Search Documents

By AIME AIME

AT bottom of this page is a photograph recently taken by a student-John E. Stewart-of the most northerly situated college in the world, the Alaska Agricultural College and School of Mines. It is situated at College, near Fairbanks, Alaska, approximately on the 65th parallel of latitude, and therefore just south of the Arctic Circle. It is farther north than Hudson Bay, and in about the same latitude as southern Greenland.

Jan 1, 1932

By Blake M. Caldwell, Thomas C. Poulter

A new approach to an old problem has made it possible to do in a a tively short period what has not been accomplished in the past three quarters of a century using strictly experimental methods. A theoretical study was made of the underlying principles whereby a jet is formed by a shaped charge and of the mechanism of the penetration of the target by that jet. It was found that there are more than 10, and perhaps as many as 15 variables affectin!? the performance of the shaped charge. Only a few calculations are necessary to show that it is physically impossible to investigate all of these variables experimentally. The shaped charge theory has been extended to include a previously little-understood mechanism in high explosive phenomena; namely, low order detonation. By superimposing a high order detonation on a zone already undergoing low order detonation, all appreciable improvement in performance is accomplished. The development of a design wherehy these phenomena are coordinated in such a way as to develop a jet which is tailored to meet the specific target requirement will be described in detail. The shortcomings or even impossibility of strictly experimental techniques will be illustrated by a discussion of the development of a special-purpose explosive charge. INTRODUCTION In an article appearing in the May, 1888 issue of Scribner's Magazine, Charles E. Monroe described his early experiments with gun cotton (Fig. 1) which led to his name being most fre-quently connected with our present-day shaped charge. Although the sunken letters or "cavities" in Mon- roe's gun cotton were not lined, they produced some penetration of an iron plate. The credit for the lined shaped charge, however, should rightfully go to Dr. R. W. Wood of the Physics Dept. of Johns Hopkins University, who was responsible for first discovering the fact that a metal liner in a cavity of explosive gave high velocity fragments and/or jets of metal. This discovery was made by Dr. Wood inadvertently while investigating an accidental death resulting from an electric blasting cap. He discovered that a jet of high velocity copper particles was ejected from the dimple

Jan 1, 1958

By J. Koskinen, P. Vanninen, T. Leskinen, A. Leppala

Continuous and accurate analysis of slurries has become a critical requirement in mineral processing. With on-stream assay data, automation procedures can be employed to obtain higher recovery and improved control of production. The Courier system was developed by Outokumpu Oy, taking advantage of mineral processing know-how, to provide means for achieving these objectives in the company's ore concentrator operations. It became evident, based on early experience with on-stream analysis, that the Courier should be a complete system to fulfill all functions of the analysis operation. The system includes equipment and techniques for primary sampling, sample preparation for assaying, and processing of data for final assay results. In addition, the on-line X-ray spectrometer unit was developed specifically for industrial use, incorporating a number of technical advances. A new system for converting spectrometric data to assays is based on a physical model programmed on a digital computer. The Courier system is furnished on a turn-key installation basis incorporating all elements needed for operation including calibration. The experience to date with the Courier system at the Pyhäsalmi concentrator is summarized. Reference is also made to recent results with installations at the Outokumpu and Vihanti concentrators.

Jan 1, 1972

Albert Arents, Alameda, Cal.: From Mr. Furman's description of his crucible-assays I infer that he regards iron nails as a necessary or advisable adjunct. Against such a notion I must beg leave to protest. Nails should not be used in

Jan 1, 1896

Extractive Metallurgy Division Institute of Metals Division Iron and Steel Division OFFICERS AND COMMITTEES W R Hibbard, Jr , President J C Kinnear, Jr , Past President John Chipman, Vice-President T D Jones, Treasurer R W Shearman, Secretary AIME, 29 West 39th Street New York 18, N Y

Jan 1, 1958

By M. A. Roche

AST fall over half a million tons of ore and rock were broken in one blast at the open pit of the Hudson Bay Mining & Smelting Company's operation, at Flin Flon, Manitoba. The following particulars of the blast, and details of the preparatory work, indicate how an operation of this scope is carried out. The data given, in essentially the present form, were first published by The Canadian Mining Journal. The area blasted was 150 ft. wide and about 700 ft. long. A total of 123 tons of 50 per cent forcite gelatin, in 5 by 16-in. cartridges, was used for the charge. Drilling for the blast was started on May 29, and was completed late in August, requiring 1297 machine shifts for drilling only. Total footage drilled for the shot was over 5 miles of 6-in. hole. The main blast consisted of 232 holes spaced on 17.5-ft.

Jan 1, 1934

By G. G. Biggar

A MATERIAL contribution to the success of our Armies in the field has been the portable pipe-line system. These are the words of Brigadier General R. F. Fowler, chief of the supply division of the War Department. The portable pipe line is one of the "secret weapons" the American forces employed in their swift advances through Tunisia, Sicily, and Italy. Constructed of a light steel so flexible it can be snaked around trees, it can be laid at a rate of ten to thirty miles daily right up to the fighting fronts. It has played a major role in supplying combat troops with products varying from petroleum to water.

Jan 1, 1943

By Robert Glass Cleland

[CAPITAL EXPENDITURES TWENTY YEARS, 1934-1950 Morenci Branch $ 67,261,000 New Cornelia Branch 24,677,000 Copper Queen Branch 7,766,000 United Verde Branch 11,037,000 Miscellaneous Total Mining Division Refining Division 5,584,000 Fabricating Division 17,032,000 Total Capital Expenditures $135,823300]

Jan 1, 1952

IN order not to deviate from the proposed order both in speaking of melts and of things necessary for guns, I shall tell you at present the method by which iron balls are made. This is surely a very fine invention and a horrible one because of its very powerful effect. It is a new thing in warfare,* because (as far as I know) iron balls shot from guns were never seen in, Italy before those that King Charles of France brought here for the conquest of the Kingdom of Naples against King Ferrandino in the year 1495. Now, although I spoke to you briefly of these when I told you above of the purification of iron, it seems to me necessary to show you again in more detail here how they are made. Therefore I tell you that in addition to iron, bellows, blast furnace, and charcoal, it is necessary to have the moulds, without which they could not be cast. At first, when this work was begun in Italy, it was customary to make these moulds of bronze so as not to be obliged always to be making them of clay. Now the present masters cast the moulds of the same iron in order to save expense. Although I am aware that you should already know how to make these from the methods of moulding taught you before, still I shall tell you the method that is followed in making these, because in the practice of every particular thing there is some divergence from the general procedure. For these balls, first make a ball of wood or of clay, or have one made of lead or iron, round and of exactly the dimensions that you wish. This is if you wish to make only one in your mould; otherwise take as many as you wish it to contain. Bury half of this, or these, in a board or in clay and, having greased them with oil or lard, make a mould over them of plaster of Paris, or of clay if you have no plaster, exactly as you wish it to be in iron or bronze. Then make the other half opposite this. After having taken out the balls make little openings for the gates and vents and like- wise four holes for pegging the parts together. At the back make a stud or

Jan 1, 1942

By WILLIAM E. NEWNAM

THE molding and loading of pig lead has, in the past, been accomplished mainly by the strong arm method and, as the pigs are usually loaded directly into the cars, it has been a hot and laborious task. Of late years it has been difficult to obtain men willing to perform such labor and the need has been felt for loading and molding machinery which would eliminate all manual handling of the hot pigs and which would be sufficiently compact to permit of installation in existing plants with little or no

Jan 1, 1924

By E. F. Johnson, F. H. Brinkman, H. J. Welge, A. L. Hicks

A method is presented for predicting the character of gas or water displacement in a radial system, which can be either horizontal or inclined. The latter case would comprise cone-shaped or dome-shaped symmetry. The method conriders the one dimension of radial distance, taken parallel to the bedding planes. Approximate allowance can be made for segregation of the two fluids perpendicular to the bedding planes. A complete saturation history can be obtained in about a day's time with the use of a desk calculator. Results of an example calculation agree well with the performance of simulated gas drive in a large model representing a section of a cone. This pie-shaped, sand-packed model was 8-ft long and 4-in. thick. The method of solution is useful in handling other partial differential equations of first order and first degree. INTRODUCTION A new analytical method has been developed for predicting the performance of gas or water drive in a reservoir having radial or cone-shaped symmetry (see Fig. 1). In addition, this new development offers a general method of handling partial differential equations of first order and first degree. This work extends those methods developed previously'- "or predicting the displacement of oil by gas or water in linear systems. The method of calculating oil recovery in a radial system involves two major parts. The first part is a calculation of the distribution of saturations at various times of depletion. The second part is the calculation of oil recovery and producing gas-oil or water-oil ratios through volumetric balance on the saturation distributions obtained in the first part. This second part differs only slightly in principle from similar calculations made with linear systems, for instance. The basic assumptions used in the calculations are as follows. 1. One-dimensional radial flow. An approach is explained later for approximating a second vertical dimension. (With- drawals of oil, and of the driving fluid after breakthrough, are assumed uniform around the periphery of the dome.) 2. Constant-volume fluid flow. Thus, in a gas drive there is no change in gas solubility, or in oil or gas volume due to viscous and gravity pressure drops. 3. Capillary forces are negligible. 4. Constant rate of injection. A program has been written for carrying out the calculations needed on a digital computer. However, a prediction can also be arrived at using a desk calculator; this latter method of work requires about a day's time for each prediction made. CALCULATION OF SATURATION DISTRIBUTION For definiteness, we describe the development of our method for the case of gas drive from the crest of the structure. The reader will note, however, that the method is just as applicable to an advancing radial water drive. The equation describing gas flow over an infinitesimal

By Leo Behr

RECENT years have seen important practical advances in the construction of recording instruments for use with thermocouples. The difficulties of the problem will be appreciated when it is remembered that a 10° F. change in temperature of a base-metal couple at 1500° means a change in the electromotive force of about 0.00035 volt. In a circuit having a resistance of 350 ohms, this means a change in the current of 0.00000,1 amp.; and despite this requirement of great sensitivity the instruments must be sufficiently robust to withstand the rough usage which is so often their lot. Two methods are in common use for the measurement of the electromotive force produced by a thermocouple: 1. The milliammeter method, in which the current produced by the thermocouple in a circuit of known resistance is measured and from. this the electromotive force is deduced by Ohm's law. 2. The potentiometer method in which a known potential difference is opposed to the thermocouple electromotive force. The use of thermocouple and milliammeter for measuring temperature introduces some possible sources of error, for the reading depends on a number of factors, including the following: (1) Electromotive force set up at the hot junction, (2) electromotive force set up at the cold junction, (3) resistance of the circuit including thermocouple, lead wires, and meter, (4) field strength of magnets, (5) strength of controlling springs in meter, (6) friction at pivots, of pointer on paper, etc. It is obviously necessary to so design and maintain the installation that the reading is independent of all the factors except the first. The electromotive force set up at the cold junction can easily be taken care of provided it is constant. This has been approximately accomplished by burying the cold junction in the ground or actually secured by locating it in a container, the temperature of which is kept constant by means of a thermostat.

Jan 9, 1919

By S. Weinig, E. S. Machlin

THE mechanism of the martensitic transformation has been the subject of a remarkable number of papers in recent years.' Because the task of evaluating all the available theories is a formidable one, the authors will confine themselves merely to the presentation of results of an experimental investigation of the habit orientation, lattice relations, magnitude and direction of average transformation shear strain, and orientation of subband markings for a single variant of the possible habit systems in an 11 pct Mo-Ti alloy. It is hoped that these data will assist in the establishment of a rigorous theory for the mechanism of the martensitic transformation. Experimental Procedure Specimen Preparation: A sample, approximately 1/2 x 1/4 x 1/4 in., was cut from a double arc-melted ingot composed of commercial-process A titanium and high purity molybdenum (nominally, 11 pct Mo). It was capsuled in evacuated Vycor at 10.-3 mm Hg subsequent to a double argon wash and homogenized for 48 hr at 1100°C. After a direct quench into H2O at room temperature, a large-grained specimen resulted, which, by X-ray diffraction and metallographic means, was subsequently shown to be in the body-centered-cubic phase, ß. Two adjacent, approximately perpendicular faces were polished and the ends of the specimen were ground parallel in a V-block. Fiducial lines were inscribed at 45" to the common edge of the polished surfaces in order that they would be perpendicular to the habit traces of the subsequently formed a plates.2 The specimen was then compressed between the ground ends in a Buehler press to stress induce the transformation ß to a'. Experimental Measurements: The habit-plane orientation, the orientation of subband markings, the orientation relation between the parent ß and the product a', and the transformation strain for the same plate were determined. To further establish the nature of the subbands, one surface was repol-ished and etched. The bands in the a' were still visible and were found to be optically anisotropic under polarized light. Back-reflection Laue patterns were obtained from the ß matrix and from a region comprising both a' plates and adjacent ß matrix (a Cu target was used). By superposition of the two X-ray diffraction patterns, it was possible to obtain a tentative orientation relationship between the two phases. This result was confirmed by a pattern taken after the specimen was rotated to make the basal-plane pole of the hexagonal a' phase strike the film. This necessitated cutting the specimen to expose the a' plate in the new position relative to the X-ray beam. Analysis of Experimental Measurements On the basis of the aforementioned X-ray patterns, the orientation between parent and product

Jan 1, 1955

By S. J. Hruska

Rate expressions for the formation of two-and three-dimensional nuclei on foreign substrates are developed, taking into account previously neglected contributions to the standard Gibbs free energy of formation of critical nuclei. The temperature dependence of critical super saturation data predicted using these expressions is in accord with data for cadmium on copper and sodium on CsCl. EXPERIMENTAL data on the heterogeneous nuclea-tion of metal crystals from the vapor phase1&apos;2 exhibit the temperature dependence predicted by a nucleation rate equation derived by Pound et al.3 In their treatment, the critical nuclei are visualized according to the Volmer4 model as cap-shaped (three-dimensional). Accordingly, it seems desirable to compare these data with a nucleation rate equation which is derived on the assumption of disk-shaped (two dimensional) nuclei. Further, Lothe and Pound5 have recently shown that the standard Gibbs free energy of formation of these critical nuclei contains a contribution which has heretofore been neglected. Thus it is necessary to re-examine these nucleation data using a rate equation which contains this contribution. The van&apos;t Hoff isotherm relates n(i), the concentration of nuclei of critical size i (i = number of atoms), to nil), the concentration of adsorbed single atoms: where standard Gibbs free energy of formation of critical nuclei given by is temperature insensitive and is the bulk free energy change/volume of transformed material], T = substrate temperature and k = Boltzmann&apos;s constant. Previously,3 was determined by considering only the contributions of bulk and surface free energies in transforming i atoms from the population nil) to a cluster of i atoms. It has been shown5 that this procedure does not take into account the free energy contribution arising from the multiplicity of sites, q, where the clusters can be situated. If this contribution, -kT In q/n(l),is added to iG3 [Note that this increases n(i) by a factor q/n(l).] Since the above does not affect the remaining terms in the rate expression of Pound et al., the details are referred to their paper. The resulting nucleation rate is If the experimental AGV and T values at some common value of are employed, a plot of vs T(ln C3/l + In p&apos;) should yield a straight line of slope k/B<p and intercept . The corresponding plots for / = 1 nucleus per sq cm sec and C3 = 1018 are shown in Figs. 1 and 2 for cadmium on copper1 and sodium on CsCl2 and the values of obtained therefrom are entered in Table I. It is apparent that the data yield reasonable straight lines with about the same scatter as found using the equation of Pound et al. When the configuration of minimum free energy for a nucleus is a circular monatomic layer, the standard free energy of formation is

Jan 1, 1963

By G. Aertsen

THE CHAIRMAN (HENRY D. HIBBARD, Plainfield, N. J).-This excellent paper fills a gap in our Transactions and is most acceptable. In the early days another way of casting tire ingots, sometimes called cheeses, because of their shape, was to use a 22-gage sheet-iron cylindrical can for each ingot of the proper size to give the weight desired. These cans were bottom cast in groups, usually of four, each can being surrounded by a heavy iron ring somewhat taller than itself the top of the can being covered by a circular cast-iron plate having a small conical riser in the center, about 2 ½ in. in diameter at the bottom and 10 in. high. The top plate was clamped down to resist the upward pressure of the fluid metal and the space between the can and the outer ring, usually about 2 in. wide, was filled with dry sand. The riser permitted the escape of some of the air displaced by the steel and also increased the pressure in the steel when the mold was filled, and so diminished somewhat the tendency for gas holes to form. But little was known of segregation and pipe in those days, though the center of an ingot was understood to be the worst part, and it was separated in part in the disk which was punched out in perforating the ingot. This disk was about 8 in. in diameter and from ¾ to 2 in. thick, the variation in thickness being to rectify the weight. When an ingot was too -heavy, a thicker disk-was made by not driving the punch in quite as far as when the ingot-weight was right. Then the bloom was turned over and the punch driven in on the other side, which finished the punching and detached the disk. The tire bloom was then" becked" and later reheated and rolled as described in the paper. The forging was done with a 10-ton double-acting steam hammer. The steel generally speaking had lower carbon, from 0.45 to 0.55 per cent., than tires today have, and the tires were smaller, the most common size of ingot weighing 1,060 lb. each. BRADLEY STOUGHTON, New York, N. Y.-This paper was specially requested by the Iron and Steel Committee, because that Committee thought so important an industry should have its history written by one who was familiar with it, and before he had forgotten, or all the rest of the world had forgotten, its early stages. Mr. Aertsen has said that it is not an exhaustive research. I think it would not be any different if it were an exhaustive research, because our library made a careful attempt to find some written light on the history of these tires, but very little was found.

Jan 4, 1917

By Lewis W. MacNaughton

The North Texas district, as herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wil-barger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature are in traps, which, although localized by structures incident to the regional uplift, are usually modified by stratigraphic changes in the sediments. Excepting the fields in southeastern Baylor, southern Archer, and southwestern Clay Counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsylvanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1940 The encouraging outcome of exploration and development in Montague and Cooke Counties and generally greater activity throughout the district resulted in the drilling of some 1700 wells during 1940, about 350 more wells than were drilled in 1939. Approximately 1250 of these tests were completed as oil wells. Production likewise increased during I940 to the extent of 8 million barrels more than the 25 1/2 million barrels produced in 1939. In spite of this large increase in production, known oil reserves again increased substantially. As is usually characteristic of this district, the new reserves were from a large number of fields, none of which were of such magnitude as to be important to the oil industry. Nevertheless, the Fargo field, Wilbarger County, deserves mention as one of the more important discoveries in this district during 1940. Following seismic surveys, the hmerada Petroleum Corporation located its No. I Goodpasture in sec. 35, block IS, H. and T. C. R. R. Co. survey, and drilled it to a total depth of 6717 ft. This well was completed in July 1940 through perforations in the casing from a pay between 3230 and 3252 ft. for an initial production of 241.5 bbl. on an 8-hr. pumping test. Other potential producing horizons were found in the Pennsyl-vanian at depths of 3960 to 3995 ft., 4208 to 11.234 ft., 4407 to 4422 ft., and in the Ordovician at 6300 ft. Wells completed to date in the several Pennsylvanian horizons have an average daily potential of 600 bbl. of oil. Although no wells have yet been completed in the Ellenburger dolomite (Ordovician), the discovery well swabbed I5 bbl. per hour from this formation before plugging back for completion in an upper horizon.

Jan 1, 1941

By Lewis W. MacNaughton

The North Texas district, as herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wil-barger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature are in traps, which, although localized by structures incident to the regional uplift, are usually modified by stratigraphic changes in the sediments. Excepting the fields in southeastern Baylor, southern Archer, and southwestern Clay Counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsylvanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1940 The encouraging outcome of exploration and development in Montague and Cooke Counties and generally greater activity throughout the district resulted in the drilling of some 1700 wells during 1940, about 350 more wells than were drilled in 1939. Approximately 1250 of these tests were completed as oil wells. Production likewise increased during I940 to the extent of 8 million barrels more than the 25 1/2 million barrels produced in 1939. In spite of this large increase in production, known oil reserves again increased substantially. As is usually characteristic of this district, the new reserves were from a large number of fields, none of which were of such magnitude as to be important to the oil industry. Nevertheless, the Fargo field, Wilbarger County, deserves mention as one of the more important discoveries in this district during 1940. Following seismic surveys, the hmerada Petroleum Corporation located its No. I Goodpasture in sec. 35, block IS, H. and T. C. R. R. Co. survey, and drilled it to a total depth of 6717 ft. This well was completed in July 1940 through perforations in the casing from a pay between 3230 and 3252 ft. for an initial production of 241.5 bbl. on an 8-hr. pumping test. Other potential producing horizons were found in the Pennsyl-vanian at depths of 3960 to 3995 ft., 4208 to 11.234 ft., 4407 to 4422 ft., and in the Ordovician at 6300 ft. Wells completed to date in the several Pennsylvanian horizons have an average daily potential of 600 bbl. of oil. Although no wells have yet been completed in the Ellenburger dolomite (Ordovician), the discovery well swabbed I5 bbl. per hour from this formation before plugging back for completion in an upper horizon.

Jan 1, 1941

By Arthur F. Taggart

This paper proposes two units (believed to be new) for designating, respectively, capacity and efficiency for primary and intermediate crushers. Capacity Operators know that the tonnage of rock that can be put through a particular crusher in a given time depends primarily upon the crusher setting (open setting for jaw and primary gyratory types; closed setting for cones and rolls), and secondarily on the lithological character of the feed, its maximum size, the amount of fines that it carries, its moisture content, and the method of feeding. The proposed capacity formula states a relationship between all of these factors in one empirical equation, as follows: Tr = TR80K&apos;K" [I] in which Tr, called "reduction tons per hour" is the new capacity unit; T = tons of feed per hour requiring crushing; R80 = "80-per cent reduction ratio"; and K, K&apos;, and K" are constants that approximate quantitatively lithological character, moisture content and method of feeding, respectively. T is the hourly weight of material in the feed that is coarser than the coarsest discharge of the crusher. (For marked departures from the normal specific-gravity range—2.5 to 2.7—T should be adjusted to corresponding volumes.) In the crushers under consideration, discharge from the crushing zone is limited by the minimum dimension of a particle. Passage of the particle through a square-mesh screen is limited by its intermediate dimension. Sheppardl has shown that the ratio of maximum: intermediate: minimum average dimensions of broken rock fragments may be taken as about 1.5:=:0,6 for nonslabby rocks such as are normally crushed, while for slabby rocks, such as thin-bedded sedimentaries, foliated schists and gneisses, and the blocky metamorphics, the ratio is of the average order I.3:I:o.3, with the possibility of an even smaller relative value for the thickness. Gaudin2 finds the corresponding ratio for —I50 + 200-mesh pyrite to be I.4: I:0.6. The hourly tonnage of crusher-plant feed, therefore, should be diminished by the amount thereof that would pass a square-mesh screen of which the aperture is S times the crusher setting, where S is a shape factor with the value 1.7 for rocks that break exceptionally cubic; 2 for ores and rocks that exhibit no appreciabie tendency to slabbiness; and 2.5 to 3, or, in exceptional cases, even larger, when the tendency to slabbiness is marked. R80 is the quotient of the theoretical square-mesh aperture that would pass 80 per cent of the feed, divided by the aperture that would pass 80 per cent of the product. It is best determined from screen tests. If, as is usual with primary crushers, a sizing test of feed is not available, the

Jan 1, 1943

By Arthur F. Taggart

This paper proposes two units (believed to be new) for designating, respectively, capacity and efficiency for primary and intermediate crushers. Capacity Operators know that the tonnage of rock that can be put through a particular crusher in a given time depends primarily upon the crusher setting (open setting for jaw and primary gyratory types; closed setting for cones and rolls), and secondarily on the lithological character of the feed, its maximum size, the amount of fines that it carries, its moisture content, and the method of feeding. The proposed capacity formula states a relationship between all of these factors in one empirical equation, as follows: Tr = TR80K&apos;K" [I] in which Tr, called "reduction tons per hour" is the new capacity unit; T = tons of feed per hour requiring crushing; R80 = "80-per cent reduction ratio"; and K, K&apos;, and K" are constants that approximate quantitatively lithological character, moisture content and method of feeding, respectively. T is the hourly weight of material in the feed that is coarser than the coarsest discharge of the crusher. (For marked departures from the normal specific-gravity range—2.5 to 2.7—T should be adjusted to corresponding volumes.) In the crushers under consideration, discharge from the crushing zone is limited by the minimum dimension of a particle. Passage of the particle through a square-mesh screen is limited by its intermediate dimension. Sheppardl has shown that the ratio of maximum: intermediate: minimum average dimensions of broken rock fragments may be taken as about 1.5:=:0,6 for nonslabby rocks such as are normally crushed, while for slabby rocks, such as thin-bedded sedimentaries, foliated schists and gneisses, and the blocky metamorphics, the ratio is of the average order I.3:I:o.3, with the possibility of an even smaller relative value for the thickness. Gaudin2 finds the corresponding ratio for —I50 + 200-mesh pyrite to be I.4: I:0.6. The hourly tonnage of crusher-plant feed, therefore, should be diminished by the amount thereof that would pass a square-mesh screen of which the aperture is S times the crusher setting, where S is a shape factor with the value 1.7 for rocks that break exceptionally cubic; 2 for ores and rocks that exhibit no appreciabie tendency to slabbiness; and 2.5 to 3, or, in exceptional cases, even larger, when the tendency to slabbiness is marked. R80 is the quotient of the theoretical square-mesh aperture that would pass 80 per cent of the feed, divided by the aperture that would pass 80 per cent of the product. It is best determined from screen tests. If, as is usual with primary crushers, a sizing test of feed is not available, the

Jan 1, 1943

By H. A. Deans

A three-parameter mathematical model for one-dimensional flow in porous media is developed. The objective of the model is to predict accurately the longitudinal dispersion associated with the flow of either gases or liquids over a wide range of Reynolds number. A qualitative analysis of the model parameters is given. Published experimental pulse-response curves are compared with results predicted by the model. Several general types of problems are given for which the model can be used. INTRODUCTION The problem of multicomponent single-phase flow through porous media is encountered in the study of petroleum reservoirs, gas chromatographic and ion-exchange columns, industrial fixed-bed con-tacters and elsewhere. These particular examples span the wide range of flow conditions possible; Reynolds numbers of less than l0-4 are not unusual in oil-production problems, while values in excess of 103 are common in large fixed-bed operations. The study of flow-dependent transport phenomena is complicated both by the changes in the character of the flow over this range, and by the irregularity of the flow boundaries inherent to porous media. Dispersion is one of the important phenomena known to depend fundamentally on flow conditions as well as on fluid and medium properties. As used in this paper, the term "dispersion" refers to the observed mixing of fluid elements of different composition which occurs in flow systems. The actual mechanism may be one or more of a number listed below. Only dispersion in the direction of the mean flow (referred to as axial or longitudinal dispersion, or mixing) is considered here, although lateral dispersion arises as part of certain coupled mechanisms. MECHANISMS FOR LONGITUDINAL DISPERSION A number of distinct mechanisms are known3,5,7,8 to contribute to the phenomenon of longitudinal dispersion. The more important of these are as follows. 1. Molecular diffusion in the flow direction. 2. Turbulent (cell) mixing. 3. Lateral transport processes coupled with velocity and/or residence time distributions, including: (a) "Taylor" diffusion caused by the interaction of velocity profiles in individual voids with lateral molecular diffusion; (b) separation and remixing or interdiffusion of streams having different velocities around particles; and (c) the couplipg of gross velocity profiles, caused by viscous instability or inhomogeneous porosity, with lateral dispersion. 4. Finite mass-transfer rate between a porous matrix and the flowing phase, and finite diffusion rate inside elements of the porous matrix. It is a well documented fact that these mechanisms, whether acting individually or in combinations, produce essentially similar integral effects. The observed dispersion can be described approximately by solutions of the diffusion equation with a properly chosen dispersion coefficient. Necessary conditions for equivalence between dispersion and diffusion are discussed by Klinkenberg and Sjenitzer.7 Apparently these conditions are not satisfied exactly in many real systems. "Best fit" solutions of the diffusion equation often depart appreciably from measured breakthrough curves for the usual pulse- or step-forced experimental systems. In particular, pulse response curves usually show some degree of asymmetry and "tailing" which cannot be reproduced by the one-parameter diffusion model. The three-parameter model proposed herein attempts to produce these effects in a realistic manner. Asymmetry and tailing are predicted for certain sets of parameter values, while for other sets the new model agrees with the diffusion model. VELOCITY DEPENDENCE OF DISPERSION Molecular diffusion apparently controls at sufficiently low Reynolds number in both gas and liquid systems.*l3 At Re > 20, turbulent cell mixing is dominant for gases flowing at low pressure; the data of McHenry and Wilhelm8 show that the mixing cell is approximately 1 particle diameter long in random sphere packs. on the other hand, the data