The sampling of disseminated copper deposits has been described often but the method of combining assays to give the true shape and value of the orebody as it will be mined has received less attention. As the ore mined during five or ten years at several of the great disseminated properties has averaged materially lower in grade than the published estimates, the question of the sampling and estimating of these orebodies seems timely. In this paper, attention is given particularly to factors that may cause errors in the final estimate. Sampling of diamond-drill holes, churn-drill holes, and underground workings is briefly described in the first part of the paper; then the method of combining assays to give the average grade and tonnage that will be mined is taken up in some detail. The necessity of study of the geology of the deposit and of probable costs is emphasized. Finally, the methods of calculating tonnages are outlined.
There are three main requisites for accurate diamond-drill sampling. First, the core should be removed and the hole cleaned out at the beginning of every sampling interval, usually 5 ft. (1.5 m.) . After the rods are let down, water should be run through them until it becomes clear. The water must be clear before drilling starts. In this way the material knocked down from the sides of the hole by the descending rods is washed away, instead of being left to salt the sludge sample.
The second requisite is to save all the sludge and all the core from every sampling interval. Where the material is uniformly heavy, the cuttings will settle sufficiently in a box, through which the sludge flows slowly. Where part of the material is too light to settle readily, the sludge should be run into barrels, and allowed to settle until the water becomes clear. Then the clear water is siphoned off, and the sludge evaporated to dryness over a slow fire, sacked, and assayed. To obtain the core assay, it is best to split every piece of core, sending one half of it to the assay office and retaining the other half in a marked box or bag for record. It is convenient to keep the core in oblong tin boxes, marked on one end, in racks, so that any box is easily accessible. A portion of the sludge, returned from the assay office, should be kept with the core.
The third requisite is to combine core and sludge assays for every sampling interval in such a proportion as to give the assay content of all material removed from the hole. This is done by measuring the length of core obtained in every sampling interval, computing the volume of core and the volume of the rest of the material removed from the hole (which has been ground into sludge), and combining core and sludge assays in proportion to the volumes. This work may be simplified by formulas, or by a very ingenious scale devised by the E. J. Longyear Co., on which the proportional weight to give to core and sludge assays for any size of bit is read directly opposite a scale showing lengths of core recovered in 5 ft. of drilling.
The drillmen and samplers should submit daily reports for every hole, giving the progress and detailed information concerning the material cut, whether or not the ground is caving, the length of core for every 5 ft. advance, and all other factors that might affect the accuracy of the samples. When a hole is finished, a chart should be prepared giving core, sludge, and accepted assay, with a graphic representation of the accepted assay, and columns showing material cut, minerals present, dates, causes of delay, factors affecting the accuracy of sample, and any other information of interest. These charts are the permanent record of the drilling; a specimen chart for one of the Ajo drill holes is given in Fig. 1.
In diamond drilling, the core assays are usually high if the values are in hard, siliceous bands, as often at Ajo, and low if in seams softer or more friable than the gangue. Sludge assays are low in the first case, high in the second. The combined assay should represent closely the average value of the rock drilled. Except in loose ground, there is little jarring down of material from the walls of the hole. It is only where the values are in very soft seams that the sludge and combined assay may be materially salted by richer material from the walls. After a few check raises or test pits have proved that there is not much of this salting, diamond-drill samples can be relied on to within the accuracy of ordinary assaying.
It is interesting to note that a little oil is carried down the hole from the drill, thoroughly churned with the sludge, and on coming out of the hole, floats away as a thin scum, carrying with it small particles of sulfides. Microscopic examination of this scum at Ajo showed quite appreciable amounts of sulfides floating with the oil on top of sludge barrels. This floating away of sulfides may give a small factor of safety to the sludge assays.
Sampling of churn drill holes has been well described by E. R. Rice. As in the case of diamond drilling, it is important to clean out the hole thoroughly at the beginning and end of every sampling interval. The process of sampling is simple, as the sludge brought up by the bailer runs through a mechanical splitter which automatically cuts it to the proper size—usually a wash tub full. It is important to wash the launder and splitter at the end of every sample, and to include a proper proportion of the wash water in the sample. As the amount of water in the sample is not excessive, it is better to evaporate off all the water instead of allowing the sludge to settle and siphoning or pouring off the water. Mr. Rice suggests drying by steam instead of coal or wood, to prevent roasting the sulfides in the samples.
As in the case of diamond-drill holes, detailed daily reports should be made for every hole; and when a hole is finished, a chart should be prepared for the permanent record, giving a graphic representation of the assay, and all features of possible interest noted during the drilling. Mr. Rice gives forms for daily reports and charts. A part of the sludge from every drilling interval, quartered out before grinding, should be kept for reference, preferably in a tin box.
Churn drilling is somewhat less accurate, in most cases, than diamond drilling. Unless the hole is cased nearly to the bottom, the frequent passage up and down of the bit and bailer knocks off material from above the sample. If the values are in soft seams, the sample will be too high grade. Even if the ore minerals are disseminated through the rock, the sample will be affected by material from higher up in the hole. As Mr. Rice suggests, if the hole is kept filled with water to above the bottom of the casing, the water pressure tends to hold material in the walls in place. The inaccuracy of churn-drill samples is lessened by the comparatively large size of the hole. A 5-ft. advance of an 8-in. (20 cm.) hole cuts out about 200 lb. (90.7 kg.) of ordinary disseminated ore. If this ore assays 1.5 per cent, copper, and if 5 lb. (2.3 kg.) of 5 per cent, ore are shaken down from crevices in the walls of the hole, salting the sample, the resulting assay would be 1.58 per cent. It is seldom that a sample would be salted more than this.
With careful work, involving casing below all caving ground, assays from churn drilling can be depended on in nearly all cases to within 0.1 per cent, copper. In every property, a large amount of raising or test- pitting should be done to check the drilling. If drilling results are high, a factor of safety is thus found to use in future drilling at that property.
SAMPLING OF UNDERGROUND WORKINGS
The best sample from underground workings is made up of all the material removed after every round is shot. On account of the great weight of the sample, the salting by rich ore falling in from friable seams in the rock is not considerable. If, as an opening advances, every tenth shovel or bucket full is thrown into a sample container, and the samples thus obtained are properly crushed and quartered—preferably by a mechanical sampler—the results are as nearly fool-proof as sampling can be. The only possible error comes from the strange impulse that moves the most ignorant and disinterested workman to throw the rich chunks into the sample. At Ajo, the large test-pit samples, made up of every tenth bucket full of ore hoisted, averaged 0.15 per cent, copper higher than corresponding channel samples. This error can be accounted for only by the fact that Mexicans have an inherited adeptness at sorting ore, which unconsciously influenced them in filling the tenth bucket. This example illustrates the fact that no sample can be blindly trusted.
Grab samples from rounds shot in underground workings are almost always high. This is partly because of the tendency to take too great a proportion of fines, and partly because of the almost magnetic attraction of the most conscientious hand toward rich pieces of ore. Grab samples should be used only as rough checks on the other methods of sampling.
Channel samples must be taken where existing underground workings must be sampled, or where it is not practicable to take a proportionate part of every round as it is mucked. The accuracy of this method of sampling depends on laying down a rigid system of sampling, and adhering to it. The location and direction of channels should be most carefully studied, and the same channel interval should be used throughout the orebody. If the mineralized seams tend to follow any prevailing structure, the channels should cross this structure. Usually these seams run in all directions, and it is safer to cut all channels in the same direction—horizontally or vertically on one or both walls—throughout the orebody. Some of these channels may follow rich seams, but the average should be about right. The channel interval chosen is usually 5 or 10 feet.
It is most important to clean off the rock before channeling. The best way is to use a pick and then a stiff brush. This cleaning removes the dust that has collected on the rock, and also tends to rub or jar out a little of the richer ore from seams before sampling begins. This loss partly compensates for the excess of rich material that falls into the sample from seams in the bottom of the channel.
The size of channel depends on the uniformity of the ore. If this is hard and uniform, channels 4 in. (10 cm.) wide by 1 in. (2.5 cm.) deep are sufficient. Often, even small samples taken with a hand pick give fair results. In very blocky and irregular ore, in which a large part of the mineral is on seams, large channels, up to 6 in. wide and 3 in. deep, should be cut. In such uneven ore, it is useful, to provide samplers with wooden blocks the width and depth of the required, cut, and to make these blocks fit in the channel at all points. With these blocks, experienced samplers cut very uniform channels even in badly jointed ore.
Where channels are small; the samples may be caught in boxes or bags. Where large, it is much better to spread large canvasses in the bottom of drifts, or on platforms in raises and test pits, and to cut the samples on them. One engineer can watch two or three crews of samplers, working on adjacent cuts, and make sure that the channels are evenly cut and that any rock from outside the channel which falls on the canvas is thrown to one side.
If crushers are available, the entire sample should be sacked, tagged, sent to the crusher, and then put through a mechanical splitter. Anything save a preliminary rough sampling of a disseminated property would justify the purchase of this equipment. If the equipment is not available, the sample may be broken to ½ in- or so by hand, and quartered, with finer hand crushing between quarterings, to a 4 or 6-lb. sample, which is sent to the assayer.
The results of all sampling should be recorded on assay maps, usually on a scale of from 50 to 20 ft. (15 to 6 m.) to the inch (2.5 cm.). Entering the assay, instead of the number of sample, on the map simplifies the later work of combining assays and estimating.
If the channels are sufficiently large for the character of ore, channel samples can be accepted with more confidence than either churn-drill or diamond-drill samples. Channel samples come from the desired place, while drill samples may be salted by ore from an upper part of the hole. Morton Webber has pointed out that there are certain errors latent in hand sampling. If the valuable minerals are harder than the gangue, the samples tend to be low; and if softer or more friable, high. These latent errors are less important in copper than in gold and silver ores. The mineral itself is less valuable, and a far greater quantity of it is required to affect the sample. A larger channel can be cut in fairly soft disseminated ore than in hard gold quartz, so that salting, by friable ore minerals, from the sides and bottom of the channel has less effect. Also the cleaning of the rock before channeling makes up for some of the ore that falls in from the bottom of the channel. If a measuring block is used, there is less chance of cutting too much of softer bands, and too little of harder bands in the ore. If there are workings enough to require several hundred samples, minimizing the effect of a few high-grade assays, channel sampling should be accurate to within 0.05 per cent, copper.
The ideal method for determining the assay content of a disseminated orebody is to check at least every fifth drill hole by a raise or test pit 50 or 100 ft. (15 or 30.5 m.). high or deep. One tenth of all material removed from each round shot in these workings should be taken as a bulk sample, and the walls should be carefully channeled. As a further check, drifts should be driven between several test pits or raises, and bulk channel samples taken in them. By this combination method, the value of the deposit is absolutely proved, and the results of future drilling, raising, or test pitting can be trusted without further checking.
As an example of results of the three methods of sampling, in the development of the New Cornelia Copper Co., at Ajo, Ariz., over 1000 ft. (304 m.) of test pitting was done to check diamond drilling. The average of diamond-drill samples and of large channel samples checked to within 0.005 per cent, copper. The bulk samples, consisting of every tenth bucketful crushed and quartered mechanically, averaged 0.15 per cent, higher than the channel and drill samples. The drill and channel samples were accepted as correct. Several million tons of this ore have now been mined and treated. All of this ore to date has averaged 1.51 per cent, copper, compared with the estimate of 1.54 per cent. The grade has been a little higher than the estimate in one part of the orebody and lower in another part. This property has proved that, in a disseminated orebody, it is possible to sample and estimate the ore correctly without reducing the grade by a factor of safety.
ESTIMATION OF ORE RESERVES
In nearly all of the disseminated copper orebodies, in the opinion of the writer, the sampling has been well done and has given accurate results. Yet in many of the properties the ore mined has averaged from 0.1 to 0.4 per cent, copper lower grade than the estimates. This is due to an error in the method of combining assays to give an average grade and length of ore in every drill hole or other opening, and to a failure to base the estimate on mining conditions. These are the difficult problems in the estimation of ore reserves. A knowledge of the geology of the deposit is necessary for the interpretation of changes in the grade of ore, and for the proper combining of assays to give the average grade. Also, a fair understanding of the size and shape of the deposit and of the character of ore is necessary for the determination of the methods of mining and of treating the ore, which in turn govern the minimum grade that can be mined with profit. The mining method and the minimum grade again modify the shape and grade of ore that will be mined. All of these factors are interdependent. Without thorough study of them, and particularly of the geology of ore occurrence, care in sampling is thrown away.
USE OF GEOLOGY IN ORE ESTIMATION
The general form of nearly all disseminated copper orebodies is tabular; that is, the horizontal dimensions are much greater than the vertical. But the fractures along which mineralization is strongest nearly always dip steeply. In the main part of most orebodies, the mineralization is so intense that the rock between the fractures is commercial ore. In outlying portions, both around the edges and underneath the main orebody, the rock between fractures is less thoroughly mineralized and is usually below the minimum grade, while along the fractures there are bands of richer ore, often several feet wide. These richer and leaner bands are too narrow to be mined separately without great expense. If rich and lean together average above the minimum, the whole mass will be mined; if below it, all will be left.
This banded character of outlying ore is exaggerated in drill holes or other vertical openings. Fifty feet of 2 per.cent, ore in a drill hole maybe caused by a 5-ft. band along a steeply dipping fracture. The next 50 ft. of 0.5 per cent, material may represent only a 5-ft. band of less thoroughly mineralized rock between fractures. If the hole is estimated to have cut 50 ft. of 2 per cent, ore, the mining grade will be far under the estimate. It should properly be figured to have cut 100 ft. of 1.25 per cent, ore, assuming that the 2 per cent, band has persisted to 100-ft. depth.
Around the edges of an orebody, even with the most careful study of ore occurrence and fractures, it is often impossible to determine just how much mineable ore a drill hole represents. A few feet to one side, the conditions may be absolutely different from those in the drill hole, depending on the regularity and frequency of mineralized fractures. For this reason, it is good practice to figure “developed ore” only to the outlying drill holes, not beyond them. Even with this limitation, estimates of outlying portions of orebodies often do not include enough of the lean bands and give too high a grade. In determining the probable bottom of commercial ore, under the main orebody, a closer approximation can be made. Where the material from the bottom of the main stretch of ore cut in a drill hole to the bottom of a lower band of ore, including rich and lean bands, averages above the minimum, it is safe to include this whole length and grade in the orebody. But if the average of lean and rich bands is below the minimum, the whole should be thrown out. Even where, the lean and rich bands below the main orebody are 50 to 100 ft. thick, it is almost never safe to estimate that leaner material can be left and the deeper ore mined. This assumption should only be made when there is definite geological evidence that a lower orebody of commercial size exists.
Fig. 2 is a typical example of a section through four drill holes that cut a lean capping, then a body of good ore, then a band of material of lower grade than the 1 per cent, minimum, and finally a lower band of ore. The average assays are given in the section. The temptation is to estimate two nearly parallel horizontal orebodies, as shown by the dotted lines. But the fractures are steep, and there is no geological structure to cause a lower horizontal orebody. Probably the alternate lean and richer
bands are caused by deep enrichment along fractures and unenriched material between them. The apparent thickness of the richer bands is caused by the steepness of the enriched fractures. Either all the material below the main part of the orebody must be mined at any point, or none, of it. Averaging lean and rich bands, in proportion to their lengths, gives the following results:
Drill hole No. 1, 230 to 370 ft., 0.99 per cent.
Drill hole No. 2, 230 to 400 ft., 1.03 per cent.
Drill hole No. 3, 280 to 450 ft., 1.25 per cent.
Drillhole No. 4, 250 to 420 ft., 0.97 per cent.
With the 1 per cent, minimum, the material below the main part of the orebody in holes No. 1 and No. 4 is below the commercial grade and must be rejected. That in holes No. 2 and No. 3 is above the minimum and will be mined.
The depth and average grade of ore estimated in these four holes should be:
Drill hole No. 1, 80 ft., 1.80 per cent.
Drill hole No. 2, 270 ft., 1.20 per cent.
Drill hole No. 3, 290 ft., 1.56 per cent.
Drillhole No. 4, 110 ft., 1.70 per cent.
If for comparison each of these holes is assumed to represent a block 200 ft. square, with 12.5 cu. ft. to the ton the holes have developed 1,800,000 tons of ore averaging 1.47 per cent, copper. The incorrect method of estimating, assuming two layers of ore separated by waste, gives 1,800,000 tons averaging 1.56 per cent, copper. Mining would probably check the first estimate and grade very closely. This case is typical. The wrong method of combining assays rarely involves a great error in tonnage, as the lean material left out about compensates for richer material included. But the grade given by the incorrect method is considerably higher than the deposit will mine; and a mining plan based on it will not be suited to the form of the deposit. Inspection of drill-hole records of several disseminated copper properties indicates that this error in combining drill-hole assays, caused by lack of understanding of the ore occurrence, is by far the most important reason for the failure of many properties to mine up to the estimated grade.
The other fact emphasized by geological study is the great variation of copper content in most orebodies of this type. A drill hole seldom really represents the ground for 100 ft. on every side of it. Close checks in small areas cannot be expected. It is therefore necessary to have a great number of drill holes, spaced regularly, not farther than 200 ft. apart. If this is done, in the whole orebody the average ore indicated by drilling will check closely with the average of ore mined.
STUDY OF MINING AND COSTS BEFORE ESTIMATING
Before an estimate can be made which will check the mining, it is necessary to know what mining method will be used, and what the total cost of producing copper, and so the minimum grade of commercial ore, will be. If steam-shovel mining is selected, in order to place the approach properly, it will be advantageous to mine and treat some material of lower grade than the minimum, and to leave in the sides of the pit some ore above the minimum grade. If a caving system is chosen, allowance must be made for mixture of ore with capping. This mixture will result in the loss of part of the ore and in the; sending of some lean capping material to the mill. The estimate must be modified to allow for this mixture; also the sending of waste to the mill will increase the charges against the ore, and so affect the minimum grade and the tonnage.
C. E. Arnold has discussed the effect of mining method on cost and extraction. The importance of the effect of a mining method on an estimate is shown by the fact that in one of the disseminated properties in which a caving system was used the manager stated that he was mining 105 per cent, of the estimated tonnage and 90 per cent, of the estimated copper. This estimate should have been recalculated.
The tonnage, grade, and form of an orebody must be known in order to determine the mining system, costs, and minimum grade of ore that can be mined; and the mining system and minimum grade must be known in order to estimate the grade and tonnage of ore that will be mined. All the factors are interdependent. The best solution to the problem is to make a preliminary estimate, based on an assumed minimum, and neglecting any influence of mining method on the outline of ore mined. This estimate will give the approximate form, grade, and tonnage in the orebody. From it the mining method, method of treatment, and approximate costs may be determined, and a more accurate minimum grade calculated. Using this new minimum, a final estimate is made, making the proper allowance for the effect of the mining method chosen on form of orebody and cleanness of mining. This final estimate should agree almost exactly with the tonnage and grade that will be mined. The only material difference will be caused by improved operating methods, process, or recovery, which will make it possible to lower the minimum grade of profitable ore and so to increase the tonnage.
CALCULATION OF TONNAGE
The calculation of tonnage is a simple matter. Where the deposit is developed by drill holes on coordinates, the average depth of ore in holes on the four corners of every square, multiplied by the area of the square, gives a sufficiently close approximation to the volume of ore in the square block. The sum of the products of assay times depth of ore in the four holes divided by the sum of the depths of ore gives the average grade of ore in the block. If drill holes are not on coordinates, the deposit is usually divided into triangular vertical prisms, with a drill hole at every corner. The volume and grade of ore in every prism are found just as in the case of the square prisms described. As pointed out by J. E. Harding, this method is not accurate when the triangles are not equilateral, but averaged over the whole deposit, the approximation is close enough unless drill holes have been purposely placed in richer parts of the ore. Whether the deposit is divided into square or triangular prisms, the tonnage of ore in the whole orebody is found by adding the tonnages in all the prisms, and the grade of ore in the deposit is found by dividing the sum of the products of tonnage and grade in all the prisms by the total tonnage.
In order to reduce cubic feet of ore in the various blocks to tons, specific gravity tests should be made on samples of coarse and fine ore from workings in various parts of the deposit. By weighing the samples in and out of water, subtracting the weight of the container in each case, the weight of ore per cubic foot is found by the formula:
Weight per cubic foot = 62.5 x Weight of ore in air/Weight in air minus weight in water
Disseminated copper ore averages about 12.5 cu. ft. per ton. The average factor found in any deposit is used for that whole orebody.
The final estimate, based on the calculated minimum and the plan of mining adopted, is often made by passing parallel vertical, sections through the orebody along coordinate lines. These sections show all the ore recoverable by the method chosen. The areas of sections of the orebody thus outlined are measured, and the average grade of ore in each section is obtained by dividing the sum of the products of grade times depth of ore in all drill holes in the section by the sum of depths of ore. The volume between adjacent sections is computed by multiplying the average between the areas of the sections by the distance between them, and the grade of this ore is the average in proportion to areas between the grades in the two sections. If one section is much smaller than the next, the prismoidal formula maybe used. (Volume of prismoid equals distance between sections multiplied by one-sixth the sum of the two end areas plus four times the area of the section midway between them.) It is seldom necessary to use this formula. If the drill holes are not on coordinates, it is simpler and sufficiently accurate to make the final estimate like the first by dividing the orebody into triangular vertical prisms, making the areas and shapes of the prisms conform with the outlines of ore that will be mined.
If the deposit is developed partly by vertical and partly by horizontal workings, the method of estimating must be decided by careful study of the individual case. The orebody is usually divided into simple geometrical figures, with workings along as many of the edges as possible. Great care must be taken not to give undue weight to assays in drifts that follow the mineralized structure; it must be remembered that workings on one level may be at the horizon of greatest enrichment. Assays from them must not be given too much weight compared with those from raises or winzes. In general, samples from workings on coordinate lines are much more reliable than those where the plan of workings is not regular, as, in the latter case, it is almost certain that the richer portions of the orebody have more than their share of workings. An estimate in such a case depends entirely on the judgment of the engineer.
If there is likely to be a mixture of ore with capping, the final estimate should be modified by factors that allow for the loss and dilution of ore and for the resulting lowering of grade.
The sampling of a disseminated copper orebody is simple and should be very accurate. The estimation of tonnage and grade of ore in the deposit, once the length and grade of ore in every opening has been figured, is a simple mathematical problem. There is no excuse for great errors except where the irregularity of workings suggests the probability that richer portions of the orebody have been more thoroughly developed. The combination of individual assays in a drill hole or other opening to give the length and average grade of ore that will be mined is the difficult part of the problem of estimation. To solve it, the engineer must have an intimate knowledge of the geological occurrence of the ore, of the mining method to be used with its effect on recovery of tonnage and of copper, and of the total probable costs per ton of ore and per pound of copper, indicating the minimum grade of ore that will be treated at a profit. The failure to study these factors properly is responsible for the fact that the ore mined in many disseminated copper properties has averaged from 0.1 to 0.4 per cent, copper lower than the estimates. This is an unnecessary error. The final estimate should check the tonnage mined almost exactly, and the grade of ore mined within less than 0.1 per cent, copper.