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By A. C. England, William F. Haney, Paul B. Crawford, Bobby L. Landrum

The creation of unsymmetrical vertical or horizontal fractures in a producing well will result in a unique distortion of the normal shut-in pressures existing at the four surrounding wells. An electrical model study has been made to show how the shut-in pressures at the wells surrounding the fractured producing well may he used to estimate the size and orientation of vertical or horizontal fractures. The pressure differences at the four surrounding wells are recorded during production from the fractured well. The resulting pressure dato are matched from a table of several hundred possible fracture combinations. The table refers to the figure showing the effective size and orientation of the commercially created fracture. INTRODUCTION The creation of commercial fractures about oil and gas wells has led to considerable speculation as to the size and shape of the fractures. It is important that the size and shape be known in certain instances, especially when pressure maintenance programs are to be initiated. It was shown that if knowledge of a vertical fracture could be found that such information may be utilized in planning a waterflooding or gas cycling program and that in some cases the fractures might be utilized very effectively.' Other work showed that it may be desirable to create "pancake" fractures in certain reservoirs but that they should exist in a desirable range.' If the fractures are too large, they should be plugged prior to initiating a pressure maintenance program. If an irregular shaped "pancake" fracture is created, it is desirable to know the orientation of this fracture because similar but unreported studies have shown that "pancake" fractures may or may not substantially affect the sweep efficiencies and performance of the flooding or cycling program. Consequently, it may be desirable in some instances to estimate the effective size and orientation of the fracture. ANALOG An electrical model was used in making this study. The electrical model consisted of a circular reservoir approximately 8 in. in diameter, 1 in. thick and was filled with a dilute salt solution. A copper band formed the periphery of the reservoir. A vertical fracture was simulated by a copper strip soldered to the wire well located in the center of the reservoir. Vertical copper strips of various lengths and orientation were soldered to the wire well to represent vertical fractures in the reservoir. In studies reported here on vertical fractures it was arbitrarily assumed that two fractures originated at the well and extended out into the reservoir. An electrical potential was imposed between the wire well and the periphery of the tank. Plots of the iso-potentials are shown in Figs. 1 through 9. This model provides the steady-state isopotentials existing in a uniform, homogeneous circular reservoir having a vertically fractured well at its center. The permeability of the fracture is much greater than the permeability of the matrix proper. The effects of gravity are neglected. In preparing Tables 1 and 2, four symmetrically located unfractured wells were assumed to exist around

Jan 1, 1956

By Charles H. Behre

This paper discusses education and training for economic geologists other than petroleum geologists. Candidates enter economic geology through liberal arts colleges, engineering schools and university graduate study. Whatever their backgrounds, rigorous courses are desirable—now conceded in theory, but not adequately recognized in practice. Besides basic sciences (each studied long enough to give a fair comprehension of its basic tenets), a functional command of English and two modern foreign languages is needed, as well as a broad understanding of mining, milling and metallurgy. A year of economics and finance is recommended. Surveying and drafting are essential skills. Yet geology should be represented in each term; otherwise the initial enthusiasm for the science, once contact is broken, may never be regained. A five-year curriculum is thus designed to take care of all major requirements and culminate in the M. S. degree. This curriculum reduces "cultural" courses below the average liberal arts requirements, but this is regarded as necessary. The pursuit of "culture" is assigned, as in most engineering and medical curricula, to extra college years or extracurricular time. To avoid the danger of over-crowding the schooling, the Doctorate in geology is preferred wherever possible. Its two added years should permit wider professional education; more browsing in "cultural" pastures; due attention to broader social implications; and some training in the research now increasingly required of the mineral industry. "In-course" training through cooperation between school and industry is especially advo- cated. The Institute should take the initiative in stimulating this practice. Introduction Training a student in geology for a career in the mineral industry is still a moot question, one that is likely to be looked at from many different angles, each of which will reflect the background of the individual considering it. From what follows, the training of petroleum geologists is omitted since, although theirs is an equally important phase of economic geology, it is based upon different essentials. The general subject was recently effectively discussed, but from a somewhat different viewpoint, by Professor McKinstry.' The practical problems that confront the young mining geologist are highly varied and in the eyes of his employer apparently almost any demands seem justified. The mining executive wants from the mining geologist results related mainly to overall operations, reports or forecasts that are largely recordable on paper and chiefly in terms of "discovery thinking." The local mining engineer may have many specific questions of his own, chiefly relating to details of geology that apply to mining practice, which he will address to the mining geologist; these usually deal with production quantities; frequently also they necessitate the immediate handling of pressing but apparently minor matters: shall the drill be moved; how soon will we encounter the watercourse which made so much trouble for us above? The client employing a consultant often wants advice or good judg-

Jan 1, 1949

By R. G. Powell, R. Schuhmann, E. J. Michal

Liquidus surfaces in the ternary system FeO-Fe2O3-SiO2, were determined from 1250' to 1450°C by the procedure of equilibrating small samples in platinum crucibles, quenching, and microscopic examination. The experimental results were combined with previously published information to construct a ternary diagram for the system showing the entire temperature-composition range of stability of iron silicate slags. Metallurgical applications of the diagram, especially in copper smelting, are discussed briefly. IRON oxides are almost unique among the common oxide constituents of metallurgical slags in that the iron occurs in two different states of oxidation, ferrous and ferric. Moreover, in liquid slags the degree of oxidation of the iron is readily changed by reactions of the slags with oxidizing agents or reducing agents. This behavior of iron oxides in slags accounts, for example, for the effective transfer of large quantities of oxygen through slag layers in open hearth steelmaking. In this process, oxygen supplied by reactions at the gas-slag interface is dissolved in the slag with the oxidation of ferrous iron to ferric. Ferric oxide is transported across the slag layer by convection, and at the slag-metal interface the oxygen reacts with liquid metal while the ferric iron is reduced back to the ferrous state. Another group of processes in which variation in degree of oxidation of iron has great practical importance is in copper smelting. In matte smelting and converting, such large proportions of the iron are oxidized to the ferric state that problems are encountered in preventing or controlling the formation of solid magnetite. The ferrous-ferric relationship also affects the attack of iron oxides on high-SiO2 refractories, which appears to be most severe under reducing conditions for which ferrous iron predominates. Darken and Gurry' determined the chemical properties and phase equilibria of pure iron oxide slags. Their data show that iron oxide melts can have compositions ranging almost all the way from FeO to Fe2O3. The melts of lowest oxygen contents, which exist in equilibrium with metallic iron, approach ferrous oxide in composition but still have a small percentage of ferric oxide. The melts of highest oxygen contents, which have oxygen dissociation pressures of 1 atm, are above magnetite in oxygen content, with over two-thirds of the iron in the ferric state. The previously established phase diagrams for silicate slag systems all show FeO as the iron oxide component. However, Bowen and Schairer? who determined the FeO-SiO2 diagram and many of the other diagrams used by slag chemists, have been careful to point out that their systems always contained both ferrous and ferric iron. Thus, their data are for limiting mixtures with minimum contents of ferric iron, obtained by melting and equilibration in iron crucibles. Under these conditions, the Fe2O3 percentages found by analysis were small enough to justify simplification of the published phase diagrams by calculating the Fe2O3 to equivalent FeO and ignoring Fe2O3 as an additional component. On the basis of experimental measurements of melting points of iron oxides on silica in the presence of various gas mixtures, Darken3 worked out phase diagrams for the Fe-Si-0 system which show the important phase equilibria in terms of temperature and gas composition. This study clarified many aspects of the application of the phase rule to the FeO-Fe2Oa-SiO2 system and was an important basing

Jan 1, 1954

By Charles H. Behre

This paper discusses education and training for economic geologists other than petroleum geologists. Candidates enter economic geology through liberal arts colleges, engineering schools and university graduate study. Whatever their backgrounds, rigorous courses are desirable—now conceded in theory, but not adequately recognized in practice. Besides basic sciences (each studied long enough to give a fair comprehension of its basic tenets), a functional command of English and two modern foreign languages is needed, as well as a broad understanding of mining, milling and metallurgy. A year of economics and finance is recommended. Surveying and drafting are essential skills. Yet geology should be represented in each term; otherwise the initial enthusiasm for the science, once contact is broken, may never be regained. A five-year curriculum is thus designed to take care of all major requirements and culminate in the M. S. degree. This curriculum reduces "cultural" courses below the average liberal arts requirements, but this is regarded as necessary. The pursuit of "culture" is assigned, as in most engineering and medical curricula, to extra college years or extracurricular time. To avoid the danger of over-crowding the schooling, the Doctorate in geology is preferred wherever possible. Its two added years should permit wider professional education; more browsing in "cultural" pastures; due attention to broader social implications; and some training in the research now increasingly required of the mineral industry. "In-course" training through cooperation between school and industry is especially advo- cated. The Institute should take the initiative in stimulating this practice. Introduction Training a student in geology for a career in the mineral industry is still a moot question, one that is likely to be looked at from many different angles, each of which will reflect the background of the individual considering it. From what follows, the training of petroleum geologists is omitted since, although theirs is an equally important phase of economic geology, it is based upon different essentials. The general subject was recently effectively discussed, but from a somewhat different viewpoint, by Professor McKinstry.' The practical problems that confront the young mining geologist are highly varied and in the eyes of his employer apparently almost any demands seem justified. The mining executive wants from the mining geologist results related mainly to overall operations, reports or forecasts that are largely recordable on paper and chiefly in terms of "discovery thinking." The local mining engineer may have many specific questions of his own, chiefly relating to details of geology that apply to mining practice, which he will address to the mining geologist; these usually deal with production quantities; frequently also they necessitate the immediate handling of pressing but apparently minor matters: shall the drill be moved; how soon will we encounter the watercourse which made so much trouble for us above? The client employing a consultant often wants advice or good judg-

Jan 1, 1949

By Andrew B. Crichton

THE oft repeated statements of the United States Geological Survey and the Bureau of Mines that the coal reserves in the United States are sufficient for 3000 yr have given us all a sense of security hard to disturb. If we discount that statement 66 pct, which to the uninformed seems drastic, we would still have 1000 yr supply, and why should mortal man worry about the difference between 1000 and 3000 yr supply of coal. That is exactly the attitude which many who should be better in- formed have taken toward the problem. A recent brochure "How Strong is America," by the New York Herald Tribune, states there is "no end to coal * * The truth is staggering * * U. S. has enough coal to last 4000 years." What the statement actually means is that the calculator got as high as 4000 yr and decided it was pointless to go on. The President's ERP Committee on Natural Resources and others in high places continue to assure the country of our superabundance of coal. In the past few days the “Wall Street Journal" carried an item from Director Boyd of the Bureau of Mines saying that within a hundred years we would need to triple our annual coal production of 6oo,ooo,ooo tons, making it 1,800,000,000 tons annually, and at that rate we had coal reserves sufficient for 1000 yr. In my humble opinion, we cannot now or ever produce 1,800,000,000 tons annually, be- cause we do not have the reserves in the producing districts to do it. Past reckoning in geology may be, as in the Psalms, a thousand years are as yesterday, but the future must be considered more realistically, and "a thousand years" is really a "heck" of a long time. In most developed areas, mining engineers can count the coal reserves in terms of a hundred years or less, and in some important areas now producing large annual tonnages in much under fifty years. They think when they hear of thousands of years coal reserves, reference is made to distant fields and "the fields are always green far away." The estimates of our coal reserves upon which we are relying were made in 1907 under the direction of Marius R. Campbell, Director of the United States Geological Survey. It is apparent this work was not well done. It was necessarily based on rather meager data because of the little development and prospecting as of that date. There were mistakes in the correlation of seams, and they assumed the continuity of thick seams throughout large coal bearing areas where coal often did not exist. The overstatement of coal bearing areas in the Campbell figures are common. The 1907 survey includes all coals over 14 in. in thickness to a depth of 3000 ft. The total coal reserves according to Campbell were 3157.2 billion tons. The production and mining losses that year would amount to -570 million tons and

Jan 1, 1948

By D. Turnbull, R. E. Cech

THE supercooling behavior of pure liquid metal droplets has been described.' The solidification behavior of small droplets of Cu-Ni alloys as a function of composition is described herein. The Cu-Ni system is of interest for such an investigation because the components are miscible in all proportions in both the liquid and solid state and the phase diagram of the system, Fig. 1, is a type often encountered in metal systems. It was noted by Van Riemsdyk2 and others that the nature of the "blick" of gold droplets during assaying is not perceptibly affected by the content of the platinum group metals that are soluble in both liquid and solid gold. With the exception of these very qualitative observations there appear to have been no prior investigations of the supercooling of alloy droplets. A series of nine alloys varying in composition by 10 pct (nominal weight) steps was made using certified OFHC copper, 99.996 pct purity, obtained from the American Brass Co., and electrolytic nickel pellets, 99.92 pct purity, obtained from the International Nickel Co. The alloys were melted and cast in vacuo in a high frequency induction furnace. Segregation was minimized by chill casting into 1-in. diam steel molds. Each alloy rod was homogenized at a temperature 50°C lower than the solidus for 100 hr in dry hydrogen. Samples for solidification experiments and chemical analysis were machined from the same portion of each rod and at a depth of in. from the rod surface. A Car-boloy tool was used in taking turnings to minimize contamination of sample by the cutting tool. As a check, a number of samples for microscopic observation were chipped from the ingot with a fragment of pyrex glass. The resultant data in all cases agreed, within experimental error, with the data obtained from machined turnings. A number of small particles, 30 to 50 micron diam, of a Cu-Ni alloy were placed in a quartz vial 1/32 in. diam x % in. long. This was inserted into a platinum ribbon heater and mounted in a high temperature microscope stage. The general procedure followed in inserting samples into the stage and measuring the temperature of melting and solidification was the same as described in an earlier paper.' A chromel-alumel thermocouple was used to study alloys of 88.93 pct Cu, 80.62 pct Cu, and 72.27 pct Cu. A platinum-10 pct rhodium thermocouple was used for the remainder of the alloys. Procedure The assembled high temperature microscope stage was first evacuated and the sample given a 2 min in situ treatment at 900 °C in dry hydrogen to remove surface oxides which might otherwise catalyze crystal nucleation. After this treatment the atmosphere was changed to purified helium and melting and solidification were observed microscopically. It was not possible to determine the solidus with certainty. However, the liquidus temperature was measured very accurately since the surface of the particle changed in appearance from coarse and uneven to smooth, mirror-like within a few degrees. The visually determined liquidus temperature was checked by finding the highest temperature to which the particle could be heated such that it did not supercool upon lowering the temperature. This temperature which checked within experimental error with that found by observing surface change was assumed to be characteristic of the thermody-namic liquidus. In order to minimize the effect of selective evaporation of copper from the alloy, samples were changed frequently and the droplets were heated no more than 50 °C in excess of the liquidus temperature T,. When the latter conditions were fulfilled, T, values were reproducible. After melting, the temperature was decreased slowly until the particles solidified. The sudden release of heat of fusion on solidification caused the

Jan 1, 1952

By Richard Franchot

DISCUSSION of a paper is sometimes more in-teresting in what has not been said than in what is said. In the present case the paper is mainly directed to certain thermo-dynamic relation-ships in the blast furnace. Careful reading of the dis-cussion fails to show a single use of the term, heat unit, or its equivalent. If we wish to know very-much about the furnace action it is necessary to count calories or B.t.u. Nothing much is. said about the availability of heat at high temperatures, although it will be generally admitted that in seeking underlying limiting factors in the furnace economy the hearth heat relations offer-the most promising clues. Those discussing the paper, with exceptions of course, apparently have failed to recognize an outstand-ing fact. It is a fact that the heat actually generated by the air oxygen in CO formation (including the blast heat) is in excess, after charging off radiation, etc., by from 70 to .90 per cent over the heat absorbed in melting the iron and slag and calcining the stone reduction by CO absorbing no heat. The fact stands out as plainly as does the fact that the furnace functions largely as a gas producer. The surplus heat is there. It is in the picture. Why not take a look at it, face the fact? That the surplus heat is necessitated by the hearth conditions admits of very little if any doubt. The furnace is really two separate pieces of apparatus: the hearth, doing certain work, and the superimposed shaft, doing certain other work. The combustion of fuel in the hearth, primarily serving the hearth pur-poses, generates much more heat and gas than the shaft requires, or can use, in smelting work. The result is surplus heat makes still more gas in the heat-absorbing reaction between CO, and coke; what is left of the surplus going to top heat. Here we have a simple yet adequate sketch of the furnace action. Having obtained a fairly comprehensive view of the existing heat relations of both hearth and shaft, the way to improvement seems quite plain. Either do more of the work above the hearth or put more heat into the hearth. Since there is already a great surplus of heat above the hearth, probably little needs to be done by way of increasing the proportion of the work done in the shaft. The shaft can, however, probably do much more work than it is now doing provided that a way, can be found to get more work, done in the hearth. The hearth heat is nicely balanced. Losses by radiation and water cooling and other losses are already taken care of. Any increase of hearth heat development could be utilized in taking care of increased smelting work. Aside from the possibility of increased blast heat, there is one sure way of putting more heat into the hearth, and this is to blow more air. And since the shaft already has more gas than it needs, the increased gas resulting from the greater blast volume can be withdrawn from the bosh after it has done its work in the hearth. Now an increase of burden will cool the shaft, cut down solution loss and thereby supply addi-tional coke in the hearth to burn with the additional air blown. The hearth heat per pound of coke charged will be proportionately increased. The balance between hearth and shaft will be better. Gruener's ideal will be more nearly attained, if not exceeded. Most inter-esting of all perhaps, the more the burden is increased, the more coke will reach the hearth and the more burden can be added. The effect is to be cumulative.

Jan 3, 1927

By M. F. Goudge, R. V. Tomkins

Sodium sulfate is an important chemical raw material that is being used in ever increasing quantities in modem industry. It comes on the market mainly in three forms: (1) Salt cake (Na2SO4), a relatively crude form of the anhydrous salt containing up to 3 pct impurities, and comprising about three-quarters of the North American production; (2) anhydrous sodium sulfate (Na2SO4), a refined form containing less than 0.3 pct impurities; (3) Glauber's salt, the decahydrate (Na2SO4.10H2O) containing 55.9 pct water of crystallization. Competing with salt cake from natural sources is byproduct salt cake from a number of industrial operations. For instance there is Mannheim cake resulting from the manufacture of hydrochloric acid by the reaction of salt (NaCl) and sulfuric acid in Mannheim furnaces; rayon cake, a high-quality product, resulting from the process of making rayon by the viscose process; chrome cake from the processing of sodium chromate to dichromate; phenol cake from the manufacture of phenol; also byproduct sodium sulfate resulting from the conversion of lithium sulfate to lithium carbonate; from the processing of sodium tetraborate to boric acid; from converting sodium formate to formic acid; and in the manufacture of cellophane. Sodium sulfate is also obtained as a byproduct in the manufacture of isosebasic acid. In addition strong competition has resulted from imports of byproduct salt cake from the chemical industries of a number of highly industrialized European countries. However in recent years due to technological changes the output of byproduct salt cake is rapidly diminishing and the natural deposits are becoming the most important source of sodium sulfate used in North America. For instance, the production of hydrochloric acid in Mannheim plants has become obsolete and thus the greatest single source of byproduct salt cake will disappear. Also viscose rayon is meeting strong competition from nylon and other synthetic fibers and production of byproduct salt cake from this source may do little more than remain at the present level. These factors together with increasing demand for sodium sulfate point to increased production from natural sources. In 1958, 36 pct of the total United States production was derived from natural sources and in addition 97,000 short tons was imported so that over 40 pct of the total consumption was supplied by natural sources whereas in 1953 the proportion was only 24 pct. The rapid growth in production is shown in Table 1. Principal Sodium Sulfate Minerals There are many minerals in which sodium sulfate is a constituent but those of commercial importance at the present time, and consisting wholly of sodium sulfate in either the hydrous or anhydrous states, are mirabilite and thenardite. Minerals of potential importance but consisting in part of compounds other than sodium sulfate are glauberite in which sodium sulfate is combined with calcium sulfate, and blödite in which sodium sulfate is combined with magnesium sulfate. Mirabilite (Na2SO4.10H2O) the decahydrate, consists of 24.8 pct SO3, 19.3 pct Na2O, and 55.9 pct H20. It is a colorless to opaque, soft, water-soluble mineral with a slightly bitter taste. It has a hardness of less than 2 and a specific gravity of 1.48. It forms long needle-

Jan 1, 1960

By Ferid Kromer

Geography: The Tagtepe district of the Vilayet of Eskigehir is about 20 miles northeast of the city of Eskigehir (approximately midway between Ankara and Istanbul) in western Anatolia. The area is a mountainous one, the highest peak being Tagtepe Mountain (5200 ft) which is approximately in the center of the district. The mountains drop off to the deep valley of the Sakarya River on the north and to the plain of Eskigehir on the south. FERID KROMER, Junior Member AZME, is a Consulting Mining Engineer and General Manager, Bagtag Turk Maadin Ltd., Istanbul, Turkey. New York Meeting, February 1950. TP 2629 H. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received Dec. 29, 1948. For the most part, the watershed is on the northern side of the mountain barrier, draining into the Sakarya River, which in turn empties into the Black Sea midway between Zonguldak and the mouth of the Bosphorus. The approximate area covered by the Tagtepe district is shown in fig. 1. Transportation to shipping points is available via the Istanbul-Ankara railroad. The station on this line nearest the mining district is Alpikoy station, about 20 miles by road southwest of Tagtepe Mountain. Interior roads within the district are poor. Being of dirt, the winter rains and snows render them almost impassable for trucks from about the middle of December until the end of March, thus presenting a considerable transportation problem. However, the roads from the Bagoren and Tagtepe chromite mines to the railroad shipping point at Alpikoy station have recently been repaired and will be maintained for all-weather truck transportation. Detailed climatic data are not available. However, in general the spring, summer, and early autumn months are dry, and good weather may be expected from May until early November. Then the winter rains commence, and heavy snow is usual during January and February. Geology: The mountainous structure of Tagtepe belongs to basic rocks of serpentine (Variscan Orogeny) which is in contact with Paleozoic schists at west, and an Oligocene outcrop of red clays in Margi-Sepetci region (see fig. 1) at southeast. The northwest and southwest borders of Tagtepe district are, respectively, surrounded by Paleozoic schists and pebbly gray and yellow Neogene clays. More recent formations of alluviums overlay the plain of Eskigehir. Dark basic rocks of trachytes with hornblende are visible on Turkmenbaba Mountain, at the west of Tagtepe. Mineral Occurrences: Chromite: the most important mineral found in any quantity in the Tagtepe district. The alignment of the deposits of chromite is in general along the line Bagoren-Tagtepe (see fig. 1). The first mines in the area were those of Tagtepe and Bagoren, which were developed over 20 years ago with Swedish capital. Other deposits of chromite, more recently discovered and so far of less importance, are being worked at Kurucor, Komurcu, Gelinmezari, and Lacin (see fig. 1). Deposits average generally between 46 and 48 pct chromic oxide, with the exception of the Bagoren mine which averages 44 pct. However, a new lode, very recently plotted, in the Tagtepe mine averages 50 pct Cr,O,, 4.6 pct SOz, and 7 pct FeO. Geological character of the chromite occurrences in the Tagtepe mine may be considered typical of most chromite lodes in this area. The indications are that the formations of ore lenses are developed by the segregation of chromite crystals intruded into the serpentinized rock, and exposed later to tectonic movement within the zone of crystallization. All lenticular masses are more or less regular in shape and follow each other in southeast-northwest direction and dip generally 70" NE. Ore lenses do not seem to persist in depth, average depth of two lenses is 60 ft below surface. Three lodes .have been mined as open-pit. The average dimensions of individual lenses are as follows: pitch length, 100 ft; breadth, 27 ft; and width, 20 ft. The lenses and their enclosing rocks are broken by parallel fractures in approximately east-west direction. These joints are filled, except in one lode, with cementing material, which gives to the ore a

Jan 1, 1951

By T. M Morris

THE rate of flotation of solid particles determines the percentage recovery of these particles which can be obtained during a given time interval. It is an established fact that the recovery is greatest in the fine sand size range and falls off on either side of this size range. It is also a fact that the history of the development of concentrating devices has been marked by a desire to recover the small particles: tables were developed to treat material too fine to recover in jigs; flotation recovers material too fine to be recovered on tables. As our ores become more complex and require finer grinding, a greater proportion is in the slow-floating size range. It is therefore of economic importance that the effect of size of particle upon rate of flotation be studied. Many studies have been made along this line. The present investigation attempts to quantify the rate of flotation by means of a rate equation, and then compares the effect of size upon the rate of flotation. It was found that the flotation rate constant increases with increase in diameter of particle in the size range smaller than the optimum size particle. The flotation rate constant decreases with an increase in diameter of particle in the size range coarser than the optimum size particle. This suggested two different actions taking place, and these are discussed. Suggestions for further work in order to improve the flotation rate of both fine and coarse particles are made. The usual method of expressing rate is to plot cumulative percent recovery vs time. If we knew the equation of this kind of curve we could replot it as a straight line, and the slope of the line would be an index of the magnitude of the flotation rate. It is easier to compare straight lines than curves. The basis used for obtaining the equation of the recovery vs time curve is the law of mass action. This law states that the "rate of a chemical reaction is proportional to the 'active masses' of the reacting substances present at any given time." This, of course, implies a constant temperature. We can modify this for our use by using the term flotation reaction instead of chemical reaction and the term floatable particle instead of active masses. dC Thus----— kc [1] where C denotes concentration of particles, t denotes time, k denotes a proportionality constant. If the exponent of C is 1, then we have a first order rate reaction. If the exponent of C is 2, then we have a second order rate reaction. For a first order rate reaction, we obtain, after integration, where k is again a proportionality constant and has the dimension of the reciprocal of time. C, is the original concentration or weight or percentage of floatable particles. C, is the concentration or weight or percentage of floatable particles remaining in the flotation cell after time t. If all particles of the mineral to be floated were capable of floating we could take C, as 100 and C, would be 100 - R, where R is the cumulative percentage recovery of mineral at time t. But it is not usual for all of the particles to be capable of floating, because of surface oxidation, etc. Therefore, we must introduce a factor x which is the percentage of un-floatable mineral. Hence the first order equation is It has been proposed by various workers1-' that this equation describes the flotation rate. More recently N. Arbiter4 states that a second order rate equation fits the recovery vs time curve more closely than does a first order rate equation. Morris- as discussed the evidence presented for this statement. It has been concluded that the first

Jan 1, 1953

By M. A. El-Aouar

Drilling muds are complex colloidal systems. In an effort to analyze the physical properties that affect their performance at high temperature, an investigation was made of the hydrothermal stability of the monoionic hydrogen, calcium and magnesium forms of montmorillonite and attapulgite. Samples were heated to 400°1F in a simple autoclave and analyzed for cation exchange capacity, c-axis X-ray diffraction spacing and pH factor us sodium hydroxide titration dependence. Out of the six monoionic clay minerals tested, calcium montmorillonite and magnesium attapulgite showed the least base exchange capacities and were relatively unaffected to heat. It is concluded that, of the six clays studied, these two clays were the most suitable forms for use in drilling fluids. INTRODUCTION The drilling of deep wells is dependent upon the drilling mud, and problems frequently arise concerning the effect of mud temperature and prolonged heating. Drilling muds are complex colloidal systems. In an effort to analyze their behavior in deep, hot boreholes, it was thought desirable in this investigation to study suspension of pure, monoionic montmorillonite and attapulgite clays before and after hydrothermal heating. Chemically, clays are hydrated aluminum silicates, such as montmorillonites and attapulgites. The structure of montmorillonite is composed of units made up of two silica tetrahedral sheets with a central alumina octahedral sheet. Attapulgite consists of double silica chains running parallel to the c-axis with the chains linked together at their longitudinal edges. The apexes of the tetrahedrons in successive chains point in opposite direc-tions.4,7,10 One of the most important characteristics of clay minerals is their property of sorbing certain anions and cations and retaining them in exchangeable state. The property of exchange capacity is measured in terms of milliequivalents (meq) per 100 gm of clay. The cation-exchange capacities are taken at pH 7 from titration curves which show the relation between pH and milliequivalents of added NaoH.9,11 The following are causes of cation exchange: (1) broken bonds around the edges of the silica alumina units would give rise to unsatisfied charges, which would be balanced by adsorbed cations; (2) substitution within the lattice structure of trivalent aluminum for quadrivalent silicon in the tetrahedral sheet and of ions of lower valence; and (3) the hydrogen of exposed hydroxyls may be replaced by a cation which would be exchangeable. The primary techniques employed to study the effects of hydrothermal treatment were titration curves and X-ray diffraction analyses. Titration curves were useful in characterizing the nature of the clay mineral surface and the stability of the various samples to attack by acid or alkali before and after hydrothermal treatment. X-ray diffraction analyses were used to determine changes in the nature and crystal structure of the minerals present and to determine the cations in exchange positions on the montmorillonite samples. EXPERMENTAL PROCEDURE PREPARATION OF SAMPLES Selected samples of Wyoming bentonite and attapulgite clay from mines along the Georgia and Florida border were purified by centrifugation to remove all particles larger than 2 microns. In preparing magnesium attapulgite, first a 1.00-normal solution of magnesium acetate was prepared. The pH of the solution was adjusted to 7.0 by adding magnesium oxide. One hundred grams of attapulgite clay were mixed in a blender for 30 minutes with the magnesium acetate solution. The attapulgite solution was left overnight, and then filtered in a Buchner funnel. The suspension was leached with further quantity of magnesium acetate solution and then washed with distilled water for 20 days, after which the filtrate was free from magnesium ions. The concentration of magnesium attapulgite in the clay slurry was adjusted and determined quantita-

By E. W. Newman

During 1943 and 1944, there was an urgent need for certain grades of optical calcite (Iceland spar) for instruments for ' military uses. To find a supply of this material, prospecting was carried out in Montana, California and Colorado. Although some production was obtained by the work in California, the best results were from prospecting the large calcite veins of south central Montana. The bulk of the optical calcite mind during World War II has come from that area. The Bureau of Mines took an active part in the search for optical calcite in Montana. It examined most of the known calcite veins in the 70-mile distance between Wilsall, on the Shields River: and Absarokee, on the Still water River, and conducted exploration on several of the deposits. The Geological Survey also took an active part by mapping many of the veins. Actual mining of the calcite was performed at first by Calcite Operators, Inc., and later by the Metals Reserve Co., through an agent. A sorting plant was established at Clyde Park, where custom material could be sold. These activities stimulated mining by private operators. To be suitable for military uses, the calcite mined had to meet rigid specificstions as to both size and quality. Individual crystals had to be clear and transparent and if in the form of rhombs had to measure at least 7/8 in. on each edge. Some color and a few inclusions in the calcite were allowable, but material with incipient or developed cleavages, or showing twinning other than parallel to the base, was unacceptable. History of Deposits The existence of large veins of calcite in south central Montana has long been known, and for many years the farmers of this region have used the common vein calcite for producing grit for chicken feed. According to reports, the fist optical calcite produced from Montana came from the Cartwright deposit near Grey-cliff,' but until recently the mining of optical calcite in Montana has been limited to spasmodic searching for small crystals suitable for making nicol prisms for saccharimeters and microscopes, or for mineral specimens. The possible need of substantial amounts of optical calcite for military uses began to appear late in 1942 and early in 1943, therefore the Polaroid company began searching for a source of supply in Montana and California. Work on the Wade property near Clyde Park was started on a small scale in the fall of 1942, by .4. H. Hansen, of Clyde Park. During the winter and spring of 1943, a modest quantity of optical calcite was mined and shipped to the Polaroid Corporation, Cambridge, Mass. Most of this was produced from the "Hansen vug," which was found close to the surface. Early in the summer of 1943, mining on the Wade property was undertaken by Calcite Operators, Inc., a company organized for mining optical calcite from the

Jan 1, 1948

By E. W. Newman

During 1943 and 1944, there was an urgent need for certain grades of optical calcite (Iceland spar) for instruments for ' military uses. To find a supply of this material, prospecting was carried out in Montana, California and Colorado. Although some production was obtained by the work in California, the best results were from prospecting the large calcite veins of south central Montana. The bulk of the optical calcite mind during World War II has come from that area. The Bureau of Mines took an active part in the search for optical calcite in Montana. It examined most of the known calcite veins in the 70-mile distance between Wilsall, on the Shields River: and Absarokee, on the Still water River, and conducted exploration on several of the deposits. The Geological Survey also took an active part by mapping many of the veins. Actual mining of the calcite was performed at first by Calcite Operators, Inc., and later by the Metals Reserve Co., through an agent. A sorting plant was established at Clyde Park, where custom material could be sold. These activities stimulated mining by private operators. To be suitable for military uses, the calcite mined had to meet rigid specificstions as to both size and quality. Individual crystals had to be clear and transparent and if in the form of rhombs had to measure at least 7/8 in. on each edge. Some color and a few inclusions in the calcite were allowable, but material with incipient or developed cleavages, or showing twinning other than parallel to the base, was unacceptable. History of Deposits The existence of large veins of calcite in south central Montana has long been known, and for many years the farmers of this region have used the common vein calcite for producing grit for chicken feed. According to reports, the fist optical calcite produced from Montana came from the Cartwright deposit near Grey-cliff,' but until recently the mining of optical calcite in Montana has been limited to spasmodic searching for small crystals suitable for making nicol prisms for saccharimeters and microscopes, or for mineral specimens. The possible need of substantial amounts of optical calcite for military uses began to appear late in 1942 and early in 1943, therefore the Polaroid company began searching for a source of supply in Montana and California. Work on the Wade property near Clyde Park was started on a small scale in the fall of 1942, by .4. H. Hansen, of Clyde Park. During the winter and spring of 1943, a modest quantity of optical calcite was mined and shipped to the Polaroid Corporation, Cambridge, Mass. Most of this was produced from the "Hansen vug," which was found close to the surface. Early in the summer of 1943, mining on the Wade property was undertaken by Calcite Operators, Inc., a company organized for mining optical calcite from the

Jan 1, 1948

By H. D. Outmans

In steady vertical flow, the interface of an immiscible liquid-liquid displacement is horizontal for any flow rate below the critical. In nonvertical flow, however, the shape of the interface in the steady state does depend on the flow rate, and the purpose of this paper is to calculate the unsteady interfaces during the transition of one steady state of flow to another. A knowledge of these transient interfaces is of considerable importance in reservoir engineering where the calculation of breakthrough recovery depends on the instant the interface reaches the producing wells and on the shape of the interface at that time. Although the emphasis is put on transient interlaces, which eventually approach stable equilibrium, it is shown that if the displacement exceeds a critical rate no equilibrium is possible. The interface is then unstable and viscous fingers are formed during the displacement. The critical rate and the shape of the transient and equilibrium interfaces are affected by the effective interfacial tension; but since this effective interfacial tension appears in the calculations only in combination with the inverse square of the thickness of the medium, its effect in the reservoir would appear to be negligible compared to its significance in model experiments. INTRODUCTION Stability criteria and the early growth of interfacial disturbances in a plane parallel to the boundaries of a dipping formation in which oil is displaced by an incompressible fluid were described in a previous paper.l This type of instability is significant in thin reservoirs. However, if the reservoir has appreciable thickness, then interfacial stability in vertical planes, normal to the upper and lower boundaries, also becomes important (the displacement is supposed to be parallel to these vertical planes). The difference between the two stability problems is that, in the first case, the intersections of the interface with planes parallel to the boundaries are normal to the direction of the displacement; in the second case, the intersections, this time with vertical planes, are not normal to the displacement. Instead, they are tilted at an angle which depends on the displacement rate. The tilt of steady interfaces was calculated by Dietz2 who also determined the critical rate of displacement for stability in the vertical plane by assuming that this rate would coincide with an interfacial tilt equal to the dip of the formation. The critical rate thus calculated is the same as has been found for thin reservoirs (see Eq. 1.1 of Ref. 1 and of the present paper). Dietz's calculation of the stable tilt was verified by laboratory experiments and the agreement was found to be fairly good.3 It is doubtful, however, that stable tilts actually exist in the reservoir because a change in production rate is not followed by an instantaneous adjustment of the interface to the new rate but, rather, by a transition period during which the interface changes from one equilibrium tilt to the other. The principal objective of this paper has been to describe these transient interfaces without putting any restrictions on the flow conditions or the shape of the interface, as had been done previously. The second objective was to compute the critical velocity, taking into account capillary effects, and the third was to evaluate, at least qualitatively, the shape of the front at rates above the critical, again without making the simplifying assumptions introduced by previous investigators.2,3 In the following sections two examples are given of the calculation of interfacial motion. The first describes this motion for an initially horizontal interface in a dipping layer, and the second for a vertical interface in a horizontal layer. The mathematical formulation of the problem is nonlinear in the boundary conditions, and this prohibits its solution in closed form. Instead, the solution is obtained in the form of higher-order approximations. 1 Before proceeding to a description of the mathematical model, however, we define two quantities

By L. W. Pommier, F. B. Brien

The Rheological properties of pulps are non-Newtonian in character and more than one viscosity parameter is necessary to describe their behavior, therefore, the single term 'apparent viscosity' which has been used in the past may be misleading. The study reported in this paper uses a dimensional analysis based on the Ostwald-de Waele shear stress-rate of shear model for non-Newtonian liquids to develop velocity and resistance equations for falling spheres. An electronic monitoring apparatus was assembled for determining the velocity of metallic bodies as they fall through opaque liquids and suspensions. By means of this apparatus the behavior of the viscosity parameters of the Ostwald-de Waele model and the applicability of the proposed equations were examined for a number of non-Newtonian liquids. The validity of the equations for these liquids was confirmed. Preliminary data collected using solid-liquid suspensions established the validity of the form of the basic equations for these systems. The differential movement of solid particles through solid-liquid pulps and suspensions is very important LO many branches of engineering, such as minerals processing, soil mechanics, ceramic slip processing, oil well drilling-mud technology, materials-handling in pipelines, and many others. There is a dearth of fundamental knowledge on the flow resistance encountered by immersed bodies moving through solid-liquid suspensions. The resistance offered by Newtonian liquids to the movement of free settling spheres is well described for laminar and turbulent conditions by Stokes' and Newton's Laws, respectively. However, problems are encountered when attempts are made to extrapolate these simple relationships into solid liquid suspensions. The rheological properties of pulps are such that they are non-Newtonian in character;'" that is, the applied shearing stress and resulting rate-of-shear are related by non-linear functions, and thus, in the simplest case two viscosity parameters are necessary to describe their rheological properties. For this reason the single term 'apparent viscosity' which has been commonly used to explain the flow resistance of suspensions and non-Newtonian liquids may be misleading. It is realized that a rigorous analysis of the rnechanisms of momentum transport of liquid-solid systems is complex indeed. There are many variables that affect the rheological properties of the systems such as density, size, shape, and surface energy of the suspended solid and density and viscosity of suspending liquid, as well as the solid to liquid ratio. However, it was felt that a useful contribution to the knowledge of the behavior of suspensions could be made by examining the systems in terms of the basic fundamentals of nowNewtonian flow. This has led to the development, by means of dimensional analysis, of velocity and resistance equations, using two viscosity parameters to describe the velocity of penetrating bodies and the flow resistance encountered by these bodies, as they pass through non-Newtonian systems. THEORY In order to examine the effects of the rheological properties of solid-liquid suspensions on the movement of immersed bodies it is appropriate to start with non-Newtonian liquids and develop equations, analogous to those of Stokes and Newton, for laminar and turbulent flow respectively, from which quantitative information may be obtained. Further investigation would then be directed at the complex suspension systems, and the effects of the many variables on the velocity and resistance equations. Liquids are classified on a basis of viscosity which may be defined as the relationship between applied shear stress and resulting rate of shear?-'* Pure single phase liquids composed of small light molecules behave as Newtonian liquids, having a single viscosity parameter since the shearing stress and rate-of-shear are related by a linear function. Bingham plastics are similar but have a yield stress. Of particular importance in our investigation are dilatant (shear thickening) and pseudoplastic (shear thinning) non-Newtonian liquids, with and without yield values.

Jan 1, 1968

By A. T. Corey, C. H. Rathjens

INTRODUCTION Although the oil industry has been aware of the directional variability of permeability in porous rock, the directional variability of relative permeability has been largely ignored. Yet it is apparent that such an effect must be present in a system in which the distribution of oil and gas within the porous matrix is controlled by capillary forces. It is easy to visualize a rock composed of layers of fine and coarse material such that gas flow across the bedding planes would take place only after the average oil saturation had been reduced to a very low value. The fine layers, because of their greater capillarity, would remain saturated and act as barriers to the flow of gas after the coarse layers had been desaturated. Flow of gas parallel to the bedding planes would obviously take place at a much greater liquid saturation. Without more complete information concerning the geology of a reservoir than is generally available, it is not possible to predict exactly how such phenomena would affect the over-all performance of an oil field. It is possible, however, to predict qualitatively the effect of stratification on relative permeability measurements made on laboratory cores. In this investigation the effect of stratification was studied analytically by assuming that two porous materials with different capillary pressure-desaturation curves (but identical relative permeability curves) were in contact and in capillary equilibrium. As a qualitative check on the analytical results, cores having various degrees of visible stratification were used for relative permeability measurements made with fluids flowing both parallel and perpendicular to the bedding planes. A quantitative check was considered impractical because of the difficulty of devising models in which two materials of predetermined properties could be joined without the plane of contact becoming a discontinuity. THEORETICAL CONSIDERATIONS AND ASSUMPTIONS The assumption of capillary equilibrium in an oil-gas system implies that the difference in pressure between oil and gas is everywhere the same. This means that the curvature of the interfaces must be everywhere the same in order to satisfy the equation where PC is the pressure difference between phases, y the interfacial tension and r, and r2 are the major and minor radii of curvature. Depending on the pore size distribution of coarse and fine layers, the volumetric percentages of oil and gas in these layers will differ when equilibrium exists. The exact relationship can only be determined by obtaining the complete capillary pressure-desaturation curves for each of the porous materials in contact. It has been pointed out elsewhere' that the capillary pressure-desaturation curves of sedimentary porous materials can often be approximated by the relation where C is a constant and Soe is the effective saturation to oil based on a percentage of the pore volume effective to flow. In the same paper it was indicated that, as a first approximation, the values of oil relative permeability are given by and the values of gas relative permeability by For this analysis Eqs. 2, 3, and 4 were assumed to apply to each of two components of a hypothetical porous rock in capillary equilibrium. It was also assumed that each of the components had a residual wetting phase saturation of 20 per cent so that 80 per cent of the total pore volume was effective to flow. The permeability of the coarse stratum was taken as 100, and its displacement pressure was such that C in Eq. 2 had the numerical value of 1. The corresponding values for the fine stratum were 10 for the permeability and 10 for C. Units are not specified because they do not enter into the final results. The choice of the permeabilities and displacement pressure ratios was made to expedite the calculations. Any reasonable rock properties could have been chosen without changing the results qualitatively. Several arrangements of the two components were studied. Table 1 summarizes the resultant permeabilities obtained for four types of arrangement. RELATIVE PERMEABILITY CALCULATIONS The first step in the computation of relative permeability for the composite cores was the plotting of the capillary pressure-desaturation curves and the relative permeability curves for the individual components according to Eqs. 2, 3, and 4. At arbitrary

Jan 1, 1957

By R. L. Slobod, H. A. Blum

A semiquantitative method for measuring the wettability of reservoir rocks has been developed. These data are needed for reservoir analysis and for interpretation of laboratory displacement studies. The wettability of a core sample is measured by the contact angle for the system oil-water-solid. These contact angles are calculated from the displacement pressure (threshold pressure) obtained by use of the centrifuge, using first oil-water and second air-oil in the same core sample. This method is based on the assumption that the air-oil and oil-water interfaces occupy similar positions in the porous medium when desaturation of the wetting phase is initiated. The assumption is also made that the Contact angle for the air-oil-solid system which is close to zero in value does not change appreciably even when the contact angle for the oil-water-solid system experiences marked changes. "Apparent contact angles'' for five different solids ranging from 31" to 82" have been determined, and changes irr the "apparent contact angle" of a given sample with laboratory use from 33" to 53' {lave been observed. INTRODUCTION Reservoir rocks vary in their wettability, 1,2,3,4 some being preferentially water wet while other are apparently preferentially oil wet. The degree of wettability, in theory, is measured quantitatively by the contact angle for the system solid-oil-water, hut in 1)practice this quantity is extremely difficult to determine." The need for obtaining some measure of this quantity has become obvious in recent years as a result of both laboratory. and field observations. Several reservoir.: such as the Bradford Sand in Pennsylvania and the Wilcox' at Oklahoma City are reported to be oil wet. If these report:: correctly reflect the true nature of the surface of the rock in the ground, then these reservoirs probably will not perform as predicted on the basis of a water wet rock. In the laboratory many core samples have been Observed to be oil wet. These samples, while perhaps not correctly representing the reservoir, have markedly different properties from water wet rock. The location of the phases is different (oil is in contact with rock instead of water), and other quantities such as the connate water, the capillary pressure curve; residual oil. relative permeabilities. and the recovery of oil by water flooding are markedly affected by the value of the contact -4 A further complication observed in the laboratory is the chang-ing of the wettability of a rock specimen with use. such changes mean that repeat runs on the same core are not the duplicate tests desired, but represent new experiments on a more oil wet material. The changes in surface characteristics are sometimes so rapid that by the time an experiment requiring several days is completed, the results may not be representative of the core as originally described, The, rock material itself (Silica. carbonates. etc.), whell Clean and uncontaminated, is water wet. There seems b( : little evidence of the presence of oil wet minerals such as heavy metal sulfides. The oil wetness of reservoir samples, therefore, is believed to be caused by the accumulation of an adsorbed film in which the polar group of a large organic. molecule is adsorbed on the surface leaving the organic or hydrocarbon part of the molecule projecting out from the solid. Such a surface is much more readily wet 17" oil than by water. These considerations indicate the need for a method which will provide some measure of tile wettalbility (Contact(angle if possible) for reservoir rock ..samples) The method should be capable of (1.1 distinguishing between tile wettalility of dif. ferent formation,.. (2) detecting (change. ill wettalbility of a core with use. and (3) measuring the changes in Wettability which may be accomplished with cleaning operations. such as the use of sodium silicate for increasing water wrettalbility." A preliminary report on such a method is preseted below. not with the idea that this procedure alone will Solve the wettabil-ity problem. but rather that it may provide encouragement to

Jan 1, 1952

By T. R. A. Gokcen

THE possibilities of separating and purifying metals by high vacuum distillation were examined by Kroll.1 He suggested vacuum treatment for the removal of zinc from the lead produced after Parkes desilverizing. The St. Joseph Lead Co. developed the first commercial vacuum dezincing process at their Herculaneum refinery, as described by Isbell.² The Broken Hill Associated Smelters at Port Pirie, Australia, has, after several years of pilot plant operations and fundamental investigations, developed a continuous process, which will be described briefly in a forthcoming publication." As the full-scale continuous vacuum dezincing plant at Port Pirie is still experimental, publication of full practical details of the plant will be deferred until the unit is operating as a normal part of the continuous refinery. This paper deals only with theoretical aspects of vacuum distillation processes, with particular reference to vacuum dezincing. The method of mathematical analysis is of general interest as it may be applicable to other metallurgical separations which have been investigated recently.4-6 Evaporation Processes At about atmospheric pressure, or higher, most liquids possess a boiling point—a temperature at which any heat put into the liquid is absorbed only as latent heat, not as specific heat. If a steady heat input is supplied, the liquid's temperature rises to this value, then remains constant while bubbles of vapor form beneath the surface. The rate of evaporation is determined solely by the rate of heat transfer to the liquid; the temperature of boiling is determined by the partial pressures of the volatile constituents in the liquid, and the total pressure above the surface. If the rate of heat transfer to the liquid is increased, the temperature remains constant, and the rate of boiling increases. When evaporating metals under vacuum, however, the partial pressures concerned are generally so small that boiling does not occur, because at even a fraction of a millimeter below the surface the hydrostatic pressure is usually too great to permit the formation of a pocket of vapor. In addition, the high thermal conductivity of metals tends to prevent the local superheating which is necessary for bubble formation.' Although this effect is doubtless also exerted when boiling metals at higher pressures, the magnitude will be less because the degree of superheat required to form bubbles is very much less at the higher temperatures involved. Under vacuum, therefore, evaporation of volatile constituents takes place only from the exposed surface, and the rate of evaporation depends upon the surface area, the surface concentration of volatile constituents, the surface temperature, and the partial pressures of volatile constituents immediately above the surface. If the heat input is raised above a certain level, the effect is not to increase the evaporation rate at constant temperature, but to raise the temperature of the liquid until at some higher level an increased rate of evaporation (and thus of latent heat absorption) again balances the heat input rate.? Many substances (including metals) have a very large intrinsic evaporation rate at quite low temperatures—far below their normal boiling points. However, at atmospheric pressure, the large numbers of atoms evaporated are almost completely deflected back into the liquid (or solid) surface by air molecules. Thus the back condensation rate is practically equal to the gross evaporation rate, and the net evaporation rate is practically zero. It can therefore be seen that an overall distillation rate depends not only upon the intrinsic evaporation rate, but also upon the ability of the volatile atoms to move away from the evaporating surface. This movement is facilitated by the provision of a condensing surface close by. Vacuum Distillation: The function of the vacuum above the evaporating surface is to remove foreign molecules, so that the chances of deflection of an evaporated atom back into its source are reduced. When the residual gas pressure is reduced so far that the evaporated atoms have a high probability of reaching a nearby condensing surface without suffering collision with a foreign molecule, the state of affairs is termed "molecular distillation." This process is practiced commercially today for the purification of numerous organic chemical products of high unit value, but not, to the writer's knowledge, for any metallurgical separation. When the degree of vacuum produced in a still is not sufficient to promote molecular distillation, then the evaporated molecules must diffuse through the

Jan 1, 1954

By Ferid Kromer

Geography: The Tagtepe district of the Vilayet of Eskigehir is about 20 miles northeast of the city of Eskigehir (approximately midway between Ankara and Istanbul) in western Anatolia. The area is a mountainous one, the highest peak being Tagtepe Mountain (5200 ft) which is approximately in the center of the district. The mountains drop off to the deep valley of the Sakarya River on the north and to the plain of Eskigehir on the south. FERID KROMER, Junior Member AZME, is a Consulting Mining Engineer and General Manager, Bagtag Turk Maadin Ltd., Istanbul, Turkey. New York Meeting, February 1950. TP 2629 H. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received Dec. 29, 1948. For the most part, the watershed is on the northern side of the mountain barrier, draining into the Sakarya River, which in turn empties into the Black Sea midway between Zonguldak and the mouth of the Bosphorus. The approximate area covered by the Tagtepe district is shown in fig. 1. Transportation to shipping points is available via the Istanbul-Ankara railroad. The station on this line nearest the mining district is Alpikoy station, about 20 miles by road southwest of Tagtepe Mountain. Interior roads within the district are poor. Being of dirt, the winter rains and snows render them almost impassable for trucks from about the middle of December until the end of March, thus presenting a considerable transportation problem. However, the roads from the Bagoren and Tagtepe chromite mines to the railroad shipping point at Alpikoy station have recently been repaired and will be maintained for all-weather truck transportation. Detailed climatic data are not available. However, in general the spring, summer, and early autumn months are dry, and good weather may be expected from May until early November. Then the winter rains commence, and heavy snow is usual during January and February. Geology: The mountainous structure of Tagtepe belongs to basic rocks of serpentine (Variscan Orogeny) which is in contact with Paleozoic schists at west, and an Oligocene outcrop of red clays in Margi-Sepetci region (see fig. 1) at southeast. The northwest and southwest borders of Tagtepe district are, respectively, surrounded by Paleozoic schists and pebbly gray and yellow Neogene clays. More recent formations of alluviums overlay the plain of Eskigehir. Dark basic rocks of trachytes with hornblende are visible on Turkmenbaba Mountain, at the west of Tagtepe. Mineral Occurrences: Chromite: the most important mineral found in any quantity in the Tagtepe district. The alignment of the deposits of chromite is in general along the line Bagoren-Tagtepe (see fig. 1). The first mines in the area were those of Tagtepe and Bagoren, which were developed over 20 years ago with Swedish capital. Other deposits of chromite, more recently discovered and so far of less importance, are being worked at Kurucor, Komurcu, Gelinmezari, and Lacin (see fig. 1). Deposits average generally between 46 and 48 pct chromic oxide, with the exception of the Bagoren mine which averages 44 pct. However, a new lode, very recently plotted, in the Tagtepe mine averages 50 pct Cr,O,, 4.6 pct SOz, and 7 pct FeO. Geological character of the chromite occurrences in the Tagtepe mine may be considered typical of most chromite lodes in this area. The indications are that the formations of ore lenses are developed by the segregation of chromite crystals intruded into the serpentinized rock, and exposed later to tectonic movement within the zone of crystallization. All lenticular masses are more or less regular in shape and follow each other in southeast-northwest direction and dip generally 70" NE. Ore lenses do not seem to persist in depth, average depth of two lenses is 60 ft below surface. Three lodes .have been mined as open-pit. The average dimensions of individual lenses are as follows: pitch length, 100 ft; breadth, 27 ft; and width, 20 ft. The lenses and their enclosing rocks are broken by parallel fractures in approximately east-west direction. These joints are filled, except in one lode, with cementing material, which gives to the ore a

Jan 1, 1951

By T. M. Morris

THE rate of flotation of solid particles determines the percentage recovery of these particles which can be obtained during a given time interval. It is an established fact that the recovery is greatest in the fine sand size range and falls off on either side of this size range. It is also a fact that the history of the development of concentrating devices has been marked by a desire to recover the small particles: tables were developed to treat material too fine to recover in jigs; flotation recovers material too fine to be recovered on tables. As our ores become more complex and require finer grinding, a greater proportion is in the slow-floating size range. It is therefore of economic importance that the effect of size of particle upon rate of flotation be studied. Many studies have been made along this line. The present investigation attempts to quantify the rate of flotation by means of a rate equation, and then compares the effect of size upon the rate of flotation. It was found that the flotation rate constant increases with increase in diameter of particle in the size range smaller than the optimum size particle. The flotation rate constant decreases with an increase in diameter of particle in the size range coarser than the optimum size particle. This suggested two different actions taking place, and these are discussed. Suggestions for further work in order to improve the flotation rate of both fine and coarse particles are made. The usual method of expressing rate is to plot cumulative percent recovery vs time. If we knew the equation of this kind of curve we could replot it as a straight line, and the slope of the line would be an index of the magnitude of the flotation rate. It is easier to compare straight lines than curves. The basis used for obtaining the equation of the recovery vs time curve is the law of mass action. This law states that the "rate of a chemical reaction is proportional to the 'active masses' of the reacting substances present at any given time." This, of course, implies a constant temperature. We can modify this for our use by using the term flotation reaction instead of chemical reaction and the term floatable particle instead of active masses. dC Thus----— kc [1] where C denotes concentration of particles, t denotes time, k denotes a proportionality constant. If the exponent of C is 1, then we have a first order rate reaction. If the exponent of C is 2, then we have a second order rate reaction. For a first order rate reaction, we obtain, after integration, where k is again a proportionality constant and has the dimension of the reciprocal of time. C, is the original concentration or weight or percentage of floatable particles. C, is the concentration or weight or percentage of floatable particles remaining in the flotation cell after time t. If all particles of the mineral to be floated were capable of floating we could take C, as 100 and C, would be 100 - R, where R is the cumulative percentage recovery of mineral at time t. But it is not usual for all of the particles to be capable of floating, because of surface oxidation, etc. Therefore, we must introduce a factor x which is the percentage of un-floatable mineral. Hence the first order equation is It has been proposed by various workers1-' that this equation describes the flotation rate. More recently N. Arbiter4 states that a second order rate equation fits the recovery vs time curve more closely than does a first order rate equation. Morris- as discussed the evidence presented for this statement. It has been concluded that the first

Jan 1, 1953