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By L. Adler

The author recently proposed a technique for handling the effect of planes of weakness on failure in geologic material.1 The technique employed an "extended" Mohr's rupture envelope, on which was superimposed a generalized three dimensional stress representation. Subsequently, the method was applied to so-called two-dimensional stress states" which were in reality degenerate three-dimensional ones. Since a two-dimensional stress solution usually refers to a plane stress condition, the terminology was confusing. The distinction between a plane stress state and a degenerate three-dimensional one is shown in Fig. 1. The solution of problems involving a generalized three-dimensional stress state is greatly aided by continual reference to the basic principle that no stress components can act on a plane, oriented as is the weakness plane, which lies outside of the weakness plane's rupture enVelope.2 This is shown in Fig. 2; and if it is also remembered that the radii of the Mohr's Circles give the orientation of such a plane, solutions are easier to follow, and perform. Sample Problem 1: Site Location (generalized three-dimensional case).' Given: 1) Both rupture envelope for the solid and plane of weakness. 2) Existing principal stresses and orientations in space (?12, ?13) obtained from a stress analysis of the proposed structure. Find: Permissible orientations of the weakness plane in order to select a suitable site.

Jan 1, 1963

By M. I. Kabir, R. S. Schechter, L. W. Lake

This paper presents the development and application of a novel scaling technique that, when used with a streamline model, causes a "bundle" of one-dimensional (1-D) problems to reduce to a single 1-D calculation. The 1-D bundle is the streamline representation of a two-dimensional (2-D) problem. The 1-D calculation accounts for chemical-rock interactions and the streamline model for areal sweep. The scaling technique significantly reduces computation time, is readily modified to desktop calculations, and can be applied to both absorbing and reacting species. The work was sponsored by the US Bureau of Mines.

Jan 1, 1986

By F. W. von Batchelder

The principles of microradiography and their application practically coincided with the discovery of X-rays. These principles were first used in the metallurgy field by Heycock and Neville1 in a study of the dendrite structure of alloys of Au-Na, Au-A1, Cu-A1, and Ag-A1. The method was introduced in the USA by clark2 after a visit to France. Scores of papers have been written, and a very complete bibliography on this subject was compiled by the Eastman Kodak company. Although a number of papers have discussed X-ray

Jan 1, 1959

By T. KIRKE ROSE

A Discussion of the paper by H. O. Hofman and M. G. Magnuson, read at the Lake Superior meeting, September, 1904. (British Columbia Meeting, July, 1905.) T. KIRKE ROSE, London, Eng. (communication to the Secretary*`) :-The authors have shown that, under certain conditions, the rate of dissolution of gold by chlorine and bromine is re¬duced by the addition of 10 per cent. of silver to the gold, and that the action is almost stopped when the silver amounts to 30 or 40 per cent. of the alloy. Even if full recognition is given to the practical way in which the work was done, how¬ever, it is to be regretted that Prof. Hofman and Mr. Magnuson did not determine the temperature at which the experiments were carried out. From the details given it may be inferred that the temperature was raised by chemical action by about 20° C. when 21 g. of sulphuric acid were added, and that the mixture was then slowly cooled down during the experiment. When bromine or very weak chlorine solutions were used, there could not have been any perceptible heating action. As the action of both chlorine and bromine is aided by heat, it follows that the stronger solutions of chlorine were given an unfair advantage over the weaker solutions and over bromine. If the temperature had been the same in each case, I do not think that the conclusions given oil p. 432 of the Bi-Monthly Bulletin, March, 1905, 1 would have been found to be justified. (This is speaking generally. In barrel-treatment the conditions are similar to those in the experiments.) The superior speed of bromine as compared with chlorine at equivalent strengths is not yet disproved, and the differences noted between strong and weak solutions of chlorine may have been largely a function of the temperature. Moreover, the authors used somewhat coarse particles of gold

Sep 1, 1905

By Ikuya Takase

INTRODUCTION Since the occurrence of the first oil crisis, coun-tries of the world, especially oil-importing countries have made sustained and vigorous efforts to lessen the dependency on oil as a source of energy supply. The adoption of "Principles of Coal Policy" by the IEA Ministerial Governing Board Meeting in May, 1979 was the first formal action taken by major energy consuming countries. At the Venice Summit in June, 1980, it was agreed that production and use of coal should be doubled over the next ten years. In fact, the world coal use in 1980 showed around a 10 percent increase over the previous year. Recently, we have seen an indication that the balance of oil supply and demand in the short term have eased. But I believe that it remains vital that we continue to encourage the development and introduction of alternative energy sources. Because, from the medium and long range viewpoint the recovery of the worldwide economy will lead us to increased oil requirements and thus we will be faced with the cyclical, structural tightening situation between the supply and demand of oil. Moreover, we are still convinced that the constraint of the supply capabilities of the Middle-East nations may be increasing in the long-term, since there still remains political uncertainties among these nations. Consequently, above all, coal is viewed as an alternative energy resource available for immediate expansion of use and is given as high a priority as nuclear power. In Japan, we regard coal as the most reliable alternative energy resource to replace oil. According to the "Alternative Energy Supply Targets" approved by the Cabinet in November, 1980, the level of coal imports is estimated to approximately double by 1990, while our domestic coal production will remain nearly at the same level. The transition from oil to coal is found in the recent import levels of coal---73 mil¬lion tons in 1980, a 23 percent increase over the 59 million tons imported in 1979. There was an upsurge in steaming coal imports, reflecting the transition in feedstocks---7.2 million tons in 1980, four times over the previous year's amount. Henceforth, from the medium to long range view, the demand for coal, especially that of steaming coal is forecast to continue to grow. The timely expansion of supply capabilities is our utmost concern and should be one of the most significant goals of our comprehensive policy. The Overseas Coal Investigative Committee, a privately organized advisory panel to the Director-General of the Natural Resources and Energy Agency of the Ministry of International Trade and Industry (MITI), investigated means to secure a stable supply of overseas coal. The panel presented its interim proposals in August, 1981, recommending the diversification of coal import sources, extensive use of low rank coal, as well as enhanced international cooperation between coal producing and importing countries. THE CONTENTS OF THE COMMITTEE'S REPORT Four Points for Major Consideration In order to ensure a stable supply of overseas coal, Japan needs adequate policy measures consistent with the characteristics of coal resources and environmental requirements, giving consideration to Japan's status and the role she is expected to play in the areas. From the above, great importance should be attached to the following four points: All the components of the "Coal Chain" (Namely, the development of mine sites, construction of railroads, port loading facilities, coal shipping vessels, port receiving facilities, including coal centers and international transport facilities etc.) should be reviewed and reformed with steps taken to assure efficiency consistent with the entire coal chain system. The complete formation of a coal chain system requires such lengthy lead times and huge amounts of investment that necessary measures should be undertaken well in advance utilizing long-range projections of future demands and various economic surveys. Policy planning should be conducted taking into account of harmonizing stability and economics of the supply structure. For ensuring the long-term stability and expansion of the coal trade, international cooperation on a bilateral and multi-national basis should be encouraged. Mutual understanding and close relationships are essential to facilitate the formation of the supply system and to promote the extensive use of coal. Direction and Problems Related to Supply Stability Expansion of Supply Capabilities. World coal imports in 1979 amounted to 229 million tons, of which Japan's share amounted to 59 million tons, or one fourth of the entire amount. The imports of European and Asian countries accounted for 83 million tons and 7 million tons respectively. According to the examination of the Investigative Committee, Japan's coal requirement is estimated to be between 140-150 million tons by 1990, nearly the same level as announced in the Provisional Long-Term Energy Supply and Demand Outlook in 1979. This fore¬cast is-to be revised in April, 1982. Japan's demand is expected to be met through fiscal 1985; however, by 1990, the supply is estimated to fall short of demand, particulary, in the field of steaming coal. For the expansion of supply capability, first, mine development should be accelerated. The proposed

Jan 1, 1982

By E. DeGolyer

THE petroleum production of the world for 1924 again passed the billion-barrel mark, as it did in 1923. A preliminary estimate of production is 1,016,000,000 bbl., a decrease of 1,100,000 bbl., or less than 1 per cent. from the 1,017,100,000 bbl. produced in 1923, the year of greatest production. FIG. 1.-TOTAL WORLD AND UNITED STATES PRODUCTION. Production in the United States decreased 18,500,000 bbl., the. first decrease in yearly production since 1906. Mexican production decreased almost 10,000,000 bbl. Russia, Persia, Roumania, Venezuela, and Peru increased their production by an amount almost great enough to offset the decline in the United States and Mexico. The decline in the production in the United States and Mexico was considerably less than anticipated by leading geologists, economists, and statisticians; nor did the increase in consumption entirely meet the expectations of estimators. Early in the year, the statistical department of one of the most important oil companies forecast a draft on stocks, from an excess of demand over supply, of about 80,000,000 bbl. Instead of decreasing our stocks, they were increased by about 33,000,000 barrels.

Jan 3, 1925

By Albert R. Ledoux

Discussion of the Paper of Albert R. Ledoux, read at the Atlantic City Meeting, February, 1904. ARTHUR JARMAN, Sydney, New South Wales, Australia' (communication to the Secretary*): Some remarks upon. Dr. Ledoux's interesting paper from one who has not visited America may, I hope, be of interest to members. It appears to me that there is considerable difference between the training of the American and of the British mining engineer. Not that the subjects are different, but rather in the way in which they are handled, the illustrations being, as far as possible, mining in character. Colloquial instruction is unknown in English curricula, but could be introduced with advantage. Students here assure me that an hour of conversation is of tar more use to them than an hour of the best lecturing. In England a school-year of 6 or 7 months would be considered very short indeed; but Americans do not consider it so, for the reason that the rest of the year is mostly spent in acquiring practical acquaintance with their subjects in works or in the field, and the shorter courses, when coupled with this large amount of outside expe¬rience, produce an essentially practical-minded engineer, who is also more of a business man; whereas the English system, though excellent from a scholastic point of view, produces the theoretical rather than the practical man. British schools are waking up, however, and the practical aspect of the engineer's training is receiving greater consideration. Once launched upon his career, the American engineer is immediately called upon to exercise his self-reliance and ingenuity, if he is to retain the confidence of his employers; but what can we say of English directors? In how many cases is the engineer allowed to guide the destinies of his company? Witness several recent cases of gross waste of money upon unsuitable plants, and the perpetuation of prehistoric methods of

Mar 1, 1905

By L. D. HUNTOON

MY first article on Canadian Gold, published in the Canadian Mining Magazine in 1911 expressed the view that the Hollinger mine would repay all the money invested and that other mines would be developed in this area. Many published forecasts have since been made. Quoting from the Northern Miner of Oct. 29, 1931: "It will be noted in studying the chart prepared by this engineer that his forecast for 1931 at $50,000,000 was too modest, as the output for this country this year will be closer to $54,000,000."

Jan 1, 1932

By AIME AIME

THE MILLING PROGRAM on Monday required a morning and afternoon session with a special luncheon of the Milling Committee in the Engineers Club at noon. Grinding and flotation were the main subjects of the papers which drew an attendance of fifty or more at each session. Under the direction of Chairman Arthur F. Taggart in the forenoon, all papers on flotation and general milling were considered, leaving the, after- noon free for crushing and grinding, with Dr. Galen H. Clevenger in the chair. The high spot was the first public presentation of the idea of size reduction of minerals by explosive shattering.

Jan 1, 1932

By HARRY H. SMITH

IT IS my understanding that, speaking broadly, the function of the engineering profession is to find how to do the thing required better for less money. Mechanical engineers, mining engineers, and the various other kinds of engineers are engaged in discovering and effectuating new and improved methods .of producing better goods and services at less cost to industry. The savings and advantages, thus, accruing ace reflected from time' to time in increased productive powers of industry and lower costs to the public which consumes the goods and services.

Jan 1, 1931

By T. A. Rickard

Technology has no recognized rank in what is called polite literature; the subject-matter of engineering is not supposed to lend itself to artistic treatment; we are the hewers of wood and drawers of water to the high-priests of learning that live on the cold summit above our humbler dwellings. Therefore the hierophants smile at the notion of 'style1-" that curiously personal thingy-in technical writing. The "great art" of Pater, the "inevitable phrase" of Raleigh, the "note of distinction" that Arnold demanded are said to be beyond the scope, as they are supposed to be beside the need, of a writer on geology or engineering. This is a narrow view. Science, no less than belles lettres, calls for the best exercise of the human intelligence; the art of writing should be employed as skilfully and as earnestly in a description of the structure of the Sierra Nevada, or of the construction of a tunnel through the range, as in a rhapsody welcoming the rosy fingers of the dawn. The idea still lingers that fine writing does not befit technology, even though the masters of the Victorian period-Huxley, Tyndall, Ruskin-proved that science is worthy to be arrayed in the best robes that the looms of thought can weave. At the beginning of these lectures I quoted Barrie's remark touching the inability of the scientific man to express himself. That imputation has been passed to the technologist, whose utilitarian pursuits are supposed to make him too clumsy for the refinements of human speech. We may not have acquired the self-consciousness of those writers on Art whose "power of expression is so cultivated that their sensual caterwauling may be almost mistaken for the music of the spheres"; nor can we imitate the politicians, who have the ability to speak far beyond anything that they may have to say; but we too have a litera-

Jan 1, 1931

By H. Foster Bain

FROM time to time geologists and mining engineers, impressed by the heavy demands made on our mineral reserves' by modern industry, and particularly by the steadily mounting rate of production necessary to meet that demand, have issued warnings as to the danger of exhaustion. There can be no dispute as to the fact that mineral deposits are exhaustible. New mineral, is not created to replace that taken from the earth and when a crop of mineral is once harvested another cannot be grown in the same area. The evidence of exhaustion 'of particular oreshoots, deposits, or even of whole districts is familiar to all who have mined. If one were to judge solely from the abandoned mills and prospect holes he would rightly conclude that mining is but a short-lived industry. If one were, furthermore, to assemble the data as to known reserves of almost any of the commonly used minerals, and divide them by the annual tonnage mined, he would come to the same conclusion. If, again, one were to consider the most carefully made estimates of competent men seeking to measure the earth's reserves of minerals and plot against them a projection of the curve of past consumption, he would be justified in viewing the situation with alarm.

Jan 1, 1930

By AIME AIME

THE non-ferrous 'metals industry of the Soviet Union found itself in a very low position at the beginning of the reconstruction period in 1922, due to the absence of modern smelters and the run-down condition of the existing ones. Up to. 1924 there was no great demand for newly smelted non-ferrous metals due to the considerable stocks' of copper, zinc, lead, tin and aluminum in the courtry and also to the undeveloped condition of Soviet industries. However, in 1925 it became necessary to obtain new stocks of non-ferrous metals and in that year 12,000 tons of zinc, 14,000 tons of lead and 2,000 tons of tin and aluminum were imported into the U. S. S. R.

Jan 1, 1929

By Edward W. Parker

This plant was built in 1907 at the Bankhead mines to manufacture briquettes by the Zwoyer process under license from the Zwoyer Fuel Go., of New York, N. Y. The building was constructed to contain two units, each of a capacity of 10 tons per hr.; one unit was installed at the time the building was constructed, and the second unit is now being built. The coal used is an anthracite, which is more friable than that of Pennsylvania, and, as a consequepce, a larger percentage of dust or waste is produced, which was formerly thrown upon the slack-pile as waste, but is now passed to the " dust-bin " in the breaker, from which it is conveyed to the briquette-plant. An average analysis of the coal, published by Lewis Stockett and 13. R. Warden,' is as follows: Per Cent. Moisture,.........0.50 Volatile,..8.00 Fixed carbon,... 83..50 Ash,.......8.00 Total,.100.00 Sulphur,.........0.40 per cent. Specific gravity,...... 1.40 Color of ash,.white Heat value,.......14,000 B.t.u. The plant is run under two 12-hr. shifts, the force consisting of 1 superintendent for both shifts, 1 engineer for each shift, 1 briquetter for each shift, 1 helper for each shift, 1 laborer cleaning up for each shift. In the pitch-melting house, 2 men are on duty for one shift. The steam for the engine is furnished from a central boiler-plant, which also supplies steam for the breaker, the electric light and power-plant, machinery-shop, and boiler-shop. During March, April, May, and half of June, in 1907, the

Jan 1, 1909

By William J. Coulter

WITHIN the past thirty years the United States has been involved in two tragic, vicious, and costly world wars. To make the world safe for democracy was the reason given for our participation, but the confusion and misunderstanding that prevails all over the world today suggests that war is not the proper approach to the attainment of that utopia. These conflicts were conceived and prosecuted by nations far advanced in civilization and culture. Their best manhood was sacrificed, a staggering tax burden was saddled on their peoples, huge financial losses were incurred, destruction of property was appalling, and cultural and peaceful scientific advancement received a setback that may require centuries to retrieve. Therefore, some basis is established for the conclusion that progress in the past fifty years has been most outstanding in the development of instruments used for death and destruction, and that progress in this direction between the two World Wars would indicate that the next war will go far toward total destruction of world civilization.

Jan 1, 1946

By R. F. Hehemann, D. J. Cometto, G. L. Houze

The w transformation in the Zr-Nb system was studied using X-ray diffraction, dilatometric, re-sistornetric, hardness, and metallographic techniques. w forms in a diffusionless, completely reaersible manner on quenching and in a diffusion-controlled manner- on aging. The temperature at which w begins to form on quenching was determined as a Junction of composition and was found to decrease with increasing solute content. w formed bv aging establishes a metastable equilibrium with an enriched ß phase. The ß/w + ß transus has been determined for this metastable equilibrium and employed to rationalize retrogression and reversion phenomena observed in these alloys. The decomposition mechanism is discussed in terms of a gradual or continuous transformation from ß to the w state. BETA- stabilizing alloying elements lower the MS temperature of the martensitic bcc (ß) to hcp (a') transformation in zirconium and titanium alloys. In certain titanium alloys, a lower symmetry modification of the martensitic structure, termed (a"), also has been reported.1,2 These martensitic transformations are suppressed when the amount of the ß-stabilizing element exceeds a critical level. However, the high-temperature ß phase cannot be quenched to room temperature without change. At alloy contents just above the critical level, |ß trans-forms to the w phase when cooled rapidly.3-6 The amount of w in quenched alloys is reduced by increasing alloy content, and this phase virtually disappears above a critical composition.5 In addition to the transformation during cooling, w also can be formed by aging ß at temperatures below approximately 500°C, and significant alloy enrichment of retained 13 accompanies the isothermal transformation.1-8 The structure of LC is closely related to that of the ß from which it forms.9-15 The bcc (ß) lattice can be generated using a hexagonal cell with three atoms located at (000) and ±(2/3, 1/3, 1/3). This cell has an axial ratio of 0.612 and is oriented with respect to the cubic cell such that (0001)H (111)C and [1120]H [101]C. Consequently, there are four possible orientations of the hexagonal cell, associated with the four (111) planes of the bee lattice. Formally w can be obtained from 0 by allowing the two atoms at the ±(2/3, 1/3, 1/3) positions to approach the coordinates ±(2/3, 1/3, 1/2) and there are four equally probable orientations of w for each 0 grain. In titanium alloys w retains the cubic axial ratio of 0.612" and hence also can be indexed as triply cubic, but this is not the case for aged Zr-Nb alloys where w is clearly hexagonal with an axial ratio of 0.622." The lattice parameters and atomic positions of w depend on thermal history and alloy content. The atomic positions (000), ±(2/3, 1/3, 1/2) provide reasonable agreement between calculated and observed diffracted intensities for w in the fully aged condition.10,14 In the quenched condition, on the other hand, the atoms appear to be displaced from the central plane12,13,15 and assume positions ±(2/3, 1/3, Z = 0.42-0.48) rather than ±(2/3, 1/3, 1/2). This results in a structure with trigonal rather than hexagonal symmetry. The readily detectable parameter and axial-ratio changes of w in Zr-Nb alloys make this system especially attractive for studying the structural changes that occur in the formation and aging of w. Particular attention in this investigation has been directed to the relationship between the structure of w in the quenched and aged conditions, and to certain aspects of the reaction kinetics. MATERIALS AND PROCEDURE Zr-5, 12, 17.5, and 25 pct Nb alloys were prepared by a double arc-melting practice, encased in stainless-steel cans and hot-rolled to 1/8-in.-thick sheet.* Charged weights have been employed for the niobium contents and interstitial analyses are reported in Table I. Dilatometric, X-ray diffraction (filtered CuK, and MoK, radiation), metallographic, and hardness techniques have been employed to follow the transformations during isothermal and quench-aging heat treatments. In quenched specimens, the electrical resistivity also was studied. Betatizing was conducted for 1 hr at 900°C. With the exception of the isothermal dilatometric studies, samples were

Jan 1, 1965

By K. C. Gilbart, E. Stansfield

This test was described in a privately circulated First Progress Report on Slacking Characteristics of Coal, by A. C. Fieldner and W. A. Selvig, May 1, 1928. The test was described in detail in U. S. Bureau of Mines Report of Investigation 3055, in November, 1930,1 The test, in brief, is conducted as follows: A sample of freshly mined coal consisting of 18 to 25 pieces approximating 1 1/4 cubes, and weighing 500 to 600 grams, is taken for the test. The sample is subjected to a "blank sieving" of carefully regulated degree, on an 8-in. circular sieve with 0.263-in. square openings, and the undersize and oversize weighed. The oversize is placed on a sheet-iron pan and dried for about 24 hr. in an A.S.T.M. air-drying oven maintained at 30" to 35" C. through which a current of warm air is drawn. The sample is then cooled to room temperature and immersed for one hour in water at the same temperature. The water is then drained off, the sample dried for 24 hr. as before, cooled, sieved as before, and the oversize and undersize weighed. The percentage weight of the undersize is calculated and reported as the first cycle loss. This loss, corrected by subtracting the percentage loss in the blank sieving, is termed the slacking index. The sample may be subjected to further cycles of wetting, draining, air-drying, sieving and weighing. In a letter (August, 1932) W. A. Selvig approved making the blank sieving on a duplicate sample, rather than on the sample used for the test, where sufficient coal was available. This method is now employed in these laboratories. The accelerated weathering test has been employed in the laboratories of the Research Council of Alberta, at Edmonton, since 1928, but not found entirely satisfactory as repeat determinations with samples taken from the same or adjacent mines frequently showed serious differences. Differences must be expected as the coal may vary in the seam, and the selection of a typical set of lumps approximating 1 1/4-in. cubes

Jan 1, 1934

By H. A. McKinstry, F. F. Lange

A vector analysis of orientating single crystals using the Laue back-reflection X-ray technique is given. Briefly, the analysis involves using a few data taken from a Laue photography and defining the crystal co- ordinate axes in a reference coordinate system. After a few matrix multiplications, the proper goniometer angles can then be determined to orient the crystal coincident with the reference frame. This analysis is easily programed for a digital computer to provide a fast, precise, and efficient method of orienting many crystals which are identical. The general procedure is as follows. The crystal is mounted on a goniometer. Laue photographs are taken until an array of diffraction spots is observed that includes a Laue spot that represents a rotational axis of symmetry. The rotation angles of goniometer are recorded. These angles are defined as positive for a counterclockwise rotation. When the axis of symmetry is located on the Laue photograph, the crystal coordinate axes can be defined in the reference coordinate system* as follows. Two Laue spots are chosen, one of which corresponds to the rotational axis of symmetry and the other to a set of planes whose zone axis is a known crystallographic direction and normal to the rotation axis of symmetry. The Laue spots are used to determine these two crystal directions in the reference coordinate frame. This is done by placing the Laue photograph on a sheet of polar coordinate graph paper and determining the polar coordinates (r, o) of these two diffraction spots in the reference coordinate frame. Their third coordinate is the distance between the crystal and the film (-D). The coordinates Xni of the two crystal directions Nn, (n = 1, 2) in the reference frame are then calculated by the following equations: Xn1 = -D X2n = Ancos on X3n = A, sin on where -tan- 1 rn/D An =Dtan(tan-1rp/D/2) By taking the proper cross products of these two directions (normalized to unit vectors), the crystal coordinate axes 3 (i = 1, 2, 3) can be determined in the reference frame. This is illustrated in Fig. 1. The next step is to determine the relation between

Jan 1, 1969

By J. G. Koenigsberger

The electrical specific resistance of rocks in the field is measured by sending a current through a medium of great volume, compared to the electrodes, whose resistivity should be measured. The whole resistance can be determined by the Wheatstone bridge and the specific resistance calculated by a well-known formula. The resistivity of some rocks in place in Germany and in Switzerland is given; first, of a rock near the surface, and especially near electrodes. Practical applications are made in the determination: (1) of the continuity of a conducting orebody; (2) of the surface ares of an orebody; (3) in the detection of a water-bearing fault in a salt mine. Preliminary 'observations are described: (1) on the influence of the depth of ground-water table; (2) on the detection of gas under high pressure in coal seams. The observations in this paper of the electrical resistivity of rocks and soil in place are along the lines of the very interesting method and results of the Messrs. Gish, Rooney, Hotchkiss and Fisher. 1,2 All the work described has been done since 1920. Method Used The very simple method consists in the application to the rock of two plane circular electrodes of iron or brass of a suitable diameter, with the aid of a contact substance, and in measuring the resistivity in a Wheatstone bridge with alternating current of 100 to 400 Hertz frequency per sec.). The general formula is known to be R= R0 +d/4(1/a+1/b-1.7/l+0.8(a+b)/l2) (1)

Jan 1, 1929

By F. H. Callaway, W. O. Keller

The various theories as to the well spacing-recovery relationship are reviewed in considerable detail and these theories analyzed in terms of their consistency with modern reservoir engineering concepts. It is concluded that the well spacing problem must be analyzed in terms of recovery efficiency and that a positive answer to the relation between well density and recovery efficiency is not available from direct comparisons of the production histories of wells and fields. The results of an engineering analysis designed to permit approximate calculation of recovery efficiencies as a function of well spacing in a depletion type reservoir from basic reservoir data is presented. Results of this type analysis indicate that the effect of well spacing on recovery efficiency in depletion type reservoirs can be expected to be very small. Limitations of this approach are pointed out, particularly with respect to its application in lenticular reservoirs. Testing techniques are outlined which should indicate whether or not a reservoir is continuous between wells and whether or not satisfactory drainage is being obtained with present spacings. A mass of data of this type indicates continuity to exist in most fields. INTRODUCTION The purpose of this paper is to review critically the engineering aspects of the well spacing problem, both from the standpoint of certain concepts and from the standpoint of reservoir mechanics. The well spacing problem is primarily an economic problem in which the optimum well density for a particular field is that density which will yield the greatest oil recovery consistent with justifiable development costs. The well spacing answer in terms of economic conditions, however, is extremely sensitive to the variation in recovery efficiency with well density. The variation in recovery efficiency with 'References given at end of paper. Manuscript received at the office of the Petroleum Branch October 2, 1949. Paper presented at the Petroleum Branch Meeting in San Antonio. Texas, October 5-7. 1949. well density is properly an engineering problem. Different opinions as to the correct answer to this engineering problem is the basis for most of the wide difference in opinion among various members of the industry as to optimum well spacing. This paper will be confined to the engineering problem of the relation between well density and ultimate oil recovery; economic considerations necessary for the evaluation of optimum well density for any particular field will not be discussed. The paper can be logically divided into two parts. The first part deals with a critical examination of the background and logic of the Cutler Rule and of similar studies by other authors and of related well spacing concepts. It is indicated that the variations in recoveries with well density* observed by Cutler and. others can be logically attributed to regional migration. Theoretical justification of the Cutler type relation wherein observed variations in recovery with well density in the same field is attributed to variations in recovery effiiency, in terms of energy relations, is refuted. The second part consists of a review of concepts of reservoir mechanics with regard to the well density-recovery relation. It is indicated that little variation of recovery efficiency with well density can be expected in a depletion type reservoir, unless lenticular conditions prevent communication between wells. The significance of field test data with regard to the existence or non-existence of lenticular conditions is pointed out. THE CUTLER RULE The first published article concerning the engineering aspects of the well spacing problem to receive wide attention was the work of W. W. Cutler' of the U. S. Bureau of Mines, published in 1924. In a study of decline curves from a large *The expression "well density" as utilized herein refers to the number of acres attributed to each well in a uniform well pattern, and is expressed in acres per well. The term "well spacing" Is utilized to denote the average distance between adjacent wells in a uniform well pattern. †Although the Cutler rule is treated critically in this discussion the authors intend no personal criticism of W. W. Cutler or of his hark The currently accepted concepts of reservoir mechanics were no": existent at the time of Cutler's work, as were even the moat basic tools (such as the bottom hole pressure bomb) for observing reservoir behavior.

Jan 1, 1950