inclusion could be degraded biologically in 2 days if it is exposed somewhere at the coal particle surface (a 58% probability if the inclusions are randomly distributed).

All of these questions can of course be resolved by experiment, but there are difficulties with a purely experimental approach. The rate of chemical and bacterial processes depends critically on the surface area of exposed pyrite and this is a difficult quantity to measure. Measuring the fraction of the pyrite that can be removed by bacteria is relatively simple but time consuming. There are even practical difficulties in the measurement of float/sink curves for finely ground coal. The ability to predict these quantities, approximately but quickly, for a particular coal from knowledge of its pyrite content and inclusion size distribution could be extremely useful. This paper describes a computer model of the coal/pyrite system that represents a first attempt to provide such predictions. The potential uses of this model, after appropriate testing, valida- tion and improvement include the rational selection of the coal top size for a given process and a quick way of comparing the performance of various depyritization processes on a particular coal. Even fairly obscure phenomena such as the reduction in coal particle size during bacterial depyritization can be calculated approximately.

This computer model is related to the "liberation models" available in the mineral processing literature. These are based on various assumptions about the size distribution of the inclusions, the structure of the solid, and what happens when it is ground. Klimpel and Austin [ 1 ] provide a useful review and present a model for the case where fracture planes pass randomly with equal ease through the solid matrix and the inclusions. Analytical solutions are available for several simple inclusion size distributions [ 2 ] but could not be used for the coal/pyrite system. The sizes of pyrite inclusions in coal follow a more complex distribution [ 3 ] and the mechanical properties of coal and pyrite are very different, so a fracture plane is more likely to follow the inclusion boundary than to go through it. This leaves the inclusion whole but emerging from a coal particle.

A MODEL FOR COAL DEPYRITIZATION 287

THE MODEL

Assumptions

No computer model (except perhaps one based on fractals) can give a realistic description of the complexity of the coal/pyrite system revealed by electron microscopy [4]. The model described here treats the coal as a ho- mogeneous solid and the pyrite as spherical inclusions of various sizes distributed randomly throughout the coal. ("Inclusions" is used here as a generic term for the many different forms of pyrite in coal). The justification for this highly simplified picture is that the main problems in pyrite removal are due more to the inclusion size distribution than to the details of the pyrite structure. The starting point must be a model in which the former is correct; deviations between its predictions and experimental data can then be attributed to the latter.

Measurements of the pyrite size distribution show considerable variation between coals [3,5,6]. The most common mathematical form used to fit the data is the log-normal distribution. Mazumdar et al. [ 5 ] provide parameter values for this distribution for several Ohio coals. This form is used here although one important reservation must be noted. The size distribution is usu- ally measured by polishing a flat surface on a coal sample and measuring the size or area of an inclusion under the microscope. Use of this projected diameter produces an obvious systematic error; monosized spherical inclusions of radius R would show a distribution of sizes between zero and R because the flat surface would cut different inclusions at different heights. It may be possible to reduce the error using the transformation equations developed (for a different purpose) by Miller and Lin [7] but this has not been at- tempted here.

Program structure

The computer program requires only two parameters to describe the coal/ pyrite system. They are the volume fraction of the pyrite in the coal, E, and the standard deviation, a, of the log-normal pyrite size distribution. The mean of the distribution,/ t , need not be provided because all dimensions in the program are normalized with respect to the mean inclusion size (e ~ microns; all p and a values given here are the natural logarithms of sizes expressed in microns). A # value must, of course, be known in order to convert the program output into real coal particle sizes.

The program divides the inclusion size distribution into 56 discrete sizes, spread 2.8 standard deviations each side of the mean size. It then sets up a cube of coal large enough to contain approximately one thousand inclusions,

288 G. ANDREWS

calculates how many inclusions of each size there must be, and distributes them randomly throughout the cube, checking that they do not overlap. Knowing the total volume of these 1000 inclusions and the volume fraction of pyrite in the coal, E, allows the size of this cube of coal to be calculated (again normalized based on the mean inclusion size).

This large cube of coal is then "ground" by dividing each side by 4. The inclusions are assumed to be hard and remain unbroken by the "grinding". The computer program then examines each of the 43--- 64 small cubes in turn to determine the exact shape, size and density of the particles that have been produced by these "grinding rules". There are several possibilities:

( 1 ) An inclusion was centered inside the small cube and was large enough to completely fill it. This becomes a spherical liberated inclusion.

(2) Inclusions were centered outside the small cube but were large enough to reduce its volume when they were removed. This produces a small cube of coal missing one or more spherical segments. In the limit a neighboring inclusion may be so big that the small cube may not produce a particle at all.

(3) Inclusions were centered inside the small cube that were large enough to emerge from one or more of its faces.

(4) Inclusions were centered inside the particle and were small enough to be totally submerged within it.

For each particle the total inclusion volume, submerged inclusion volume, exposed surface area of inclusions and total particle volume are calculated. Whether it would float or sink in liquids of different specific gravities is also determined. The entire procedure is then repeated, dividing the large cube into 8, 16, etc. along each side.

This type of mathematical representation always involves edge effects. For example a large inclusion centered just outside the large cube of coal may, when it is removed, leave a large depression in the side of the cube. This is accounted for by having the program "wrap around". The region just outside one face of the cube is assumed to be identical to the region just inside the opposite face.

The "largest inclusion "problem

The "wrap around" procedure described above in effect assumes that coal in the ground can be represented by a stack of such cubes extending to infinity in all directions. The question arises whether a cube containing one thousand inclusions is an adequately representative sample of the coal. A cube containing ten thousand would obviously be more representative but would use up far more computer time (a factor of approximately 103 ). The choice of one thousand inclusions is a compromise with several implications that must be understood. The most serious is the constraint it puts on the largest inclusion that will be put into the coal and the implications of this constraint for pyrite removal processes.


The problem can be illustrated by reference to Fig. 1 which shows the number and volume distributions for the pyrite in a middle Kittanning coal (DGS 1389 ) for which Mazumdar et al. [ 5 ] give/z = 3.753, tr= 1.019. This coal, like most coals, contains very many small inclusions and relatively few large ones but, since volume is proportional to size cubed, the large-diameter "tail" of the number distribution makes a disproportionately large contribution to the total pyrite volume in the coal. In theory this "tail" continues to infinity and it is a reasonable representation of reality. Many run-of-mine coals contain the occasional large lump or sheet of almost pure pyrite (the so-called second- ary pyrite ), whose removal will significantly reduce the sulfur content of the coal.

Unfortunately the sample size needed to include these large lumps of pyrite is impractically large for computational purposes. In the cube of coal containing one thousand inclusions set up in the computer program, there is a 50/50 chance that there is one inclusion of size between 2.9 and 3.0 standard deviations above the mean. For the Middle Kittanning coal of Fig. 1 this means one inclusion between 0.818 m m and 0.906 mm, whose volume would be 19% of the total pyrite volume in the cube. The program actually takes the largest inclusion as one with a 90% chance of being present in the cube, which is one between 2.8 and 2.9 standard deviations above the mean (0.740 < d < 0.818 m m ). Increasing the size of the coal cube to one containing ten thousand inclusions would increase the largest inclusion to one of size between 1.36 and 1.15 mm. (3.4 to 3.5 standard deviations). It would clearly be desirable in future work to relate the size of the computer 's coal cube to the amount of processing the subject coal has undergone. Run of mine coal, which may contain the occasional large inclusion, would start with a much larger cube than washed coal, which should not.

Number / ~ ~ distdbution / ~

/4--- Volume / distribution ~"

/ / / / / Middle KIUenning Coal /z = 3.75 o = 1.02

d I : I I I I I 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

d m m

Fig . 1. I n c l u s i o n s i z e d i s t r i b u t i o n s f o r m i d d l e K i t t a n n i n g c o a l .

290 G. ANDREWS

The problem discussed above is the computer simulation analog of that faced by the analytical chemist in deciding the minimum sample size required for a realistic pyrite analysis, or the experimenter who finds an unusually large piece of pyrite in a sample being prepared for a depyritization experiment. (Should it be left in knowing that its presence will give high results for pyrite removal?) The program described here can be used to give considerable in- sight into these practical questions.

R E S U L T S

Model predictions

Results are given for the Middle Kittanning coal whose inclusion size distribution is shown in Fig. 1 [5]. The mean inclusion size is e~=42.6/tm and the known pyritic sulfur content of 2.82% is converted to a pyrite volume fraction e =0.0202 by assuming that the ratio of the density of coal pyrite (which is less than that of pure crystal pyrite [ 8 ] ) to the density of all the non-pyrite material is 2.7.

Figure 2 shows the pyrite surface area (per unit volume of coal) that is exposed when the coal is ground to different particle sizes, it is plotted against the reciprocal of the particle size, because, as a first approximation, it may be expected that the exposed pyrite area is proportional to the total surface area,

E 0.3

o. 0.2

0

w

• "~ 0.1

1 •0 Middle Kittanning Coal |

= o.o2o2 |--

• • _ ~ 0 . 6 ~

0.4 ~ • U.

,/ 0.2

/ • I e l I 2 4 6 8

(Coal size) -~ (mm -1)

f I I I I I 18 35 45 60 80 100

Mesh size

Fig. 2. P y r i t e l i b e r a t e d a n d py r i t e su r f ace a rea .


which would give a straight line on such a plot. This approximation is seen to be reasonable at large particle sizes but the exposed pyrite area tends to level offas the coal is ground finer. It would reach a max imum value if the coal was ground to the size of the smallest inclusion ( < 1 a m ) so that all of the pyrite was liberated. However, this predicted max imum would be a consequence of the assumption that grinding does not break the pyritic inclusions, which would be unrealistic for this very fine grinding. The ability of the model to predict the trend of the exposed pyrite area is extremely important. This parameter is very difficult to measure directly and yet it is one of the major factors in determining the rate and effectiveness of bacterial depyritization and surface-area dependent physical processes such as froth flotation and oil agglomeration.

The three points shown in Fig. 2 for each particle size (some points overlap so only one or two may appear) were obtained from three different runs of the program and correspond to three different random arrangements of the inclusions in the cube of coal. These different arrangements produce little scatter in the surface area prediction showing that for this purpose the size of the original "1000 inclusion" cube of coal is large enough to be statistically significant. This would clearly not be true for the other quantity shown in Fig. 2, the fraction of the pyrite that is liberated by grinding. Predictions of this quantity appear unrealistic but this is largely a result of the problems discussed in the previous section, and the way "liberation" is defined in the computer. After the program has divided the large cube of coal it examines each of the small cubes produced in turn. If one such cube is completely occupied by a pyritic inclusion then it labels that inclusion as liberated (and removes appropriate sectors from neighboring cubes). With this definition no inclusions can be "liberated" if the coal particle size is greater than the size of the largest inclusion divided by x/~ (approximately 0.5 m m for the coal shown in Fig. 2 ). The scatter found with smaller coal particle sizes shows how, as discussed in the previous section, the behaviour of a few large inclusions can have an overwhelming effect on the results. If a large inclusion happens to be located near the center of a small cube the program will label it as "liberated", whereas if it is centered near a corner the program may decide that it is not liberated but a large sphere of pyrite with small pieces of coal attached to it. This difference has a large influence on the fraction of pyrite liberated, but should have very little effect on the predicted fate of the inclusion in a depyritization process.

This expectation was borne out by the predictions of pyrite removal and loss of calorific value in float/sink and bacterial processes. The results showed scatter between computer runs similar to that shown in Fig. 2 for the exposed pyrite area which, given the other uncertainties in the problem, is small enough to be ignored. The results of three computer runs were averaged and plotted in Fig. 3. Fractional beneficiation is defined by

292 G. ANDREWS

Pyrite content in product coal Fractional = 1 ( 1 ) benefication Pyrite content in feed coal

The liquid specific gravity for the float/sink curves are defined in terms of the equivalent solid densities. Thus, 0.1 means a liquid having the same specific gravity as a coal containing 10% (v/v) pyrite. True float/sink curves would be obtained by cross-plotting the fractional beneficiation and calorific loss data from Fig. 3 with particle size as the parameter.

Figure 3 shows the expected behavior. No process will give good pyrite removal with coarsely-ground coal, while a gravity separation (including hy- drocyclones ) with a media density corresponding to e = 0.025, or the bacterial process can potentially (the computer considers only ideal processes) give 99% pyrite removal from coal ground to 80 mesh or smaller. At first glance this figure seems surprising; 80 mesh (0.2 mm) is five times the mean of the number distribution of the pyrite inclusions, so only a small fraction of the inclusions could be liberated from, or exposed at the surface of, a particle of this size. Once again, this results from the shape of the log-normal distribution. The mean of the pyrite volume distribution is close to 1 mm (see Fig. 1 ) which is five times larger than 80 mesh. At this particle size only a small fraction of the inclusions are removed, but these few large inclusions contain the great majority of the pyrite.

Figure 3 also shows that for any particle size, a bacterial process will give a higher pyrite removal with lower calorific value loss than a gravity-based physical process. This is as expected because the two processes are very dif-

1.0

0.8

0.6

0.4

0.2

0.1

Middle Kittanning Coal p. = 3.75

\ Oa,a Fractional ~ ~ " ~G'~ 1"6

Bensficiation X ~ X %,

LOSS of Calorific Value ~

0.2 0.5 1 2 Coal size (mm)

I I I I I I I I 140 1 O0 60 40 30 20 14 10

Mesh size

Fig. 3. Pyrite removal by float/sink and bacterial processes.


ferent. Physical depyritization processes are separation processes that remove only those inclusions that happen to be concentrated in one particle suffi- ciently to raise its density above a certain value. They inevitably result in some loss of coal organic matter. Bacterial processes involve the selective deg- radation of any pyritic inclusion that is exposed at the particle surface. Figure 3 may actually understate the advantage of the bacterial process because when coal is ground it tends to fracture along planes weakened by the presence of inclusions. This effect, which is not included in the model, increases the probability that even small inclusions will be exposed to bacterial attack.

Comparison with experimental data

A complete confirmation of the model would require that all of the following be known about a coal; its pyrite content; the mean and standard deviation of its inclusion size distribution; the densities of the pyritic inclusions and the non-pyrite material; complete float/sink curves and data on bacterial pyrite removal for coal whose particle size distribution is known precisely. The data can then be compared with a suitably weighted average of the model's predictions for the actual particles sizes involved. This is not possible at present, but some approximate comparisons can be made. Shown in Fig. 3 is the float/sink fractional beneficiation result given by Carlton [9] for a 14 X 28 mesh fraction of the Middle Kittanning coal in a liquid of specific gravity 1.6. Without exact knowledge of the coal and pyrite densities, it is difficult to translate this specific gravity into a volume fraction figure, but the result would be of order 0.08. Thus Fig. 3 suggests that the model is approximately correct, but underestimates the actual pyrite removal. This is as expected since the model ignores the tendency of coal to fracture along planes weakened by the presence of inclusions and therefore underestimates the amount of pyrite liberated during grinding.

Data on the ultimate bacterial removal of pyrite from well-characterized coals as a function of particle size is even more sparse. Andrews and Maczuga [ 10] give 73.5% at 60X 100 mesh, 93.1% at 100X 140, 95.7% at 140-200 and 98.1% at 200X 325 from a Pittsburgh seam bituminous coal. This is consis- tent with the trend of the results of Fig. 3. More detailed comparison must await the results of bacterial experiments with well-characterized coals.

CONCLUSION

Many of the problems associated with analyzing and removing the pyritic sulfur in coal are due to the form of the size distribution of the pyritic inclusions. This becomes particularly important as pyrite removal requirements become more stringent: 70 ~ 80% removal (a very approximate and coal specific number) can be achieved by removing relatively few, large inclusions.

294 G. ANDREWS

The final 20 ~ 30% calls for the removal of very large numbers of very small inclusions (the finely dispersed pyrite) which requires very fine grinding of the coal if they are to be separated physically.

Thinking about the optimum design and operation of depyritization processes for a particular coal can be facilitated by a geometric model of the coal structure. A first attempt to produce such a model was based on the log-normal distribution for pyritic inclusion sizes but was otherwise highly simplified, treating the coal as a two-component coal/pyrite system with cube-shaped coal particles and spherical pyritic inclusions that remain intact during coal grinding. This model correctly predicts the trends in experimental data on pyrite removal as a function of coal grind, although it appears to generally underestimate the removal because it necessarily ignores the tendency of coal to fracture along planes weakened by the presence of inclusions. It suggests that bacterial depyritization can produce higher removal for a given coal size then a gravity-based physical process and gives predictions of the exposed surface area of pyrite which is important in the flotation, agglomeration and bacterial processes.

The work has suggested several modifications to the model. It is now being improved to give predictions for any pre-determined distribution of coal particle sizes. The computer time required by the present routine, which divides a coal sample into small cubes and examines each sequentially, is proportional to (coal particle size) -3 which becomes excessive for finely ground coal. The efficiency of the routine needs to be improved. Finally the relationship between the coal "sample" size, the standard deviation of the inclusion size distribution, the largest inclusion present in the sample and the predicted pyrite removal of a process needs to be examined. These studies are the nu- merical equivalent of the problem of finding the smallest coal sample that will give statistically significant results in a physical experiment.

ACKNOWLEDGEMENT

This work was supported by Contract No. DE AC07 761D0570 from the US Department of Energy Advanced Research and Technology Development Office to the Idaho National Engineering Laboratory.

REFERENCES

1 Klimpel, R.R. and Austin, L.G., 1983. Binary liberation model. Powder Technol., 34:121. 2 Klimpel, R.R., 1984. Applications of a model for the analysis of liberation from a binary

system. Powder Technol., 39:117. 3 Shah, N., Keogh, R.A., Huggins, F.E., Huffmann, G.P. Shah, B., Granguly, B. and Mitra,

S., 1990. Coal Mineralogy, Forms of Sulfur and Iron, and Coal Liquefaction Properties for the Argonne Premium Coals. 200th ACS National Meeting, Washington DC, August 1990.


4 Greer, R.T., 1977. Coal microstructure and pyrite distribution. In: T.D. Wheelock (Edi- tor), Coal Desulfurization, Chemical and Physical Methods. A.C.S. Symp. Ser., 64: 3.

5 Mazumdar, M., Carlton, R.W. and Irdi, G., 1988. Statistical relationship between pyrite grain size distribution and pyritic sulfur reduction in Ohio coal. Int. J. Coal Geol., 9:371.

6 Ki, S., Ciocco, M., Morsi, B.I., Chiang, S.H., Cheng, Y.S., Sharkey, A. and Blachere, J., 1990. Effects of Surface Modification Reagents on the Performance of a Selective Agglom- eration Process for Coal Beneficiation. 7th Annual Pittsburgh Coal Conf., Pittsburgh, PA, September 1990.

7 Miller, J.D. and Lin, C.L., 1988. Treatment of polished section data for detailed liberation analysis. Int. J. Min. Process., 22: 41.

8 Meyers, R.A., 1977. Coal Desulfurization. Dekker, New York, 1977. 9 Carlton, R.W., 1985. Image analysis of pyrite in Ohio coal; relation between pyrite grain

size distribution and pyritic sulfur reduction. In: K.A. Attia (Editor), Processing, and Uti- lization of High-Sulfur Coals. Elsevier, Amsterdam, pp. 3-18.

10 Andrews, G.F. and Maczuga, J., 1982. Bacterial coal desulfurization. Biotech. Bioeng. Symp. Ser., 12: 337.

A model for coal depyritization

Documents

Transcript of A model for coal depyritization