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By T. K. Smith

The comments contained in the discussion of the paper concerning the prediction of fracture gradients are of considerable interest, since the subject is of a very controversial and timely nature. It is regrettable and Fairhurst2 contradicts the author's statement in the third paragraph of Other Applications. These references create significant doubt that Eaton's Eq. 1 predicts fracture pressure during the injection of fluid into old wells. 3. No evidence is presented in this paper to support the author's Conclusions 2 and 3. While an empirical coefficient related to back-calculated field data is correlated with depth (Eaton's Fig. 4), there is no reason to suspect that this coefficient might be the Poisson's ratio of the various formations involved. 4. Until the field data supporting the empirical approach proposed by the author are presented and evaluated, the accuracy claimed in Conclusion 5 is without substantiation. References 1. Geertsma, J.: "Problems of Rock Mechanics in Petroleum Production Engineering", Proc., First Intl. Symposium on Rock Mechanics, Lisbon (1966) 585. 2. Haimson, B. and Fairhurst, C.: "Hydraulic Fracturing in Porous-Permeable Materials", I. Pet Tech. (July, 1969) 811-817. that the comments are those of a critic and do not offer an alternative and better method for the prediction of fracture gradients. Nevertheless, a reply is in order.

Jan 1, 1970

By G. R. Mansfield

THE geologic structure of the Idaho phosphate field has an important bearing on the classifica-tion and the exploitation of the lands that contain phosphate. Maps and structure sections1 recently made available show that the phosphate is mainly preserved in downfolded or downfaulted areas. Since the phos- phate beds are generally rather soft and lie between harder and thicker formations they have been forced to adjust themselves to these formations during epochs of disturbance of the earth's crust, so that they are frequently affected by minor folds and by faults which may help exploitation by producing undue thickness at certain places or may hinder it by cutting out the phosphate at other places where according to expecta-tion it should be present. A particularly important structural feature which affects both the distribution and the exploitation of the phosphate beds is the great Bannock overthrust by which one or more slices or blocks of the earth's crust have been pushed over other blocks like ice cakes on a pond. Thus in this region a great flap of folded rocks lies across other rock structures for a distance of approximately 35 miles. Most of the commercially accessible phosphate deposits, shown in the maps that accompany the report cited, are in this flap, which con-stitutes the upper block of the overthrust. In some places, however, the phosphate in the lower block is also accessible. In both blocks post-phosphate rocks exposed at the surface here and there indicate that phos-phate beds may lie at greater or less depth below. The presence of the Bannock overthrust beneath much of the area reported is known by the occurrence of windows in the upper block both within the quadrangles mapped and in areas farther west. The portions of the lower block exposed in these windows show stratigraphic dis-cordance with the surrounding formations. The depth of the fault plane at most places, however, can be told only by drilling or actual mining. Some of the folds in the upper block are relatively deep and it seems fairly certain that the phosphate that may originally have been present in their deeper parts has been removed by thrust faulting. The estimates of phosphate reserves in folds liable to be affected by the Bannock overthrust may therefore need ultimate revision depending on the depth of this fault plane, as it may subsequently be ascertained.

Jan 1, 1928

By Fred D. Wright, Philip B. Bucky

FOREWORD By E. D. Gardner[$] THE present known petroleum reserves are limited, and unless important new fields are discovered the Nation will be dependent, in the not too distant future, upon imports or upon synthetic liquid fuels to supplement domestic petroleum supplies. As a national defense measure, it would appear desirable to develop a substitute source of liquid fuels within the borders of the country if new discoveries of petroleum should prove disappointing. Congress undoubtedly had this in mind when it passed the Synthetic Liquid Fuels Act (78th Congress, approved April 5, 1944). The act directed the Bureau of Mines to construct and operate demonstration plants for producing synthetic liquid fuels from coal and oil shale, and from forestry and agricultural products. As a part of this program, the Bureau of Mines has built a demonstration plant at Anvil Points, near Rifle, Colo., for retorting the oil shale, and has developed a mine to supply the plant with oil shale. At the beginning of mining operations, the physical qualities of the oil shale, which would have a bearing upon the selection of mining methods and practices for exploiting the deposits, were largely unknown. A comprehensive mining-research program has been set up to determine the best methods and practices to follow to obtain the lowest overall practicable mining cost for producing the oil shale on a large scale. Unusually low mining costs will be necessary for shale oil to be produced commercially. Consideration now is being given to exploiting a series of flat-lying beds 70 ft thick by a room-and-pillar method of three benches with the advance heading at the top. This report is one of a series giving the results obtained in research on mining problems. INTRODUCTION The structure and physical qualities of the oil shale indicate that the 70-ft interval of the oil-shale measure can be safely mined in open stopes; studies indicate that this method would be the most economical one to use.1 As labor will be a major item of expense, the largest equipment that could be operated efficiently in the workings would be required to obtain the lowest practicable mining cost. It was therefore desirable to know the maximum safe span of unsupported rooms and the size of pillars necessary to support the overburden. This paper describes the work done at the Columbia School of Mines Barodynamic Laboratory in determining the maximum safe unsupported roof spans and the minimum safe pillar dimensions for the oil-shale mine at Rifle, Colo.

Jan 1, 1947

By William Carton, Cyril U. Cooledge

BecauSe the rich La Colorada orebody of the Cananea Consolidated Copper Co. does not outcrop at surface, after its discovery (by churn drill) and before mining was begun, a large amount of development work was done to learn the shape and extent of the ore and to provide for economic and effective mining. As these openings progressed, the actual shape of the orebody became known and with this knowledge came the realization that mining this rich and unusual deposit without loss of ore or danger to workmen presented several difficult problems. This paper will describe one of these problems; namely, the handling of an inverted cone-shaped core of barren rock, on the periphery of and below which the ore occurred. It mas clear that as the ore was mined out from around and under this inverted cone of rock, weighing about 3,000,000 tons, it would hang over the workings, held suspended only by its own tensile strength and threatening to crash into the stapes below with disastrous results to men and mine. The method of mining developed during the years 1928,1929 and 1930 anticipated and provided for the eventual collapse of this core of rock. In November 1936 the core settled down gradually on the edges of the stopes, descending a total of about 50 ft. vertically. The men in the stopes had ample warning and no lives were endangered. There were no air blasts in the mine. The core broke loose from its top support at the 500-ft. level along old fracture planes and evidently is crushed to the ninth level. Movement was of short duration; the following shift went to work in the stopes as usual. No ore was lost. Geological Structure The shape of the orebody is illustrated in Fig. 1. The geology of the Colorada orebody has been described by V. D. Perry1 and by W. G.

Jan 1, 1940

By Cyril U. Cooledge, William Carton

BecauSe the rich La Colorada orebody of the Cananea Consolidated Copper Co. does not outcrop at surface, after its discovery (by churn drill) and before mining was begun, a large amount of development work was done to learn the shape and extent of the ore and to provide for economic and effective mining. As these openings progressed, the actual shape of the orebody became known and with this knowledge came the realization that mining this rich and unusual deposit without loss of ore or danger to workmen presented several difficult problems. This paper will describe one of these problems; namely, the handling of an inverted cone-shaped core of barren rock, on the periphery of and below which the ore occurred. It mas clear that as the ore was mined out from around and under this inverted cone of rock, weighing about 3,000,000 tons, it would hang over the workings, held suspended only by its own tensile strength and threatening to crash into the stapes below with disastrous results to men and mine. The method of mining developed during the years 1928,1929 and 1930 anticipated and provided for the eventual collapse of this core of rock. In November 1936 the core settled down gradually on the edges of the stopes, descending a total of about 50 ft. vertically. The men in the stopes had ample warning and no lives were endangered. There were no air blasts in the mine. The core broke loose from its top support at the 500-ft. level along old fracture planes and evidently is crushed to the ninth level. Movement was of short duration; the following shift went to work in the stopes as usual. No ore was lost. Geological Structure The shape of the orebody is illustrated in Fig. 1. The geology of the Colorada orebody has been described by V. D. Perry1 and by W. G.

Jan 1, 1940

E. D. TILLYER,* Southbridge, Mass. (written discussion?).-It is quite generally known that there is very little that is standard about a mercurial thermometer at temperatures above 212° F. (100° C.) because so many precautions must be taken-precautions that are rarely realized in practice-such as depth of immersion, aging, elastic fatigue, separation of mercury column, and accidental deformation from very slight excess temperature. One cannot help wishing that Mr. Brown would dwell at greater length on the practical side of both radiation and optical pyrometey, both of which have great possibilities as commercial instruments. In the radiation pyrometer we have ideal conditions for a permanent instru-ment, no materials being exposed to excessive temperatures or subjected to contamination from the furnace fumes which may raise such havoc with an ordinary pyrometer. The development of a radiation pyrometer requires a thermocouple having a relatively high electromotive force but which need stand temperatures of only 200° F. or 300° F. instead of 1500 to 2000° F., which is required of even a base-metal couple. The galva-nometer, if located near the thermocouple, does not need to have a high resistance as at such low temperatures no changes can occur in the thermocouple that will affect its resistance and, consequently, the in-dicated temperature.

Jan 11, 1919

By A. P. Svenningsen

IN the early stages of design it was not considered necessary that separate crushing plants be built for the new sulphide concentrator and smelter until sometime in the future. The plan was to use the existing crushing facilities for both oxide and sulphide ore. A few additions were contemplated for the existing plants, such as increased bin capacity, and possibly two new secondary crushing units. The more the problem was studied and discussed with the plant operators, the more it became evident that it was complex. It involved the classification of different kinds of ore from the open pit mine -sulphide, oxide and mixed-and how best to separate them so that each kind of ore was given the proper processing and treatment. It also involved the problem of keeping the different ores from being contaminated in bins, hoppers and chutes. Added to these, transportation became complicated and would involve additional handling and loading of ore from crushing plants to conveyors, to bins, and finally to railroad cars which were to be hauled to the concentrator and dumped into the fine ore bin. General In the early part of 1951 it was decided that the concentrator be constructed with ten grinding units instead of seven as originally authorized. The smelter was to be increased proportionally and naturally also the overall tonnages of ore to be handled by the new sulphide plant. Due to this increase in plant capacity and the larger tonnages involved, the difficulties which would arise by using the existing crushing plants were increased to a point where it became evident that the building of new crushing plants for sulphide ore exclusively was technically, as well as economically, advantageous. Authorization was, therefore, given by the company to construct new crushing plants to handle 30,000 tons of ore per day, and capable of reducing the run-of-open-pit ore to the proper size feed for the 10x14-ft rod mills in the concentrator. The ore, mined in the open pit, sometimes comes in pieces as large as 6 to 7 ft diam. The rod mills may call for ore crushed to 3/4 in. The large .size of ore delivered from the open pit determined that a 60-in. gyratory crusher be used as primary breaker. Such a crusher will have a capacity considerably in excess of 30,000 tons per day. The crusher will be a single discharge unit driven by a 500-hp electric motor through a tear coupling and a floating shaft. This type of drive has proven successful at a number of other crusher installations which our company has operating in the United States, Mexico and South America. The tear coupling will protect both the crusher and motor against damage in case of overload. No new features are incorporated in the design of the crusher itself, except that the, discharge chute is made the full width of the crusher with parallel sides instead of the usual converging sides. This change in detail should eliminate, a feature which has been a bottleneck in some of the operating plants and has caused loss of production due to ore hanging up and blocking the chute. The secondary crushing plants will have three 7-ft standard Symons cone crushers and six 7-ft short head Symons crushers. Between the primary and secondary crushing plants a coarse ore bin will be constructed with a nominal draw-off capacity of 30,000 tons of ore. The standard Symons and the short head Symons will be in separate buildings. All the crushing plants and the coarse ore bin are interconnected with conveyor belts for transporting the ore to the crushers at the tonnage rate desired. The final product of the new crushing plants is produced by the short head crushers. It will be delivered onto a conveyor belt leading to the top of the fines ore bin in the concentrator. A separate conveyor belt running the full length of the fines ore bin and provided with a movable tripper of rugged design will discharge the sulphide ore into the bin. The concentrator bin is planned and designed so that the installation of this additional conveyor will not interfere with the operation of the two railroad tracks on which crushed ore is brought from the existing oxide plant. Thus when completed the bin can be filled simultaneously by ore from the new crushing plant and by ore from the existing leaching plant.

Jan 1, 1952

By Raja V. Ramani, Ralph W. Barbaro

This paper presents an application of a Mixed Integer Programming (MIP) model to the problem of locating a centralized coal preparation plant and determining the production schedule for the mines. The system used for illustrating model application is hypothetical but realistic. It consists of three mines, two potential preparation plant sites, heavy media processing plant, and one market. The goal is to maximize the total profit of the system while satisfying the coal delivery schedule over a three year period meeting both quantity and quality requirements (ash, sulfur, and heat content). In addition to the base case, four different scenarios are analyzed. These four modifications are: (1) removing the flotation circuit from the preparation plant and sending all of the fines directly to the clean coal, (2) lowering the quality of coal from one of the mines, (3) applying discounts to the unselected site to improve its competitive position, and (4) adding a new mine. A detailed discussion of the base case and the effect of these four alternatives is presented.

Jan 1, 1983

By L. A. Panek, F. D. Wang, M. C. Sun

A method of stability analysis of underground opening by the limiting equilibrium approach is presented. The Coulomb shear failure criterion is employed to find possible fracture surfaces and to evaluate the shear strengths along them. The normal stresses required for the calculation of shear strength, and the shear stresses for the calculation of total shear force along the fracture surfaces, are obtained by the finite-element method of plane-strain analysis. The factor of safety against Coulomb shear failure is calculated as the ratio of the shear strength to the shear force along a fracture surface, similar to the practice in slope stability analysis. Four shapes of openings are analyzed, with three ratios of horizontal lithostatic stress and four coefficients of internal friction. The critical fracture surfaces found by this method of analysis are consistent with the arching of roofs and slabbing of ribs commonly observed.

Jan 1, 1972

Jan 1, 1925

By J. Moore Samuel

THE prospective change in ore receipts at the Copper Queen reduction works necessitated a careful study of conditions to determine the most economical method of smelting. The first step, calculating the known, probable, and possible results, showed the economy of a unimetallurgical flow sheet f which the three pyrometallurgical stages would be roasting, reverberatory smelting, and converting. The past and future ore receipts (not including converter flux) are as follows: AVERAGE MONTHLY FUTURE MONTHLY RECEIPTS, 1918 RECEIPTS TONS PER PER CENT. OF TONS PER PER CENT. OF MONTH TOTAL RECEIPTS MONTH TOTAL RECEIPTS Ore 84,553 82.3 43,000 44.0 Gravity concentrates 16,375 15.9 25,500 26.0 Flotation concentrates 1,883 1.8 29,400 30.0 Total 102,811 100.0 97,900 100.0 Of the 102,811 tons per month received in 1918, only 28,945, or 28 per cent., was treated in the roasters and an average f 14.1 roasters out of 20 were in operation; the remaining ore was treated in the blast furnaces. The change to "all reverb." practice, therefore, called for considerable additional roaster capacity, which could be obtained either by building additional units, or by remodelling the present units so as to give increased unit capacity. In view of the progress in roasting practice since the construction of the Copper Queen roaster plant and the heavy investment in that roaster plant, the second plan seemed to be the more desirable. The Copper Queen roaster plant consisted of twenty six-hearth, McDougall roasters, 18 ft. in diameter, equipped with cast-iron arms that originally were water cooled but now are air cooled. They have no top dry hearth and the feed is discharged through the top arch, near its periphery, by plunger feeders from two bins at opposite sides of the roaster.

Jan 7, 1921

By Parke A. Hodges

CHROMIUM, one of the most vital of the strategic metals, has constantly increasing importance as research expands potential uses in alloy steel metallurgy. All signs point to a steadily growing use for chrome ore, and the general subject has received a great deal of attention recently.1 A relatively little known country, Southern Rhodesia produced a total of 5.949 million tons, or 18.6 pct of the total world chrome output, between 1906 and 1950, according to figures from the U. S. Dept. of Commerce. According to U. S. Bureau of Mines figures, Southern Rhodesia produced 291,525 tons in 1950 and 300,267 tons in 1951, or approximately 13 and 11 pct, respectively, of world production for the two years. In 1953 the Rhodesian Vanadium Corp. produced about 85,000 tons of which probably 7,000 tons were concentrate. Production by other companies was high. Large in themselves, the figures assume even greater significance because most of this output is of metallurgical grade.

Jan 8, 1954

By Rudolf Gahl

Page Tests Conducted in Small Test Mill................... 577 Demonstration Tests Conducted by Minerals Separation Co....... 577 Flotation Tcsts Conducted by Inspiration Co............. 577 Sampling of Orebody........................ 578 Other Results Obtained in Small Test Mill.............. 580 Tests Conducted in Large Test Mill................... 580 Flow Sheet............................. 580 Discussion of the Value of Preliminary Table Treatment......582 Callow Flotation Installation..................... 585 Flinn-Towne ~nstallation...................... 587 Cole-Bergman Installation...................... 588 Methods Followed in Competitive Tests................ 590 Advantage of Pneumatic Flotation Machines.............. 591 Pneumatic Machines of Minerals Separation Co............. 591 Float Skimming Device......................; 594 Experimental Inspiration Flotation Machine.............. 596 Arrangement of Callow Cells in Series ................ 598 Variations of Flow Sheet....................... 599 Coal Tar as Flotation Agent..................... 600 Experience with Primary Slime.................... 602 Influence of Iron on Flotation..................... 605 Influence of Chemicals on Primary Slime............... 607 Fineness of Crushing Desired.................... 607 Operation of Large Concentrator..................... 608 Flow Sheet of Callow Sections.................... 608 Flow Sheet of Inspiration Sections.................• 609 Inspiration Flotation Machine of Steel Construction.......... 610 Minerals Separation Section..................... 613 Filter Plant............................ 613 Results Obtained in Commercial Concentrator............... 616 Tonnage............................... 616 Air and Power Consumption...................... 616 Floor Space............................ 617 Water Consumption......................... 617 Recovery............................. 618 Oil Consumption.......................... 618 Operating Costs for Flotation..................... 620 Discussion of Results Obtained.................... 620 Prospects for Futurc Development of the Flotation Process......... 621 Porous-Bottom Experiments..................... 622 Raising the Grade of Concentrates.................. 624 Recovering Carbonates by Flotation................. 624 Recovery of Silicates by Flotation.................. 627 General Theory......................... 628 Conclusion............................... 630

Jan 1, 1917

By A. P. Anderson, J. H. Jensen, W. E. Breckoff

Bromine is the intermediate member of the halogen family of elements between iodine, a solid, and chlorine, a gas. The name is derived from the Greek "bromos," meaning stench. Bromine is the only nonmetallic element that is liquid at room temperatures with a melting point of -7.2° C and a boiling point of 58.78º C. Reddish brown in color, it dissolves easily in water to yield a red solution. Bromine volatilizes at ordinary temperatures to a red vapor that is very irritating to the eyes, nose, and throat. Density of the liquid is 3.12 and gas weighs 7.59 gpl at standard conditions. As the element is highly active, it exists in nature only as bromide compounds. Bromine was discovered by Antoine Jerome Balard in seawater bitterns in 1826 and first prepared in quantity in 1860. Distribution Bromine is widely distributed in nature and compounds occur in solution in natural brines, in seawater, saline lakes, oil and gas well brines, and in evaporite chloride minerals. The concentration of bromine salts ranges from 60-65 ppm in seawater to several thousand ppm in oil well brines and saline lakes. The distribution of bromine in marine evaporite minerals and in the solutions from which they crystallized was determined many years ago by H. E. Boeke (1908). Theoretical aspects regarding the geochemistry of bromine have been published in numerous papers (Raup and Mite, 1969). Bromine occurs in solid solution in carnallite and sylvite associated in potash deposits; in halite in salt beds; salt in oil shales; and in trona deposits. Its presence is useful as a guide in geochemical exploration. The analysis of small amounts of bromides in the presence of large amounts of chlorides is discussed by W. Schwerdtner (1963). Manganese, iron, and iodine may interfere with the determination. Other analytical methods are discussed at length in the literature (Stenger and Atchison, 1964). Sources and Reserves The sources and reserves of bromine, given in Table 1, appear ample to meet present and foreseeable requirements in all producing countries. With the occurrence of bromine salts in seawater and other brines, the potential for bromine production is worldwide. It has been estimated that 99% of all commercially recoverable bromine is in the ocean. However, actual subterranean brines having a higher bromine content than seawater will continue to be the preferred sources of bromine for the foreseeable future. [ ]

Jan 1, 1983

By J. Gordon Parr, D. H. Polonis

IN a previous study of hypereutectoid Ti-Ni alloys' a substructure was observed in quenched powder specimens when the constitution was 100 pet retained ß body-centered-cubic phase. The alloy powders were quenched from 1000°C by a blast of helium gas and precautions already described were observed throughout the work, to minimize contamination. Ogden et al.2 have previously observed subboundaries in the ß phase of a Ti-Mn-N alloy; but this structure was attributed to nitrogen-rich a precipitation. The nitrogen content of the Ti-Ni alloys does not exceed 0.02 pet and the quenching rate was sufficiently rapid to suppress precipitation reactions. Since X-ray diffraction results have confirmed the absence of any second phase which might account for this phenomenon, it seems unlikely that this substructure is explicable in terms of nitrogen content. Fig. 1 shows the substructure in adjacent grains of 100 pet ß phase in a quenched 6 atomic pet Ni alloy. Fig. 2 shows adjacent ß grains in a similarly treated alloy; one grain contains marked intracrys-talline boundaries and the other is completely free from any substructure. The suberystals appear to have fairly regular shapes, suggesting a regular orientation relationship among them. Tempering the retained ß structure at temperatures below the eutectoid eliminates the substructure at an early stage of ß decomposition. At the present time it is possible only to guess at an explanation for this subboundary phenomenon, since very little work has been reported on substructures resulting from phase changes. It is believed that the present phenomenon is due to poly-gonization resulting from unrelieved stresses set up

Jan 1, 1957

By J. S. Owens, R. W. Marsden, J. W. Emanuelson, R. F. Werner, N. E. Walker

The iron ores of the Mesabi Range occur in a 340 to 750-foot thick, Precambrian cherty iron formation termed "taconite." For about 65 years, extensive natural iron ore bodies were mined, and the ores either shipped as a direct ore or processed by gravity methods to a shipping grade iron ore. Since 1956, magnetite taconite ores, occurring in magnetite-rich horizons in the Biwabik iron formation, have been commercially concentrated and agglomerated. The transition from natural ores to concentrating-grade ores is progressing rapidly so that, in the near future, a major percentage of the iron ore shipped from the Mesabi Range will be as iron ore pellets produced from taconite. Natural iron ores of the Mesabi Range occur in the Biwabik formation as trough ore bodies in elongated channels and as irregular and tabular deposits in fractured areas associated with faults and folds. Ore bodies range in size from a few thousand tons to hundreds of millions of tons and may occur in any part of the iron formation. In some areas of strong ore development, ore was formed from the hanging-wall argillite to the footwall quartzite. The natural ores and beneficiating-grade natural crude ores were formed by the oxidation of the iron minerals, magnetite, greenalite, stilpnomelane, minnesotaite, and siderite, to hematite and goethite and by the removal of much of the silica in the cherty quartz and in the associated silicates by leaching. The ores are believed to have formed by the oxidizing and leaching action of surface waters. Magnetite taconite ores occur as stratigraphic zones in the Biwabik formation where it contains sufficient magnetite to be concentrated profitably, by magnetic methods, to give a magnetite concentrate that is agglomerated into a high quality product. Unoxidized taconite has an extensive distribution away from and between channels of oxidation and leaching but only a part of the unoxidized taconite is of ore grade. Two general types of magnetite taconite ore occur: ( 1) magnetite taconite of the Main Mesabi Range, generally west of Mesaba, which is composed of magnetite associated with cherty quartz, greenalite, stilpnomelane, minnesotaite, and carbonates and (2) magnetite taconite of the Eastern Mesabi, generally east of Mesaba, composed of magnetite associated with quartz, cummingtonite, actinolite, ferrohypersthene, hedenbergite, fayalite, hornblende, pyroxene, garnet, and biotite. The Mesabi taconite is a metasediment derived from an iron- and silica-rich chemical sediment that has been regionally metamorphosed and, on the eastern end, additionally metamorphosed by the Duluth Gabbro Complex.

Jan 1, 1968

By J. Husson, R. Iffly, M. Gondouin

A systematic variation of well deliverability, as reflected from isochronal back-pressure tests performed at regular intervals, has been observed in some gas condensate wells producing at high rates. The same effects have been obtained using a numerical model of gas and condensate flow which takes into account secondary gasoline deposited in the pore space as a result of pressure reduction, and non - Darcy flow of gas in the vicinity of the wells. Matching calculated values with previous test results has been possible, and future predictions have been obtained. An application of this method to the Hassi Er R'Mel gas-condensate field in Algeria is tentatively shown. INTRODUCTION Flow capacity of gas wells is generally derived from an analysis of back-pressure tests. The empirical equation q = C (?p2)n used by Rawlins and Schellhardtl can be derived rigorously assuming that steady-state radial flow of a dry gas of constant viscosity and compressibility is established during each flow period of the well tests. Furthermore, when Darcy's law applies in the entire flow region, the theory predicts that the exponent n is equal to 1. In low-permeability reservoirs, it was soon discovered that the time required to reach a stabilized flow often exceeded the duration of the flow periods normally available for testing wells. Consequently, transient gas flow had to be considered instead of the steady-state assumption previously used. This led to the isochronal testing procedure established by Cullender2 which has largely replaced conventional back-pressure testing. For dry gas fields, this method yields definite values of C and n equivalent to those of the empirical equation. These values should remain constant for each well as long as the permeability of the formation and the characteristics of the gas (viscosity and compressibility) do not change appreciably. This is the case when reservoir pressure remains -close to the original value and when the formation near the wellbore remains free of plugging. Under those conditions, stabilized flow potential curves of gas wells can be established from a single sequence of isochronal flow and shut-in periods. An analysis of a pressure build-up following a longer production period provides additional data on the transmissivity (k h/ u) of the reservoir, and eventually on the 'drainage radius rd of the well, which can be related to the value of C so that future performance of the well can be predicted using the concepts developed by A. Houpeurt.3 At high flow rates, Darcy's law no longer applies in the vicinity of the wellbore, and inertial effects in the high velocity gas flow introduce additional pressure drops. As a consequence, exponent n of the backpressure tests becomes smaller than 1, and a slight curvature of the log-log plot of ?p2 vs q can be predicted when going from very low to high rates of flow (Elenbaas and Katz).5 The effects of variations of viscosity and compressibility with pressure on the radial flow of dry gas in an infinite reservoir were taken into account by Jenkins and Aronofsky.7 Numerical solutions of the transient flow of an ideal gas in finite radial reservoirs were presented by Bruce, Peaceman, Rachford and Rice.8 In the case of gas condensate wells, however, the presence of gasoline in the pore space as soon as reservoir pressure is reduced below the dewpoint pressure further complicates the interpretation of flow tests so that the prediction of stabilized well performance becomes very difficult. Field observation shows that both C and n derived from isochronal tests vary in time, even when reservoir pressure has not changed appreciably. Such a variation cannot be attributed to any change of the gas characteristics, and must result from the effect of a gasoline saturation on the gas flow.

By Lyall Zickrick

As a result of the studies on recrystallization and crystal growth made in this laboratory, certain theories have been developed. These are expressed briefly in a paper by Dean and Hudson.1 One of the principal points brought out in that paper is that in the deformation of a crystal, the energy supplied is distributed to the atoms of the lattice, probably by the forced formation of molecules. It is found that a Maxwellian distribution of the energy among these atoms will account for the grain growth at various temperatures. According to such a distribution the number of atoms with energy above a certain critical value, E, necessary for recrystallization at the absolute temperature T is given by n Ne(-E/kT) where N is the total number of atoms. It is apparent that if this line of reasoning is correct, a metal which has been cold-worked and reheated to a temperature below that of complete annealing will have the atoms with the higher energy recrystallized, that is, reduced to normal energy and there will remain only atoms below a certain energy. If this metal is again cold-worked the peak in the number-energy distribution curve will be displaced toward the regions of lower energies, that is, higher temperature of recrystallization. By a repetition of this process the position of this maximum and hence the recrystallization temperature of the metal could be raised considerably. In order to' check this theory, experiments have been made on copper wire. The wire was drawn from 1/4-in. rod to 22 B & S gage and then sample lots were annealed at 400 and 220° C., respectively. The wire annealed at 400° C. gave an elongation of 34 per cent., whereas that annealed at 220° C. gave only 23 per cent. These wires were then drawn by identical practice to 34 B & S gage and the elongation determined after an anneal of 3 mm. in an oil bath held at various temperatures.

Jan 1, 1927

Jan 1, 1926

By C. A. Wert

THE solid solubility of cementite in a-iron has been investigated a number of times and there is now general agreement on the solubility of about 0.018 wt pct at the eutectoid temperature, 720°C. With decreasing temperature, the solubility falls off so rapidly and to such a low value that no data obtained by standard metallurgical methods are available below 500°C. Using a new technique, however, Dijkstral has obtained apparently accurate solubilities down to 400°C; which data agree well with previously measured solubilities in the 600" to 700°C temperature range.' The present paper has in part the purpose of extending his work to still lower temperatures. Earlier work of Low and Gensamer3 on iron has established that the presence of a relatively small amount of carbon can play a tremendous role in affecting the mechanical properties. In particular they found that the yield point remained high as they reduced the amount of carbon in the iron; the yield point dropped only after the carbon content had fallen to something less than 0.003 wt pct, the point where their carbon analysis failed. It seemed desirable to the present author to see if some means could not be found to extend this part of their work. This investigation has then the additional purpose to determine the range of carbon concentration in which the major change occurs. Solubility The method used in the present work to measure small percentages of carbon in a-iron utilizes internal friction. Since this method may not be fa-miliar to the reader, the following explanation will be given (a part of this procedure is from unpublished results of Dijkstra): It is known that the internal friction associated with the diffusion of

Jan 1, 1951