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By James B. Cathcart

The potash mine of the International Minerals and Chemical Corp. is about 18 miles east of Carlsbad, New Mexico, in sec 1 and 12, T 22 S, R 29 E, N.M.P.M. Potash is produced from two zones in the Salado formation of late Permian age. The lower zone, consisting of a mixture of sylvite (KCl) and halite (NaCl), lies at a depth of about 900 ft, and the upper zone, in which the principal potassium mineral is langbeinite (K2S04.2MgS0d), lies at a depth of about 800 ft. Because of the plastic nature of the material, fractures in the Salado formation are extremely rare and have been noted only on the 800 ft level of the International mine. The open fracture described below is almost unique. Only one other open fracture has been noted, and it was on a working face in the same general area as the one described, but was destroyed before the writer had a chance to examine it. According to J. E. Tong, foreman on the 800 level, this fracture was similar to, but smaller than, the one herein described.

Jan 1, 1949

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Jan 1, 1938

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Jan 1, 1938

By C. R. King

Most of the acid volcanic glasses such as obsidian, perlite, pitchstone, pumice, and pumicite (volcanic ash) are susceptible to some expansion if suddenly subjected to a suitably high temperature in a properly designed furnace, and subsequently suddenly cooled. Expansion results from the action of chemically combined or dissolved water expanding as a vapor within the softened heated rock particles. This expansion forms countless minute bubbles within the pasty mass of the natural glass particles. If the particles are cooled before these bubbles can escape, the resulting products are cellular, more or less spherulitized glass froths or hollow glass spheres of many types. Chemically, they are essentially aluminum silicates containing about 70 to 75 pct silica, 10 to 16 pct alumina, and 2 to 7 pct sodium plus potassium oxides. They are relatively resistant to attack by acids or alkalies, are resistant to heat up to over 1000°F, and are completely inert to insect or fungus attack.

Jan 1, 1949

By Robert M. Weidenhammer

For years before the war, Coal had the reputation of being a sick industry. Currently it is operating at peak production and succeeding pretty well in keeping out of the red. But, says Mr. Weidenhammer, it will have a relapse as soon as the war ends unless (1) working capital can be built up; (2) it gets the support of the people and Congress; and (3) a truly long-range national fuel policy is formulated.

Jan 1, 1943

Institute of Metals Division Iron and Steel Division Extractive Metallurgy Division Council J H Scaff (IMD) Chairman, Robert W Shearman, Secretary, J S Smart, (IMD), P T Stroup, (EMD), A W Schlechten, (EMD), J S Marsh, (ISD), A W Thornton, (ISD), M E Violin, (MED), D S Eppelsheimer, (MIED) Journal of Metals Editorial Advisory Committee J S Smart, Jr, Chairman, W A Dean, J C Kinnear, Jr, T D Jones, Evan Just, John Marsh, M Tenenbaum Pacific Northwest Regional Conference A Y Bethune, General Chairman, Frank N Marr, Chairman, General Arrangements, R J Lapee, Chairman, C P Love, (EMD Program), W M Armstrong, Chairman, Physical Metallurgy Program, L W Heinzinger, Chairman (ISD Program), J P Spielman, Chairman, (MIED Program) New England Regional Conference K H Mairs, Chairman, W A Backofen, Vice-Chair¬man, Delmar E Trout, Secretary, G W Coleman, Treasurer, F H Wilson, Past Chairman, Members at Large Sidney Siegel, Boston, G F Donahue, Connecti¬cut Representatives from Connecticut Frank Chudy, J E Chafey Representa¬tives from Boston N L Reed, E Gordon

Jan 1, 1955

By S. G. Bankoff

INCE1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. [ ] In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (-200 mesh) and 50 c.c. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments [c] through g are more insoluble than lead carbonate, therefore should prevent the formation of lead carbonate on the galena surface. In experiment [i] the calcium oxalate, which presumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments [j] through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1941

By S.G. Bankoff

Ince1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (—200 mesh) and 50 C.C. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments c through g are more insoluble than lead carbonate, there- fore should prevent the formation of lead carbonate on the galena surface. In experiment i the calcium oxalate, which precumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments j through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1943

By S. G. Bankoff

Ince1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (—200 mesh) and 50 C.C. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments c through g are more insoluble than lead carbonate, there- fore should prevent the formation of lead carbonate on the galena surface. In experiment i the calcium oxalate, which precumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments j through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1943

By E. R. Dean

A wire-feed mechanism has been employed to fabricute metal alloy film resistors to various sheet resistivities on oxidized silicon substrates. The effect of several thousand hours storage in air at elevated temperatures on the resistance and temperature coefficient of resistance is presented. Unprotected films of- sheet resistivity between 100 and 500 ohms per sq fabricated at 300°C substrate tenzperatures were unstable when stored at 150°Cfor extended periods. The higher sheet resistivity films exhibited the greatest instability; however, even the 100 ohms per sq films drijted excessively for device application. When stored at still higher temperatures, the normalized resistance increases to maximum, then decreases until a minimum value is obtained, then finally increases in resistance until open. The use of a protective overcoating of SiO has had considerable benejicial effects on the film stability, so that 250 ohms per sq films deposited on 300°C substrates are now stable after 1000 hr storage at 250°C and possess a temperature coefficient of resistance less than 200 ppm per C. The use of a low substrate temperature during depositon (100°C) enables the preparation oj resistors with very low tenperature coefficients of resistance (10 to 20 ppnl per 'C). However, these films are less stable than their higher substrate temperatuve counterparts. During extended storage, the resistance of the protected films always decreases with lower substrate films exhibiting larger normalized resistance decreases. This resistance decrease is accompanied by a linearly related increase in the temperature coefficient of resistance. The electrical behavior of these films may be explained by postulating That the structure of the films is in the transition region between thick continuous films and ultrathin island structure films so that the conductivity is the restlt of both electron scattering and tunneling-activated charge carrier creation between neighboring grains. The annealing behavior when thermally aged is the result of defect anneal, grain growth, and selective oxidation. TheRE is a considerable interest in thin metallic films for use as resistor elements in microelectronic circuits.1,2 These resistor films must be stable when exposed to elevated-temperature storage or operating ambient, possess low temperature coefficients of resistance (hereafter referred to as T.C.R.), and be of a high enough sheet resistivity to be useful. The resistivity and T.C.R. of a thin metallic film are determined by the structure and thickness of the film. Hence the stability of the film when exposed to stress would depend on the stability of the structure. The resistivity of a thin film is the result of the electrons' interaction with the lattice vibrations (electron-phonon scattering), scattering of electrons due to impurities, defects, and grain boundaries and specula reflection from the film surfaces.3' All of these effects serve to reduce the electron mean free path and result in a resistivity higher than the ideal bulk. In ultrathin films possessing essentially an island structure consisting of a planar array of aggregates separated by a few to a few tens of angstroms, conduction is dominated by a combination of tunneling and activated charge carrier reation. Thin films would be characterized by relatively low resistivity, positive T.C.R., and reasonable structure stability whereas ultrathin films possess unstable structures, negative T.C.R., and exhibit high resistivity. Feldman6 has investigated films intermediate between the two regions and postulates that the resistivity of a film in the transition region is composed of two linearly additive parts: that due to the resistance of the grains and that due to the gaps. The grain resistivity would represent the scattering of the conduction electrons by defects, surfaces, and phonon interaction while the gap term represents the tunneling contribution. For gold and platinum films, he found as the film structure becomes progressively less continuous, corresponding to thinner films, the absolute value of the T.C.R. becomes progressively smaller until negative values are observed with respective zero T.C.R.'s at about 35 and 150 ohm per sq, respectively. Recently the author7 investigated the behavior of a multicomponent alloy of nickel, chromium, and iron and found the T.C.R.'s of these films decrease with decreasing substrate temperature during deposition. The lower T.C.A. associated with lower substrate temperatures was attributed to an increased contribution to the total resistivity from the negatively temperature-dependent gap tunneling since it is well-known that thin films deposited on low-temperature substrates consist of a higher density of smaller grains than the same sheet resistivity films deposited on higher-temperature substrates. Under conditions of thermal anneal, the author found that, when various sheet resistivity films fabricated at 300°C substrate temperature are exposed to extended storage in air at 300°C, the thinner films increase in resistance until open, while the thicker films

Jan 1, 1967

By Frederick H. Williams

The object of this paper is to bring to the attention of those members of the Institute who are interested in the subject, a method for the estimation of manganese, which has been frequently used in the labratory of the Vulcan Steel Works during he last eight months, and which is deemed worthy of more general use. It is simply an adaptation of well-known processes, for the purpose of determining this element in pig iron and steel. In general, the method consists in precipitating the manganese as binoxide dissolving in dilute sulphuric acid in the presence of an excess of a standardized solution of oxalic acid, and titrating the remainder of the oxalic acid left unoxidized with permanganate of potash. For this method, therefore, two standardized solutions are needed, viz., a permanganate solution and an oxalic acid solution. The permanganate solution is made so that 1 C.C. is equivalent to 1 mgr. of iron. By using so weak a solution and keeping tile bulk of the solution to be titrated down to 75 C.C. or a little leas, the accuracy of the process is greatly increased, since the final reaction is almost if not quite as sharp as if a stronger solution were used. The oxalic acid may be of almost any strength, but if made so that 1 c.c. requires 3 O.C. of the permanganate to oxidize it, it will auswer well. The process is then, as follows: from 1 to 2 grams of. pig iron or steel ate dissolved in 40 to 50 C.C. of concentrated nitric acid with the aid of heat. As soon as solution is erected, in the awe of steel, add gradually and cautiously, the solution being kept boiling, sufficient pulverized chlorate of potash to precipitate the manganese as binoxide. Two grams will be a great abundance. In the case of pig iron, first remove the carbon and silica by filtering the solution through asbestos and washing with concentrated nitric acid. Filter the strong acid solution in which the binoxide has been precipitated, through asbestos with the aid of the filter pump. When it has entirely passed through wash well with water. Blow the contents of the funnel into the beaker in which the precipitation was made and rinse the funnel with a little water.

Jan 1, 1882

By S Bankoff

INCE1 proposed that electrostatic attraction between oppositely charged particles was responsible for slime-coating. Del Giudice2 postulated the metathetic formation of a cementing compound. Wark3 suggested that prevention of slime-coating was related to peptization of the slime. [ ] In the experiments of Table I the technique employed was essentially that of del Giudice, with the difference that the particle was examined under a film of water rather than dry.4 In general, the polished particle was agitated for 2 min. in a pulp consisting of 12.5 grams of the slime (-200 mesh) and 50 c.c. of distilled water, washed in three baths of distilled water, and examined at 220 diameters with the Leitz Ultropak. Observations of Brownian movement were made at 850 diameters with dark-field illumination. Several of these experiments do not jibe with the metathesis theory. According to published solubilities,5,6 the lead salts of the anions in experiments c through g are more insoluble than lead carbonate, there- [ ] fore should prevent the formation of lead carbonate on the galena surface. In experiment i the calcium oxalate, which presumably was on the calcite surfaces, should have permitted the formation of a lead carbonate cement by virtue of its greater solubility. Experiments j through m show that the addition of lime accelerates the deposition of quartz onto a galena surface. The writer is unable to postulate a satisfactory cementing compound, according to the metathesis theory, to explain this effect. These experiments led to the conclusion that the metathetic formation of a cement-

Jan 1, 1941

Jan 1, 1969

The following is an incomplete list of members and guests who called at Institute headquarters during the period Feb. 10, 1918 to Mar. 10, 1918: W. G. Anderson, St. John, N. B., Canada. Charles E. Locke, Boston, Mass. L. M. Banks, Camp Meade, Md. E. T. Lednum, Joplin, Mo. P. E. Barbour, Albany, N. Y. C.' K. McDonald, Washington, D. C. Alan M. Bateman, New Haven, Conn. C. T. Malcolmson, Chicago, Ill. Graham Bright, Pittsburgh, Pa. Stuart B. Marshall, Badin, N. C. J. F. Callbreath, Washington, D. C. T. C. Merriman, New Haven, Conn. J. E. S. Clark, Riverside. Cal. Arvid E. Nissen, Gary, Ind. G. H. Clevenger, Palo Alto, Cal. Herbert G. Officer, Conway, S. C. George C. Crossley, Trenton, N. J. J. E. Parker, Bulawayo, Rhodesia, S. Afr. R. H. Eagles, Palmerton, Pa. Francis R. Pyne, Elizabeth, N, J. Charles Enzian, Pottsville, Pa. Alfred Hull Ramage, Joplin, Mo. Albert H. Fay, Washington, D. C. H. H. Stoek, Urbana, Ill. David B. Gemmill, Crown King, Ariz. G. M. Taylor, Colorado Springs; Colo. Ronald Harris, London, Ont., Canada. Charles Tubby, St. Paul, Minn. Wm. J. Hayes, Colombia. So. America. J. B. Tyrrell, Toronto, Canada. B. B. Hood, Chrome, N. J. Edmund W. Westervelt, Ymir, B. C. 0. P. Hood, Pittsburgh, Pa. Carl Zapffe, Brainerd, Minn. H. M. LaFollette, LaFollette, Tenn. W. S. Boyd, formerly superintendent of mines of the Ray Consolidated Copper Co., has been appointed assistant general manager. William Campbell, Professor of Metallurgy, at Columbia University, is acting as metallurgist at the New York Navy Yard.

Jan 4, 1918

By A. L. Holley

There is a growing demand for pure and cheap material for fine open-hearth steel; a material not only very free from phosphorus, but from carbon and silicon; so that it may he rapidly converted into steel. Iron and steel scrap are not trustworthy as to quality, and they are often dear. There are three methods of purifying cheap materials for the open hearth. 1. Mechanical puddling, as done at Creusot, which removes 90' per cent. of the phosphorus from the pig iron. 2. Krupp's washing process (the conduct and results of which 1 fully described in a former paper*), which eliminates 70 to 80 per cent. of the phosphorus and most of the sulphur and silicon from pig iron. Neither of these processes would sufficiently purify, for very fine steel, those very impure pigs which are cheapest in many parts of the United States. 3. The process of producing directly from the ore an iron which is practically pure chemically, although mechanically mixed with the impurities of the ore. This is the oldest of iron processes ; one form of it, the CataIan forge, employed to produce charcoal blooms, is still in use, but its great cost is rapidly throwing it out of competition. Among the modern attempts to produce iron direct from the one, on a large scale and at a cheap rate, several have been in various respects successful. Dr. Siemens's process of treating a ton and a half or more of ore and the coal to deoxidize it, in a rotating gas furnace, and bringing out, in some four hours, a ball of chemically pure iron so soft that the fluid and impure slag may be sqneezed out of it, is the most attractive and the most highly developed of all the modern direct processes. I hare watched it, from time to time, since 1874, and have noted a steady improvement. It may now be said to have passed the experimental stage, although, like older processes, it must be adapted by practice to special materials. The cause which has been more potent than all others, including the defects of the best direct processes, to bring these processes into disrepute, is the wasteful treatment of the direct product. With one or two exceptions (when failure mas due to other and obvious causes), the direct product has been made into wrought iron (weld iron). Even Dr. Siemens has, at Towcester, in England, and at Park, Bro. & Co.'s, in Pittsburg, set up his apparatus for this purpose. Is it likely that

Jan 1, 1880

By A. L. Holley

THERE is a growing demand for pure and cheap material for fine open-hearth steel ; a material not only very free from phosphorus, but from carbon and silicon; so that it may he rapidly converted into steel. Iron and steel scrap are not trustworthy as to quality, and they are often dear. There are three methods of purifying cheap materials for the open hearth. 1. Mechanical puddling, as done at Creusot, which removes 90' per cent. of the phosphorus from the pig iron. 2. Krupp's washing process (the conduct and results of which I fully described in a former paper*), which eliminates 70 to 80 per cent. of the phosphorus and most of the sulphur and silicon from pig iron. Neither of these processes would sufficiently purify, for very fine steel, those very impure pigs which are cheapest in many parts of the United States: 3. The process of producing directly from the ore an iron which is practically pure chemically, although mechanically mixed with the impurities of the ore. This is the oldest of iron processes ; one form of it, the Catalan forge, employed to produce charcoal blooms, is still in use, but its great cost is rapidly throwing it out of competition. Among the modern attempts to produce iron direct from the one, on a large scale and at a cheap rate, several have been in various respects successful. Dr. Siemens's process of treating a ton and a half or more of ore and the coal to deoxidize it, in a rotating gas furnace, and bringing out, in some four hours, a ball of chemically pure iron so soft that the fluid and impure slag may be squeezed out of it, is the most attractive and the most highly developed of all the modern direct processes. I have watched it, from time to time, since 1874, and have noted a steady improvement. It may now be said to have passed the experimental stage, although, like older processes, it must be adapted by practice to special materials. The cause which has been more potent than all others, including the defects of the best direct processes, to bring these processes into disrepute, is the waste-ful treatment of the direct product. With one or two exceptions (when failure was due to other and obvious causes), the direct product has been made into wrought iron (weld iron). Even Dr. Siemens has, at Towcester, in England, and at Park, Bro. & Co.'s, in Pittsburg, set up his apparatus for this purpose. Is it likely that

Jan 1, 1880

By Floyd E. Bliven

A century ago, Thomas Carlyle sketched the Emblem of the Wasting Candle in one of his papers. "Terar Dum Prosim" he wrote under the candle-" May I be wasted so that I be of use." The application of his reasoning is an excellent guide for a discussion of the scrap problems of today. The General Electric Co. has addressed itself to the need of proper and careful preparation of scrap metals for many years. A supervisor of salvage directs this work in each of the works. Generally he is an engineer and has had broad factory training. He gives general direction to the collection, preparation and disposition of scrap materials. He operates the extensive facilities which each works has provided for the centralization and control of scrap accumulations, and also initiates studies leading to the reduction of scrap accruing from machining and assembly operations. r We recognize that each industry, each factory, each locality faces a different set of conditions. Irrespective of size, in a plant employing 20 men or a large works with 15,00 employees-certain fundamental principles can be applied for organization and the collection of scrap. The manufacture of electrical apparatus is a highly complicated intricate business. In one area we make electronic tube and adjacent buildings house the manufacture of steam turbines. Both are instruments for power-different in size and in many cases serving different fields of application. Unlike the great industries that build automobiles, trucks, or engines where repetitive operations, once solved, set the stage, electrical manufacturers' plants are large jobbing shops. Therefore, we must carefully plan every step in handling the scrap that "in so wasting to produce the finished motor or locomotive-we can return this product to reprocessing and ultimate use." ESSENTIALS FOR SALVAGE EFFICIENCY The essential steps for an efficient salvage department are: I. Selection of Personnel.-An able foreman would be a man of broad experience and understanding-one who commands the respect of the entire foreman group as well as that of his own men. In the interest of clean scrap, it is necessary to acquaint the foremen in the separate manufacturing units with the need of careful segregation in the shop and the best methods of obtaining it. At least 40 per cent contact time should be devoted for this purpose. 2. The physical equipment of the salvage department should be devised and selected to handle complete, at one point, all scrap operations. Bulky materials as produced by some large shops can be economically placed in salable shape at the divisional point. Because salvage

Jan 1, 1943

Extractive Metallurgy Division Institute of Metals Division Iron and Steel Division Council R R McNaughton, Chairman (EMD), Ernest O Kirkendall, Secretary, J H Scaff, (IMD), Morris Cohen, (IMD), T J McLoughlin, (ISD), J S Marsh, (ISD), P T Stroup, (EMD), R D Parks, (MED), D S Eppelsheimer, (MIED) Journal of Metals Editorial Advisory Committee J S Smart, Jr, Chairman, W A Dean, T D Jones, Evan Just, J C Kinnear, Jr, J S Marsh, M Tenenbaum Pacific Northwest Regional Meeting F X Cappa, General Chairman, W W Wiltschko, Chairman (Metals Branch), Program Chairmen H E Lee (EMD), S E Maddigan (IMD), G R Heffernan (ISD), L C Richards (Ind Min Div), James Bell (Finance Committee), Ed Vestica (Registration), Donald Johnson (Special Events)

Jan 1, 1954

By E. S. Machlin

THE function of this paper is to present certain results based on the fact that the strain energy arising from the solution of out-of-size solute atoms into the solid matrix is free energy and not internal energy, and that this strain energy is almost wholly shear strain energy as Zener1 pointed out. One natural consequence of this fact is an expression for the excess entropy of mixing due to the strain energy. Also, a derivation of the integral molar free energy of mixing partitioned to strain energy will be made using the model of Lawson2 and thermodynamics. This derivation has the advantage of showing in a simple way the assumptions involved in Lawson's treatment. The excess entropy of mixing partitioned to strain energy can be derived in two ways. The first way makes use of the fact that the strain energy is almost wholly in the form of shear strain energy. In this case, as Zener1 pointed out, the change in entropy due to the addition of shear strain energy is to a first approximation given by ?S/?? p,T = - ?lnµ/?T p,? Hence, the excess entropy of mixing partitioned to strain energy will be given by Sx ? = ?S/?? p,T Gx ? = - ?lnµ/?T p,? Gx ? where, Gx ? is the relative integral molar free en- ergy partitioned to strain energy; S is the entropy; is the shear strain energy; µ is the shear modulus; T is the absolute temperature; p is the pressure; and ? is the shear strain. Zener,1 as well as others, has pointed out that the shear strain energy stored in a compressible isotropic solid due to the insertion of an off-size incompres-sible sphere into a spherical hole in the solid, is approximately given by 2/3 µ/O (O°I - O)2 where a is the volume of spherical hole and no , is the volume of sphere. If we now consider the introduction of one mol of such spheres into an infinite volume of solid, then the relative partial molar free energy excess due to strain energy alone is GM ? = 2/3 µ/v (v ° 1 - v)2 where v is the molar volume of solvent and v°1, is the molar volume of pure solute type 1. Let us consider that these spheres are the two types of atoms in a binary solution, then there will be a similar relation for solute 2. The total relative integral molar free energy excess due to strain is then, to the approximations stated above GM ? = GM ? x1 + GM2 ? x2 = 2/3 µ/v [(v ° 1 - v)2 x1 + (v ° 1 - v)2 x2]. Lawson's relation for the strain energy can be de-

Jan 1, 1955

By G. Thodos, R. B. Grieves

A method has been developed for the accurate calculation of the cricondentberm and cricondenbar temperatures of multicomponent hydrocarbon mixtures of known composition. The mixtures may contain any number of components including paraffins and isoparaffins, olefins, acetylenes, naphthenes and aromatics. This approach is based upon the mole fraction of the low-boiling component in the mixture and graphically presents the ratios of the cricondentherm and cricondenbar temperatures to the pseudocritical temperature as {unctions of a boiling-point parameter. The only requirements are the critical temperature, normal boiling point and the approximate vapor pressure behavior of each component. For mixtures of more than two constituents a stepwise calculation procedure is necessary where the pseudocritical temperature is based upon the critical temperature of the pure low-boiling component and upon the actual cricondentherm or cricondenbar temperature of the mixture of all the remaining higher-boiling components. From an analysis of 22 binary systems (123 compositionsl, the average deviation of calculated cricondentherm temperatures from reported values is 0.87 per cent, based on degrees Rankine; and for 10 multicomponent mixtures containing from three to six components, the average deviation is 0.98 per cent. From an analysis of 18 binary systems (104 compositions) the average deviation of calculated cricondenbar temperatures from reported values is 0. 79 per cent; and for 15 multicomponent mixtures, 1.47 per cent. Equations, derived from the graphical relationships, are presented which enable rapid calculations for both binary and multicomponent systems. INTRODUCTION With the increasing tendency towards the use of high pressure processes, the need for an accurate method of calculation of the properties of a multicomponent hydrocarbon mixture in the critical region is becoming more essential. Critical region phase relations are also significant in gas condensate reservoirs, for which a knowledge of the fluid phase boundaries and regions of retrograde condensation make it possible to evaluate optimum operating conditions. The possibility of liquefaction in the underground structure may be established, and information on the feasibility of the use of repressurizing may be determined. A typical phase diagram for a multicomponent hydrocarbon mixture is presented as Fig. 1. This figure also shows the regions of retrograde behavior encountered by following lines AB and AC. If accurate methods of calculating the temperatures and pressures at the critical, cricondentherm (maximum temperature) and cricondenbar (maximum pressure) points of multicomponent hydrocarbon mixtures of known composition were available, it would be possible to estimate closely the entire phase diagram of any mixture. Several methods have been presented in the literature for the estimation of the critical temperatures and pressures of multicomponent mixtures containing all types of hydrocarbons and including the fixed gases.4-8,21 Considering the cricondentherm and cricondenbar points, the work is more limited. Etter and Kay5 have developed rather complex equations for