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By R. V. Smith

The theoretical background for calculating friction factors for flow in gas wells by two methods is presented. The first method, requiring pressures, temperatures and specific volumes of the flowing fluids at various depths in the well bore, shows how the mechanical-energy-balance equation for vertical flow may be graphically integrated over the actual path of the expansion of the fluid in the well. Thus, assumptions regarding the effective temperature and effective compressibility of the fluid in the well are avoided. The second method presents an equation derived on a basis of the assumptions that both the temperature and the compressibility are fixed at constant effective values throughout the flowing column of gas. The second method provides a convenient and practical means of calculating friction factors for gas wells and lends itself readily to the problem of calculating subsurface pressures in a flowing gas well. The application of both methods to actual test data taken on a flowing gas well is illustrated in the paper. INTRODUCTION As friction factors for the producing strings of flowing gas wells cannot be measured directly and must be calculated from flow-test data, study of the methods of arriving at friction factors is a necessary adjunct to understanding the characteristics of flow in gas wells. There are two methods of calculating friction factors for gas wells; they differ from one another mainly in the treatment of the path of expansion of the fluid in the well. In the flowing well, the energy consumed in lifting the fluid from the bottom to the top of the well, overcoming the friction between the moving fluid and the pipe walls, and increasing the velocity of the fluid as it flows up the producing string is supplied by expansion of the flowing fluid. The available energy is determined by the expansion of the fluid that follows a path determined by conditions of temperature, compressibility and phase changes of the fluid during the expansion. A means of evaluating the available energy in a flowing gas well and determining the proportion of the available energy used in lifting the gas, overcoming friction, and increasing the velocity of flow is developed in this report. Knowing how much energy is consumed in overcoming friction makes it possible to calculate friction factors for given flow rates in given sizes of pipes in wells. Friction coefficients, as used in this report, are dimension- less proportionality multipliers used in the flow equations to satisfy the equality between the terms of the equation. The square root of the reciprocal of the friction coefficient is termed the friction factor. It has been known for many years that friction factors may be computed directly from mathematical formulas based on certain assumptions regarding the temperature and compressibility of the moving fluid in a well. A general equation is presented in this report without assumptions for vertical flow of fluids and a conventional-type equation is derived on the basis of assumptions that fix the temperature and compressibility at constant values. Accurate pressures at the sand faces in wells are required in the method of determining the productivity of gas wells, as outlined by Rawlins and Schellhardt1 in Bureau of Mines Monograph 7. Where measurements are not made with subsurface-pressure gauge; or static gas columns are unavailable, flowing pressures customarily are calculated at the sand face in the well by the use of the well-known Weymouth formula1. Natural gas engineers have realized that errors introduced by the use of friction factors as given by the Weymouth formula are relatively unimportant in testing low-capacity gas wells; they also know that such factors are important considerations in testing large-capacity gas wells. Accordingly. present research on the productivity of gas wells at the Petroleum Experiment Station of the Bureau of Mines, Bartlesville, Okla., is being directed toward measurement of the pressure loss due to friction in flowing gas wells. It is beyond the scope of this report to show how friction factors vary with rate of flow and in pipes of different diameters, as it is intended only to develop and illustrate the use of mathematical expressions for calculating friction factors from flow-test data. The equations presented apply only to turbulent flow in circular pipes. ENERGY RELATIONS FOR FLOW OF FLUIDS2 The concept of conservation of energy is usually the basis of any study of fluid flow through vertical pipes as in gas wells, horizontal pipe lines, or orifices. In deriving equations, the following symbols are used:

Jan 1, 1950

By H. I. Meyer, D. F. Searcy

INTRODUCTION The analysls of our previous paper' on the behavior at two immiscible fluids separated by gravity into two dlstinct saturated zones in the porous medium was shown to be theoretically valid only if one of the two fluids was immobile. The practical problems associated with flow of both phases have so far been impossible of solution by these analytic methods. We, therefore, decided to resort to a simulator study to answer the following pertinent questions: 1. If the lighter fluid is produced from a point above the fluid-fluid interface, how long will it take for the heavier fluid to come up to the point where production of both fluids is taking place? 2. After steady-state two-phase production is established, what is the relative production rate of each phase, on what physical variables does this depend, and what are the boundary conditions at the outflow face? 3. A third question was at least partially answered in the course of this investigation: that of the shape of the interface under flow conditions. These questions are of fundamental importance in the fields of hydrology and the reservoir mechanics of oil and gas production. In order to simplify equipment used and still retain a fair physical representation of these phenomena, it was decided to use a Hele-Shaw type of analogy in which the flow took place between two vertically mounted pieces of plate glass. The advantage of this system is that it eliminates any surface effects between the matrix of the porous medium (e.g. packed sand) and also allows equilibrium conditions to be established more quickly. The principle disadvantage (apart from the obvious one of being one more step removed from the prototype) is that our equipment limited us to two dimensional flow studies. In spite of these limitations answers to the questions were obtained which seem adequate for our purposes. We would like to see more work of this nature done to verify and to improve our conclusions. DESCRIPTION OF EQUIPMENT AND PROCEDURE A drawing of the equipment used in this study is shown in Fig. 1. Fluid flow takes place between the two 36 in. x 12 in. pieces of plate glass held apart at the long edges by two spacers of cellulose acetate sheet (Kodapac IV) which is available in several thicknesses. This sandwich was clamped together by small c-clamps whose stress was distributed by long pieces of 3/8-in. keystock. Accurate spacing was obtained by tightening these clamps as indicated by micrometer measurements on the outside of the glass. At the upstream end of the plates a piece of 6-in. diameter pipe simulated an infinite reservoir, while at the downstream end a 2-in. Lucite cylinder with a small hole near the top of the flow region served to drain the fluid. Sealing was achieved by O-rings, the whole system being tightened by pressure on the Lucite tube provided by set screws (not shown in the drawing). The total head

Jan 1, 1957

By Kenneth B. Ray, George R. Gardner

The application of wet cleaning processes for the beneficiation of bituminous coal has created in some localities a problem in the recovery and disposal of fine solids in the washery water. The maximum allowable concentration of these solids in the washery circuit that is consistent with satisfactory operation of the cleaning units remains a controversial point. It has, however, been generally recognized for a number of years that some degree of control should be exerted over the concentration of such material. Early methods of control involved intermittent or continuous discharge of a portion of the plant slurry into near-by streams or settling ponds, and this persisted even after the adoption of settling tanks or cones. The practice is not always economical, for two reasons: first, because of the waste of coal, and, second, because it is sometimes difficult and expensive to obtain an adequate supply of water. The latter condition often is aggravated by chemical treatment of the make-up water that is necessary to prevent excessive corrosion of plant equipment. The modern approach to this problem has been the adoption of continuous thickening devices. However, because such equipment occupies considerable plant space and is somewhat expensive to construct, the practice of loading these thickeners beyond their rated capacity is widespread, therefore often the performance of such units is not altogether satisfactory. In recent years, European washeries have increased the rate of settling of the fine coal from the slurry by the addition of specially prepared starch solutions. These reagents cause flocculation of the solid particles and thereby increase the rate of sedimentation. The first important work on the flocculation and clarification of coal slurry was done by Henry, who developed the Henry process and used it successfully in Belgian preparation plants. Soon after the initiation in Belgium, the process was introduced into England, where subsequent investigation developed similar processes, which were successfully used in

Jan 1, 1940

By George R. Gardner, Kenneth B. Ray

The application of wet cleaning processes for the beneficiation of bituminous coal has created in some localities a problem in the recovery and disposal of fine solids in the washery water. The maximum allowable concentration of these solids in the washery circuit that is consistent with satisfactory operation of the cleaning units remains a controversial point. It has, however, been generally recognized for a number of years that some degree of control should be exerted over the concentration of such material. Early methods of control involved intermittent or continuous discharge of a portion of the plant slurry into near-by streams or settling ponds, and this persisted even after the adoption of settling tanks or cones. The practice is not always economical, for two reasons: first, because of the waste of coal, and, second, because it is sometimes difficult and expensive to obtain an adequate supply of water. The latter condition often is aggravated by chemical treatment of the make-up water that is necessary to prevent excessive corrosion of plant equipment. The modern approach to this problem has been the adoption of continuous thickening devices. However, because such equipment occupies considerable plant space and is somewhat expensive to construct, the practice of loading these thickeners beyond their rated capacity is widespread, therefore often the performance of such units is not altogether satisfactory. In recent years, European washeries have increased the rate of settling of the fine coal from the slurry by the addition of specially prepared starch solutions. These reagents cause flocculation of the solid particles and thereby increase the rate of sedimentation. The first important work on the flocculation and clarification of coal slurry was done by Henry, who developed the Henry process and used it successfully in Belgian preparation plants. Soon after the initiation in Belgium, the process was introduced into England, where subsequent investigation developed similar processes, which were successfully used in

Jan 1, 1940

By G. Krauss, J. M. Thompson, H. Y. Kumagai

Boron-doped p-type and arsenic-doped n-type source materials were used to deposit thin silicon films on amorphous fused quartz substrates by cathodic sputtering in argon atmospheres. All as-sputtered films were found to have high electrical resistivities of about 104 ohm-cm, despite controlled variation of the substrate temperature from 50O to 400°C. The high resistivity of the n-type films persisted even after postdeposition heat treatments as high as 1000°C, while p-type films showed a sharp decrease in re-sistivity to values on the order of 1 ohm-cm or lower after heat treatments above 650°C. X-ray and electron diffraction, together with transmission electron microscopy of the p-type films, revealed that the improved electrical properties resulted from two distinct processes. A primary crystallization or recovery within the pains, which were approximately 200Å diam in the as-sputtered films, accompanied the initial sharp drop in resistivity at 650°C. Following this process, a secondary recrystallization or discontinuous grain growth was nucleated in films heated at 1000°C. The resulting significantly increased size of certain grains and the corresponding decrease in grain boundary area accompanied an additional decrease in resistivity after heat treatment at 1000°C. The properties of thin silicon films are of interest because of their possible application in device technology. Although evaporated silicon films on amorphous substrates1-3 and both sputtered and evaporated germanium films4-' have been studied in some detail, sputtered silicon films have not been widely investigated. It has been observed that evaporated silicon films deposited at substrate temperatures below approximately 600°C are amorphous.1,3,9,10 At substrate temperatures higher than this, the films are polycrys-talline, sometimes exhibiting a fiber texture with the fiber axis normal to the substrate surface.' Similar results have been obtained with germanium films, although in this case the substrate temperature for the amorphous to crystalline transformation is reported to be as low as 150OC.5 The mechanism of film deposition by cathodic sputtering differs markedly from that of thermal evaporation. It might be expected, therefore, that the properties of sputtered and evaporated silicon films would also differ. The purpose of our study was to determine the effects of deposition conditions and heat treatments on the electrical resistivity, structure, and composition of thin silicon films sputtered on fused quartz substrates. EXPERIMENTAL DETAILS Apparatus. A schematic diagram of the sputtering apparatus is shown in Fig. 1. The vacuum chamber was enclosed by an 18-in.-diam by 12-in.-high Pyrex bell jar mounted on a stainless-steel base plate. Access holes in the base plate were used to supply argon gas to the chamber, to allow for various electrical feedthroughs, and to provide mechanical motion to the shutter between the source material and substrate. The chamber was evacuated by a pumping system consisting of a 720 liter per sec oil diffusion pump backed by a 13 cu ft per min mechanical pump. Ultimate pressures of less than 1 x 10-6 torr could be achieved. The substrates were securely mounted on the stainless-steel substrate holder by quartz tabs held in place by stainless-steel screws. Temperatures of the substrate holder were measured by a thermocouple inserted within the holder. A quartz lamp was used to heat the holder and temperatures as high as 420°C could be maintained. Deposition Conditions and Procedure. The substrates used were polished fused quartz slides 116 by 1-12 by 3 in. and were outgassed at 200°C for 1 hr at a pressure less than 1 x 10-5 torr before film deposition. This was followed by a presputtering period of 2 hr during which the movable stainless-steel shutter was so positioned that deposition on the substrate was prevented. At a sputtering voltage of 5000 v dc and an argon pressure of 0.03 torr, the cathode cur-

Jan 1, 1967

By Edward Martinez

Although the copper segregation process has been known as a method for treating oxide copper ores since the 1920's, the reactions involved in this process are still a matter of conjecture. However, the evidence turned up in a recent series of experiments at Asarco's Central Research Laboratories strongly indicates that some of the proposed reactions may not be occurring. Experimental work on oxide copper ores from the Sagasca mines in Chile led to the discovery of the copper segregation process in 1923. It was found that the reduction of the copper with coal at about 700°C occurred on the surface of the coal instead of remaining disseminated in the ore. The unusual behavior of the copper, which caused it to migrate from the ore particles to the coal, was traced to the presence of a small quantity of sodium chloride occurring in the ore. Further experiments with oxide copper ores proved that the presence of a halide, either occurring naturally or admixed with the ore, caused the copper to migrate from the ore particles and to segregate in the charge.

Jan 8, 1966

[Abrahamson, Guy C., (5'43) Lt., 0-880861, Hammer Field Fresno Calif. Adamec, LAW, (8'42) c/o Braden Copper Co., Rancagua, Chile. Adams, Karl S., (9'43) Univ. of New Hampshire, Durham, N. H. Agnilar, Roperto Q., (9'43) Texas College of Mines, El Paso Texas. Ainge, B'onald Farra, (943) Otago University, Dunedin, New Zealand. Akaran, Cevdet A,, (9'44) Pennsylvania State College, State College, Pa. Albala, Americo, (5'44) School of Mineral Industries, The Pennsylvania State College, State College, PA.]

Jan 1, 1946

By Arthur H. Leigh

Anode mud, the residual material collected from the bottom of the electrolytic cells during the refining of copper is leached, roasted, fire-refined and cast into Dore1 metal anodes. Dore1 metal is a gold-silver-copper alloy containing 80 percent silver. The metal is processed electrolytically using the Moebius system to refine silver and separate gold, platinum and palladium. The Moebius cell cathodes receive a deposit of silver crystals which are melted and cast into 1000 ounce silver bars with 999 Fine minimum purity. Gold mud is collected in fabric bags and cast into gold anodes for further refining in the Wohlwill cells. Wohlwill cells are unique in that gold, the noble metal, can be put into solution electrolytically without the use of aqua regia. Gold is collected on high purity gold foil cathodes and cast into 400 ounce bull ion with 999.7 Fine minimum purity. Platinum and palladium remain in the electrolyte progressively increasing in concentration and are finally separated and purified by precipitation.

Jan 1, 1973

By N. E. Maccallum

(Cleveland Meeting, October, 1912.) ALMOST half a century has passed since the Siemens brothers, after tedious and costly experiments, finally began the manufacture of open-hearth steel. The furnace of that time was very small, having a hearth-capacity of from 3 to 4 tons, and we can appreciate the wonderful development that has taken place in those 50 years by the knowledge that to-day furnaces of 50 times the original capacity are in operation. As the new steel process assumed importance, and furnaces began to grow in number and in size, a question arose, to which no satisfactory answer has ever been given, and that was: ?What is the safe and economical limit of the open-hearth furnace?" Various stopping-places have been suggested, and 20, 30, 40, and 50 tons have each been advocated, but all such arbitrary restrictions have been passed, and 60 tons would probably represent the average furnace, although in a few instances from 70 to 80 tons are regularly tapped into one ladle. The furnaces which are the subject of the present paper have gone far beyond even these limits, and since, in my opinion, they mark another step in the progress of open-hearth steel, they will be considered fairly and frankly, in order that those to whom the matter may be of interest may be able to judge and form their own Conclusions. Short accounts of the work of these furnaces have appeared from time to time in various technical journals, of which the following is a brief résumé. These furnaces are the property of the Phoenix Iron Co., of Phoenixville, Pa., and their distinctive and important feature is, that they charge to twice the capacity of one ladle, and tap simultaneously into two ladles, with a device for controlling the flow into either. In this way the capacity of the furnace is not limited, as formerly, but heats of any size within the capacity of two ladles may be charged.

Oct 1, 1912

By T. A. Dungan

THE thermal processes for the production of metallic magnesium can be divided into two general classifications, the direct reduction of magnesia with carbon and the indirect reduction of compounds of magnesium by reducing agents that are themselves products of carbon reduction. The latter are so chosen as to cause reduction of magnesium compounds wherein only the magnesium is liberated in the vapor phase. Reducing agents used are: calcium carbide, silicon carbide, silicon, aluminum, various silicides or combinations of calcium, aluminum, silicon in iron. All of these are products of highly endothermic reactions and, with the exception of scrap aluminum, can be produced in an open, submerged arc furnace; that is, the arc is covered only by the charge itself. The more investment in energy required to prepare such a reducing agent, the less is the energy required in the subsequent step to reduce the magnesium compound to the metal. It is impossible, however, to avoid the laws of thermodynamics, no matter how much circumambulation is resorted to in the preparation of successively more powerful reducing agents. Since each such step carries forward its own inefficiencies, it appears evident that the ultimate status of such processes is dependent upon the development of by-products. EARLY EXPERIMENTS IN DIRECT REDUCTION The direct reduction of magnesium oxide by carbon has a decided appeal to both the scientist and the industrialist. The successful production of the carbothermic plant at Permanente is a significant fact in the substantiation of this concept. Like most developments, however, the history of carbon reduction of magnesia is not one of triumph after triumph, or immediate heady success to the investigators. It is understood that one of the early investigators conducted an experiment wherein he placed carbon and magnesia in one end of an evacuated tube and managed to heat this end to a temperature high enough that magnesia and carbon deposited at the other end of the tube. The charge, unreduced, appeared to have been completely transported from the hot to the cold end of the tube. This raised doubt for some time as to whether magnesia could be reduced at all with carbon. It was correctly suspected, however, that the magnesia was in fact reduced and the resultant magnesium vapor and carbon monoxide reacted upon one another upon reduction in temperature to reform the starting ingredients. Attempts were then made to dilute the two vapors by passing a considerable stream of hydrogen through an arc furnace charged with magnesia and carbon. Thus by dilution of the products it was expected to obtain metallic magnesium. The results were positive and metallic magnesium was

Jan 1, 1944

By P. D. Bush, E. H. Gates, M. D. Vijayaraghavan, L. F. Engle

The process developed over the last few years by Republic Steel Corporation in conjunction with Colorado School of Mines Research Institute has been used as a basis for the conceptual engineering of full size plants. The paper will cover the equipment design criteria, equipment design itself, and the integration of the complex unit operations. There are unique features of agitation and use of gas media through- out. The paper will provide an illustrative example of the process requirements for a variety of raw material feeds. It will discuss the materials of construction approach required.

Jan 1, 1973

By W. F. Stowasser

A downdraft traveling grate process to agglomerate pelletized iron ore concentrates has been successfully demonstrated in a pilot plant at Carrollville, Wis. Work there followed several years of development in the Allis-Chalmers Mfg. Co. laboratories, and the pilot plant phase was carried out in co-operation with Arthur G. McKee & Co., consultants and engineers to the iron and steel industry. End result of the process is conversion of iron ore concentrates into a form which can easily be transported and smelted in the blast furnace.

Jan 5, 1955

By H. E. Rorschach

Activity in Oklahoma fields declined in 1938 from the banner year of 1937. During the year, 1768 wells were completed as compared to 2632 completed during the year 1937. The following tabulation sets out details regarding the wells completed during the year: These computations do not take into account the wells drilled for repres-sure and salt-water disposal, and other nonexploratory wells. Purchasers' reports filed with the Corporation Commission of the State of Oklahoma show a total of 168,789,229 bbl. of oil purchased from Oklahoma leases in 1938, or a daily average of 462,436, a decrease of about 25 per cent from the year 1937. The outstanding operation of the year was the further development of the Ramsey pool, in western Payne County, the producing horizon being classified as the Wilcox. This pool was discovered on the last day in the year 1937, by the Mid-Continent Petroleum Corporation drilling on a unitized block in see. 18, T. 18 N., R. 2 E. The map in Fig. 1 shows the development at the end of the year 1938. An important discovery of the year was the Champlin Refining Company's No. 1 Boehm, in Garfield County, sec. 4-24N-8W., the producing horizon being the second Wilcox found at a depth of approximately 6700 ft. This pool was assigned the name of Hillsdale. Some of the offsets to this discovery well had not come up to expectations at the end of the year, but the discovery seems to be important as indicating that the Wilcox sand is productive in the Anadarko Basin area, providing that the right structural conditions are present.

Jan 1, 1939

By H. E. Rorschach

Activity in Oklahoma fields declined in 1938 from the banner year of 1937. During the year, 1768 wells were completed as compared to 2632 completed during the year 1937. The following tabulation sets out details regarding the wells completed during the year: These computations do not take into account the wells drilled for repres-sure and salt-water disposal, and other nonexploratory wells. Purchasers' reports filed with the Corporation Commission of the State of Oklahoma show a total of 168,789,229 bbl. of oil purchased from Oklahoma leases in 1938, or a daily average of 462,436, a decrease of about 25 per cent from the year 1937. The outstanding operation of the year was the further development of the Ramsey pool, in western Payne County, the producing horizon being classified as the Wilcox. This pool was discovered on the last day in the year 1937, by the Mid-Continent Petroleum Corporation drilling on a unitized block in see. 18, T. 18 N., R. 2 E. The map in Fig. 1 shows the development at the end of the year 1938. An important discovery of the year was the Champlin Refining Company's No. 1 Boehm, in Garfield County, sec. 4-24N-8W., the producing horizon being the second Wilcox found at a depth of approximately 6700 ft. This pool was assigned the name of Hillsdale. Some of the offsets to this discovery well had not come up to expectations at the end of the year, but the discovery seems to be important as indicating that the Wilcox sand is productive in the Anadarko Basin area, providing that the right structural conditions are present.

Jan 1, 1939

By H. J. Struth

In these trying times of proration and low oil prices, it is decidedly necessary for all branches of the petroleum industry to accord full recognition to the economic phenomena that contribute to its varying state of welfare. Perhaps no other single factor has a more important bearing upon the general oil situation than the supply and demand of gasoline. Year after year, the records have shown that the degree of prosperity or depression accompanying the industry's developments has been to a large extent influenced by the degree of balance maintamed between the supply and demand of gasoline. More and more it is being realized within the industry that equilibrium between the supply and demand of gasoline forms the basic structure of crude and product market values and, consequently, the deciding factor in the financial results of the industry as a whole. The influence of the gasoline situation upon the market and financial structure of the petroleum industry was effectively demonstrated during 1930, when excess accumulation of gasoline undermined not only the refined oil market but the crude market as well. In fact, it was a top-heavy gasoline situation that defeated the realization of benefits that might have accrued from an otherwise favorable statistical position in the producing branch of the industry. Indicative of this is the fact that crude oil production was curtailed to the extent of 98,323,000 bbl. last year, while refinery runs to stills were maintained at an excessive rate until late in the year, creating an excess gasoline production of 6,663,000 bbl. above actual requirements. Nevertheless, the movement to curtail refinery operations during the closing months of the year prevented a far worse situation, although it came too late to turn the ebbing momentum of the general oil market. Despite the severe depression of the market values that accompanied 1930 developments, it can be said that the results attained during the closing months of the year, in the direction of production control, marked a decisive turn in the industry's economic affairs. In fact, a review of the oil situation from every angle points definitely to a better general understanding and recognition of the workings of the economic law of supply and demand. As a result, the year closed with crude production in

Jan 1, 1931

By Y. Takahashi, I. Iwasaki, S. Tanabe

Supported by the vigorous capital investment of the heavy and chemical industries and by the ever-increasing demand for durable consumer goods in the past decade, Japan has now emerged as the world's third largest steel producer, surpassed only by the United States and the Soviet Union. In 1968, the crude steel production is expected to exceed 50 million tons; the per capita steel consumption at that time will reach 886 lb, approaching the level of Western Europe. Characteristics of the Japanese steel industry is the high dependence of raw materials on overseas sources. Before World War II the industry relied on North China and Manchuria for coking coal, and on middle China, Hainan Island, the Philippines and the Malayan Peninsula for iron ores. After the war, the major sources of iron ores were shifted to the Philippines and the Malayan Peninsula, supplemented by shipments from the United States, Canada, India and Goa. The United States, in addition, became the primary source of coking coal.

Jan 1, 1967

The Army Reorganization Act, which became effective July 1, 1916, contains a provision authorizing the organization of an Officers' Reserve, in which will be included a Corps of Reserve Engineers. There will also be an Enlisted Reserve of skilled workmen in technical lines. The special provisions of the bill relating to the Engineer Officers' Reserve were formulated with the help of the Joint Committee of the several national engineering societies, which has been at work on the matter for over a year with the War Department and Committees of Congress. Recognizing that engineering science is the basis of success in modern

Jan 8, 1916

G. M. TAYLOR,* Colorado Springs, Co1o.-I do not think the plan outlined in this paper would work at Cripple Creek. Most of our men have had a pretty good education. The Cripple Creek district is a lessee district-I do not think there is one mine operating in Cripple Creek to-day that does not have the leasing system. We have as many men leasing on our property as we have mining and every plan who is working for wages is looking for n lease-everyman has mined for him- self, he has been his on7n boss on n lease, either on our own property or

Jan 1, 1919

By Charles H. Morgan

Jan 1, 1905

By C. Norman Cochran

The pllnse diagvam for the NaF-AlF3 system was used to calcutate an ionic model for the NaF-AlF3 system. Assuming an ideal solution,a series of simultaneous equations expressing equilibria be-tween solid and liquid phases at the euleclic, perilec-tic, and melting points were solved for the activities of the ionic species, the dissociation constants, and the entropies and heats of fusion. The calculations suggest the existence of A13F1415 ions in addition to the F-1+AlF6-3 , and AlF4-4 ions previously proposed by others. The calculaled valnes give better agreement with vapor pressures than the previous model without Al3Fl14-5. Additional possible vefinements of the model are proposed. CRYOSCOPIC1 investigations and density data2 for the NaF-A1F3 system have previously been used to study the dissociation mechanism of Na3A1F6 and to derive equilibrium constants for its dissociation to NaF and NaAlF,. Depending primarily on the heat of fusion assumed for cryolite, the dissociation constants ranged between 0.02 and 0.18 from cryoscopic studies, and from 0.09 at 1273°K to 0.16 at 1363°K from density data. In most cases the values were unable to reproduce satisfactorily the experimental liquidus lines very far on the A1F3 side of the Na3A1Fe composition. This suggested the existence of at least one other ionized compound in the melt besides NaA1F4 in the Na3A1F6-A1F3 side of the system. This is assumed to be liquid Na&13F14 (chiolite), which is already established as a stable solid in phase studies of this system. MODEL FOR THE MELT The melt is assumed to be an ideal solution with ion activities equal to anion fractions. The only cation in the model is sodium so that Temkin and simple anionic activities are identical. Although the compounds are completely ionized to Na' and the respective anion in the melt, molecular rather than ionic notation is used throughout this work. The Na3A1Fe is assumed to dissociate to NaA1F4 and NaF as in the former model, and Na&13F14 to dissociate to Na3A1Fe and NaA1F4. Other valid dissociation equilibria can be written involving these four compounds, but all of these can be obtained by combinations of the two described dissociation reactions and, thus, are automatically considered in these calculations. The model allows for no free AlF3 so that compositions for NAIF3 > 0.5 (mole fraction A1F3 on the NaF-A1F3 basis) cannot be treated. The question of the existence of free AlF3 in the melt will be discussed again later. The constants in the model were evaluated from points along the entire known liquidus line of the NaF-A1F3 system. Previous work employed only the liquidus line or densi- ties near the Na3A1F, composition. The liquidus line compositions used in the solution of the model are from unpublished work by Mr. P. A. Foster, Jr., for compositions between the Na3A1F6 melting point and the Na&13F14-A1F3 eutectic, and from the published works of Grjotheim,1 Phillips,3 and Foster4 for the remainder of the system. The relationships used in solving for the desired dissociation constants and heats and entropies of fusion are listed in Table I, and the points along the liquidus line at which each apply are indicated to the right of the relationships. The mole fractions of each of the separate species in the melt are symbolized by N. Relationships [I] and [2] are the respective dissocia-ation constants, Kl and K2, of Na3AIF6 and Na5A13F14 for this model. For simplicity, these constants will be assumed to be independent of temperature. Relationship [3] follows from the assumption of the ideal solution. The expression relating the values of N to the experimental values of NAIf3, is given in Relationship (41. Relationships [5], [6], and [7] each state the equilibrium between a compound in the melt and its pure solid phase for the portion of the liquidus lines where it precipitates. The heats of melting, AH,, and entropies of melting, AS,, used in [5], [6], and [7] are assumed to be independent of temperature. The compositions and temperatures of all five invariant points (two melting points, two eutectics, and one peritectic) along the liquidus lines from NAIF3 = 0 to NAIF3 = 0.5 were employed in the solution. The eutectic and peritectic compositions were particularly useful because each of these is involved in one more equation than other points along the liquidus lines and thus reduces the number of points required to solve for the constants. Also, their use assures that the inflection points in the derived liquidus line will correspond exactly with those on the experimental liquidus line. The total number of equations is 5k1 — 1, where n is the number of experimental composition points used. The number of unknowns is 4n + 5 (4n- 3 values of N, 3 values each of AH, and AS,, and 2 values of K). Thus, six points must be used in the solution to obtain an equal number of equations and unknowns. The one additional required experimental composition was taken on the liquidus line between the Na3A1Fe melting point and the Na3A1F6-Na5A13F14 peritectic. Previous work indicated this was a difficult portion of the curve to fit. The temperature used for the point was 1161°K, the same as for the NaF-Na3A1Fe eutectic. This choice of temperature gave two points with identical NNa3AIF6 values which simplifies the algebraic solution. The second point at this temperature is denoted 1161°'K. PROCEDURE FOR SOLUTION OF EQUATIONS Values were assumed for NNa,AIF and NNaF at the NaF-Na3A1F6 eutectic at 1161°k. By an iterative procedure, the corresponding values for NNa5A13F14 and NNaAlF4 at 1161°K were determined from 131 and 141. A value was assumed for NNaAlF4 at 1161°'K and

Jan 1, 1968