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E. W. Stutchbury (Internationa~ Oombustion Aust. Ltd.) : Mr. Callcott made particular mention in his paper of erosion in primary air fans which are placed after the mill discharge. He adds that subsequent reduction in plant performance and resulting increased maintenance costs occur. It is generally assumed that this statement is substantially correct as the fan handles the complete output from the mill, but with modern materials, reduction in performance and subsequent .maintenance are not now a problem. This consideration of handling the pulverised coal in the fan is more than offset by the advantage of operating the mill under suction which results in cleaner operating conditions, simpler feeder arrangements and elimination of complicated seals on the mill.and feeder unit. It should be specially noted that whereas mill exhausters in the past have used chequer plate blades (sometimes with the addition of hard facing by electrode deposit) it is modern practice to provide fan blades of up to 1 in·. thick Ni-hard suitablyheat treated, with the circumferential section of the fan also in Ni-hard. By the use of this material large power...

Jan 1, 1957

By Allen D. Look

Uninterrupted shaft operations are an important economic factor in mine operation, and good shaft support is an important aid in preventing accidents and interruptions. More permanent supports can cut the hazards, costs, and delay incident to replacement of conventional timbers, especially where subject to decay. Installation of prestressed, precast concrete shaft supports in 100 feet of shaft at the Banner mine, Lordsburg, N. Mex., nave a satisfactory permanent installation in a section of shaft that had given trouble with conventional timbering. Use of rock bolts supporting gunited wire netting around the rock walls of the shaft prevented sloughing. No attempt was made in this paper to arrive at comparative costs of installation of various types of support. However, it was indicated that use of a lighter weight aggregate would be desirable in further use if prestressed precast members as placed in the Banner mine.

Jan 1, 1957

By Eugene T. Sheridan

The United States has extensive reserves of peat. Peat and muck lands are estimated at approximately 79 million acres, with reserves of 13.8 billion net tons. Within the past decade domestic production of peat has increased 2-1/2 times, and apparent consumption has tripled. During the same period imports have increased greatly, and in 1955 they almost equaled domestic production. The substantial increase in the demand for peat in the United States was due chiefly to expanding markets in agriculture and horticulture, for the reason that in this country peat is used primarily as a source of organic matter to improve the physical condition of mineral soils and as a mulch for shrubbery. A valuable constituent of any soil is its organic matter, and its depletion will injure cultivated soils and subject them to greater erosion.

Jan 1, 1957

By R. A. Bloom, John Birtalan

CONSIDERABLE interest has been shown in recent years toward determining the crystal structure, mode of formation, and chemical composition of the x phase, designated as such by Andrews,' who was the first to establish its presence in Fe-Cr- Ni-Mo alloys . Later work2 by the same author has shown that the occurrence of x depends on the presence of some molybdenum in the alloy. The phase, which appears to be identical or very similar to a manganese, has a body-centered-cubic structure and is closely related to s phase. Koh observed a similarity in composition between x and s and speculated as to whether x might be an ordered structure of u which is known to have a tetragonal crystal

Jan 1, 1957

By P. F. Allen

WITH capacity of 51,000 tpd, the Morenci concentrator produces approximately 49,000 tons of tailing for final deposition. Disposal involves distribution of thickened tailing to dams in such a manner that solids can be used for dam construction and water can be impounded for reclamation. During early operation, although tonnage treated was lower, it was necessary to use orthodox disposal practices in the areas available for tailing. Trestles mounted on a series of dams, constructed of borrow material, carried the pipelines from which tailing were spigoted behind the dams. When adequate disposal areas were finally established, it became desirable to look for more efficient methods. The idea of placing the distribution pipe or manifold directly on the crest of the dam was advanced in 1945. After a period of testing, that procedure in modified form replaced the older trestle arrangement. Marked economies resulted, and time required to prepare dams for succeeding storage cycles was greatly reduced. The tailing disposal area for the Morenci concentrator lies south and southwest of the concentrator building. Ample storage space is available. A wide valley contains three sharply defined ravines lying on an average slope of 4 pct. The more central of these ravines, and the largest of the three, is known as Morenci canyon, which provides substantially more tailing storage area than the other two. Stargo canyon lies to the west; the other is appropriately named East canyon. Total area of the tailing disposal site is nearly 31/4 sq miles, or about 2000 acres. The storage area in use was somewhat more than 850 acres at the end of 1954, or 16 acres per 1000 tons of tailing to be stored daily. At the present time none of the east side dams are in regular use but they are available in emergency. There are five dams on the west side (in Morenci and Stargo canyons) as well as two auxiliary dams adjacent to No. 4 West and No. 5 West. This has made it possible to concentrate men and equipment in a smaller area with consequent savings in both manpower and machinery. Tailing Thickening: Tailing from the flotation process reaches the thickeners with a solid content of about 18 pct. The launder carrying this pulp is subdivided at a central point into seven launders carrying a proportional share to each of seven tailing thickeners, which are located in Morenci canyon close to the concentrator. Five of these thickeners are 300 ft diam and two are 325 ft diam. Thickeners are of the peripheral traction type and rakes travel at the rate of one revolution in 37 to 39 min. The entire installation provides 500,000 sq ft of settling area, or approximately 101/2 sq ft per ton of tailing to be thickened daily.

Jan 1, 1957

By L. D. Wooddy, Robert Moscrip

The simultaneous solution of the volumerric balance and the unsteady-state equation has been used for several years to make performance calculations for combination drive reservoirs. This method makes possible the calculation of volumetric changes of fluids in the gas cap, oil zone, and aquifer which occur as a result of withdrawals and reservoir pressure changes. It does not provide a means for the determination of reservoir fluid distribution changes corresponding to these vollrmetric changes. A knowledge of the fluid saturation distribution in the reservoir at various stages of depletion is important for the determination of the efficiency of gas and water as oil-displacement media and, therefore, for the reliable predicrion of ultimate oil recovery. To provide this knowledge, the displacement equations are solved simultaneously with the volumetric balance and unsteady-state equations. The described calculation procedure has been used satisfactorily to analyze the past performance and to predict the future behavior of combination drive reservoirs under both primary and pressure-maintenance operations. INTRODUCTION The three basic mechanisms by which oil is displaced from a reservoir are: (1) dissolved gas drive—the displacement of oil by the expansion of liberated solution gas, (2) water drive—the displacement of oil by water which enters the oil zone from the aquifer, and (3) gas cap drive—the displacement of oil by gas which ex- pands into the oil zone from the gas cap. The action of gravitational forces may be effective in increasing the efficiency of the basic drive mechanisms. Gravitational forces favor the segregation both of gas and oil and of oil and water, thus tending to shorten the transition zone between oil and displacing fluids. Most reservoirs produce under the influence of a combination of these drives and are designated "combination drive reservoirs". Fig. 1 is a cross section of a typical combination drive reservoir. A calculation procedure for analyzing the performance of combination drive reservoirs has been developed by combining the displacement equations' with the volumetric balance equation' and the unsteady-state equations. The pressure-production performance and the positions of the gas-oil and oil-water contacts are calculated for several stages of reservoir depletion by solving these equations simultaneously, thus affording a basis for: 1. Determining instantaneous and ultimate oil, gas, and water production under various operating conditions. 2. 'Establishing a maximum efficient rate of production, 3. Determining the advantages of pressure maintenance and unitization, and 4. Designing surface installations necessary for primarv and pressure-maintenance operations. DEFINITIONS The calculation procedure for combination drive res-

Jan 1, 1957

By I. F. Avery

The productive capacity of natural gasoline and cycling plants in the United States on January 1, 1956, was 46.4 million gallons per day, according to the Bureau of Mines r biennial survey. This represented an increase of 7.5 million gallons per day during the 2-year period since the last survey. In the previous 2-year period, capacity had increased 4.8 million gallons per day. The total number of plants increased from 535 on January 1, 1954, to 600 on January 1, 1956. The number of operating plants increased from 521 to 571. The major increases in capacity took place in Texas, Louisiana, New Mexico, and Oklahoma, with the absorption-type plants continuing to account for most of the new construction. All types of plants showed construction gains with the exception of charcoal which showed no change.

Jan 1, 1957

By J. T. Dewan

An experimental setup is described whereby the responses of Neutron logging instruments have been determined opposite formations of different porosities and under various borehole conditions. The results of these tests are presented in several charts which show how the Neutron log is affected by the following factors: hole diameter, casing, cement, salinity and weight of drilling mud, and position of logging tool with respect to the wall of the hole. The responses in the case of empty holes are also shown. A chart is furthermore presented which shows the shapes of the Neutron log, as a function of logging speed and time constant, at the boundaries between two formations with different porosities. These were derived mathematically using as a basis laboratory determination of the shape of the curve under static conditions, i.e. at very low logging speed. Corrections for the readings made opposite thin beds are given by these computations. The correction is found negligible under usual logging conditions for beds thicker than about 4 ft. INTRODUCTION The Neutron log is used in borehole surveys both for the delineation of porous formations and for the quantitative estimation of their porosities.1,2,3,4,5 It is common practice to calibrate the response of the Neutron log in terms of porosity values for each given geological unit by means of empirical comparisons between the deflections of the neutron curve and the porosity values given by the core analysis in a sufficient number of wells. Usually, the plots of the porosity values vs Neutron log deflections show a definite trend. It is therefore possible to trace an average line across the plotted points. This average line constitutes a calibration curve which can be used to evaluate the porosities from the Neutron logs in the other wells drilled in the same region. Futhermore, when the porosity values are plotted on a logarithmic scale and the Neutron log deflections on a linear scale, the calibration curve is practically a straight line. Accordingly the calibration curves are often determined by simply tracing a straight line between two points corresponding to two widely different porosities. Different choices are made for these two points, depending on local conditions. For example, one point will be defined by plotting the deflection of the Neutron curve opposite a formation known to be very tight, for which an average porosity value of 1 or 2 per cent is assumed. The other point may correspond to shale sections, to which a porosity of around 40 per cent is ascribed. The information provided by the eletrical logs — in particular the Laterolog, Limestone log or Micro-Latero-log — is also very often a help in the calibration of the Neutron logs. Empirical approaches such as these make possible the derivation of fairly reliable porosity values from the Neutron logs in many cases, at least in open holes and in essentially clean formations. There are, however, several causes of uncertainty which may sometimes entail appreciable errors. On the one hand, the Neutron log readings are influenced by the borehole conditions: hole diameter, presence or absence of casing and cement, presence or absence of drilling mud, characteristics of the mud, and position of the logging instrument with respect to the wall of the hole. The amplitudes of the curves opposite thin beds are furthermore atfected by the bed thickness,

Jan 1, 1957

By Thaddeus B. Evans

This information circular is one of a series describing mining methods and costs, being published by the Bureau of Mines. The Sunbright mine of the Foote Mineral Co. at Sunbright, Va., is the southernmost underground limestone mine in the State. It is a comparatively recent operation, and a description of its rapid development to production stage may have particular interest for the limestone-mining industry. ACKNOWLEDGMENTS Acknowledgment is made to the executives of the Foote Mineral Company including F. B. Shay, vice president in charge of production, W. B. Towner, general production manager; and to the members of the company staff at Sunbright for their assistance in preparing this paper.

Jan 1, 1957

By P. E. Cavanagh

THIS REPORT is not intended to be a ?comprehensive survey of the steel industry in Europe. For the past ten years the Ontario Research Foundation has been interested in several developments in the steel industry in Europe which it was felt would be of particular interest in Canada and might possibly find application in this country. This is an account of the present status of some of these developments. The economies of steel making in Canada are somewhat different than in the United States because of the nature of the market and the relative costs and availability of such raw materials as metallurgical coke and electric power. There are cases in Europe where a great deal of effort and money has been spent in trying to make steel profitably by methods which take advantage of locally available and cheap raw materials by modifying standard practices. ln cases wl1ere the investigations have been successful and the data are available to allow translation of the results into Canadian conditions, it is felt that such information may be of great benefit in the future in Canada and at !east should be known to all those in the steel industry in this country. The field to be covered in this report only comprises the steps from concentration and treatment of iron ores to production of iron and is only concerned with those commercially operating processes well known to us and judged to be of present interest in Canada.

Jan 1, 1957

Up to the end of World War n, flat-back cut and fill stoping with or without square sets was the universal method of ore extraction. Rapid changes in practice occurred during the post-war years; first, ore extraction was fully mechanized; secondly, the stope design for new levels, notably No. 17 Level Zinc Corporation Ltd. and No. 19 Level New Broken Hill Consolidated Ltd., was modified to suit this mechanization; and thirdly, sub-level and shrinkage stopes were developed in orebodies where cut and fill methods would be uneconomical. The following is a brief survey of the changes that have occurred-most of which were inaugurated during the last five years.ROCK DRILLINGDuring 1951 open stoping was investigated in detail. In order to reduce steel handling problems, forged steel onepass detachable bits were introduced, but were soon superseded by the "Swedish method". Investigation showed that when using a bar and arm mounted 3-in. drifter the overall drilling time was approximately 6 min. per ft. compared with 4 min. per ft. using the light jackhammer-airleg combination with 1-in. hex. by 4-in. collared shank tungsten carbide-tipped steel.Although competitive with tipped steels on a cost per foot drilled basis (excluding miner's time), detachable steel bits proved most unsatisfactory for hard drilling conditions.Rapid blunting necessitated frequent bit changes and thus caused lost drilling time. This, together with rapid gauge...

Jan 1, 1957

By Homer N. Mead

This report develops equations for decline curve analysis based upon the premise that the rate of change of the reciprocal of decline for succeeding time intervals is constant when the reservoir is produced under a fixed set of conditions. A method is shown for predicting maximum production rate against cumulative production for any reservoir. A method is also presented for predicting future production rate by an analysis of past production performance after decline has been esrahlished. INTRODUCTION No significant contribution to the analysis of decline curves by the loss-ratio method has been made since J. J. Arps paper1. The concept of loss-ratio that was developed by Arps and his contemporaries has been redefined in another way and the concept of instantaneous loss-ratio at time zero has been added. In the mathematical developmerit by Arps, production rate was related as a continuous function with time and his equatlons were developed on that basis. In this paper, production is considered to be a series of segments for equal time intervals and equations have been developed based upon these finite differences. It is realized that decline curve analysis is not the answer to all predictions of reservoir behavior. However, as production must decline from an initial maximum rate to zero in any reservoir, if such decline can be expressed as an infinite series, this series should accurately predict production. Decline curve analysis should be considered a valuable tool that may be used in conjunction with predictions of future recoveries by other methods. Various uses of the decline curve method will be discussed in this paper. Equations predicting production rate at any time and cumulative production by exponential and hyperbolic decline will be developed. Characteristic values of b related to various types of drive will be discussed. After that a hypothetical reservoir will be studied and ultimate recovery by natural depletion and pressure maintenance compared, then actual field examples will be shown and discussed. The rate-cumulative curve introduced by H. N. Marshs in 1928 is an important one for use in estimating future production rate and ultimate recovery. This graphical method is the one that is used in conjunction with the equations to be developed for predicting production behavior. EXPONENTIAL DECLINE In exponential decline each succeeding production rate per unit of time is a constant percentage of the production rate just before it. Since (1 — r) is the common ratio, where r is the constant decline rate, this condition may be expressed as a geometrical progression; thus Pn = P (1 - r)n-1 . ......(1) Where r is less than unity, r Since P1 (1 - r)n = Pn+1 P1 - Pn+1 C =P1-Pn+1/r........(2) LOSS-RATIO In this paper the calculation for loss-ratio has been changed from the method presented by Johnson and Bollens2. The first loss-ratio to be calculated is a,; it is the initial production per unit of time after decline has set in divided by the difference between the initial and the second production rate. This loss-ratio is for the first time interval. After b (which is the constant change

Jan 1, 1957

UP TO and including 1931, the twelve mines that were treated in THE PORPHYRY COPPERS had produced 17.4 billion pounds of copper worth $2,820,000,000. With a little help from six others (three of them did not start output until 1954) that record had been increased at the end of 1955 to 60.5 billion pounds worth $10,440,000,000. Today, ten billion dollars is not as impressive as it once was; but it still represents a lot of value. It must be remembered that this is newly-created wealth, produced entirely from material considered worthless when the Porphyry era started about fifty years ago. At that time "rock" that contained less than forty pounds of copper per ton was regarded by competent mining engineers as value- less. It was not "ore" in the economic sense. Today, ore is being successfully exploited that contains less than twelve pounds of copper per ton. Also, in Peru, a typical Porphyry operation is being launched by a partnership of four United States mining companies that will involve an initial capital investment of $200,000,000 for mine development, plant construction, and the provision of related facilities. Of this project more will be said at the end of the chapter. The point I want to make now is twofold: (1) that phenomenal progress has been made in Porphyry engineering and technology; and (2) that exploitation of an important Porphyry copper deposit has become an industrial enterprise of truly great magnitude. Much had been accomplished by 1931; but that progress has been dwarfed by the achievements of the past 25 years- a fact that, in the nature of things, is as it should be.

Jan 1, 1957

The Western New South Wales Electric Power Proprietary Limited is the central generating authority for distribution of power to the majority of the Broken Hill mining companies and the Broken Hill Water Board. This station supplies the whole of the power to North Broken Hill Ltd and Broken Hill South Ltd. It also supplies, power to the Southern Power Corporation for distribution to the Zinc Corporation Ltd. The Southern Power Corporation has a generating station which is tied in with the central generating authority.

Jan 1, 1957

By Nicholas J. Grant, Chih-Chung Wang

TO phase of the Ti-0 system has the structure of NaCl and has a wide range of solid solubility.' In the course of studying the Ti-Cr-0 ternary system, binary alloys were made of iodide titanium and high purity TiO,. It was found from X-ray studies of the binary alloys that a transformation of the TiO appears to take place at a temperature near 925°C. Evidence of this phase change is best seen in Fig. 1. Fig. 1A shows the X-ray spectrometer pattern (CUKa radiation) of an alloy of 25 wt pct 0 corresponding to the stoichiometric composition of TiO.

Jan 1, 1957

By M. Prats

This paper presents a method for obtaining the correct values of the breakthrough sweep efficiency of the staggered line drive, taking into account the proper shape of the breakthrough streamline. Results obtained were different from those previously published, which were obtained by using an inexact shape of the breakrhrough streamline. INTRODUCTION In Section 9.31 of Muskat's' The Flow of Hotnogeticous Fluids Through Porous Media, it is stated that in a staggered line drive flood "the streamline of highest average velocity [is] the line of centers between input and output wells" (see Fig. I). Muskat used this concept to determine the relationship between the breakthrough sweep efficiency and the geometry of the staggered line drive pattern. Although it is clear from symmetry considerations that the breakthrough streamline passes through the midpoint between input and output wells, it is equally clear, as shown in Fig. 239 of Ref. 1, that the breakthrough streamline is not represented very well by the straight line joining the input and output wells. Therefore, it is desirable to determine the proper relationship between the breakthrough sweep efficiency and the pattern geometry by using the proper shape of the breakthrough streamline. METHOD OF SOLUTION It was found that the effect of the geometry of the staggered line drive on the breakthrough sweep efficiency can be investigated easily by making use of the method developed in Ref. 2. With this method, it can be shown that the general complex potential for the staggered line drive, which can be considered as a rectangular five-spot, is given in the coordinate system of Fig. 1, by O(z) = In cn(z\m) = +(x,y) + i $(x, y) . (1) where z = x + iy, +(x, y) is the potential distribution and $(x, y) is the stream function. The function cn (zm) is a Jacobian elliptic function of parameter m and has simple zeros at z,. = (2n + 1) K + 21iK and simple poles at z, = 2nK + (21 + 1)iK. Thus, the complex potential behaves like a(z) = ln(z - zr.) in the neighborhood of the production wells and behaves like a(z) = - ln(z - Z,) in the neighborhood of the injection wells. Since (z - z1.v) = rll.ei, we note that the potential + has the proper logarithmic behavior near the two wells, while the stream function $ varies with the angle, decreasing clockwise around the production well and increasing clockwise around the injection well. The functions K(m) and K'(tn), related by K(m) = K'(m,), where m + m, = 1, are known as the complete elliptic integrals of the first kind. By use of other properties of the Jacobian elliptic functions, the general stream function distribution for the staggered line drive can be obtained from Eq. 1: From the Jacobian elliptic function values, sn(0lm) = 0 dn(O(m) = cn(0jm) = 1, and f[K'(m)Iml = 03, it follows that the stream function given by Eq. 2 satisfies the proper symmetry conditions near a production well P located at [K(m), 01 and an injection well I located at [0, K' (m)]. That is, the line IOP in Fig. 1 is a streamline with value G (0. 0) = -0. and the straight lines connecting I and P to the point [K(m), K' (m)] is a streamline of value $[K(m), K' (m)] = -7/2. Similar symmetry conditions are obtained near other wells. It should be nuled that for m = m1, = 0.5, Eq. 2 reduces to the stream function distribution of the regular five-spot given in Ref. 7. SHAPE OF THE BREAKTHROUGH STREAMLINE It is apparent, from symmetry considerations, that the breakthrough streamline ($,) passes through the point [K(m)/2, K' (m)/2]. Its value there is so that the shape of the breakthrough streamline $,, is given by

Jan 1, 1957

By R. J. McNally

THERE are three primary plant nutrients—nitrogen, phosphorus, and potassium—expressed in any fertilizer compound as percent N, percent P 2 O 5, and percent K 2 O, in that order. This article will be concerned with the first two. The chief source of P 2 O 5 is phosphate rock. As found in the western states phosphate rock is essentially tricalcium phosphate-calcium fluoride (fluor-patite). As such, it is quite water insoluble.

Jan 1, 1957

By S. M. Brisbane

THE life of refractory linings in rotary cement kilns can be shortened by uneven or inadequate support of the kiln and its shell and by variations in the conditions of operation. Alteration of these factors may, according to their nature, bring about mechanical deterioration of the lining or promote chemical attack. Chemical attack has been described elsewhere.1-4 The distortion of cement kilns has been discussed in a general manner by Rochow,6 ho indicates the amount of distortion which may occur in an unlined shell, and by Rosenblad: who states that the deformations of the shell are greatest above the trunnions. The present article indicates the extent of the distortion of a kiln to an oval shape in certain selected positions and the deviation from a straight line of the kiln along its length between two supports. The cement kiln is a long, hollow, rotating cylinder consisting of steel plates which may be either welded or riveted together. This shell is supported on tires, frequently 60 ft apart, which roll on trunnions. The large mass of the kiln causes distortion of its cross-section; it becomes slightly oval, i.e., diameters lengthen as they become horizontal and shorten as they become vertical. There is also a tendency for the shell to bow between supporting tires; this bowing may be upwards or downwards depending on the position of the weight forces and the supports. The extent of the deviations from the ideal kiln shape was investigated. Observations described in this paper were made on the shell of the clinkering zone between the first and second tires of two of the kilns at the Geelong works of Australian Portland Cement Pty. Ltd. The kilns were both 400 ft long and 10 ft diam with a welded enlarged burning zone 11 ft 6 in. diam. The shell was fabricated from mild steel and in this section its thickness was 1 in. It was lined with 41/2 in. of chemically bonded magnesite-chrome bricks which were jointed with mild steel plates. The kilns operate on a 4 pct slope and the speed may be varied between 0.75 and 1.68 rpm. The wet process is used; kilns are coal fired and are fitted with integral coolers. Temperatures within the kiln are difficult to determine with any accuracy because of the absence of black body conditions, but surface temperatures are probably in the range 1420° to 1470°C. Average shell .temperatures at the two positions at which the deformation studies were made were 370°C and 355"C respectively. Methods: In determining the ellipticity it was necessary to measure the lengths of the vertical and horizontal diameters while the kiln was in operation; data obtained from a stationary kiln would not have the same practical significance. For this purpose the four points V, W, X, and Y at the ends of two mutually perpendicular diameters were marked on one kiln. The point X is shown in Fig. 1. For the measurement of the length of the vertical diameter a vertical column, to which a horizontally aligned telescope was attached, was placed 10 ft from the kiln. The telescope could be racked up and down in a vertical plane. Two sets of readings were taken, one set when each of the points V, W, X, and Y was at its maximum height above the

Jan 1, 1957

By T. M. Morris, W. E. Horst

W. E. Horst—In regard to the flotation rate being described as "first orcler" for flotation of quartz particles below 65 p in size (or any size studied in this work) in this paper, it appears that the authors' conception of rate equations is not in agreement with cited references. A first order rate equation has as one of its forms the following: a In.=a/a-x=kt where a = initial concentration, a—x = concentration at time t, t = time, and k = constant. The constant, k, has the dimension of reciprocal time which is similar to the specific flotation rate, Q. described by Eq. 2 in the authors' article, as has been previously discussed by Schumann (Ref. 1 of original article). The plotted data presented in Fig. 4 of the article utilizes the specific flotation rate, Q (min.'); however, there is not adequate data given to indicate the order of the rate equation which describes the flotation behavior of the quartz system studied. Results from the experimental work indicate that the relationship between rate of flotation (grams per minute) and cell concentration (provided the percent solids in the flotation cell is less than 5.2 pct and the particle size is less than 65 p) is described by an equation of the first order (R, = k c+", n being equal to 1 in this size range) and the use of the first order rate equation does not apply. Similarly the relationship for other particle size ranges studied is expressed by equations of the second or third order depending on the magnitude of n. T. M. Morris—The authors are to be commended for the experiments which they performed. As they state in their discussion the concentration of collector ion In solution did change with change in concentration of solids in the flotation cell. Since for a given slze of particle, flotation rate increases with concentration of collector until a maximum is reached, the effect of concentration of particles in their experiments was to vary the concentration of collector ions. A collector concentration which insures maximum supporting angle for all particles eliminates the unequal effect of collector concentration on various sized particles and the effect of size of particles and concentration of particles upon flotation rate could be more clearly assessed. I believe that if the authors had increased the concentration of collector to an amount sufficient to attain a maximum supporting angle for all particles they would find that the specific flotation rate of particles coarser than 65 p would be constant with change in the concentration of solids in the flotation cell, and that a first order rate would apply to the + 65 as well as to the —65 p sizes. It might also be discovered when this change in collector concentration was made that the maximum specific rate constant would be shifted toward a coarser fraction than when starvation quantities of collector are used since this practice favors the fine particles and penalizes the coarse particles. P. L. de Bruyn and H. J. Modi (authors' reply)—The authors wish to thank Professor Morris for his kind remarks and for mentioning the influence of equilibrium collector concentration on flotation rate. With a collector concentration sufficient to insure maximum supporting angle for all particles, a first order rate equation may indeed be found to be generally applicable irrespective of size. Such a concentration would, however, lead to 100 pct recovery of the fine particles and consequently defeat the essential objective of the investigation to derive the maximum information on flotation kinetics. To establish absolutely the validity of any single rate equation for a given size range, the ideal method would be to work with a feed consisting solely of particles of that size range. Use of such a closely sized feed would also eliminate the possibility of the interfering effect of different sizes upon one another. The authors do not believe that increasing the collector concentration would shift the maximum specific flotation rate (Q) towards a coarser fraction. Experimentation showed Q to be independent of solids concentration for all particles up to 65 µ in size, whereas the maximum value of Q was obtained in the range 37 to 10 p. Professor Morris contends that the addition of starvation quantities of collector favors fine particles at the expense of coarse particles, but the reason for this is not entirely clear to the authors. The comments by Mr. W. E. Horst are concerned only with the concept of the term "first order rate equation." According to the usage of this term in chemical kinetics, time is an important variable, as is shown in the equation quoted by Mr. Horst. All the experimental results reported by the authors were obtained under steady state continuous operations when the rate of flotation is independent of time. To be consistent with the common usage of the "first order rate equation," it would be more satisfactory to state that under certain conditions the experimental results show that the relation between flotation rate and pulp density is an equation of the first order.

Jan 1, 1957

By R. W. Cahn, C. D. Graham

The rate of growth of a single grain growing into a strained aluminum single crystal, measured by the conventional heat-cool-etch technique, is shown to decrease with time at temperature. The growth rate measured by means of X-rays, with the sample continuously at temperature, is found to be linear. Evidence is presented to show that the decreasing growth rate obtained by the conventional technique is due to abnormal recovery in the strained grain, and that the recovery in turn results from the heating and cooling cycles, rather than from the effects of etching. The experimental apparatus is described in an appendix. FREQUENTLY, the rate of grain boundary motion during recrystallization is determined by heating a sample to a known temperature for a given time, cooling to room temperature, and etching to reveal the boundary position. The cycle of operations is repeated as many times as necessary to establish the rate of boundary motion. Although this heat-cool-etch technique has been used by a number of workers over a period of many years,'-!' other investigators have encountered difficulty with the method."'. " They have attributed the erratic results to the effects of repeated heating and cooling, or of etching, or both, and have adopted an alternative experimental procedure in which a number of identical samples are employed, each sample being cooled and etched only once. This alternative method ove1.comes some difficulties, but introduces others. In particular, the incubation periods of the observed grains are unknown: any effect of crystal orientation on growth rate cannot be determined easily. A preferable method would be to measure the motion of a recrystallizing grain boundary with the sample at temperature without etching," but such measurements have in the past been restricted to nonmetals. This paper describes the construction and operation of a device, the goniometer furnace, with which the position of a moving grain boundary between a recrystallizing grain and the strained single crystal into which it grows can be measured by means of X-rays, with the sample maintained continuously at temperature. Goniometer Furnace The operating principle of the goniometer furnace is shown in Fig. 1. The sample, in the form of a bicrystal strip, is surrounded by a furnace, not shown in the sketch, and can be rotated about the two axes A and B which intersect at the point where the X-ray beam strikes the strip. The strip is oriented so that one of the two grains gives a strong Bragg reflection, which is detected by a suitably placed Geiger-Miiller counter coupled to a counting-rate meter When the strip is moved parallel to its own length in the furnace, arrow C, so that the X-ray beam strikes the second grain, there is in general no strong reflection. By noting the position of the strip at which the drop in Geiger counter reading occurs, it is possible to determine the position of the boundary. Measuring the change in boundary position with time at temperature gives the rate of growth of the recrystallizing grain. Details of the construction and operation of the goniometer furnace are given in the Appendix. Measurements showed that the temperature in the furnace was uniform within ±10°C over its working length of about 28 cm. The temperature at the measuring position, i.e., at the point where the X-ray beam struck the sample, was estimated to be constant within ±2oC. Using the goniometer furnace, the position of a stationary boundary could be measured with a reproducibility of ±0.3 mm. At elevated temperatures, 500" to 625"C, with the boundary in motion and the X-ray reflection less sharp, the estimated accuracy of each measured boundary position dropped to about ±1 mm. Experimental Results The test pieces were single crystals of 99.6 pet A1 —principal impurities 0.19 pet Fe and 0.12 pet Si— 1 mm by 1 cm in cross section and 6 to 10 cm in length, grown by the strain-anneal method. This relatively low purity material was used because of the difficulty encountered in producing strain-anneal single crystals of very high purity—99.996 pet—

Jan 1, 1957