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By Robert H. Richards

This is in part a review paper, indicating the various steps that have been taken in developing hindered-settling apparatus, some of the standard data that have been obtained, and some of the conclusions one is led to as to the effect of it in improving concentrating-methods and machinery, and in part it brings in some unpublished work. Causes oF Loss in ORe-ConcEntration. In making a study of the separation of valuable minerals from the waste gangue, particularly by water concentrators, it is necessary to define, first of all, what are the causes of loss that are likely to interfere with the concentration. Having made this definition, we can then study to see in what may the machines make their losses, and plan remedies for them in an intelligent way. Losses may be stated to occur as included grains, as flat or long grains, as fine free mineral, and as absolute slime. We will take these up one by one, as follows: Included Grains.—Fig. 1 shows by a set of diagrams how included grains may occur : first, where the heavy mineral grains attached to the quartz are of large size; secondly, where they are of small size; and thirdly, where very fine particles of heavy mineral are included in the quartz. We have to decide in regard to included grains whether they are rich enough to go direct to the furnace, or poor enough to throw away, or whether they lie between these two points and require recrush-ing as the only means of severing the values from the waste. This last case is the orlly one requiring special treatment at our hands. We will therefore consider that next.

Jan 1, 1911

By G. M. Ikeda, J. G. Sibakin

An investigation was carried out to determine the variables affecting the coiling temperature of strip in the 56-in. hot strip mill. After statistical treatment, equations have been derived to determine the temperature drop between mill and coiler for both full spray (top and bottom) and top spray only practices. The individual influences of each variable in the temperature drop were derived for both practices. Limitations of the present practices were shown and adjustments in cooling for increased rolling speeds were suggested. A method of estimating the required number of sprays, their spacing, pressure, etc., to achieve a desired temperature drop is developed. MAXIMUM finishing temperature of a hot strip mill is mainly determined by the rolling speed, gage, and the temperature of the bar entering the mill. This finishing temperature may be limited by the maximum admissible coiling temperature in cases when either the cooling facilities on the runout table are not adequate or, more generally, when the cooling capacity of the runout table and the production capacity of the continuous mill are out of balance. Some time ago, the balance between these two factors was not considered detrimental to production. Recently, a new drafting schedule was introduced which increased the production rate, the entry temperature, and hence the finishing temperature. Thus, the restriction of the maximum specified coiling temperature became an important factor for many of the thicker gages. An investigation of the factors determining the coiling temperature may be, therefore, of considerable importance. A brief description of the available equipment will be a useful illustration of the techniques and methods used for this investigation. The 56 in. continuous hot strip mill is composed of six 4-high stands each containing two 221/2-in. diam work rolls and two 45-in. diam back-up rolls. Either of the last two stands can be used as the finishing stand. Which stand is used is dependent on the total percentage of reduction to be taken over the whole train, i.e., on the entry thickness and the final gage. The characteristics of these last two stands are given in Table I. Table I. Operational Characteristics of Nos. 5 and 6 Stands No. .5 NO. 6 Maximum voltage GOO 600 Power, hp 30(10 W00 I normal, kilonmp 4.35 3.73 Rpm of motor and rolls ISO 15 0 ITS to 300 Spettl ot strip, fpm 333 6 to 376T.2 103) to 2062 The speed of the finishing stand varies with the amount of reduction, strip width, and the exit gage. Finishing speeds in general use for varying gages are shown in Table 11. These speeds may change with an increase or decrease in the entry temperature of the strip. Even though the maximum speed of No. 6 stand is shown as 2062 fpm, this has so far never been attained,

Jan 1, 1957

By E. D. Fields, R. W. Sayers, M. C. Tippett

The Duval Corp. porphyry copper deposits at Copper Canyon and Copper Basin, though widely separated, form an econornic unit requiring integrated exploitation. Contrasts in mineralization, host rocks, and mode of occurrence present unique mining and milling problems. Mixed oxide-sulfide ore is treated in extensive dump leaching facilities in both areas. Complex Cu-Au-Ag ore is treated in a 4000-tpd mill at Copper Canyon. In both areas, hypogene metallization occurs within large aureoles of metamoiphism and hydrothennal alteration related to quartz monzonite intrusions of mid-Tertiary age. Supergene processes fitrther altered the rocks and enriched the hypogene protore. At Copper Canyon, hypogene copper and iron sulfides with gold and silver occur in fractures, as partial replacement of favorable beds, and as disseminations in Paleozoic sedimentary rocks. The lower part of the Pennsylvanian Battle formation was a particularly favorable host. Metallization occurs to a lesser extent in quartz monzonite. Metal zoning is well-developed. The deposits at Copper Basin consist principally of supergene copper minerals in arenites of the Cambrian Harmony formation. Oxidation of hypogene copper and iron sulfides in tactite zones has formed at least two commercial deposits; intersections of fractures with favorable beds exerted important ore controls. Recently, the Copper Canyon and Copper Basin properties of Duval Corp. have been added to the list of porphyry copper mines in Nevada, marking the first new copper open pit in this state in 15 years. The properties are situated in the Battle Mountain

Jan 1, 1970

By Arthur Philips

THE purpose of this paper is to present certain data and observations resulting from a series of experiments dealing with the heat treatment and microstructure of commercial white cast iron and its derivative, malleable iron. In planning the experimental work, particular pains were taken to secure for the tests white cast iron of "normal" composition; i.e., within the composition limits commonly prescribed by manufacturers of malleable castings. A review of the literature leads us to believe that much data of a fragmentary character treating of the graphitization of white cast iron have been of little value, mainly because of the diversity in chemical composition of the materials employed in the tests. Moreover, when feasible, annealing periods at least comparable to those of current practice have been adopted. We wish to acknowledge our indebtedness to the members of the research department of the Eastern Malleable Iron Co. for the white cast iron used in the tests and, particularly, for their active cooperation during the experimental stage of the work. In this paper the following subjects will be discussed in the order indicated: Data on the thermal critical points of white cast iron and malleable iron. Changes produced in tensile properties and microstructure of white cast iron by annealing at different temperatures within the range, 760 to 1100° C. Relation of thickness of wall section of hard iron to microstructure and tensile properties of malleable iron obtained under normal annealing conditions. Notes on mechanics of graphitization of normal white cast iron as observed in specimens quenched after various periods of anneal at approximately 800° C.

Jan 1, 1922

By R. E. Pollard

The National Bureau of Standards received, in August 1940, a number of samples of bridge wire taken from the cables of the General U. S. Grant suspension bridge over the Ohio River at Ports- mouth, Ohio. These cables were 7% in. in diameter under the wrapping and each was made up of 1458 ungalvanized wires of No. 8 gage in 3 parallel-wire strands. The choice of ungalvanized wire was based on the previous satisfactory performance of similar wires in other bridges over periods of 20 to 50 yr. of service(1).2 After about 12 yr. of service a number of breaks were discovered in the Portsmouth bridge cables, most of them at the anchor- age shoes, and they were replaced by cables made up of galvanized wire(2).

Jan 1, 1945

By Cyril Stanley Smith

IsolatEd alloys of copper and silicon were prepared and examined by chemical methods more than one hundred years ago, but it was not until the work of Rudolfi l that the equilibrium relations were studied. The early history of the alloys was well described by Baradue-Muller 2 and need not be further discussed here. The diagram of Rudolfi, based entirely on thermal observations, showed sillcon to be soluble in copper up to 4.5 per cent. at 849" C., at which temperature there was a peritectic horizontal resulting from the formation of a ß phase with about 7.4 per cent. silicon from a and liquid with 7.85 per cent. silicon. The ß phase was believed to form a eutectic with Cu3Si at 820" C. and 9.8 per

Jan 1, 1929

By K. E. Gray, A. Podio

ABSTRACT Berea and Bandera sandstone samples were impacted with both 3/4-in. and 1/2-in. long wedges, each having a 60° included angle and a 0.05-in. flat, at various confining pressures, with borehole and pore pressures held fixed at atmospheric pressure. Samples were saturated with air, water, glycerine-water, solirol, mineral oil and soltrol-mineral oil mixtures to obtain a wide range of pore fluid viscosity. Penetration depth was held constant at 0.1 in. Dry and soltrol-mineral oil-saturated Berea samples were impacted at depths of penetration from 0.01 to 0.04 in. under 1,000 psi confining pressure to study crater initiation. Results indicate that viscosity of the pore fluid is influential primarily during the early stages of crater formation. Differences in bit force, crater volume and blow energy for tests parallel and perpendicular to bedding were significant, but decreased as the stress state was elevated. Crater volume, blow energy and bit force were nonlinearly related with depth of penetration. Crater volume was nonlinear with energy of blow. Fixed-penetration tests on saturated Berea yielded greater crater volume than did similar tests on dry samples. Differences in the nature of deformation for low values of bit penetration were noted between saturated and unsaturated samples. INTRODUCTION Rock failure during bit-tooth impact and scouring action constitutes a vital part of the drilling process and a difficult problem for researchers. Much study has been devoted to various aspects of the problem, and much has been learned about mechanics of rock failure. However, analytical treatment of drilling at depth remains difficult, partly because there are so many factors involved and because valid simulation of downhole conditions is extremely difficult. Forming individual craters by a bit tooth or chisel impacting, or indenting, a rock mass has been studied by many investigators.1-18 Similarity between single-tooth chisel impact and the corresponding action of a rotary bit has been discussed by Appl and Gatley, Garner, Podio, and Gatlin l8 compared the similarity in single-blow impact tests with microbit drilling data reported by Cunningham and Eenink.l9 Maurerll has used single-tooth impact data to develop a "perfect cleaning" theory of rotary drilling. Individual roller cutter-tooth impact data have been reported by Young. 20 Single-tooth tests in all of the cited literature were carried out on dry rocks. Inasmuch as any subsurface rock of oilfield interest is saturated with some fluid, it seemed desirable to study crater formation in permeable rocks saturated with a viscous pore fluid as a step, however short, toward more realistic simulation of subsurface conditions. This paper presents results of single-blow chisel impact studies on Berea and Bandera sandstones, both dry and saturated with pore fluids of various viscosities at confining pressures to 10,000 psi. EXPERIMENTAL APPARATUS AND PROCEDURE EXPERIMENTAL APPARATUS The same basic apparatus for single-blow chisel impact at elevated stress states, described in earlier papers was used in this study. l6. l8 Fig. 1 shows the complete experimental system; Fig. 2 shows a cross section of the pressure cell, with a sample ready to be impacted. EXPERIMENTAL PROCEDURE Two different rocks, Berea and Bandera sandstones, were used in this study. Both rocks have been used extensively in research, and rock descriptions can be found in a paper by Gnirk and Cheatham.15 Permeability to air of Berea is about 300 md normal to bedding and 540 md parallel to bedding. Bandera had vertical and horizontal air permeabilities of 18 and 57 md, respectively.

Jan 1, 1966

By C. Scala, M. Gondouin

Published laboratory data have established that very significant streaming potentials can exist across mud cakes subjected to pressure differentials such as exist between a mud column and formation fluids. Since shale is similar in kind and in properties to a well-formed mud cake, it appeared possible that streaming potentials might also arise across shales. A practical consequence would be that the streaming potential contribution to the SP would be smaller than might otherwise be assumed since the SP is measured with respect to the "shale bare line". The resultant contribution would be the difference between the streaming potential across the shale and that across the mud cake. In order to investigate this possibility, a laboratory apparatus was devised for measuring streaming potentials under pressure conditions normally encountered in wells. Reported data on streaming potentids across mud cakes were verified. More important, appreciable streaming potentials were found across shale samples. As in the case of mud cakes, the shale potentials varied with the concentration and nature of the impregnating electrolyte. Dependence on pressure was In a different rela-tion than that for mud cakes, possibly because of the lower compressibility of shales. The differences in streaming potentials between the shales md mud cakes were generally small, although they might vary considerably in practice depending on the relative electro-kinetic properties of the particular shale-mud cuke combination. A "poorly eflective" shale with a "very eflec-tive mud cake" would produce the largest negative addition to the electrochemical component of the SP. Results of field experiments with pressurized wells were considered in the light of the laboratory results. INTRODUCTION Field experiments wherein the pressure of the mud column in a borehole was varied have often indicated the presence of a streaming potential, but its magnitude was not easily predictable and its sign sometimes changed from one formation to another in the same well.' In the interpretation of SP logs from standard surveys, nevertheless, the correct value of R,, is very frequently obtained, within the limits of field accuracy, using only the simple electrochemical expression of the SP provided that proper corrections are made for bed thickness, ion activity, etc.' Accordingly, it was apparent that the streaming potential component of the SP in a borehole was considerably more complex than commonly assumed and clarification was indeed necessary The close similarity in nature and constitution of a shale to a well-compacted mud cake suggested that a streaming potential might also exist across shales as pointed out by M. P. Tixier in 1953 and as recently emphasized by Wyllie." e practical consequence would be that the streaming potential across the mud cake would be canceled, at least in part, on electrical logs since the SP is recorded with respect to the shale potential as a base line. This appeared to be a plausible explanation for many of the effects observed but no supporting data were available. In 1955 preliminary experiments at low pressures were conducted in our laboratories which supported the hypothesis of the shale streaming potential and formed the basis for later studies at borehole pressures.* EARLY LOW PRESSURE EXPERIMENTS The early experiments were conducted primarily to determine the possibility of a streaming potential across shales. The shale used was a compact type designated as No. 7 from Reagan County, Tex. (Permian). Cut samples were saturated for over one month in .2 to 2.0-N NaCl solutions. In order to eliminate all electrode polarization effects, a dynamic method was used. A transient pressure of about 1 atm was applied across

By Cyril Stanley Smith

IsolatEd alloys of copper and silicon were prepared and examined by chemical methods more than one hundred years ago, but it was not until the work of Rudolfi l that the equilibrium relations were studied. The early history of the alloys was well described by Baradue-Muller 2 and need not be further discussed here. The diagram of Rudolfi, based entirely on thermal observations, showed sillcon to be soluble in copper up to 4.5 per cent. at 849" C., at which temperature there was a peritectic horizontal resulting from the formation of a ß phase with about 7.4 per cent. silicon from a and liquid with 7.85 per cent. silicon. The ß phase was believed to form a eutectic with Cu3Si at 820" C. and 9.8 per

Jan 1, 1929

By J. J. Crowe, G. K. Burgess

PAGE, Theories of Allotropy of Iron........... 667 Previous Determinations of A2 and A3 in Iron........ 668 Critical Ranges as Determined by Expansion........ 669 Critical Ranges by Thermoelectric Observations........ Critical Ranges in Terms of Crystalline Structure....... 670 Critical Ranges as Detected by Mechanical Methods...... 670 Critical Ranges as Given by Electrical Resistance....... 670 Critical Ranges as Determined Magnetically........ 671 Critical Ranges as Determined Calorimetrically....... 673 Critical Ranges from Heating and Cooling Curves....... 673 Summary of Previous Determinations of A3 and A2 in Pure Iron.... 675 The Present Investigation............ 678 The Experimental Method........... 678 Arrangement of the Apparatus.......... 679 The Measurements of Temperaturc.......... 679 The Measurement of Time........... 679 The Thermocouples............ 681 Temperature Scale and Calibration of Thermocouples...... 681 Mounting of Thermocouples........... 682 The Differential Measurements.......... 682 The Furnace and Accessories........... 682 The Vacuum Pump............ 683 The Energy Supply............683 The Rheostat.............. 683 The Materials Investigated............ 685 Sources of Iron............. 685 Preparation and Description of Samples......... 685 Chemical Analyses............. 687 The Experimental Data............. 688 The Preliminary Observations.......... 688 The Definite Series............691 Description of the Plotted Curves........... 694 The Effect of Plotting at Different Intervals........ 694 The Curves of the Definite Series.......... 695 . The Curves of the Preliminary Series......... The Existence of Other Critical Ranges......... 696 The Microscopical Examination........... 697 Summary and Conclusions............ 698 Bibliography............... 701 Plates................ 704

Jan 1, 1914

By M. N. Short, I. A. Ettlinger

M. N. Short,? Washington, D. C., and I. A. Ettlinger, New York', N. Y. (New York Meeting. February, 1926) The Pioneer mining district, better known as the Superior district, from its principal town, is located in Pinal County in south-central Arizona about 80 miles east of Phoenix and 22 miles west of Miami. The region embraces a, confused series of mountain ranges of moderate height but precipitous slopes, between which lie irregular valleys filled with alluvial detritus. The average elevation is about 2800 ft. in the valleys and the summits of the ranges reach 2000 ft. above this. Superior is situated on the north bank of Queen Creek where it emerges from one of those ranges into a more or less basin-shaped valley. The drainage of Queen Creek is to the southwest and the flood waters spread out and lose themselves in the desert northeast of Florence, the county seat of Pinal County. The Magma copper mine (Fig. 1) is the only producer in the district. Although discovered in 1875, its production has been important only

Jan 1, 1927

Adams, Benjamin C., Jr., Student, Univ. of Oklahoma Norman, Okla. '36 Adams, Ernest C., Student, Univ. of Illinois 908 W. Green St., Urbana, Ill. '35 Adams, George H., Student, Colorado School of Mines Golden, Colo. '36 Adams, Robert Keller Mitchell Hotel, No. 18, Golden, Colo. '35 Afshar, Hadji Khan A., Student Box 63, Univ. Sta., Moscow, Idaho. '36 Ahrenholz, Herman William, Jr., Student, Lehigh Univ Bethlehem, Pa. '35 Alger, Robert P., Student, Missouri School of Mines & Met.Rolla, Mo. '36 Allen, Paul W., Student, Mass. Inst. of Tech Cambridge, Mass. '35 Allen, R. M., Jr., Student, Virginia Polytechnic Inst., "G" Co.Blacksburg, Va. '35 Alley, John Arnold, Student, Montana School of Mines Butte, Mont. '36 Amberger, R. H., Student, Michigan College of Min. & Tech Houghton, Mich. '35 Ambrosiani, F. Peter, Student, Michigan College of Min. & Tech Houghton, Mich. '36 Andersen, Burton Lee, Student, School of Mines, Univ. of Washington Seattle, Wash. '36 Anderson, Carlos, Student, Univ. of Oklahoma Norman, Okla. '36 Anderson, J. Wendell, Student, Pennsylvania State College State College, Pa. '36 Anderson, Joseph S. Cornelia Hotel, Ajo, Ariz. '35 Anderson, R. C., Student, Univ. of Washington Seattle, Wash. '35 Anderson, Roy A., Student, Washington State College Pullman, Wash. '35 Anderson, Willard. Student. Univ. of Oklahoma Norman, Okla. '36

Jan 1, 1936

By Sidney Powers

CONTENTS PAGE Distribution of fields 4 History of development 6 Origin of oil 7 Structure, accumulation and migration 8 Reservoir rocks 9 Methods of drilling and exploration 10 Oil-field statistics : 12 Description by regions: United States: Appalachian region ; 12 East-central states 17 Kansas 18 Oklahoma : 19 Texas : 24 Arkansas : 32 Louisiana 33 Mississippi ....... 34 Rocky Mountain region : 34 California 37 Canada 41 Mexico 43 Cuba 46 Bibliography 46 THE purpose of this brief account- of the occurrence of petroleum in North America is to make available to those who have a knowledge of geology, but who are not engaged in the petroleum industry, a few salient facts about the location of oil and gas fields, their productivity, the important structural types of accumulation and the age of the rocks containing petroleum. A few useful data and statistics are furnished, yet not complete statistics that are available elsewhere. Geology has been treated in simple terms because the reader is presumed to have little interest in the names of formations and of oil sands. Mineral deposits are more or less analogous. Whether oil or metals, minerals are found in rocks, largely in sedimentary rocks which carry water or have at one time carried it. A genetic or accumula-

Jan 1, 1931

By T. L. Joseph

THE invention of the Bessemer converter process in 1856 added great impetus to the manufacture of steel and is one of the outstanding contributions to process metallurgy. Although the process of refining pig iron by passing air through the molten metal bears the name of Henry Bessemer, it should be mentioned in passing that William Kelley of Eddysville, Ky., worked on the process as early as 1847. Kelley was granted a patent on the process in 1857, inasmuch as he was able to prove priority in discovery.1 After considerable litigation in 1865 the respective interests of Kelley and Bessemer were combined. On Sept. 10, 1856, Robert Mushet of England obtained his first patent on the application of manganese to cast steel. Mushet anticipated trouble in purifying iron by passing currents of air through it. His patent specified that steel made in this way often contained flaws and was red short or cold short. Mushet understood the refining of pig iron into steel well enough to realize the difficulties likely to be encountered from oxidation of the iron. Mushet was not only an inventor but he was also an investigator. He understood the principle of selective oxidation which takes place in the converter process, arid he realized therefore that the remedy for over-oxidation was attainable if a suitable metal could be found at a reasonable cost and in sufficient quantities. His first experiments were made in small crucibles holding a few ounces of metal. Later his work was conducted on a larger scale and with complete success. Manganese had been used in making steel a quarter of a century before the converter

Jan 5, 1927

CONTENTS PAGE HESSE, A. W,-Safeguarding Coal-mining Operations against Danger from Oil and Gas Wells. Discussed by A. W. Hesse, T. G. Fear, George H. Ashley, George S. Rice, W. E. Fohl, R. V. Norris, S. A. Taylor, F. B. Tough, C. W. Gibbs, A. Hurlburt, S. W. Meals 1 DAWSON, THOS. W.-Belt Conveying of Coal at H. C. Frick Coke Company Mines. Discussed by F. F. Jorgensen, Thos. W. Dawson, Graham Bright, A. W. Hesse 13 OTTO, HENRY H.-Ultimate Recovery from Anthracite Coal Beds. Discussed by R. V. Norris, S. A. Taylor, Henry H. Otto, Douglas Bunting, Graham Bright, Howard N. Eavenson, J. B. Warriner 15 HOSLER, Rush N.-Schedule Rating Coal Mines in Pennsylvania for Compensation Insurance Rates. Discussed by E. A. Holbrook, W. W. Adams 17 ARCHBALD, HUGH.-Application of Gaussian Curve to Mining Industry. Discussed by Donald A. Laird, T. T. Read 19 ASH, SIMON H.-System of Coal Mining in Western Washington. Discussed by Eli T. Conner, Simon H. Ash 21 MILLER, J. S.-Method of Mining a Steeply Pitching Anthracite Vein by Successive Skips. Discussed by Eli T. Conner, J. S. Miller, J. B. Warriner 22 HARRINGTON, GEORGE B.-New Orient, an Unusual Coal Mine. Discussed" by George S. Rice, Eli T. Conner, John A. Garcia, George B. Harrington, F. F. Jorgensen, Graham Bright, W. M. Hoen, George N. Simpson, W. C. Adams, R. W. McNeill, Chas. C. Whaley, Carl Scholz, E. T. Gott, Andrews Allen 23 PERROTT, G. ST. J.-Properties of Liquid-oxygen Explosives. Discussed by George S. Rice 48 Safeguarding Coal-mining Operations against Danger from Oil and Gas Wells Discussion of the paper of A. W. HESSE, presented at the New York Meeting, Feb-ruary, 1925, and issued, as Paper No. 1412-F, with MINING AND METALLURGY, February, 1925. A. W. HESSE.-The well under investigation, No. 101, Fig. 2, was started about Sept. 5, 1921, and drilled-in in November. The first hole was started with a 13-in. bit and reached the Pittsburgh coal at a depth of 563 ft.; at 602 ft. the 10-in. casing was run in and the well was continued with a 10-in. bit and 1400 ft. of 8-in. casing was put in. It was then continued to a depth of 1770 ft. and 6-in. casing put in; then continued to a depth of 2555 ft. where the gas was struck. As the well produced only about 100,000 cu. ft. per day. 2-in. tubing was used to conduct the

Jan 6, 1925

By J. E. Hilliard, J. W. Cahn

calculation has been made of the standard deviations to be expected in the measurement of volume fractions by areal analysis, lineal analysis and four point-counting Procedures. The effect of experimetztal errors is not included. Our conclusion is that a point count using a two-dimensional grid will be the most efficient method of volume fraction analvsis providing the grid spacing IS coarse enough. The predicted standard deviation for such an analysis is shown to he in good agreement with that determined experimentally. A metallurgist wishing to estimate a structural property by means of quantitative metallography is often faced with a choice between several different procedures. In such a case, he will naturally wish to know: a) Which procedure is the most efficient in the sense of requiring the least effort for a given precision? b) For a given procedure, what are the conditions for maximum efficiency? c) Under these conditions, how many measurements are required to attain a given precision? It is our aim in this paper to provide at least partial answers to these queries as they relate to the estimation of volume fractions from measurements on a random two-dimensional section of an opaque specimen. The commonly used techniques1,2 for volume-fraction analyses are based on one or more of the following principles: i) For an areal or Delesse3 analysis: That the areal fraction of a three-dimensional feature intercepted by a random plane provides an unbiased estimate of the volume fraction of that feature. ii) For a lineal or Rosiwal4 analysis: That the fractional intercept on a line passing at random through a two-or three-dimensional feature provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. iii) For a point-count analysis: That the fractional number of randomly or regularly dispersed points falling within the boundaries of a two-dimensional feature on a plane, or within the boundaries of a three-dimensional feature in a volume, provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. The absence of bias referred to in these principles does not, of course, imply that the results of an analysis will be free of error, but only that the expected result is equal to the true one. Application of the foregoing principles provide the following six possible experimental procedures: a) An Areal Analysis—This involves the measurement with a planimeter (or other means) of the area of a constitutent intercepted by the plane of polish b) A Two-Dimensional Random Point Count—Apos-sible experimental procedure for this analysis is to superimpose a sheet of transparent graph paper on a micrograph, and then use a table of random numbers to select coordinates for the points. c) A Two-Dimensiotuzl Systematic Point Count-Similar to b) except that the points are distributed in a prescribed manner, usually at the corners of a lattice superimposed on a micrograph or the screen of a projection microscope. d)A Lineal Analysis—A measurement of the fractional line length intercepted. It is usually performed by traversing the specimen under the cross hairs of a microscope and recording the distance travelled in each constituent. e) 4 One-Dimensional Random-Point Count— This could be performed by traversing the specimen with stops at random intervals to identify the constituent then present under the cross hairs. f) A One-Dimensionul Systematic Point Count— Similar to e) except that the traverse is stopped at prescribed (usually equal) intervals. It will be noted that the point-counting procedures b) and c) can be regarded as methods of estimating the areal fraction. Similarly, e) and f) are indirect methods of making a lineal analysis. All of the six procedures described above involve at least one stage of sampling. Thus, quite apart from any experimental errors, there will always be a statistical uncertainty associated with the final results. It is with the calculation of this uncertainty that we will be concerned. To avoid unnecessary repetition, the statistical relationships that will be used in the calculations are collected together in the appendix. For a fuller discussion reference should be made to one of the many textbooks5,6 on statistics. For symbols relating to the specimen structure we will follow as far as possible the terminology used by Smith and Guttman.7

Jan 1, 1962

By G. E. Perry, J. F. Bruskotter, D. G. Russell, J. H. Goodrich

The depletion performance of gas wells has been investigated by mathematical simulation techniques. The gas well model which was studied consisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity on pressure was considered in studies of well performance at both constant mass flow rate and constant flowing pressure conditions. To carry out the investigation, the nonlinear, second-order, partial differential equation which describes Darcy flow of a nonideal gas through porous media was solved numerically. Some of the previous investigations of gas well performance have been of limited general use, because assumptions were introduced to simplify either the gas properties or the basic differential equation. Other studies have been rigorous in these respects but have presented a very limited set of calculated results. The present study was attempted to present a rigorous theoretical model and sufficient numerical results to permit meaningful conclusions to be drawn. It was found that all terms must be retained in the partial differential equation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balance errors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thickness product of the formation, the more pronounced are these deviations. For example, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gas in place) at a constant rate of 993 Mcf/D, the rigorous solution predicts a bottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. If higher-order terms are neglected in the differential equation, this decline in pressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equation as a basis, simple, easy-to-use approximations for predicting gas well performance for Darcy flow conditions have been developed. These simple approximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree of accuracy and enable the prediction of long-term gas well performance to be made quickly and accurately without the use of a digital computer. Both transient and stable flow period approximations were developed. INTRODUCTION In recent years income from the sale of natural gas and associated products has represented an ever-incre as ing fraction of the industry's total revenue from operations. To meet the surge in demand for natural gas, the industry has depended heavily upon established reserves and has actively pursued development of new reserves. The search has progressively led to reservoirs which yesterday were too tight and/or deep to yield the desired return on invested capital. More than ever before, evaluation accuracy is now required to forecast the criteria upon which engineering recommendations and management decisions are based. Considerable effort has been expended by both research and operations personnel on the development and application of methods for analyzing and predicting the performance of gas wells. Fundamentally, the problem is the familiar one of extracting data during the drilling, testing and early production life of a well and applying these data within an accurate simulation model to predict long-term behavior. During the past 30 or more years a voluminous literature dealing specifically with gas field problems has been generated. A recent book' lists a comprehensive bibliography of published material through 1959. Over 1,200 references are cited. Since then 39 additional articles on natural gas technology have been published in Transactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that one or more idealizations (e.g., steady-state flow, ideal gas of constant viscosity, small and constant compressibility and constant-viscosity fluid) be applied. Although existing theory may apply directly or be adapted by various artifices to describe specific gas well and reservoir behavior, no widely applicable method is available, and existing methods appear to be subject to appreciable error unless better limits of applicability are defined. The objectives of this paper are (1) to present numerical solutions to the partial differential equation describing gas flow under conditions of general interest in gas well performance prediction work, (2) to present solutions which possess a high order of accuracy for both transient and stabilized flow periods of a well producing at constant rate or constant pressure, and (3) to develop and present simplified relationships which can be used as high-order approximations to the exact numerical results for fast and accurate predictions of gas well performance at the operating level. Combined, these objectives are designed gen-

Jan 1, 1967

By P. J. Jacquard, C. Jain

Interpreting pressure measurements is one of the fundamental problems in the operation of oil reservoirs. The principal methods and means of study zuhich are currently used are reviewed. Emphasis is placed on the necessity of improving the quality of the information to turn it to the best possible account. One of the important aspects of the problem is the development of a system of automatic interpretation of the pressure measurements. The proposed method aims at this objective: starting from the relation which exists between a local perturbation of permeability and its effect on the velocity potentials in the wells, we determine by successive approximation the modifications to be made to the permeability map by fitting the least squares between the measured pressures and the pressures indicated by the mathematical model. The method has already been successfully employed in the case of heterogeneous reservoirs of radial- circular symmetry. Its application is extended here to the two-dimensional case, and is illustrated by two examples, for which the results are presented. The conditions required for the method to become fully operational are likewise analyzed. I — INTRODUCTION One of the basic problems of production and recovery from oil fields is interpreting pressure measurements made in wells in the single-fluid-phase regime. Simplifying assumptions, for example supposing the reservoir to be homogeneous, make it possible to use more or less simple methods which permit the estimation, from these pressure measurements, of a mean value of the permeability around the wells. Considering the actual heterogeneity of the majority of reservoirs, and the phenomena of interference between wells, these methods are only indicative. Much has been published on the studies of different cases of comparatively simple heterogeneity: some have discussed the radial heterogeneity around a single wel1,l or vertical heterogeneity.2 The results of these works have shown the influence of variations of permeability on the pressure, but unfortunately they are not very useful in practice because they all are concerned with the phenomena around a single well, without interference between wells, and they correspond to relatively simple and theoretical schemes. These studies of reservoirs or parts of reservoirs on a larger scale are made by the electric analyzer or digital model. We define a permeability map and a porosity map, then reproduce the production history of the wells on the wells of the model, and note the corresponding pressures. These pressures are then compared with actuality, and the discrepancies observed are analyzed. From this analysis we deduce the modifications to be made to the maps of permeability and porosity, and repeat until the coincidence between the pressures indicated by the model and the actually observed pressures is considered adequate. We have adjusted the model. Obviously, in this method of investigation, everything depends on the formula which permits the modification of the permeability to approach the adjustment. Considering the complicated nature of the problem, some oversimplified formulas are poorly adapted to reaching a good adjustment. For example, we have shown that the elementary operation of increasing the permeability not far from a producing well to compensate for too low pressures in the well can, in certain cases, express itself by an effect exactly opposite. 3 The project described here is for a system where we begin with the pressure measurements and the several known parameters of the reservoir, and develop the most probable permeability map, taking account of the measurements available and a subdivision of the reservoir fixed a priori. Ideally, this system is conceived as one in which no manual intervention would be necessary. The model simulating the reservoir is only one part of the whole system, and it is neither the longest nor the most complex part. The need to integrate the model into an aggregate of much more extensive processes has led to the adoption of the digital solution, even though a solution combining the digital and the analog is perfectly conceivable. The simulating model is in that case no more

Jan 1, 1966

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By Lawrence Wright

ON the steep slopes of the Kootenays, 15 to 20 miles south of Nelson, B. C., are a number of ore occurrences (Fig. 1). One that has many features of mining and geological interest is the Ymir Yankee Girl Gold Mines Limited. Discovery of this property was made in 1899 at an outcrop on the hillside, some 2500 ft. above the village of Ymir. This proved to be a branch vein 20 ft. long leading to two main veins, the Yankee Girl and the Spur (Fig. 5). The ore pattern as now delimited shows a remarkable increase in ore area with depth below the outcrop. This recent development is of interest particularly in view of the fact that the property was nearly con-demned, professionally. Another interesting feature, which has a bearing upon its history, is the persistent excess of tonnage produced from period to period over visible reserves. This is not ascribed to lagging mine development, but to detailed vein characteristics, which we will endeavor to make clear by giving a description of the veins and their surroundings.

Jan 1, 1938