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By C. M. Wayman, R. Bullough

The selection rules fir twinning in fcc, bcc, and hcp lattices as established in Part I are used to predict the positions, relative to the matrix (untwinned) reciprocal lattice, of reflections due to double diffraction from the twins. These doubly diffracted reciprocal lattice points, which often coincide with ordinary matrix reciprocal lattice points, are deduced from kinematical considerations. 1. INTRODUCTION. A Bragg diffracted beam under certain conditions may be rediffracted to produce a third beam i .e., the incident beam, the first diffracted beam, and the rediffracted beam). In such a case an initial incident beam is diffracted by a set of planes; the diffracted beam may then be rediffracted by a second set of crystallographically different planes. The initially diffracted beam acts as an incident beam for the second set of planes, thus resulting in a twice-diffracted beam. This twice-diffracted beam may be regarded as a singly diffracted beam from a set of lattice planes whose structure factor is zero. In order to find the reciprocal lattice point corresponding to the doubly diffracted beam, it is customary1,2 to combine vectorially the component reciprocal lattice vectors which head to the extra reflections. For example, hcp metals may exhibit the forbidden (0001) reflections.* As Fig. 1 shows, the (0001) reciprocal lattice point results from: (1010) + (1011) = (0001) Similarly, combination of the beams (1011) and (1010) gives rise to: (1011)- (1010) = (0001) As Pashley and stowell2 have pointed out, even if in fact the double diffraction points lie on the Ewald sphere, they may not actually represent observed doubly diffracted beams because the initially diffracted primary beam, i.e., the source, must also correspond to a reciprocal lattice point which lies on the sphere of reflection; however, the reciprocal lattice point corresponding to the planes causing the rediffraction need not lie on the sphere. A little consideration of the Ewald construction in Fig. 2 makes this argument clear. In Fig. 2 the incident beam is represented by the wave vector ko. This beam is initially diffracted by the lattice planes (hkl) which are represented by the reciprocal lattice vector r(hk1) The reciprocal lattice point (hkl) of course lies on the Ewald sphere in order that the Bragg condition be satisfied. The initially diffracted beam is represented by the wave vector kl. If now kl is rediffracted by a second set of planes (h'k'l') resulting in k2 the lattice point (h"k"l") must lie on the Ewald sphere if the double diffracted beam k2 is to be observed. It is clear that (h"k"l") is the vector sum of (hkl) and (h'k'l'), and that (h'k'l') need not in fact lie on the Ewald sphere. In the usual1,2 analysis the origin (000) of the reciprocal lattice is shifted to the point (hkl). However the translation (000)— (hkl) automatically shifts the point (h'k'l') to the Ewald sphere, i.e., (h'k'l')— (h"k"1"). It is to be seen that (hkl), the source reflection, must lie on the Ewald sphere; if it does not the translation (000) — (hkl) places the "new" origin off the sphere, not satisfying the Ewald construction and hence the Bragg condition. The point (h"k"1") of course must lie on the sphere if it corresponds to an observed doubly diffracted beam. It is to be noted that crystals having the hcp structure, as just discussed, are intrinsically capable (i.e., without lattice defects such as twins) of double diffraction, as contrasted to fcc and bcc crystals which are extrinsically capable (requiring lattice defects or reoriented lattice regions). The "allowed" bcc reciprocal lattice points (which comprise an fcc lattice) are (110), (2001, (211), (220), (310), (2221, (321), (4001, and so forth. The combination

Jan 1, 1967

By E. F. Johnson, F. H. Brinkman, H. J. Welge, A. L. Hicks

A method is presented for predicting the character of gas or water displacement in a radial system, which can be either horizontal or inclined. The latter case would comprise cone-shaped or dome-shaped symmetry. The method conriders the one dimension of radial distance, taken parallel to the bedding planes. Approximate allowance can be made for segregation of the two fluids perpendicular to the bedding planes. A complete saturation history can be obtained in about a day's time with the use of a desk calculator. Results of an example calculation agree well with the performance of simulated gas drive in a large model representing a section of a cone. This pie-shaped, sand-packed model was 8-ft long and 4-in. thick. The method of solution is useful in handling other partial differential equations of first order and first degree. INTRODUCTION A new analytical method has been developed for predicting the performance of gas or water drive in a reservoir having radial or cone-shaped symmetry (see Fig. 1). In addition, this new development offers a general method of handling partial differential equations of first order and first degree. This work extends those methods developed previously'- "or predicting the displacement of oil by gas or water in linear systems. The method of calculating oil recovery in a radial system involves two major parts. The first part is a calculation of the distribution of saturations at various times of depletion. The second part is the calculation of oil recovery and producing gas-oil or water-oil ratios through volumetric balance on the saturation distributions obtained in the first part. This second part differs only slightly in principle from similar calculations made with linear systems, for instance. The basic assumptions used in the calculations are as follows. 1. One-dimensional radial flow. An approach is explained later for approximating a second vertical dimension. (With- drawals of oil, and of the driving fluid after breakthrough, are assumed uniform around the periphery of the dome.) 2. Constant-volume fluid flow. Thus, in a gas drive there is no change in gas solubility, or in oil or gas volume due to viscous and gravity pressure drops. 3. Capillary forces are negligible. 4. Constant rate of injection. A program has been written for carrying out the calculations needed on a digital computer. However, a prediction can also be arrived at using a desk calculator; this latter method of work requires about a day's time for each prediction made. CALCULATION OF SATURATION DISTRIBUTION For definiteness, we describe the development of our method for the case of gas drive from the crest of the structure. The reader will note, however, that the method is just as applicable to an advancing radial water drive. The equation describing gas flow over an infinitesimal

By Fred C. Bond

Many grindability tests have been made in the Allis-Chalmers laboratory since the tabulated results were last published.' The lists of standard ball-mill and standard rod-mill grindability tests are brought up to date in this paper, and considerable new material is added. This includes a tabulation of open-circuit grinding tests, with impact and compression-crushing tests. The standard ball-mill grindability tests (Table I) were made in a standard laboratory ball mill, 12 by 12 in. inside, running at 70 rpm, with a charge of 285 iron balls ranging from 1½ to 3/4 in. in diameter and weighing 20,125 grams. Seven hundred cubic centimeters of minus 6-mesh stage-crushed dry feed was used, and the circulating load was maintained constant at 250 pct by adjusting the number of mill revolutions for each grinding period. Tests were made at all mesh sizes from 28 to 200, and the grindability is the number of net grams of screen undersize produced per revolution. The table includes 479 tests. It has been calculated that the ball mill does 52.3 joules of useful work on the ore per revolution2 with 93 joules input to the mill. The standard rod-mill grindability tests (Table 2) were made in a laboratory tilting rod mill, 12 in. in diameter by 24 in. long inside, with a wave-type lining, running at 46 rpm. The grinding charge consisted of six I1/4-in. diameter and two 13/4-in. diameter steel rods, all 21 in. long and weighing 33,380 grams. The mill was rotated level for eight revolutions, then tilted up 5' for one revolution, down 5° for one revolution, and returned to level for eight revolutions. It was discharged by tilting downward at 45° for 30 revolutions. Feed consisted of 1250 cc of minus in. stone and the circulating load was maintained constant at 100 pct by adjusting the number of mill revolutions for each grinding period. Tests were made at all mesh sizes from 3 to 65, and the rod-mill grindability is the number of net grams of screen undersize produced per revolution. The table includes 105 tests. The impact and compression-crushing tests (Table 3) are given in a table that is an extension of a previous publication8 in which the method of testing was described in detail. Two equal hammers weighing about 30 lb each were arranged to strike simultaneous blows on opposite sides of the test specimen. Broken pieces of rock passing a 3-in. square and retained on a 2-in. square were set up with the smallest dimension between the hammers, and this distance was measured. The height of the hammers was increased slightly before each blow until the specimen broke, and the foot-pounds per inch of thickness was calculated. Ten pieces

Jan 1, 1949

By H. W. Hitzrot

THE new 4800-ton fine-grinding plant at the Hollinger Consolidated Gold Mines property at Timmins, in the Porcupine district of northern Ontario, went into operation in November 1937, and represents the culmination of an experimental program. The plant is a moderately low rectangular building of hollow tile on a steel frame, large enough to house four 7 by 15-ft. ball mills, with a 12 by 27-ft. classifier beside each mill. At one end is space for the addi-tion of another mill and classifier or a mill and classifier for the regrinding of table concentrates. This regrinding is now done in the old grinding department of the main mill building. Also within the new building are the four 6-in. sand pumps for lifting the product from the low-dis-charge ball mills up to the classifier feed launders and the containers and appurtenances of a complete dust-collecting system. Together with the usual overhead crane, these constitute the major units of equipment within the new plant. The location is at the lower end of the main mill buildings toward the old tailings pond, now so neatly leveled off and sodded to rival the very best of our own W.P.A. projects. Close by the new grinding plant is a large dome-shaped structure-the new fine-ore bin designed and built by Mr. Longmore and the Hollinger milling and engineering staffs. There are four separate automatically loaded inclined belt conveyors leading up from the bottom of the bin to the grinding plant. Each belt is equipped with a recording weightometer, in the grinding building. The whole structure and the machinery within it give the impression of permanence and a carefully integrated design with close attention to details, giving the operators every advantage for consistently good work.

Jan 1, 1939

By William Campbell

In the olden days the making of alloys was an art, and the secrete of the craft were jealously guarded. To-day it has become a science, though the old ideas in regard to the secrets and formulæ are dying hard. Modern progress may be attributed to scientific research and testing of materials, and the substitution of chemical analytical control for " cook-book " methods. We know to-day a great deal about the constitution of alloys, the reasons of the change in structure and physical properties by heat and mechanical treatment; and this new knowledge is due for the most part to the physical chemist and metallographist, who have shown us that alloys are simply solutions, and as such obey definite laws. The application of the theories of solutions and of the phase rule tells us what ought to happen when our alloys are in a state of equilibrium. The working-out of the temperature-composition diagram (thermal diagram) for numerous alloys has thrown a light on the structure and constitution which has dispelled most of the darkness in which we labored before the advent of metallography. The work began with the determination of the freezing-point curves, and here the research of Le Chatelier,' Gautier,2 Roberts-Austen,3 and the other pioneers broke the ground. Next the physical chemists, Tammann,4 Rooseboom,5 Bancroft,6 and their colleagues, showed us the complete thermal diagram and its meaning. Then the researches of Heycock and Neville7 on the Cu-Sn series and of Shepherd 8 on the

Jan 1, 1913

By R. C. Allen

ABOUT four years ago the writer proposed a revision of the correlation of the Huronian formations in Michigan, and noted the bearing of the question on the correlations of the Huronian rocks in Wisconsin and Minnesota.1 Dr. C. K. Leith opposed this revision and argued for the retention of the correlations of the United States Geological Survey, published in 1911,2 for which he and Dr. Van Hise were mainly responsible. As late as June, 1917, Harder and Johnson, following Leith, thought it "premature to change radically a correlation based on years of careful field work."3 The work of Wolff on the Mesabi and Cuyuna Ranges, of Hotchkiss on the Gogebic Range (unpublished), and of the writer and assistants on the Michigan ranges, together with data developed by exploratory and mining operations, has introduced so many pew facts not recognized in the scheme of the U. S. Geological Survey that the correlations of 1911 must be considered, in some important respects, obsolete. Indeed new data are accumulating so rapidly that any classification, which for the moment may seem best to explain the facts, is almost immediately modified or refined by further observations. The problem of Huronian correlations is difficult, but interesting and important. With the aid of fossils, stratigraphers of the post-Algonkian formations have been able to show that slight disconformities may separate strata of vastly different ages, and that within physically conformable strata may be concealed a hiatus of great magnitude. In the non-fossiliferous Huronian group, minor physical breaks in the strata are

Jan 9, 1919

By O. B. Hopkins

The total production of oil in Peru in 1940 was 12,127,135 bbl., or about 10 per cent less than in 1939. Most of the reduction can be attributed to the fact that the export market under war conditions is much restricted and naturally is more than ordinarily competitive. Development and Exploration in Older Areas As evidenced by Table I, almost all production continued to come from the three established fields in coastal northwestern Peru. Zorritos Field.—Exploration in this small field, which was purchased by the Peruvian Government in 1939, continued with that in near-by areas in the adjoining National Reserve. Several wells were drilled, regarding which details are not as yet available. It is estimated that the production rate for a total of some 45 old and 15 new wells approximated zoo bbl. per day, or about 3 bbl. per well per day. Lobitos Fields.—The Lobitos area produced 2,435,504 bbl.; about 10 per cent less than the amount for 1939. La Brea-Pari9zas.—This property of International Petroleum Co. continued to account for nearly 80 per cent of Peru's production. During the year, drilling was stepped up to 139 wells, as compared with 73 wells completed in the previous year; 123 were producers and aggregated a total of 287,867 ft. Of this total, more than 85 per cent was drilled by rotary tools, which are steadily displacing other equipment. Although most of these wells were drilled in the proved or semiproved areas, eight

Jan 1, 1941

By O. B. Hopkins

The total production of oil in Peru in 1940 was 12,127,135 bbl., or about 10 per cent less than in 1939. Most of the reduction can be attributed to the fact that the export market under war conditions is much restricted and naturally is more than ordinarily competitive. Development and Exploration in Older Areas As evidenced by Table I, almost all production continued to come from the three established fields in coastal northwestern Peru. Zorritos Field.—Exploration in this small field, which was purchased by the Peruvian Government in 1939, continued with that in near-by areas in the adjoining National Reserve. Several wells were drilled, regarding which details are not as yet available. It is estimated that the production rate for a total of some 45 old and 15 new wells approximated zoo bbl. per day, or about 3 bbl. per well per day. Lobitos Fields.—The Lobitos area produced 2,435,504 bbl.; about 10 per cent less than the amount for 1939. La Brea-Pari9zas.—This property of International Petroleum Co. continued to account for nearly 80 per cent of Peru's production. During the year, drilling was stepped up to 139 wells, as compared with 73 wells completed in the previous year; 123 were producers and aggregated a total of 287,867 ft. Of this total, more than 85 per cent was drilled by rotary tools, which are steadily displacing other equipment. Although most of these wells were drilled in the proved or semiproved areas, eight

Jan 1, 1941

By W. C. McClain

In the design of underground excavations, rock mechanics considerations are nearly always based on an elastic behavior of rock. Most rocks do exhibit a certain amount of elasticity, and the application of principles and concepts of elasticity to rock mechanics problems has been largely responsible for progress in the field over the past 10 or 15 years. NO doubt the theory of elasticity will remain the most useful analytical tool available for both the design of underground openings and the interpretation of phenomenological data. Dr. Cook's analysis of rock behavior based on energy considerations represents a significant new approach to mining rock mechanics problems. Although the foundations of this analysis are somewhat broader and more general than elastic analysis, the development and applications are grounded almost entirely in the theory of elasticity. It has long been known1,2 that all rocks, even granites and dense limestones, exhibit nonlinear time-dependent strain properties to a greater or lesser degree. Creep strain (that is, deformation under constant stress) in salt, potash, and trona can be several orders of magnitude greater than instantaneous elastic strain. Design of underground workings in these materials must incorporate provisions for these strains and must therefore go considerably beyond elastic analysis. Some of the principles of underground design in highly plastic materials will be discussed in this paper. Since all rocks, especially when highly fractured, exhibit a certain amount of creep-type strain, these concepts should be at least recognized in any rock mechanics problem. The discussion will be illustrated largely, but not entirely, by examples drawn from

Jan 1, 1967

Crushed limestone is now being "de-dusted" at the Warner Co. plant in Bellefonte, Pa., by a new high-efficiency classifier utilizing aerodynamic principles not previously employed in classifiers. Crushed limestone for certain glass industry requirements must not have more than 10 pct fines in the overall aggregate, and it is the function of the new-type classifier to separate these fines from the coarse material. During the development of this classifier by the Buell Engineering Co. of New York, it was found to have possible applications for separating pulverized coal, sintered metals, ores, mineral flours, and fillers, among other items. Limestone from Warner's deep mine is initially crushed and particles larger than 3/8-in. mesh are burned in kilns to provide calcium oxide for the chemical industry. The 3/8-in. screenings are dried and crushed to -16 mesh for use by the glass industry. For those applications requiring a minimum of fines, no more than 10 pct -100 mesh material is allowable in the end product. Hence the need for high-efficiency separation.

Jan 11, 1960

By Ralph Arnold

IN OPENING the symposium under the auspices of the Petroleum and Gas Committee of the American Institute of Mining and Metallurgical Engineers, I wish to call to your attention the following, among other subjects, which it is hoped may receive proper attention: 1. The recording of as accurate an appraisal of the oil possibilities of the various countries as is possible, with information as to the immediate availability of their supply. 2. The development of further support for the move-ment to bring about active cooperation among Ameri-can oil companies in their foreign exploration and development work. 3. The furtherance of the efforts of the industry in securing governmental assistance in foreign oil develop-ment: (a) along the lines of a modification of our domestic oil policy, so that we can go to foreign coun-tries and consistently ask fair treatment as to royalties and bonuses; (b) by a closer cooperation between the State and Commerce Departments and the oil industry. 4. The calling of attention to the unjustifiably drastic action of the price-fixing group of the oil industry during the last year or so, with the hope that it will use gentler methods in the future. None of these subjects are new, and some of them have been discussed before various organizations for years. Our justification for again bringing them forward is the hope that by everlastingly harping on them the industry, the Government, and the people who shape the destinies of this country may some time, some how, realize their importance and take effective constructive action.

Jan 6, 1922

By I. Iwasaki

In the flotation of iron ores and nonmetallic ores desliming is the key to a successful operation; the technology of flotation of well-deslimed ores has become fairly well established. When finely disseminated ores are ground to liberation, however, conventional desliming of the fully dispersed pulp results in an excessive loss of valuable constituents. Selective flocculation of iron oxides followed by removal of dispersed siliceous slimes is a new development and is one of the most promising approaches to the treatment of finely disseminated, oxidized iron ores, available in vast quantities both here and abroad (1,2,3). To apply selective flocculation to the variety of refractory iron ores or to cope with the fluctuations in an individual ore and the make-up water, the factors governing this technique must be clearly formulated. For the removal of siliceous and clayey slimes from oxidized iron ores by selective flocculation, the optimum conditions are extremely sensitive to the mineralogical characteristics of the ore, the type and the amount of soluble salts in pulp solutions, and the mesh-of-grind. Certain starches appear to function better than others (4, 5). Selection of the proper reagents and their judicious use is important not only for their efficient utilization but also for minimizing the adverse effects they might exert on the flocculation and flotation steps, and the pollution the effluents might cause when discharged, either intentionally or accidentally, into lakes and streams. In the present article some of the major factors that influence the selective flocculation of iron ores are summarized.

Jan 1, 1979

By R. W. Raymond

The death of Professor Blake removes the oldest of American economic geologists and mining engineers, and deprives this Institute of one of its earliest and most illustrious members. To many of us it brings a personal loss also, the loss of a friend. William Phipps Blake was born June 21, 1826, in New York City. His father, Elihu Blake, was a surgeon-dentist of eminence, a direct descendant of William -Blake, who settled in the Massachusetts Bay Colony about 1630. He was prs pared for college at private schools in New York, and entered the Sheffield School of Yale, where he was graduated as Ph.B. in the chemical course, class of 1852, the first graduating-class of the institution. In the same year he became chemist and mineralogist of the New Jersey Zinc Co., and chemist of chemical works at Baltimore, Md. In 1853, he started the Department of Mineralogy of the World's Fair at New York City. In 1854, 1855 and 1856, he was mineralogist and geologist of the United States Pacific Railroad Surveys of Willianlson, Pope, and Whipple, and for the War Department at

Jan 1, 1911

By G. C. Broadhead

THE lead district of Southeast Missouri covers an area of over 3000 square miles, including Maries County on the west, Jefferson on the east, Franklin on the north, and part of Madison on the south, or parts of ten counties. A general section of the rocks of the southeast part of this region would be about as follows, numbering from the top 1. Sandstone (the second of Missouri geologists), - 20 feet. 2. Cbert beds-beds of passage below, - 125 feet 3. Magnesian limestone, chert, and quartzite, - 100 to 300 feet 4. Lower magnesian limestone, - 100 to 150 feet 5. Gritstone and lingula beds, - 50 feet 6. Ozark marble beds, - 5 to 20 feet 7. Sandstone and conglomerate, - 5 to 90 feet 8. Porphyry, Archaean. 9. Granite, The thickness is approximate, for it is not possible to obtain the correct thickness of the various beds. No. 1 may be seen as de¬tached outliers or loose masses of a hard sandstone or quartzite, and is found on the hilltops in the southern part of Madison County, in like topographical position in Reynolds County and the western part of Washington County. No. 2 consists of alternations of chert, clay, and quartzite. It is the formation which contains most of the limonite deposits of Central and Southern Missouri. In Reynolds County shafts have pene¬trated it 75 feet. Outcrops there and in Madison would indicate it to be at least 125 feet thick. Fossils obtained in various places prove it clearly to be of the age of the calciferous sandrock of the New York system, and Nos. 1 and 2 may also be referred to the age of the second sandstone of Missouri. No. 3 consists chiefly of thick beds of ash, drab and flesh-colored magnesian limestone, both coarse and fine-grained. These beds, where they occur, in Washington, Jefferson, and the southern part of Madison Counties, contain a good deal of quartz in drusy cavities. In Washington County the limestones are beautifully ramified by a system of connected drusy cavities generally lined with minute quartz crystals arranged in botryoidal and mammillary forms, and called u mineral blossom " by the miners. This is the lead-bearing rock of Washington County, but in the southern part of Madison it does not appear to be galeniferous. It is also undoubtedly the equivalent of

Jan 1, 1877

By G. C. Broadhead

The lead district of Southeast Missouri covers an area of over 3000 square miles, including Maries County on the west, Jefferson on the east, Franklin on the north, and part of Madison on the south, or parts of ten counties. A general section of the rocks of the southeast part of this region would be about as follows, numbering from the top: 1. Sandstone (the second of Missouri geologists),.... 20 feet. 2. Chert beds—beds of passage below,...... 126 " 3. Magnesian limestone, chert, and quartzite,. .. 100 to 300 " 4. Lower magnesian limestone,......100 to 150 " 5. Gritstone and lingula beds,....... 50 " 6. Ozark marble beds,........5 to 20 " 7. Sandstone and conglomerate,. .. .. 5 to 90 " 8. Porphyry, Archæan 9. Granite, The thickness is approximate, for it is not possible to obtain the correct thickness of the various beds. No. 1 may be seen as detached outliers or loose masses of a hard sandstone or quartzite, and is found on the hilltops in the southern part of Madison County, in like topographical position in Reynolds County and the western part of Washington County. No. 2 consists of alternations of chert, clay, and quartzite. It is the formation which contains most of the limonite deposits of Central and Southern Missouri. In Reynolds County shafts have penetrated it 75 feet. Outcrops there and in Madison would indicate it to be at least 125 feet thick. Fossils obtained in various places prove it clearly to be of the age of the calciferous saudrock of the New York system, and Nos. 1 and 2 may also be referred to the age of the second sandstone of Missouri. No. 3 consists chiefly of thick beds of ash, drab and flesh-colored magnesian limestone, both coarse and fine-grained. These beds, where they occur, in Washington, Jefferson, and the southern part of Madison Counties, contain a good deal of quartz in drusy cavities. In Washington County the limestones are beautifully ramified by a system of connected drusy cavities generally lined with minute quartz crystals arranged in botryoidal and mammillary forms, and called " mineral blossom " by the miners. This is the lead-bearing rock of Washington County, but in the southern part of Madison it does not appear to be galeniferous. It is also undoubtedly the equivalent of

By Charles Y. Clayton

THE general public does not know that there is such a thing as metallurgy and it is very seldom that you see the word metallurgy in print except in technical magazines. Perhaps it is more to the front now than in former years; the Dee. 30, 1929, issue of Time mentioned under the heading of "Science7' certain new achievements in metallurgy, which may be cited as a rare instance of the use of the word in anything but the technical press. Too often the part the metallurgist plays in the advancement of the different branches of engineering is overlooked. To say that the public does not know there is such a profession as metallurgical engineering seems to be a bold statement, but had there beep time a questionnaire could have proved this beyond doubt. Suppose a carefully-planned questionnaire had been sent to all high school students asking them, among other questions, to list the different branches of engineering, I believe that the several professions would have been listed in this manner: (1) Electrical engineering; (2) mechanical; (3) civil, and (4)' mining. One in each hundred might have listed metallurgy as an engineering profession. Even the Society for the Promotion of Engineering Education in its Bulletin No. 10-"Investigation of Engineering Education" lists Civil, Mining, Mechanical, Electrical, and Chemical, leaving out Metallurgical Engineering.

Jan 1, 1930

By E. S. Mardock, Robert E. Bush

The object of this paper is to report recent developments in the quantitative interpretation of radioactivity logs. The use of reference lines is described in the application of the new zero radioactivity reference line for the determination of neutron derived porosities is discussed. Illustrated examples are shown of logs from the reef limestone of the North Snyder Field and from the Lansing-Kansas City limestone of central Kansas. A method of using an interrelation factor calculated from the neutron and gamma ray curves, called the neutron Productivity number, for the estimation of productivity from sandstone formations is discussed. When used in a relative manner the neutron productivity number has aided in Predicting whether a given zone will produce gas or liquid or whether it is too shaly to produce. Examples of logs from wells in the Freites District, Venezuela, and in East Texas are shown to illustrate the application of the neutron productivitv number. INTRODUCTION The petroleum industry was introduced to some of the preliminary results of investigations into the quantitative interpretation of radioactivity logs in October, 1949." It was stated at that time that the methods presented were entirely relative because they involved the use of reference points obtained from the radioactivity log, i.e., shale reference lines, dense zone reference lines, or a combination of both shale and dense zone reference lines. These relative methods offered many advantages to the industry in interpreting radioactivity logs in terms of porosity with particular application to limestone and dolomite reservoirs. However, these relative methods did not offer the wide range of applicability desired because the esta1)lishment of reliable reference points from shale in some areas were difficult. It was recognized that a more reliable mean; of establishing reference lines was vitally needed. Such a method is now available through the introduction of an instrumeutal zero device. It is the purpose of this paper to discuss the application of this new zero reference to the quantitative interpretation of radioactivity logs. Previously all applications of quantitative interpretations of radioactivity logs have been made in limestone reservoirs with little or no emphasis placed on sandstone reservoirs. A brief resumé of investigations into the quantitative interpretation of radioactivity logs in sandstone reservoirs is presented here. This discussion deals primarily with the interrelation of the gamma ray and neutron curves and the response of the latter to the density of the fluids filling the pore space in relatively homogeneous sandstones of uniform porosity. The authors believe that the methods presented herein are only applicable locally to specific fields and reservoirs, and that they probably do not offer a wide range of applicability. However, tile authors believe that the wider use of the new instrumental zero references in sand areas will reveal more information about the specific response of the gamma ray and neutron curves to changes in lithology and saturation. Two applications of quantitative interpretation using the new instrumental zero references are presented. Examples are given which show the comparison of logs and porosity in the limestones and dolomites of West Texas and Kansas. Logs of wells in 'Venezuela and East Texas are compared with the drill stem test data, production data, etc.. to illurtrate the interrelation of the gamma ray and neutron curve: and the rise of methods involving these interrelations to determine certain saturation variables. THE QUANTITATIVE APPLICATION OF RADIOACTIVITY LOGS TO LIMESTONE AND DOLOMITE RESERVOIRS Tile theoretical basis for the gamma ray and neutron curves has been discussed elsewhere.9 he method of recording the logs and apparatus involved has also been thoroughly covered and will not be discussed here.'."".'" It has been shown that the neutron curve responds exponentially to liquid filled porosity over the 1 1/2 to 35 per cent

Jan 1, 1951

By Robert E. Bush, E. S. Mardock

The object of this paper is to report recent developments in the quantitative interpretation of radioactivity logs. The use of reference lines is described in the application of the new zero radioactivity reference line for the determination of neutron derived porosities is discussed. Illustrated examples are shown of logs from the reef limestone of the North Snyder Field and from the Lansing-Kansas City limestone of central Kansas. A method of using an interrelation factor calculated from the neutron and gamma ray curves, called the neutron Productivity number, for the estimation of productivity from sandstone formations is discussed. When used in a relative manner the neutron productivity number has aided in Predicting whether a given zone will produce gas or liquid or whether it is too shaly to produce. Examples of logs from wells in the Freites District, Venezuela, and in East Texas are shown to illustrate the application of the neutron productivitv number. INTRODUCTION The petroleum industry was introduced to some of the preliminary results of investigations into the quantitative interpretation of radioactivity logs in October, 1949." It was stated at that time that the methods presented were entirely relative because they involved the use of reference points obtained from the radioactivity log, i.e., shale reference lines, dense zone reference lines, or a combination of both shale and dense zone reference lines. These relative methods offered many advantages to the industry in interpreting radioactivity logs in terms of porosity with particular application to limestone and dolomite reservoirs. However, these relative methods did not offer the wide range of applicability desired because the esta1)lishment of reliable reference points from shale in some areas were difficult. It was recognized that a more reliable mean; of establishing reference lines was vitally needed. Such a method is now available through the introduction of an instrumeutal zero device. It is the purpose of this paper to discuss the application of this new zero reference to the quantitative interpretation of radioactivity logs. Previously all applications of quantitative interpretations of radioactivity logs have been made in limestone reservoirs with little or no emphasis placed on sandstone reservoirs. A brief resumé of investigations into the quantitative interpretation of radioactivity logs in sandstone reservoirs is presented here. This discussion deals primarily with the interrelation of the gamma ray and neutron curves and the response of the latter to the density of the fluids filling the pore space in relatively homogeneous sandstones of uniform porosity. The authors believe that the methods presented herein are only applicable locally to specific fields and reservoirs, and that they probably do not offer a wide range of applicability. However, tile authors believe that the wider use of the new instrumental zero references in sand areas will reveal more information about the specific response of the gamma ray and neutron curves to changes in lithology and saturation. Two applications of quantitative interpretation using the new instrumental zero references are presented. Examples are given which show the comparison of logs and porosity in the limestones and dolomites of West Texas and Kansas. Logs of wells in 'Venezuela and East Texas are compared with the drill stem test data, production data, etc.. to illurtrate the interrelation of the gamma ray and neutron curve: and the rise of methods involving these interrelations to determine certain saturation variables. THE QUANTITATIVE APPLICATION OF RADIOACTIVITY LOGS TO LIMESTONE AND DOLOMITE RESERVOIRS Tile theoretical basis for the gamma ray and neutron curves has been discussed elsewhere.9 he method of recording the logs and apparatus involved has also been thoroughly covered and will not be discussed here.'."".'" It has been shown that the neutron curve responds exponentially to liquid filled porosity over the 1 1/2 to 35 per cent

Jan 1, 1951

By W. A. Tiller

The unidirectional freezing of a semiinfinite liquid from one end has been treated by calculating the solute and temperature distributions in the liquid and solid phases with time, when the solid-liquid interface advances at a rate proportional to (time)lt2. The nucleation probability for new grain formation is calculated as a function of the constitutional and thermal properties of the alloy, the pouring conditions and the catalytic efficiency of the nucleating agents. The transition from columnar crystal formation to equiaxed crystal formation is assumed to occur at a critical nucleation frequency for a particular alloy and the quantitative dependence of the ratio (columnar zone length/equiaxed zone length) upon the freezing conditions has been predicted. The effects of (i) fluid flow in the liquid, (ii) heat transfer through a mold wall, and (iii) a finite ingot length, have been explicitly tveated as departures from ideality. These departures from ideality are found to have very important consequences on the ingot stmcture. In Part I&apos; of this series, a qualitative description of the general ingot structure was developed. The factors that determine i) the ratio of the equiaxed zone length to columnar zone length and ii) the grain sizes in these zones, were discussed. In the present paper, topic (i) will be treated quantitatively, and it is intended that topic (ii) will be treated quantitatively in Part 111. The complete treatment has been split in this manner for ease of development and coherency of presentation. The treatments are quite mathematical in nature and, although some of the conclusions to Part 11 depend upon the treatment presented in Part 111, it was felt that the intended audience would find the material more readable and more useful in its present form. To this same end, it seems worthwhile to reiterate some of the qualitative aspects of grain nucleation during ingot solidification before embarking on the mathematical description. QUALITATIVE ANALYSIS In the conventional method of casting, a liquid alloy with a certain degree of superheat is poured into a mold. The outer rim of liquid metal cools rapidly to the liquidus temperature of the alloy and begins to undercool. As the degree of undercooling increases, nuclei of solid begin to form in this chill layer, this nucleation being catalyzed by certain heterogeneous particles in the liquid. The grains in the chill layer which are generally of random orientation, begin to grow inwards because of heat conduction through the mold. The grains usually develop a columnar shape since the frequency of nucleation of new grains in the liquid ahead of the advancing interface is generally insufficient to seriously impede the growth of the original grains. Due to the slow diffusion rate of solute in the liquid, a solute distribution is formed in the liquid adjacent to the interface which is either an excess or a depletion if the partition coefficient, ko, of the solute is < 1 or > 1, respectively. Thus, the liquidus temperature of the liquid adjacent to the interface is a function of position. The actual temperature in the liquid is also a function of position and the temperature gradient at the interface decreases as the interface moves away from the mold wall. Since the rate of advance of the interface decreases with time, the equilibrium temperature distributions and the actual temperature distributions as a function of interface position, X, can be illustrated as in Fig. 1. Thus, a region of liquid may exist in which the actual temperature is below the liquidus temperature. This liquid is contitutionally supercooled and therefore unstable with respect to the nucleation of new grains. Now, since the supercooling in Fig. 1 increases as the interface moves further away from the mold wall, the nucleation rate of new grains will increase. When the nuclea-

Jan 1, 1962

By Alec M. Crowell, Thomas D. Bailey

Although natural gas was first discovered in Northwest Arkansas in 1887, . near Fort Smith, Sebastian County, the literature contains very little information on the region, which is separated distinctly from the oil area of Southern Arkansas. For that reason this brief and concise report is a summary of developments from discovery to the present time. Northwest Arkansas produced 5,736,-ooo,ooo cu. ft. of natural gas during 1942, the trend of production having been generally upward over the past five years, as is shown in Fig. I. Since 1904 a reserve of 237 billion cubic feet of natural gas has been discovered in Northwest Arkansas, of which approximately 162 billion cubic feet have been expended, leaving a reserve of approximately 75 billion cubic feet available as of Jan. 1, 1943. A prolific new field discovered in Pope County Oct. 23, 1942, will add to the reserve of the region materially. Per well reserves, over-all, are unusually high because of the practice of multiple completion. As yet no commercial deposits of oil have been discovered in Northwest Arkansas. but the gas deposits have proved of immense value industrially, principally in the processing of zinc ore mined in the local area as well as that imported from distant states. With the war, new interest in the exploitation of the metallic ores of the region lends new significance to the gas reserves tabulated herein. Geological Discussion The region covered in this report comprises the Arkansas Valley from Pope County weslward to the Arkansas-Oklahoma state line as shown in Fig. 2. This valley is a westward trending structural trough with sharp-topped ridges and mesa-like mountains rising above the valley&apos;s undulating surface. It is bounded on the north by the Ozark Highlands and on the south by the Ouachita Mountains. The sedimentary beds of the Arkansas Valley are composed mainly of noniossil-iferous shales and sandstones. The rocks contain a high content of carbonaceous material and many coal beds are found in the region. The Gxed carbon ratios (ratio of fixed carbon to volatile combustible matter of surface coals) are very high and average about 80 per cent over the region covered in this report. Little or no calcareous material is present. Rocks of the Arkansas Valley are sharply folded, and igneous intrusive rocks cut the sedimentary beds at a few places. The Arkansas Geological Survey&apos; made a detailed reconnaissance survey of the Arkansas Valley province in 1927, the purpose being to delineate the major structural features (Fig. 3) and to point out the possibilities of discovering addi. tional gas deposits. More than fifty anticlines were mapped as a result of this survey. The information gained by this

Jan 1, 1943