Although direct comparison of table performance with jig performance gives only a general idea as to the efficiency of tables, a better understanding of the subject can be obtained from a consideration of table efficiencies in relation to the washing difficulties reflected in the washability curves of various coals. Numerous methods of interpreting washability curves have been suggested by coal-washing engineers from time to time, and one method, which has become fairly well known in the last 8 or 10 years, is capable of giving a rather definite measure of the difficulty of washing any given coal to any desired ash content. Credit for developing this method should be given B. M. Bird, Chief Concentration Engineer, Battelle Memorial Institute, Columbus, Ohio, and those associated with him in his work at the Northwest and Southern Experiment Stations of the Bureau of Mines in 1928 and 1929. The method was first described by Bird in 1928. A more detailed explanation of the curves on which this method of interpretation is based has been presented by Coe. The method is based on the simple principle that production of a washed coal of a certain ash content depends almost entirely on how the various constituents in the feed to a washer are distributed with respect to specific gravity.
The first requisite for the application of this principle is to have a specific-gravity curve and cumulative-ash curve of the feed and to base the specific gravity of separation on the ash percentage in the washed coal and the corresponding values on the cumulative-ash and specific-gravity curves of the feed coal. This method of determining the specific gravity of separation is illustrated in Fig. 9.
To obtain from the coal represented by the curves in Fig. 9 a washed coal of 11 per cent ash, the separation between washed coal and refuse would have to be made at 1.56 sp. gr., as shown by the dashed line. Suppose that with a certain feed the separation has to be made at 1.50 sp. gr. to get a washed coal of the desired ash content. The difficulty of making the separation at this gravity will depend almost entirely on how large a percentage of the feed coal lies in approximately the specific-gravity range between 1.40 and 1.60. In other words, if we consider the range of specific gravity from 0.10 unit below to 0.10 unit above the specific gravity at which the separation is to be made, the percentage by weight of the total feed within this ±0.10 range determines how difficult the separation will be. The specific gravity at which the separation is made is always taken as the middle point of the ±0.10 range. If a separation is to be made at 1.55 sp. gr., for instance, the quantity of material between 1.45 and 1.65 sp. gr. should be the basis for judging the difficulty of the separation.
It is obvious that if a large percentage of the feed occurs in the ±0.10 range, an efficient separation will be difficult, owing to the tendency of washed coal and refuse to overlap. Conversely, if a very small percentage of the feed occurs in this range an efficient separation will be easy to make. When a specific-gravity curve is available it shows, of course, what percentage of the total feed occurs in any specific-gravity range.
An important detail of this system of coal-washability analysis must be noted at this point; namely, that the values read from the specific-gravity curve should be divided by a correction factor, this factor being 100 per cent minus the percentage of the total feed that is sink material at 2.00 sp. gr. What this means can be illustrated very simply. Assume that in a given case a table has to make a separation at 1.50 sp. gr. to obtain the desired grade of washed coal, and that 5 per cent of the feed is in the range between 1.40 and 1.60 sp. gr. Assume, furthermore, that 20 per cent of the feed sinks in a solution of 2.00 sp. gr. In judging the difficulty of this separation, we would consider the percentage in the ±0.10 range as being not 5 per cent but 5 divided by (100-20), or 6.25 per cent. The reason for the use of such a correction factor is that constituents in the feed of higher specific gravities than approximately 2.0 are so easy to eliminate from the coal that usually they do not affect the difficulty of a washing problem. Since the percentages of this heavy material vary a great deal in different feeds, the difficulty of any washing problem should be judged on the basis of the constituents in the feed, exclusive of such heavy material. The purpose of the correction factor is to eliminate from consideration the heavy material and put all coals on a more nearly common basis for the evaluation of their washability characteristics.
Although the data available as to the relationship between the amount of material in the ±0.10 range and the difficulty of a separation are not yet as comprehensive as might be desired, nevertheless they are sufficient so that some fairly definite statements can be made as to what results will be obtainable by table treatment of a coal for which washability curves are available. The statements made here will be general rather than specific in character and will be confined to a consideration of the tabling of the ¼-in. to 0 size. An effort will be made to explain how to estimate the lowest specific gravities at which efficient separations can be made on various coals by tabling. The specific-gravity and cumulative-ash curves, as illustrated in Fig. 9, are so correlated that the washed-coal ash content corresponding to any given specific gravity of separation can be read directly on the cumulative-ash curve. Hence, if we know the lowest specific gravity at which it is practical to make a separation, the cumulative-ash curve will give the corresponding ash percentage in the washed coal, and this, for any given coal, will be the lowest ash content to which it can be cleaned efficiently.
There may be some difference of opinion as to what should be considered an efficient separation. In this discussion the expression will be taken to mean any separation in which the recovery of coal is at least 95 per cent of what is shown to be theoretically possible by the cumulative-ash curve. For instance, if this curve and the specific-gravity curve show that 85 per cent of a coal floated in a solution of 1.50 sp. gr. and analyzed 8 per cent ash, to make an efficient separation at 1.50 sp. gr. a table would have to recover 95 per cent of this 85 per cent; in other words, not less than 80.75 per cent by weight of the total feed, as washed coal analyzing 8 per cent ash. Only table feeds that have been given no preliminary treatment such as classification or special screen sizing will be considered in this discussion.
It is a well-known fact that on a feed that has been subjected to hydraulic classification or one from which all of the extremely fine material has been removed, a table will give better results both as to ash reduction and recovery efficiency than it will on feeds without such preliminary treatments, but there is not yet enough information available to show just how much the results can be improved by a classification or screening treatment of the feed. Furthermore, it is not customary in this country to resort to any such classification or screening. To the writer’s knowledge, classification of the table feed has not been practiced at more than two or three plants in this country, and in each of these instances only small tonnages of classified feed were treated. Some indications of the advantages to be gained by preliminary classifications may be obtained from reports published by the Bureau of Mines and the A.I.M.E.
Although the relationship between the percentage of material in the range of ±0.10 sp. gr. and the difficulty of separating the coal from the refuse is dependent to some extent on the proportion of bone coal and the proportion of fines in the table feed, it may be stated as a general rule that on an average ¼-in. to 0 raw-coal feed the lowest specific gravity at which tables will make an efficient separation is the one that shows a 10 per cent value in the ±0.10 range. An efficient separation at this gravity usually requires the right table adjustments and correct operating conditions. If the operation is at all haphazard one of two things is likely to happen—either the washed- coal ash will exceed by 0.5 per cent or more the ash corresponding to this minimum specific gravity of separation, or the recovery of washed coal will fall short of 95 per cent of the available coal in the feed. This general rule can be applied quite safely except when the coals are either abnormally high or abnormally low in bone content.
Effect of Fines on Shaker Table Performance
Another factor, already referred to, that can influence the relationship between the lowest specific gravity for efficient separation and the value in the ±0.10 range is the proportion of fines below approximately 100 mesh contained in the feed and the ash analysis of this fine material. If its ash analysis is as high as 20 or 25 per cent and if the proportion of it in the feed is as much as 7 or 8 per cent of the total feed, it can easily be responsible for increasing the ash in the washed coal by an additional 0.5 to 1 per cent beyond what would be a normal ash increase due to the minus 100-mesh fines. The lowest specific gravity at which an efficient separation can be made may be a gravity showing about 5 per cent in the ±0.10 range, rather than 10 per cent, as a result of such an increase in the washed-coal ash content. The minus 100-mesh material almost invariably increases the percentage of ash in the washed coal to some extent because in the tabling process it receives virtually no cleaning, even when a size range of only ¼-in. to 0 is tabled. If the minus 100-mesh material in the feed has 20 per cent ash, for instance, this same size in the washed coal probably will be about 17 or 18 per cent ash. The increase of ash in the washed coal due to the presence of these fines probably would be on the order of 0.5 to 1 per cent. This means that if the minus 100-mesh fines were removed from such a feed before tabling, the washed coal would analyze from 0.5 to 1 per cent less ash than when it is not removed, with virtually no change in the recovery efficiency on the basis of the actual feed. If the proportion of the 100-mesh fines in the feed and their ash analysis are abnormally high the increase in ash content of the washed coal due to the minus 100-mesh fines may be twice this amount. It is usually not practical to remove these fines from the feed before tabling, but if they are removed the lowest specific gravity for efficient separation of coal from refuse probably would be one showing approximately 20 per cent in the ±0.10 range rather than 10 per cent, assuming a raw-coal feed of average washability characteristics.
It must not be assumed from the foregoing statements that there is a definite line of demarcation, such as the 100-mesh size, above which the table cleans efficiently and below which virtually no cleaning is effected. In tabling ¼-in. to 0 coal, however, efficient ash reduction may be expected on all sizes down to about 48 or 65 mesh; and from this size down to 100 mesh efficiency declines very rapidly and is almost zero below 100 mesh. The reason for this rather abrupt loss of cleaning efficiency in passing from the 48-mesh to the 100-mesh size is not certain and would not be easy to explain on the basis of mathematical and physical derivations, but it is probably closely connected with the transition from the law of eddying resistance to the law of viscous resistance, which, according to Richards and Locke would be expected to occur in a size range close to 65-mesh. Gravity concentration processes, including tabling, function on the basis of differences in the settling rates of particles of varying sizes and specific gravities and, as explained by Richards and Locke, the ratio of settling rate to particle size for all sizes above a certain minimum follows the law of eddying resistance, and below this minimum it follows the law of viscous resistance. The minimum size of particle to which the law of eddying resistance applies depends to some extent on the specific gravity of a mineral, and it was not determined by Richards and Locke for particles having the same specific gravities as coal and impurities associated with it. However, according to these investigators the transition from one law to the other occurs at a particle size of approximately 0.2 mm. for quartz. Quartz has virtually the same specific gravity as shale and other common rock impurities in coal, and a particle size of 0.2 mm. would correspond approximately to the openings in a 65-mesh screen.