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By Keith Leonard Sutherland

THIS paper is a study of the differential flotation of the sulphide minerals in the presence of salts of silver, lead and zinc. In practice, accidental activation due to these salts is more important than their use as reagents to replace copper sulphate. The general method of investigation has been based upon contact tests, the temperature of 35°C. being chosen in conformity with earlier work. Potassium ethyl xanthate and potassium amyl xanthate were selected as collectors and pure sulphide minerals were used. The experimental procedure has been outlined in earlier papers and all solutions were kept carbonate-free.'' Contact, or spreading of an air bubble, at a mineral surface indicates the presence of an adsorbed collector film. PURITY OF REAGENTS The xanthates were purified in the usual manner.1 Neither the cyanide nor the sodium hydroxide solutions contained sufficient carbonate to give a precipitate with barium chloride solution. The silver sulphate was prepared from pure silver nitrate by evaporation with concentrated sulphuric acid until there was no evidence of brown fumes. This solution was diluted and the difficultly soluble sulphate washed with water so that unchanged nitrate was dissolved. The resultant crystal-line powder was pure white. The lead and zinc salts were prepared by dissolving especially pure lead and zinc in C.P. nitric and sulphuric acid solution and the crystals drained. The standard solutions were checked by titration. It was felt desirable to use the sulphate radical wherever possible, but since lead sulphate was insufficiently soluble for the purpose of the experiments, it was necessary to use some other lead salt. A.R. copper sulphate was used without further purification. RESULTS The results are presented in the accompanying figures; the areas of noncontact (nonflotation) are shaded in Figs. 8, 9, 10 and 11; in the remainder they lie to the right of the curve. Zinc Sulphate The curves in Fig. I are to be compared with those for Fig. 2, for which zinc sulphate is absent. This comparison shows that the influence of the zinc ion is usually small. Its influence is more marked, however, for chalcopyrite in the absence of cyanide. The influence of zinc sulphate is also marked for copper-activated sphalerite, for which tests were made only in the absence of cyanide. The results are of importance in the separation of pyrite from copper-activated sphalerite when zinc sulphate is added in the lead flotation section (p. 204 of ref. I). Sphalerite does not adsorb the collector (i.e., become floatable) under the conditions chosen.

Jan 1, 1942

By B. L. Averba

THE determination of retained austenite by X-ray diffraction uses the following relationship:"" Pa = constant . RVaA (8) [1] where: P is the diffracted power from phase a; R, the calculated intensity factor; A, the absorption correction; 8, the diffraction angle; and Va, the irradiated volume of phase a For a flat sample making a glancing angle + with the incident beam the absorption correction is calculated as: * 1 sin (28 - 4) A .= 1 [2] µ sin, (28 — 4) + sin 4 where µ is the linear absorption coefficient. Beu3 has proposed that the computed absorption correction be combined with the constant and that the experimental observation of the absorption correction used in the original method be eliminated. This procedure is permissible only if: 1—There is no preferred orientation in the sample, and 2—The geometric requirements have been met precisely. If these conditions are not met the validity of the determination is questionable. Unfortunately the necessary conditions must be tested experimentally for each determination, and this is done most easily by observing whether the apparent absorption has the form of Eq. 2. In practice it may be convenient to plot P/R vs the parameter sin (2? — )[sin (28 — +) + sin +] to obtain straight lines for the ap- parent absorption correction. Deviations from straight lines indicate either that the sample has not been positioned correctly or that the relative intensities are incorrect. Geiger counter spectrometer methods also have been used successfully for retained austenite determinations. In the usual spectrometer arrangement the sample makes equal angles with the incident and diffracted beams (8 = ); thus the absorption correction is simply 1/2µ and independent of 8. The retained austenite is then easily calculated from integrated intensity measurements on austenite and martensite lines. If the austenite content is not too low and if excessive fluorescence is not encountered it is possible to use filtered radiation and a recording spectrometer. The integrated intensities are then proportional to the areas of the diffraction peaks. For lower austenite contents the following technique was used: A bent quartz monochromator and a Geiger counter spectrometer are employed. The monochromatic radiation is focused on the front slit, and the counter slit is made broad enough to include the entire line. A series of readings are taken in the vicinity of the diffraction peak. The highest reading includes the diffraction line plus background. The background is obtained from the average of several readings on each side of the peak. The integrated intensity is obtained by subtraction. CrK, and FeKa have been used for such determinations. This technique has been found to be as sensitive and as accurate as the photographic methods. In the spectrometer methods the ratio austenite/ martensite may be obtained from readings on austenite and martensite lines and the application of Eq. 1. It is also possible to use external standards and to obtain the austenite contents from measurements on the austenite lines alone. The small correction for carbides then becomes unnecessary. The best standards are probably samples with known

Jan 1, 1954

"Butte is in many ways an ideal location for a mining school. The student lives in the atmosphere of his intended profession. By the time he has spent four years at the school and in the community he has a fairly clear idea of what kind of a business he is entering upon, and is freed from any illusions about its being a primrose path he is about to follow. The mines and mills and smelters are his lecture rooms in part, and the shovel, pick and drill form part of his equipment. Most of the students work in the mines during part of their school life, which serves the double purpose of assisting them financially and increasing their practical knowledge.The School of Mines is a state institution, amply endowed and exceptionally well equipped. The school is strictly technical and no attempt is made to prepare men for any other work but mining engineering. The mining men of the community take an active interest in the welfare of the school and are of much assistance in securing employment for its graduates.The teaching staff is entirely composed of men who have had practical, commercial experience in their various specialties, and no expense is spared in securing suitable men for the faculty."

Jan 1, 1913

By A. A. Smith, J. S. Smart

NUMEROUS investigations of the effects of the various impurities common to commercial coppers have been published, and the data have found wide use in industry. Naturally, emphasis has been placed on the oxygen-bearing coppers of the tough-pitch variety, but need is now evident for data covering the oxygen-free condition as well. Furthermore, relatively few of the important reactions between oxygen and the various impurities are well understood, and often the data at hand are not applicable to the low concentrations encountered in commercial coppers. This paper presents the changes in conductivity and softening temperature derived from individual additions of the group VIII triad, iron, cobalt and nickel, to high-purity copper, and constitutes a portion of the copper-research program being conducted at the Central Research Laboratory of the American Smelting and Refining Co. The method of preparation of high-purity copper and its alloys in either the oxygen-free or oxygen-bearing form has been described previously.1 The purity of this material, and the methods developed to produce it, provide the means for direct investigation of the very low concentration range in which the various impurities generally exist in commercial coppers. The usual necessity for extrapolation to this range using the results obtained from higher concentrations, and the interfering effects of extraneous impurities, are thus simultaneously circumvented. Since previously published data have adequately presented the effects of higher concentrations of iron, cobalt and nickel, the present investigation has been confined to the composition range 0 to 0.05 per cent. All alloys were initially prepared in the form of oxygen-free continuous cast rod, the weighed alloying additions in suitable form being charged with the pure copper to the continuous casting crucible. The best of the available high-purity alloying materials were used, and spectrographic analyses confirmed the absence of interfering elements from the alloys formed. Each series was compounded in the direction of increasing concentration, starting with pure copper in a new crucible and finishing with the 0.05 per cent alloy. Composition was closely controlled by adding the alloying element in the form of a carefully compounded and analyzed master alloy rendered uniform by continuous casting. The accuracy of this method of synthesis was proved by chemical analysis of the more concentrated alloys, and, accordingly, there is every reason to credit the stated composition of the very dilute alloys in the range where chemical analysis becomes highly uncertain. Oxygen-free samples for measurements of conductivity and softening temperature were obtained by drawing the continuous cast rod to wire of 0.081-in. diameter, employing a number of intermediate anneals to refine the grain structure. The

Jan 1, 1942

The engineering personnel shortage, present and impending, so well brought out in the article in Mining Engineering in the August, 1951 number, both in the editorial lead and the article by William B. Plank and Henry J. Petrie, has left untapped and has ignored a potential source of supply that would fill the need ably and with complete satisfaction. This source is comprised of the women engineers- and geologists, both presently, trained and able to handle work at all levels, and the many who would make splendid engineers and geologists if they could hope for even a modest taste of the square deal that should be theirs, but, as we all know, is not. I write from experience. It is not pleasant or sensible to have to urge borderline cases among men students to consider engineering and geology as careers to fill the need, when I have far more able, interested and suited young women students whom I must divert into other channels. It does not make sense to scrape the bottom and sides of the barrel to induce potentially second or third rate male engineers and geologists to enter the profession when we have superior material among the women, eager to do good work in these fields. It does not make sense for these men to become second or third rate in these fields when they might be first rate salesmen, musicians, advertising copywriters or policemen. Nor does it make any more sense to force potentially first rate female geologists and engineers to become second or third rate and very frustrated typists, kindergarten teachers, dress sales-women or clerks. At this point I am willing to admit that where superstitious -miners object to women in underground workings, men are available for the jobs. Moreover, it is not necessary for women to be sent into the most difficult country, if there is reluctance on either side of the contract. There may be fewer of them eager for the roughest assignments, in proportion to the men, but women are so accustomed to discrimination far more complete than that against any racial or religious group, that a reasonably tough assignment would seem like a heaven-descended joy. In my own experience, I have found that my girl students majoring in geology, could keep up with me in the field in the roughest terrain, but. the men, all but the best students and the most physically fit young men, complained that they could not keep up with me and that I always "walked their-legs off. The women, a few men and I always returned with bags heavy with well chosen specimens and proper notes. Most of the men carried no specimens and-but poor scraps of notes on loose bits of paper. Yet the men were urged to prepare for a career in engineering or geology if their examination marks were reasonably good. When we find that we still have a shortage of engineers and geologists, after putting all the qualified women to work, then we may begin to worry. Until then, we are simply fooling ourselves as we wander in, a forest of outmoded tradition and emotional habit reactions. MARY W. GARRETSON ASSOC. MEMBER, AIME SCARSDALE, N. Y.

Jan 1, 1952

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By Oscar Weiss

An aerial magnetometer survey was carried out by the author&apos;s geophysical organization over the Vrede-fort dome, where Witwatersrand beds are wrapped around a granite plug 25 to 30 miles in diameter. The well-known magnetic shales of the Lower Witwatersrand system (to be referred to as LWW) give strong negative anomalies over the out-cropping portion of the dome. This is unusual as these same shales cause positive anomalies over large areas near Johannesburg and along a strike of 130 miles between the East Rand and Klerksdorp. It is suggested that the negative polarization is caused by heat and stresses connected with the doming. This negative polarization of sedimentary beds, which usually cause positive anomalies, is a good example of how "magnetic lows" can be caused by "structural highs." Significant magnetic anomalies should be tested by gravity and seismic methods irrespective of the sign of the anomalies. South of the line X — Y (see Fig 2 and 5) the gravity anomalies are smaller over the LWW beds and magnetic anomalies suddenly become weaker and even change signs by becoming positive. This peculiar phe- nomenon is explained by faulting which truncated the nearly vertical LWW shales at depth. In this manner the mass of the LWW beds has been reduced together with the weakening of the negative magnetic anomalies by positive poles which occupy the truncated end. Furthermore, by uplifting the beds between f1 and f2 (Fig 2) positive polarization becomes predominant, thus causing positive magnetic anomalies. General The Vredefort dome is one of the internationally known geological structures, which, among others, has attracted the attention of numerous American geologists. It was for this latter reason that our aerial magnetic results over this structure were selected by us for publication in the United States of America. A full description of the exposed geology has been published by Nell and readers are referred to this paper, which is subject to only slight modifications inasmuch as the subdivision of the Witwatersrand system (to be referred to as WW system) is concerned. The Vredefort dome is about 60 miles southwest of Johannesburg. The WW system, after being exposed in the vicinity of Johannesburg, plunges with southerly dips beneath the Vent-ersdorp and Transvaal systems. Along a section southwest from Johannesburg, as shown diagrammatically in Fig 4, we see no outcrops of the WW system until the Vredefort dome, where the Upper and Lower WW system are wrapped around an almost circular arc of a granite mass. Here the whole WW system is overturned around the perimeter of a huge granite plug 25 to 30 miles in diameter. Less than half of the circumference of this dome is exposed; the rest is covered by Karroo dolerites and sediments. The determination of the exact shape of the concealed part of the dome has been a matter of considerable interest and obviously geophysical methods were eminently suited for obtaining this information. A good start was made with a gravimeter survey carried out by the Geological Survey of the Union of South Africa.2 Our own

Jan 1, 1950

By Cheri Eby, William R. Eby

INTRODUCTION Pneumatic conveyance systems provide for material placement at high compaction rates in confined spaces. This method of conveyance provides proper roof support and ground stabilization important to underground mining activities. Today underground mining activities are conducted far differently than those of our ancestors, in that the reclamation process is the final step in any mining activity. Responsible mine owners are constantly seeking innovative methods to assist them in their reclamation procedures. During the last few years, particular attention has been paid to previously mined areas, as many of these abandoned areas lay open, imposing a constant threat to humans and animals. Considerable attention is being directed to applying proper methods for the filling and sealing of underground slopes, drifts, tunnels, and adits, because today we are experiencing the effects of past mining activities such as subsidence, acid mine water run-off, buring refuse piles, and underground mine fires. Furthermore humans and animals who have ventured into abandoned mine openings have died from exposure, suffocating gases, and mine collapse. This paper explains the method of pneumatically filling and sealing these openings and underground works by means of employing pneumatic equipment and proper backfill material together, thus achieving high material compaction and thereby providing the complete filling of the voids and alleviation of the mentioned dangers. NEUMATIC SYSTEMS The use of air to transport material is widely used; however, conveying abrasive material (e., rock, earth, and cement) requires certain pneumatic transport systems designed to handle the abrasiveness as well as the size of these materials. The Eby pneumatic transport sys tem, known as a Mobile Stower, in mounted on a 42-foot trailer pulled by a Kenwor th tractor. This arrangement allows for quick mobilization and project set-up. The pneumatic system, composed of several components assembled together, produces the volume and pressure of air required to transport the material. Knowledge of elevation, ambient temperature, and material composition at the locations to be backfilled play a big part in the design and useage of the pneumatic system. In this particular system design, material is placed by a front-end loader into an eight (8)-yard hopper which is located over a belt conveyor. The conveyor transports the material up to an air lock feeder, which is the metering devise used to feed the material into the Tee Injector located directly below. Air is supplied by a positive displacement blower which, in this instance, delivers up to 4400 CFM&apos;s of air at 8 to 12 PSI. Horse power requirements to drive the blower are met with the useage of either a diesel engine or an electric motor. A diesel engine enables the Mobile Stower to operate in remote areas. As the air flows through the upstream air piping, it passes through the Tee Injector and picks up the material and conveys it through the material conveyance pipe, (referred to as down-stream pipe), and out the placement nozzle. Depending upon material composition and the amount of tonnage to be moved, either mild carbon steel pipe or specially heat- treated hardened pipe is used for the material conveyance line. The entire pneumatic system is controlled from the operator&apos;s console. With the aid of instrumentation, only one person is required to operate the system. Tonnage rates vary in accordance with horse power and air supply, as well as

Jan 1, 1982

By J. D. Forrester, Erich Sarapuu, T. C. Cheasley

John G. Tripp-—The concept of converting fuel deposits in-situ to useful forms of energy and chemical raw materials has important possibilities as a means of stretching out our fuel resources. The authors have worked in this field for years and in fact are among the pioneers in developing in-situ techniques based on underground electrocarbonization. Their efforts have aroused great interest in this subject and their contributions will undoubtedly gain even more significance as time goes on. The 4 to 5 billion tons of petroleum are proved reserves, that is, they are completely defined and could be produced economically with present methods of recovery. Reserves of coal, tar sands, and oil shale shown in Table I are not equivalent to proved reserves as the term is used in the oil industry. Incidentally, the 4.3 billion tons of oil shown in the tabulation is equal to about 28 billion barrels of oil and, therefore, presumably does not include reserves of natural gas liquids estimated at about 5 billion barrels. The relative comparisons would be more complete if these liquids together with the reserves of natural gas were included in the tabulation. It is stated in the report that production costs of the order of 10c per million Btu&apos;s could be expected from a large industrial electrocarbonization installation. The authors state that the operation probably could be operated successfully and at a profit. I would like to express my view that for the operation to be profitable extremely favorable conditions would have to prevail. For example, the coal seam would have to be thick and close to the surface in order to minimize drilling costs; the deposit should be dry and so situated that there would be little, if any, inflow of ground water; and the seam would have to be relatively gas tight to avoid excessive gas leakage. Notwithstanding the tremendous strides that have already been made, it is my hope that the authors plan to continue their development work. Experiments on underground electrolinking and initial carbonization at Gorgas, Ala., indicate a need for improved control over the operation. Subsequent examination of the underground system at Gorgas has shown that the gasification zone did not always follow a direct path between the electrodes. Undoubtedly the control of the in-situ thermal processes can be improved by further development work. With respect to the electrocarbonization of oil shale it may be well to point out that the cost of mining oil shale is estimated to be 50c to 60c per ton. These are low mining costs as compared to coal. Thus it would appear that there is less economic incentive for applying in-situ thermal methods to oil shale than there is for applying these methods to coal. As is the case with in-situ methods for petroleum, the product from the shale having the most economic interest would be liquid oil rather than gas. The authors point out that for distances up to several hundred miles it is cheaper to transmit energy as electricity than it is to ship energy as coal. This is a very important point, and with coal shipping rates rising periodically, it could prove increasingly important in the future. I believe that the authors deserve great credit for their outstanding work on underground electrocarbonization. The knowledge resulting from their efforts is of great value to our fuels technology. James L. Elder—The experimental work conducted by the authors on the electrolinking-carbonization of carbonaceous materials in situ is of great interest. The method is of great importance in the development

Jan 1, 1955

By AIME

To be born in the East, reared and educated in the West, to do graduate work in Germany, leading to the doctorate in metallurgy, and to wind up-for the time being at least-in the Middle West as head of one of the outstanding mining and engineering schools of the country, is a unique career. Curtis Laws Wilson, dean (and in most respects, president) of Missouri School of Mines and Metallurgy at Rolla, is a native of Baltimore. He came to Anaconda in 1918 and in due course was graduated from Montana School of Mines, with an exceptional record. In 1921, after experience in metallurgical research at Anaconda, he became instructor in metallurgy at his alma mater. Because of his ability as a teacher, he rose rapidly to head of the department after special work at Columbia in 1923-24. In 1927, Wilson was granted leave of absence to study physical metallurgy under the great Tammen at Goettingen, and returned with his doctorate to his work at Montana School of Mines. His major metallurgical interest was then in age-hardening of copper alloys. Also after his return to Montana Mines, Wilson started

Jan 1, 1948

By Norman F. Schulz, Emert W. Lindroos, Strathmore R. B. Cooke

DURING the course of an investigation of the effects of various starch products on hematite and quartz in regard to their separation by flotation, it was found that whereas most starches flocculated suspensions of hematite in water, they did not flocculate similar suspensions of quartz. However, a derivative of whole corn starch containing approximately one tenth aminoethyl group (-—CH,CH2NH2) per glucose unit proved to be an exception. This aminoethyl starch was a very good flocculant for both hematite and quartz, and also possessed the property of depressing both minerals in cationic flotation tests. In view of the widespread use of starch as a flocculating agent of solids in tailing water, pulps, and for coal slimes, ore and various other purposes in sulphide and nonsulphide flotation, attention is called to the effective surface activity of aminoethyl starch in flocculating suspensions of the two minerals investigated. Test Materials The starch products employed included Globe Pearl starch No. 144 and fresh aminoethyl starch, both supplied by the Corn Products Refining Co. Dr. A. L. Elder" has kindly furnished a description The minerals used in the various tests are listed in Table I. Their specific surfaces were determined by the air permeability method, which gave results reproducible to within plus or minus 3 pct. Surface areas obtained by krypton adsorption were greater than the air permeability values by a factor of 2.0 for quartz and 62.4 for hematite. Starch Adsorption on Mineral Surfaces Starch adsorption data were obtained by agitating for 1 hr measured volumes of neutral starch solutions of known concentrations with weighed quantities of finely divided mineral of measured specific surface. The mineral then was separated from the pulp liquor by centrifugation and the residual starch content determined by chemical analysis. The analytical procedure consisted of oxidizing the starch with an excess of dichromate in acid medium at elevated temperature and titrating the excess dichromate by the ferrous ammonium sulphate—potassium permanganate method. Analytical results were reproducible to within less than 1 pct. Adsorption data obtained in unbuffered solutions near the neutral point are plotted in Fig. 1. The adsorption on either mineral was far greater for the aminoethyl starch than for the Pearl starch. Flocculation The degree of flocculation was determined for a given pulp by measuring the time required for the supernatant liquid to reach a certain degree of clarity. This was accomplished by passing a standard light beam through the pulp, contained in a glass settling tube, and measuring the time required after agitation ceased for the intensity of the transmitted beam to reach a predetermined value. Starch reagent was added to each pulp in small uniform increments, and the settling time was determined after each such addition. Increase in pulp liquor volume due to the added starch reagent was ignored in these tests. Pulps were maintained at or near neutrality. of the preparation of the aminoethyl starch: "Three hundred and sixty grams of powdered unmodified corn starch was slurried in 3 liters of water and stirred during gelatinization. Eighty-six grams of ethylenimine was added slowly during reflux which was continued for 4 hr. The yellow solution set to a gel upon cooling. This was broken up and neutralized with HC1. The thick paste was dried on hot rolls. Adsorbed polyethylenimine and salts were removed from the yellowish products by washing first with acidified aqueous &apos;60 per cent&apos; alcohol. The white product contained nitrogen corresponding to about one aminoethoxy group per ten glucose residues." Only laboratory samples of this starch derivative have been prepared. The starch reagents for use in flocculation, flotation, and adsorption tests were made up by dispersing the appropriate quantities of air-dry starch in cold water, adding boiling water, and heating for 30 min at 120°C under pressure. When used ip adsorption tests, the starch solutions first were cleared of insoluble matter by centrifugation.

Jan 1, 1953

By W. J. Rogers, L. J. Dwiggins, R. O. Williams

THERE has been comparatively little work on the importance of strain rate and temperature as variables in the formation of deformation textures. For this reason the present work was started, the choice of compression being in part that of convenience and in part because of the absence of quantitative data in this area. These do not turn out to be important variables within the range studied which permits the results to be condensed into this note. Samples 1/4 in. in diam and 1/2 in. long were machined from 99.9 pct pure commercial aluminum and recrystallized to a fine grain size. A set of five samples were deformed between a spring-driven weight and an anvil resulting in roughly 20 pct strain each time. The strain rate varied because of decle-ration and shortening of the sample but would average about 10&apos; per min. Deformation at temperatures over the range of -76" to 150°C were obtained by heating or cooling the samples. Complete lubrication could be obtained by oil since the short time of contact did not permit its escape. The samples were compressed to a total true strain of 1.4 to 1.6. A larger sample was prepared similarly with spiral grooves in the ends to hold paraffin which provided essentially complete lubrication. This sam ple was compressed slowly at room temperature at a rate of about 2 per min to a total strain of 1.0. Cylindrical samples were carefully machined from these discs with a radial direction as an axis. They came from the center half of the samples and were roughly 1/16 in. in diam. The samples were etched down 15 pct to remove any surface effects. Diffraction data were then obtained for six different kinds of planes by the use of the Norton technique as applied to a fiber texture. Direct comparison between the raw data failed to reveal any significant difference between any of the samples and consequently the data from only one sample was completely reduced. The particular sample had been deformed at O°C The background was subtracted from the intensity data which were averaged over the four quadrants and then normalized to random. These data were then used to obtain fiber-axis distribution charts as previously described.2 For this sample the (422) plane was also run to assist in this inversion. The final result, Fig. 1, provided a comparable fit to that previously obtained from fiber data. About 85 pct of the material forms an elliptical texture around the <110> direction. The radius (at half height) is 5.5 deg along the (111) boundary and 8 deg along the (100) boundary. The remaining 15 pct forms a ridge running from this texture to near the <311> direction. The regions around the (100) and (111) planes are devoid of material. The earlier qualitative results of ~arrett~ are in complete agreement with the present results. The possibility has been dis-cused that the material around the <311> results from friction between the sample and compression plates.4 The present results are considered proof that such is not the case because of the uniformity of sample deformation and the requirement of axial symmetry before fiber-axis distribution charts can be accurately obtained. Recently results have been obtained to show that strain rate and temperature are important variables in the extrusion of aluminum.5 Perhaps the most important observation was that the partial recrystal-lization occurred even at room temperature. Strain rate was considered to be a factor only in that it produced a temperature change. There are many differences between the two experiments, the most important possibly being that their material was roughly ten times the purity of the present material. The present experiment, however, may not be as definitive as desired in this respect since it has been shown that compressed aluminum recrystallizes without a texture change6 although supplementary

Jan 1, 1961

By Edward H. Robie

SHOULD the name of our Institute be changed? Perhaps one should say, should it again be changed, for until 1919 the name was the American Institute of Mining Engineers. When the American Institute of Metals joined our ranks we became the American Institute of Mining and Metallurgical Engineers. To make it a full mouthful, and strictly legal, one should add the word "Incorporated." At the June meeting of the Board of Directors it was suggested that this name was not a particularly happy one, especially so far as members of the Petroleum Branch, comprising a quarter of our membership, were concerned-not particularly appropriate as the name for the professional society for petroleum engineers. Apart from the petroleum group, the present name is felt by some not to be sufficiently comprehensive. Most geologists and many metallurgists, ceramists, and fuel technologists, for instance, are not engineers. They could never qualify as registered professional engineers under the licensing laws and yet they are valued and fully qualified Members of the AIME. The Directors, at the June meeting, thought the idea of a change in name should be presented to the membership for discussion, and suggested this column as the avenue of approach. Nine years ago Dean Steidle, of Penn State, recommended among other things that the name of the Institute be changed to "American Institute of Mineral Technologists and Engineers." In an editorial in Mining and Metallurgy in January 1944 objection was offered to this name but "American Institute of Mineral Engineers" was suggested. A special committee appointed by the Board to review Dean Steidle&apos;s suggestions (W. B. Heroy was Chairman) suggested that if the AIME were starting from scratch, the American Institute of Mineral Engineers might be a preferred name. It was not thought that the change suggested by Dean Steidle was one of major importance, and the comment was made that "the present name has gained prestige through many years and is cherished by our membership. An important element of &apos;good will&apos; is attached to it and some of this would be unquestionably sacrificed by any change." In M&M for February 1945, Oliver C. Ralston went into the derivation of the terms mineralogy and metallurgy, and pointed out that both Mining and Metallurgical mean "digging," etymologically. He went on to show, with tongue in cheek, that if we want a short and all-inclusive name it should be American Institute of Geo-urgists, or, for euphony, Geolurgists. Oliver&apos;s brilliant development seems to have been received with speechless wonder! Should a decision ever be made to change the name, we think most members will agree that the American Institute of Mineral Engineers is to be preferred over anything yet suggested. "Mineral" has become, through usage, a much broader term than is indicated in the dictionary. Webster states that a mineral, in the true sense, must be inorganic, but Murray&apos;s Oxford English Dictionary seems more liberal, defining "mineral" as "any substance which is obtained by mining; a product of the bowels of the earth;" and "mineral oil" as any oil of mineral origin, as petroleum or shale oil. Certainly "the mineral industry" is ordinarily taken to include those activities based upon processing all the metallic and nonmetallic ores and deposits found in the ground, including the fuels. One advantage of this title is that the familiar abbreviation, "AIME" need not be changed. The advisability of maintaining a well-known abbreviation is evident, and was recognized, for instance, when the Committee for Industrial Organization became the Congress of Industrial Organizations some years ago. But if the petroleum engineers are the ones to be chiefly considered in revising the name of the Institute, it is by no means certain that they would feel that they are much more adequately recognized in a group of Mineral Engineers than in a society of Mining and Metallurgical Engineers. &apos;And then there remain, of course, the considerable number of professional members of the Institute who are not engineers at all. Comment from readers is invited.

Jan 1, 1952

By Strathmore R. B. Cooke, Emert W. Lindroos, Norman F. Schulz

DURING the course of an investigation of the effects of various starch products on hematite and quartz in regard to their separation by flotation, it was found that whereas most starches flocculated suspensions of hematite in water, they did not flocculate similar suspensions of quartz. However, a derivative of whole corn starch containing approximately one tenth aminoethyl group (-—CH,CH2NH2) per glucose unit proved to be an exception. This aminoethyl starch was a very good flocculant for both hematite and quartz, and also possessed the property of depressing both minerals in cationic flotation tests. In view of the widespread use of starch as a flocculating agent of solids in tailing water, pulps, and for coal slimes, ore and various other purposes in sulphide and nonsulphide flotation, attention is called to the effective surface activity of aminoethyl starch in flocculating suspensions of the two minerals investigated. Test Materials The starch products employed included Globe Pearl starch No. 144 and fresh aminoethyl starch, both supplied by the Corn Products Refining Co. Dr. A. L. Elder" has kindly furnished a description The minerals used in the various tests are listed in Table I. Their specific surfaces were determined by the air permeability method, which gave results reproducible to within plus or minus 3 pct. Surface areas obtained by krypton adsorption were greater than the air permeability values by a factor of 2.0 for quartz and 62.4 for hematite. Starch Adsorption on Mineral Surfaces Starch adsorption data were obtained by agitating for 1 hr measured volumes of neutral starch solutions of known concentrations with weighed quantities of finely divided mineral of measured specific surface. The mineral then was separated from the pulp liquor by centrifugation and the residual starch content determined by chemical analysis. The analytical procedure consisted of oxidizing the starch with an excess of dichromate in acid medium at elevated temperature and titrating the excess dichromate by the ferrous ammonium sulphate—potassium permanganate method. Analytical results were reproducible to within less than 1 pct. Adsorption data obtained in unbuffered solutions near the neutral point are plotted in Fig. 1. The adsorption on either mineral was far greater for the aminoethyl starch than for the Pearl starch. Flocculation The degree of flocculation was determined for a given pulp by measuring the time required for the supernatant liquid to reach a certain degree of clarity. This was accomplished by passing a standard light beam through the pulp, contained in a glass settling tube, and measuring the time required after agitation ceased for the intensity of the transmitted beam to reach a predetermined value. Starch reagent was added to each pulp in small uniform increments, and the settling time was determined after each such addition. Increase in pulp liquor volume due to the added starch reagent was ignored in these tests. Pulps were maintained at or near neutrality. of the preparation of the aminoethyl starch: "Three hundred and sixty grams of powdered unmodified corn starch was slurried in 3 liters of water and stirred during gelatinization. Eighty-six grams of ethylenimine was added slowly during reflux which was continued for 4 hr. The yellow solution set to a gel upon cooling. This was broken up and neutralized with HC1. The thick paste was dried on hot rolls. Adsorbed polyethylenimine and salts were removed from the yellowish products by washing first with acidified aqueous &apos;60 per cent&apos; alcohol. The white product contained nitrogen corresponding to about one aminoethoxy group per ten glucose residues." Only laboratory samples of this starch derivative have been prepared. The starch reagents for use in flocculation, flotation, and adsorption tests were made up by dispersing the appropriate quantities of air-dry starch in cold water, adding boiling water, and heating for 30 min at 120°C under pressure. When used ip adsorption tests, the starch solutions first were cleared of insoluble matter by centrifugation.

Jan 1, 1953

By AIME AIME

OUR new Director from the 15th District is Robert W. Thomas; of Ray, Ariz., general manager of the Ray Mines division, Kennecott Copper Corp. In electing him to this office his fellow engineers pay tribute to his ability as an engineer and express appreciation for his service to the A.I.M.E. and its Arizona Section. ?Bob? Thomas was born April 1, 1886 at St. James Minn. received his early education in the public schools of Topeka Kans. and was graduted from Topeka High School in 1905. Already he had decided upon mining engineering as a profession. so he entered the mining school of the University of Kanas from which he was graduated with the degree of B.S. in hlining enginrering. While in college he became a Student Associate of the A.I.M.E. After graduation, lution and isolated mining camps wel-e not the most desirable places in w

Jan 1, 1944

By C. O. Dale, W. J. Rundle

THE upper Mississippi Valley zinc-lead area was the first major lead-producing section in the United States. The lead ore, found near the surface in crevices, was relatively pure galena that could be smelted directly into lead, at first in log hearth furnaces and later in more efficient blast type furnaces. French Canadian fur traders encouraged the Indians to mine the lead ore and showed them how to smelt it into lead that had a high value for bullets1 Nicholas Perrot found lead ore on the Mississippi River bluffs near the junction of Wisconsin and Illinois and in 1690 established a trading post on the Wisconsin side of the river opposite the present site of Dubuque, Iowa.2 Shortly after 1720 discovery of Mine La Mott in Missouri diverted considerable attention from the Upper Mississippi area. Mining continued on a desultory basis with operations concentrated in the Galena, Illinois-Dubuque, area. In 1740 at least 20 miners were at work in the Fever River area around Galena and are reported to have shipped 2500 70-lb pigs of lead to Kaskaskia in 1741." Julien Dubuque established a mining and smelting operation in 1790 near the city that bears his name and was granted sole right to exploit the mining operations on the lands of the Sauk and the Fox Indians. He is reported to have produced 30,000 70-lb pigs of lead in 1805. Following the death of Dubuque in 1810 the Indians refused to let the white miners enter their lands, and little was done on the Iowa side of the river until the Indians were removed by treaty with the United States government in 1832." Early mining was entirely for lead but as the crevices were followed down, increasing percentages of zinc sulphide and zinc carbonate were encountered and at first discarded. Later a market became available for the zinc ores, and hand jigging devices were made to separate the lead, the zinc, and the rock or waste materials. The first record of zinc production from the area is for 1860. Production of zinc passed that of lead before 1900, reached a peak of 64,000 short tons in 1917, fell off rapidly and continually to about 2000 short tons in 1938, and since 1940 has ranged from 11,000 to 19,000 short tons. Lead has been of considerably less importance since 1900, and at present only about 10 pct as much lead as zinc is produced. Practically all of the zinc ore has come from orebodies that are rather flat and wide with considerable length as compared to width. Most of the early lead came from the crevice type deposit, but present production is from the predominately flat zinc orebodies. The Graham-Snyder orebody, scene of Eagle Picher operations, is practically all zinc with little or no lead being recovered. Marcasite, present in varying amounts, makes production of finished concentrates by gravity separation impractical. Satisfactory lead and zinc concentrates have been produced since flotation was introduced in the area in 1927. An acid recovery plant was operated for about 20 years after World War I, but it has been dismantled, and no recovery of the iron sulphides in the ores of the district is being made at the present time. In June 1950 there were three companies operating mines and mills, Tri-State Zinc Co., Calumet & Hecla Consolidated Copper Co., and Eagle Picher Mining and Smelting Co. The Vinegar Hill Zinc Co. had completed a shaft at a new orebody and had started to develop the mine which will supply the Cuba City mill. The Cuba Mining Co. was holding the Andrews Mine inactive. The Dodgeville Mining Co. was not operating but was exploring for additional reserves. Several small mines were selling ore to the Eagle Picher mill. A general area map is given in Fig. 1. The Eagle Picher Mining and Smelting Co. entered the area in 1946 with an active exploration campaign. Leases on a block basis were secured for the area south from the Wisconsin-Illinois line near

Jan 1, 1953

By Marston G. Fleming

E. C. Peterson (Anaconda Copper Mining CO., Darwin, Calif.)—A study of this quite comprehensible and interesting paper by Dr. Fleming brings to mind several observations in the practical application of alkalinity and related factors to the actual practice of lead mineral flotation. Soda ash has long been a widely used and a very helpful alkaline conditioning agent in the flotation of galena from the usual run of lead-zinc ores. Soda ash is one of the common "standard" conditioning agents tried in any laboratory investigation of lead-zinc ores because it has so often proved helpful to galena flotation. However, the use of soda ash in the actual flotation of oxidized lead ores is certainly not widespread. In the flotation of certain lead-zinc ores from the Park City district of Utah, it was found in the usual cyanide-zinc sulphate-xanthate circuit that soda ash had an effect of producing a very condensed and flat froth regardless of the many frothers tried and that substitution of lime for soda ash to produce the same pH (8.0 to 8.4) improved the froth condition. However, the flotation of coarse particles of galena became so critical that some would pass through into the tailing, but caustic soda as a substitute for either soda ash or lime produced a very desirable froth condition in the same pH range and greatly improved the metallurgical outcome. Milling was carried out in typically "hard water" from watersheds of limestone and other calcareous rocks and the ore also apparently contributed magnesium and calcium salts to the pulp. Certain lead-zinc ores of Mexico have shown their greatest flotation response in circuits conditioned with sodium bicarbonate, and such actual mill use was also believed to be related to the water necessarily used in milling. On other lead-zinc ores the optimum has been obtained in actual milling treatment by use of caustic soda in both circuits of the operation. In flotation of oxidized lead ores in which sulphidi-zation is employed by addition of sodium sulphide, very high pH&apos;s exist in the flotation circuit. With the usual oxide lead ores, demanding 5 to 15 lb of sodium sulphide per ton of ore, pH&apos;s in the circuit (closed and open water-circuits) may range from 9.5 to 12, and for ores that contain much anglesite or a high percentage of iron oxide minerals, sodium sulphide consumption may reach as much as 30 lb per ton of ore and the resultant pH will be correspondingly higher. Yet in such flotation treatment employing either xanthate or oil (high-sulphur crude oil or diesel oils) as the collector, satisfactory to excellent grades of concentrate and lead recovery are obtained. Although there have been great studies and accomplishments in the investigations of flotation fundamentals and flotation theory, and although an investigation to determine the effect of all factors entering into the actual plant flotation of sulphide and oxide ores must become very complicated, as Mr. Fleming has mentioned in his caution regarding the drawing of general conclusions for other ores, it seems that it would be of greater interest if the techniques and investigations could, with time, approach the conditions of actual practice and lead the way to improved and more efficient flotation plant performance. Marston G. Fleming (author&apos;s reply)—The gulf between fundamental flotation research and plant operation is, perhaps, less wide than Mr. Peterson suggests. For example, the work described in my paper developed from an extensive investigation of a complex lead-vanadium ore from southwest Africa. This investigation started as a standard ore-testing problem but, at almost every stage, results were obtained which could not be interpreted in terms of previous experience. A program of fundamental research was therefore undertaken and was closely interlocked with the ore testing. This coordinated investigation resulted in a flotation process which has now been proved by two years of successful plant operation, and although the grade and mineralogical constitution of ore as well as smelter requirements have altered more than could have been anticipated, our knowledge of the fundamental character of the problem has made it possible to meet each change in conditions with much more confidence than would have been the case had we neglected this aspect of the investigation.

Jan 1, 1954

By C. O. Dale, W. J. Rundle

THE upper Mississippi Valley zinc-lead area was the first major lead-producing section in the United States. The lead ore, found near the surface in crevices, was relatively pure galena that could be smelted directly into lead, at first in log hearth furnaces and later in more efficient blast type furnaces. French Canadian fur traders encouraged the Indians to mine the lead ore and showed them how to smelt it into lead that had a high value for bullets1 Nicholas Perrot found lead ore on the Mississippi River bluffs near the junction of Wisconsin and Illinois and in 1690 established a trading post on the Wisconsin side of the river opposite the present site of Dubuque, Iowa.2 Shortly after 1720 discovery of Mine La Mott in Missouri diverted considerable attention from the Upper Mississippi area. Mining continued on a desultory basis with operations concentrated in the Galena, Illinois-Dubuque, area. In 1740 at least 20 miners were at work in the Fever River area around Galena and are reported to have shipped 2500 70-lb pigs of lead to Kaskaskia in 1741." Julien Dubuque established a mining and smelting operation in 1790 near the city that bears his name and was granted sole right to exploit the mining operations on the lands of the Sauk and the Fox Indians. He is reported to have produced 30,000 70-lb pigs of lead in 1805. Following the death of Dubuque in 1810 the Indians refused to let the white miners enter their lands, and little was done on the Iowa side of the river until the Indians were removed by treaty with the United States government in 1832." Early mining was entirely for lead but as the crevices were followed down, increasing percentages of zinc sulphide and zinc carbonate were encountered and at first discarded. Later a market became available for the zinc ores, and hand jigging devices were made to separate the lead, the zinc, and the rock or waste materials. The first record of zinc production from the area is for 1860. Production of zinc passed that of lead before 1900, reached a peak of 64,000 short tons in 1917, fell off rapidly and continually to about 2000 short tons in 1938, and since 1940 has ranged from 11,000 to 19,000 short tons. Lead has been of considerably less importance since 1900, and at present only about 10 pct as much lead as zinc is produced. Practically all of the zinc ore has come from orebodies that are rather flat and wide with considerable length as compared to width. Most of the early lead came from the crevice type deposit, but present production is from the predominately flat zinc orebodies. The Graham-Snyder orebody, scene of Eagle Picher operations, is practically all zinc with little or no lead being recovered. Marcasite, present in varying amounts, makes production of finished concentrates by gravity separation impractical. Satisfactory lead and zinc concentrates have been produced since flotation was introduced in the area in 1927. An acid recovery plant was operated for about 20 years after World War I, but it has been dismantled, and no recovery of the iron sulphides in the ores of the district is being made at the present time. In June 1950 there were three companies operating mines and mills, Tri-State Zinc Co., Calumet & Hecla Consolidated Copper Co., and Eagle Picher Mining and Smelting Co. The Vinegar Hill Zinc Co. had completed a shaft at a new orebody and had started to develop the mine which will supply the Cuba City mill. The Cuba Mining Co. was holding the Andrews Mine inactive. The Dodgeville Mining Co. was not operating but was exploring for additional reserves. Several small mines were selling ore to the Eagle Picher mill. A general area map is given in Fig. 1. The Eagle Picher Mining and Smelting Co. entered the area in 1946 with an active exploration campaign. Leases on a block basis were secured for the area south from the Wisconsin-Illinois line near

Jan 1, 1953

By Ralph V. Higgins

This paper concerns the magnitude of the amount of supersaturation that occurs in an underground reservoir during the flow of oil and gas to wells and to the amount of undersaturation that occurs during repres-suring of an oil reservoir where some effective permeability to gas exists. The study is based on earlier laboratory findings of other investigators on the rate of diffusion of gas in oil as a function of the depth of oil. Utilizing these relationships and the principles of reservoir mechanics, a quantitative estimate of undersaturation and super-saturation was calculated. The results showed that the diffusion of the gas is rapid enough that for all practical purposes no supersaturation exists during the flow of oil to wells or undersaturation during repressuring in reservoir sands having some effective permeability to gas. The reason diffusion of the gas virtually keeps the oil saturated is the long time required in radial flow for oil to reach the well and the slow rate at which pressure in reservoirs is increased during repressuring. INTRODUCTION Knowledge of the phase relationships during flow of gas and oil in an underground reservoir is essential to operating the reservoir in the most efficient manner. In material-balance calculations and in fluid-flow studies, the oil is assumed to contain all the gas that it will dissolve at given temperature and pressure. Pressure-volume-temperature relationships are normally obtained in the laboratory using "bottom-hole" or combined samples of the reservoir fluids. In such laboratory determinations equilibrium is obtained between the oil and gas in the pressure cells by mechanical agitation. During the flow of oil and gas in reservoirs, however, no comparable agitation occurs to mix thoroughly these fluids to aid in effecting equilibrium between the two phases. During repressuring of a partly depleted underground reservoir, the gas is usually injected into the reservoir faster than the oil can absorb it; consequently, the oil is undersaturated. On the other hand, as the oil flows through the reservoir to the wells during producing operations the pressure decreases faster than the gas in solution can diffuse through the oil to the gas phase. The oil therefore is supersaturated with gas. Where the oil is undersaturated, gas diffuses away from the gas-oil interface, and where it is supersaturated the gas diffuses toward the interface. In either case the gas moves from a higher to a lower saturation. This report contains the results of a study of the factors influencing the degree of nonequilibrium of the phase relations of oil and gas in porous mediums during the flow of oil through reservoirs to wells and also during the injection of gas into partially depleted sands. Data from an underground reservoir are presented and the degree of supersaturation during the flow of the oil through the reservoir to the well is approximated. Also data from another reservoir are used and the degree of undersaturation during the repressuring operation is calculated. In addition, the flow rates of oil in laboratory experiments and in underground reservoirs are compared, as data from the laboratory are often used to interpret events in the reservoir, and the rates of flow influence appreciably the degree of nonequilibrium. Much of the contents of this report was prepared in 1943; but, because of other activities during and since the war, the manuscript was left untouched until 1952, when it was decided to include an estimate of the amount of undersaturation during repressuring as well as supersaturation during flow.

Jan 1, 1955

By H. M. Myers, J. E. Funk

The two-phase flow of a drilling fluid in a diamond drill bit is investigated by deriving and solving the steady-state continuity and momentum equations. Parameters in this analysis are rotational speed of the bit, local rate of addition of drill solids, non-Newtonian nature of the drilling fluid and drilling rate. The describing equations relate the flow and pressure drop to the design characteristics of the bit. The equations are integrated numerically yielding the flow-rate pressure drop characteristics for the bit, flow distribution in the bit and velocity and static pressure as a function of position in each flow channel of the bit. Results are presented for a particular bit design. This paper shows that under normal drilling conditions certain parameters may be neglected in the hydraulic calculations for a diamond drill bit. Therefore, shortened forms of the equations presented can be used to fit the proper diamond bit to the drilling fluid hydraulic system. INTRODUCTION Like the conventional bit, the diamond drill bit is a key component in the circulating system of a well. The conventional rock bit is fitted to the circulating system by selecting the flow nozzles which provide the system with the proper flow-rate pressure drop relationship. Fluid behavior across the face of the diamond bit must be better understood so the bit can also be fitted to the circulating system. Data from field-operated diamond bits are presently available and do yield some information regarding the flow-rate pressure drop relationship. However, the number of factors affecting this relationship is quite large. Drilling parameters and conditions such as bit penetration rate, bit weight and rotational speed are important. Moreover, flow channels in the bit are part of the cutting head, and introducing drilled solids into the flow channels reduces the flow area, causes additional drag and influences the pressure drop. Many tests would have to be performed if field tests were required to study all parameters which might influence fluid behavior in the bit. A logical approach to this problem is to investigate analytically the fluid behavior in the bit, including parameters that are present under normal drilling operations. This approach, which seems to offer the best method for future studies, is presented in this paper. Following is the general procedure. 1. Equations describing the most general flow channel are written and include the addition of drilling solids (which is related to penetration rate), rotation of the bit, design parameters of the bit and non-Newtonian properties of the fluid. 2. A typical bit is designed and the bit parameters are substituted into the equations. 3. Parameters are assumed (penetration rate, rotational speed of the bit, mud weight, etc.). 4. The describing equations are numerically integrated to obtain the pressure drop across the face of the bit as a function of flow rate. 5. The pressure-drop contribution of each component (friction, acceleration, etc.) is obtained from the numerical solution, and those factors which largely influence the total pressure drop are identified. Classifying the drilling fluid is important in establishing the friction factor relationship since the frictional pressure losses are the main contributors to the total pressure drop. High-density drilling fluid is commonly assumed to be a Bingham plastic. 1-3 Govier4 presented a method for selecting a friction factor in the laminar flow region from the rheology properties of the mud and a modified Reynolds number. Metzner5 presented a criterion for selecting the friction factor in the turbulent flow region. The bit design used in conjunction with the solution of the equations has divergent flow channels. Stall, which is the backflow of fluid in the channels due to eddies that occur on the outer perimeter of the flow stream, can occur in these divergent channels (or diffusers). When stall does occur the static