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By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy's law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By R. S. Handy

DOES hand-sorting of mill feed pay? The fact that the practice is so general would seem to indicate that there must be good reasons for following it; yet, to my mind, the advantage in many cases is doubtful enough to invite a thorough discussion of the subject, in an effort to determine under what conditions hand-sorting does pay. A typical sorting plant in the Coeur d'Alene district handles about 800 tons of mine-run ore per day. The material is run over a grizzly with about 4-in. opening; the oversize is crushed to about 4-in. size and joins the undersize, and the whole product is washed and screened on trommels with about 1 ½ -in. openings. The oversize from these trommels is spread on a belt and the waste and first-class ore are sorted out by hand, the residue being further crushed, and passes, together with the trommel undersize, into the mill feed bins. About 50 tons of shipping ore and 150 tons of waste are sorted out per day, leaving about 600 tons of mill feed. To sort out this material requires 20 ore sorters and five bosses and repairmen. The normal cost of hand-sorting is about 16 c. per ton of run-of-mine ore, or 65 c. per ton of material sorted out. I believe that straight crushing and milling of the run-of-mine ore, in this case, is not only cheaper, but is metallurgically moree canonical and efficient than hand-sorting followed by milling of the residue. At one of the Bunker Hill rock-houses, 1250 tons of run-of-mine ore are reduced to pass 30-mm., or about 1 ¼ -in. opening in six hours, requiring five men. The equipment and the power consumed are not greatly different from that required in a sorting plant of the same capacity, and the normal cost of thus preparing the feed for milling is under 3 c. per ton of mine product. The relative cheapness of this method as against hand-sorting is thus clearly established, the saving being about 13 c. per ton. If there is any virtue in hand-sorting, then, it must lie in the metallurgical results achieved.

Jan 4, 1918

By W. T. Nightingale

The three gas-producing "pools" discussed in this paper are in Sweet-water County, southwest Wyoming, and Moffat, County, northwest Colorado. Hiawatha, North Baxter Basin and South Baxter Basin gas fields became economically important in 1929 when a 330-mile gas line connected them with Salt Lake City, Ogden and towns en route. This development immediately focussed attention on the gas-producing fields and the efforts of the producing company to develop them in an orderly, economical manner. Several outstanding interests were acquired and working agreements made with others. Thus the interference of natural drainage areas was avoided, the pernicious practice of drilling direct

Jan 1, 1930

By C. F. Park

Hog Mountain is in the north central part of Tallapoosa County, Alabama, about 13 miles northeast from Alexander City. The Hog Mountain Mining and Milling Co. controls 1658 acres of land and is the only company operating in the district. The principal mine workings are in sections 10 and 15, T.24N., R.22E. The region has been visited by geologists many times, has been briefly described in several papers,' and mentioned in many others. No detailed map of the mine or vicinity has been published. The field work for this report was started in March, 1934, as part of the Public Works reemployment program. About a month and a half was spent mapping both the surface and underground geology. The mine owners and operators have cooperated in every way possible to facilitate the work. N. 0. Johnson, the mine engineer, E. W. Ellsworth, J. E. McCoy and J. G. Englebert have acted as assistants for part of the work. The University of Alabama and the State Geologist's office have aided materially by permitting free use of their libraries and laboratory equipment. Geography Hog Mountain forms a conspicuous ridge that rises to a height of a little more than 1000 ft. above sea level, and about 400 to 500 ft. above the adjacent country. The ridge is composed of granitoid intrusive rock and silicified schist that are more resistant to erosion than the surrounding softer schist. The topography of the area around the ridge is gently rolling and is typical of the subdued forms of the deeply eroded Southern

Jan 1, 1935

By C. F. Park

Hog Mountain is in the north central part of Tallapoosa County, Alabama, about 13 miles northeast from Alexander City. The Hog Mountain Mining and Milling Co. controls 1658 acres of land and is the only company operating in the district. The principal mine workings are in sections 10 and 15, T.24N., R.22E. The region has been visited by geologists many times, has been briefly described in several papers,' and mentioned in many others. No detailed map of the mine or vicinity has been published. The field work for this report was started in March, 1934, as part of the Public Works reemployment program. About a month and a half was spent mapping both the surface and underground geology. The mine owners and operators have cooperated in every way possible to facilitate the work. N. 0. Johnson, the mine engineer, E. W. Ellsworth, J. E. McCoy and J. G. Englebert have acted as assistants for part of the work. The University of Alabama and the State Geologist's office have aided materially by permitting free use of their libraries and laboratory equipment. Geography Hog Mountain forms a conspicuous ridge that rises to a height of a little more than 1000 ft. above sea level, and about 400 to 500 ft. above the adjacent country. The ridge is composed of granitoid intrusive rock and silicified schist that are more resistant to erosion than the surrounding softer schist. The topography of the area around the ridge is gently rolling and is typical of the subdued forms of the deeply eroded Southern

Jan 1, 1935

Hog Mountain is in the north central part of Tallapoosa County, Alabama, about 13 miles northeast from Alexander City. The Hog Mountain Mining and Milling Co. controls 1658 acres of land and is the only company operating in the district. The principal mine workings are in sections 10 and 15, T.24N., R.22E. The region has been visited by geologists many times, has been briefly described in several papers,' and mentioned in many others. No detailed map of the mine or vicinity has been published. The field work for this report was started in March, 1934, as part of the Public Works reemployment program. About a month and a half was spent mapping both the surface and underground geology. The mine owners and operators have cooperated in every way possible to facilitate the work. N. 0. Johnson, the mine engineer, E. W. Ellsworth, J. E. McCoy and J. G. Englebert have acted as assistants for part of the work. The University of Alabama and the State Geologist's office have aided materially by permitting free use of their libraries and laboratory equipment. Geography Hog Mountain forms a conspicuous ridge that rises to a height of a little more than 1000 ft. above sea level, and about 400 to 500 ft. above the adjacent country. The ridge is composed of granitoid intrusive rock and silicified schist that are more resistant to erosion than the surrounding softer schist. The topography of the area around the ridge is gently rolling and is typical of the subdued forms of the deeply eroded Southern

Jan 1, 1935

By C. F. Park

Hog Mountain is in the north central part of Tallapoosa County, Alabama, about 13 miles northeast from Alexander City. The Hog Mountain Mining and Milling Co. controls 1658 acres of land and is the only company operating in the district. The principal mine workings are in sections 10 and 15, T.24N., R.22E. The region has been visited by geologists many times, has been briefly described in several papers,' and mentioned in many others. No detailed map of the mine or vicinity has been published. The field work for this report was started in March, 1934, as part of the Public Works reemployment program. About a month and a half was spent mapping both the surface and underground geology. The mine owners and operators have cooperated in every way possible to facilitate the work. N. 0. Johnson, the mine engineer, E. W. Ellsworth, J. E. McCoy and J. G. Englebert have acted as assistants for part of the work. The University of Alabama and the State Geologist's office have aided materially by permitting free use of their libraries and laboratory equipment. Geography Hog Mountain forms a conspicuous ridge that rises to a height of a little more than 1000 ft. above sea level, and about 400 to 500 ft. above the adjacent country. The ridge is composed of granitoid intrusive rock and silicified schist that are more resistant to erosion than the surrounding softer schist. The topography of the area around the ridge is gently rolling and is typical of the subdued forms of the deeply eroded Southern

Jan 1, 1935

By Irving Fatt, R. M. Weinbrandt

Efforts have been made for many years to observe pore structure of sedimentary rocks on a microscopic scale. A better description of the pore structure in reservoir rock would aid in the development of relations between flow through tube network models and flow in consolidated reservoir rock. The unique qualities of the scanning electron miscroscope (SEM) make it the ideal tool to use in a study of pore structure. Previous methods of studying pore structure included plastic casts of pore space and optical microscopy.l-7 There is now available a new method to observe three-dimensional flow channels in reservoir rock: a scanning electron microscope having variable magnification from X20 to X20,000 and approximately 1000 times the depth of focus of the conventional light microscopes. This microscope also can obtain stereoscopic images and can measure and diagram flow channels so that it is possible to construct a network of tubes that will model consolidated reservoir rock. THEORY OF THE SCANNING ELECTRON MICROSCOPE The scanning electron microscope (SEM) functions by projecting a beam of electrons through magnetic focusing lenses at a specimen and recording secondary electrons excited by the primary beam. The amount of secondary electron emission portrays the topography of the specimen because more secondary electrons are emitted from high points than from low points. A schematic of the SEM is shown in Fig. 1. The property of the SEM that is of most importance in this study is its great depth of focus. The depth of focus results from using electrons

Jan 1, 1970

By AIME AIME

COMPLETION of the Rainbow Bridge across the Niagara River and Gorge this fall marks a new page of achievement in the annals of bridge- building. Symbolic of the amity between two great nations, the new bridge provides an additional gateway across the most peaceful border in the world. Ground was broken for the project May 16. 1940, at a site close to that formally occupied by the Falls View Bridge which was destroyed by a record ice jam in 1938. At this point, about 2000 ft. deep and 1000 ft. downstream from the American Falls, the gorge is about 200 ft. deep and 1000 ft. wide. The great steel arch of the bridge has a span of 950 ft. and rises from its supporting abutments on the American and Canadian sides of the river to the level of the top of the gorge. This is said to be the longest hingeless arch in the world.

Jan 1, 1941

By Hendon R. Johnston

In the Tennessee Valley Authority's program of investigation and treatment of foundations for major structures, many chert, or flint, bodies have been encountered during the diamond-drilling operations. These chert bodies occur most frequently in the Knox dolomite and

Jan 1, 1948

By Hendon R. Johnston

In the Tennessee Valley Authority's program of investigation and treatment of foundations for major structures, many chert, or flint, bodies have been encountered during the diamond-drilling operations. These chert bodies occur most frequently in the Knox dolomite and

Jan 1, 1948

By G. K. Manning, M. C. Udy, L. W. Eastwood

Those who have examined beryllium and beryllium-rich alloys under the microscope have noted the results of the difficulties encountered when preparing these materials for examination. Hard constituents are readily chipped and pulled out of the matrix, and the soft ones are easily gouged out or embedded with abrasive or other material. The matrix is easily deformed, which makes it very difficult to remove the effects of scratches. Furthermore, the matrix and some of the constituents are also readily pitted during etching, which makes the structure difficult to develop. The metallographic techniques designed to avoid these difficulties are neither radically new nor necessarily the best possible procedures. They were developed at Battelle to fill immediate requirements as part of a study of the preparation and pouring of beryllium melts as described in a separate paper. A part of the research program on the causes of gas unsoundness in beryllium castings entailed a study of the effects of such gases or gas formers as oxygen or oxides, nitrogen or nitrides, and carbon or carbides. These gases or gas formers, if dissolved in the melt, might be an important factor in the study of unsoundness caused by gas evolution in beryllium. Because it was necessary to be able to distinguish these gases or gas formers, if present as alloy constituents, from metallic phases also present as alloy constituents, a series of alloys was prepared with additions of the various possible metallic and non-metallic constituent formers. It should be emphasized that the constituents referred to as gases or gas formers are important in the study of gases in beryllium only if they form a part of the alloy, that is, if they dissolve in the liquid or solid metal. During the first part of the development of metallographic techniques, the Massachusetts Institute of Technology, unpublished report (TC 3315, Nov., 1945) by Paul Gordon, describing various microconstituents in beryllium, was quite useful. Of particular interest in this report is the confirmation of one of the conclusions drawn from the present investigation, that is, that a distinct oxide phase apparently does not occur in beryllium. The Preparation of Metallographic Specimens GRINDING PROCEDURE The original specimen is either sawed or cut on an abrasive wheel to a convenient size. For best results, the surface to be polished should not be more than about 1/4 in. square, and it is convenient to mount the specimens in bakelite to facilitate handling. Two alternative grinding procedures have been developed. As one alternative, specimens are ground successively on 120-, 240-, and 400-grit, wet-or-dry metallographic discs. The abrasive discs are revolved at 1750 rpm on a conventional pedestal grinder. The coarsest disc (120 grit) is used either wet or dry, and in most instances, it can be eliminated from the procedure. Grinding on the two finer discs (240 and 400 grit) is accompanied by the application of kerosene. The technique consists of holding an oil can, containing kerosene, in one hand and the mounted specimen in the other hand. While the grinding is being done, several drops of kerosene are applied every few seconds close to the center of the disc. Carbon tetrachloride serves at least as well as kerosene as a lubricant; perhaps it is slightly better, but it volatilizes so readily that an additional health hazard is involved. Light oils and water are not satisfactory for the finer grinding operations. The second procedure is perhaps slightly slower than the first and requires a more careful technique, but it eliminates the use of kerosene. The specimen is first ground wet on a 240-grit disc, followed by dry grinding on a 400-grit disc. Finer grinding does not appear to be necessary with either of the two alternative procedures. The pressures used throughout either grinding operation must be extremely light, that is, barely sufficient to hold the specimen in contact with the disc; otherwise, flow and chipping are almost certain to occur. In both procedures, it is essential that the discs be sharp and that they be discarded as they show evidence of becoming dull or loaded. In general, not more than four or five specimens can be ground on a disc before the disc becomes dull enough to warrant discarding it.

Jan 1, 1950

By W. O. Crosby

The crystalline belt of the Atlantic Seaboard, south of New York, attains its maximum breadth of 220 miles on the northern border of North Carolina; arid in this State it is most widely characterized by the occurrence of gold in workable deposits. Half a dozen auriferous belts have been recognized by Nitze and Hanna.' These are, in the main, coincident in position and trend with the NE.—SW. zones of metamorphic slates and schists, which, more than any other feature, give character to the geological map of North Carolina. The central gold-belts, accompanying the main zone of slates and as-

Jan 1, 1908

By John W. Bell

In the introduction to an excellent pamphlet, John Gross' makes the following statements: Although marked progress has been made along mechanical lines, the theory and conception of underlying principles have not advanced so rapidly. This lack of advance in theory may be attributed to the unfortunate situation resulting from the controversy as to whether the Rittinger or Kick law is applicable to crushing. Many pages of the technical literature are burdened with theoretical discussions in favor of one or the other of these laws, which have tended to cloud rather than to clear the atmosphere. Realizing the situation, the Milling Committee of the American Institute of Mining and Metallurgical Engineers, through its secretary, E. A. Hersam, studied the milling industry and, because of the apparently hopeless lack of agreement in the Kick versus Rittinger dispute (5, 13, 14, 0, i8, 19, 21, 22, 23. 24, 30. 34), concluded that a foundation for the theory of crushing was of primary importance. The numbers in the paragraph quoted refer to papers listed by Mr. Gross in his Bibliography on Crushing and Grinding.1 One is obliged to infer that these papers show "hopeless lack of agreement in the Kick versus Rittinger dispute." No. 22 is a paper by Arthur O. Gates2 and No. 23 is one by the writer.3 Employing the subject matter contained in papers Nos. 22 and 23 2,3 the writer will show that their authors formulated identical conclusions, based solely on experimental evidence. Exactly the same defect in the Stadler hypothesis was described in each of the two papers, although entirely different experimental methods were employed in uncovering it. Both of the authors, independently, formulated the conclusion that Rittinger's was a true hypothesis and Stadler's false. The evidence in a third paper4 will be employed to prove that Stadler's hypothesis, when examined experimentally, is worthless. STADLER'S HYPOTHESIS WORTHLESS It is the writer's opinion that the evidence available in 1915 and the corroborating evidence in 1916 was amply sufficient to eliminate the need for any further consideration of Stadler's hypothesis. Certainly the evidence produced in 1918 dealt this hypothesis its coup de grace. It follows, therefore, that in the year 1918 there was only one credible hypothesis left-the Rittinger hypothesis. Gates' Opinion What information is available in Mr. Gates' paper?2 His conclusions are not consecutively summarized, none the less they are perfectly clear. On page 876, Gates says, and it is a very significant utterance: But my results show, among other things, that many more of Stadler's energy units are obtained per foot-pound-applied in coarse than in fine crushing. This suggests a doubt as to the correctness of his unit, since one would expect a foot-pound-applied to produce the same number of "energy units," whether the feed and resulting product were coarse or fine. When Rittinger's theory is applied, the number of mesh-tons (my unit of surface produced) is

Jan 1, 1942

By C. Y. Garber

INTEREST in the sink-float plant operated by the Bunker Hill and Sullivan Mining and Concentrating Co. at Kellogg, Idaho, has recently been largely confined to the preparation and reconditioning of the galena medium. The ease and simplicity of these operations in a concentrating mill producing a flotation lead concentrate has occasioned enough comment to possibly justify a brief description. The subject is treated from an operator's viewpoint only; no effort is made to discuss it in a theoretical or technical manner. PLANT AT BUNKER HILL The sink-float plant was first operated in December 1941. It was built for the purpose of quickly increasing mill capacity with a minimum of equipment. It is the Huntington-Heberlein sink and float process using galena medium and is operated under license from the Sink and Float Corporation, New York city. Lead-zinc ore from the Bunker Hill mine is crushed to pass a I ¼ in. screen and is then washed and separated on vibrating screens having 4 ½ -mm. round-hole punched plates. The screen undersize, amounting to 33 per cent of the mill feed, is dewatered and sent to the ball-mill feed bins. The screen oversize goes to the sink-float plant, where 50 per cent of the oversize, or 33 per cent of the mill feed, is float, which is washed free of medium and disposed of as a tailing. The remaining 33 per cent is sink, which, after washing, is crushed to pass ½ in. and joins the undersize in the ball-mill feed bins. The normal plant capacity is 1700 tons per 24 hr. About 1.7 per cent of the total lead and 3.3 per cent of the total zinc in the feed is lost with the sink-float tailings (Table I). [ ] More complete descriptions of the H. H. process and Bunker Hill sink-float plant are given in several recent articles, listed at the end of the paper. PREPARATION OF MEDIUM AT BUNKER HILL New medium is made intermittently as needed, usually 12 hr. in each 6 days. A small portion of the current mill flotation concentrate is diverted from the lead cleaner cells to a I-in. vertical sand pump and pumped to a two-cell 36-in. Agitair flotation machine, where NaCn and ZnSO4 are added and the grade of concentrate is improved as shown in Table 2. Tailing from this operation is returned by gravity

Jan 1, 1946

By Henry A. Wentworth

Electrostatic separation of ores in its present form is generally known as the Huff process, from the name of Charles H. Huff, of Boston, Mass., through whose constant and persistent labors (with the invention of Clinton E. Dolbear as a basis) the successful commercial process embracing separative machinery and the various electrifying devices has been developed step by step, and the finances for the long period of development provided, and the method finally established and recognized throughout the world as an important and successful addition to the ore-dressing department of metallurgy. The permanent field-success of electrostatic separation began in 1908 with a 20-ton Huff experimental mill built specially for the purpose by the American Zinc, Lead & Smelting Go., in Platterille, Wis., a plant which was a success from the start and was gradually increased in capacity as the market-conditions warranted to 100 tons of concentrates per day. Much credit is due to the above-mentioned company for its initial

Jan 1, 1913

By John W. Bell

In the introduction to an excellent pamphlet, John Gross' makes the following statements: Although marked progress has been made along mechanical lines, the theory and conception of underlying principles have not advanced so rapidly. This lack of advance in theory may be attributed to the unfortunate situation resulting from the controversy as to whether the Rittinger or Kick law is applicable to crushing. Many pages of the technical literature are burdened with theoretical discussions in favor of one or the other of these laws, which have tended to cloud rather than to clear the atmosphere. Realizing the situation, the Milling Committee of the American Institute of Mining and Metallurgical Engineers, through its secretary, E. A. Hersam, studied the milling industry and, because of the apparently hopeless lack of agreement in the Kick versus Rittinger dispute (5, 13, 14, 16, 18. 19. 21, 22, 23, 24, 30, 34). concluded that a foundation lor the theory of crushing was of primary importance. The numbers in the paragraph quoted refer to papers listed by Mr. Gross in his Bibliography on Crushing and Grinding.I One is obliged to infer that these papers show "hopeless lack of agreement in the Kick versus Rittinger dispute." No. 22 is a paper by Arthur 0. Gates2 and No. 23 is one by the writer.3 Employing the subject matter contained in papers Nos. 22 and 232,3 the writer will show that their authors formulated identical conclusions, based solely on experimental evidence. Exactly the same defect in the Stadler hypothesis was described in each of the two papers, although entirely different experimental methods were employed in uncovering it. Both of the authors, independently, formulated the conclusion that Rittinger's was a true hypothesis and Stadler's false. The evidence in a third paper4 will be employed to prove that Stadler's hypothesis, when examined experimentally, is worthless. Stadler's Hypothesis Worthless It is the writer's opinion that the evidence available in 1915 and the corroborating evidence in 1916 was amply sufficient to eliminate the need for any further consideration of Stadler's hypothesis. Certainly the evidence produced in 1918 dealt this hypothesis its coup de grace. It follows, therefore, that in the year 1918 there was only one credible hypothesis left—the Rittinger hypothesis. Gates' Opinion What information is available in Mr. Gates' paper?2 His conclusions are not consecutively summarized, none the less they are perfectly clear. On page 876, Gates says, and it is a very significant utterance: But my results show, among other things. that many more of Stadler's energy units are obtained per foot-pound-applied in coarse than in finc crushing. This suggests a doubt as to the correctness of his unit, since one would expect a foot-pound-applied to produce the same number of "energy units," whether the feed and resulting product were coarse or fine. When Rittinger's theory is applied, the number of mesh-tons (my unit of surface produced) is

Jan 1, 1943

By John W. Bell

In the introduction to an excellent pamphlet, John Gross' makes the following statements: Although marked progress has been made along mechanical lines, the theory and conception of underlying principles have not advanced so rapidly. This lack of advance in theory may be attributed to the unfortunate situation resulting from the controversy as to whether the Rittinger or Kick law is applicable to crushing. Many pages of the technical literature are burdened with theoretical discussions in favor of one or the other of these laws, which have tended to cloud rather than to clear the atmosphere. Realizing the situation, the Milling Committee of the American Institute of Mining and Metallurgical Engineers, through its secretary, E. A. Hersam, studied the milling industry and, because of the apparently hopeless lack of agreement in the Kick versus Rittinger dispute (5, 13, 14, 16, 18. 19. 21, 22, 23, 24, 30, 34). concluded that a foundation lor the theory of crushing was of primary importance. The numbers in the paragraph quoted refer to papers listed by Mr. Gross in his Bibliography on Crushing and Grinding.I One is obliged to infer that these papers show "hopeless lack of agreement in the Kick versus Rittinger dispute." No. 22 is a paper by Arthur 0. Gates2 and No. 23 is one by the writer.3 Employing the subject matter contained in papers Nos. 22 and 232,3 the writer will show that their authors formulated identical conclusions, based solely on experimental evidence. Exactly the same defect in the Stadler hypothesis was described in each of the two papers, although entirely different experimental methods were employed in uncovering it. Both of the authors, independently, formulated the conclusion that Rittinger's was a true hypothesis and Stadler's false. The evidence in a third paper4 will be employed to prove that Stadler's hypothesis, when examined experimentally, is worthless. Stadler's Hypothesis Worthless It is the writer's opinion that the evidence available in 1915 and the corroborating evidence in 1916 was amply sufficient to eliminate the need for any further consideration of Stadler's hypothesis. Certainly the evidence produced in 1918 dealt this hypothesis its coup de grace. It follows, therefore, that in the year 1918 there was only one credible hypothesis left—the Rittinger hypothesis. Gates' Opinion What information is available in Mr. Gates' paper?2 His conclusions are not consecutively summarized, none the less they are perfectly clear. On page 876, Gates says, and it is a very significant utterance: But my results show, among other things. that many more of Stadler's energy units are obtained per foot-pound-applied in coarse than in finc crushing. This suggests a doubt as to the correctness of his unit, since one would expect a foot-pound-applied to produce the same number of "energy units," whether the feed and resulting product were coarse or fine. When Rittinger's theory is applied, the number of mesh-tons (my unit of surface produced) is

Jan 1, 1943

By J. R. Cahoon, H. W. Paxton

The possibility of using unidirectionally solidified, two-phase alloys as an approximation to fiber composite materials is investigated. The short-term me.chanical properties and failure modes of unidirectionully solidified A1 (rich)-Cu alloys containing ap -Proximately 0, 17.5, and 27.7 vol pct of 0 phase 'fibers" are determined at temperatures from 25" to 500" and compared with those obtained for conventionul SAP alloys. In a previous publication,' hereafter referred to as I, the possibility of understanding some of the room-temperature mechanical properties of unidirectionally solidified castings was explored. For Al(rich)-Cu and Al(rich)-Mg two-phase alloys over a substantial range of compositions, the yield and ultimate strengths and common ductility measures were very adequately predicted from the principles of fiber strengthening4 and the analysis of ductility outlined by Gurland and Plateau." The results obtained in I suggest the possibility of using unidirectionally solidified, two-phase alloys to simulate fiber composite materials where the inter-dendritic second phase or constituent acts as the reinforcing material. Recent attempts concerning the fabrication of fiber conlposites have concentrated on producing composites with a good bond between fiber and matrix and with very long fibers so that their maximum contribution to the strength of the composite may be realized. However, these objectives are difficult to attain in practice and present fabrication processes are either extremely laborious or costly.13 The slow, unidirectional solidification of eutectics has received considerable attention as a method for producing composite materials. 5,6 This method can fulfill both of the above objectives but it is currently laborious, expensive, and has the additional disadvantage that the volume fraction of reinforcing phase cannot be easily varied. On the other hand, unidirectionally solidified, two-phase alloys, also with a good bond between the phases, are relatively easy to make and the volume fraction of reinforcing "fibers" can be easily varied by changing the average composition of the alloy. The disadvantage of the cast alloys is that the mechanical effectiveness of the "elongated interdendritic reinforcements" (EIR)* may be reduced due to their rela- tively short lengths, the w factor in Eq. [2] of I. However, if the EIR have a high strength their contribution can be considerable. For composite materials containing discontinuous cylindrical fibers of various lengths the ultimate strength is given by1 where it is assumed that the composite fractures when the fibers fail. In Eq. [I], a, is the stress in the matrix just prior to failure of the composite, Vf is the total volume fraction of fiber reinforcing constituent, Vf(l+) is the volume fraction of fibers whose lengths exceed the critical length, I,, which is defined as the shortest length of fiber in which the stress can build up sufficiently to break the fiber. af is the fracture strength of the fiber material, w is a factor accounting for the discontinuity of those fibers whose lengths exceed I,, 1-/d is the average aspect ratio of those fibers whose lengths are shorter than I,, and t is the shear stress in the matrix at the fiber-matrix interface. The factor w is dependent on the length of the fibers and also on whether deformation of the matrix occurs plastically or elastically. However, for a given length of fiber, w is smaller when elastic deformation of the matrix is assumed.' It is of interest to consider the properties of simple unidirectionally solidified, two-phase alloys at elevated temperatures in view of the possibility of using suitable modifications for high temperature service. Knowledge of the creep behavior of these materials is still rudimentary (although under active investigation) and the present paper concerns itself with short time tensile properties of some alloys similar to those investigated in I (i.e., unidirectionally solidified Al(rich)-Cu alloys). Unidirectionally solidified alloys containing 5.6, 17, and 23 wt pct Cu were tested parallel to the direction of solidification at temperatures from 25" to 500°C. In the present investigation, the alloys were homogenized for 2 days at 535°C giving a matrix of homogeneous a phase (5.2 wt pct Cu) and an interdendritic constituent (EIR) which was completely Q phase (53 wt pct Cu). EXPERIMENTAL Alloys of nominal composition 5.6, 17, and 23 wt pct Cu (containing approximately 0, 17.5, and 27.7 vol pct 8 phase, respectively, after homogenization at 535°C) were prepared by melting 1200 g of A1 (99.99 pct) in a high purity graphite crucible and adding the appropriate amount of freshly cleaned copper chips (99.9 pct). The molten alloy (at 700°C) was poured into a preheated graphite mold (also at 700°C) and the ingot unidirectionally solidified by impinging water on the steel baseplate of the mold. The alloy was degassed immediately

Jan 1, 1970

NAME AND OBJECT. SEC. 1. This Institute is incorporated under the Membership Corporation Law of the State of New York ; its corporate name is AMERICAN INSTITUTE OF MINING ENGINEERS; and its objects are such as are stated in its Certificate of Incorporation. ARTICLE II. MEMBERS. SEC. 1. The membership of the Institute shall comprise four classes, namely (1) Members ; (2) Honorary Members , (3) Associates , and (4) Honorary Associates Only Members and Associates residing within the United States of America, Republic of Mexico and Dominion of Canada shall be entitled to vote at the meetings of the Institute. SEC. 2 All Members, Honorary Members, Associates and Honorary Associates of the American Institute of Mining Engineers as the same existed on the day of the incorporation of this Institute, are Members, Honorary Members, Associates and Honorary Associates, respectively, of this Corporation SEC. 3. The following classes of persons shall be eligible for membership in the Institute, namely, as Members and Honorary Members, all professional mining engineers, geologists, metallurgists or chemists, and all persons practically engaged in mining, metallurgy or metallurgical engineering ; as Associates and Honorary Associates, all persons desirous of being connected with the Institute who, in the opinion of the Council, are suitable. SEC 4. Every candidate for election as a Member or Associate of the Institute must be proposed for election by at least three Members or Associates; must be approved by the Committee on Membership, as prescribed in the By-Laws ; and .must be elected by the Council. Not less than three-fourths of the votes cast shall be necessary to an election Every person so elected shall become a Member or Associate, as the case may be, upon payment of his first dues as herein-after prescribed Each candidate for Honorary Member or Honorary Associate, must be recommended by at least ten Members or Associates ; must be approved by the Council ; and must be elected by ballot at a meeting of the Board of Directors by the unanimous vote of all the Directors present ; provided, however, that the number of Honorary Members and Honorary Associates shall not at any time exceed twenty SEC. 5. If any person elected a Member or Associate does not, within sixty days after notice of his election, accept the same and pay his initiation fee and dues for the current year, his election may be cancelled at the discretion of the Council.

Jan 1, 1917