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By W. Hurst

What is entailed here is the extension of the sinzplified material balance formulas to encompass interference between oil fields. As previously reported, the ex-plicitness as so revealed for the cunzulative pressure drop as a function of all factors contributing to its change in the material balance equation, is now transcribed through the inter-conzmunicating aquifer to effect an increased pressure drop on an adjoining field by interference. Such is performed by mathematical analyses and the application of the Laplace transformations. What is accomplished is that the reiteration problems previously associated with interference studies are nullified, since volumetric changes for the fluids in situ are automatically adjusted by the explicitness so expressed, and what pertains to the superposition principle applies only to the impeded water drive upon a su.bject field, which is likewise incorporated in the over-all pressure drop that results. The mathematics treats with the rigorous solution of the problem, as well as with methods easily amenable to numerical interpretation by the practicing engineer. In all cases, however, what is deduced for areal extents, reveal interference between wells when time becomes large that further substantiate the analyses. Probably of equal significance, all variables and for/nation characteristics are accounted for. This applies to the differences in PVT analyses that occur from field to field and the physical parameters associated with the lithology of the reservoirs. The latter is deduced from a rigorous interpretation of the unsteady-state flow problem for sands of different permeabilities in series. Thus, what purports to be a trial-and-error calculation to include variations in sand conditions within the intercommunicating aquifer to define water drive has little importance compared to the designation of such paranzeters at the reservoir to constitute the essential criteria. INTRODUCTION In a recent publication, the reader has been introduced to the simplified material balance formulas,' It has been shown that the complexities formerly associated for identifying and determining reservoir pressure in the material balance relationship can be resolved by treating with the Laplace transformations, the inversion of which reveals pressure as an explicit function of all factors contributing to its change. For an under saturated oil reservoir, this constitutes an integrated effect from the inception of production; and for a saturated oil reservoir, such represents a survey traverse. However, what is most important, for the first time we are able to express the pressure change in a reservoir directly to the oil, gas and water produced, and to the physical parameters of the formation, in the same manner that reservoir pressure has served in the past to define well interference — which opens up this avenue of endeavor for investigating interference between oil fields. The occurrence of interference is by virtue of the juxtaposition of two or more oil reservoirs producing in the same aquifer. Thus, in any one field, the extended production so incurred creates a pressure lowering in the field, as well as in the aquifer, which can now be transcribed by these simplified material balance formulas to the adjoining reservoir to observe the increased pressure change so induced. These effects are retroactive from field to field, to reveal a pressure drop far in excess of normal depletion to evidence the interference pattern that can result. Such is the purpose for the present undertaking — to develop the mathematical physics treating with this phenomenon of interference between oil fields, employing the simplified material balance formulas. Since Ref. 1 often will be referred to in the text, it is identified as "The Simplification", in the same connotation that another paper has been referred to as the "Laplace Trans-formation. However, the amount of material to be covered in these passages is substantial; therefore, the total emphasis will be placed upon developing these fundamental ideas treating with interference rather than attempting to offer work curves, which always can be prepared. For the practical application of these simplified material balance formulas that form the framework of the present development, the reader will find a comprehensive treatment in the Appendix of Ref. 1, illustrating a factual field example. In essence, what is proposed by this presentation is to make available to the practicing engineer a simplified means to treat with interference between oil fields, independent of the complex machine computations that have attended such undertakings in the past. As the problem unfolds, a common pattern will be discernible, whereby the many reiteration processes that previously required computing devices are eliminated.

By AIME AIME

A PAPER prepared by James A. Adams, development engineer of the fitline & Smelter Supply Co., and presented at the last Annual Meeting of the A.I.M.E. in New York City, de- scribed a new automatic pulp density controller which has had a most favorable reception. Manual control has until now been the universal practice in spite of its shortcomings; samples of pulp for density determination were often improperly taken, and only at the operator's convenience, so that the trend in density changes was frequently missed, and the grinding circuit al- lowed to operate under something less than the most efficient conditions.

Jan 1, 1940

By AIME AIME

M ODERN metallurgy properly belongs to this century. The great advance made in this science is directly attributable to the discovery of the Roentgen rays. Application of the results of this discovery, together with the more recent corroborating studies in electronic diffraction have definitely and for all time established this science. Metallurgists today speak with familiarity of the atoms of the different metals in terms of their orientation, atomic volumes, lattice structures, dimensional lattice constants distance of nearest approach, and the like. One matter of profound interest, which is quite staggering to the imagination of the human mind, is the enormity of the number of atoms even in a small particle of metal. As an illustration, let us compute the number of atoms in the volume of one cubic centimeter in a single grain of absolutely pure copper. Eighteen and a fraction cubic centimeters equal the volume of one cubic inch.

Jan 1, 1940

By AIME AIME

WITH the example of the steel open-hearth men and their round table conference before the copper men, the query naturally arose "Why cannot we do likewise?" The advantage of pooling and comparing knowledge on smelting in the copper reverberatory furnace seems particularly pertinent at this time when all metallurgical economies possible must be rigorously enforced. A great deal of data had also been obtained and filed during the period of litigation over the Carson patent, and it would naturally be available with the cessation of further suits. With these ideas in mind, H. Foster Bain took up the advisability of holding such a conference directly with the heads of all the companies in the United States operating copper reverberatories, and found a nearly unanimous response. The mining companies appointed representatives directly, or indicated to the heads of various metallurgical operations what members of their staffs should be sent to such a conference.

Jan 1, 1930

By C. B. Foster, S. I. Freedman, E. M. Jamgochian

Coal-oil mixture (COM) combustion technology is regarded by the US Department of Energy (DOE) as near term and Potentially applicable to existing utility and industrial steam generators and for injection into blast furnaces. From work done previously, it has been established that COM can be burned in existing boilers and blast furnaces. Therefore, the issues being addressed by the current DOE program are: (1) determination of best available technology to achieve environmentally acceptable long-term reliable operation and (2) determination of applications for which COM can be utilized economically. Some of the technological options have begun to be determined by projects already under way. However, many projects are still in the early stages of development.

Jan 1, 1980

By H. Y. Bassett

THIS paper attempts to show the various major operations used in nonferrous tube mills and does not necessarily represent the current practices at the two plants of the Wolverine Tube Div., of Calumet and Hecla Consolidated Copper Co. Inc. The operations now utilized in the production of tubing are quite varied and show the continual interest and advance metallurgically and mechanically to produce the best quality at the lowest cost. Naturally, any advance or lowering of cost is dependent on large production runs, which mean longer machine running time with maximum worker productivity. Standardization of tube sizes and elimination of unnecessary alloys are therefore very necessary, otherwise the development of costly new production machines would be of little benefit to the consumer as a whole. It should be noted that in such a short presentation it is impossible to describe in any detail the major operations. The short descriptions, it is hoped, will enable all who are interested to obtain a general idea of present, day practices in the copper tube producing field. Fig. I is a flowchart or sequence of operations showing the steps usually employed in tube production. RAW MATERIALS Quality starts with the raw material, and it is absolutely necessary that raw material be controlled and held to rigid specifications. Little need be said, however, regarding the raw materials for the casting of bars or billets, as the material always is purchased and checked against the various governing A.S.T.M. specifications. CASTING Casting, as is indicated in Fig. I, is quite varied and for convenience can be classified into two groups: The casting of solid billets, and the casting of hollow tubes, each of which is the base for subsequent operations. In the melting of the raw materials various types of furnaces are used, and the selection of any one is dependent on many factors outside the scope of this paper. However, as of general interest, a short description will be made of each. Induction Furnace (Low Frequency) This is popular in the melting of copper-base alloys, Fig. 2. In the induction furnace the principle of an inefficient transformer is used for the production of the necessary melting heat. The primary coil is.arranged around a transformer core made of high permeability silicon steel sheet. The secondary circuit is through a melting channel around the primary coil and opens into a hearth which contains the main charge. The heat is generated only in the melting channel, but because of the stirring action there is a constant flow of metal around the channel, which when mixing with the charge causes very rapid melting. The volatilization losses are very low as the furnace atmosphere above the charge is heated only by the heat from the melting metal. The stirring action, however, makes the use of any slag cover difficult. Such furnaces- must be started with molten

Jan 1, 1951

By L. A. Cranson

WHEN I came out of Stanford University in 1922, the out-look for men trained in geology, petroleum engineering, and mining was indeed dismal; in fact, so much so that most of us looked upon our future in those fields as pretty hopeless. Neither our professors nor those men in industry with whom we came in contact gave us any enthusiastic encouragement as to the future of ourselves or the fields we had chosen for our labors. I believe that the attitude of pessimism which saturates everyone about graduation time is lament able and short-sighted, and may often start a young man on his way with an attitude of defeatism. Instead, he should be starting out knowing that he can expect hard work and keen competition, but that the fields of his labours are expanding at an accelerated rate, and that strong, energetic efforts will as always accomplish highly satisfactory results.

Jan 1, 1941

By R. A. Deju, R. B. Bhappu

The basic structural unit of all silicate minerals is a tetrahedron with a silicon atom at the center and four oxygen atoms at the corners. The oxygen-silicon distance is about 1.6 & and the oxygen-oxygen distance about 2.6 &. The different types of oxygen-silicon frameworks in the various silicates are based entirely on the combinations of the tetra-hedral oxygen-silicon groups through sharing of oxygen atoms. In recent years, infrared spectroscopy has permitted estimation of the ratio of the ionic character of the oxygen-silicon bond to be a few times that of the oxygen-carbon bond and the ratio of electro-negativity of the two bonds has also substantiated this finding. On this basis, it is generally accepted that the oxygen-silicon bond is the strongest one occurring in silicate minerals. As the oxygen-silicon ratio increases from quartz to the olivines, a greater percentage of the oxygen bonding power is available for bonding to cations other than silicon. Hence, with an increasing oxygen-silicon ratio, there is increasing oxygen-to-metal bonding. Upon the fracturing of a silicate mineral crystal, the oxygen-metal bond, which is almost entirely ionic in character, should break more easily than the stronger oxygen-silicon bond, resulting in a greater number of unsatisfied negative forces on the surface. If, then the mineral is immersed in a liquid containing hydrogen ions, these negative forces should tend to be neutralized by hydrogen ions from solution, resulting in a change of the pH of the solution. An increase in the degree of adsorption of hydrogen ions is to be expected as the oxygen-silicon ratio in the crystal structure increases. This study attempted to correlate the oxygen-silicon ratio for various representative silicate minerals to the adsorption of hydrogen ions. Experiments to determine the effect of surface area on this adsorption and to investigate the effect of surface iron were also conducted. It is believed that such studies of the surface properties of silicate minerals will supply pertinent information about their behavior in froth flotation systems. EXPERIMENTAL PROCEDURE Ion Exchange: Carefully selected, hand-picked samples of the minerals investigated were dry-crushed in a ceramic ball mill and sieved to obtain a minus 100 plus 200-mesh sample. The sized samples were then run through the electro-magnetic separator to remove any iron-bearing particles. A 10-g sample of each mineral was placed in 100 ml of freshly deionized water previously adjusted to a pH of 3.50 with HCl. The beaker containing the sample and the water was placed under a bell jar from which the air was displaced at once by nitrogen gas from a tank. All experiments were carried out in a nitrogen atmosphere. The sample and solution were stirred gently but continuously during the entire experiment, the stirring speed being kept about the same for all runs. Changes in pH were followed with a Beckman Zeromatic pH meter and recorded on a

Jan 1, 1967

G. A. Moore—The tin-fusion method has been a very favorable possibility for many years. The authors apparently have settled the question that delayed the method for a long time by showing that no hydrogen is absorbed in the tin. This, of course, is very important. I want to make a few remarks concerning the absolute accuracy of analysis, which must be the final basis for deciding among the various methods. From the figures in the paper, there seems to be some re-maining slight discrepancy on the actual amount of hydrogen present in various samples which may be presumed essentially identical. (This is of the order of the precision of individual analyses but appears in averaged results.) From the analyst's viewpoint, the tally of hydrogen content can be regarded as occurring in three portions. First is a large portion which comes off easily and automatically during sample storage and later on heating in the apparatus. This is fairly easily analyzed. Second is an item which may be either positive or negative in the tally sheet. In warm or hot evolution, this is a portion which, in practice, can never be re-

Jan 1, 1951

By J. F. Olk, E. D. Spaulding, R. E. Thurmond, G. A. Komadina, R. W. Hernlund, J. A. Journeay

THE Pima pit is a 1700x1400-St oval, the long T axis parallel to the strike of the orebody. The north side of the pit is carried as a final pit slope that coincides with the footwall of the orebody. The south side and east and west ends of the pit are working slopes continually being stripped back toward the final slopes. An inclined roadway extending from the natural ground surface on a 5 pct grade down to the north- east corner provides access to the pit. This road enters the pit 130 ft below the natural surface and continues as a pit ramp on a 5 pct grade to the 3150-ft bench (roughly the base of the alluvial cover). At this point the ramp system is steepened to a 12 pct grade and continues to the pit bottom. The 5 pct grade is maintained in the alluvial section to facilitate scraper haulage out of the pit. In addition to this main access ramp, temporary working ramps in the alluvial areas allow shorter routes to dumps. These are left on top of working benches and do not change the overall working slopes. Below the base of the alluvium, haulage is by truck down to the skip loading point or up from the bottom to the skip loading point.

Jan 4, 1958

By Bunting S. Crocker

EBBLE grinding at Lake Shore is not a temporary BlE wartime substitute. The tube milling plant, with a 1000 ton per day capacity, grinds a hard siliceous ore to 90 pct — 325 mesh. The plant, prior to using pebbles, was consuming 4.3 lb of 11/4-in. grinding balls per ton of ore, which amounted to 785 tons of balls per year. At September 1951 prices, $132.60 per ton, this steel cost amounted to $104,400 per year, or $0.285 per ton milled. By the Lake Shore method of substituting screened rock for this steel, all of this cost is saved. This is one of the major economies in Lake Shore mill practice. Regardless of the ultimate price of grinding balls, a change back to steel balls is not considered. The present pebble plant is more flexible than a steel ball plant and equally efficient. For example, if it is desired to change the size of grinding media, the pebble charge in any mill can be changed completely in 4 to 5 days, as against 76 days to change completely a 1-in. steel ball charge. To change pebble size it is necessary only to change two sets of screens and clean out the rock feed storage bin. This will take 8 to 10 days as against 3 to 4 months to clean out the customary supply of grinding balls kept on hand. Also it has not always been possible to purchase all desired sizes of balls at any price. In an analysis of savings effected by the use of the pebble mills, the flexibility of the Lake Shore grinding plant should be discussed, as it has a direct bearing on these savings. The plant has always used several units to handle tonnage rather than sending all the tonnage through a single unit. This principle may result in using small diameter mills, but no objection to that is seen. At no time has any advantage been found in cost per ton ground in large diameter mills. Both the capacity and the power of any mill varies as the diameter raised to the 2.6th power. Consequently large or small mills are equally efficient, and a plant, should be designed to use as many units or combination of units as is consistent with reasonable operating practice. Mills under 5 ft diam are harder to reline, etc. To define the case at Lake Shore, 2600 tons per day formerly were milled in seven 7x6-ft ball mills and twelve 5x16-ft (and two 6x16-ft) tube mills.* This gave an excellent test plant and an extremely efficient one. In this plant the ratio of ball mills to tube mills was 1:2. When the much cheaper pebble mills were substituted for the tube mills, this ratio was changed to one ball mill to four pebble mills to take the greatest possible advantage of the cheaper operating mill, i.e., the pebble mill. This flexibility without loss in efficiency has been an important item in the cost savings. It is interesting to note that the use of pebbles for fine grinding was proved first in the laboratory in a 12-in. ball mill. In fact, since 1934 all testing on — 8 mesh material has been done in this 12-in. mill. Scope of the Tests A paper on fine grinding at Lake Shore Mines was published in July 1940.' This paper covered 7 years of intensive research on fine grinding as well as sizing methods and equipment, plant scale grinding tests on 5x16-ft tube mills with and without grate discharges both with 1-in. and -in. balls, the use of laboratory mills to evaluate plant changes, and several reports on classifiers and classification. In the following July the addendum report2 was added in which the idea of series-circuit grinding was introduced, and the results of running five stages of tube mills and bowl classifiers were shown. Since 1940, the ball milling end of the plant has been altered extensively as a result of tests on the use of 3-in. rods in 7x6-ft mills and the use of the Tyler repulping screen with from 7 to 14 mesh screens. These tests are lengthy and may be covered in a separate report later. The scope of this report is confined to ore ground by rod milling and ball milling until it passed through an 8 mesh Tyler Ty-rod screen. The —8 mesh screen undersize then was pumped to a primary bowl classifier in open circuit and the sands from the bowl sent to the primary pebble mills, see Fig. 1. In the pebble mill circuit the ore is ground to 90 pct —325 mesh (24 pct + 28 microns). In studying the flowsheet, attention should be paid to the efficiency of the classification equipment used. The Tyler repulping screen is an efficient machine on the 8 to 10 mesh separation, and the bowl classifier is equally efficient at the 325 mesh separation. Efficient classification is a necessity for series-circuit stage grinding. The ore is hard siliceous porphyry, 60 pct SiO,, 80 pct insoluble. Its grindability at different meshes has been shown near the top of the list in F. C. Bond's grindability tests.' Lake Shore is not shown, but an adjacent mine with identical ore, Wright-Hargreaves, is. Reasons for the Changeover Since 1936 grinding balls have been rising steadily in price with no sign of stopping. For a mill that used 4.5 to 5.2 lb of grinding balls for every ton of ore ground this rise represented an alarming increase in grinding costs. In many cases the quality of the grinding balls fell off as the scrap steel became more difficult to obtain. The ratio of tube mills to ball mills increased with the use of the Tyler repulping screen in the ball mill circuit. Originally only 3.0 lb of balls per ton were used in the tube mills, and this

Jan 1, 1953

By Bunting S. Crocker

EBBLE grinding at Lake Shore is not a temporary BlE wartime substitute. The tube milling plant, with a 1000 ton per day capacity, grinds a hard siliceous ore to 90 pct — 325 mesh. The plant, prior to using pebbles, was consuming 4.3 lb of 11/4-in. grinding balls per ton of ore, which amounted to 785 tons of balls per year. At September 1951 prices, $132.60 per ton, this steel cost amounted to $104,400 per year, or $0.285 per ton milled. By the Lake Shore method of substituting screened rock for this steel, all of this cost is saved. This is one of the major economies in Lake Shore mill practice. Regardless of the ultimate price of grinding balls, a change back to steel balls is not considered. The present pebble plant is more flexible than a steel ball plant and equally efficient. For example, if it is desired to change the size of grinding media, the pebble charge in any mill can be changed completely in 4 to 5 days, as against 76 days to change completely a 1-in. steel ball charge. To change pebble size it is necessary only to change two sets of screens and clean out the rock feed storage bin. This will take 8 to 10 days as against 3 to 4 months to clean out the customary supply of grinding balls kept on hand. Also it has not always been possible to purchase all desired sizes of balls at any price. In an analysis of savings effected by the use of the pebble mills, the flexibility of the Lake Shore grinding plant should be discussed, as it has a direct bearing on these savings. The plant has always used several units to handle tonnage rather than sending all the tonnage through a single unit. This principle may result in using small diameter mills, but no objection to that is seen. At no time has any advantage been found in cost per ton ground in large diameter mills. Both the capacity and the power of any mill varies as the diameter raised to the 2.6th power. Consequently large or small mills are equally efficient, and a plant, should be designed to use as many units or combination of units as is consistent with reasonable operating practice. Mills under 5 ft diam are harder to reline, etc. To define the case at Lake Shore, 2600 tons per day formerly were milled in seven 7x6-ft ball mills and twelve 5x16-ft (and two 6x16-ft) tube mills.* This gave an excellent test plant and an extremely efficient one. In this plant the ratio of ball mills to tube mills was 1:2. When the much cheaper pebble mills were substituted for the tube mills, this ratio was changed to one ball mill to four pebble mills to take the greatest possible advantage of the cheaper operating mill, i.e., the pebble mill. This flexibility without loss in efficiency has been an important item in the cost savings. It is interesting to note that the use of pebbles for fine grinding was proved first in the laboratory in a 12-in. ball mill. In fact, since 1934 all testing on — 8 mesh material has been done in this 12-in. mill. Scope of the Tests A paper on fine grinding at Lake Shore Mines was published in July 1940.' This paper covered 7 years of intensive research on fine grinding as well as sizing methods and equipment, plant scale grinding tests on 5x16-ft tube mills with and without grate discharges both with 1-in. and -in. balls, the use of laboratory mills to evaluate plant changes, and several reports on classifiers and classification. In the following July the addendum report2 was added in which the idea of series-circuit grinding was introduced, and the results of running five stages of tube mills and bowl classifiers were shown. Since 1940, the ball milling end of the plant has been altered extensively as a result of tests on the use of 3-in. rods in 7x6-ft mills and the use of the Tyler repulping screen with from 7 to 14 mesh screens. These tests are lengthy and may be covered in a separate report later. The scope of this report is confined to ore ground by rod milling and ball milling until it passed through an 8 mesh Tyler Ty-rod screen. The —8 mesh screen undersize then was pumped to a primary bowl classifier in open circuit and the sands from the bowl sent to the primary pebble mills, see Fig. 1. In the pebble mill circuit the ore is ground to 90 pct —325 mesh (24 pct + 28 microns). In studying the flowsheet, attention should be paid to the efficiency of the classification equipment used. The Tyler repulping screen is an efficient machine on the 8 to 10 mesh separation, and the bowl classifier is equally efficient at the 325 mesh separation. Efficient classification is a necessity for series-circuit stage grinding. The ore is hard siliceous porphyry, 60 pct SiO,, 80 pct insoluble. Its grindability at different meshes has been shown near the top of the list in F. C. Bond's grindability tests.' Lake Shore is not shown, but an adjacent mine with identical ore, Wright-Hargreaves, is. Reasons for the Changeover Since 1936 grinding balls have been rising steadily in price with no sign of stopping. For a mill that used 4.5 to 5.2 lb of grinding balls for every ton of ore ground this rise represented an alarming increase in grinding costs. In many cases the quality of the grinding balls fell off as the scrap steel became more difficult to obtain. The ratio of tube mills to ball mills increased with the use of the Tyler repulping screen in the ball mill circuit. Originally only 3.0 lb of balls per ton were used in the tube mills, and this

Jan 1, 1953

By R. T. Hukki

THE accepted basis of comparisons between mills of different diameter is the percentage critical speed. If n = actual mill speed, rpm, nc = calculated critical speed, rpm, np = calculated percentage critical speed, and D == inside diameter of the mill in feet, then n, In the following analysis capacity, T, is expressed in short tons per hour, tph, and power consumption, P, in kilowatts, kw. Accordingly power consumption per unit of capacity, P will be expressed in kilowatt hours per short ton, or kw-hr per ton. In all equations D refers to the inside diameter of the mill in feet and v to the peripheral speed of the mill in feet per minute inside the liners. ' Comparison between separate mills must be based on equivalent grinding conditions, i.e., same feed, same size distribution of feed, same size distribution of product, and same percentage of solids. In addition, comparisons between separate rod mills must be based on the same rods, same type of liners, and same percentage rod load. Comparisons between separate ball mills presuppose the same balls, similar liners, and same relative ball load. The practical np-range through which the equations apply varies, being narrower for fine grinding in ball mills and wider for coarse crushing in rod mills. The Relationship between Capacity and Speed It is the general belief that the capacity, T, of a tumbling mill is directly proportional to the speed of the mill, other things remaining constant.' Mathematically this is represented by the equation T - c¹ n tph [4] where c, is a factor related with the grinding characteristics of the ore, method of reduction, and the units chosen. It is proposed here that the general equation relating mill capacity and speed should be of the form T = c¹ nm tph [5] In other words, the capacity should be proportional to the mill speed raised to power m, the numerical value of the exponent being 1 5 m 5 1.5, depending on the circumstances. Eq. 5 can also be written in the following forms: T = c, (np)m tph, and [6] T=Ca vm tph, [71 where v = peripheral speed of the mill in feet per minute. If the observed capacity of a mill at speed n¹ is = T¹ tph, the capacity T² of the same mill at speed n² should be T² = T¹ (n²/n¹)tph [8] The Relationship between Power Consumption, Mill Diameter, and Speed The only well known theoretical deduction relating power consumption, P, and mill diameter appears to be the formula of duPont introduced by Gow, Guggenheim, Campbell, and Coghill.' According to duPont, the power required to operate a mill is a function of the mass of the balls, of the lever arm of the ball mass, and of the speed of the mill. The ball mass per unit of mill length is proportional to the square of the diameter, the lever arm is directly proportional to the diameter, and the critical mill speed or any percentage thereof is inversely proportional to the square root of the mill diameter. Following this reasoning, the original duPont formula is of the form P = c4D² c D • c6D-0.5 = c7D2.5 [9] If the mill speed in the above equation is expressed in terms of Eq. 3, the duPont formula may be written as follows: P=f1(D2) f2(D) f³(—np) or [10] vD P = c np D2.5 kw [11] Eq. 11 may also be derived from the mechanical principle of force, which is equal to mass x acceleration. Power necessary to operate a mill may be considered to be an homogeneous linear function of the force developed. Ball or rod mass per unit of mill length is a function of D2. The acceleration factor of the ball or rod mass is a function of the peripheral speed of the mill. Thus P = f4(F) = /x(D2) f5(v) Indicating that v = nDn, and n = c9 np /vD, the above equation becomes P = f2 (D2) -fa (D ca np/vD

Jan 1, 1955

Discussions of the paper of Mr. Gayley read by title at the Lake Superior hieeting, but first presented at the New York meeting of the Iron and Steel Institute, October, 1904 (see p. 746). With the exception of Mr. Pourcel's discussion (p. 1038), these papers are here published under a mutual agreement between the Councils of the two Institutes, and will also be found, with others, in the Journal of the Iron and Steel In-slitute for the pear 1904, Mr. E. Windsor Richards, Past-President,' said that in 1799 Mr. Dawson, of Low Moor, read a paper before a scientific society in York pointing out the great diff'erence in the moisture of the air going into the blast-furnace in the hot months of the year and in the winter months. A cold blast-furnace was a very sensitive instrument, and showed this very clearly, for in June, July and August the furnace did not drive so well; it did not make the quality of iron and required more fuel; so that Mr. Gayley was on the right road to effect an enormous improvement in this direction. He considered that Mr. Gayley was on the way to great success, and hoped that the apparatus would not be a very expensive one. He supposed it mas too early for Mr. Gayley to let them know what the saviug was

Jan 1, 1905

By H. T. Hildage

ALTHOUGH Greater New York does not bear any resemblance to a great mining district, the mining operations that are being conducted in and about the city are both extensive and interesting in character. With regard to the extent, it may be mentioned that, at. present, there is more dynamite used in New York than in any mining district in the United States; that there are under construction about 38 miles of tunnel, and that 66 miles more are projected, most of which must be constructed in the near future ; that since 1902 at least 2,000,000 tons of earth has been removed in underground work, in addition to about 3,500,000 tons that has been removed in, open-cut in connection with tunnel-work, and many times this quantity that has been removed in excavating foundations for buildings not connected with tunnel-work; and that there are to-day probably more than 5,000 men engaged in mining-work in and about New York City. These undertakings include almost every operation connected with underground work, from exploration by means of trench and boring, to the sinking of large shafts and the driving of large tunnels through every kind of ground from hard rock to soft, semi-fluid silt and quicksand. It is proposed in this paper to give a general description of some of the methods and appliances used in the opening-up ,of a "mine" in a large city, and a brief description of some of the "mines" now being developed in New York, connecting as far as possible the methods described with the particular work for which they were designed, in order to give a general idea of the

May 1, 1907

By AIME AIME

T HE Executive Board of the American Engineering Council held its fourth meeting at St. Louis on the first anniversary of the organizing conference which met in Washington on June 3,1920. Representatives of a number of the leading engineering organizations in the vicinity of St. Louis were present by invitation. The members of the Executive Board were guests of the Associated Engineering Societies of St. Louis. They were given a delightful ride about the city and were entertained at the Glen Echo Country Club at dinner. The special committee that had been appointed to draft resolutions to Mr. Hoover submitted the following, which were adopted : WHEREAS, our President, Herbert Hoover, has been appointed Secretary of Commerce in the Cabinet of the President of the United States, and WHEREAS, in consequence of his acceptance of this high public office, he has deemed it necessary to tender his resignation as President of The Federated American Engineering Societies.

Jan 1, 1921

By L. L. Wyman

SINCE the observations of Heyn,1 relative to the embrittlement of copper after having been heated in hydrogen, this subject has received considerable attention from later investigators. The published works of Archbutt2 and of Bengough and Hill3 give the reasons for this embrittlement-the formation of steam by the reaction between cuprous oxide and hydrogen. From Ruder,4 Pilling,5 Moore and Beckinsdale,6 Bassett and Bradley,7 and from Smith8 can be obtained quantitative data concerning the action of hydrogen and other reducing gases on copper samples having various oxygen contents. This problem has been discussed from a practical standpoint by Fuller9 who calls attention to some of the instances of this embrittlement encountered in the manufacturing field. The examples he cites may be considered typical cases of copper embrittlement which were incident to the process of manufacture. In many cases, such difficulties are overcome by changes in the manufacturing process.

Jan 1, 1931

By James T. Gow, Oscar E. Harder, Anton de S. Brasunas

THIS paper deals with the results obtained and the techniques employed in determining: I. Liquidus and solidus temperatures of the HH and HT type heat-resistant alloys. † 2. The relation of true temperatures (thermocouple) to apparent temperatures (optical pyrometer) for the molten HH and HT type alloys. This work was the outgrowth of needing to know something definite about these temperatures in order to study the effect of pouring temperatures, shake-out times, and heat-treatments on the properties of some heat-resistant alloys. The information developed is thought to be of interest to industry for guidance in foundry practices and the industrial heat applications of the alloys. This paper is based upon work that has been done for the Alloy Casting Institute at Battelle Memorial Institute. LIQUIDUS AND SOLIDUS TEMPERATURES OF HH AND HT TYPE ALLOYS Experimental Procedures Temperature-time curves were obtained during the cooling and solidification of several HH and HT type alloys. The metal was melted in an Ajax high-frequency induction furnace and poured into a coresand mold for cooling. The temperature measurements were obtained by means of a platinum, platinumrhodium thermocouple contained within a fused silica sheath, which was extended through the side wall of the dry core-sand mold to a point at about the center of the mold cavity, which was 3 in. in diameter by 5 in. deep. The cold junction of the thermocouple was kept in an ice bottle, and the temperature was recorded automatically on a direct-reading potentiometer recorder. Through a switching arrangement, the temperature recorded was checked occasionally with a portable Leeds and Northrup potentiometer indicator. Less than a 5°F. variation in the two instruments was always found. This is within the limit of accuracy of readings. The thermocouple used was checked for accuracy against a standard couple, both before use on this work and after completion of the work, by the instrument laboratory. Temperature-time Cooling Curves Fig. I is an enlarged reproduction of a part of one of the cooling curves over the temperature range of 2600° to 2200°F. for an alloy of the HT type with 0.45 per cent carbon, 16 per cent chromium, and 36 per cent nickel. This is a typically shaped cooling curve as obtained for the alloys. It will be noted that two temperatures are shown on Fig. r for the liquidus temperature. It is thought likely that the higher temperature, A, at the point at

Jan 1, 1945

By Robert F. Mehl

THIS essay is an attempt to present the elementary facts and ideas concerning the growth of crystals, especially of metals. Freezing, like all heterogeneous processes, is a process of nucleation and growth; it manifests itself in metallurgy primarily in the freezing of ingots. The preceding paper in this volume discusses nucleation; the paper to follow describes ingot solidification. The present paper will treat of the growth of nuclei to large crystals, embracing a long series of phenomena, many of which are familiar to metallurgists.† Crystal growth, it will be immediately noted, occurs not only in the freezing of metals, but in the freezing of all substances; and it is a prominent and familiar phenomenon in crystallization from solutions, aqueous or otherwise, and in crystallization from the vapor phase. It will be necessary to include such systems in this discussion, for so much of value to metallurgists has been learned from their study. Apart from this, so far as metals are concerned, it will be simpler to limit the discussion to the freezing of pure metals and of solid solutions. Other types of freezing-eutectic, peritectic, etc.-will be excluded, though they have much of interest and of importance. BASIC MECHANISM OF FREEZING Ideally, nucleation and growth processes can best be considered from the point of view of isothermal reaction and upon the assumption of random nucleation. In. such an ideal case, nuclei form at random, and at a characteristic rate either constant or changing with time, and grow to spherulites at a characteristic rate, constant or changing with time, Fig. I.. On the simplest assumption, the reaction rate-in this case the rate of freezing-is a resultant of these two component rates. The reaction rate equation may be written in terms of these two component rates. The formation of pearlite from austenite closely approaches this ideal case. The ideal case forms a very useful point of departure in considering real cases. Various factors of reality produce deviations from this assumed ideality. In freezing, the isotropic medium, the melt, passes to the anisotropic solid, the crystal. Crystals are lattices of atoms, and the unit cell is often referred to as a crystal unit. Rosenhain, many years ago, represented the nucleation and growth process on freezing in the manner shown in Fig. 2, feeling, intuitively, that there must be some crystal unit in crystal growth. It now appears that this may be true, though his picture requires much elaboration. The greatest deviation from ideality lies in the nonisothermal nature of the freezing process in metals. To approach this properly it should be recalled that many nonmetallic substances freeze slowly. Tammann, to whom we owe the classic approach, studied complex organic materials in which (as in the case of eutectoid steels at high

Jan 1, 1951

By William B. Plank

AGAIN the records show an unprecedented enrollment of students in the mineral technology schools of the United States and Canada. In the current year, 1938-'39, 9619 students were resident in the 53 schools of the United States arid 1014 in the six schools of Canada. These data are from my fifth study of the mineral technology schools of the United States and Canada. the last previous study having been made for the year 1936-'37. The undertaking as previously was made under the auspices of the Mineral Industry Education Division of the A. I. M. E. The data or, the various schools were collected in the same way as for former studies.

Jan 1, 1939