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By A. Alonso, J. Daubenspeck

In the nickel extraction process at Nicaro, Cuba, dried and ground nickel bearing laterites are reduced at 1300-1400F in multiple-hearth furnaces. Nickel is leached from the reduced ore by aeration in an aqueous solution of ammonium carbonate. Nickel carbonate is precipitated from the liquor and calcined to yield nickel oxide. The following are the more important modifications of the Nicaro process since plant rehabilitation and expansion. Ten percent increase in tonnage was achieved without decreasing the fineness of the ore by minor mechanical modifications of the grinding plant. Another five percent increase in tonnage was attained by intentionally overloading the ore prepration and leaching circuits in an effort to control cobalt extraction. Modifications at the sintering plant allowed it to handle the entire output of the expanded plant. A fifty percent increase in leach liquor cooling facilities alone provided an increase in nickel production of five percent. Stronger fresh leach liquor for increased nickel washing efficiency was obtained through improved distribution of water to the ammonia absorption towers. Advantage was taken of the reduced calcine's capability to precipitate cobalt, and modifications in the leach liquor circulation provided controlled cobalt solubility with minimum harm to nickel extraction. Several process changes at the drying plant brought about a ten percent reduction in the fuel oil consumption at this pint. Controlled air addition to the reduction furnaces' upper hearths burned formerly wasted combustibles thereby reducing oil consumption by twenty percent. The nickel extraction process successfully emplayed on the extensive but lowgrade lateritic ores of Eastern Cuba at the U. S. Government owned Nicaro plant, has been previously described in various publications. The large mine and plant operated by the Nickel Processing Corporation, located on the northeastern shore of Oriente Province, have been recently expanded to a yearly capacity of about 50 million pounds of nickel. Essentially, the operation involves open pit mining of a limonite-serpentine ore mixture containing 1.3 to 1.4 percent nickel and 34 to 38 percent iron. The comparatively lumpy, wet (25 to 30 percent moisture) ore is first dried and ground prior to chemical treatment, to which the entire 7,000 tons per day feed must be subjected. In the initial chemical action the dried and ground ore is reduced with carbon manoxide and hydrogen at 1300-1400° in multiple-hearth furnaces. The resulting metallic nickel is selectively leached from the reduced calcine by aeration in an

Jan 1, 1961

By Henry S. Washington

I. INTRODUCTION. DURING the last twenty years or so the chemical investigation of rocks has made great advances, and it is now generally recognized that a knowledge of the chemical composition is as essential as that of the texture or mineral composition-if not more so-for the proper classification of rocks and study of their origin and relationships. Rock-analyses have vastly increased in numbers and, what is of greater importance, in quality. New and improved methods permit of greater accuracy than was possible in the early days, and the list of chemical constituents frequently determined has risen from the seven or eight of the greater part of the nineteenth century to twenty or more. Indeed, rock-analyses with determinations of so many constituents are now commonly made by the chemists of the United States and Australia, while in Germany, Great Britain, France, and Italy the rarer constituents are determined more frequently than formerly. As a consequence of this modern, accurate work, it has been discovered that some elements which were formerly supposed to be rare are of wide-spread occurrence and are often present in considerable amount. The fact is further being developed that the elements tend to show certain relations of occurrence or abundance in connection with each other. This is a fact which is applicable to the rarer elements, and which also finds a broad geological and petrological expression in the recognition of petrographic provinces. We are beginning to obtain some definite, though as yet rudimentary, knowledge of the distribution of the elements among igneous rocks. Some of the results along these lines obtained by study of the vast accumulation of analytical data now available are well known to petrologists, while others do not seem to be so gener-

Sep 1, 1908

By A. Timur

Fluid flow properties of porous media have long been of interest in such varied disciplines as geology, geophysics, soil mechanics, and chemical, civil, and mechanical engineering. This interest has resulted in numerous models of porous media that have been proposed, tested, and found to be useful under, at best, only special circumstances. A critical review of most of these models is given by Scheidegger. 1 The application of each new tool to the study of porous media has helped to test some of the existing theories and to form new ideas based on the new parameters being measured. In the application of nuclear magnetic resonance (NMR) techniques to the study of the properties of fluids in porous media, the theoretical studies of Korringa et al.2 resulted in a model for the relaxation of spin polarization of protons in a hydrogenous fluid in a pore of a solid. Seevers3,4 verified this model, established a method for measuring the surface-to-volume-ratio distribution in a porous medium, and proposed a technique for determining specific permeability in sandstones. In the present investigation, the uses of NMR methods are extended and a simple model of porous media is developed from an analysis of pulsed NMR measurements. In this model, the pore spaces of a porous medium are divided into three groups on the basis of their surface-to-volume ratios. To evaluate predictions of the NMR model, laboratory measurements of spin-lattice relaxation time, porosity, permeability, and residual (irreducible) water saturation were conducted on more than 150 sandstone samples obtained from four oil fields in North America. Applications are discussed for estimating the volume of movable fluid, ?p, and the specific permeability, k, of sandstone samples. The former parameter, which can be considered as producible porosity, is expressed by ?p = [1 -- (Swr/100)]? , .... (1) where + is porosity in percent of bulk volume and Swr is the residual (irreducible) water saturation in percent of pore volume at a capillary pressure of 50 Psi. Fast, nondestructive laboratory methods are described for determining porosity, movable fluid, and permeability of sandstone samples from measurements with a pulsed NMR (spin-echo) apparatus. Procedures are given for adapting these methods to samples of irregular shape and small size. Theory General In the Korringa, Seevers, and Torrey2 (KST) model the observed decrease in the spin-lattice relaxation time, T1, of protons of a hydrogenous liquid contained in the pore spaces of a porous solid is attributed to an increase in the correlation time for the random motion of the water molecules and to the presence of paramagnetic centers at the liquid-solid interface. This KST model predicts the observed relaxation time of a hydrogenous liquid in a pore of a solid through

Jan 1, 1970

By Richard E. Chism

Jan 1, 1902

By Philip B. Bucky

CONTENTS [PACEPACE r. What Is a Rock Burst?2 4. How Can Rock Bursts Be Predicted? . 35 Jack Spalding2Jack Spalding35 A. F. Robertson 2, 5A. F. Robertson35 W. R. Crane 2A. B. Yates and P. J. Shenon. . . . 35 G. S. Rice 2W. R. Crane 35 P. J. Shenon 2G. S. Rice 35 L. C. Graton 2B. F. Tillson 36 2. What Are the Causes of Rock Bursts? 6 5. How Can Rock Bursts Be Controlled?. 36 Jack Spalding6Jack Spalding36 A. B. Yates and P. J. Shenon . 7, 12, 29A. F. Robertson 36 A. F. Robertson 12, 28W. R. Crane37 W. R. Crane 15A. B. Yates and P. J. Shenon. . . . 37 G. S. Rice 15Oscar Weiss38 Oscar Weiss15G. S. Rice37, 42 P. B. Bucky21R. D. Hoffman42, 43 P. H. Bird 21, 26, 28R. D. Hall 42 M. K. Hubbert26R. H. Cromwell42 G. Wheeler 26. J. Shenon 42 B. F. Tillson26, 28P. B. Bucky42, 44 T. T. Read 27B. F. Tillson 42, 44 A. B. Yates 43, 44 3. How Can Rock Bursts Be Prevented? . 30P. H. Bird 43 Jack Spalding. . . . • . • • • • . 306. General Discussion . A. B. Yates and P. J. Shenon. . . . 31Jack Spalding44 A. F. Robertson32R. D. Parker49 W. R. Crane 35C. Baring Horwood 51 G. S. Rice 35P. B. Bucky 52] FOREWORD THIS symposium brings together points of view, experiences and ideas on rock bursts from a goodly portion of the globe. Some conceptions, particularly those regarding the necessity of depth, have been fairly well shattered, as we find that they are present in the water tunnels of New York, on the surface at marble quarries in Vermont, and in the coal mines of the United States, as well as in the deep mines of the South African and Kolar gold fields, and in the nickel, copper and gold mines of Canada. Their occurrence under such a variety of conditions is, therefore, a challenge,

Jan 1, 1942

By Lawrence Addicks

T HIS has been a most momentous year in the annals of the Institute. We have been in the midst of a situation which, were it not for the convulsions of social unrest with which life is surrounded on every side, would have attracted the attention of the world at large. I do not refer to the desperate campaign for new members. That has gone on much as usual except that, this being leap year, the annual proposal to the M. & M. Society has been omitted. Nor do I refer to the desperate situation which we found in other directions, the spread of Bolshevism, the burning of the Engineers' Club, the fact that the selling of copper appears to have become one of the lost arts. No, I speak of the great question which has to be. settled once and for all, as to whether this great Institute should adopt simplified spelling. The whole trouble started in the ranks of the California Hysterical Society. It appears, while most of the San Francisco members can read and write, several of them cannot spell. It also appears that the Secretary, in editing the Transactions, has perhaps made just a little bit too much of a point of employing the correct Stoughton idiom. At any rate, the rebels filed an amendment to the constitution, and the stage was set for civil war, with perhaps more stress on war than on civil.

Jan 1, 1920

By W. A. Tiller, J. D. Harrison

HOT pressing of powder particles has gained importance recently, since it affords a method in which high densities are rapidly attained. In a recent study on hot pressing of alumina powders, Mangsen, Lam-bertson, and Best1 have shown within the limits of their experiment, the validity the rate equation for densification in hot pressing, originally proposed by Murray, Livey, and Williams.2 i.e., where D = fraction of theoretical density, t = time, P = pressure and 77 is the viscosity, all in appropriate units. This equation was derived from earlier work of Shuttleworth and Mackenzie3 which is based on the closing of spherical pores under the action of surface tension. The integrated form of this equation yields a straight-line relation between log (1 - D) and t. Such conditions were found by Felten4 to be true only after extended periods of pressing. In an endeavor to quantitatively evaluate the exactitude of this equation in the initial sintering stage, i.e., prior to sealing of the pores, spherical anti-

Jan 1, 1962

By J. H. Bain, D. C. Haigh, L. C. Parsons

Jan 1, 1964

Q: It is May 1961 at Bill Wrather's Washington house. Bill, think back to your first job after college. Wrather: Perhaps I ought to go back a little bit further than my first job. I entered the University of Chicago with the idea of studying law. My intention was to take a 4-yr liberal arts course and superimpose a law degree on that. But during my undergraduate work I fell under the influence of R. D. Salsbury. He decided I had some talent as a geologist and influenced me to take a geological course. Nevertheless, I did not give up the idea of law. While in school I took a spell of typhoid fever and almost died. The doctor recommended outdoor exercise, so a geological job seemed logical. W. H. Emmons was a graduate student in the University and he interceded with Dr. Hayes of the USGS. I went on the payroll as assistant packer at $60 a month. I had one of the most glorious summers I ever spent in my life. That fall and the following year I took law courses and became thoroughly convinced that I was cut out for a geologist rather than a lawyer. I finished up my law work in 1908 while waiting for a job with Bill Emmons, who was doing a careful study of Goldfield and Tonopah.

Jan 4, 1964

By Thomas Leonard Watson

Jan 1, 1906

By H. H. Bein

Most western industrial sands are feldspathic and contain feldspars in variahle amounts. A few deposits will show alumina contents of less than one per cent while others will contain over twelve per cent alumina. Some industries are not especially concerned with the amount of contained feldspar but are interested only in color and in size gradations. Other industries, however, are very much interested in alumina content and set up quite rigid specifications as to this content. Several western plants are beneficiating crude sands both to reduce the iron content and to control the feldspar content. At present, most of these plants are using flotation processes for both controls although a few plants do use magnetic separators for the reduction of iron content. Some work has also been done with electrostatic separators for the feldspar-quartz splits. The Sand Division of Del Monte Properties Company, Pebble Beach, California, has been operating a flotation plant for iron removal and the separation of quartz and feldspar since 1950. As mentioned before, control of alumina, especially in the quartz product, is very important. Some users require an alumina content of less than two per cent and others will demand a product of less than one per cent Al2,O3,. The standard Quinolate method for determining alumina is lengthy and time consuming. The HF —H2SO4 evaporation step is especially critical and, if forced, spattering is apt to occur with a resulting loss of sample. Standard procedure is to evaporate to dry ness overnight at a low temperature. Even with forcing under optimum conditions the procerlnre will take two or three hours to complete. A new method has been developed which allows an alumina determination to be made, in 10 or 15 minutes, on a sample of the quartz product as it is being produced. This pocedure, although simply an approximation, has been most helpful in showing whether or not the product being formed is meeting specifications. This procedure has also allowed a great reduction in samples formerly taken and analysed by the orthodox method. Whether a sample assays 1.75% A12O3, or 1.95% .41,0, is not so important as the fact that it is below the allowable maximum of 2.00%. Similar thinking would apply to products required to contain less than 1.00% A1,0,. The step by step procedures for the method are as follows: 1. Collect sample, drain or filter, and dry. 2. Split sample through standard Jones sample cutter to quarter or eighth sample, depending on size of original sample taken, then split down to about 5 grams through Sepor micro-splitter. 3. Screen through 50 mesh sieve (U.S. Series) and reject undersize. 4. Weigh out 2 grams and place in platinum crucible. 5. Etch with 3-5 mls 38.40% HF for 1 minute at room temp. 6. Decant and wash. 7. Stain for two minutes in same crucible with a 1% water solution of Nigrosene dye. 8. Decant and wash well. 9. Dry.

Jan 1, 1961

By Raymond E. Davis

LET'S imagine we are at the Grand L Coulee Dam, where daily 15,000 barrels of low-heat Portland cement and 27,000 tons of processed aggregate in various sizes are mixed to produce 30,000 tons of concrete. Inspect the autographic records which show for each 4-cu-yd. mixer batch of concrete the weights of its constituent materials including its several sizes of aggregate, cement, and water, and which also show the period of mixing and the consistency of the mix. Watch the inspectors sample and test the aggregate for gradation and moisture content of sand, and sample the concrete for homogeneity. Watch the huge buckets deposit the concrete in the forms. It looks too dry to handle, but the concrete vibrators make it melt away. Just enough vibration fully to com- pact the mass, but not enough to produce segregation of the materials; the inspector says when. See the sprinkler system covering all hardening concrete with a spray so that it may not thirst for water. Watch the cleaning of the top of an old lift preparatory to placing a new lift; the sand blasting; the blow-down; the mop-up; the minute inspection.

Jan 1, 1939

By TENNEY C. DeSOLLAR

TRADITION tells us that the earliest use of Alabama iron was to make shoes for the horses of General Andrew Jackson and his men during the first part of the nineteenth century. The first recorded incident in the making of iron was the request of U. S. Indian Agent Benjamin Hawkins "that a crew of blacksmiths be sent to the Creek Nation in the lower Mississippi territory." These frontiersmen made up the first body of pioneer iron makers in the territory. The first known blast furnace was built by Joseph Heslip in 1818 at Russellville, named after Major William Russell, who was General Jackson's chief of scouts. The Tannehill furnace was built in 1830 in what is now Tuscaloosa County and its ruins, as shown above, can be seen today.

Jan 1, 1937

By M. J. R. Morris

THE year 1939 has seen the iron and steel industry driving for efficiency with unabated zeal. "Efficiency" is here used in the sense of enabling the customer to do more with less, either supplying him with more economically priced steels or with higher priced steels that will do a job more economically. The plain carbon steels have been improved tremendously in quality be- cause of recent control tests. All steel companies have been urged to hold to .closer chemical control, closer standards, soundness, and more control on grain size, and now attention is being directed to closer control of hardening properties. Better control of open- hearth operations undoubtedly will result in an increase in the application of special carbon steel. Further, with a better understanding of quenching, the present trend to study the quenching of this class of steels will be ex- tended. These steels will then be used for purposes to which they are best suited. Utilization of special carbon bars and large shapes seems to be developing less slowly than special car- bon in the form of strip. There are many reasons for this and the future development of this trend will be important. Continued development of the manufacture of parts from strip and sheet to replace forgings, and of formed; structural members such as channels or welded pipe, is notable. Special carbon sheets with nonaging properties have been produced during the year; they maintain a higher degree of ductility over a longer time and are less sensitive to the changes which took place in the former product when stocked.

Jan 1, 1940

By Sam Tour

WHAT is a die-casting and what is the die-casting industry? From the literal translation of the words "die" and "casting"' one concludes that a die-casting is a casting made in a die. The casting may be of any metal or alloy or, for that matter, may be of some nonmetallic material capable of being cast, such as plaster of paris or glass. The die may be of any material that will take successive casts so it need not necessarily be metallic in nature. The term "die-casting," therefore, is indeed broad, though in practical usage it has come to mean the casting of metals and their alloys in metallic molds or dies. Even this limitation of the term leaves -a broad field, for castings may be made in a number of different ways. For example, the molten metal may be allowed to run into the die by gravity it may be sucked into the cavity of the die, it may be forced to take the contour of the cavity in the die by centrifiugal force, or it may be forced into the cavity under hydrostatic pressure. In England, castings made by practically all of these

Jan 1, 1935

By H. R. Cooper

Beginning from the point of view that process control of ore flotation can be approached by on-line analysis of processing behavior, an equation was developed which has characteristics useful for a multi-variable feedback loop. The application of this equation to optimizing control with a data acquisition system will be discussed in Part 11. OBJECTIVE OF CONTROL The purpose of developing a feedback method for concentrator control is to provide a means for determining ore processing behavior in order that data describing the ore can be used to make appropriate changes in control conditions while the ore continues to flow through the flotation circuit. In absence of simple linear relationships between pairs of variables in the flotation process, attention is directed to the need for a generalized relationship which possibly would incorporate all pertinent variables. It would be possible to apply such an equation to the control of variables in a concentrator in real time according to operational requirements as ore gradually changes in quality and processing behavior. To meet this objective, it is necessary to define relationships describing flotation performance in terms of performance variables capable of being measured on-line, either with on-line instruments and analyzers or with manual methods lending themselves to quick determination of meaningful information. Relationships derived to meet this objective form a model for the flotation process. The evaluation of flotation parameters of the ore and the execution of control on the basis of the derived information while the ore is continuing through the process would constitute a feedback control system. Data for the following control and performance variables can be made available: 1) ore feed rate, 2) collector addition rate, 3) lime addition rate, 4) pulp density, 5) assay or multiple assays in feed, tails, or concentrate sufficient for material balancing, 6) particle size distribution in flotation feed, 7) froth height, and 8) frother addition rate. Other process variables, such as flotation air input and mechanical agitation intensity, are usually not considered as control variables and were not taken into account in this analysis. Other data, such as that describing the ore, would be useful for concentrator process control. However, information of this type (such as ore hardness, grain size of the mineral, chemical species of the mineral, and ore surface properties) being not presently measurable in the on-line sense, has the effect of causing disturbances in the system which can be detected only indirectly. The process control system being sought must recognize disturbances by their effect on measured performance followed by determining control changes to compensate for them in meeting the objectives of improved performance (perhaps higher throughput, maximum return, etc.). A suitable model for the process having capability of recognizing the effects of ore disturbances should provide the means for introducing proper compensation through control changes. This would be done by processing on-line data with the model to calculate coefficients reflecting ore characteristics. This procedure can only be applied in a typical flotation system when on-line data can be processed at faster rates than the usual rate at which the ore in flotation feed takes on significantly different characteristics. For example, material balance data can be accumulated in approximately 5-min intervals using on-line X-ray fluorescence analysis. The flotation system time constant might be 15 min including grinding. Ore changes having time constants longer than 1 hr could be accommodated using on-line feedback control by this procedure. FORM OF A FLOTATION MODEL A suitable form for mathematical expression of the flotation process is an equation involving rates, when each of the components entering into the separation can be treated independently by a rate equation. A first-order, kinetic rate equation can be written on

Jan 1, 1967

By Henry Rawdon

THE following note describing the behavior of copper under rather unusual conditions is offered here for its suggestiveness rather than as a complete study of the question. The examinations described were made because of a request for information concerning the embrittlement of copper when heated in a molten salt bath (sodium chloride) for the purpose of cleaning it, as well as for softening it. It is well known that metals may be rendered very brittle by electrolytic action, in aqueous solutions, in all probability by the action of nascent hydrogen, and it was suspected that perhaps the embrittlement of the copper by means of the molten salt was produced in a somewhat similar manner. It was found that the copper was in contact with iron (or steel) while immersed in the molten salt, through the occasional use of an iron stirring rod, iron forceps for handling the pieces, and an iron pot for containing the fused salt. In the electrochemical potential series iron and copper stand some distance apart, copper being electronegative to the iron. Assuming that the two metals bear a similar relation to each other, when immersed in a bath of molten salt, as they do in an aqueous solution, they would be expected to form a galvanic couple, the copper being the cathode. By this means the copper might be embrittled, as often happens in aqueous solutions, by the action of the liberated hydrogen. In this case, however, the embrittlement must be attributed to some other agent than hydrogen. To demonstrate how copper may be embrittled under these conditions, two small rods, one of copper and the other of mild steel, approximately 3/8 in. (9.5 mm.) in diameter, were immersed in a bath of sodium chloride that had been heated somewhat above its fusion point (melting point of sodium chloride is 819° C.) and an electromotive force of approximately 6 volts from a storage battery was impressed upon the system. The copper was made the cathode and the action was continued for

Jan 2, 1920

By George F. Becker

(San Francisco Meeting, October, 1911.) A MERE record of Emmons's professional career would very inadequately represent the man. That he was eminent we know, and our successors will realize in due time; but they must depend upon us for knowledge of a singularly wholesome, modest, unselfish personality, and of a character that did honor to a profession in which trustworthiness is indispensable: Those members of the Institute who met Emmons are his friends, and I never knew one of these who was not the better for that friendship. Emmons was born in Boston, Mar. 29, 1841, the son- of Nathaniel H. and Elizabeth (Wales) Emmons, and was named Samuel Franklin after an ancestor who was of the same family as Benjamin Franklin. He took the degree of Bachelor of Arts at Harvard in 1861, and soon afterwards went abroad to complete his education. From 1862 to 1864 he attended the courses at the École Impériale des Mines at Paris, lie e Beaumont and Daubrée being among his professors. The year 1864-1865 he spent at Freiberg under Cotta and other famous teachers; after which he spent another year in traveling through Europe. Like many other renowned geologists, he approached his ultimate profession from its economic side, and was thus from the first imbued with a sense of high responsibility in the promulgation of scientific opinions or conclusions. With hypotheses which were interesting merely because. they were ingenious or even plausible, he would have nothing to do. In 1867 he joined the Geological Exploration of the Fortieth Parallel at its organization under Clarence King, serving at first as a volunteer, but soon receiving a regular appointment. This expedition was the first one of purely geological character sent out by the United States Government. As Emmons has shown in his admirable presidential address on " The Geology of Government Explorations," its work was founded on a com-

Sep 1, 1911

By R. G. Vardiman, M. R. Achter

Observations of dislocation structure in niobium are presented using two techniques. Triangular pits developed by electroetching are confined to orientations in the stereographic triangle between the (111) pole and planes of the (1ll) zone and require the presence of carbon. Some unusual electroetching phenomena at other orientations are noted. A chemical etch of dislocations decorated by the addition of carbon to 50 ppm reveals the complete dislocation line structure in a surface layer up to 30 p deep, with a resolution of less than 1 p. This effect is independent of surface orientation. The structure of subboundary nets may be resolved for misorientations up to about 1'. Dislocation structures found in strain anneal grown crystals, such as helices, prismatic loops, and high-density areas, are observed. The measurement of dislocation density is discussed and values obtained in different ways are compared. IN the course of some work on the response of refractory metals to thermal-mechanical treatments, it was desired to examine the defect structure of relatively low dislocation density crystals of niobium in bulk form. Surface and bulk methods for the observation of dislocations have been reviewed by ~melinckx,' and include etch pitting, decoration, and various X-ray techniques. The dislocation line structure has been developed by decoration in a few metals, although observations were limited to certain orientations, or by the coarseness and nonselectivity of the precipitate. The most commonly used technique is etch pitting. In niobium, etch pits have been developed chemically'0," in material of high impurity content and electrolyti-cally'' in relatively pure material. In this paper, etch pits developed electrolytically, and the dislocation line structure of a surface layer developed by decoration and chemical etching, are examined, and observations are presented from both techniques. EXPERIMENTAL METHODS Our starting material was electron-beam-melted niobium, swaged to 4 or -in.-diam rod. Chemical analysis is given in Table I. Single crystals were grown by a strain anneal technique using 1 to 2.5 pct of strain and growth temperatures of 1700" to 2300"~.'~ Some crystals grown by zone melting were also examined. The desired surface orientation was exposed either by spark machining or by sectioning with a cut-off wheel and prepared for etching by electro-polishing.

Jan 1, 1969

By K. Leutwyler

The key to realistic casing stress analysis in thermal recovery installations is accurate knowledge of the temperatures involved. Much information leading to prediction of heat losses from tubing string to wellbore has been published. This .same information permits calculation of casing temperature under certain conditions. This paper reviews the basis for most of the published work, the line source solution to the diflusivity equation and examines some of its application criteria in the light of unsteady-state conditions. An alternate finite differences method is presented for correlation, and experimental data pertaining to the heat transfer mechanism in the annulus is reported. In the light of the information presented in the paper, it appears that the assumption of a line source for the tubing-wellbore system is valid even for reasonably short periods of heat flow, .such as "steam soak" operations. The empirically modified equation presented earlier matches computer derived results of the finite differences approach lor periods as short as 50 hours. Previously predicted cas ing temperatures and the associated stress levels are thus verified based on these correlative computations and the reported experimental information. Fall out from the computer output resulting in some studies of the influence of insulating cement properties on casing temperature, and experimentally studied effects of nitrogen placed in the annulus at various pressures., are described. INTRODUCTION Generally speaking, predictions of average casing temperatures have been based on an idealized model involving a centralized tubing string at uniform constant temperature radiating energy towards the casing under steady-state conditions.'. ' Heat is transferred away from the casing to the formation by unsteady-state conduction across thermal barriers consisting of cement and the mud sheath. Heat balances written on the casing permit prediction of instantaneous casing temperatures. During early periods of injection, casing temperature varies appreciably as a function of time; however, for long injection times this variation decays as heat flow from the wellbore to the formation stabilizes, and it becomes virtually negligible as conditions surrounding the wellbore become quasi-steady-state (Fig. 1). Carslaw and Jaeger -escribe a solution to the diffusivity equation for a line source (Fig. 2). A constant supply of heat is introduced into the medium from the line placed into the origin of the x-y coordinate system and parallel to the z-axis. Heat spreads outward in the infinite cylindrical solid and the temperature increase on a line going through point (x, y) parallel to the z-axis at a distance r can be predicted by: The following criterion must be considered: the Carslaw and Jaeger equation is obtained on the basis of a large

Jan 1, 1967