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By William Glenn

In their account of chromium, Roscoe and Schorlemmer (Treatise on Chemistry, London, 1879) state that "In 1762 Lehmann, in a letter to Buffon, de nova minerœ plumbi specie crystalline rubra, described a new mineral from Siberia, now termed crocoisite." In 1786 Lehmann analyzed it (Nicholson's Jour., Dee., 1798) and found that it contained chiefly lead, and that the " mineralizers " were arsenic and sulphur. It was next examined in 1189 by Macquart and Vauquelin, who stated that it contained an intimate mixture of iron, alumina, and lead peroxide. The account of their work was published over the name of Macquart. Vauquelin (Louis-Nicolas) was a Norman peasant, who had studied in the village school, and at the age of fourteen was a laboratory-boy in a pharmacy at Rouen. Later, he found his way to Paris, and in 1789 was assistant to Fourcroy, a pharmacist and a teacher of note. It was here that he met Macquart, with whom he did the work on Siberian red lead, and at this time his friend Cheradame taught him his Latin.

Jan 1, 1896

By Kenneth L. Cook

GEOPHYSICAL exploration is continuing to expand in scope and variety of methods, in experimental studies of specific applications, and in development of theory for complex situations. Aerial surveys have been made economically more attractive by simultaneous recording of magnetic and radioactivity data, and aerial electromagnetic surveys have been attempted. The most significant success of mining geophysics was the discovery of huge lead-zinc-copper sulphide ore deposits in New Brunswick, Canada. Spectacular geophysical astivity has occurred in the area as a result of these discoveries, and geophysics is expected to continue to play a large role in this drift-covered area. Other developments this year find the Atomic Energy Commission making available monthly reports of the location of anomalous radioactivity detected in aerial and ground surveys and the AEC is installing supersensitive radioactivity assaying instruments in about 25 localities in the U. S. Interest in helicopters is being aroused because of potentialities for near-ground surveys and better location control of anomalies. Japan can be added to the list of countries using geophysical surveys extensively.

Jan 2, 1954

By H. N. Eavenson

In a discussion in the Transactions of the Institute (vol. Xl, page 835 et seq.) the writer gave some data about the explosions of gas and dust in the coal mines of the United States, Canada, and Mexico…

Jan 1, 1915

By M. Prats, D. G. Russell

The performance of a well in a bounded, layered reservoir with interlayer crossflow has been investigated mathematically. The system studied comprises a centrally located well in a bounded cylindrical reservoir composed of two layers of contrasting physical properties. The reservoir contains a single fluid of small and constant compressibility. In the case of a well producing at constant pressure, the production rate of the crossflow system declines exponentially after the early transient behavior dies out. For wells which produce with constant rate, the pressure-time relationship is linear following the transient. For very early production time, the production rate of the two-layer crossflow system behaves as that of the two-layer stratified system (the case in which the layers are in communication at the well only). Except for early time, in most practical cases the performance of a two-layer reservoir with cross-flow can be duplicated by that of a single-layer reservoir. The equivalent single-layer reservoir must have the same pore volume and the same drainage and wellbore radii as in the two-layer case. In addition, the equivalent reservoir must have a "kh" (permeability x thickness) product equal to the sum of the "kh" products of the respective layers in the crossflow system. If the porosity and permeability distributions are known, the production and pressure behavior of a well with and without crossflow can be predicted. From a comparison of the observed pressure or production performance of a well and the theoretical behavior, the occurrence of interlayer crossflow can be detected. INTRODUCTION When flow is possible across the bedding plane from a low-permeability layer into an adjacent layer of moderate or high permeability, the earlier depletion of the more permeable layer will cause such flow to occur. If this situation exists, the oil recovery from tight layers can be appreciable; thus, the economic ramifications of interlayer crossflow are apparent. The possible importance and extent of flow between adjacent and connected layers — whether resulting from capillary, gravitational, or viscous forces — have been the subject of considerable speculation for many years. Jacquard1 presented a rigorous analysis of the crossflow due to single-fluid expansion occurring between two adjacent and connected layers when the well produces at constant rate. His presentation was entirely mathematical, however, and no numerical results from evaluation of the mathematical solutions were presented. Our objectives in the preparation and presentation of the present paper are essentially twofold— (1) to analyze the behavior of a well which produces a single compressible fluid from a bounded, layered reservoir with interlayer crossflow, and (2) to present practical numerical results and simplified formulas to facilitate engineering analysis of reservoirs with crossflow. The constant-terminal-pressure case was analyzed rigorously, whereas the constant-terminal-rate case was treated only for semisteady-state conditions. DESCRIPTION OF THE IDEALIZED TWO-LAYER RESERVOIR The reservoir to be studied is assumed to be bounded and cylindrical in shape, with a completely penetrating well at its center. The reservoir is composed of two adjacent horizontal layers between which fluid is free to flow. Each layer is assumed to be homogeneous, isotropic and completely filled with a fluid of small and constant compressibility. The total thickness of the reservoir is small enough

By Edward Keller

Someone some time ago remarked that some chemists still insist on telling us how to determine copper by the electrolytic method. The writer must confess that he believes that everything is not known definitely as yet as to how the exact amount of copper is determined in such material as purest commercial electrolytic copper. Some of us are not yet convinced that the pure copper atom is at all times deposited from an acid solution and that no oxygen or hydrogen will, under certain conditions, accompany it. Difficulties with impurer material are frequent, but erroneous results are not always apparent, since these do not speak so readily for themselves as those in the first case. By this is meant that if a chemist finds 100 per cent. of copper in electrolytic copper it is pretty certain that he perceives the result to be wrong, while if he finds 0.1 per cent. of copper too much in a very impure material he is far more likely to be unconscious of his error. These, in a wide experience, are frequent happenings and the writer has always looked with interest to publications on this subject. In turn, he feels justified in giving to others a few of his own observations. Up to a few years ago there were two methods of electrolytic copper assay in technical use, which had in common, that the amount of copper deposited on the cathode did not exceed 2 g., and they differed in that, for the one a large sample1 (20 to 80 g.) was taken from the general sample by a splitting device, dissolved, and from the solution a small portion (to contain 1 or 2 g. of copper) measured out for the electrolytic deposition; in the other method the copper was determined, generally in 1-g. portions of the separated coarse and fine portions of the sample, all of which passed a 16 or 20-mesh screen, being accomplished by a 40-mesh screen,

Jan 1, 1914

By T. W. Guy

THE increased moisture due to water¬spraying for coal dust control is of interest even for mines from which the coal is to be wet-washed before screening, because in many cases wet coal dust materially decreases the loading efficiency of men an equipment at the faces. It also causes serious increase in the normal wear and deterioration of all equipment with which it comes in contact. It is important to the consumer if it increases his as-receive moisture. No attempt will be made in this paper t cover the entire subject of water-spraying of coal for dust control. It will be confine to discussion and data on (r) percentages c dust in bituminous coals, (2) moisture increases due to spraying for dust control in mines or plants by methods which have proven satisfactory for periods of one to five or more years, and (3) a few suggestions for research. SIZE AND PERCENTAGE OF COAL DUST The U. S. Bureau of Mines1 classifies a coal dust all bituminous coal passing 20-mesh sieve (0.0328 in. square opening; The percentage of such dust to be found is ROM coal, of course, varies widely wit. the characteristics of the seam, and with the methods used in the mining and in the preparation of the coal. ROM screen analyses of 12 U. S. coals selected at random from personal files given in Table I show: A few other screen analyses examined indicating 40 pct or more of 2o-mesh X o dust in 3/8 in. X o-sizes were not included because of uncertainty that they were representative. The number of results in Table I is not sufficient to give a reliable estimate of the average, or of the range to be expected, but it indicates that in every case the coal dust is a relatively large percentage of the total ROM coal, and, of course, a progressively larger percentage of resultants as the larger sizes are separated for marketing.

Jan 1, 1948

By N. A. D. Parlee, I. D. Shah

ThIS reports on some work done on the solubility and diffusivity of oxygen in liquid silver. Solubility. Improvements in the measurement of the solubility of oxygen in silver and silver alloys were made because precise data were needed for calculating diffusion coefficients of oxygen in these alloys. The apparatus and the procedure used were similar to those of Parlee and Sacris.' The main improvement was in the temperature-measuring technique. A MV30 mullite protection tube containing a calibrated Pt-Pt, 10 pct Rh thermocouple was inserted in the reaction tube from the top through a vacuum-tight swage-lok fitting. The protection tube was well-immersed in the liquid silver, which was heated by induction. A Leeds and Northrup potentiometer was used in connection with the thermocouple. All runs reported were made at 1 atm. The temperature range investigated varied from 940" to 1200°C. The ternary point in Ag-0 phase diagram2 is at 939°C and 0.32 wt pct O. This point was reinvestigated using the above-described apparatus and was found to be at 939°C and 0.315 wt pct 0. It was determined by observing the sudden evolution of oxygen at this point while the solubility measurements were made. The point was easily reproducible if precautions were taken to keep the liquid silver essentially in equilibrium with oxygen and to lower the temperature very slowly. All of the results of this new solubility investigation are plotted in Fig. 1. They are represented by the "least-squares" line shown in the figure and the following equation for solubility at po2 = 1 atm: log% O =695.4/T - 1.086 This equation differs only slightly from that proposed by Parlee and sacrisl and that of Diaz, Masson, and Richardson.3 The points of Parlee and Sacris, using an optical pyrometer, are shown for comparison.

Jan 1, 1968

By Alexander L. Holley

The 400-ton testing machine, ordered in June, 1875, by the United States Board appointed to test "iron, steel, and other metals," has lately been completed at the Watertown Arsenal, thoroughly proved and accepted by the Board. The excellence of the machine in every respect is more than satisfactory, and its accuracy is at first sight astonishing, although an investigation of its principles must show that if the weighing apparatus will weigh at all, it must do so with perfect accuracy, because all its movements are absolutely without friction. The proof experiments were numerous, and the effects of recoil after sudden ruptures at maximum loads, were watched with great care, but without much anxiety, because the weighing parts affected are by no means delicate in structure, and their motion is almost infinitely small. Among the tests were the following : A forged link of hard, wrought iron, 5 inches in diameter between the eyes, was slowly strained in tension, and broke short off with a loud report at 722,800 pounds. The diameter before breaking at the point of fracture was 5.04 inches; after breaking, 4.98 inches. In order to see if the weighing parts had been disturbed by the recoil, which was obviously near the greatest recoil the machine will ever suffer, a horse-hair was next tested; it was 7-1000ths of an inch in diameter; it stretched 30 per cent., and broke at 1 pound. Other horse-hairs vary in tenacity between 1 and 2 pounds. Of course, the accuracy of the machine on such delicate specimens, and indeed on specimens having some hundreds of pounds tenacity, has been checked and proved by other weighing machines. A 5-inch round bar, turned down to 38 inches diameter along the centre, was pulled apart at 430,200 pounds tension. Then some more horse-hairs were tested ; also copper wires 191/2-1000ths of an inch in diameter, which averaged 25 pounds tenacity..

Jan 1, 1879

By David Reger

THE value of carbon ratios in determining the boundaries of possible oil deposits appears to have passed the hypothetical stage. The theory that the ratio of fixed carbon in pure coals is an, invariable index of incipient metamorphism in both, surface and underground rocks and that it may be applied in defining the limits of petroleum, advanced by David White,1 has been received with keen interest by many petroleum geologists. Detailed isocarb maps have been prepared of the Pennsylvanian area of North Texas and Eastern Oklahoma by M. L. Fuller.2 A similar map of the coal-bearing area of West Virginia is given here. An isocarb3 is a line showing an equal fixed-carbon percentage, pure coal basis; the term has been proposed by David White to supersede a less expressive nomenclature. The term carbon ratio is applied to the percentage of carbon in pure coal after water and ash have been eliminated. As a comparatively small number of analyses have been made on this basis, it is usually necessary to compute the ratio by dividing the fixed carbon of the proximate analysis by the sum of the fixed carbon and volatile matter of the same analysis. Many thousands of proximate analyses have been made by the West Virginia Geological Survey, covering nearly every county in which coal is found. Numerous others have been made by the. U.S. Geological Survey and the U. S. Bureau of Mines, but as uniformity of results is

Jan 2, 1921

By Reuben B. Ellestad, Fremont F. Clarke

In the early days of the lithium industry most of the production was from lepidolite, zinnwaldite, and amblygonite. Nearly all the early extraction processes described in the literature involve heating the finely ground mineral with sulphuric or hydrochloric acid. On subsequent water leaching most of the bases present in the mineral (especially aluminum) are dissolved as sulphates. As a result, the leach solution required extensive chemical purification before the lithium could be precipitated as carbonate. Following the remarkable growth of the lithium industry to its present size, zinnwaldite and amblygonite ores must be considered of minor importance only. Attention is now focused on spodumene, abundant enough in North America to be a major source of supply, and there are important supplies of lepidolite and petalite in Africa. The extraction processes described below all apply to spodumene, although several will also operate on other lithium minerals, such as petalite. Base Exchange with Alkali Sulphates: A distinct advance was made with the disclosures of Wadman and von Girsewalt. In these methods the finely ground silicate ore (spodumene or lepidolite) is intimately mixed with an excess of alkali sulphate (usually K2S04) in at least a 1 to 1 proportion, and the mixture was heated to a relatively high temperature. Base exchange results, with the formation of lithium sulphate. A water leach dissolves the lithium sulphate, together with the excess potassium sulphate. Successful operation of this type of process requires very thorough grinding and mixing, as well as careful temperature control. The use of K,SO, is objectionable from cost considerations since purification of lithium carbonate re- quires the use of potassium carbonate, if the K2S04 is to be recovered and recycled. The lower solubility of K,SO, as compared with Na,SO, is also objectionable, since it limits the concentration of the Li,SO, solution to be precipitated by K,CO,. Early laboratory-scale investigation of this process by Lithium Corp. was not encouraging

Nov 1, 1955

By W. A. Boyer

MINE hoisting ropes can be loaded to capacity only when the strength of each component is exactly known. Characteristic curves provide this information. When load and rate of acceleration are specified for an individual rope, the characteristic curve assumes a predetermined shape. The factor of safety, is the value drived by dividing the breaking strength of the rope by the total stress on the rope where it goes over the sheave wheel. Total stress is made up of the weight of skip and cage, weight of ore, weight of rope between sheave and rope clevise or attachment, friction load, and acceleration force. Bending stresses are neglected in this discussion, as sheaves and drum di- ameters are assumed to be large enough to reduce these stresses to a negligible value. Fig. 1 gives a family of characteristic curves for 13/8-in. improved plow steel hoisting ropes of 6 x 19 or 6x21 construction with hemp core. The curves will hold for all rope sizes of this specified quality when they are subjected to an acceleration rate of 1.608 ft per sec2. As acceleration rates of most deep shaft hoists are close to this value, this family of curves is presented as a standard. Deviation is slight for other rope sizes. Note that for 0, which is the most important, the deviation is within the width of the line on the graph. In a comparison of values for ropes of 5/8-in. and 21/4-in. diam the deviation ranges from a maximum 1.2 pct at 0 ft to 0.6 of 1 pct at 5000 ft. The value of 5.55 is the same for all ropes at 2500 ft. The tabulated columns to the left of the curves are values of total connected load for each size of rope from 5/8-in. to 21/4-in. diam inclusive. With each of these connected loads the safety factor characteristic curve for the rope will be as indicated.

Jan 1, 1957

Jan 1, 1968

Executive JVW REYNOLDS, Chairman SYDNEY H BALL E DEGOLYER WILLIAM H BASSETT SAMUEL A TAYLOR Finance GEORGE D BARRON, Chairman H A GUESS GEORGE OTIS SMITH Membership ] H CALLOW, Chairman GEORGE D BARRON WILBER JUDSON JOHN A CHURCH, JR H N SPICER Alternates LEWIS W FRANCIS LOUIS D HUNTOON F T RUBIDGE

Jan 1, 1923

By Frances Jane Cromwell, D. J. McAdam, G. W. Geil

INTRODUCTION IN a series of papers, the authors and their associates have shown that the technical cohesion limit is affected by the same four factors that affect the flow stress, namely, the stress system, plastic deformation, temperature, and the strain rate.16-28 Moreover, each of these factors affects the technical cohesion limit in the same way that it affects the flow stress.‡ The influence of any one of these factors may be represented by a curve of cohesion limits, although only one point on the curve may represent actual fracture. As the term "fracture stress" has come into use with the same significance as "technical cohesion limit," the authors are here using the shorter term with the understanding that it does not always refer to actual fracture. This paper presents the results of an investigation of the flow of notched and unnotched specimens between yield and fracture. A study has thus been made of the flow and fracture of metals as affected by the stress system, and of the ductility of metals as affected by the stress system throughout plastic deformation. Since two of the principal stresses were equal (S2 = S3), the stress systems can be represented in terms of the radial stress ratio, the ratio of the transverse radial stress S3 to the longitudinal stress Sl.* The results of the experiments are represented by a series of complete flow-stress curves for each of the metals investigated, and these diagrams have been used for the development of other diagrams of various types. Ludwik was the first to suggest that fracture occurs when the flow stress becomes equal to a technical cohesion limit. Although Ludwik was incorrect in his view that the technical cohesion limit depends only on the amount of plastic deformation and not on the stress system, he was correct in his view that the flow-stress curve for any stress system terminates at a point representing a technical cohesion limit. The authors have seen some recent references to assertions by other investigators that a point representing the fracture stress need not be on the flow-stress curve. The Ludwik principle, however, would seem to be axiomatic, provided that the flow stress and fracture stress are properly defined and that the fracture stress is properly determined. Disregard of this principle has led to some untenable theories of criteria for fracture. When a metal is very ductile, the conventional method of determining the ductility and fracture stress by dividing the breaking load by the sectional area after fracture, generally gives values that are much too high. With some metals and in some conditions, the fracture stress thus determined may be two or more times the

Jan 1, 1948

By George Rice

THE A.I.M.E. Ground Movement and Subsidence Committee, pro-posed in 1920, held its first technical meeting in February 1923, under the able chairmanship of Mr. H. G. Moulton. The following list of papers and discussions, indicating the scope of the problems and relation to various conditions and method of mining, were given at that meeting by the distinguished mining engineers: J. Parke Channing, on Subsidence at Miami, Arizona; Howard N. Eavenson, on Mining an Upper Bitu-minous Seam after a Lower Seam Has Been Extracted; J. J. Rutledge, on Subsidence in Two Oklahoma Coal Mines; Benjamin F. Tillson, on Caving Cracks at the Franklin Mine, New Jersey; Dr. F. W. McNair, on the Dome Theory; William Kelly, on disadvantageous effects in Mining and Back-filling Working Upward a Steep-Pitching Iron-ore Bed; Eli T. Conner, on the good results of Back-Filling by Hydraulic Means in Preventing Destructive Subsidence in the Anthracite District; Thomas H. Claggett, on the merit of Systematic Pillar Drawing in Preventing Cracks in an Upper Seam; Henry H. Otto, successful results in the anthracite district in Mining Lower Seams before Upper Seams; Douglas Bunting, on Leading Factors Incident to Successful Mining of an Overlying Seam; Edwin Ludlow, on there being "less damage to buildings when there was complete removal of coal with complete packing than when room and pillar is used without extracting the pillars"; Edward O'Toole on "bumps" in eastern Kentucky mines, which he thought were the result of geologic stresses: H. A. Buehler, on Upheaval of Surface in an Illinois Case in Advance of the Face; and R. Dawson Hall, on The Mechanics of Subsidence from Mining. The author of this paper discussed various kinds of problems of ground movement and subsidence in both metal mining and coal mining; the production of great landslides by workings near an outcrop, as at Turtle Mountain, Alberta, Canada; and general

Jan 1, 1939

By J. A. Woolf, E. S. Leaver

The presence of soluble base metals in precious-metal ores usually precludes cyanidation as the best method of treatment. The laboratory experiments described in this paper show the possibility of cyanidation of gold-silver ores containing less than 0.5 per cent. of cyanide-soluble copper and the effect of zinc in the cyanide solution. Part I.—Copper in Cyanidation The proposed process of cyanidation of precious-metal ores containing copper is based on the regeneration of about 80 per cent. of the cyanide used in the dissolution of the copper. The method of regeneration involves a combination of the sulfide and the acid precipitation of the copper and silver. The resultant solution is made alkaline with lime, and the gold is precipitated with zinc dust. Solubility of Copper Minerals in Cyanide Solution In order to determine the solubility of copper minerals, including metallic copper, under the usual conditions for cyanidation, experiments were conducted with synthetic ores. Each ore sample was prepared by mixing the particular pure copper mineral with barren sea sand. Both the mineral and sand were ground to pass 100 mesh before they were thoroughly mixed. The percentage of copper in each head sample was determined by direct assay, excepting the metallic copper sample, which was computed on weights before mixing. Table 1 gives the results. Azurite, bornite, chalcocite, cuprite, malachite and finely divided metallic copper are readily and completely soluble under the usual conditions for cyanidation. Enargite and tetrahedrite are sufficiently soluble to cause an excessive loss of cyanide, and they also cause fouling of solutions with arsenic and antimony. Precious-metal ores containing small percentages of chalcopyrite or chrysocolla may give satisfactory returns with the usual cyanidation.

Jan 1, 1930

NEW MEMBERS The following list comprises the names of those persons who became members during the period of Mar. 10, 1917, to Apr. 10, 1917. ADKINS, HARVEY S Adkins & Denham, Engineers, Box 291,. Hazard, Ky. ANDERSON, ARTHUR P .... Leaser, Gibson Copper Co., Box 1978, Miami, Ariz. ARNOLD, EDWARD C... Min. Engr., Chief Engr., Federal Lead Co., Flat River, Mo. ASKIN, THOMAS B. H., Ball Mill Expert, Inspiration Cons. Copper Co., Miami, Ariz. BAIN, C. KREMER Butte & Superior Mining Co., Butte, Mont. BAKER, WILLIAM A.,.JR., Vice Pres. & Sales Mgr., The Georges Creek-Parker Coal Co., 306 North Gay St., Baltimore, Md. BOOTH, GEORGE H Mech. Engr., Inspiration Cons. Copper Co., Miami, Ariz. BRIDGMAN, G. TEMPLE, Asst. Consulting Mining Engr., Guggenheim Bros., 120 Broadway, New York, N. Y. BROOKS, CHARLES A Mine Surveyor, Homestake Min. Co., Lead, So. Dak. BUTCHER, FREDERIC E., Secretary, Missouri Metals Corpn., 1945 Railway Exchange Bldg., St. Louis, Mo.

Jan 5, 1917

By R. L. Huntington, D. T. MacRoberts, Charles R. Hetherington

Since the equation of continuity governing transient flow of gases through porous media cannot be integrated mathematically into a simple usable expression free from series terms, empirical and approximate equations have been advanced relating cumulative production and future production rates from gas reservoirs with time. In order to check the accuracy of these empirical equations and to obtain an insight into the initial conditions pertinent to the solution of the fundamental equation of continuity, experimental work has been conducted on a vertical 2-in. tube, 91.6 ft. high, packed with unconsolidated Wilcox sand. The results presented in graphical form show the accuracy of the approximate relations. Data from unsteady-flow runs on the 2-in. experimental tube are presented graphically, and are applied to obtain an equation for this specific case, and are offered as an aid in future investigations of this basic equation. The close agreement between equations calculated for steady-state flow and the experiments indicates that the decline of actual gas reservoirs may be treated by an application of these equations without serious error. Introduction The steady-state flow of gas through a porous material—that is, flow wherein the boundary conditions do not vary with time—is subject to analytical solution. Muskat1 has shown that the general differential equation is simply the La Place equation in P2. Direct solutions may be at once obtained. The unsteady state, on the other hand, is not analytically reducible. Since nearly all phenomena of practical interest in gas production involve flow in the unsteady rather than in the steady state, it has been necessary to derive approximate Solutions to the general equation. The validity of such approximations has not hitherto been adequately tested. In the experiments to be described a simple, closed, linear system is substituted for the real complex gas field. The general results, however, are independent of the geometry Of the system' The problem studied is the rate of production, and the accompanying variations in pressure, when one end of a linear porous system is opened to the atmosphere and permitted to produce to exhaustion. An approximate solution to the general differential equation, based upon the assumption of an "infinite series of steady states," is then applied to the results to determine the validity of this method of dealing with actual reservoirs. Theoretical Considerations The fundamental differential equation governing the flow of a gas through a Porous medium can be derived easily from the equation of continuity, Darcy's law, Boyle's law and a statement of the thermo-dynamic nature of the flow. For isothermal flow it is: d2P2/dx2 + d2p2/dy2 + d2p2/dz2 = 2fµ/K dP-dT

Jan 1, 1942

By R. L. Huntington, D. T. MacRoberts, Charles R. Hetherington

Since the equation of continuity governing transient flow of gases through porous media cannot be integrated mathematically into a simple usable expression free from series terms, empirical and approximate equations have been advanced relating cumulative production and future production rates from gas reservoirs with time. In order to check the accuracy of these empirical equations and to obtain an insight into the initial conditions pertinent to the solution of the fundamental equation of continuity, experimental work has been conducted on a vertical 2-in. tube, 91.6 ft. high, packed with unconsolidated Wilcox sand. The results presented in graphical form show the accuracy of the approximate relations. Data from unsteady-flow runs on the 2-in. experimental tube are presented graphically, and are applied to obtain an equation for this specific case, and are offered as an aid in future investigations of this basic equation. The close agreement between equations calculated for steady-state flow and the experiments indicates that the decline of actual gas reservoirs may be treated by an application of these equations without serious error. Introduction The steady-state flow of gas through a porous material—that is, flow wherein the boundary conditions do not vary with time—is subject to analytical solution. Muskat1 has shown that the general differential equation is simply the La Place equation in P2. Direct solutions may be at once obtained. The unsteady state, on the other hand, is not analytically reducible. Since nearly all phenomena of practical interest in gas production involve flow in the unsteady rather than in the steady state, it has been necessary to derive approximate Solutions to the general equation. The validity of such approximations has not hitherto been adequately tested. In the experiments to be described a simple, closed, linear system is substituted for the real complex gas field. The general results, however, are independent of the geometry Of the system' The problem studied is the rate of production, and the accompanying variations in pressure, when one end of a linear porous system is opened to the atmosphere and permitted to produce to exhaustion. An approximate solution to the general differential equation, based upon the assumption of an "infinite series of steady states," is then applied to the results to determine the validity of this method of dealing with actual reservoirs. Theoretical Considerations The fundamental differential equation governing the flow of a gas through a Porous medium can be derived easily from the equation of continuity, Darcy's law, Boyle's law and a statement of the thermo-dynamic nature of the flow. For isothermal flow it is: d2P2/dx2 + d2p2/dy2 + d2p2/dz2 = 2fµ/K dP-dT

Jan 1, 1942

By R. W. Fenn, H. A. Lepper, W. R. Hibbard

THIS paper reports the results of static tension and torsion tests made on single crystals of alpha brass for the purpose of determining its elastic coefficients. 70-30 alpha brass was chosen because it has been used extensively in the study of the plastic deformation and because it has the following desirable characteristics: (1) face-centered cubic structure, (2) marked elastic anistropy, (3) low elastic modulus. In 1928 Masima and Sachs' using static methods reported the following values for the elastic coefficients of 72-28 pct alpha brass: S11 = 19.4 X 10-13' cm2 per dyne S12 = —8.35 X 10"' cm2 per dyne S44 = 13.9 X 10-13= cm2 per dyne These values were obtained from the measurements shown in fig. 1. The experimental points for both tension and torsion lie consistently below the lines drawn to represent them. Fig. 2 shows the stress-strain curves for their specimens. Only a few points in the elastic range of these curves were available to obtain their values for Young's modulus. Therefore, it was considered that a re-evaluation of these data was desirable. In addition a variation of from 1.13 to 1.485 kg per mm2 was found in the values of the critical resolved shear stress for 70-30 alpha brass reported by Burghoff,² Treuting and Brick: Martin,4 Maddin, Mathewson and Hibbard5,6 and von Goler and Sachs.' Therefore, it was desired to evaluate the conclusion of Boas and Schmid8 that a constant resolved shear stress and not a constant elastic shear initiates plastic deformation. Theoretical Considerations*: The elastic deformation of cubic crystals may be defined by three elastic coefficients (S11, S12, S44,) or three elastic parameters (C,,, C,, C,,). These coefficients or parameters are sufficient to define the stress and strain relations for cubic crystals in the generalized form of Hooke's law referred to Cartesian coordinates. Elastic parameters and coefficients in the cubic system are related by the expressions: C11 —S11+S12/(S11-S12)(S11+2 S12) C12=-S12/(S11-S12)(S11+ 2 S12) (S11 — S12) (S11 + 2 S12) [2] C44 =1/S44 PI It is possible to determine all the elastic coefficients for a cubic metal by measuring two of the three elastic constants: Young's modulus (E), torsion modulus (G), or compressibility (S). The following relations exist between crystallographic orientation and E, G and S for cylindrical crystals of the cubic system: 1/E = S11 — 2 [(S11 - S12) — Su] (?1² ?2² + ?2²?83 + ?3² ?1²) [4]

Jan 1, 1951