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By Charles Jones

IN the winter of 1902, while occupying the position of mining and examining engineer for the Mountain Copper Co., Ltd., of Keswick, Cal., I had occasion to discuss with the General Manager, among other things, the question of the enormous waste of sulphur in smelting cupriferous, pyrite ore, and to cast about for means to utilize this waste or to render the fumes innocuous to vegetation. The decreasing rate of production of California farms, the consequent need of fertilizers, and the opportunity thus offered to utilize large quantities of sulphuric acid in the manufacture of superphosphates naturally brought the subject to the practical and commercial side of phosphates. I was informed that the company had made efforts to find phosphates in the West, without success. I advised as a start placing inquiries for phosphate deposits on the Pacific coast in the current mining ,journals. This was done, with the result that in January, 1903, from an advertisement in the Mining and Scientific Press we got track of a deposit in Rich county, Utah, through T.J . Wilson, of the Southern Pacific railroad in San Francisco. As soon as snow in the mountains would permit, in May, 1903, I undertook an examination of the property, with the result of recognizing the importance of the find, in spite of its lack of facilities for transportation at a commercial figure. On June 15, 1903, I concluded my report by saying, "This may be one of the world's deposits of phosphates." On Nov. 17, 1903, I concluded my report for the season in the following words : " I have now no hesitation in saying that I believe the Carboniferous formation so largely developed in the Wasatch mountains of Utah and the mountains of the Great Basin will prove to be one of the greatest storehouses of phosphoric acid in the world."

Jan 10, 1913

Jan 1, 1970

By Austin E. Dwight

IT has been shown by Oelsen and Wever' that the effect of a solute element on the allotropic transformation in iron is dependent upon the quantity

Jan 1, 1957

By P. G. Hallof

Only recently has the term Induced Polarization found its way into geophysical literature. Schlumberger first mentioned the possible use of the induced polarization effect in one of his early papers. Later, induced polarization was the subject of several university theses, such as Seigel's at the University of Toronto and Bliel's at the Michigan School of Technology. In addition, a group at the New Mexico School of Mining and Technobgy has done work on induced polarization. There is very little to be found in print on the subject of induced polarization. Several papers have been presented at meetings, the 1958 AIME and SEG* conventions, for instance, on laboratory measurements of the effect and theoretical considerations useful in the interpretation of field results. This paper is the first attempt to present actual field results which show the usefulness of induced polarization as a prospecting technique. There are several phenomena that can cause polarization when electrical current is passed through the ground. In a paper presented at the 1958 SEG* meetings Professor T. R. Madden of M. I. T. demonstrated that only two of these gave rise to appreciable effects. The first is a result of the membrane and diffusion effects in a sandstone that contains appre- ciable amounts of clay minerals. The unbonded charges associated with the clay mineral forma material that passes positive and negative ions with different mobilities. When current is passed through such a system for some period of time, polarization results. The second phenomenon, which gives rise to very much larger polarization effects, is the one used in the new prospecting technique. These effects are a result of the blocking action or polarization of metallic or electronic conductors in a medium of ionic solution conduction. This electrochemical polarization, called "the over-voltage effect" by electro-chemists, occurs whenever electrical current is passed through a volume of rock which contains metallic minerals such as base metal sulphides. This polarization at metallic interfaces in ionic solutions depends upon the chemical energies necessary to allow the ions to continue the flow of current by giving up or receiving an electron from the metallic surfaces. The energy stored in this reaction isanalogous to that stored when a condenser is charged. If a d. c. current flowing through such a system is interrupted, the polarization can be detected as a small, decaying current that flows after the applied current is discontinued. The decaying potential measured is a result of the current flow caused by charges returning to their equilibrium positions from the positions they assumed under the applied potential field. Because of the polarization, there is an excess of change at each metallic interface. There is an alternate method of measurement of the induced polarization effect. The electrical

Jan 1, 1961

By H. N. Egan

Faced with a severe disposal problem of their fines from a coal mine in the heart of the Appalachian Mountains of extreme eastern Kentucky, Eastern Coal Corporation has built a special plant to pelletize the fines into high quality coal pellets meeting the requirements of the metallurgical market. These low-ash, low-sulfur pellets measuring 3/4 x 3/8 in. contain less than 1.5% moisture and have the same stability as raw coal of the same size. Although Eastern Coal is mining 6000 tpd, the company had, until recently, no provision to recover the fine coal which was included with the plant effluent pumped to a 12-acre refuse pond. The pond, impounded behind the coarse refuse dump, rose 15 ft last year and obviously no pond can stand many years at this rate. Limited pond space in this rugged area of steep hills and narrow valleys dictated a revised disposal method.

Jan 11, 1967

By R. S. Montgomery

Laboratory experiments simulating rock drilling were conducted on a number of commercial grades of tungsten carbide in order to determine their wear rates when they are used as inserts in percussive rock drill bits. The test rock was Barre granite and tests were made at conditions similar to those of the carbide buttons near the periphery of a large, down-hole, button bit. In addition, some wear rate measurements were made at a low blow energy. Wear rates of these carbide buttons were an extremely sensitive function of their cobalt contents and hardnesses and were proportional to e-°.57Hup to a hardness of about 91 RA. The point of minimum wear rate, which occurs at about 92 RA, corresponds to the point of maximum compressive strength. Modern percussive rock drill bits have inserts of cemented tungsten carbide on their wear faces. These inserts have drastically reduced bit wear in comparison to that of earlier all steel bits. The most common cemented carbide grade used in percussive rock drill bits contains about ten weight percent cobalt, although grades containing more or less cobalt are also used. Contrary to the case with carbide in metal-cutting tools, alloying materials are rarely used in mining grades. There are a number of designs of rock bits in current use. The most common form is an X bit which has four chisel-form radial wings. The button bit is another important design and one which has been recently developed. This design uses a flat steel face studded with relatively small hemispherically tipped carbide buttons. These types are illustrated in Fig. 1. Studies have been made of the sliding wear of cemented tungsten carbide on rock 1-4 and multiple-impact fracture', 5-6, b~t there has been comparatively little published on the percussive wear of this material although the wear of the impact face is the most important. There is some available data on the rate of dulling of rock bit inserts in actual drilling 7 but no laboratory studies. Sliding wear studies are useful for understanding the wear of coal and mineral cutting tools and gauge wear of percussive drill bits. but the

Jan 1, 1970

By J. B. Dyess

TARNISH films on some of the common metals (particularly on copper and silver) have been of much scientific and commercial concern for a long time, but before the development of the electrical method1 of measuring film thicknesses there was no satisfactory quantitative approach by which to study the separate parts of these complex films. This method has been adapted to the measurement of duplex (cuprous-cupric) oxide films on copper .2 In the present work it has been used to measure tarnish films on copper when they were mixtures of cuprous oxide and cuprous sulphide, and also when they contained cuprous oxide, cupric oxide and cuprous sulphide, each component part being measured at a different potential value. Oxide-coated copper specimens, prepared by heating copper in air at chosen temperatures for given periods, were exposed to moist hydrogen. sulphide in air to form the various oxide-sulphide films studied. The comparative resistances afforded by (1) different thicknesses of oxide films, and also (2) equal thicknesses of oxide and sulphide films, against severe attacks of hydrogen sulphide were measured. The electrical method requires that the time be observed for the cathodic reduction of each part of the film substance, and these respective time values multiplied by the constant current give the corresponding quantities of electricity expended. Then each millicoulomb per square centimeter represents a film thickness of T= MX10 8 2D X 96,494 X 103 (a) where M is weight of oxide (or sulphide) giving one gram-atom of oxygen (or sulphur) for cathodic reduction, D is density of the oxide (or sulphide) and t is the thickness in Angström units per millicoulomb per square centimeter. The value of t for cuprous sulphide (cubical) is 14.27, and is obtained by substituting 5.78 for D and 159.20 for M in equation a. Previous values2 of t for cuprous and cupric oxides (12.36 and 6.39, respectively) were used in the present work.

Jan 1, 1939

By R. G. Turner, M. G. Hubbard, A. E. Dukler

Gas phase hydrocarbons produced from underground reservoirs will, in many instances, have liquid phase material associated with them, the presence of which can affect the flowing characteristics of the well. Liquids can come from condensation of hydrocarbon gas (condensate) or from interstitial water in the reservoir matrix. In either case, the higher density liquid phase, being essentially discontinuous, must be transported to the surface by the gas. In the event the gas phase does not provide sufficient transport energy to lift the liquids out of the well, the liquids will accumulate in the wellbore. The accumulation of the liquid will impose an additional back pressure on the formation that can significantly affect the production capacity of the well. In low pressure wells the liquid may completely kill the well; and in the higher pressure wells there can occur a variable degree of slugging or churning of the liquids, which can affect calculations used in routine well tests. Specifically, the calculated bottom-hole pressures used in multirate backpressure tests will be erroneous if the well is not removing liquids on a continuous basis, and gas:liquid ratios observed during such a test may not be correct. Several authors1,3,8,14 have suggested methods to determine if the flow rate of a well is sufficient to remove liquid phase material. Vitter14 and Duggan' proposed that wellhead velocities observed in the field would be adequate for keeping wells unloaded. Jones8 and Dukler3 presented analytical treatments resulting in equations for calculating, from physical properties, the minimum necessary flow rate. An analysis of these studies indicates the existence of two proposed physical models for the removal of gas well liquids: (1) liquid film movement along the walls of the pipe and (2) liquid droplets entrained in the high velocity gas core. Although there probably is a continuous exchange of liquid between the gas core and the film, they will be treated separately for the purposes of this study. The development and comparison of these separate models with experimental data will permit the determination of which, if either, is the controlling mechanism for the removal of liquids from gas wells. The Continuous Film Model Liquid phase accumulation on the walls of a conduit during two-phase gas/liquid flow is inevitable due to the impingement of entrained liquid drops and the condensation of vapors. The movement of the liquid on the wall is therefore of interest in the analysis of liquid removal from gas wells. If the annular liquid film must be moved upward along the walls in order to keep a gas well from loading up, then the minimum gas flow rate necessary to accomplish this is of primary interest. The analysis technique used follows Dukler2 and Hewitt5 and involves describing the profile of the velocity of a liquid film moving upward on the inside of a tube. The minimum rate of gas flow required to move the film upward is then calculated.

Jan 1, 1970

By B. W. Prof. Frazier

I PROPOSE in this paper to treat of the chimney merely as a heat engine, as one of the devices resorted to in practice for the conversion of heat into mechanical work. For the sake of simplicity and clearness in the discussion, let us consider the subject in its simplest form. Conceive a chamber, heated from without, in free communicatioH at one end with the external atmosphere, and at the other end opening into a vertical chimney. Let the. cross-section of the chamber be so great, relatively to that of the chimney, that we can neglect the actual energy of the air passing through the chamber. We will neglect, also, all passive resistances to the passage of the air. We will assume that the cross-section of the chimney is constant, and that the air in passing through it neither gains nor loses heat. The following symbols will be employed in the discussion : Po = the normal pressure of the atmosphere, which, it is assumed, is the pressure existing at the level of the chamber. Po = 10332.96 kilograms per square meter. P2 = the pressure of the external atmosphere at the top of the chimney. To = the, absolute temperature of melting ice by the centigrade scale. This is assumed to be the temperature of the external air at the level of the chamber. To = 273°. T2 =the absolute temperature of the air as it passes from the chamber to the chimney. T3 =the absolute temperature of the air as it issues from the chimney. to, t2, t3 are the temperatures, as recorded on the centigrade ther¬mometer, corresponding to the absolute temperatures To, T2, T3 re-spectively to = 0° C. In general, t = T- 273. Io, I2, I3, represent the intrinsic energy of the air at the temperatures To, T2, T3 respectively.

Jan 1, 1882

A record $18.7 billion worth of metals, non- metals and fuels was produced in the U.S. during 1962, according to a year-end estimate from the USBM. The 1962 total value, based on preliminary statistics compiled by the Bureau, was nearly $600 million more than in 1961. Most minerals gained both in value and volume of production during 1962 according to information collected by the Bureau. All mineral fuels except anthracite showed increases. Among nonmetallic minerals- other than fuels-gains exceeded losses by two to one. Metal production held steady as gains and losses balanced.

Jan 2, 1963

The pellet plant, built by Dravo Corp, in Groveland, Mich., for the Hanna Mining Co., is now in full operation. Although using jasper, a type of iron ore with low iron content (approximately 28% Fe), the plant has a rated capacity of 1,250,000 tans of pellets per year. In its four years of existence, the nearby concentrating plant has seen its capacity increase from 700,000 tons to 1,500,000 tons a year as part of a major expansion program at Groveland. Utilizing the Dravo-Lurgi continuous grate process, the pellet plant produces %a-in. pellets of more than 60% iron content. The fully-hooded pelletizing grate, largest in the U.S., is 9 ft. 10% in. wide and 223 ft. 1% in. tong over 34 windboxes, with an effective hearth area of 2195 sq. ft. Drying, firing, and cooling functions are all carried out on this single piece of equipment.

Jan 4, 1964

By John Ward Smith

Dawsonite-bearing oil shale of Colorado's Green River formation offers a unique and vast (more than 5.9 Gt of A120 j) resource of easily extractable alumina. The processing methods required by the thermal reactions of dawsonite and its oil-shale carrier also require production of shale oil, soda ash, and nahcolite as marketable coproducts. These production methods are presented. The alumina production process is contrasted with the Bayer process to describe technical advantages of extraction of alumina from oil shale which may offset the problems associated with processing a relatively lean ore. While alumina production from oil shale requires development of new technology, the technical problems appear solvable. Only the political problems arising from the now onerous and completely unnecessary federal oil-shale withdrawal appear less solvable.

Jan 1, 1982

By J. van Lookeren

In the case of a reservoir where the oil underlies a large gas cap and overlies bottom water, production can be inzproved considerably if wells are perforated below the water-oil contact rather than opposite the oil-bearing section. The theoretical arguments for this improvement, which in some cases may be tenfold, are supported by experimental evidence. INTRODUCTION Reservoirs frequently consist of one sand body containing an oil layer underlying a thick, gas-bearing section and overlying bottom water (Fig. 1). Wells in such reservoirs are customarily opened up opposite the oil-bearing interval or, rather, opposite the lower part of this interval (Fig. 2). More often than not, it is inefficient or prohibited to blow off large quantities of gas with the oil. This im-psses a severe limitation on the drawdown, which results in low oil-production rates. Because of the small difference in specific gravity between oil and water, the latter will easily cone upwards, so that the production of water together with the oil is not prevented by this completion method. In such a situation wells should be opened deeper, in the originally water-bearing zone. The gas can be shut off by not perforating over the upper part of the interval (Fig. 3) or by a tubing hung close to the bottom of the interval (Fig. 4). Initially much water will be produced, but when steady-state conditions have been established (as depicted in Figs. 3 and 4) larger drawdowns are permissible than in a conventionally completed well, and correspondingly higher oil-production rates will result. Water cuts are only slightly higher because of the small effect of gravity on the water-oil flow distribution. CALCULATIONS The ratio of improvement has been estimated by means of approximate calculations. The completion depicted in Fig. 4 is the most convenient basis for these calculations. By postulating that vertical flow gradients can be disregarded, the Appendix shows that the well-known Dupuit formula can be obtained except for some complication due to the presence of two fluids rather than one. The Appendix makes the reasonable assumption that, for suitable boundary conditions, the oil layer occupies a constant fraction of the total fluid height throughout the reservoir. The oil- and water-production rates can thus be related to the liquid levels in the borehole as follows:

Jan 1, 1966

Executive A R LEDOUX, Chairman ARTHUR S DWIGHT CHARLES F RAND E P MATHEWSON J V W REYNDERS Membership E DEGOLYER, Chairman W Y WESTERVELT, Vice-chairman WILLIAM H BASSETT H G MOULTON C MINOT WELD Finance WALTER H ALDRIDGE, Chairman GEORGE D BARRON GALEN H CLEVENGER Library GEORGE C STONE,' Chairman JOHN H JANEWAY ALEXANDER C HUMPHREYS, ROBERT LINTON FREDERICK F SHARPLESS

Jan 1, 1923

By V. H. Whihelm

Since 1935 California has enjoyed a remarkable cycle of discovery, which has placed the state in a very satisfactory position in regard to oil reserves. Most ol the geophysical plays have been drilled and it is possible that new discoveries must be made by the application of careful geologic and stratigraphic studies. During 1940 only one new field was discovered, which, although not of major importance, may lead to additional discoveries. During the year, 113 wildcats were drilled. New discoveries, extensions and a reappraisal of discoveries made in 1939 will not approximate over 50,000,000 bbl., as against an estimated withdrawal during the year of 224,000,000 barrels. Demand in terms of crude for 1940 was 632,000 bbl. per day as against 626,000 bbl. per day for 1939. Demand for gasoline was the same as in 1939, but the demand lor fuel oil increased 3.8 per cent. Compared with 1939, Japanese shipments decreased from 75,786 bbl, per day to 61,000 bbl. per day, but the balance of Pacific foreign shipments increased from 59,409 bbl. per day to 61,304. Total with-drawals from storage during the year will approximate 7,000,000 bbl., almost all of which is fuel oil. Drilling activity was slightly greater than in 1939 and accounted for 890 new producing wells as against 851 for 1939 (Table 3). Production averaged 611,900 bbl. per day as compared with 614.,842 bbl. per day for 1939. The productive acreage figure of the state was increased by 4000 through discoveries and extensions. New Discoveries Los Angeles Basin District Del Vdle Field.—Northwest of Newhall, where the first oil well in California was drilled, R. E. Havenstrite completed his Lincoln No. I well, flowing 390 bbl. of 50" gravity oil together with 7000 M CU. ft. of gas. Later the well was recompleted, after cutting off the gas, for 950 bbl. of 34" gravity oil. The type of structure from which this production is coming is a plunging anticline, complicated by faulting. The Lincoln No. I well uncovered approximately 180 ft. of net sand. This field contains a gas cap and its indicated productive area approximates 500 acres. An intensive wildcat drilling campaign is expected during this coming year in the district in the vicinity of the Del Valle field. Extensions and Deeper Sand Developments Los Ange1es Basin District Athens Field.—On the northwest plunge of the Athens structure, the Thorley Oil Co. completed its No. 12-1 well, flowing 250 bbl. of 3 2" gravity oil from a depth of 8097 ft. The area in which the well is located is complicated by faulting and it is impossible at this date to determine the importance of this deep-zone discovery.

Jan 1, 1941

By V. H. Whihelm

Since 1935 California has enjoyed a remarkable cycle of discovery, which has placed the state in a very satisfactory position in regard to oil reserves. Most ol the geophysical plays have been drilled and it is possible that new discoveries must be made by the application of careful geologic and stratigraphic studies. During 1940 only one new field was discovered, which, although not of major importance, may lead to additional discoveries. During the year, 113 wildcats were drilled. New discoveries, extensions and a reappraisal of discoveries made in 1939 will not approximate over 50,000,000 bbl., as against an estimated withdrawal during the year of 224,000,000 barrels. Demand in terms of crude for 1940 was 632,000 bbl. per day as against 626,000 bbl. per day for 1939. Demand for gasoline was the same as in 1939, but the demand lor fuel oil increased 3.8 per cent. Compared with 1939, Japanese shipments decreased from 75,786 bbl, per day to 61,000 bbl. per day, but the balance of Pacific foreign shipments increased from 59,409 bbl. per day to 61,304. Total with-drawals from storage during the year will approximate 7,000,000 bbl., almost all of which is fuel oil. Drilling activity was slightly greater than in 1939 and accounted for 890 new producing wells as against 851 for 1939 (Table 3). Production averaged 611,900 bbl. per day as compared with 614.,842 bbl. per day for 1939. The productive acreage figure of the state was increased by 4000 through discoveries and extensions. New Discoveries Los Angeles Basin District Del Vdle Field.—Northwest of Newhall, where the first oil well in California was drilled, R. E. Havenstrite completed his Lincoln No. I well, flowing 390 bbl. of 50" gravity oil together with 7000 M CU. ft. of gas. Later the well was recompleted, after cutting off the gas, for 950 bbl. of 34" gravity oil. The type of structure from which this production is coming is a plunging anticline, complicated by faulting. The Lincoln No. I well uncovered approximately 180 ft. of net sand. This field contains a gas cap and its indicated productive area approximates 500 acres. An intensive wildcat drilling campaign is expected during this coming year in the district in the vicinity of the Del Valle field. Extensions and Deeper Sand Developments Los Ange1es Basin District Athens Field.—On the northwest plunge of the Athens structure, the Thorley Oil Co. completed its No. 12-1 well, flowing 250 bbl. of 3 2" gravity oil from a depth of 8097 ft. The area in which the well is located is complicated by faulting and it is impossible at this date to determine the importance of this deep-zone discovery.

Jan 1, 1941

By Henry M. Howe

PART I. § 1. Introduction. After giving certain definitions, this paper gives the reasons which led to Roozeboom's form of the diagram of the freezing-point curves and general equilibrium of the iron-carbon compounds, steel and cast-iron ; and then those which led to replacing it with the present or double diagram, in which graphite is at all temperatures held to be the more stable and cementite the less stable (metastable) form of carbon. Next in § 10 the evidence supporting this greater stability of graphite is examined, then in § 17 that which seems to oppose it, and in § 22 a summary of the evidence is presented. The second part of the paper considers the topography of the graphite-iron diagram, rejecting summarily the solubility-lines based on the data of Charpy and Grenet and of Mannes-mann, on the ground that the data even on their face do not really point toward these lines, and that they are wholly incompetent to determine any solubility-lines whatsoever, because they report together with the dissolved carbon also an indeterminate quantity of cement-carbon, and because even such carbon as is actually dissolved, only in part represents the solubility of graphite, and in another and indeterminate part represents the solubility of cementite, or at least of carbon in presence of cementite as distinguished from graphite. It might be thought that graphite is but slightly soluble in iron, because of the absence of any suggestions of eutectoid graphite, corresponding to the eutectoid cementite of pearlite in very many cases in which the cast-iron seems to consist of ferrite and massive graphite only, and because of the micrographs of Goerens and Gutowsky. In these the primary austenite of cast-iron quenched but little below the eutectic freezing-

Jan 7, 1908

By R. L. Grunes, F. K. Kies, C. D&apos, Antonio

THE several studies concerned with the annealing of thin nickel films have largely been restricted to films of a single thickness.1-4 It is well-known, however, that both physical and mechanical properties depend upon film thickness.5, 6 The strength-thickness relations found in vapor-deposited nickel films in the annealed and as-deposited states, as an example, are at least partially due to the density and arrangement of imperfections within the films.7, 8 For these reasons, the annealing characteristics of thin nickel films as a function of thickness were investigated. Electrical resistance was chosen to monitor annealing behavior since resistance changes are partially dependent upon defect structure. In addition, the equations predicting film resistivity as a function of thickness are already available.9, 10 Further advantages afforded by electrical-resistance measurements are its adaption to continuous readings during annealing and its relative simplicity. Nickel films were vapor-deposited, at average rates of 60Å per sec, on Vycor substrates held at room temperature in vacuums of about 10-5 torr. Afterwards, deposition-thickness measurements were made using a multiple-beam interferometric technique. A more detailed description of deposition procedures and the interferometer appear elsewhere.7, 8 The four-probe method was employed in measuring electrical resistance since this technique measures film resistance without contributions from lead wires and contacts. Resistance measurements were made before, during, and after annealing to temperatures of 700°C under vacuums of approximately 10-4 torr. Measurements were made every 25°C or more often when necessitated by unusual resistance changes. Cooling and heating rates were maintained at approximately 5°C per min. Typical resistivity vs temperature curves are shown in Figs. 1 through 4. It is apparent from these

Jan 1, 1965

By Eugene Stephenson

CRITICAL analyses of the work expended in producing oil by the utilization of gas energy have appeared in the publications of Shaw,1 Pierce and Lewis,2 and Herold,3 authors who have ably discussed the factors which must be taken into consideration in comparing energy consumed per barrel in various wells which are flowed by means of gas-lift. However, two distinct phases of oil production are concerned with the ratio of gas energy consumed to oil produced. One of these phases is the gas-lift, which utilizes the differential gas pressures for the purpose of flowing oil, whether these pressures be natural reservoir pressures or be induced by artificial compression of gas or air. The other phase has to do with prorating oil production in pools which are operated either as units, or are subject to such restrictions as those imposed at Oklahoma City by the Corporation Commission, or, by similar controlling groups in other fields. An abundance of literature is available relative to the problems of flowing wells by gas-lift, but the first suggestion that the energy of the gas within the oil and gas pool might serve as a basis for proration, appeared in the timely article by McWilliams.4 Much of the. dissatisfaction with proration in certain fields is because some operators feel that besides the hazard to the wells which accompanies the test, the method of allocating production on the basis of the "potential" gage is inequitable and gives some operators a distinct advantage over others.5 The most severe penalty may be exacted from the most progressive operators or those who attempt to produce their oil with a minimum quantity of reservoir gas. If :no difficulties ever

Jan 1, 1931

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