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By J. D. Vincent, Paul A. Weyler

Climax Molybdenum's plan for the Henderson 30,000 tpd molybdenite plant didn't just happen. It slowly evolved over a period of 3% years. Many plants cannot afford similar delays, but the Henderson project will take about 10 years to complete from the time the orebody was first discovered until production begins. Pilot plant testing results with both the single stage and two-stage semi-autogenous grinding circuits were highly favorable in terms of operating costs reduction-so much so, that the Amax subsidiary made the decision to go with semi-autogenous grinding for the Henderson mill.

Jan 5, 1972

By JOHN R. SUMAN

TONIGHT I want to speak of the current problems and the postwar difficulties facing American industry. American industry has done an outstanding job in adjusting its operations to wartime necessity. The national income for 1942 was nearly $120,000,090,000 and of this outlay approximately $55,000,000,000 went for war material. The enormity of the expenditures for war material is indicated by the fact that the expenditures for war purposes alone were greater than the annual gross national income in the period 1931-34. This tremendous production job in turning out a record output of war products was accomplished by industry in spite of a large number of restraining and hampering influences, and I want to mention several of the more important problems.

Jan 1, 1943

By Keats, J. L.

IN THE literature on the elimination of metalloids in basic open-hearth practice, there are a great many heats recorded in which excellent data on changes in slag and metal composition during refining are given, but in almost all of these heats either temperature data or weights and analysis of charge are unrecorded and observations on the physical charac- teristics of the slag are almost always lacking. With these points in mind, a test heat was made in which as complete as data possible on all the factors that affect the elimination of metalloids were obtained.

Jan 1, 1957

THE sessions of the Institute were opened on Tuesday evening, October 26th, at Garrett's Hall, by Mr. Charles A. Otis, Chairman of the Local Committee of Arrangements, who welcomed the Institute to Cleveland, and introduced Col. Charles Whittlesey, who ad¬dressed the Institute briefly on the coal deposits of Ohio. Col. Whittlesey described the situation and character of the coal-beds of the State, and gave a short history of the use of raw coal in the manufacture of pig-iron, and spoke of the excellent quality of metal produced. The aid that a body of scientific miners and metal¬lurgists were capable of giving in the development of coal and other mineral resources was dwelt upon, and the hope expressed that the visit of the Institute to Cleveland might be profitable as, well to its members as to the citizens of the State. The President, Mr. A. L. Holley, responded to the welcome of Mr. Otis and of Col. Whittlesey, and read an introductory address on Some Pressing Needs in the Iron and Steel Manufacture. The following members and associates, duly proposed and indorsed by the Council, were then elected MEMBERS. Alfred S. Bertolet, - Youngstown, Ohio. Henry Binnse, - Chicago, Ill. John Birkinbine, - Philadelphia. Andrew A. Blair, - Watertown Arsenal, Mass. Ogden Bolton, - Canton, Ohio. Lloyd Booth, - Youngstown, Ohio. E. Borda, - Philadelphia. N. P. Bowler, - Cleveland, Ohio. Alexander E. Brown, - Cleveland, Ohio. C. F. Brush, - Cleveland, Ohio. S. M. Carpenter, - Cleveland, Ohio. James Cartwright, - Youngstown, Ohio. Henry Chisbolm, - Cleveland, Ohio. Wilson B. Chisbolm, - Newburgh, Ohio. W. H. Clarke, - Millertown, Pa. James E. Clayton, - Ore Knob, N. C.

Jan 1, 1876

The sessions of the Institute were opened on Tuesday evening, October 26th, at Garrett's Hall, by Mr. Charles A. Otis, Chairman of the Local Committee of Arrangements, who welcomed the Institute to Cleveland, and introduced Col. Charles Whittlesey, who addressed the Institute briefly on the coal deposits of Ohio. Col. Whittlesey described the situation and character of the coalbeds of the State, and gave a short history of the use of raw coal in the manufacture of pig-iron, and spoke of the excellent quality of metal produced. The aid that a body of scientific miners and metallurgists were capable of giving in the development of coal and other mineral resources was dwelt upon, and the hope expressed that the visit of the Institute to Cleveland might be profitable as well to its members as to the citizens of the State. The President, Mr. A. L. Holley, responded to the welcome of Mr. Otis and of Col. Whittlesey, and read an introductory address on Some Pressing Needs in the Iron and Steel Manufacture. The following members and associates, duly proposed and indorsed by the Council, were then elected MEMBERS. Alfred S. Bertolet,.. .. . Youngstown, Ohio. Henry Binnse,. Chicago, Ill. John Birkinbine,.. .. . Philadelphia. Andrew A. Blair,. .. .. Watertown Arsenal, Mass. Ogden Bolton,. .. .. Canton, Ohio. Lloyd Booth,..Youngstown, Ohio. E. Borda,..Philadelphia. N. P. Bowler,.. .. . Cleveland, Ohio. Alexander E. Brown,.... Cleveland, Ohio. C. F. Brush,.. .. .Cleveland, Ohio. S. M. Carpenter,.. .. . Cleveland, Ohio. James Cartwright,.. .. . Youngstown, Ohio. Henry Chisholm,.. .. . Cleveland, Ohio. Wilson B. Chisholm,.. .. . Newburgh, Ohio. W. H. Clarke,.. .. . Millertown, Pa. James E. Clayton,. .. .. Ore Knob, N..C.

By Howard N. Eavenbon

The low-volatile, or smokeless, coal field of southern West Virginia is in Fayette, Raleigh, Wyoming, Mercer, Summers and McDowell counties, in the extreme southern portion of the state, and extends into the adjacent counties of Tazewell and Buchanan in Virginia. McDowell County is the largest producer, with Fayette and Raleigh counties next. The total area of the field (Fig. 1) is approximately 1600 square miles, or 1,024,000 acres. The percentage of volatile matter in the various seams ranges from 15 to 26 per cent, The upper limit of true low-volatile coal is usually considered to be 23 per cent volatile matter; above this point, the coal usually is classed as medium volatile. This limit will be used in this paper. Geological Position of Seams The smokeless seams are among the oldest coal seams in the country, as the Pocahontas group of rocks is the lowest member of the coal-bearing series and rests on top of the Mauch Chunk red shale, in or below which no coal seams of any importance occur. The Pocahontas group, or Lower Pottsville measures, has a thickness of 750 ft. in southern McDowell County, which decreases to about 350 ft. at Prince, on the New River, in Fayette County, 50 miles to the northeast. In this group, at various points, 12 coal beds have been found, of which 4 have been found in workable thickness and are now being mined. The New River group, or Middle Pottsville measures, is just above the Pocahontas group and varies in thickness from 1300 ft. in southern McDowell County to about 700 ft. along New River. At various places, 16 beds of smokeless coal have been identified in this group, of which 5 have been found in workable thickness and are now being mined. A general columnar section of these strata is shown on Fig. 2. The workable seams in these strata, arranged in geological sequence, are as shown on page 77.

Jan 1, 1932

By Karl V. Lindell

THE Jeffrey mine of the Canadian Johns-Manville Co., Asbestos, Que. has operated for a number of years, supplying the parent company, Johns-Manville, raw material for asbestos products. The mine is situated in the 70-mile-long serpentine belt running from Asbestos, Que. on the west to East Broughton on the east. This district is the most important producing area in the world of quality spinning-fiber asbestos, with 11 operating mines supplying 70 pct of the world's needs. The Jeffrey mine, located 90 miles from Montreal and approximately 35 miles southwest of Thetford, accounts for 50 pct of the Canadian asbestos output. Production from the Canadian serpentine belt is the chrysotile asbestos, which is considered the best available for spinning. Consumers in the United States prefer the clean, fine fibers of the Canadian chrysotile of the type produced by the Jeffrey mine. Mining In 1881, when the mine was first opened, all work, including drilling, was done by hand. The deposit, located on a hillside, was first worked as a sidehill cut by hand drilling 15-ft holes and blasting with black powder. The fiber was chiselled from the broken rock. Hand derricks, later powered by horses, were used to raise the rock as the pit deepened. Eventually, the pit became so deep that derricks were, by necessity, replaced by aerial tramways. In the late 1930's, further deepening of the open pit, with the resulting constriction of the pit bottom brought about the need for altering the mining system then in use. The high ratio of overburden to be handled to mill ore mined and the value of surface structures, not company property, that would be destroyed in expanding the area of the pit, definitely indicated vertical rather than horizontal expansion would have to be used. One exception to this was that a small area on company property to north and east of the pit could be opened up. The mining problem then resolved itself into two phases; make the small lateral expansion and as rapidly as possible choose a mining method that would expand the mine vertically. Several methods for vertical expansion were studied and rejected. Methods considered included shrinkage stoping, block caving, glory holing, and various modifications of open workings. Block caving was finally accepted as the most suitable method of underground development. Cost factors and production were important factors in the decision, also, the asbestos mines in the Thetford area were already having success with this method. Original plans provided for the lateral expansion of the open mine where possible and beginning the underground operation. This program was based on the open pit being worked out in 1954, with the underground development and production gradually increasing until the open mine was depleted. In 1949, the plan was changed to allow underground development to progress at maximum so that underground output would be 550 tons per hr by 1951. Any deficit in ore would be mined from the open pit. This change permitted extending the life of the open pit through 1964 and in this time would make available a large quantity of readily attained ore. Block Caving at The Jeffrey Mine Plans for the underground operation were formulated on a 12,000-ton-per-day basis, and the adaptability of block caving methods to high production presented a desirable situation. As shown in the main-haulage plan, a continuous loop was laid out for smooth operation of the underground railroad from the loading points to the underground crusher. A feature encountered at the Jeffrey mine, as well as other asbestos mines using caving methods, is the large size of caved material, requiring that ore be crushed before hoisting.

Jan 1, 1952

By J. C. Reed

CINNABAR was discovered in southwestern Arkansas on Little Missouri River in sec. 1, T.7S., R.26W., in April, 1930, and near Antoine Creek in sec. 28, T.6S., R.23W., some 15 miles farther east in May of the same year. It was not, however, until June, 1931, that cinnabar was identified as such in a specimen from the original discovery area sent to W. M. Weigel1 by Walter F. Hintze of Murfreesboro. Almost simultaneously2, in July, 1931, Moritz Norden of Hot Springs identified specimens from the Antoine Creek area as cinnabar. Immediate interest in the district followed the identification of cinnabar and by January, 1932, the district was known to extend as a mineralized belt about one mile wide trending east-northeast from sec. 13, T.7S., R.27W., in Howard County-across central Pike County and into Clark County to sec. 19, T.6S., R.23W., thence extending southeast into sections 33 and 34 of the same township. Since then, cinnabar has been found in sec. 6, T.7S., R.22W., thus giving a total east-west length to the district of approximately 30 miles. Interest focused mainly on the two discovery areas, with the result that mining development has progressed most rapidly in those localities. In the Antoine Creek area the Arkansas Quicksilver Co. has done con-siderable exploration work and has retorted the high-grade ore so .obtained. In the Little Missouri area the Southwestern Quicksilver Co. has had a 12-ton rotary furnace in more or less continuous operation since April, 1932, and has been the largest producer in the district.

Jan 1, 1935

By Charles Will Wright

ITALY is by- far the poorest in mineral resources of the so-called great pou7ers of Europe. Before the World War this shortage was not so serious as the essential minerals that could not be mined domestically at a profit were bought in the world markets. In those days tourist trade and remittances from Italians abroad helped to provide Italy with foreign exchange. During the World War, when certain mineral products were scarce and when prices rose in some instances to several times normal, the Italian Government began to regulate consumption and imports. It was not until later, when the Fascist regime established the corporate state, that Italy seriously considered adopting a of self-sufficiency. Private industry was grouped under separate corporations, for the principal industries; including mining and metallurgy and the heads of the large producing companies, became members of these corporations. Industrialists were thus able to regulate their own affairs and to advise the Government as to the measures necessary to meet domestic or foreign trade demands upon their industry. Labor was or-

Jan 1, 1939

By Cyril Smith

IN the study of the structure or the properties of a series of alloys or nonmetallic compounds, it is often advantageous to express the com-position not as percentage by weight, according to which the material is always made up and analyzed, but as the atomic percentage of the two constituents. The conversion from the one to the other is repre-sented by the formulas: 100A 100x or 1 x/A+100-x/B B(100-x) _ 100yA 100y [2] X. yA + (100 - y)B or y (100 - y) where x and y are the weight and atomic percentages respectively of the element of atomic weight A, and (100 - x) and (100 - y) are the per-centages by weight and by atoms respectively of the element of atomic weight B. While calculations according to these formulas are simple, they are time consuming if several conversions have to be made. In 1931 Water-man1 constructed a nomograph for performing the conversion, but this did not permit an accuracy greater than about 1 per cent to be obtained in the neighborhood of 50 per cent. Ölander2 has proposed a graphic method simpler than Waterman's and one that gives a uniform precision throughout the entire scale. The possible accuracy is about 0.5 per cent of the whole, depending on the size and accuracy of the coordinate paper used. Recently, Hermann3 has described a slide rule for making the calculations. These devices make use of the simple rearranged equation

Jan 1, 1933

By Cyril Smith

IN the study of the structure or the properties of a series of alloys or nonmetallic compounds, it is often advantageous to express the com-position not as percentage by weight, according to which the material is always made up and analyzed, but as the atomic percentage of the two constituents. The conversion from the one to the other is repre-sented by the formulas: 100A 100x Y x 100 ? x/A A [1] A+ B x + A/B(100-x) X _ 100yA 100y [2] yA+(100-y)B or y+A(100-y) where x and y are the weight and atomic percentages respectively of the element of atomic weight A, and (100 - x) and (100 - y) are the per-centages by weight and by atoms respectively of the element of atomic weight B. While calculations according to these formulas are simple, they are' time consuming if several conversions have to be made. In 1931 Water-man' constructed a nomograph for performing the conversion, but this did not permit an accuracy greater than about 1 per cent to be obtained in the neighborhood of 50 per cent. Olander2 has proposed a graphic method simpler than Waterman's and one that gives a uniform precision throughout the entire scale. The possible accuracy is about 0.5 per cent of the whole, depending on the size and accuracy of the coordinate paper used. Recently, Hermann3 has described a slide rule for making the calculations. These devices make use of the simple rearranged equation:

Jan 1, 1933

By H. J. Wogner

STORAGE of natural gas in underground reservoirs is one of the most important developments in the natural gas industry in recent years. However, it is only when we consider this development together with proved fuel reserves, the know-how of the fuel technologist, and the possibility of making manufactured gas available over large areas, that we begin to appreciate fully the impact that underground storage of gas may have on the future growth and development of large areas in the United States. During the past winter, shortages of natural gas in the industrial East were given wide publicity and domestic consumers were requested to reduce their requirements to a minimum, so that war plants might have sufficient gas to continue operations. Curtailments would have been more drastic except for the fact that large volumes of natural gas had previously been stored in underground reservoirs. Storage of natural gas in depleted or partly depleted gas or oil sands is not new, having originally been tried, as far as I know, about 1915. About five or ten years later an attempt was made to store manufactured gas in a depleted gas sand. This proved unsuccessful at first because the gas was not properly cleaned and the impurities plugged the pores in the sand.

Jan 1, 1945

By George H. Jones

NO STRANGER phenomenon exists in the American mining industry today than the so-called bootleg anthracite industry in Pennsylvania which now produces probably close to 15 per cent of the total hard coal out- put of the State. Instead of being what - was first thought to be a temporary condition, countenanced because of the desperate condition of some of the miners at the depth of the depression. it is thriving now as never before. Re- ports of it have penetrated all over the world, as exemplified by inquiries concerning it in Durban, South Africa mentioned by John C. Cosgrove in his article in the July MINING AND META LURGY.

Jan 1, 1939

By Edgar L. Weinberg, W. Horatio Brown

The Austinville-Ivanhoe lead-zinc deposit occurs in the Lower Cambrian Shady dolomite. This deposit is located in southwestern Virginia in the faulted and folded Appalachian Valley and Ridge province. The ore bodies resemble the chimmey and manto deposits of northern Mexico and are formed by replacement and filling. They are confined to certain favorable zones of the Austinville and Ribbon members of the Shady. Structural and stratigraphic factors combine to control the location and form of the ore bodies. In certain places secondary oxide enrichment of the zinc minerals has contributed to the economic development of the area. It is concluded that the ore is epigenetic and is deposited by hydrothermal solutions rising through the fault "plumbing." Classification is epithermal-telethermal.

Jan 1, 1968

By Philip D. Wilson

SPEED is essentiaI in this war program and it is hard to keep up with developments. When the title of this paper was chosen, the contemplated magnesium production for which plants were then under construction was some 200,000 tons of metal per year or sixty times the 3350-ton production in prewar 1939. A few- days later an analysis of the President's 185,000-plane pro-gram, incendiary bomb schedules, and the additional requirements of the Army. Navy and Maritime Commission made it apparent that a much greater amount of magnesium must be provided in 1943. The new figures are huge but the censor will not per-mit their disclosure.

Jan 1, 1942

By A. C. Lane

Relations de la profondeur de plissement avec la gravita-tion et la hauteur des montagnes dans les Alpes. Par A. Heim (Zurich) 50me Anniversaire, Livre Jubilaire Soc. Geol. De Belgique, Rome, Fascicule 1, 17 to 28. Measurements show a negative anomaly, less densities of .the material below sea level. The author expresses it in terms of the thickness of rocks of an arbitrary density, 2.4, which might be considered wanting. The accordant heights of the summits, the depths of the folds, the deficiency in .gravity, and denudation he finds to be connected. The Alps float on the lightness of the folds of "sal" of weight 2.6 to 2.75 plunged into the heavier "Sima" according to a for-mula: P = h (2.7/2.8-2.7) where - P is the depth of fold-ing below sea level; 2.7 is the weight of the material accu-mulated in folding; 2.8 is the weight of the material dis-placed by it; and h is the mean height of the mountainous regions. For instance, between the valley of Saar and the Val de Bagne in Valais the depth of the folds according to Ar-gand's profiles is between 30 and 40 kilometers. The loss of gravity has been estimated in this region as 1450 X 2.4 = 3480 in units of weight. Obviously errors in the densities would profoundly affect the estimates of the thickness of folding, but his depths of folds are obtained from sections, and from them he works back to the densities. Of course other densities might be placed in the formula. Zur Dichte bestimmung von Tonen. By J. Koenigsberger, Berg u. Hüttenmannisches Jahrbuch, 75, I. Discusses Dr. B. Wilser's investigations as to the best way of obtaining the weight of rocks per unit volume. The use of mercury for rocks affected by water as there recom-mended may easily give too large volumes unless 1 to 3 atm. pressure is used. Thick machine oil is recommended for large lumps of clay.

Jan 4, 1928

By AIME AIME

ON Thursday a most interesting symposium on "Gases in Metals" was held, with both morning and afternoon sessions. The morning was devoted principally to the considerations of the steel maker, the nonferrous field being taken up in the afternoon period. Dr. John Johnston, as chairman, introduced the subject with "A Short Analysis of the Gas-metal Problem and Its Practical Importance." He then introduced P. H. Brace who explained in considerable detail the various vacuum fusion and other methods in use at present, both here and abroad, in the study of "gases" in metals. He was fol¬lowed immediately by H. W. Graham on "The Effect of Oxygen in Steel." The papers elicited considerable discussion, the point being particularly noted by both Dr. Rawdon and Dr. Sauveur that a knowledge of "total oxygen" alone is not sufficient information for the metallurgist, distribution of oxygen being probably the more important. Dr. Johnston, in commenting on the lack of agreement among many of the methods now in use, such as the Ledebur and vacuum fusion, spoke of the contemplated plan of the Iron and Steel Division to have a number of standard samples analyzed by many laboratories by the various methods, the Bureau of Standards acting as a clearing house, so that more definite information may be obtained on the comparative accuracy of the method.

Jan 1, 1933

By Joachim J. Hauser

William F. Hosford, Jr. (Massachusetts Institute of Technology)—Dr. Hauser has used a very interesting method to study the interaction of dislocations on different slip systems, but it should be pointed out that the analysis of the experiments is subject to a serious criticism. He states that "the effect of the compression can be adequately described by one slip system." The effect of frictional constraint during the compression makes this quite unlikely. When a block of metal is compressed its lateral expansion requires a sliding of the metal over the compression platens. The role of friction in the interface between the deforming metal and the platens is to increase the normal force required for the compression. Analyses1213 have shown that, in general, the additional force, p, required for the compression is a function of l/h where is the coefficient of friction, I is the length of the speci- men in contact with the platens. For a constant COefficient of friction, isho' shows that P should increase exponentially with pl/h for both plane strain and axially symmetric compression. For a compression specimen, Fig. 7, whose cross section perpendicular to the compression axis is a rectangle whith one dimension L, much larger than the other W, a much larger force would be required for appreciable flow parallel to L than for flow parallel to U7. Therefore lateral strain in the W direction, EW, should be much greater than the lateral strain in the L direction EL. Since L/H = 14.5 for Dr. Hauser's crystals, and since no lubrication was used, it seems questionable that appreciable lengthening of the crystals could occur. Because the theories of frictional constraint have been derived for isotropic polycrystalline materials, it was decided to make experimental measurements on a single crystal. A section 3.590 in. long was sawed from an aluminum single crystal with a square section of 0.249 in., so that L/W= 14.4. This crystal was tested in compression between dry ground steel platens. Fig. 8 shows the orientation of the crystal and the axis of compression. The face for compression was chosen so that the operation of the single-slip system which would be predicted in the absence of friction would lead to a larger strain in the length direction than in the width direction. The dimensional changes of the width and length as well as the height were measured frequently during the compression with micrometers. Width strains were calculated from the average of readings near each end and at the center. A plot of the length strain, EL, against the width strain E w is given in Fig. 9. The slope indicates that the EL amounted to only 2.5 pct of cw. Other compression tests on similar crystals with shorter lengths also showed severely limited elongation. Even for a crystal with L/W = A.0, EL was only about 26 pct of cw. Because of the frequent interruptions of the tests for dimensional measurements should have decreased the frictional constraint by allowing a reseating of the platens, even smaller elongations under continuous testing seem probable. These tests on long narrow crystals show that essentially plane strain conditions prevailed. We may assume that Dr. Hauser's crystals deformed similarly. That the compression can be described by the

Jan 1, 1962

By Jack R. Elenbaas, Donald L. Katz

A radial turbulent flow formula has been developed which permits the computation of the pressure drop for radial flow in gas wells whether the flow is laminar, turbulent, or partially laminar and partially turbulent. Using the formula a complete back-pressure curve has been calculated and analyzed by a comparison with existing back-pressure curves. A procedure is presented for computing the permeability of the porous media when the porosity, sphericity and average particle diameter are known. Introduction Recent studies on the flow of fluids through porous media have provided new methods for computing flow under turbulent conditions. The present study was initiated as an investigation of pressure -drop computations for flow through porous sands in gas wells and as an analysis of present-day back-pressure tests. Although laminar flow exists in the producing formation of gas wells under normal flow rates, turbulent flow does take place adjacent to the well bore. As the flow rate is increased, turbulent flow exists further and further into the producing formation and under open-flow conditions in relatively deep wells a considerable portion of the flow through the sand will be turbulent. In order to calculate a complete backpressure curve for relatively deep wells without resorting to extrapolation of curves drawn from data obtained in back-pressure tests or calculations made in the completely laminar region, it was necessary to have some means of calculating pressure drop for flow through porous sands under turbulent conditions.4.6 As a result, a radial turbulent flow formula was derived from the equations recently presented by Brownell and Katz.1 A rigorous solution of this equation involves a trial and error graphical integration. By making the assumptions of average viscosity, temperature and compressibility factor of the flowing gas, it was possible to graphically integrate the relation for the general case of radial flow of gases through the porous sand of gas wells. A chart has been prepared relating the value of the integral to the radius of the well bore and to the Reynolds number of the flowing gas. The chart actually performs the graphical integration and the solution of the formula is then reduced to a simple trial and error calculation. A typical back-pressure curve is calculated to show the transition from laminar to turbulent flow. This paper will briefly describe the pro-cedurcs for computing flow through porous media, including a method for predicting sand permeability from porosity and grain size and shape. Flow through Porous Media Brownell and Katzl recently reported a correlation for computing flow of fluids through porous media by the use of an enlarged Reynolds number and friction factor in which the porosity of the bed is included as an additional prime variable. The enlargcd Reynolds number com-

Jan 1, 1948

By Donald L. Katz, Jack R. Elenbaas

A radial turbulent flow formula has been developed which permits the computation of the pressure drop for radial flow in gas wells whether the flow is laminar, turbulent, or partially laminar and partially turbulent. Using the formula a complete back-pressure curve has been calculated and analyzed by a comparison with existing back-pressure curves. A procedure is presented for computing the permeability of the porous media when the porosity, sphericity and average particle diameter are known. Introduction Recent studies on the flow of fluids through porous media have provided new methods for computing flow under turbulent conditions. The present study was initiated as an investigation of pressure -drop computations for flow through porous sands in gas wells and as an analysis of present-day back-pressure tests. Although laminar flow exists in the producing formation of gas wells under normal flow rates, turbulent flow does take place adjacent to the well bore. As the flow rate is increased, turbulent flow exists further and further into the producing formation and under open-flow conditions in relatively deep wells a considerable portion of the flow through the sand will be turbulent. In order to calculate a complete backpressure curve for relatively deep wells without resorting to extrapolation of curves drawn from data obtained in back-pressure tests or calculations made in the completely laminar region, it was necessary to have some means of calculating pressure drop for flow through porous sands under turbulent conditions.4.6 As a result, a radial turbulent flow formula was derived from the equations recently presented by Brownell and Katz.1 A rigorous solution of this equation involves a trial and error graphical integration. By making the assumptions of average viscosity, temperature and compressibility factor of the flowing gas, it was possible to graphically integrate the relation for the general case of radial flow of gases through the porous sand of gas wells. A chart has been prepared relating the value of the integral to the radius of the well bore and to the Reynolds number of the flowing gas. The chart actually performs the graphical integration and the solution of the formula is then reduced to a simple trial and error calculation. A typical back-pressure curve is calculated to show the transition from laminar to turbulent flow. This paper will briefly describe the pro-cedurcs for computing flow through porous media, including a method for predicting sand permeability from porosity and grain size and shape. Flow through Porous Media Brownell and Katzl recently reported a correlation for computing flow of fluids through porous media by the use of an enlarged Reynolds number and friction factor in which the porosity of the bed is included as an additional prime variable. The enlargcd Reynolds number com-

Jan 1, 1948