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By M. R. Annis, P. H. Monaghan

The control of mud properties affords two practical means of tnitigating pipe sticking caused by differential pressure: (I) teducing weight and, therefore, differential pressure; and (2) reducing the friction berween the pipe and mud cake. This paper describes investigation of the second of these—the friction between the pipe and the mud cake. Friction between a steel plate and a mud cake, held in contact by a differential pressure, was measured in the laboratory while maintaining a constant area of contact. Experiments were performed to determine how this friction varied with changes in mud composition and with changes in experimental conditions such as the differential pressure, time of contact of plate and mud cake, and filter-cake thickness. It was found that the apparent coefficient of friction, or the "sticking" coeficient, was not a constant; instead, it increased with increased time of contact between plate and mud cake, and with increased barite content of the Mud. The sticking coeficient varied from about 0.05 to 0.2 afer 20 , and eventually reached values of 0.1 to 0.3 after two Hours. Quehracho or ferrochrome lignosulfonate reduced the sticking coefficient at short .set times but did not reduce the maximum value. Carboxy-~t~etlz~lcellulose had no effect on the sticking coeficient. Emulsification of oil in the mud reduced the sticking coefficient. Some oils reduced the sticking coefficient to about one-third of its Value in the oil- free base mud, while other oils reduced it only slightly. Addition of certain surfactants with the oils further reduced the sticking coefficient. Spotting a clean fluid over the stuck plate caused a reduction in sticking coefficient only if the differential presslrrr was reduced, either temporarily or- permanently. INTRODUCTION Often during drilling operations the drill string becomes stuck and cannot be raised, lowered, or rotated. This condition can be brought about by a number of causes, such as sloughing of the hole wall, settling of large particles carried by the mud, accumulation of mud filter cake during long stoppage of circulation and, finally, sticking by pressure of the mud column holding the pipe against the filter cake on the hole wall. This paper is concerned with the last-mentioned phenomenon. Helmick 2nd Longley' in 1957 suggested that a pressure differential from the wellbore to a permeable formation covered with mud cake could hold the drill pipe against the borehole wall with great force. This situation occurs when a portion of the drill string rests against the wall of the borehole, imbedding itself in the filter cake. The area of the drill pipe in contact with filter cake is then sealed from the full hydrostatic pressure of the mud column. The pressure difference between the mud-column pressure and the formation pressure acts on the area of drill pipe in contact with the filter cake to hold the drill pipe against the wall of the borehole. Helmick and Longley also presented laboratory cxperiments which showed that the force required to move steel across a mud cake increased with increasing differential pressure and with the time the stcel and mud cake had been In cuntact. Their data indicated that replacing the bulk mud with oil reduced the force required for movement. Field evidence was rcported that spotting oil over the stuck interval sometimes freed the pipe. Outmans- in 1958 presented a theoretical paper which described the sticking mechanism and explained the increase of sticking force with time with equations derived from consolidation theory. Since publication of these papers, there has been interest in the differential pressure sticking of drill strings, and several mud additives to reduce sticking or special equipment to free stuck pipe have been proposed."" Haden and Welch" have recently reported laboratory evidence showing that the composition of the filter cake influences the force necessary to move steel on the filter cake. There seems no doubt that differential pressure sticking is a real phenomenon and that its severity depends on the magnitude of the pressure differential across the mud cake, the area of contact and the friction between pipe and mud cake. The mud weight required to control a well is determined by the highest formation pressure in the well: hence, the magnitude of the differential pressure opposite normal or subnormal pressure formations cannot bc reduced. The area of contact may be minimized in several ways (control of filter-cake thickness, use of stabilizers and spirally grooved drill collars), but there arc practical limitations which prevent reduction of contact area from becoming a complete solution of the problem. However. the mud composition might bc altered to reduce the friction between pipe and mud cake. This paper presents quantitative measurements of the friction between steel and mud filter cake and shows how the friction varies with mud composition for given experimental conditions.

By Malcolm J. McPherson, Michael Hood

Sunnyside Mines, owned and operated by the Kaiser Steel Corporation, are situated near the city of Price, Utah. The complex comprises three adjacent mines, named simply Nos. 1, 2 and 3, all connected underground. Two seams, the upper and lower Sunnyside have been worked. These dip at about 10 percent to the north-east. The surface cover is variable due to the mountainous nature of the topography. The Sunnyside upper seam varies from 5 1/2 ft (1.7m) to 9 ft (2.7m) In thickness whilst the lower seam remains at about 6ft (1.8m). The separation between the two seams has ranged from 7 to 45 ft over the mined area (2 to 14m). Longwall mining has been practiced at Sunnyside for over 20 years due to difficulties of roof control encountered when using the roan and pillar system. Number 3 mine is bounded on the north and south sides by mines Number 1 and 2 respectively. Whilst current production is concentrated into Number 1 mine, much of the future of the complex lies in the further development of deeper reserves in Number 3 mine. Workings in this latter mine were curtailed in 1978 due to difficulties in ventilation. Present developments are ventilated partially from the neighboring Number 2 mine where no workings are in progress. The layout of Number 3 mine is illustrated on the schematic Figure 1. Trunk airways extend down dip from the surface at No. 2 Canyon and the Water Canyon for a distance of some 9,600 ft. (2930m). The area between the two sets of trunk airways has been worked extensively in both seams as have the corresponding reserves on either side in the connected adjacent mines. At the present time exhausting fans are sited at the top of a shallow shaft in No. 2 Canyon and an 8 ft (2.4m) diameter shaft sunk to a depth of 1013 ft (310m) closer to the current developments (Figure 1). The current airflow system, even with an additional 116,000 cfm (55m3/s) entering from No. 2 Mine, is adequate only for the development work now in progress but will be unable to support new longwall faces further downdip. The basic ventilation problem of this mine may be stated quite simply. In a situation where all intake and return airways pass through extensive old workings, a ventilation system design was required that would be effective, efficient and economic for the foreseeable future of the mine. ORGANIZATION OF THE PLANNING PROCEDURE The procedure followed during the study is illustrated on Figure 2. Initial ventilation surveys established the current state of the airflow system and provided the necessary data for setting up a Basic Network File in a computer store. The data in this file was a mathematical model of the ventilation system of the mine. The basic network was analysed by a ventilation network analysis program in order to correlate the measured and computed airflows and to establish the basic network as a true representation of the mine as it stood at the time of the surveys. The network model could then be extended to simulate the future development of the mine and alternative ventilation designs investigated. The remaining sections of the paper outline the work involved in each of these main phases of the planning procedure. VENTILATION SURVEYS Conduct of Surveys Two types of measurements were conducted simultaneously throughout the air-carrying routes of the mine: (i) Airflow measurements were made by anemometer traverse or smoke tube at 221 selected stations. Anemometer traverses were repeated at each station until at least three gave results to within 5 per cent. (ii) Pressure drop measurements were made across ventilation doors, regulators and, wherever possible, across stoppings. Additionally, frictional pressure drops were measured along airways where such pressure drops were significant (above 0.01 inches of water gauge or 2.5 Pa over a 100m distance). The trailing hose method was used to determine these frictional pressure drops. This involved laying out 100m of abrasive resistant plastic tubing (3 mm internal diameter) with a 4 ft. pitot-static tube facing into the airflow at either end and a low range pressure gauge connected into the line. The trailing hose method was preferred to the alternative barometer technique for this study because of (a) the relative ease of access between measuring points and (b) the greater accuracy within individual airways. The anemometers used were Davis Biram Type A/2-3" (30 to 5,000 ft/min) and Airflow Developments AM-5000 digital (50 to 5,000 ft/min). The pressure gauges employed were Dwyer magnehelic instruments. These were preferred to liquid in glass manometers because of their portability and dependability under adverse mining conditions. A checklist of the equipment used in the survey is given in Appendix 1. The instruments were calibrated before and after the surveys in the mine ventilation laboratory at the University of California, Berkeley. The survey occupied two teams, each of three men, for ten working days. The work consisted

Jan 1, 1982

By H. W. Knott, M. H. Mueller

The crystal structures of Ti2Cu, Ti2Ni, Ti4Ni2O, and Ti4Cu20 have been determined using powder specimens examined by X-ray and neutron diffraction. Lattice constants have been determined for all four phases using X-ray powder diffraction films. Atom positional parameters of all four phases have been determined from observed neutron intensities. X-ray diffraction calculated intensity data have been presented also for the phase Ti2Cu to point out the particular suitability of neutron diffraction in this case. Interatomic distances have been determined using the positional parameters obtained from neutron diffraction. ALTHOUGH some investigations of the crystal structures have been made of these four compounds previously,'-13 it was the purpose of the present investigation to expand the previous work in order to locate the various atoms, determine their coordinates, and to confirm or to correct some of the previous work. It was convenient to group these four compounds together since they are related chemicallv and/or structurally. The compound Ti2Cu is tetragonil; and Ti2Ni, Ti4Ni2O, and Ti4CU2O are all large fees of the same space group. Ti2Cu has been previously reported as a fee phase by Laves and Wallbaum;1 and Rostoker2 which was possibly the oxide phase, Ti4Cu20. Joukainen, Grant, and Floe;3 and Trzebiatowski, Berak, and Ramotow-ski4 have also reported a phase of this composition. karlsson5 has reported a small fct phase of the composition Ti3Cu which may be the presently discussed Ti2Cu phase. More recently Ence and Margolin6 have reported a small fct phase for Ti2Cu and the present authors7 together with Nevitt8 have briefly reported it to be a bet related to the fct with a co three times the length of the co of the fct and have also reported that this phase has a very limited composition. Further refinements will be reported which have varied some of the parameters of this bct structure slightly. Ti2Ni has been reported as a fee phase by Laves and wallbaum;1 Duwez and taylor;9 Rostoker;2 Poole and Hume-Rothery;10 and Yurko, Barton, and parr.11 In a later paper Yurko, Barton, and parr12 have given the complete structure of this phase based on an X-ray diffraction study which was independently confirmed with neutron diffraction by Mueller and knott.7 Additional crystal structure information will be given. Ti4Ti2O, Ti4Cu2O, and a number of other compounds including Ti4Fe2O have been reported as fcc phases by Rostoker,2 and more recently Nevitt13 has confirmed the Ti4Ti2O phase. Rostoker,2 however has reported diffraction lines for Ti4Fe2O which do not have all odd or all even indices. These lines, therefore, cannot be observed if this compound has a fee structure. This same error has crept into the diffraction results reported for TiNi2O and Ti4Cu20 in the ASTM powder data which has been credited from Rostoker's data. Complete crystal structures of these two phases will be presented. Although all four of these structures have large unit cells and hence do not lend themselves for completely resolved neutron powder patterns, a sufficient number of individual reflections was observed for solving the structure. They also serve as good examples of some of the advantages to be gained by using both neutron and X-ray diffraction techniques. EXPERIMENTAL PROCEDURE All of the alloys were prepared by arc melting. The starting metals had the following purity: Cu 99.999 pct, Ni 99.83 pct, and Ti 99.92 pct. Oxygen was introduced into the two oxide phases as chemically pure TiO2, with the remainder of the titanium coming from the above mentioned metal. All of the sample buttons were annealed in evacuated Vycor tubes, the two binary phases for 5 days at 700°C and the two oxide phases for 3 days at 900°C. Oxygen analyses were performed on all four phases by two independent laboratories with the following amounts of oxygen present in atomic percent; Ti2Cu-0.06, Ti2Ni-1.03, Ti4Ni2O-13.95, and Ti4Cu20-13.87. The stoichiometric amount for the oxide phases is 14.29 at. pct. Since all of the samples were very brittle they were easily reduced to a powder for diffraction measurements. The lattice constants given in Table I were determined for the four compounds from X-ray diffraction patterns of powder samples exposed to filtered copper radiation using a 114.59 mm diam Debye-Scherrer type camera using the Straumanis loading. None of the patterns showed a detectable amount of a second phase. The lattice constants were obtained from an IBM 704 computer program employing a least squares treatment with systematic correction terms as previously reported.14

Jan 1, 1963

By A. N. Holden

A DISLOCATION mechanism has been described by Cottrell' by which metals can yield locally, I. form Liiders bands, giving rise to a characteristic stress-strain curve with a sharp yield point and appreciable strain at constant or decreasing stress. It is undoubtedly the best mechanism that has been suggested to date." In its present development, however, the dislocation mechanism provides a more satisfying explanation for the sharp yield point than for the extensive localized flow occurring at the lower yield stress. The primary objective in this paper is to extend the dislocation mechanism to account for localized cataclysmic flow by a dislocation collision process and to give experimental evidence to support such a process. Only the yielding of iron containing carbon -will be discussed, although other metal-solute systems are known to behave similarly. Cottrell Mechanism In brief, Cottrell explains the yield point in the following way: The dislocations in iron which must propagate to produce slip usually lie at the center of local concentrations of carbon atoms, since segregation about these dislocatlons relieves some of the local stress resulting from them. A dislocation surrounded by a "cloud" of carbon atoms is thus anchored, and a higher stress is required to set it in motion than to move a free dislocation. Considering all available dislocatlons to be anchored in this fashion, the iron exhibits a yield point when the first dialocations break free and move through the lattice causing slip. This first breaking away of a dislocation enables other dislocations to break loose by "interaction" and the process becomes a cataclysm producing local deformation or Luders bands. The yield point in the stress-strain diagram for iron is absent in freshly deformed material, but returns gradually with time; the phenomenon is one aspect of what is called strain aging. The rate at which the yield point returns following straining depends on the temperature of aging. According to Cottrell the rate of return of the yield point in strained iron is limited by the rate of diffusion of carbon at the aging temperature, the mechanism is onr: of reforming the solute atmospheres around carbon-free dislocations that had stopped moving coincident with the removal of stress. If the specimen is retested immediately after straining and unloading, carbon will not have had time to diffuse to, and re-anchor, dislocations and the yield point will not occur. The carbon diffusion limitation for the rate of strain aging apparently applies if the criterion for strain aging is either the change in hardness" or the change in electrical resistance" of the strained speci- men with aging time. The possibility exists, however, that the yield point actually returns to strained iron at some rate other than that deduced from hardness or electrical resistance data. Therefore, as a preliminary experiment, the rate of yield point return in a rimmed sheet steel strained 6 pct in tension was measured at 27°, 77°, and 100°C. A plot of yield-point elongation for each of these temperatures against aging time appears in Fig. 1. The aging process is described by curves which rise to a plateau value of elongation that seems independent of temperature, but at a rate that depends on temperature. Very long times lead to a further rise in the yield-point elongation above the plateau value. However, if the later increase in yield-point elongation is ignored and the log of the time to reach half the plateau value of elongation is plotted against 1/T, a straight line results for which an activation energy of about 25 kcal pel- mol may be assigned. Within the accuracy of this sort of experiment this is approximately the activation energy for the diffusion of carbon in iron (20 kcal per mol), and the carbon diffusion limitation suggested for the yield-point return on strain aging is valid. The Cottrell mechanism thus explains in a qualitative manner the occurrence of a yield point in iron and its return with strain aging. It fails, however, to explain some of the other experimental observations that have been made of the yielding behavior of iron. For example, it is known that the yield point in iron becomes less pronounced with increasing grain size. Annealed single crystals of iron have very small yield-point elongations .if indeed they have any,' compared to a polycrystalline steel. If the only requirement for a yield point is that the dislocations in the lattice of the annealed. material be anchored by carbon atoms, the difference in the behavior of single crystals and polycrystals is not explained. That a dislocation mechanism may be entirely consistent with little or no yield point in an annealed single crystal will become apparent later when dislocation interaction is discussed. Strain aging produces a definite yield point even in single crystals. This accentuation of the yield-point phenomenon in single crystals after strain

Jan 1, 1953

By N. A. Gokcen, J. Chipman

Aluminum and oxygen dissolved in liquid iron were brought into equilibrium with pure alumina crucibles and atmospheres of known H2O and H2 contents to study the reactions: 1—Al2O3(s) = 2 Al + 3 0; 2—Al2o3(s) + 3H2(g) = 2Al+ 3H2o(g); and 3—H2(9) +O = H2O(g). Aluminum strongly reduces the activity coefficient of oxygen and similarly oxygen reduces that of aluminum. Values of the product [% All" • [% O]3 are much smaller than those found in previous experimental studies and are of the order of magnitude of the calculated values. ALUMINUM is the strongest deoxidizer commonly A used in steelmaking, but the extent to which it removes dissolved oxygen has been debatable. The relationship between aluminum and oxygen has not been determined reliably not only on account of the usual experimental difficulties at high temperatures but also because of uncertainties in the analyses of very small concentrations of oxygen and aluminum. The earliest experimental attempt of Herty and coworkers' was followed by a more systematic study of Wentrup and Hieber.' These authors added aluminum to liquid iron of high oxygen content in an induction furnace and considered that 10 min was sufficient to remove the deoxidation products from the melt. Parts of the melts thus obtained were poured into a copper mold and analyzed for total aluminum and oxygen (soluble plus insoluble forms), assuming that the insoluble parts were in solution at the temperatures from which samples were taken. It is conceivable that the furnace atmosphere in their experiments, consisting of mainly air at 20 mm Hg pressure, was a serious source of continuous oxidation and therefore that their oxygen concentrations were correspondingly high. Scattering of their data was explained to be well within the maximum inaccuracy of 10°C in the temperature measurements and errors of ±0.002 pct each in the oxygen and total aluminum analyses. Maximum and minimum deoxidation values, i.e., values of the product [% All' . [% O] differed by factors of 10 to 15; mean values of 9x10-11 and 7.5x10-9 ere reported at 1600" and 1700°C, respectively. Hilty and Craftsv determined the solubility of oxygen in liquid iron containing aluminum, using a rotating induction furnace. Pure alumina crucibles used in their experiments contained the liquid iron which in turn acted as a container for slags of varying compositions consisting mainly of Al2O3, Fe2O3, and FeO. The furnace was continuously flushed with argon, and additions of aluminum and Fe2O3 were made in the course of each experimental heat. The inner surfaces of their alumina crucibles were covered with a substance other than pure Al2O3, containing both iron oxide and alumina. Although frequent slag additions can change the composition of slag in the liquid iron cup formed by rotation, the inner surface of the crucible must depend upon the transfer of oxygen or aluminum through the liquid iron for any adjustment in composition. It is not clear that their metal was in equilibrium with the crucible wall, but it is clear that it was not in equilibrium with Al2O3. Their deoxidation product, [% A].]" • [% O]3, varied by a factor of more than 50; the average values of 2.8x10- and 1.0x10-7 were selected for temperatures of 1600" and 1700°C, respectively. Aside from the experimental determinations, attempts have been made to calculate the deoxidation constant for aluminum indirectly from thermody-namic data. Schenck4 combined the thermodynamic data for Al2O3 and dissolved oxygen in liquid iron by assuming an ideal solution. His calculated values are 2.0x10-15 and 3.2x10-13 at 1600" and 1700°C, respectively. Later, Chipman5 attempted to correct for the deviation from ideality and derived an expression which led to deoxidation values of 2.0x10-14 and 1.1x10-12 at 1600" and 1700°C, respectively. The errors in these treatments originate mainly from inaccuracies of thermal data and uncertainties regarding the activity coefficients of dissolved oxygen and aluminum. The purpose of this investigation was to study the equilibria represented in the following reactions in the presence of pure alumina: Al2O3(s) = 2Al + 3O K = aAl2.ao3 [1] Al2O3(s) + 3H2(g) = 2Al + 3H2O(g) H2O K2 = aAl2(H2O/H2 ) [2] H2(g) +O = H2O(g) K3 = 1/ao (H2) [3] The experimental method consisted of melting pure electrolytic iron, usually with an initial charge of aluminum, in pure dense alumina crucibles under a controlled atmosphere of H,O and H2 and holding

Jan 1, 1954

By R. M. Waterstrat, E. C. van Reuth

BINARY- alloy phases having the A15-type crystal structure have been described as occurring at a simple and more or less invariant stoichiometric composition (A3B) which corresponds to the relative number of atoms occupying each of the two crystallographi lattice sites in this structure.1,2 It is frequently assumed, therefore, that each crystallographic site is occupied exclusively by one kind of atom. In most cases, however, there have been insufficient experimental data to establish whether atomic ordering is, in fact, complete. Recent studies have shown that binary A15-type phases are sometimes stable over an appreciable composition range3''* and, occasionally, the composition range of stability does not even include the "ideal" A3B stoichiometric composition.5-7 We have observed the existence of nonstoichiometric A15-type phases in the binary systems Cr-Pt and Cr-Os. This has not been reported in previous work on these alloy systems.1,8-11 A series of alloys, each weighing approximately 30 g, was prepared by are-melting in an Ar-He atmosphere using 99.999 pct Cr, 99.999 pct Os, and 99.99 pct Pt as starting materials. Each alloy was melted four times with a total weight loss of less than 1 pct. The stoichiometric (A3B) alloys were sealed in evacuated quartz tubes and annealed at 1200°C for periods of time ranging from 3 days to 2 months. Examination of the alloy microstructures revealed that little change had occurred over this time interval and it was therefore assumed that the microstructures were fairly representative of equilibrium conditions. No evidence of contamination was observed although there was apparently some loss of chromium which was confined to a thin layer at the surface of the specimens. The quartz tubes were quenched from the annealing temperature into cold water. X-ray diffraction and metallographic examination of the stoichiometric alloys revealed an estimated 10 to 30 pct of second phases which were tentatively identified as phases previously reported in these binary-alloy systems.8-11 A second series of alloys was prepared by mixing -325 mesh metal powders having a nominal purity of 99.9 pct and compressing these mixed powders in a cylindrical die at a pressure of 43,000 psi. These alloys, each weighing 15 g, and some of the arc-melted alloys were annealed in a high-temperature vacuum furnace heated by tantalum strips at a pressure of 10-8 Torr and were rapidly cooled by turning off the furnace power. X-ray and metallographic examination of both series of alloys served to establish the composition ranges of the A15-type phases. Although some chromium losses occurred during the vacuum annealing, they were largely confined to a thin layer on the outer surfaces of the samples. It was established that the A15 phases occur in the Cr-Pt system at 21 ± 1 at. pct Pt after 1 week at 1200°C and in the Cr-Os system at 28 ± 1 at. pctOs after 1 day at 1400°C (see Table I). We also observed that an arc-melted stoichiometric (A3B) alloy in the Cr-Ir system was single-phase (A15-type) in the "as-cast" condition in agreement with previous work.8,13 In addition we obtained a sample of the Cr-Os A15-type phase from Argonne National Laboratory. This alloy contained less than 1 pct second phase12 and was submitted to a density measurement. The density measurement yielded a value of 11.14 g per cu cm in comparison to a theoretical value of 11.25 g per cu cm calculated using the observed lattice constant (4.6806Å) of this alloy. The uncertainty in measurement was 0.1 pct but the sample may have contained some cracks or minor imperfections which could account for the low experimental value. We have also studied the atomic ordering in these phases by means of integrated line intensity measurements using thick, flat, rotating powder samples and CuK a radiation in an X-ray diffractometer. We have obtained order parameters of 0.90 for the Cr-Pt phase, 0.89 for the Cr-Ir phase, and 0.64 for the Cr-Os phase using the formula: where s is the usual Bragg and Williams order parameter, ra is the fraction of chromium atoms in A sites, and FA is the fraction of chromium atoms in the alloy. The values obtained are estimated to be accurate within ±4 pct. If the unusually small value for the order parameter of the Cr-Os A15 phase were due to the existence of lattice vacancies on the "B-atom" sites, then a density of 10.04 g per cu cm would be expected in contrast to the observed value of 11.14 g per cu cm. We, therefore. conclude that the fraction of lattice vacan-

Jan 1, 1967

By C. L. Prokop

A laboratory investigation has been made of the effects of mud hydraulics upon the formation and erosion of mud filter cakes. The tests were conducted to simulate drilling conditions as nearly as possible. The formation of mud filter cake in a drilling well does not proceed at a uniform and unbroken rate. Instead, the rate of cake accumulation depends upon whether or not the mud is being circulated. If the mud column is quiescent, filter cake formation is a smooth function of the filtration characteristics of the system. If the mud is being circulated filter cake formation depends not only upon the filtration characteristics of the mud but also upon the erosive action of the flowing mud column Filter cakes formed during continuous mud circulation were observed to reach an equilibrium thickness after several hours' circulation. Mud circulation was maintained at a constant volumetric rate throughout each experiment. The fluid velocity at equilibrium cake thickness was dependent upon the thickness of the filter cake. Muds having exceptionally high water loss deposited thick filter cakes in spite of very high eroding velocities. The muds having good filtration characteristics deposited thin filter cakes at equilibrium circulating velocities well within tile range of those in a drilling well. It was observed that filter cakes deposited during stagnant filtration were quite difficult to erode by mud circulation. The - rate of crosion computed from the rate of filtrate accumulation after equilibrium cake thickness had been reached was in reasonable agreement with the rate of erosion obtained by direct observation. Continuous mud circulation usually caused the permeability of the filter cake to decrease with time. INTRODUCTION Many of the difficulties encountered during tile drilling of a well have been attributed to the loss of water from the mud and the attendant deposition of solids upon the walls of the hole. Past experience has shown that a reduction of the filtration rate of the drilling fluid eliminates or greatly reduces these difficulties. Definite filtration requirements, however, are hard to establish for a given set of conditions. This is due. in part, to the fact that the usual filtration test performed upon mud doe? not simulate well conditions as closely as desirable. The filtration characteristics of a mud are customarily determined by means of the standard low-pressure API wall-building tester.' In this instrument a filter cake is deposited upon a horizontal bed under a pressure differential of 100 psi. The rnud is quiescent during the filtration period. In actual practice. mud filtration occurs within a well under quite different conditions. One of the major differences is that mud flows upward across the filter bed as the filter cake forms. This undoubtedly produces a change in the filter cake which cannot be reflected in the results of the API test. The laboratory work described in this paper had as its primary objective a better understanding of the influence of mud circulation upon the thickness and ,characteristics of the filter cakes deposited under conditions similar to those existing in a drilling well. ANALYSIS OF PROBLEM Once a permeable formation is penetrated by the bit, filtrate from the mud flows into the formation. 'he mud solids plaster against the walls of the hole, forming a filter cake. If the mud column is stagnant, that is, if it is not being circulated. the filter cake will increase in thickness until the hole is filled. Prior to the time that the hole is filled, the thickness of filter cake existing at any given time will be a function of the filtration characteristics of the mud, the temperature, and the pressure differential. The effects of these variables have been investigated in the past for both flat bed filtration2'3 and for radial filtration.' When the mud is circulated in a hole in which a filter cake i. being deposited. some of the solids that would ordinarily deposit in the filter cake will be carried away by the eroding action of the mud. This will limit. filter cake thickness. Some work has been done to determine the effect of flow upon the filtration rate in a circulating mud system' but little work has been done upon the factors which determine the filter cake thickness existing in a circulating system. On first sight it would appear that the major factors controlling filter cake formation in a circulating system should be: 1. The rate of deposition of solids from the mud. 2. The erosive force that the flowing mud exerts upon the filter cake. 'A. The erodabilitv of the filter cake. 4. Any change in filter cake characteristics attributable to the scouring action of the mud. The rate at which solids are deposited from the mud will be controlled to a large degree by the filtration characteristics of the mud, the pressure differential. the temperature under

Jan 1, 1952

By D. E. Marks, Arnold, C. W, R. J. Robinson, A. E. Hoffmann

The efficiency of operation of a fixed-bed adsorption unit is infEuenced both by the absolute adsorption capacity of the bed and by the rate of adsorption. This paper describer studies of adsorption rate which were conducted in an experimental unit designed such that conditions existing in the treatment of high-pressure natural-gas mixtures could be duplicated. Variables investigated included pressure, temperature, gas composition, adsorbent particle size, depth of packed bed and gas velocity. The adequacy of a simplified mathematical model for predicting the observed phenomena was tested. A correlation is preserited which relates adsorption rate to the process variables stlldied. This correlation is useful in combination with the matheinatical model. INTRODUCTION Of the techniques available for contacting adsorbent particles with fluid streams to be treated, fixed-bed adsorption columns offer definite advantages in simplicity and ease of operation. As a result, they are often used in preference to others for such petroleum industry applications as dehydration and purification of natural gas and hydrocarbon recovery. Fixed-bed adsorption units usually consist of two or more towers filled with a desired adsorbent and operated in a cyclic manner. While one is being used to process the main flow stream, the others are undergoing regeneration to remove the adsorbed phase. When the tower on stream becomes saturated with the preferentially adsorbed material, the roles of the towers are switched, and the freshly regenerated tower is placed on stream. Cacle duration is determined by the bed capacity under the process conditions and by the flow rate through the bed. The sharpness of separation which can be effected is a function of both the absolute capacity of the bed and the rate of adsorption in the bed. The effect of rate for a particular set of conditions is evidenced by the sharpness or diffuse-ness of the adsorption front as it advances through the bed. Since data needed for design of adsorption units to treat high-pressure natural-gas systems were not available, an experimental program was designed to investigate the effects of different variables upon adsorption rate in fixed beds. In the present paper, effects of gas composition, column length, temperature, pressure, adsorbent particle size and flow rate (actual linear flow rate of the gas) are shown, and utility of a simplified mathematical model for describing the process is discussed. As gas enters the top of a cool, clean bed of adsorbent, preferentially adsorbed materials are stripped from the main flow stream by the uppermost particle layers. As these layers become saturated with a particular component, new supplies of this component are carried further down the column until fresh adsorbent is encountered. An adsorption wave thus moves through the column as material is supplied to saturate succeeding elements of the bed. Adsorption from a Multicomponent gas stream occurs as a succession of such moving waves corresponding to the different components in the gas. The leading edge of an adsorption wave for a component of a natural-gas stream moving through a bed of a common commercial adsorbent such as silica gel would be sharp but for the influence of certain broadening fac tors. These factors include a nonuniform velocity profile in the bed, longitudinal dispersion or mixing in the main gas stream, and the time required for a molecule to migrate from the main gas stream and be adsorbed at a site within the body of an adsorbent particle. If packing is uniform and the ratio of column to particle diameter is greater than approximately 15:1, the first factor is relatively unimportant' Longitudinal mixing is of importance only for the case of moderately high mass transfer with extremely slow flow rates.' The sharpness of an adsorption front, therefore, is, primarily a function of the rate of adsorption or the time required to saturate a particle of zdsorbent. Two methods for defining adsorption rate are used in this work. The first is a normalized or relative rate which describes the rate of saturation of a differential element of the packed bed. This can be measured by observing the time required for the concentration of the preferentially adsorbed material in the effluent gas from the bed to rise from zero to a value equal to that in the inlet gas stream. The second definition describes the absolute rate of mass transfer from the gaseous to the adsorbed phase. This definition is used in a mathematical description of the adsorption process. If the concentration of a component in the gas strcam leaving an adsorption column is measured and plotted as a function of time, a curve such as that shown in Fig. I results. It is seen that for a period of time the effluent gas is devoid of the component under consideration. As the bed approaches saturation, a small percentage of this material will appear in the effluent gas. The concentration will then rise with time, or increasing cumulative gas flow, until it is equal to that in the inlet gas stream. If adsorp-

By J. B. Cheatham, J. W. McEver

A laboratory investigation of the behavior of casing subjected to salt loading indicates that it is not economically feasible to design casing for the most severe situations of nonuniform loading. When the annulus is completely filled with cement, casing is subjected to a nearly uniform loading approximately equal to the overburden pressure, and, although the modes of failure may be different, the design of casing to withstand uniform salt pressure can be computed on the same basis as the design of casing to withstand fluid pressure. Failure of casing by nonuniform loading in inadequately cemented washed-out salt sections should be considered a cementing problem rather than a casing design problem. INTRODUCTION Casing failures in salt zones have created an interest in understanding the behavior of casing subjected to salt loading. The designer must know the magnitudes and types of loading to be expected from salt flow and he must be able to calculate the reaction of the casing to these loads. In the laboratory study reported in this paper, short-time experimental measurements of the load required to force steel cylinders into rock salt are used as a basis for computing the salt loading on casing. These results must be considered to be qualitative only since rock salt behaves differently under down-hole and atmospheric conditions and also may vary in strength at different locations. The beneficial effects of (1) cement around casing, (2) a liner cemented inside of casing, and (3) fluid pressure inside of casing in resisting casing failure are considered. ROCK SALT BEHAVIOR UNDER STRESS The effects of such factors as overburden loading, internal fluid pressure, and temperature on the flow of salt around cavities have been studied extensively at The U. of Texas. Brown, et al.1 have concluded that an opening in rock salt can reach a stable equilibrium if the formation stress is less than 3,000 psi and the temperature is less than 300°F. At higher temperatures and pressures an opening in salt can close completely. These results indicate that calculations based upon elastic and plastic equilibrium for an open hole in salt should be applied only at depths less than 3,000 ft. In most oil wells the tem- perature will be less than 300F in the salt sections, therefore no appreciable temperature effects are anticipated. Serata and Gloyna2 have reported an investigation of the structural stability of salt. .They assume that the major principal stress is due to the overburden. Other stresses can be superimposed if additional lateral pressures are known to be acting in a particular region. In the present analysis an isotropic state of stress is assumed to exist in the salt before the hole is drilled, since salt regions are generally at rest. This assumption is partially verified from formation breakdown pressure data taken during squeeze-cementing operations in salt. Experimental measurements of the elastic properties of rock salt indicate a value of 150,000 psi for Young's modulus and a value of approximately 0.5 for Poisson's ratio. A value of % for Poison's ratio with finite Young's modulus would indicate that the material was incompressible. Values ranging from 2,300 to 5,000 psi have been reporteda for the unconfined compressive strength of salt. These variations may be due to differences in the properties of the salt from different locations or at least partially to differences in testing techniques. Salt is very ductile, even under relatively low confining pressures. For example, in triaxial tests reported by Handin3 strains in excess of 20 to 30 per cent were obtained without fracture. When casing is cemented in a hole through a salt section, the casing must withstand a load from the formation if plastic flow of the salt is prevented. To determine the forces which salt can impose on casing, circular steel rods were forced into Hockley rocksalt with the longitudinal axis of the rods parallel to the surface of the salt. The force required to embed rods 0.2 to I in. in diameter and 1/2 to 1 in. long to a depth equal to the radius of the rods was found to be F/DL =28,700 psi (± 3,700 psi) , .... (1) where D is the diameter, and L is the length of the rod. CASING STRESSES Since an open borehole through salt at depths greater than 3,000 ft will tend to close, cemented casing which prevents closure of the hole will be subjected to a pressure approximately equal to the horizontal formation stress after a sufficiently long time. As a first approximation the horizontal stress can be assumed to be equal to the overburden pressure. This is in agreement with the suggestion by Texter4 that an adequate cement job can prevent plastic flow of salt and result in a pressure on the casing approximately equal to the overburden pressure. He also advocated drilling with fully saturated salt mud

Jan 1, 1965

By G. D. Oxx, L. F. Coffin

The concept of using a phase that is liquid at service temperatures as a component of coatings for refractory metals has been described. The liquid, an alloy of gold and silicon, is retained on a molybdemum surface by a capillary system made of molybdenum disilicide. The coating has the advantage of good thermal shock and has a self-henling chracteristic. In order for highly stressed structures to exceed a service temperature of 2000°F, it has become apparent that a development that does not depend on the traditional iron, cobalt, or nickel-base alloy is needed. Alloys of the refractory metals, i.e., molybdenum, tungsten, tantalum. niobium (colum-bium), and rhenium are potentially useful at extremely high temperatures that more conventional alloys would never be expected to achieve. A new alloy of molybdenum has become available that has a 100-hr rupture strength of 35,000 psi at 2200°F.1 As a result of this work, it may be assumed that a material with adequate mechanical properties at 2200?F is now available. Unfortunately, this alloy and all other known alloys of the refractory metals suffer from not being; serviceable in an oxidizing atmosphere for a very long time. In order to permit general use of refractory metals at high temperatures, it is necessary to prevent destructive oxidation by appropriate alloying or by protective coatings. The liquid phase coating reported here is representative of a concept for the protection of metals that permits higher service temperatures and introduces a new group of materials for selection as coatings. Coating Requirements—Service conditions that represent potential applications for refractory metals vary considerably: however, it is possible to consider two conditions that are usually present. The refractory metal1 component must be heated to the service temperature at least once and usually frequently. When a solid coating is used, usually the coating and basis metal do not have the same coefficient of expansion. This difference causes thermal stress in the coating that is aggravated by rapid heating and cooling and eventually causes coating failure. The second consideration is the probability that there will be damage to the coating by some environmental condition. In jet engines, for example, it is expected that large particles, stones, metal parts, and so forth, will strike a bucket at high speed and cut a hole in the coating. In addition to the above considerations, the coating must also have other fundamental properties. Obviously, it must be oxidation resistant. In addi- tion, it must prevent permeation of oxygen and subsequent oxidation of the basis metal at the interface. Also, diffusion of the basis metal to the outside surface and subsequent oxidation there must be prevented. Finally, the coating must not react with the basis metal to form a weak bond at the interface. It should be noted that the coating need not support a load: it must only remain intact. Liquid Phase Coating Design Factors—In the use of a liquid as a principal coating constituent, it would be expected that the two service conditions mentioned above would be satisfied. A liquid would flow under the influence of the thermal strain developed by coating-basis metal expansion mismatch such that failure from this source would not be expected to occur. It is also probable that the ability of a liquid to flow would provide a self-healing effect. Thus, damage caused by particles in the atmosphere would be repaired. A third advantage is evident in that vapor pressure rather than melting point limits the service temperature. This latter advantage permits use of low melting but oxidation resistant metals such as gold or copper that would be quite useless if the solid state was required. A low viscosity liquid alone. however, is a totally unsuitable coating because it will simply flow off a component, particularly under the influence of a high acceleration field. A method of preventing liquid loss must be devised. In this case, it is desired that the liquid have a low viscosity so that it may easily flow into flaws; thus, raising the viscosity is not a satisfactory solution. One other inherent difficulty is caused by the high mobility of atoms in the liquid state as compared to the solid state. Because of this mobility, it would be expected that gases would diffuse more rapidly through a liquid. It is also probable that the solubility of oxygen in the liquid would be comparatively high. These factors would tend toward rapid permeation of oxygen and oxidation of the substrate. It is most reasonable that this problem could be solved by incorporating a solid phase, which is impermeable to gases, as a component of the coating. To overcome the tendency of a liquid to flow easily, it is possible to use surface tension to advantage. If the surface were made up of a large number of capillary tubes of sufficiently small diameter, then surface tension would hold the liquid even against the acceleration of a centrifugal field.

Jan 1, 1961

By F. G. Jones, R. D. Pehlke, H. E. Gardner

The solubility of nitrogen in liquid Fe-18 pct Cr-8 pct Ni-0. 7 to 2.3 pct A1 alloys has been measured up to the solubility limit for the formation of aluminum nitride in the temperature range 1600° to 1700°C uszng the Sieverts' method. The solubility of nitrogen in 18-8 stainless steel increases with increasing aluminum content. Based on a nitride composition, AlN, the standard free energy of formation of aluminum nitride from the elements dissolved in liquid 18-8 stainless-steel alloys has been determined to be: ?G° = -42,500 + 20. IT in the range from 1600° to 1700° C. EVANS and pehlke1 have measured the equilibrium conditions for the formation of aluminum nitride, AlN, in liquid Fe-A1 alloys. The present study extends that work to the more complex solvent, liquid 18 pct Cr-8 pct Ni (18-8) stainless steel. Recent work by Small and pehlke2 has dealt with the effect of fourth-element additions on the solubility of nitrogen in 18-8 base alloys. They found the effect of aluminum additions, up to 0.74 pct, on the solubility of nitrogen to be small. The present study covered the range from 0.74 to 2.28 pct aluminum, and by extending the composition range may be used to better define the effect of aluminum on the nitrogen solubility in these alloys. EXPERIMENTAL PROCEDURE The Sieverts' method was used to measure the equilibrium solubility of nitrogen gas in liquid 18-8 stainless steel alloys containing 0.74, 1.49, 1.93, and 2.28 pct Al. The solubility was measured as a function of the nitrogen gas pressure at temperatures of 1600°, 1650°, and 1700°C. The apparatus used is the same as described by Small and Pehlke.2 The 100-g melts were made from Ferrovac-E high-purity iron, Crucible Steel Co.; 99.95 pct Cr, Union Carbide Corp.; 99.9 pct Ni, International Nickel Co.; and 99.99+ pct Al, Aluminum Co. of America. The aluminum was charged at the bottom of the crucible, surrounded by nickel and iron. The chromium was packed into the interstices to minimize vapor transport of the aluminum during initial melting. The hot volume of the system, measured for each melt with argon, ranged from 45 to 55 standard cu cm with a temperature coefficient of —8 x 10-3 cu cm per °C. The melt temperature was measured with a Leeds and Northrup disappearing-filament type optical pyrometer sighted vertically downward on the center of the melt surface. The temperature calibration of the system by Small and pehlke2 was assumed. Two problems are involved in determining the solubility product of a solid, metal nitride phase in liquid iron alloys. These are: 1) establishing the point of departure from Henrian behavior at the solubility limit of the metal nitride phase; and 2) determining the composition of the solid nitride which is precipitated. Determination of the solubility product of AlN was made by admitting small amounts of nitrogen into the reaction bulb until the deviation from Sieverts' law was clearly evident in the form of a pressure halt. To obtain the solubility product at several temperatures during one run the following procedure was used: 1) add increments of nitrogen to determine the Sieverts' law line at the lowest desired temperature; 2) continue to add nitrogen to precipitate a small amount of the nitride phase; 3) increase the melt temperature 50°C to dissolve the precipitated nitride; 4) repeat step 2 until either a nitride formed or the system reached ambient pressure; if a nitride formed at 1650°C, the sequence was repeated at 1700°C. The composition of the precipitated phase was checked by an X-ray diffraction pattern obtained from powder scraped from the surface of the solidified 1.93 pct A1 melt. RESULTS AND DISCUSSlON Solubility Measurements. Fig. 1 is a typical nitrogen-absorption curve obtained from measurements on a 1.93 pct A1 alloy. Since the initial absorption of nitrogen follows Sieverts' law the nitrogen solubility is plotted as a function of the square root of the pressure of nitrogen gas in the reaction bulb. The results of the solubility measurements for all alloys studied are summarized in Table I. The slope of the Sieverts' law line for each alloy was determined. Since this is also the solubility of nitrogen at 1 atm pressure of nitrogen gas, the latter designation is used for the data. It should be noted. however, that in most cases the value lies above the solubility limit for AlN. Fig. 2 shows the effect of aluminum on the solubility of nitrogen at this reference pressure and as a function of melt temperature. The solid portions of the lines represent attainable solutions; the dashed regions lie above the limit for precipitation of AlN.

Jan 1, 1969

By E. J. Rapperport, J. P. Pemsler

The thermodynamic activities of zinc in six solid solution Cu-Zn alloys ranging from 5 to 35 at. pct Zn were determined experimentally in the temperature range 400° to 600°C. This low temperature investigation was canducted in order to evaluate techniques developed to utilize the inherently high sensitivity of atomic absorption flocesses in the measurement of thermodynamic activities. Analytical expressions ,for the activity and actizlity coeflcient are given for the six alloys in the temperature ranges investigated. RELATIVELY few experimental methods are available for investigation of thermodynamic activities of alloys, especially in the solid state. The techniques most frequently used have been the electrochemical potential and the effusion methods, both of which have severe limitations in many instances. It is therefore desirable to expand the ability to perform such measurements in order to obtain new information as well as to provide an additional independent verification capability. In this work, we present a significant improvement in the spectrophotometric method for sensing small vapor pressures in static absorption cells. Similar techniques have been used previously;1"5 however, applications had been limited to relatively high pressures, often greater than 1 torr. Prior investigators have, for the most part, used broad spectral sources such as xenon or mercury lamps, and high intensity arcs. Hollow cathode sources were first suggested in 1956 6 and were used soon afterwards.4'5 These sources offer significant improvements in sensitivity and freedom from interfering spectral lines.'-' EXPERIMENTAL High purity zinc was obtained from Cominco Products, Inc., and copper from American Smelting and Refining Co. Both elements were of 99.999 pct purity. Copper-zinc alloys were vacuum melted in a high fired carbon crucible with each alloy pulled from the melt as a 4 -in. diam bar. The bars were swaged to -1/4 in. rods and vacuum annealed for 160 hr at 800° + 1°C. Samples for gross chemical analysis were taken at intervals along the length of the rods to ascertain the axial zinc gradient. Electron microprobe analysis of homogenized specimens indicated that the alloys had uniform compositions over their cross sections on a macro (200 p) and micro (1 u) scale to better than *1 pct (20) of the gross composition. This tolerance was determined by counting statistics, rather than assured composition fluctuations. All SiO 2 windows were high-ultraviolet-transmission grade to minimize intensity losses. Silica absorption cells were scrupulously cleaned consecutively in organic solvents, dilute HF, and distilled water before use. The empty cells were then flamed while under a dynamic vacuum, cooled, and removed to an argon-filled glove bag. Alloy pieces were cut and filed in the glove bag to produce fresh surfaces, and then loaded into the cells. The loaded cells were temporarily sealed, removed from the glove bag, reevacuated to 10-5 torr or better, and permanently sealed. The instrument used is schematically shown in Fig. 1. The spectral emission from a commercially made hollow cathode lamp (A) of a selected element is focused through an absorption cell (B) inside a well-controlled furnace (C). The intensity of the transmitted beam is measured using the spectrometer* (D) 'Techtron model AA4 atomic absorption spectrometer. which contains a grating (E) that disperses the light prior to impingement on the photomultiplier (F). The monochromator grating is adjusted so that only the wavelength of interest is measured. The power supply delivered an interrupted voltage to the lamp, causing a chopped radiation output to be transmitted. The detector read only the intermittent component of radiation incident upon it, so that all continuous noise signals (furnace radiation, and so forth) were eliminated. Three recording thermocouples contained in the muffle furnace were positioned along the length of the absorption cell: one at each end and one at the center. An effort was made to keep the ends of the cell several degrees hotter than the center to avoid window condensate. Appropriate thermal corrections were then necessary to relate cell pressure to radiation attenuation. Water-cooled heat shields, as shown in Fig. 1, were found to aid signal stability by protecting the hollow cathode and the photomultiplier from furnace radiation. The furnace had a 2-in. diam muffle, Kan-thal wound, with SiO 2 windows at its ends to minimize convective effects. The hollow cathode radiation was masked and focused to form a conic beam that was a maximum of { in. diam within the furnace. Thus, the 1.5 in. diam absorption cell easily contained the entire beam. The furnace was mounted on ball-bearing slides with positive positioning detents. This arrangement allowed the removal of the entire furnace assembly from the radiation path, position [I], Fig. 1, so that frequent sampling of the unattenuated beam intensity could be obtained. In all cases the beam intensity was kept constant to 0.1 pct as judged by readings taken immediately before and immediately after data collection. Only data for absorptions of less than 80 pct were utilized, as systematic deviations from linearity were found for greater absorptions.

Jan 1, 1970

By O. N. Carlson, S. A. Bradford

Discontinuous yielding in tensile tests was observed in V-O alloys in the temperature ranges of 150° to 175°C and also 350° to 400°C. The magnitude and intensity of the serrations were found to vary considerably with oxygen content. Maxima were observed in tensile and yield strengths and in the strain-hardening coefficient at the higher temperature only. The strain rate sensitivity was observed to be negative between 150° and 400°C. THIS investigation was undertaken to study the effect of oxygen on the tensile properties of iodide vanadium in the temperature range of 25o to 450°C. Brown1 observed an increase in strength between room temperature and 400°C in vanadium metal, and found that oxygen and nitrogen had a rather pronounced effect on the strength and ductility. A maximum in the tensile strength was observed by Rostoker et al.2 near 300oC and by Pugh3 around 450°C for calcium-reduced vanadium. Pugh also found a maximum in the yield strength and in the strain-hardening exponent, and minima in the elongation and strain rate sensitivity at the same temperature. Eustice and Carlson4 reported the appearance of serrations in the stress-strain curves between 140° and 180°C in iodide vanadium containing 600 ppm O. These anomalies in the mechanical properties indicate that strain aging occurs in vanadium, but the impurity or impurities responsible for the above-mentioned effects have not been identified. The phenomenon of strain aging is usually characterized by the return of the yield point after interruption of a strength test. In the temperature range where strain aging occurs, the yield and tensile strengths attain maximum values, elongation and strain rate sensitivity exhibit minima, and discontinuous yielding is generally observed in the stress-strain curve. Cottrell5, 6 has postulated that strain aging is due to the migration of solute atoms to dislocation sites to produce locking after the dislocations have broken free from their impurity atmospheres during the initial yielding. At the strain-aging temperature the process is a dynamic one in which the solute impurity atoms diffuse to the vicinity of the moving disloca- tion producing "locking" which gives rise to maxima in the tensile strength and serrations in the elongation curves. Cottrel17 has noted that discontinuous yielding in iron occurs when the diffusion coefficient of nitrogen, D, and the strain rate, i, are related by D = 10-9 €. EXPERTMENTAL PROCEDURE The vanadium metal employed in this study was prepared by the iodide refining process as described by Carlson and owen.8 A representative analysis of the vanadium used in this investigation was: 150 ppm O, <5 ppm N, <1 ppm H, 150 ppm C, 150 ppm Fe, 70 ppm Cr, <50 ppm Si, 30ppm Cu, 20 ppm Ni, <20 ppm Ca, <20 ppm Mg and <20 ppm Ti. Alloys containing from 200 to 1800 ppm O, all of which lie in the solid solution range of the V-O system, were prepared by arc melting vanadium together with portions of a high-oxygen master alloy. The master alloy was prepared by tamping pure V2O5 into holes drilled in a vanadium ingot and arc melting this five or six times in an inert gas atmosphere, inverting the button between each melting step. The oxygen content of the master alloy was then determined by vacuum fusion analysis. Vanadium containing less than 150 ppm O was prepared in the following manner. A bar of iodide vanadium was deoxidized by sealing it in a tantalum crucible with a few grams of high-purity calcium. This was held at 1100°C for 4 days to allow time for the oxygen to diffuse to the surface and to react with the calcium vapors. The calcium oxide product was later dissolved from the surface of the bar with dilute acetic acid. In this way vanadium containing from 20 to 50 ppm O was prepared. Sample Preparation. The are-melted ingots were cold swaged into 3/16-in. diam rods and these were machined into cylindrical tensile specimens with a reduced section of 1.00-in. length and 0.120-in. diam. The test specimens were annealed for 4 hr at 900°C in a dynamic vacuum of mm of Hg to remove hydrogen from the metal. This recrystal-lization treatment produced a uniformly fine-grained structure with a mean grain size of approximately 0.06-mm diam. The oxygen contents reported in this paper were determined by a vacuum fusion analysis of the tensile specimens after testing. Analyses for other interstitial or metallic impurities showed no significant changes from that of the original material. Tension Tests. Tension tests were performed on a screw-driven tensile machine at a constant cross-head speed of 0.01 in. per min. Tests at elevated temperatures were carried out by heating the

Jan 1, 1962

By S. N. Singh, M. C. Flemings

Results are presented of a detailed study on the combined influences of ingot dendrite am spacing and thermomechanical treatments on the structure and solution kinetics of high --purity cast and worked 7075 alloy. Solution kinetics were found to depend sensitively on ingot dendrite am spacing and on details of therrnomechanical processing, including amount of reduction and extent of&apos; solution treatment before reduction. An approximate analysis is given for rate of solution of nonequilibrium second phase in the cast and worked structres; results of the analysis are compared with experiment. MICROSEGREGATION in high strength aluminum alloys manifests itself as "coring" (composition differences within the primary aluminum-rich phase), and as interdendritic second phase. The mechanism of formation of the microsegregation is understood, and approximate prediction of the amount of second phase is possible for simple binary systems.1,2 When alloy elements or impurities are present in amounts less than their solid solubility at solution temperature, any phases forming from these elements are termed "nonequilibrium" and can be dissolved by appropriate solution treatment. The rate at which the nonequilibrium phases are removed depends sensitively on their spacing (dendrite arm spacing in the cast material, or band spacing in wrought material). When alloy elements or impurities are present in amounts in excess of their solubility at the solution temperature, second phase particles form an "equilibrium" second phase that does not dissolve in heat treatment and may, in fact, coarsen in such treatment. Usual commercial, high strength, wrought aluminum alloys contain nonequilibrium second phases that were not fully dissolved during ingot processing. They also contain equilibrium second phases resulting from impurities present in amounts greater than their solubility. As has been shown by Antes, Lipson, and Rosenthal,3 and will be demonstrated further in a subsequent paper by the authors,4 significant improvements in mechanical properties of high strength alloys can be achieved by reduction or elimination of these second phases. Methods of elimination are 1) to employ high purity materials to minimize amounts of equilibrium second phase, and 2) to employ suitable thermomechanical processing techniques to fully eliminate nonequilibrium second phases. Work reported herein comprises a study of selected thermomechani- cal processing treatments, and of their influence on solution kinetics of wrought high purity 7075 alloy. EXPERIMENTAL PROCEDURE Melting and Casting. The bulk of the work reported was performed on a single ingot of high purity 7075 alloy. The ingot was 4 in. by 4 in. by 8 in. high, uni-directionally solidified following a procedure previously described.5 The mold was heated to 1350°F before pouring the melt. The bottom chill was carbon coated stainless steel. Water was circulated through the chill after the melt was poured. The 7075 alloy was prepared from high purity virgin material (aluminum, zinc, magnesium) and from master alloys (Al-50 pct Cu, A1-15 pct Cr, A1-5 pct Ti). Final measured melt composition (wt pct) was: Zn Mg Cu Cr Ti Fe Si Al 5.70 2.28 1.35 0.18 0.15 <0.002 <0.012 bal Melting was done in a silicon carbide crucible; all tools were coated with zircon wash to minimize iron contamination; degassing was by bubbling chlorine through the melt. che-rmomechanical Treatments. Detailed studies were made on material taken from a location approximately 13 in. from the chill and 51/2 in. from the chill (i.e., from 1 in. thick slices taken between 1 and 2 in. from the chill and between 5 and 6 in. from the chill). Solution treatment was done at 860°F in an air-circulating furnace with a "bottom drop" arrangement to achieve minimum delay time between solution treatment and quench. Samples solution treated in this way were 2 in. by 2 in. by 1 in. Temperature of the quench water was approximately 10°C. Mechanical reduction was by cold rolling. Samples 11/2 and 51/2 in. from the chill were treated for 12 and 24 hr, respectively, before cold rolling. Reduction by cold rolling was then 4/1, 16/1, and 35/1. In each case, several intermediate anneals (1/2 hr at 860°F) were used to permit reaching the final thickness without cracking; two such anneals were used for the 4/1 reduction, five for 16/1, and six for 35/1. After working, materials were again solution treated for various lengths of time from 0 to 48 hr and quenched in water. Structural Measurements. Secondary dendrite arm spacings were measured using procedures previously described.&apos; For each measurement reported, five photomicrographs were first made at X75. Measurements were made of dendrite arm spacings in at least 20 different grains (grain structure was equiaxed). Grain size measurements were made by running a number of random traverses across photomicrographs of the samples and obtaining the mean lineal intercept. Measurement of the volume percent of second phase and porosity was done by quantitative metallography. A two-dimensional systematic point count was used

Jan 1, 1970

By Lloyd Pollish, Robert N. Breckenridge

SUCCESS in any underground mining operation is determined by accessibility of the orebody, which in turn is dependent upon maintenance of passageways to the mining zones and temporary support of the voids caused by extraction of ore. This is accomplished by one or a combination of the following methods: timbering, back-filling, pillaring, or, more recently, rock bolting. Timbering has usually been the principal means of maintaining these underground openings necessary for mining operations. Timber, however, does not prevent ground movement beyond the scope of localized sloughing, which is indicated by the gradual failing of the timber itself. Besides this, timbering has always been a costly process, and with the decline of available supplies of timber close to the mining areas, mining men have constantly sought other methods of controlling ground. Rock bolting is now replacing timbering at an ever increasing rate. Experience has proved that this form of ground support is just as applicable to blocky igneous rock as to stratified rock. Besides preventing sloughing of the walls and back of underground openings, Fig. 1, rock bolting has a stabilizing effect on the surrounding ground in much the same manner that steel reinforcing rods add to the strength of concrete structures. Further, rock bolting is flexible and may be applied to any shaped excavation, whereas timber sets are in a fixed pattern and the ground must often be changed to conform with this pattern. Rock-bolting installations were made in metal mines of the Northwest as early as 1939. An exhaust air crosscut was driven that year in one of the Butte mines of the Anaconda Copper Mining Co. The crosscut was rock-bolted and gunited at the time it was driven and is still being used to exhaust hot humid air from the 3400 level of the Belmont mine. It is interesting to note that no sloughing or caving has taken place in the 14 years it has been open. Even though these early installations of rock bolts were successful, few men recognized their potentiality until recent years, when the coal mines started their programs of mechanization and the great trend toward roof bolting began. In some areas of the Northwest stopes that previously required heavy timbering and close backfilling are now being mined by the more economical cut-and-fill and shrinkage methods. When used in conjunction with timbering, rock bolting increases the efficiency of the operation by decreasing hanging wall dilution and by making it possible to blast larger rounds. Most of the rock bolts installed to date in mines of the Northwest have been the 1-in. diam slot and wedge type, but there has been a recent trend to- ward using the 3/4-in. diam expansion shell bolt shown in Fig. 2. In addition to these commercially manufactured steel bolts, wooden bolts have been used with considerable success by the Day Mines of Wall&apos;ace, Idaho. Installation of the slot and wedge type requires three distinct operations, with tools for each operation: 1—drilling the hole to proper diameter and depth, 2—setting the bolt, and 3—tightening the nut. Holes are drilled and bolts set with pneumatic rock drills. A number of setting or driving tools have been used successfully, but most follow the same general pattern. Usually the driving tool is designed to accommodate a short length of drill steel on one end and the rock bolt on the other end. In this manner the hammering effect of the rock drill is transmitted through the steel and driving tool to the bolt. When machines not having stop rotation are used, slippage is allowed between the driving tool and bolt or between the drill steel and driving tool. The rock bolt nuts are tightened either with pneumatic impact wrenches or with hand wrenches. Impact wrenches are desirable because they are faster and assure adequate tightness. Expansion shell bolts have the following advantages over slot and wedge rock bolts: 1—No special equipment other than a wrench is needed for their installation. 2—Installation is faster. 3—They are removable. 4—Holes need not be drilled to a specific depth as the expansion shell will anchor anywhere along the length of the hole. These advantages are offset somewhat by the lesser strength of the bolt, since expansion shell bolts are generally made from 3/4-in. diam steel as compared to 1-in. diam steel for the slot and wedge type. One manufacturer, however, is now fabricating expansion shell rock bolts from steel of high tensile strength, which gives this ¾-in. bolt a much greater strength than that of the mild steel bolt. Table I illustrates tests made by the Anaconda Copper Mining Co. to determine the proper hole size to use with various types of bolts and to determine

Jan 1, 1955

By G. W. Ostroot, S. Shryock

Cementing deep, high-temperature oil wells where static temperatures range from 350 to 400F has become routine in the part decade. In the United States there were 271 wells drilled deeper than 15,000 ft during 1963. Many of these wells had static temperatures higher than 400F. Bottom-hole static temperatures near 700F are now realities in the geother-mal (steam producing) wells of California&apos;s Salton Sea area. The detailed planning initiated prior to drilling the wells is discussed together with the methods, materials and equipment used in solving the cementing problems which are encountered. Data are also presented that lead to development of cementing compositions that provide adequate thickening time, do not retrogress in strength, and maintain low permeability under these extreme temperature conditions. Field data include the cementing programs used on eight relatively trouble-free geothermal steam wells in the Salton Sea area. INTRODUCTION Not too many years ago cementing oil wells with temperatures in the range of 300F caused considerable anxiety. In some areas of the United States it is now fairly common to cement wells having bottom-hole static temperatures in excess of 400F. We are now confronted with the problem of cementing wells with temperatures ranging from 500 to 700F. Temperatures in this order of magnitude are often found in geothermal steam wells. From where does this extreme heat emanate? There are many theories as to the source of this steam flow. The most widely held views are: (1) heat- ing of ground water fairly close to the surface by an intrusive mass of hot rock; (2) steam generation from a reservoir of metamorphic rock, normally found below 25,000 ft and not at the shallower depths of the Salton Sea reservoir; and (3) high-temperature gases (water vapor) escaping and migrating from molten or semi-molten rock (magma) at a considerable depth. Of these. No. 3 seems to be the most generally acceptable explanation. Heat from springs and fumaroles has been used for years as a means of heating and cooking; however, significant progress in harnessing the vast power of underground steam reservoirs has been relatively slow. The first large-scale attempt to use the heat generated by steam from wells was made in Italy around the beginning of the 20th century. In excess of 250,000 kw of electrical power is now being produced from holes around Larde-rello, Italy. Another very active drilling program was initiated in the volcanic area of New Zealand in 1949.&apos; Natural steam for power projects in the United States began in the early 1920&apos;s. An early commercial steam field is located at the Geysers, approximately 75 miles north of San Francisco, an area discovered in 1847 and used for many years as a health resort. Steam originates from 15 wells that have been drilled since 1957. The present output from this project is 25,000 kw. Success of the Geysers operation has been responsible for several companies taking a careful look at the feasibility of producing steam for power generation in the Salton Sea area of Southern California&apos;s Imperial Valley. Geothermal steam activity in this latter area began in 1961 when O&apos;Neill, Ashmun and Hilliard completed Sportsman No. 1, at that time the hottest wellbore in the world.&apos; Since its References given at end of paver. completion seven additional wells have been successfully completed in this area. Many problems encountered in drilling steam wells had to be overcome to make the ventures successful. Formation temperatures encountered in the Salton Sea seemed to be a straight-line function (a gradient of 13F per 100 ft of depth).&apos; This imposed severe conditions on all aspects of drilling and completion. This varied, to some extent, from gradients in the older geothermal areas. Not to be overlooked is the effect of these temperatures on casing creep or elongation by thermal expansion (Table I), because standard API flanged wellhead equipment makes no provision for this kind of performance. Floating equipment was redesigned, and changes in types of downhole equipment were made in an effort to eliminate anticipated problems. In the later completed wells, standard oil-well cementing equipment has been used. During the early development of geothermal steam wells there were some problems resulting from blowouts. However, these were eliminated in the deeper Salton Sea wells and no problems were encountered with the drilling mud. A sodium surfactant mud was used on the Sportsman No. 1 to drill from 2,690 to total depth. Nevertheless, it was necessary that a cooling system be added and the mud cooled before circulating it back into the well. The difficulty in evaluating the size of the steam area and its potential in terms of pounds of steam and years of productivity still has not been resolved. Economic complexities have also entered into the steam play in the Salton Sea. The wells at the Geysers were drilled at a cost of $15,000 to $20,-000, whereas the Salton Sea wells will cost more than $150,000. This cost differential has to some extent been accounted for because of the heavily

Jan 1, 1965

By J. W. Edington

THE Hopkinson bar has become a popular technique for the measurement of the mechanical properties of materials deformed at high strain rate. Maximum use of the equipment is made in the arrangement first used by Kolskyl in which a short compression specimen is sandwiched between two pressure bars and is loaded by a single pulse travelling through the system. The pressure bars are used both to apply the load to the specimen and as transducers to obtain continuous strain-time histories of three pulses, incident on, reflected, and transmitted by the specimen. The data measured by the pressure bars can be analyzed in terms of the stress/strain behavior of the specimen.2&apos;3 However, one of the assumptions of the analysis of the observed pulses is that the total stress and total strain do not vary significantly from point to point within the specimen at any given instant during the deformation process. Although this assumption is generally justified for very short disc-like specimens2 the situation is uncertain for larger specimens. For example, at small plastic strains (-0.01) Hauser et al.2 have some evidence of small flucations in the total stress within the crystal during deformation, even in relatively short aluminum specimens. In addition, Karnes4 has shown that the plastic strain, and by inference strain rate, is different at each end of a compression specimen tested in a Hopkinson bar, although the length of the specimen was not specified. Recently, the mechanical properties and the dislocation substructure have been investigated in single crystals of columbium5 (length 0.25 in., diam 0.19 in.), and copper6 (length 0.5 in., diam 0.5 in.) deformed at high strain rates. As part of this research program the assumption that the plastic strain is constant throughout the specimen has been checked by measuring the total dislocation density as a function of position in the specimen. Compression specimens of the same orientations and dimensions were tested as described previously5,6 sing a split Hopkinson bar. Since any discontinuity in strain distribution is most likely to arise during the initial stages of deformation the investigation was performed on specimens deformed to plastic shear strains of 0.054 (copper) at a strain rate 1.2 x l03 sec-1, and 0.06 (columbium) at a strain rate 1.5 X l03 sec-1. The orientation of the single crystals is shown in Figs. 1 and 3. Thin foils were taken parallel to the most highly stressed slip plane, i.e., (111) in copper and (011) in columbium, using conventional disc techniques. The dislocation densities were measured using first order reflections with compensation for invisible dislocations.5&apos;6 In the copper single crystals the discs were randomly distributed throughout the cross section of the specimen. However, the dislocation density obtained from each disc was plotted vs the disc positions relative to the ends of the specimen. The results for the copper specimens are shown in Fig. 1. Clearly the dislocation density is constant throughout the main portion of specimen within the experimental error. The error bars on the dislocation densities correspond to a shear strain variation of 0.015 on the basis of previous measurements% ± of the rate of increase of dislocation density with strain in copper single crystals of the same geometry. Thus within this experimental error the plastic strain can be concluded to be constant within the specimen and the assumptions used in the analysis of the stress/time curves are therefore reasonably valid. The higher measured dslocation density near the impact end and the lower dislocation density at the bar end of the copper specimen is in agreement with the results of Karnes4 who showed that this strain/time curve rose to a maximum more rapidly at the impact end compared with the bar end. Hauser et al.2 have also pointed out that at small plastic strains (-0.01) the strain at the impact end of the specimen may be greater than that at the bar end. Thin foils taken from different points within the columbium single crystals demonstrated that the dislocation density could vary significantly within the specimen, see Fig. 2. Large areas of some thin foils up to 30 µ sq contained very few dislocations, see Fig. 2(a). However, in other parts of the compression specimen dislocation configurations like those shown in Fig. 2(b) existed over large areas (-30 µ sq). As a result, when the average dislocation density in a thin foil is plotted as a function of the position of the thin foil relative to the ends of the specimen, considerable scatter is observed, see Fig. 3. In this material then, the local dislocation density, and consequently the

Jan 1, 1970

By H. C. Brown

SINCE 1934 the steel industry has been utilizing the spectrograph for supplementing wet chemical analysis in the production control of electric and open hearth furnaces. This means of control made great strides during the war years because of the general acceptance of the spectrograph and the increased emphasis that was placed on rapid control methods. However, in the post war era, with the demand still on increased production, it became apparent that a still more rapid and economical means of production control was needed. Since the spectrograph had been used mostly in the analysis of low alloying and residual elements, it also became apparent that equipment was needed to extend the spectrographic technique to the analysis of the high alloying elements in stainless steel. For these reasons, companies manufacturing spectrographic equipment were prompted to start development work on direct reading instruments. In June 1949, the Applied Research Laboratories of Glendale, Calif., announced that a direct method of spectrochemical analysis for stainless type steels had been developed. This paper will describe the use of the Applied Research Laboratories Production Control Quantometer in the quantitative control of stainless, silicon, and plain carbon steels being made at the Butler Pennsylvania Div. of the Armco Steel Corp. The Armco Butler Div. has one 70-ton electric furnace and six 150-ton open hearth furnaces. The electric furnace is employed in the making of all types of stainless steel and the open hearth furnaces are used for the production of silicon, wheel, and plain carbon steels. The ARL quantometer was purchased primarily for the purpose of controlling the steelmaking in the electric furnace, but its use has been extended for the analysis of final tests (ladle tests) on a number of different types of stainless, silicon, and plain carbon steels. Because of this additional work by the quantometer, substantial savings in manpower and time have been realized by the laboratory. In the analysis of a set of preliminary tests from the stainless steel furnace, approximately 40 min in laboratory time are saved due to quantometric analyses. Despite the fact that more specialty grades of stainless steel are being made in the electric furnace, the average tons per hour have been increased since the quantometer was put into operation. Specialty grades require more furnace time than regular commodity grades of stainless steel. The installation of the ARL production control quantometer was completed on March 13, 1952. By May 1, 1952, the instrument was calibrated for nickel, chromium, manganese, silicon, and molybdenum, which are the elements necessary for the production control of the stainless steel furnace. Within the following month, training of personnel on the quantometer was achieved and a study of the accuracy of the instrument showed that the results obtained were sufficiently accurate for control purposes. Therefore, on June 11, 1952, the quantometer was placed on production control for all types of stainless steels. Starting September 11, 1952, the instrument was gradually placed on ladle analysis (final tests) as the analytical curves were refined and additional curves were drawn. The quantometer has been relatively free of breakdowns since placing it on production control. The samples from only one stainless steel heat have had to be analyzed by wet chemistry because of instrument trouble. The previously existing heat-time record was also bettered by 15 min on a commodity grade of 18-8 stainless steel. Scope of Control In general, the quantometer determines all elements necessary for the production control of all types of stainless steel heats and for the ladle analysis of various types of stainless steel heats. It is also used in reporting final results for silicon, manganese, chromium, nickel, molybdenum, tin, copper, and aluminum on all silicon steel grades and manganese, chromium, nickel, molybdenum, tin, and copper on several plain carbon steel grades. Table I shows the elements and the concentration ranges of these elements in the various types of stainless, silicon, and plain carbon steel that are determined on the quantometer. A study of the results obtained on ladle test samples of stainless steel types 410, 430, 430 Ti, 446, 301, 302, 304, 304L, 305, and 17-7 PH will be discussed. Also included in the study are the results obtained on ladle test samples of a number of silicon steels. Apparatus In order to take full advantage of the potentials of the production control quantometer, the unit has been placed in an air-conditioned room with relative humidity control. The temperature is maintained at 73&apos;22°F and the humidity at 45&5 pct. The air conditioning serves as a precaution to minimize the amount of adjustment and calibration needed during operation. It also reduces contaminating fumes and dust and thereby lessens the necessity for maintenance on the equipment. The quantometer is composed of three units: the high precision multisource unit, the 1.5 meter vertical spectrometer, and the console. The source unit supplies excitation conditions varying from spark-like discharges to arc-like discharges. The voltage to the source unit is supplied by a motor-generator

Jan 1, 1955

By K. E. Barrett

Exxon owns a uranium mill and holds two mining leases in Live Oak County, Texas, about halfway between San Antonio and Corpus Christi. The properties make up the Felder Uranium Operations which was reopened earlier this year. Exxon held an oil, gas, and other minerals lease on the J. C. Felder tract, which was adjacent to a relatively shallow uranium discovery by Susquehanna-Western, Inc. on the Marrs-McLean lease immediately south of the Felder property. Drilling in 1967 and 1968 confirmed the presence of reduced uranium mineralization in the basal sand unit of the Oakville formation on the Felder tract, which formed the major part of the roll-front deposit. In 1969 Exxon and Susquehanna-Western, Inc. entered into a sale and purchase agreement which provided for Susquehanna to mine and process Felder ore and purchase recovered uranium. Susquehanna moved an alkaline-leach mill from Wyoming, erected it on the Ray Point property, and placed it into operation late in 1970. Susquehanna mined and processed ore from the Felder and McLean properties through March 1973. Susquehanna ceased operations in March 1973. Exxon then acquired the mill and mill property. Exxon also purchased the mineral rights to the McLean lease, re-negotiated a mining lease for that property, and carried out shut-down programs for the mining and mill areas in the fall of 1973. The project was put on a standby basis until late 1973, when Exxon initiated mine feasibility studies for the project. MINE PLANNING EVALUATION The feasibility study for reopening the Felder Project began in late 1975 and was not completed until late 1976. I will discuss several areas of the feasibility study that required additional work prior to making the decision to renew operations. Ore Reserves Preparations for estimating the ore reserves began with the re-evaluation of more than 1500 natural radioactivity logs from exploration and pre-development drilling that had been completed on the property. These gamma ray logs of non-core rotary drill holes were the principal source of data used in making the estimate. Chemical assays of cores from the deposit were also used in the reserve determination. Electric resistivity and self-potential logs were made along with the gamma ray log. In December 1975 an additional core drilling project was undertaken to confirm the in-place density and radiometric equilibrium characteristics of the ore deposits. Comparison of chemical assays of cores with the U308 values calculated from the logs showed that the unoxidized ores were in radiometric equilibrium. In contrast, cores from anomalies occurring in near surface, weathered, and oxidized zones were in radiometric disequilibrium. Several important decisions were made in developing a mine plan or schedule of production from the Felder and McLean ore bodies. Disposal of Produced Mine Water: The ore bodies of the Felder Uranium Project occur at a point below the ground water table. The ore zones to be mined must first be dewatered to allow removal of mineralized material. In the open pit operations, this is accomplished by maintaining a perimeter ditch around the periphery of the open pit, allowing the interior of the pit to drain and collect into a sump and be pumped from the mine. In addition to anticipated water production from future mining operations, approximately 200M gallons of water was contained in three open pits left from prior mining operations. In two of these existing pits, the water was to be removed and disposed to allow for planned backfilling of waste material into these pits. The third pit would also have to be drained to allow continued mining of an area left from the prior operations. Essentially no ground water information was available for this area. The only data available was water production history from Susquehanna&apos;s mining operation. Two water wells were drilled early in 1976 on the Felder lease for use in obtaining hydrological data. A long term draw-down test was performed by pumping one water well and measuring water level drawdown in both the pumped well and the observation well. From these data, values for permeability and storage coefficient were calculated. These data were then used in modeling the aquifer to allow calculation of water influx into the mining area versus time. Once a schedule of water production, including the stored volume in the existing pits was calculated, alternate solutions for disposal were evaluated. The first system evaluated was a series of deep injection wells. The wells were designed to inject at a depth of approximately 3500 feet. Again very little information concerning reservoir characteristics of the receiving sand units was known. Using assumed values for reservoir permeability and storage coefficients, an injection well system was designed to allow for disposal of produced mine water. The biggest

Jan 1, 1979

By G. Borelius

ABOUT the turn of the century, Gibbs&apos; thermo-dynamic theory of heterogeneous equilibrium, on the one hand, and the experimental methods of thermal and microscopic analysis, on the other, gave to the physical metallurgist his first scientific tool, the equilibrium diagram. The classical equilibrium diagram of a binary alloy system shows the boundaries between ranges of homogeneous and heterogeneous equilibrium in their dependence of concentration and temperature. A homogeneous solid sohtion which on cooling passes such a boundary is assumed to precipitate, forming a mixture of two phases with different concentrations. The equilibriunl diagram and the equilibrium theory, however, give no information about the time scheme of the process or the intermediate states passed during precipitation. For this reason it satisfies neither the practical need of the metallurgist nor the curiosity of the physicist. As a matter of fact, in the heat treatment of alloys for technical use the objective very seldom is the equilibrium state. Thus good mechanical properties of construction material are connected, for the most part, with some intermediate state. As these intermediate states are thermodynamically unstable, there is, from a theoretical point of view, always to be expected a decay of the good properties with time; and it is a matter also of practical interest to know whether this natural life time of a material is of the order of, say, ten or thousands of years. Thus, for many reasons, there is a current demand to complete our knowledge of equilibrium through knowledge of the kinetics of the precipitation phenomena. From the point of view of the physicist, the most interesting question in this case is whether there are any general laws governing the kinetics. According to a generally accepted view, precipitation is ruled by two more or less independent phenomena, the formation of nuclei of a new phase and the growth of these nuclei. It is also commonly accepted that there is a tendency for the velocity of growth to increase with increasing temperature because of the increasing mobility of the atoms. There is also a tendency for the velocity of growth to decrease in the neighborhood of the two-phase boundaries. So far, however, very little is known quantitatively about this fundamental phenomenon in the case of solid metallic systems. In our laboratory attention has been directed especially toward the nucleation phenomena, and a series of measurements have been carried out with the guidance of a work- ing hypothesis (based on experiences from previous work on order-disorder transformations in alloys) about the influence on the nucleation of thermo-dynamic potential barriers. However, before discussing the experiments, the theoretical ideas will be considered. In a binary solid solution the arrangement of atoms on the lattice points approaches with increasing temperature a state of full randomness, as illustrated by the ball model of Fig. 1, that might represent a [111] plane of a face-centered alloy with 30 pct "black" and 70 pct "white" atoms. In reality the atoms are changing places continually with their neighbors so that the picture should rightly have been a moving one. On account of this thermal motion the concentration of black atoms within a certain group of, say, a hundred or a thousand lattice points fluctuates with time around the bulk concentration of 30 pct in a manner governed by statistical laws. With decreasing temperature two independent changes in this state grow more and more important. First, the mobility of the atoms decreases, and second, the forces between the atoms will have an increased influence on the fluctuations. In alloys with a tendency for precipitation, which are the concern of this lecture, the distribution function of concentration fluctuations will broaden, so that the relative probability of great local variations from the bulk concentration increases. Fig. 2 gives an example of such a fluctuation. When the alloy is supercooled below the solubility limit into the range of two-phase equilibrium, the fluctuations will now and then at some point give rise to a state that resembles the equilibrium state and thus will form a stable nucleus that is capable of growing by diffusion processes. In discussions with colleagues and in the literature, I have often encountered the idea that three or four atoms of the dissolved metal could form a nucleus of the new phase. A look at the ball model might be enough to indicate that this cannot be true. If it were true, there should be nothing but nuclei, whereas we know from experiment that nucleation must be a rather rare occurrence. In fact we have, as will be mentioned later, certain reasons to believe that the nuclei are formed by fluctuations containing some hundreds of atoms, which should be the order of the number of black balls in the fluctuating group of the figure, if it were extended into three dimensions. As a working hypothesis we have assumed that the fluctuations producing nuclei, though large and rare, still are ruled by the distribution laws of fluctuations of the supercooled solid solution in its initial state. Thus the probability of nucleation will be connected to the thermodynamic properties of the solid

Jan 1, 1952