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By H. N. Herrick

The flow characteristics of drilling muds, as described in this paper, and the method given for solving problems relating to the flow of these muds through pipe and accessory equipment, are based on a conception that drilling muds are plastic solids like paints or greases; not liquids. The data presented in this report have been obtained from studies of California muds, chiefly those used in the Kettleman Hills field, by the Producing Department of the Standard Oil Company of California. Although no claim of scientific exactness is made for the formulas and diagrams, since the data upon which they are based are not complete even for California muds, the method has proved to be a convenient means for estimating, closely enough for practical purposes, the pressures required to force muds at various rates through pipe systems in which-they are handled. Certain approximations have been made to simplify the procedures so that they can be used easily in the field. Viscosity and Shearing Strength of Mud For the purpose of this discussion a plastic solid is defined as a material in which no deformation or flow takes place when the material is subjected to shearing forces, until the shearing force reaches a value called the "yield point." With liquids, the smallest force will produce continuous deformation; that is, the yield point of liquids is zero. The difference between true liquids and muds is illustrated in Fig. 1, which shows rates of flow through a small tube under different pressures. The flow rate of the liquids is directly proportional to the pressure and that of the muds is not. The behavior of drilling mud does not conform in every detail with the definition of a plastic solid as given, because mud actually flows slightly at pressures below its yield point. However, for practical purposes the definition describes the condition adequately and has the advantage of simplicity. In order to make mud-flow calculations based on the theory that mud is a plastic solid, it is necessary to know the "yield point" of the mud, which hereinafter is defined by equation 1 under the caption "Viscosity

Jan 1, 1932

By Howard Scott

INVAR is the preeminent low-expansion metal by virtue of the fact that it can be prepared with a zero coefficient of expansion at atmospheric temperature. This fact suggests that there is little room for improvement in the expansion properties of the low-expansion nickel steels. The inference is true, however, only so far as the expansion at and near atmospheric temperature is concerned, because the expansivity of invar starts to increase rapidly on heating above 100° C. and soon reaches the value of copper. Guillaume1 met this situation by increasing the nickel content above that of invar. By that expedient, alloys having low expansivity under higher temperatures were obtained, but not without a large increase in minimum expansivity. The increase in minimum expansivity with increasing nickel content severely limits the technical applications of these alloys at high temperatures. Prospects of improving the expansion characteristics of the nickel steels is offered by alloying. Search for an advantageous alloying addition by analogy with other alloy systems, however, is not productive because the low-expansion characteristic is unique with that system. The rule of mixtures usually gives a fair value of the expansivity of other solid-solution alloys, but in the iron-nickel systems gives a value of 18 X 10-6 per deg. C. whereas the actual value is 1 X 10-6 per deg. C. Apparently suitable additions are not to be deduced from such ingenuous considerations. Recognition of the fact that the temperature range of low expansivity in nickel steels is terminated with loss of magnetism affords a more promising basis for the selection of an advantageous element. One may expect from that fact that additions of nonmagnetic elements to the iron-nickel alloys are detrimental to the low-expansion characteristic. Indeed, carbon, manganese, silicon, copper and chromium are detri-mental to the expansion properties and no nonmagnetic element is reported to be beneficial. From the same viewpoint, the addition of a magnetic metal offers prospects of improvement. As two of the three ferromagnetic elements are already present in the

Jan 1, 1930

By C. H. Herty

During the past few years frequent reference has been made to a certain type of iron known generally as "bad iron," "dirty iron," etc., both by steelmakers and producers of iron castings.' Open-hearth operators have claimed that such iron was entirely within the specified limits as to ordinary analysis but it was difficult to make good steel from it. It has been suggested that unreduced material in the iron is responsible, also that most trouble is experienced with the iron when the blast furnace is delivering a product whose analysis is more or less variable. Other reasons suggested are the use of scrap or borings, unsintered flue dust in the burden, a cold hearth, too high a proportion of unsuitable grade of ore, or the form of the carbon in the iron. Accordingly, a subcommittee was appoint at the fall meeting of the Open-hearth Committee of the Americ m Institute of Mining and Metallurgical Engineers held in Pittsburgh in October, 1926, to investigate the reasons for the occurrence of this bad iron and suggest methods for preventing its appearance. This committee enlisted the cooperation of the U. S. Bureau of Mines Experiment Station at Pittsburgh in undertaking a study of pig-iron quality as affecting the open hearth. The following is a report of the findings to date: Method of Testing Inasmuch as a "spell" of dirty iron occurs without warning and may be of short duration, it was deemed advisable to attempt to simulate the conditions existing before and during such a period and compare the quality of the steel made with the normal and with the dirty iron. The Bourne-Fuller Co., of Cleveland, which has a single furnace that supplies

Jan 1, 1929

By A. J. R. Curtis

THE Portland Cement Association was organized more than a third of a century ago by a group of cement manufacturers, to do cooperatively the educational and research work needed to ensure proper use of their product. Specifically, the Association has a threefold purpose: (1) to search out facts to ensure the best possible service from concrete; (2) to give the widest possible circulation to facts affecting the use of concrete; (3) to urge practical application of those facts on actual building projects. An organization of technically trained men conducts many research projects in the Association laboratories, interprets their findings and applies them practically in the field. The net effect of this work has been to improve the design and prolong the life of roads, bridges, industrial, commercial and public buildings, homes, farm structures and concrete products. The results of this technical research and experimentation are made available to the entire construction industry through bulletins and reports. Information is also released to the general public through newspapers, magazines and Association publications. In addition to a technical staff in the general office in Chicago, the Association has district offices in 22 cities. Field engineers cover 37 states, the District of Columbia and British Columbia, to give service to users of Portland cement. ACCIDENT PREVENTION During the early part of the century, there began a complete transformation in the processes of manufacturing cement. Electricity, with its attendant hazards, was beginning to replace steam; huge rotary kilns and tube mills were being substituted for the vertical kiln and "coffee grinder" mill. Only a few far-sighted leaders realized the import of these innovations, and they also recognized the fact that workmen must be protected against the hazards of the new machinery. By their sincerity and firm purpose they infused into the whole industry the concept of industry's responsibility for safeguarding employees. Even before effective compensation laws had been passed in most states, the Portland Cement Association had assigned to an Accident

Jan 1, 1937

By E. A. Sondreal, F. I. Honea

This paper summarizes coal and ash properties and pilot-plant results for 14 key lignite seams in the Gulf Province, as well as discusses operating problems encountered by the four Texas power plants burning Gulf Province lignite. Some consideration is given to the design of future power plants.

Jan 1, 1982

By G. J. Roe

Drawing largely on desulfurizing practices which have been developing abroad in the last several years, this paper will cover the main ways in which producing steels with low sulfur provides appreciable benefits -- beginning with improvements in ingot processing and carrying over into improved product properties, in particular cleanliness, formability, notch toughness and weldahility. Because the raw materials and fuels used in steelmaking are sources of sulfur and the removal of this element is difficult, sulfur has tended to be accepted as an unavoidable incidental contaminant of steel. Although it was early recognized that sulfur significantly affects several mechanical properties, the main concern was with its effect on hot shortness. Concentrating on countering this effect, operators have traditionally added manganese in sufficient multiples of the sulfur content to form manganese sulfide and thus avoid iron sulfide formation, the assumption being that the steel would then be acceptable in terms of both processing and mechanical properties.

Jan 1, 1972

By Alfred E. Hunt

The charge to be described was made in a seven-ton furnace, with a hearth twelve feet long and eight feet wide, with three gas and three air ports on each side. The stock of the entire heat was charged cold in one hour and five minutes, a part of the pig being first placed upon the bottom to protect it, then upon it the plate-scrap and blooms, and finally the remainder of the pig—some two thousand pounds. In fire hours and twenty-five minutes after beginning the charge the metal was melted down level, and two hundred pounds of hot twelve-per cent. spiegel was charged, care being taken to have it entirely immersed in the bath. In two hours more the bath was thoroughly melted and hot, and began to boil, i. e., the carbon began to be oxidized and evolved through the bath of covering slag as carbonic acid and carbonic oxide gases. Seventy-five pounds of lumps of Republic specular iron ore were added at this time, increasing the action, so that in ten minutes after the metal was in active ebullition. A test of the metal showed it to have about 0.90 per cent. carbon. One hour after the first ore was added a test was again taken, after thorough rabbling of the metal, and it was found to be 0.37 per cent. carbon. One hundred pounds more of lump Republic ore and about seventy-five pounds of limestone were then added, and fifty minutes later, after the bath was thoroughly rabbled, a -test showed the metal to have 0.23 per cent. carbon. Twenty-five pounds more of Republic iron ore were added and the metal allowed to boil for twenty minutes, when a test, after rabbling, showed the carbon to be 0.18 per cent. and the manganese to be 0.01 per cent.; the slag fracture was vitreous and of a very dark-green color. About forty pounds of limestone were added, and, the metal being hot and in a state of quiet ebullition, a hickory pole of twelve feet length and about four inches diameter, was run through the aperture in the centre door and held in a steady inclined position in the bath, with the end touching the bottom, the pole being shoved in further as it was burned away. The bath was carefully watched to see that the action that ensued was not too violent, the pole being several times

Jan 1, 1884

By W. P. Blake

Forging under the hydraulic press, which was introduced by Haswell in the year 1861, at the machine shops of the Imperial State Railway Company of Austria, has since been greatly improved, so that at the present time there are very few parts of machines which cannot be produced in this way, and at no greater cost than iron castings. The process is now used at Vienna chiefly for such parts of locomotives as cross-heads, link-bars, axle-box frames, etc., especially where the form is intricate, and there are many angles and projections. These objects weigh from 50 to 150 lb. or more, and it is claimed for them that they are not only much cheaper than ordinary forgings, but are much more regular in form and stronger. The results which Mr. Haswell has attained, after years of patient experimenting, were well shown in the Austrian Department of the Vienna Exhibition by a collection of the pressed objects in iron and steel, just as they left the moulds, with some of them cut asunder longitudinally and the surfaces etched, so as to show the internal structure or direction of the grain. Through the courtesy of Mr. Haswell and his son I saw the hydraulic presses in full operation at the works, drawing down large Bessemer ingots, cutting them up into blocks of convenient size, and forming various park of locomotives. They have two large hydraulic presses in use; the largest, with a piston 24 inches diameter, gives 1200 tons pressure, and the second, with an 18-inch piston, gives 600 tons pressure. The pressure in the pumps is 600 atmospheres. The action is vertical; the piston descends upon the work, and for forging ingots is armed with a hammer-like head. An ingot of No. 7 soft Bessemer steel, which was forged in my presence, weighed 2030 lbs. One end being placed upon the anvil, the piston is brought slowly down and crowded into the mass as if it were putty or dough, forcing it each way, but chiefly in the direction of the length of the ingot, this being the narrowest section of the anvil and hammer. The piston is then raised and the ingot is moved forward for a second squeeze, and so on, until the first half of the ingot has been reduced in thickness, when it is turned on edge and the operation is repeated. The ingot is then turned end for end and forged until the whole length has been re-

By F. P. Dewey

The most serious problem that confronts the lead-smelter is the waste caused during smelting by the volatilization of both lead and silver, which are consequently lost in the form of fume. It is not difficult to collect a portion of the solid materials passing out of the

Jan 1, 1890

By W. A. Ver Wiebe

The year 1939 in Kansas, with a production of 57,944,300 bbl. from 19,669 wells, shows a slight recession from the peak of oil production reached the previous year, when slightly over 59,000,000 bbl. of oil was marketed. The previous peak had been reached in 1917 with 45,451,000 bbl. marketed. Another still earlier peak had been reached in 1904, when slightly less than 5,000,000 bbl. was produced and sold. The production of gas probably reached a new peak during 1939 with a total of over 69 billion cubic feet. Between the peak of the year 1908, when over 80 billion cu. ft. was produced, and that of 1939 the production dropped to 16 billion cu. ft., in the year 1921. During the year 1458 wells were drilled. This figure is somewhat lower than that given in several trade journals, because it does not include wells that were deepened or recompleted in a different geological horizon. Nearly 75 per cent (1029) of the total number of wells were completed as commercial oil wells (824 in western and 205 in eastern Kansas). The commercial gas wells completed number 71, of which 24 are in eastern Kansas and 47 in western Kansas. The remaining completions include 154 dry holes in eastern and 204 dry holes in western Kansas. Based on daily potential capacity the new discoveries of the year accounted for a cumulative initial production of 264,000 bbl. in eastern and 1,158,827 bbl. in western Kansas. It is interesting in this connection to note that the number of wells completed in the state rose gradually to a first peak in 1904, when 2782 were drilled. The number dropped off rapidly to 368 three years later, but rose to the second and highest peak in 1918, when 4671 wells were completed. In the period between 1904 and 1912 more gas wells than oil wells were completed. Between the high peak of 1918 and the somewhat lower peak of 1937, the low point was reached during 1931 with the completion of only 470 wells. In the matter of new pools discovered, Kansas again ranks high. The exact number depends somewhat upon the interpretation of a "new" area—whether it should be called a new pool or a long extension of an older pool. In some places this determination cannot be made until more wells are drilled within the area. Therefore, the figures given

Jan 1, 1940

By W. A. Ver Wiebe

The year 1939 in Kansas, with a production of 57,944,300 bbl. from 19,669 wells, shows a slight recession from the peak of oil production reached the previous year, when slightly over 59,000,000 bbl. of oil was marketed. The previous peak had been reached in 1917 with 45,451,000 bbl. marketed. Another still earlier peak had been reached in 1904, when slightly less than 5,000,000 bbl. was produced and sold. The production of gas probably reached a new peak during 1939 with a total of over 69 billion cubic feet. Between the peak of the year 1908, when over 80 billion cu. ft. was produced, and that of 1939 the production dropped to 16 billion cu. ft., in the year 1921. During the year 1458 wells were drilled. This figure is somewhat lower than that given in several trade journals, because it does not include wells that were deepened or recompleted in a different geological horizon. Nearly 75 per cent (1029) of the total number of wells were completed as commercial oil wells (824 in western and 205 in eastern Kansas). The commercial gas wells completed number 71, of which 24 are in eastern Kansas and 47 in western Kansas. The remaining completions include 154 dry holes in eastern and 204 dry holes in western Kansas. Based on daily potential capacity the new discoveries of the year accounted for a cumulative initial production of 264,000 bbl. in eastern and 1,158,827 bbl. in western Kansas. It is interesting in this connection to note that the number of wells completed in the state rose gradually to a first peak in 1904, when 2782 were drilled. The number dropped off rapidly to 368 three years later, but rose to the second and highest peak in 1918, when 4671 wells were completed. In the period between 1904 and 1912 more gas wells than oil wells were completed. Between the high peak of 1918 and the somewhat lower peak of 1937, the low point was reached during 1931 with the completion of only 470 wells. In the matter of new pools discovered, Kansas again ranks high. The exact number depends somewhat upon the interpretation of a "new" area—whether it should be called a new pool or a long extension of an older pool. In some places this determination cannot be made until more wells are drilled within the area. Therefore, the figures given

Jan 1, 1940

By John F. Sulzbach, Donald K. Walker, John F. Abel

With the increasing military significance of the arctic, the U.S. Army Corps of Engineers' ice- tunneling research program has been instituted to determine the feasibility of excavating large under- ice openings. Such openings would provide for year- around storage of material and housing of personnel, independent of surface weather conditions. This unique ice mining operation has been carried on in the tunnels at Camp Tuto, Greenland, during the summers of 1955, 1956, 1957 and 1958 by the U.S. Army Snow, Ice, and Permafrost Research Establishment (USA SIPRE), Wilmette, Ill. Supervisory personnel for the tunneling projects principally have been civilian mining engineers and mining engineering students from Colorado School of Mines. They have been employed under contract between USA SIPRE and the Denver Research Institute (DRI) of the University of Denver, Denver, Colo. Laborers have been enlisted military personnel attached to the U.S. Army Polar Research & Development Center (USA PR&DC) , Ft. Belvoir, Va.

Jan 6, 1959

By R. Didchenko

THERE are many methods described in the older literature which claim to produce anhydrous rare-earth chlorides in general. and cerium chloiide in

Jan 1, 1960

Jan 1, 1925

By H. A. Jr. Koch, C. A. Hutchinson

Miscible phase displacement of oil from reservoirs has been emphasized in the past few years. The reason for this emphasis lies in the high oil recovery attainable by this process. Removal of capillary effects in the reservoir leads to recoveries approaching 100 per cent in the area contacted by the miscible phase. The miscible slug process is one means of obtaining a miscible displacement. Here a band or slug of I,PG is injected into the reservoir prior to gas injection. The idea is to maintain the band of LPG "wedged" between the gas and oil phases and thus achieve a miscible phase displacement. A second method lor achieving miscibility is through the injection of a gas which is not miscible with the reservoir fluid but which develops a zone of miscibility in [he reservoir through mass trans-ier with the reservoir oil.' This mass transfer results in either an enrichment of the lean injected gas by intermediates from the oil or an enrichment of the oil by intermediates from a rich injection gas or one that has been enriched on the surface by LPG addition. We are interested here in discussing the process in which miscibility is developed at the displacement front by the evaporation of interrnediatcs from the oil phase into the gas phase. This process "builds up" its own slug of miscible material at the displacement front and therefore does not require the injection of LPG to obtain miscibil-ily. Each process has its own area of applicability. Generally, the high pressure gas process is applicable only with reservoir fluids which con-!ain a high concentration of inter- mediates. If the high pressure gas process is technically feasible at pressures less than 4,500 psi, it is probably more desirable economically than the slug process. The slug process has broad applicability in the shallower reservoirs and with reservoir fluids which contain a relatively low concentration of LPG and natural gasoline constituents. This paper deals with some new concepts of the high pressure gas injection process where it is proposed that flue gas can be substituted for hydrocarbon gas without sacrificing our goal of miscibility. MECHANISM Introduction Considerable effort has been devoted to study of the mechanics ot the high pressure gas injection proc-one generalization result-ing from some of these studies was that the composition of the injected gas is relatively unimportant in establishing the miscibility pressure* for a given reservoir fluid. This generalization is correct for the composition range of gases typically encountered in the field. Two such gases are a gasoline plant tail gas containing 85 per cent methane and 15 per cent ethane, and a field separator gas containing 70 per cent methane and 30 per cent heavier components. The most important factor which sets the miscibility pressure in the operation is the reservoir fluid composition, particularly the concentration of LPG-natural gasoline constituents. The injected gas is the agent by which the LPG-natural gasoline constituents are concentrated at the displacing front to create a miscible displacement. Based on these results, it appeared feasible that some inexpensive gas, such as flue gas, might be substituted for hydrocarbon gas for use in the high pressure gas process. A re-examination of the phase relations of the high pressure gas injection process should clarify the principle behind using flue gas (essentially nitrogen) as an injection gas. Three Component Diagram The phase relations of the high pressure gas injection process have been illustrated by the use of the three component diagrams.'," In Fig. 1 we have arbitrarily represented the multi-component reservoir system by three components; methane, ethane through hexane, and heptanes plus. The solid curve ABC is the phase boundary curve. It represents the locus of compositions which have fixed saturation pressure at a fixed temperature; the lower branch AB shows bubble point compositions, the upper branch BC, the dew point compositions. Point B is the coniposition of the critical mixture at this temperature and pressure. The dashed lines (tie lines) connect vapor and liquid compositions which are in equilibrium. Let us consider Reservoir Fluid D which we wish to displace in 21 miscible manner by gas injection. Let us further restrict the discussion to the case where miscibility between an injection gas and the reservoir fluid at the displacement front is developed by gas enrichment in the reservoir. For this case, any gas whose composition lies between Points C and E on the right side of the three component diagram can be used to give a miscible displacement of Reservoir Fluid D. This is true because the more mobile injected gas moves faster than the displaced oil and is in continuous contact with virgin oil at the displacement front. This leads to a continuing enrichment 01' the gas at the displacement front by evaporation of the C, - C,

By P. E. Doherty, R. S. Davis

Sub boundaries and micropores, as well as certain other imperfections, may be revealed in aluminum by the formation of pits on the surface during cooling from elevated temperatures. The pits are attributed to the condensation of vacancies from supersaturated solution. This "vacancy pit" phenomenon has been used as an etching technique for studying the structure of aluminum specimens grown from the melt. Three fundamental structures were studied: stria-tions, cells, and dendrites. Two types of striations, as well as a crosswise structure are reported. Mic-roporosity is observed to occur in the cell walls on freezing. Subboundaries between primary, secondary, and tertiary branches are observed in dendritic growth. A special case is cited in which cellular growth suppresses the formation of striations. SMALL, well-defined pits have been observed to form on the surfaces of electropolished aluminum specimens during cooling from elevated temperatures.' This phenomenon was attributed to the condensation, from supersaturated solution, of vacancies at particular points on the surface. It was shown that the amount of cooling required for the formation of pits increased exponentially with decreasing holding temperatures in a way that was consistent with the thesis that a critical supersaturation of vacancies was required for the pits to form. Pits do not form in the vicinity of certain imperfections, namely, subgrain or normal graind boundaries, phase boundaries, certain surface irregularities, and pores. The width of the pit-free region increases with decreasing cooling rate. This observation suggests that the imperfections in question are effective sinks for vacancies and that the pit-free region around them is material that is not sufficiently supersaturated with respect to vacancies to nucleate the surface pits during cooling.

Jan 1, 1962

J. L. McK. YARDLEY,* Pittsburgh, Pa. (written dlscussion ?) .-It is interesting to observe how closely Mr. Hansen agrees with other investigators to the effect that the art of electrolytic zinc has left the realm of mystery. In his introduction, lie has said practically what Thomas French said in his paper "The Future of Electrolytic Zinc. "1 The successful electrolysis of zinc from sulphate solutions has not been an easy matter, and it is only within recent years that the difficult problem of depositing high-grade zinc has been satisfactorily: accomplished on a commercial basis. The principal requisite is. that the electrolyte shall be quite free from certain impurities. The methods by which freedom from these impurities is assured are now very well understood, and with experienced superintendents there is little difficulty in obtaining a high efficiency in that part of the process. When certain underlying principles are recognized, the difficulty encountered in dealing with the filtration of the acid and slimy solutions also largely disappears, although it has been a very serious one to the uninitiated. In the dissolving of the zinc from the roasted ore, there is nothing which any competent chemical' engineer cannot undertake, and any other operations connected with the electrolytic process are either of little or no difficulty, or are common to the retort process. Mr. Hansen also agrees with R. G. Hall's statement in " Some Economic Factors in the Production of Electrolytic Zinc:"2

Jan 10, 1918

By John Gjers

Being on a visit to your great and prosperous country, and having been favored with an invitation to attend this meeting of your Institute, the author has been requested by your Secretary to give a short account of his invention of the " soaking-pit," which he has great pleasure in doing. The object of the soaking-pit is the rolling of steel ingots with their own initial heat, that is, to supply the missing link in that chain of metallurgical operations which Sir Henry Bessemer began in 1857, when he proved how it was possible to produce malleable iron or steel direct from the fluid cast-iron out of the blast-furnace, without any further direct use of fuel. The great Bessemer invention has revolutionized iron and steelmaking throughout the world; but it stopped short at producing the ingot, which, it was found, had afterwards to be heated in a furnace to enable it to be rolled or hammered; and it is only lately, twenty-five years after Mr. Bessemer's announcement, that the author of this paper has been able to show that furnacing can be dispensed with, and that it is practicable to roll a steel ingot into say a bloom, a rail, or a billet, with its own initial heat. It has no doubt suggested itself to many that there ought to be heat enough in the ingot just cast, for the purpose of rolling; and from time to time attempts have been made to utilize this heat; but such attempts always ending in failure, it became a settled opinion in the trade that it could not be done—an opinion which the author is aware that your late lamented countryman, Mr. Holley, than whom there was none more conversant with Bessemer steel-making, also entertained. But settled opinions sometimes prove to be great fallacies. As an instance, it is not many years since the opinion prevailed in the trade that steel ingots could not be rolled successfully, that is, so as to make good rails, unless they were first allowed to get quite cold, and afterwards heated. No greater boon was ever conferred on the

Jan 1, 1885

By J. Szekely, Robert J. Fisher

A formulation is Presented and solutions are given for the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its environment. The solutions were obtained by the numerical integration of the appropriate Partial differential equation and are Presented in a graphical form by Plotting a dimensionless average temperature against the Fourier number with the radiation number as a paranreter, for various initial sphere and environment temperatures. In addition to these numerical results asymptotic analytical solutions are also given. PROBLEMS involving the transient heating or cooling of droplets and particles frequently arise and are of importance in metallurgical operations. Spray refining, vacuum degassing, high-temperature gas-solid reaction systems, and pebble heaters are but few of the numerous examples that may be quoted. The practical interest in these problems from a design or operational point of view is to evaluate the change in the particle temperature with the time given its physical properties, initial temperature, and that of the environment. At the high temperatures encountered the principal mode of heat transfer between the particles and their environment is by thermal radiation; in case of vacuum degassing due to the very low thermal conductivity of the gas space the convec-tive components are negligible and radiation is the only heat transfer mechanism. Although much work has been done on transient heat conduction problems, the special class mentioned here, in which thermal radiation is specified at the bounding surface, received little attention to date. One contributory factor to this situation may be the nonlinearity of the radiation term in temperature, which in general precludes the use of analytical techniques and requires numerical or analog solution of the appropriate differential equations. In fact the only solutions of general nature that are available at present pertain to semi-infinite media and slabs.'-3 The work on which the paper reports forms part of a program aimed at the theoretical and experimental study of transient radiative heat exchange between particles and their environment. The purpose of the present paper is to develop a formulation and solutions to the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its surroundings. The solutions, obtained by the numerical integration of the appropriate differential equations, will be presented graphically, by plotting dimensionless parame- ters covering the range of variables relevant to metallurgical interests, thus affording a ready reference for design calculations. In addition to these results, approximate analytical solutions are also given which represent asymptotes, corresponding to extreme values of the variables mentioned. FORMULATION Consider a spherical particle of radius, a, initially at uniform temperature, Ti (T measured on the absolute scale), having a thermal conductivity, k, density, , specific heat, C, and thermal diffusivity, a. At time = 0 let this particle be exposed to an environment which is at a temperature T, and subsequently let there be a purely radiative heat exchange between the particle and the environment resulting in a spatially uniform heat flux at the surface. If in addition to the above we make the assumptions that the sphere is a gray body radiator, homogeneous, isotropic, and opaque, and that the physical properties are independent of temperature, conservation of heat in the sphere may be written as follows: The boundary condition contained in Eq. [3] states that the initial temperature of the sphere is considered uniform, equalling Ti, whereas Eq. [4] is readily obtained from symmetry considerations. Eq. [5] expresses the continuity of the heat flux at the surface of the sphere, or in other words the condition that the rate of heat exchange between the sur-

Jan 1, 1969

By Joseph R. Crump, Francois Ville, Frank M. Tiller

Several simplifications have been accepted in filtration theory during the past fifty years in an effort to avoid apparently intractable mathematical problems. In effect, these simplifications ignored the variation in average cake porosity and average filtration resistance with variation in pressure drop or with time. This study examines the traditional approach and shows that, in many cases, it cannot give correct design guidance. Using a set of dimensionless parameters because of the large number of significant variables, a revised theory is developed which does not require that porosity and resistance values be set constant. Graphs developed in the traditional approach (e.g., dt/dv versus v or t/v versus V) have substantial curvature near the ordinate; but this curvature is frequently ignored in theory and is easily missed in experiments. The revised theory allows more accurate design calculations, especially for compressible cakes.

Jan 1, 1980