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By G. H. LeFevre

THE Metal Sales Department, with offices in New York, is responsible for the sale of the Company's products, with the exception of gold and coal. At present the department handles the sales of lead, zinc, silver, antimonial lead, , cadmium, bismuth, arsenic trioxide, and tellurium; gold is shipped direct to the United States Mint and coal is marketed by United States Fuel Company's own sales organization. The department keeps in close touch with the metal markets and collects information on marketing conditions, which it makes available to other departments of the Company. The electrolytic lead produced at the U. S. S. Lead Refinery, Inc., is a high-uality product marketed as corroding grade under the "U. S. S.-ELECTRO" brand. It is largely sold to manufacturers of paints, pigments, lead oxides, and storage batteries.

Jan 1, 1948

By J. R. Thoenen

THE proper classification of mining methods has received the earnest study of many mining engineers and has resulted in much technical con-troversy, depending no doubt upon the point from which classification is viewed or the use to which it is put. So far as the writer is aware, the discussion has invariably centered around the classification of under-ground mining methods, and only superficial attention has been directed to surface methods. Volume 72, page 10, of the Institute TRANSACTIONS, presents such a classification, sponsored by the Mining Methods Committee of the Institute. A similar classification by Prof. Hugh P. Nicholson appeared in MINING AND METALLURGY in October, 1934. The two classifications are quite different in their treatment of underground methods but are identical in classifying surface methods, although Professor Nicholson does suggest possible further divisions for surface mining and admits that such subdivision is more difficult than appears at first. Surface subdivisions as given by these two authorities are as follows, showing that in spite of rearrangement the two classifications are identical:

Jan 1, 1935

By John V. Beall

IKE'S amiable expression and apparent sincerity impressed AIME members as did the theme of his talk. Cautioning against the gradually increasing power of the federal government, he said: . . . "freedom as we know it is in no greater danger from without than it is from our own lack of understanding of this creeping paralysis from within." Next February, it will be three years since he uttered these words at Annual Meeting welcoming ceremonies, but the theme was oft repeated in his winning campaign. This brush with the exalted, brief though it was, makes Washington look friendlier to many AIME members than it has for years.

Jan 1, 1953

The Howe Memorial Lecture, in memory of Henry Marion Howe, Past President of the Institute, was authorized in April, 1923, as an annual address to be delivered by invitation under the auspices of the Institute by an individual of recognized and outstanding attainment in the science and practice of iron and steel metallurgy or metallography, chosen by the Board of Directors upon recommendation of the Iron and Steel Division. The following were the Howe lectures and lecturers for the years indicated 1924 What is Steel? By Albert Sauveur

Jan 1, 1952

By R. E. Stewart

The major mining companies of the world all face the problems associated with investing in new mining ventures. In particular, investment in foreign countries - whether these are advanced or developing countries - requires careful consideration. A thorough analysis of all the possible risks must be undertaken, so that realistic decisions can be made. Some of the points to be considered are outlined in this paper.

Jan 1, 1977

By William G. Kegel

Problems involved in putting the gob back underground in modern deep mines we dealt with. In particular, the problems associated with haulage of the gob back to the mine, the blown gob method of dispersion underground, and handling the refuse as slurry are discussed. Some alternative methods of disposal are presented.

Jan 1, 1976

By J. J. Rutledge

THE first method of working coal mines in the middle western states, more particularly in Illinois, Indiana and Missouri, was by means of the so-called single-entry method. In this method a single main passageway, or entry, was driven in the coal seam. with no parallel passageways, and from this pas-sageway or entry there were turned at intervals sim-ilar cross-passageways or entries, and from these cross-passageways, if the coal seam worked lay fairly horizontal, rooms were turned right and left. These crude methods of working were followed when the com-panies opening the mines were small and of very limited capital, and when the demand for coal was small and irregular. The principal desire was to produce coal in the short-est possible time and at the cheapest price. The chief evil resulting from such method of working was de-fective ventilation, although there were other serious drawbacks. There were then few or no good mining laws and no restrictions on those operating the coal mines. The hours of labor were long, the wages low, and the miners accordingly worked hard. All the coal was either sheared or undercut with a pick by hand. Very little solid shooting and no machine mining was done. What little air entered the mine, openings was introduced through the entries or. headings and thence conducted through the rooms by means of curtains; in many cases, as the workings became more exten-sive, the number of curtains added so materially to the mine resistance that ventilation was extremely in-efficient. Shots were fired by the miners at any time during the working shift and consequently there was more or less powder smoke or fumes in the mine work-ings all day long. Moreover, the working days were much longer than at present. The fine, dry coal-dust falling from the miners' picks while they were shear-ing or undercutting the coal filled the mine atmosphere and was taken into the lungs of the mine employees.

Jan 2, 1927

By M. E. Glicksman, G. S. Ansel

It has been shown by Walton and Chalmers,&apos; that the mechanism of the development of solidification textures in castings involves the preferential growth of dendrites along certain crystallographic directions as determined by the influence of prevailing heat-transfer conditions. Specifically, this growth is parallel to the direction of heat flow. The purpose of the present investigation was to determine the applicability of this mechanism to: 1) commercially pure aluminum (99.75 pct) solidified to coarse columnar crystals, 2) an aluminum-silicon casting alloy (5.25 Si, 0.38 Fe, 0.02 Cu, 0.10 Ti, 0.002 S) cast to a fine-grained structure under complex and reproducible heat transfer conditions. PROCEDURE AND RESULTS 1) Specimen Preparation—Using a technique similar to that employed by Northcott and Thomas,2 samples were melted in the directional solidification mold, Fig. 1, by heating the entire assembly to 670° C. The mold was then end cooled using a water jet. From considerations of harmonic analysis, the likely distribution of isotherm normals encountered by the growing crystals is shown in Fig. 1. 2) Orientation Analysis—The pure aluminum sample froze to large columnar crystals, nucleated close to the metal diaphragm, with the growth direction parallel to the mold axis. Using the back-reflection Laue technique, the growth direction of these crystals was determined to be a <100>, which coincided within 53 deg to the mold axis. Metallographic examination of the relatively fine-grained aluminum-silicon sample revealed a dendritic mode of growth having its primary dendrite arms along isotherm normals. Back-reflection Debye-Scherrer patterns, taken with the specimen rotating about its cylinder axis, yielded rings displaying symmetrical arcing, thus proving that the sample did, indeed, possess the solidification texture inferred from the preliminary metallographic examination. To determine the extent and orientation of the texture in the aluminum-silicon alloy, a density distribution of the (111) poles of the sample was plotted using the transmission Debge-Scherrer

Jan 1, 1960

By W. S. Morris

PETROLEUM&apos;S importance in World War II can perhaps be better realized by the recitation of a few facts and figures: Gasoline needs in this war are already eighty times greater than in the last war. It takes nearly three pounds of gasoline to deliver one pound of bombs, filled with petroleum explosives, on an enemy objective. Every American soldier overseas requires an average of more than fifty gallons of petroleum products per week, with the oil used by Navy and supply ships and America&apos;s Allies boosting the consumption of oil per soldier to an even higher figure. Every oil well in the United States now must produce each day an average of four barrels of oil for war and combat jobs. More than fifty million gallons of gasoline, fuel oils, lubricants, and other petroleum products are now going directly to the fighting forces every day.

Jan 1, 1945

By R. F. Miller, R. F. Campbell

Sixteen steels containing different combinations of chromium and molybdenum, in amounts up to 5 per cent of each element, were examined for microstructure and hardness after air cooling and after furnace cooling from suitable austenitizing temper- atures. Diagrams summarizing the structnres and hadness resulting from these two cooling rates are presented (Figs. 3, 4, 7).t Data were also obtained on the influence of these two elements, individually and in combination, on the depth of decarburiza-tion observed after furnace cooling (Fig. 8). Composition of Material The chemical composition of the steels investigated is given in Table I. The plain carbon steel was made in a 2 5-ton Heroult electric-are furnace, while the alloy steels were made in a 4.5-ton Ajax-Northrup elec- tric induction furnace. The cast ingots were hot-rolled to 1.75-in. bars. Air-cooled Series The I.75-in. bars were forged to flat plates, 0.25 in. thick, from which specimens 0.5 in. wide by 2 in. long were cut. The specimens were pretreated to improve their homogeneity by heating to 1830°F. (I000°C.) for 20 min. and oil-quenching. They were then reheated to 1740°F. (950°C.) for one hour and air-cooled, after

Jan 1, 1942

By R. F. Campbell, R. F. Miller

Sixteen steels containing different combinations of chromium and molybdenum, in amounts up to 5 per cent of each element, were examined for microstructure and hardness after air cooling and after furnace cooling from suitable austenitizing temper- atures. Diagrams summarizing the structnres and hadness resulting from these two cooling rates are presented (Figs. 3, 4, 7).t Data were also obtained on the influence of these two elements, individually and in combination, on the depth of decarburiza-tion observed after furnace cooling (Fig. 8). Composition of Material The chemical composition of the steels investigated is given in Table I. The plain carbon steel was made in a 2 5-ton Heroult electric-are furnace, while the alloy steels were made in a 4.5-ton Ajax-Northrup elec- tric induction furnace. The cast ingots were hot-rolled to 1.75-in. bars. Air-cooled Series The I.75-in. bars were forged to flat plates, 0.25 in. thick, from which specimens 0.5 in. wide by 2 in. long were cut. The specimens were pretreated to improve their homogeneity by heating to 1830°F. (I000°C.) for 20 min. and oil-quenching. They were then reheated to 1740°F. (950°C.) for one hour and air-cooled, after

Jan 1, 1942

By B. A. Cheadle, C. E. Ells

The ovienlalion of hexagonal a-zirconium crystals in cold-drawn Zircaloy-2 tubes and in both as-extruded and heat-treated Zr-2.5 wt pcl ND tubes has been rrleasured using the inverse Pole - figure technique. Uniaxial tensile tests hare shown the Zil-caloy-2 lubes to hare highly anisotropic delovmation behavior whereas heat-treated Zr-2.5 wt pet Nb tubes are nearly isotropic. The differences in deformation behavior are esbloilred from the observed textures of the tubes and the deformation systems known to oberate in Zircnloy,-3. Tlze vcsults lead to an explanation of the high effective strain observed fov the Zircaloy-2 tubes as colrzpared to heat-treated Zr-2.5 wt pet Nb tubes in restrained end burst tests at 280° to 300°C. THE Zr-2.5 wt pct Nb alloy. when heat-treated by quenching from temperatures slightly below the (a + p)/P phase boundary and subsequently aged at 500°C, has tensile strengths about 50 pct greater than those of 20 pct cold-worked Zircaloy-2.1 There is. therefore, considerable economic incentive to replace Zircaloy-2 with the heat-treated alloy in some in-reactor applications. notably for pressure tubes, where strength is a prime consideration. However, when tubes of Zr-2.5 wt pct Nb fabricated by extrusion and drawing prior to heat treatment were subjected to restrained end-burst tests at 300 °C. the circumferential expansion at failure1 was only 10 pct that of cold-drawn Zircaloy-2 tubes in similar tests,2 Table I. This result was not predicted from uniaxial tensile tests in which the ductilities of the two materials were quite similar.&apos; The detailed requirement for ductility in pressure vessels has not yet been worked out. and comparison of the relative merits of cold-worked Zircaloy-2 and heat-treated Zr-2.5 wt pct Nb is further complicated by the irradiation-induced loss of ductility and hydrogen pickup each will undergo from reactor operation.1,2 Nevertheless. the lower circumferential expansion of the Zr-2.5 wt pct Nb tubes raised serious doubts on the advisability of their use as pressure vessels. For this reason, an investigation to determine the cause for different ductilities of the two types of tubes was initiated. From a study of uniaxial tensile properties and crystallographic orientation it has been found that the fracture ductilities observed in the burst tests can be related directly to the crystallographic ori-

Jan 1, 1965

By AIME AIME

HONORARY COMMITTEE. HON. C. D. WALCOTT (Chairman.), Director U. S. Geological Surrey. HON. FREDERICK I. ALLEN, Commissioner of Patents. DR. FRANK BAKER, Superintendent National Zoological Park. MR. CHARLES A. BELL, President American Security and Trust Co. MAJOR JOHN BIDDLE, Engineer Commissioner of District of Columbia. ADMIRAL C. M. CHESTER, Superintendent U.S. Naval Observatory. GENERAL WILLIAM CROZIER, Chief of Ordnance, U. S. A. ADMIRAL GEORGE DEWEY, Admiral of the Navy. COLONEL CLARENCE R. EDWARDS, Chief Bureau. of Insular Affairs. MR. WILLIAM C. FOX, Director Bureau of American Republics. MR. CHARLES C. GLOVER, President The Riggs National Bank. GENERAL A. W. GREELY, Chief Signal Officer, U. S. A. MR. BERNARD R. GREEN, Superintendent Library Building. GEN. G. H. HARRIES, Vice-President Washington Electric Railway Co. HON. E. A. HITCHCOCK, Secretary of the Interior. COMMANDER H. M. HODGES, Chief Hydrographer, U. S. N. PROF. W. H. HOLMES, Chief Bureau of American. Ethnology. PROF. S. P. LANGLEY, Secretary Smithsonian Institution. GENERAL ALEXANDER MACKENZIE, Chief of Engineers, U. S. A. ADMIRAL N. E. MASON, Chief Bureau of Ordnance, U. S. HON. WM. M. MEREDITH, Director Bureau of Engraving and Printing. HON. V. H. METCALF, Secretary Department of Commerce and Labor. HON. WILLIS L. MOORE, Chief -U. S. Weather Bureau. HON. PAUL MORTON, Secretary of the Navy. MR. F. H. NEWELL, Chief Reclamation Service, U. S. Geological Survey. HON. S. N. D. NORTH, Director Census Office. CAPT. E. C. PENDLETON, Superintendent Naval Gun Factory. MR. GIFFORD PINCHOT, Chief Forester, Department of Agriculture. MR. HERBERT PUTNAM, Librarian of Congress. ADMIRAL CHAS. W. RAE, Chief Bureau of Steam Engineering, U. S. A: MR. RICHARD RATHBUN, Assistant Secretary Smithsonian. Institution. HON. W. T. RICHARDS, Commissioner General Land Office.

Jul 1, 1905

I HAVE previously shown you in the Fifth Book the process of making guns and gun carriages, together with other preparations and methods of moving them. If I now failed to show you more about them, it would be as if I had pointed out only the useless shadow of a thing, for I did not show the kinds and arrangement of their supplies or how the effects for which they are made are achieved. For these reasons I now wish to tell you, in addition to what I have already said, how saltpeter is made and the methods of refining it well; what it is and how without it guns and many effects of violent and artificial fires would have been discovered in vain. After this, I also wish to tell you the methods of compounding the powders for large and small guns, and finally how these are loaded and discharged. I also wish to tell you how mines are made, and fire tubes, [149v] fire pots, squibs, fireballs, rockets, shells, grapeshot, and other similar devices for shooting fire in order to bum ships, supplies, bridges, and ramparts, or, in offense, for firing on batteries. I also wish to teach you to make certain bronze balls for shooting, which carry fire and break in many pieces when they hit. For surely, besides being terrifying to the sight, they would be harmful to armies lined up in battle when they are fighting. Likewise, I wish, to enlighten you as to how artificial fires are made that last long and are difficult to extinguish. Since these are fine and useful things in wars, every captain and soldier should give them consideration and know how to use them when necessary. You will be pleased to have this information if for no other reason than that you can teach it to those who take delight in celebrating holidays with festivities and with fires.

Jan 1, 1942

By Henry R. Piehler

Continuous seven- and nine teen -filament close-packed silver-steel filamentary composites mere tested in tension. For purposes of comparison, the tensile behavior of the composite was predicted from the measured properties of the individual com-ponents. It was assumed that the axial strain is the same in both components and that the contribution of each component to the composite flow stress is proportional to its volume fraction. Good agreetnent was obtained between the observed and predicted tensile behavior. However, the composite elongation at fracture was about twice that observed when the individual steel wires were tested alone. Composites in which the filaments were widely spaced failed by the consecutive fracture of the filaments. In composites with closely spaced filaments, a composite instability preceded frachcre. These effects are explained in terms of a lateral restraint to the necking of the filaments which develops in the deforming composite. TWO-COMPONENT or composite materials are increasingly being developed and used as structural materials. Of all the composite geometries used, the filamentary configuration has proved to be the most successful. Polymer-bonded fiber-glas, the most common of the filamentary composites, has been investigated most extensively to date. One explanation of the behavior of fiberglas1 suggests that the load transfer between the glass fibers and the polymer matrix occurs primarily through friction. Bond separation between the fibers and the matrix is presumed to occur at very low stresses. Subsequently, only frictional bonding can provide for the transfer of load from the matrix to the fibers. The force normal to the fiber-matrix interface which gives rise to this friction is assumed to arise from the matrix shrinkage which occurs during solidification. The behavior of metallic filamentary-composite materials would be expected to differ from that of fiberglas in several significant aspects. Residual stresses resulting from differences in thermal contraction can be kept to a minimum by proper heat treatment. A strong wetted bond is formed between the two phases. In brazed joints,2 for example, the interphase bond is sufficiently strong that the weaker material will fail before separation occurs at the interface. Most metal filaments can undergo appreciable amounts of plastic deformation before failure. Failure by plastic instability or necking frequently occurs in metallic filaments, but not in glass fibers tested at room temperature. Differences between the behavior of fiberglas-polymer and metallic filamentary composites have indeed been observed in composites containing various types of metallic filaments in a silver matrix.3,4 At strains of the order of 10-2 pct, all the deformation was accommodated by the silver matrix. Hence, the strength of the composite depended only on the fiber concentration and not on the nature of the fiber. At higher strains, the strength of the composite increased when filaments with higher work-hardening rates were used. Surface slip line observations on a silver-mild steel composite that had been stretched 4 pct showed that an appreciable amount of deformation occurred in the filaments. Work on tungsten-copper filamentary composites5 has shown that the ultimate tensile strength for varying filament fractions followed a linear mixture rule. Assuming that the axial strains in both filaments and the matrix are equal, this linear mixture rule can be expressed as: The subscripts c, f, and m refer to the composite, filaments, and matrix, respectively. A and V are the area and volume fractions of each component. sc and of are the ultimate tensile strengths of the composite and the filaments. sm is the flow stress of matrix at a strain equal to the elongation at failure of the filaments. However, the tungsten filaments can undergo only a limited elongation before they fracture without an appreciable reduction in area. A composite containing more ductile filaments might indeed deviate from this linear mixture rule for the ultimate tensile strength, since filament failure by necking might be arrested by the matrix. SPECIMEN PREPARATION Specimens were prepared from 0.8 pct carbon steel piano wires of 0.015 in. initial diameter. The wires were given a thin nickel flash and a silver plate varying in thickness from 0.015 to 0.007 in., depending on the filament fraction desired. In order

Jan 1, 1965

By Peter A. Allen

INTRODUCTION Lac Minerals Ltd., a significant North American producer of gold and other metals for over three decades, recently completed the financing for its third discovery in an eight year period. From 1975 to 1982, three important gold deposits in Quebec and Ontario: namely Bousquet, Doyon and Hemlo, were located and tested by company geologists. When current development plans are complete, Lac will have injected $400 million into these deposits. A discussion of these projects and their financing reveals some extraordinary challenges faced by top mining management. Responses to these challenges developed by Lac management may interest executives planning to proceed with new North American gold or base metal mines. MINE DE BOUSQUET In 1976, we explored a property containing a large low grade surface gold deposit. The geologial setting was exciting and we tested recent rethinking about the volcanigenic genesis of gold and base metal occurrences. These ideas helped pus to persist in drilling a nearby conductor and 600,000 ton, 0.22 ounce/ton orebody was outlined. With gold at $Cdn.150 per ounce the feasibility was approved and work started February 1978. Availability of a company custom mill 35 miles away reduced our immediate capital needs to $8.5 million. First of all, understanding the geological significance of results at Bousquet was critical. Mine and surface exploration geologists at Lac are continually and closely working together to better understand the nature of gold deposits in the Shield. This management emphasis on both pure and mine geology meant that a much larger ore reserve could confidently be predicted. (A proposal to quickly develop and ship the ore to a nearby company mine was discarded.) Instead of designing just for the initial plan of 500 tons per day we therefore included headframe, shaft and hoisting capacity for 1,700 tons and provided a compartment for future shaft deepening. These prebuilt additions were welcomed within two years. The type of collaboration whereby surface and mine geologists make study and field projects of each other&apos;s problems sets the foundation for this predictive ability. At Lac, the traditional responsibility for and supervision of the mine geologist by the mine manager is modified by this collaboration. This adds interest and scope to the geologist&apos;s work and lets him think beyond production requirements. Besides such management considerations, dedicated, professional geologists with integrity and lots of practical experience are needed to plan successful developments like Bousquet. Second, projecting future bullion revenue was critical and our experience selling production for future delivery gave us a way to ensure that loan repayment at term would not be jeopardized by falling metal prices. Output from a single mine is often reduced or curtailed for numerous reasons, so "selling forward" is done best and with least risk by companies like Lac with more than one or two producing locations for that metal. At first, a forward marketing program was considered unwise, speculative and unorthodox by analysts and other producers. Declining markets in the early 1980s prolonged gold project capital recoveries however, and critics were better able to appreciate the usefulness of such a tool. The notion that gold miners shouldn&apos;t sell forward is rooted in the belief that long-run gold prices will rise as modern social theory implementation in democracies inevitably erodes currency values. Selling against this trend goes against this industry belief or "ethic" and is at odds with the company shareholder who expects the gold price to rise not fall. Nonetheless, an efficient tool is available to the gold producer (not to most other metal producers) to quickly disengage from adverse price trends or to lock in spot prices instantaneously for two years or more of profits. Gold had recently retreated from U.S.$200 to $104 and now had reversed to $150. Lac had been forced to close several of its producers during the late 1960s because central bank-controlled

Jan 1, 1985

By Reed W. Hyde

Some information has been published on the sulphur dioxide concentration of gases from D wight-Lloyd machines sintering lead ores but most of this relates to the customary practice in which the charge is relatively high in lead and is sintered in two passes Over the machine. It is thought, therefore, that the following observations on sintering in one pass a low-lead, low-sulphur charge may be of interest. The data were obtained in sintering lead sulphide notation concentrates mixed with minus 20.mesh oxide ore, the mixture carrying 16,8 per cent Pb and 5.3 per cent S. No returns were used because of the limited amount of sulphur available as fuel, but the mixture pelletized readily. to make a satisfactorily permeable bed on the sintering machine. As there was a possibility that the SO z might be utilized, a series of runs was made to determine the concentration ofSO2 in the gases at different points along the wind box, and the effect on this concentration of changes in the wind-box vacuum. Several runs each were made with vacuums (as measured in inches of water at the wind box) of (1 2 to 1 in., (&apos;1 4 to 3% in. and (3) 6 to 5% in. The averages of the determinations from each series are platted On the graph (Fig, 1). The vertical scale shows the percentage by volume of SOz (as determined by the Reich method), and the horizontal scale shows the time e~pressed as percentage of the total sintering time. Sintering was considered to be complete when no SOz could be detected in the gases. In all cases the depth of bed was 4 1/2 in. and the weight of dry charge per square foot of hearth area was 45.2 lb. Other data are given in the table. The volume of gases corresponding to the several points along the wind box at which SO2 determinations were made could not be measured, but has been calculated from the SO2 Content and sulphur elimination on the assumption that the volume is uniform throughout the sintering period. This is not strictly true, as with a given vacuum the volume usually will drop slightly toward the middle of the period and increase toward the end. However, this made is a reasonable approximation. several interesting features are brought out by these data. In general, the published data on SO 2 concentration in sintering under ordinary conditions show a high SO2 concentration in the early stages followed by a rapid decrease in concentration and with relatively little SOz in the gases from the last half or third of the operation. In other words, the greater part of the sulphur elimination is obtained in the first third or half of the period. In these runs, the 6-in. vacuum, which approximates the usual operating condition, gives a curve that follows this customary pattern. Maximum SO2 concentration is obtained 234 min. after

Jan 1, 1944

The Institute maintains a dual relationship with students: (1) an individual relationship with a Student Associate; and (2) a relationship with local organizations of students, known as Affiliated Student Societies or Student Chapters. 1. The conditions of Student Associateship are set forth in Section 9, Article I, of the Bylaws of the Institute (see page 62 and following pages). During 1934, sundry amendments were made for the purpose of improving the student relationship. Postgraduate students are now eligible; and associateship can be maintained, with the payment of the regular dues of $2 per year, for 18 months following graduation in June. With his regular dues, each Student Associate is entitled to receive during the year his choice of MINING AND METALLURGY, METALS TECHNOLOGY, MINING TECHNOLOGY, PETROLEUM TECHNOLOGY, or two "classes" of Technical

Jan 1, 1942

A. E. Hunt, Pittsburgh, Pa : I have heard these papers read with a great deal of pleasure. I am particularly interested, in a financial way, in the bauxites as ores of aluminum, and it is safe to prophesy that there will be many more mining engineers in the future who will be interested in these ores of aluminum, in the same way as many are

Jan 1, 1895

By G. C. Wallick

Since the appearance of the paper, "Solution of the Equations of Un-steady State Two-Phase Flow in Oil Reservoirs," by W. J. West, W. W. Garvin, and J. W. Sheldon,&apos; a two-fold investigation of this subject has been carried out. One objective of the investigation has been to deter-mine the feasibility of solving such problems 7on a medium-size com-puter such as the Datatron*, and the other objective has been to in-vestigate the application of such cal-culations to experimental and theo-retical petroleum reservoir research. In the first Datatron calculations, the fluid and rock properties published by West, et al, were used, together with the published equations describ-ing the system. Details of the formu-lation not given in the original paper are discussed in the Appendix to this note. Reference should be made to the subject paper for the complete equations and defintion of symbols. An unexpected result of this in-vestigation was the discovery that the linear solution published by West was in error. Thus, in addition to describing the Datatron solutions and to discussing certain numerical diffi-culties which will be encountered if one uses the published method of solution, the purpose of this note is to indicate the nature of this error. LINEAR FLOW Since the linear case requires a minimum amount of scaling, a fixed-decimal point Datatron program was written for the one-dimensional flow problem and an attempt was made to duplicate the solution described by West. In the case described, fluid was produced at a constant rate, Q, until such time as well pressure reached 0.04. Production was then continued at constant pressure. From the constants and curves given by West it was determined that the ini-tial constant production rate could be approximated by Q = 0.007. An ini-tial dimensionless time step ?t = 0.434 X 10 - "as used, and each suc-cessive time step was doubled until a value of = 0.444 was reached. This constant interval was then used for the remainder of the solution. In subsequent solutions, several varia-tions in the time schedule were em-ployed, including smaller time steps and slower rates of increase in the time steps. In all cases, almost identical results were obtained regardless of the time schedule employed. However, as described below, it was noted that the time schedule had some influence on the rate of convergence of the solutions. As a check on the accuracy of the solution, the cumulative production at each time step was calculated using the two methods described in the Appendix. Satisfactory agreement was observed with the differences in these two values of the order of two parts in 50,000. It should be noted that the mass balance check as described is of questionable value, particularly with regard to the well pressure and saturation. This is especially true in the radial solution where pressure and saturation values near the wellbore would make only a negligible contribution to the numer-ical integration. It is believed, how-ever, that such a comparison is ot value in determining the over-all accuracy of a solution. In comparing the Datatron solu-tion with that published by West it was discovered that in the later stages of depletion, the pressures near the well declined more rapidly in our solution than in the West solution, and that the limiting well pressure of 0.04 was reached at an earlier time than that originally reported. It thus became evident that it would be impossible to duplicate the production schedule described by West and a constant rate of production was maintained until the well pressure was equal to 0.0. A representative comparison of the results published by West with those obtained in this investigation is shown in Fig. 1, which is a plot of GOR as a function of cumulative recovery. These two curves should be in agreement until a cumulative recovery is reached which corresponds to a well pressure of 0.04 — for the Datatron solution, a recovery of approximately 5.6 per cent. Actually, a major disagreement is evident. Subsequent correspondence

Jan 1, 1958