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By C. Y. Garber

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

Jan 1, 1946

By H. E. Wilborg

This chapter deals with those sands employed by the foundries for the manufacture of cores and molds used in the casting of such common metals as steel, gray iron, ductile iron, aluminum-based alloys, and copper-based alloys. Most metal is cast in "green sand" molds in which the sand mixture, consisting primarily of silica, clay, and water, forms a plastic material. This plastic material is rammed around a pattern in a split box called a flask, then the box is separated, the pattern is withdrawn, and the metal poured. These green sand molds are broken apart when the metal has solidified. The sand is then remixed and a new mold made for the next casting. To a lesser extent silica sand is mixed with resins or oils and, after forming, the mixture is hardened either by heat or chemical reaction. In any case, the foundry mold or core is used just once before being broken up and remixed for manufacturing another core or mold. By far the greatest consumption in the foundry is of those types of sand high in silica, low in clay (under 0.5%) and occurring in numerous locations thoughout the United States.

Jan 1, 1975

By Richard H. Bube

Photoelectronic radiation detectors may be conveniently classified as homogeneous intrinsic, homogeneom extrinsic, or junction type. Highly photosensitive homogeneous intrinsic photodetectors may be prepared from a number of different II-VI, III-V, or IV materials. Such materials require the presence of specific imperfections that can act as sensitizing centers to provide long majority carrier lifetime. Homogeneous extrinsic photodetectors are of interest primarity for infrared detection, and consist principully of germaniuim and silicon with suitable inpurities. A vaviety of junction photodetectors exist, with silicon us the most common material for them all. The following extrema in performance are found: 1) highest photoconductivity gain in homogeneous intrinsic photodetectors; 2) smallest response time (highest frequency response) in p-i-n junctions; 3) largest gain-bandwidth product in avalanche diodes. ALTHOUGH the total number of materials exhibiting photoconductivity effects is very large, only a relatively few of these have appropriate properties for a practical photoelectronic radiation detector. In fact if one surveys the commercial detectors currently available, one finds that the field is dominated by some ten or fewer materials. These are summarized in Table 1 in terms of the other important variable in detector fabrication, the structure of the material, i.e., whether the material is used as a single crystal or in polycrystalline form, and whether the material is used as a homogeneous detector or whether the detector depends upon the existence of a junction or barrier in the material. The principal wavelength range for each type of material is also shown, together with an indication of the utilization of intrinsic or extrinsic excitation. For the purposes of the present comparison of various detectors, it will be convenient to discuss two main topics: homogeneous photodetectors and junction photodetectors. The performance of a photoelectronic radiation detector is measured in terms of two parameters: the photoconductivity gain, and the response time of the detector. A convenient figure-of-merit is given by the ratio of gain to response time, often called the gain-bandwidth product. The photoconductivity gain is a device parameter since it varies in many cases with the applied voltage and the detector geometry, and should be distinguished from the actual photosensitivity of the material involved. This photosensitivity can be conveniently given as the product of free carrier lifetime and mobility in the material. The photoconductivity gain is defined as the number of charge carriers which pass between the electrodes per second for each photon absorbed per second, where G is the photoconductivity gain, is the pho-tocurrent in amperes, e is the electronic charge in coulombs, and F is the total number of electron-hole pairs created in the photo conductor per second by the absorption of light. The gain may also be expressed as the ratio of the lifetime of a free carrier to the transit time for that carrier, i.e., the time required for the carrier to move between the electrodes. For a material in which one-carrier conductivity dominates, where T is the lifetime of a free carrier, ttr is the transit time for this carrier, p is the carrier mobil-ity, V is the applied voltage, and L is the electrode spacing. From Eq. [2] it follows that the photoconductivity gain is proportional to the photosensitivity of the material (tP), the proportionality constant being The photosensitivity of a material, and hence the photoconductivity gain of a device utilizing the material, depends on the lifetime of the free carriers as a critical parameter. In a homogeneous material this lifetime is determined by the nature of imperfections in the material, and in an inhomogeneous material the lifetime is determined by the specific junction structure. The speed of response, the other basic photodetec-tor parameter, is determined by factors quite similar to those important for photoconductivity gain. Imperfections are of primary importance in homogeneous materials, and the structure of the junction is a determining factor in junction devices. For infrared detectors it has become common to define another quantity designed to indicate directly how effective the detector is in distinguishing between a small photoconductivity signal and random noise due to the detector and its environment. The detectivity D* is given by

Jan 1, 1968

By AIME AIME

THIS year's Chairman of the Institute of Metals Division is a relatively rare phenomenon in the metallurgical profession; he is an expert historian of metallurgy, he is a confirmed collector and student of old works on alchemy, chemistry, and metallurgy-vide: the famous Biringuccio and he is a profound student (with a somewhat idealistic slant) of recent trends in world affairs and in what some incurable optimists call civilization; and at the same time he is still possessed of a sense of humor. Incidentally he is also one of the bestknown nonferrous metallurgists in this country and abroad, and for fifteen years has been a willing worker in A.I.M.E and the Institute of Metals Division.

Jan 1, 1943

A. H. Bromly, Zihuatanejo, Guerrero, Mexico (communication to the Secretary*):—The following criticism of what "is offered as a summary which may be found useful by mining engineers," is not dictated by any captious spirit, but in the intereet of historical and scientific accuracy. The States of Queretaro and Oaxaca have produced sufficient silver to warrant more extended notice. Referring to Pachuca, State of Hidalgo, the eomewhat loose and inexact statement is made that "the ore-depdsit is an andesite, intermixed with quartz-veins, rich from the surface." A better description mould be,—the ore-deposits consist of quartz-veins in andesite. It is notable that many of the rich shoots worked in recent days did not come to surface. In consequence, Pachuca is often quoted by the ill-informed as a camp in which values improve with depth, the truth being that the veins carry shoots, or clavos, some of which were exposed at surface and some not. The name of " electric plow," applied to the mechanical stirrer of recent use, is certainly not to be recommended. The stirrer, or agitator, consists essentially of a traversing gang-plow, operated by power through shafting; drums, and wire-rope. The fact that in certain plants the motive-power used is electricity does not make it an electric plow. Such a name suggests a machine of which the motor is an essential and integral part; which is not so in this case. A lathe in a factory driven by water-power is not called a hydraulic lathe. My experience agrees with Dr. Raymond's note as to azulapue, which in some districts is also applied to blue copper carbonate. The El Oro, Esperanza, and Mexico mines should be allocated to the State of Mexico; the Dos Estrellas being in Michoacan, as stated. The El Oro quartz certainly does not appeal to me

Jan 1, 1910

By Alan Morris

Brass rod for use in automatic screw machines is one of the major products of the brass mills. A large tonnage is consumed each year in the manufacture of an endless variety of finished articles and parts for assembly into other products. The machines that do this work have been developed to a high degree of efficiency, and their manufacturers are still striving for higher production speeds. This development has brought with it a demand for brass rod to meet the increasingly difficult machining conditions. This paper is a report of the results of tests undertaken in an effort to obtain a measure of the effects of such variables as lead content, microstructure and cold work on the machinability of brass rod. It is realized that the term "machinability" has never been well defined. Power, finish and tool life all should have a place in such a definition. In practice it is sometimes found necessary to sacrifice some of these in order to obtain a rod that will not tend to throw up a burr, or will give a burr which is easily tumbled off. Again a specially stiff rod may be necessary because of long overhang from the chuck or a rod of special characteristics is needed to take a given broaching operation without chattering. It is only through an understanding of the effect of basic mill operations on the machinability of the rod that such problems as these may be solved most economically. It is hoped that this paper, together with the discussion it may evoke, will prove to be a basis for such an understanding. Testing Apparatus The testing apparatus used was of the single-tooth milling cutter type, in all respects sirnilar to that first used and described by Airey and Oxford1 and again by Boston. The machine used in the present test is shown in Fig. 1. It is an ordinary milling machine in which a heavy pendulum has been substituted for the pulley on the arbor. If the pendulum is raised

Jan 1, 1932

By R. R. Wilson

THE Cassidy Colliery operated by the Granby Consolidated Mining, Smelting & Power Co., Ltd., is situated about 9 miles in a southerly direction from the city of Nanaimo on Vancouver Island. The coal seam worked, which is called the Douglas bed, outcrops in the western part of the property, clipping easteyrl, and is opened by a slope 7 by 14 ft. in the clear, and is timbered by 12 to 14-in. framed sets of timber, 4 ft. center to center. A separate manway provides for a traveling road and at the same time forms an intake airway. The general average of the dip of the seam at Cassidy is 18°, and varies in thickness from 1 to 25 ft., averaging about 8 ft. The main slopes follow straight down the dip a distance of 4545 ft. At the bottom of the main slope two rock tunnels were driven a distance of 1500 ft. to the south, cutting through a fault, and opening up an area in the same seam which is known as No. 7 South Section. The coal is found in this section at a vertical depth of 1560 ft., and is very soft and friable. The immediate roof is a strong, sandy shale overlain by massive sandstone while the floor is a light-colored shale, hard when freshly exposed. It does not soften materially oil exposure. In the folding of the coal measures a great thrust caused a movement along the coal seam as indicated by the slickensided nature of the coal. The floor has buckled and this has rolled and squeezed the coal-so that with rare exceptions it shows no normal bedding but curved slip planes, which frequently start at right angles to the floor, curving upward and then in the direction of the dip. As such planes are slickensided it is probable that there is a coating of clay which is more or less impervious to gas.

Jan 1, 1927

By William F. Ward

One often reads of the rich placer gravels in many of the citnoe-trav-elqd rivers of South America. The apparent richness of these gold-bearing gravels impresses the traveler, and in fact he may see batea after batea showing enough colors to figure over a dollar per cubic yard. These workings are called "playas" from the Spanish word playa, meaning shore or beach. Many workings have been reported in tropical rivers, but to my knowledge no dredge has made a success in such deposits. Investigation generally shows that the area of richness is limited and especially that the depth of the rich concentration is hardly ever more than a few inches. The Cauca river in Colombia, South America, is noted for its many rich playas. This river rises near .Popayan in the southern part of Colombia, flows north through a narrow valley between parallel mountain ranges and empties into the Magdalena river near Maganque. , The airline distance between source and mouth of this river is only about 500 miles. The rainfall is large and the lower Cauca appears to be about the size of the Missouri river in the United States. From its mouth up to Valdivia, in the State of Antioqua, it is navigable. Above Valdivia is a narrow gorge, above which the river is again navigable for some distance. The part of the Cauca where the play a panning is most noticeable is from Valdivia down to where the Nechi river enters the Cauca, a distance along the river of about 100 miles. The current in this part is swift, so that the stern-wheel river steamers make the trip with some difficulty. In the course of my work in this section of Colombia I have had the opportunity to make a study of several of these play a workings and will give in detail the conditions observed. The Island"Playa" The richest of the island playas is about 40 miles below Valdivia and a little below the old town of Caceres. The shape of the river and the location of the deposit are shown in Fig. 1, which indicates the condition at low water. The river at this place is about 600 ft. wide and the island about 75 ft. wide by 300 ft. long. The island is made up of coarse pebbles, some of which are as big as a man's head. In times of high water this island is under several feet of water and in a swift current. When the river lowers the current is still fast enough to prevent sand or silt from covering the coarse pebbles.

Jan 1, 1915

By Pradeep K. Rohatgi, Clyde M. Adams

An analysis of heal conduction in the freezing of a solution has been performed. The case considered is the semi-infinite mass of solution, bounded by a con-stant-temperature plane with one-dimensional heat flow, Numerical cooling rate and freezing rate distributions hare been calcutated for the particular case of unidirectional freezing of aqueous solutions against. a cold copper chill. The solution at each level parallel to the chill surface is subjected to a spectra of frcezing rates; the freezing rate is inilially lour., passes through a maximum, and then decreases until solidification is camplete. Arange and maximum freeeing rates are inversely proportional to the square of distance from the chill surface. The temperature of the chill surface in contact with the solution remains constant during solidification. Experimentally, it is observed that deudrite sparing increases linearly with distance from the chill surface; in the light of heat -flow analysis this means that the dendrile spacing is imersely proportional to the square root of the maximum freezing rate. SOLIDIFICATION of liquids is accompanied by rejection of latent heat at the solid-liquid interface. The over-all rate of liquid to solid transformation is governed by the rate of heat extraction. Analysis of the heat transfer in the liquid during freezing is important since it determines the freezing rate and resulting structure. A considerable amount of work has been done on metallic systems since solidification is frequently a major step in processing metals. Unidirectional freezing from heat sinks has been treated by several investigators.1-4 Much of the work has been limited to the simpler case of substances such as pure metals which freeze isothermally at a unique transformation temperature. In this case the thickness of the solid zone y, next to a chill surface. is a parabolic function of the time. 8. where a and b are constants. Eq. |1| is a close approximation giving the progress of solidification for the case in which there is a small but finite thermal contact resistance at the interface between the freezing liquid and the chill.' It has been used with some success in connection with large steel ingots4 when the therma1 contact resistance is negligibly small (as is the case when water is brought into contact with the metal chill). The constant, b. becomes zero and Eq. [l] is then exact. even when the thermal properties of the chill and the freezing liquid depend on temperature. Analysis of unidirectional solidification of solutions is more complicated since the latent heat is evolved over a range of temperatures. Next to the all-solid zone in contact with the chill surface there is a solid plus liquid zone in which solidification takes place. Although the equations presented are considered quite general the numerical and experimental results are for freezing of aqueous solutions from a copper chill. I) EXPERIMENTAL PROCEDURE Solutions of potassium chloride, sodium chloride. and lithium chloride have been used. These solutions form a eutectic: a typical phase diagram is shown in Fig. 1. A solution at its liquid us temperature is poured into a tygon tube mounted on a relatively large copper chill. The chill is immersed in a freezing mixture of dry ice and acetone at -70°C. A thermocouple connected to a high-speed recorder was mounted near the top of the chill to measure the fluctuation in the temperature of chill surface in contact with the solution. In this system the progress of solidification can be visually observed through the tygon tube. After the specimens freeze to a desired height they are removed from the copper chill and stripped from the tygon tube. Longitudinal and transverse sections are cut from the specimen for micrographic examination. Specimens in the form of a thin slice are mounted on a transparent glass slide by freezing small drops of water around the periphery. They are then polished on a series of emery papers; the final finishing is done on a soft tissue paper. A Leitz Biological microscope was used for structural observations; photography was

Jan 1, 1968

By W. T. Lundy

THE forms in which sulphur is commonly found-native sulphur, sulphides of many metals and sulphates-are widely distributed throughout the world. The two first mentioned are the principal sources of sulphur. Substantial amounts of sulphur in some form are recovered from gases from industrial plants and from gases from smelters treating other minerals. In recent years, plants have been installed in the United States to recover sulphur in elemental form from sour gases."' The amount of sulphur so produced is small at the present time but undoubtedly will increase in the future. The recovery of sulphur from gases is not covered in this chapter, which is confined to: (1) native sulphur deposits of Texas and Louisiana; (2) those of Italy; (3) other scattered deposits of native sulphur; and (4) pyrites deposits found in many countries of the world.30 Sulphur, a nonmetallic element, occurs normally in well developed bipyramidal or tabular crystals of the orthorhombic system, as well as in stalactitic and earthy masses. The mineral has a distinctive yellow color, which may be dark and discolored by impurities; the streak is white; the luster is resinous; and the fracture is conchoidal to uneven. Sulphur is translucent to opaque; has a hardness of 1.5 to 2.5, a specific gravity of 2.05, and an atomic weight of 32.06.16 The molecular weight of the solid is expressed by the symbol SS and that of the liquid and vapor ranges from S2 to S8, depending on the temperature. Sulphur melts at a temperature between 2340 and 248°F, depending on its crystalline state, to a liquid of dark amber color, the boiling point of which is 832°F. The viscosity near the melting point is about that of water and increases to 50,000 times that of water at a temperature of 380°F, subsequently falling rapidly to a low figure at the boiling point. Crystallization changes slowly from rhombic to monoclinic above 205 °F and in cooling the transformation is reversed. The mineral is a very poor conductor of heat and electricity; it is insoluble in water and nearly all acids and is soluble in cold carbon bisulphide and carbon tetrachloride. It ignites in air at a temperature of 478°F, burning with a distinctive blue flame with evolution of sulphur dioxide.47

Jan 1, 1949

By M. P. Dalton

THE problem at the Morning mill is to separate the galena, which contains a great percentage of the silver, from the sphalerite, making each into a commercial product. The ore as received from the nine is dumped into hopper-bottomed bins of 1200 tons capacity. These are divided into five sections, the first section being the regularly used section and the re-mainder used as a reserve bin. The ore is first passed through a 9 by 15-in. Blake jaw-crusher with an opening of 4 in. This allows a ham-mer head to pass through without damage. The crusher discharges to a conveyor that delivers the ore into a two-section punched-plate trommel screen with 1 ½ and 2-in. openings. The undersize is carried by means of conveyors to the mill bins. The oversize passes over a shaking feeder and through a spray or high-pressure water to a picking-belt, where waste and crude ore is hand-sorted. About 4 per cent of the ore by weight is picked out as waste, assaying about 0.6 per cent lead, and this is discarded over the dump. About 4 per cent of the ore by weight is removed as crude ore, assaying 10 oz. silver, 30 per cent lead, and S per cent zinc, and is shipped direct to the smelter. The remainder of the oversize from the picking-belt is con-veyed to a 4-ft. Symons cone crusher with 1-in. opening, which is interesting as a new introduction in this dis-trict. The machine consumes approximately 40 hp. and the pinion shaft travels 555 r.p.m. The horsepower is rather high, but the machine has an extraordinarily large capacity, and, due to the unique construction, there is no danger of tramp steel causing any damage, as in that case the discharge "opening" is automatically

Jan 7, 1927

By Frank R. Barnako

Coal mining is a hazardous occupation, but tremendous progress has been made in reducing accidental injuries and deaths in the mines. Let us take a look at the hazards in coal mining and the accident record. COAL MINE SAFETY TODAY Underground coal mining creates underground open areas, rooms, and haulageways. The roof (top) and ribs (sides) become highly stressed, and because coal and slate are very weak in tension or compression they frequently fail and fall from the roof and ribs unexpectedly. This is the most hazardous condition miners must cope with underground, and it has consistently produced the greatest number of fatal injuries in the coal mining industry. Only very sophisticated equipment, but which is not yet practical for use underground, is able to detect the buildup of stresses that may eventually lead to a roof or rib fall. Today's miner still looks for fresh cracks in the roof or rib, listens for the "drummy" sound, and feels vibrations from loose material in the roof, when tapped with a sounding stick, in order to find material which may fall. Once located, it is barred down, but if this is not possible, it is then secured to prevent it from falling. The next great& hazard is the equipment used to mine or haul coal. It is large, heavy, reacts quickly to its controls and is operated in con- fined areas with low lighting levels. The record of the last few years shows that fatalities attributable to mining and hauling equipment are about equally divided. Thorough training as part of a complete safety program is necessary to teach employees the hazards of loose roof, rib, and machine operation in order that they can work in the safest way possible. Unless there is such a program, the trade is learned by trial and error with a resulting tragic.

Jan 1, 1973

By Charles E. Locke

The little stamp-mill in the mining laboratory of the Massachusetts Institute of Technology and the work done by it have been well described by Prof. R. H. Richards and E. E. Bugbee in a paper read at the Albany meeting of the American Institute of Mining Engineers, February, 1903.' As run for student class-work the mill contains a feeder, stamps, plate, and vanner. Results in the past indicate that the work of these machines is just as efficient as that of a regular mill handling the same class of ore. It has been the custom to obtain ore principally from Nova Scotia, mainly because it is the nearest source of supply, and also because there is a considerable saving in freight-cost as compared with other districts. The gold in Nova Scotia ores is notoriously coarse, and for this reason it is almost impossible to obtain satisfactory results by sampling and fire-assay, unless an extremely large lot of ore is crushed and all of the contained gold pellets are saved. A very interesting and most extraordinary example of this fact has been presented by a recent run in the Technology stamp-mill. Since the capacity of the mill is about 60 kg. per hr., and since in about 5-hr. run the students in any one section have an opportunity to make the necessary study of machines, it usually happens that several runs are made from one lot of ore. When the shipment is received it is first dried and weighed, put through the Blake breaker, set at 1 or 1.5 in., and the crushed product is piled in a cone on the sampling-floor. When the crushing is completed the ore is usually stored away in barrels for future use; it is aimed to have each barrel of

Jan 1, 1914

BURKE BAKER, Philadelphia, Pa. (written discussion*).-The small briquetting plant of the American Briquet Co., at 25th Street and Washington Ave., Philadelphia, was built primarily as a demonstration plant. Its output per hour is 4 tons of 2-oz. briquets, which have been retailed in the, vicinity during the year the plant has been in operation. They have proved very acceptable for use in ranges, heaters and grates in-home, and in steam heating plants in apartment houses and hotels. They have not been sold for power purposes, although satisfactory tests have been made in. this field. Anthracite silt is used and is shipped direct from breaker or washery, the only preparation it receives being the removal f excess moisture by means of a Ruggles-Coles rotary dryer. Care is taken, however, to purchase silt containing less than 18 per cent. ash. The method is covered by U. S. Patent No. 941454, issued to Chas. E. Hite, and is known as the "emulsion process." The binder, which is the, basis of the patent, is composed. of 0.5 per cent. cornstarch or wheat flour; 1 per cent. asphaltum or hydrolene, and 6.5 per cent. water, on the weight of coal dust. It is prepared in a tank equipped with paddle agitators and heated by steam jets. The starch and water are first made into a paste by being brought to the boiling point with live steam; the melted asphaltum is then introduced and thoroughly beaten into the paste by the agitators. This rapid stirring breaks. the hot asphaltum into minute particles which are distributed through the paste, producing a smooth chemical emulsion. This emulsion, when dried, is not soluble in water. The binder is mixed with the dry coal dust in a horizontal paddle mixer, 8 per cent. binder to the weight of coal being used. The resultant plastic mass is then discharged into the press, which is of the simple roll type. Since the binder is a liquid and is not sticky or gummy until

Jan 3, 1918

OCHRE is a semimineral composed by Nature of earth and a tincture of yellow caused by a fumosity of lead ore. By itself it is a material without any [38] metal, although when it is used in smelting it helps to melt the harsh and sour ores of metals. I do not know that it has any other use, except to painters. Bole is also a red viscous earth which has a very astringent and drying nature. It has no very apparent smell or taste, and I think that the cause of its redness lies in the fumosities of iron ore, for it is a companion to this and is found in its mines. It is an efficacious medicine against any poison and in this capacity has an action like terra sigillata* or perhaps better. In

Jan 1, 1942

By N. W. Lord

The process of molten-zone refining is analyzed for long ingots and many zone passages. Formulas are derived which give the resultant impurity distribution in terms of finite series. A comparison with the approximate procedure of Hamming is given. HE physical principles and applications of an extremely physicalprinciple efficient form of metallurgical refinement has been described by Pfann. The purpose of the present paper is to describe a method of analyzing exactly the particular program used which enables the segregation effect to be predicted for any number of molten-zone passages in a long ingot. The method is applied to the particular case of refinement of an ingot whose impurity initially is uniformly distributed throughout its length. A number of molten zones of equal length are passed through the ingot effecting a radical redistribution of impurity. Pfann has indicated an approximate method, due to R. W. Hamming, of calculating the resultant concentration after each successive zone pass for a particular value of the segregation constant defined in his paper. Here a solution will be presented in terms of the number of zone passes and the segregation constant. The expression, though cumbersome, is exact and susceptible to ordinary numerical computation procedures. The results of a similar computation using the procedure of Hamming are presented in a table together with the exact results of the present method. The discrepancy in terms of absolute concentrations is tabulated for the first eight zone-lengths. To establish the notation (which follows that of Pfann1 as closely as possible) and physical basis of the analytical equations, the physical model and principal assumptions may be reviewed. An alloy of two elements, where there is formed a continuous range of solid solutions, usually does not melt as a simple compound. Rather, a temperature is reached where the solid solution is in heterogeneous phase equilibrium with a liquid solution of different composition. The temperature dependence of these equilibrium compositions forms part of the phase diagram. For very small concentrations of a solute B in a solvent A, this usually takes the form of Fig. 1. Sometimes the solidus and liquidus slope upward. This corresponds to a segregation constant (defined below) which is greater than unity. The segregation constant is now defined as k = Cn(x)/CnI(x) [1] where C,,(x) is the impurity concentration in the solid ingot at distance x during the nth passing of a molten zone and Cnl (x) is the impurity concentration of the liquid zone from which the solid at dis- tance x is formed (see Fig. 4 of ref. 1.) C (x) remains the same after passage of the zone. The constant k may be either greater or less than unity in general. Purification in the former case is effected only in a finite ingot and in the portion that is melted last. For k less than unity purification is effected even in an infinite ingot. The method which follows gives, in the former case, the successive increases in impurity concentration and, in the latter case, the successive decreases in concentration. The general case of impurity redistribution will be considered first, and purification will be discussed later on. The analysis rests on the following assumption: The movement of the zone is too rapid to allow appreciable atomic rearrangement in the solid sections and too slow to disturb the uniform impurity distribution in the liquid zone characteristic of equilibrium. Hence, the composition in the solid at the left solidifying interface will be determined by Eq. 1 while the impurity concentration of the liquid zone will be uniform throughout its length. The reasoning which follows closely parallels that of Appendix 11 in Pfann&apos;s paper. It is reviewed here for the case of the nth zone pass in order to make clear the meaning of an operator essential to the present method. Fig. 4 of ref. 1 shows the movement of a molten zone of length 1 in an ingot of total length d. Each Cn(x) can be determined from the condition that the amount of solute added to the zone during an incremental advance, dx, is due to the melting in of a solid portion C(x)dx and the freezing out of kCnl(x), that is d I —r- CnL (x) dx = Cn-1 (x+l)- kCnL (x) dx or, in terms of Cn(x) d k k —— C,(x) +—c.(x) =— Cn-1 (x + l). [2] dx l l This, of course, is derived from the main assumption, the fact that 1 is constant, and that the total impurity content previously present up to x + 1 is constant . A correction has to be made for the region (d — nl) < x < d. This is due to the zone length changing during the passage of the solidifying interface beyond x = d — 1. Since the general solution would be too complicated otherwise, only the region 0 < x < d — nl is considered. The general solution of Eq. 2 is

Jan 1, 1954

By G. G. Luther, C. E. Jackson

THE relationship between hardenability and weldability has been mentioned many times. The ease of making a hardness survey has led to its wide use as a criterion [ ] of weldability and with a given class or series of steels for which the ductility under weld heat-treatment is known the test is entirely suitable. However, in studying a new steel the hardness survey is of less value, since it is based on the assumption that there is a correlation between hardness and ductility. Several attempts have been made to derive indices for weldabilityl and hardenability from the chemical analysis. In most of these proposals the effects of the different elements were considered to be additive, but recently Grossmami2 proposed a novel method of calculating the hardenability of a steel from its chemical composition. In the [ ] method proposed, a steel is considered as having a base hardenability due to its carbon content and grain size, and this base hardenability is multiplied by a factor for each chemical element present, The final product is the hardenability. The purpose of the present study is to point out the possible relationship between hardenability and the effect of welding on hardness and ductility for a number of plain carbon and low-alloy steels. The composition of the 25 steels reported in this paper as determined by chemical analysis is given in Table I. To eliminate the effect of variations in finishing temperatures, the 1/2-in. plates were normalized after heating for one hour at 1650°F. in a controlled-atmosphere furnace.

Jan 1, 1942

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.&apos; THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy&apos;s Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. &apos;Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If&apos; .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By F. Brons, V. E. Marting

In the past, other authors.1, 2 have studied the influence of a skin effect on the productivity of a well. This skin effect, expressed by the skin factor S, is considered to be caused by a thin layer of impaired permeability immediately around the wellbore and extending vertically over the whole productive interval penetrated by the well. The skin factor S is defined as follows. Based on this, the impairment in productivity caused by a skin can be expressed by the fractional loss in productivity I, which is the loss in productivity divided by the total unimpaired productivity. For compressible flow in a stabilized well which drains a circular area of radius re, 1 is given by The present paper deals with a different kind of productivity impairment. Consider a well in which part of the productive formation is blocked off completely, either by incomplete penetration or by exclusion of parts of the productive zone by blank casing. In Fig. 1 (A, B and C), three examples are shown. Fig. 1(A) shows the situation where a well only partially penetrates the formation. This often is done to combat the actual or imagined danger of bottom-water coning. Fig. 1(B) shows a well producing from only the central portion of a productive interval. This type of completion is sometimes used where both water and gas coning are a problem. Although the case of a well producing through perforated casing cannot be treated in a manner similar to the previous two cases (where radial flow in the horizontal plane is assumed), Fig. 1(C) shows several intervals open to production and qualitatively describes this case (as will be discussed later). To study the loss in productivity in all these cases, two parameters are introduced which fully determine the impairment. The first is the penetration ratio "b," i.e., the total interval open to fluid entry divided by the total thickness of the productive zone. The second is the ratio hlrw. In this ratio, rw is the wellbore radius. The definition of h is more cumbersome. In Fig. 1(A), h is the thickness of the total productive interval. The streamline configuration for this case of partial penetration is basic to the other two cases considered (Views B and C of Fig. 1). It will be obvious from Fig. i (A) that the flow lines in the uppermost portion of the formation will be essentially horizontal, while those in the lower portion will curve upward toward the well. In Fig. 1(B), with only the middle portion of the zone open to production, the streamline configuration. of the upper half will be an exact mirror image of that in the lower half of the zone. Hence, for the case illustrated in Fig. 1(B), h is defined as one-half the total sand thickness. It follows, then, that in Fig. 1(C) h is one-half the distance between corresponding points in adjacent intervals. (In gun-perforated casing, h would be one-half the distance between perforations.) In a paper by Nisle4 and a paper given by the present authors5, the mathematical theory was developed for the cases under consideration. In the present publication, the emphasis is put on the results of these studies; consequently, the equations derived in Refs. 4 and 5 will be omitted, for the most part. The pressure drop p in a well producing from only a portion of the total formation thickness can, in analogy with Eq. 1, be expressed by Numerical solution of Eq. 5 by use of the IBM 650 leads to the following important conclusions. First, during a short period after starting production (usually on the order of a few minutes), the function p(b) is given by