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By C. S. Matthews, P. Hazebroek, F. Brons

A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well's production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained. To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log[?t/(t + ?t)], where At is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume). INTRODUCTION It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. 'The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir — that is, a reservoir with no water drive. In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a con- stant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties. One method which has been used in the past for obtaining an "average" pressure involves the extrapolation to infinite closed-in time of curves of pressure as a function of closed-in time. Contour maps of these extrapolated pressures are used in arriving at an average pressure. In some cases wells are shut in for arbitrary Lengths of time, and contours of these arbitrary shut-in pressures are used for calculation. All these methods are somewhat arbitrary and suffer from lack of fundamental theoretical basis. For example, no precise meaning can be given either to the extrapolated or to the arbitrary shut-in pressure. Furthermore, there seems to be no reason why either set of pressures should be contourable. It was because of the vagueness of these old methods and their lack of a sound theoretical basis that, the present method for determining average reservoir pressure was developed. SYMBOLS A = drainage area of a well, cm' A, = drainage area of well j, cm2 A , = total drainage area of all wells in a reservoir, cm2 c = coefficient of compressibility of fluid at reservoir temperature, atm-1 f = hydrocarbin-filled porosity, fraction h = net thickness of formation, cm k = permeability of formation, darcy p = pressure at a well, atm p0 = initial reservoir pressure, atm p* = pressure obtained by straight-line extrapolation of linear portion of plot of p versus log [At/(t+ At)] p = volumetric average pressure inside drainage volume of a well q = volume flow rate at a well, cc/sec a: prevailing reservoir conditions q, = total volumetric flow rate from a reservoir, cc/sec at prevailing reservoir conditions rw = radius of well bore, cm T = kt/fµcA t = corrected time of production of a well, seconds, defined by

Jan 1, 1955

TO THE BOARD OF DIRECTORS OF AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS Gentlemen:-I have the honor to present the following, report for the calendar year 1920. The activities which seem to call for special comment are: THE NEW FORM OF MAGAZINE MINING AND METALLURGY appeared every month during the calendar year and has been developed until it contains some ten departments. It has brought forth more commendatory letters than have been received at headquarters on any other subject throughout the year. Less than a dozen letters unfavorable to the change have been received, and the indications are that the magazine has met a want deeply felt, especially by members distant from headquarters. The technical papers printed by the Institute are published in abstract in the magazine and opportunity is given to members who desire them to receive full copies of any or all papers published. The Bound Volumes, as usual, contain all the papers in full and discussions thereof. FINANCES The greatly increased cost of paper and printing has put a tremendous burden on the Institute's finances, since the dues of $12 per year are only 20 per cent. greater than the members paid when the Institute was founded forty-nine years ago. This has resulted in a temporary deficit, similar to that encountered by many of our sister engineering societies. The fact that our Institute has lower dues and gives more in the way of publications to its members than any other of the national engineering societies has rendered the situation more difficult for us. MEETINGS The Annual Meeting in New York, the Field Meeting in the Lake Superior District, the meeting of the Petroleum and Gas members at St. Louis, and of the Institute of Metals Division in Columbus, Ohio, have all been described in full in the magazine.

Jan 1, 1925

By Roger M. Zimmerman

The G-Tunnel heated block experiment is being conducted on the Nevada Test Site (NTS) as part of the Nevada Nuclear Waste Storage Investigations project (NNWSI). The purpose of the ambient temperature testing ph se is to evaluate rock-mass mechanical properties of a block (- 8 m3) under biaxial stress changes up to 7.5 MPa above an initialization in situ value of 3.1 MPa. Results indicate that the modulus of deformation ranges from 9.7 to 17.0 GPa and Poisson's ratio ranges from 0.21 to 0.33. In general, the higher values of the modulus and Poisson' s ratio were influenced by fracture propagations parallel to the compressive stress field. Other measurements indicated that cross-hole compression (p) wave velocities and single fracture permeability values were relatively insensitive to stress changes above the in situ value.

Jan 1, 1984

By AIME AIME

THE 130th Meeting of the Institute was held in Birmingham on Oct. 13 to 15, with visits to other mines and districts before and after. The last visit of the Institute to Birmingham was made in 1888, thirty-six years ago, and vast development has been made in' the district since then. With proverbial southern hospitality compounding over this period of years the welcome given to the Institute was such that .it is difficult to express properly the gratification and appreciation of the visiting members and the officers of the Institute. The Birmingham News in an editorial said: Birmingham is duly appreciative of the presence of these gentlemen, not because they are all distinguished in their great services in the mining and metallurgical world, but for the further reason that our interests are very largely wrapped up in their deliberations. Birmingham is one of the great industrial centers of America. Their discussions are of vital concern to all of us.

Jan 1, 1924

After a three-year period characterized by inflation, recession, depressed metal prices, lack of demand, enormous world inventories, and rapidly escalating costs, the Canadian mining industry is showing welcome signs of recovery. A rise in world metal prices and particularly strong demand for gold, uranium, and coal have stimulated the industry in early 1979. In this atmosphere of growing optimism, over 3000 mineral industry executives, economists, geologists, and mining and metallurgical engineers convened in Montreal, April 26-29, for Canada's largest mining convention, the Annual General Meeting of the Canadian Institute of Mining and Metallurgy.

Jan 6, 1979

August 10 to 14, 1914, inclusive Headquarters will be at the Hotel Utah. The following program of the meeting has been arranged y the Local Committees: Monday, August 10.-Members and guests will register at the Secretary's desk in Room C-38, Hotel Utah, and receive the official badges, booklets and programs of the meeting. At 2:30 P. M., there will be an organ recital at the Mormon Tabernacle, after which members and guests will be taken for a trip around Salt Lake City in sight-seeing motor cars. At 8:30 P. M., the ladies will assemble in the lobby of the Hotel Utah, where they will be met by the members of the Ladies' Entertainment Committee, and will be taken for an automobile drive about the city. At 8:30 P. M., a technical session will be held in the ballroom of the Hotel Utah. The following papers will be presented: F. W. BACORN: An Amendment to Sales's Theory of Ore Deposition. C. W. GOODALE: Drumlummon Mine, Marysville, Mont. I. B. JORALEMON: The Ajo Copper-Mining District. STUART CROASDALE: Leaching Experiments on the Ajo Ore. FRANK R. VAN HORN: The Occurrence of Bournonite, Jamesonite, and Calamine at Park City. HOWLAND BANCROFT: Dip Chart. M. N. ALLING: Ancient Auriferous Gravel Channels of Sierra County, California. B. S. BUTLER AND H. D. MCCASKEY: Copper Ores of the New London Mine. GEORGE A. PACKARD: Rope Idlers in the Raven Shaft. ARTHUR CROWFOOT: Development of the Round Table at Great Falls. FREDERICK LAIST AND A. E. WIGGIN: The Slime-Concentrating Plant at Anaconda. W, L, AUSTIN: The Treatment of Copper Ore by Leaching Methods. W. L. AUSTIN: Leaching Copper Products at the Steptoe Works.

Jan 8, 1914

By Blandford C. Burgess

Mica is an orchid among minerals. It is formed in pegmatites, one of the most bizarre of igneous formations, and is exceeded by few other minerals in the perfection it may attain as to size, color, and cleavage. First used for window glazing, as an ornament and article of trade, it has become one of the most essential insulators of electricity, heat, and shock. Most internal combustion engines use mica condensers or capacitors and such machines of war as planes, tanks, and submarines are immobile without it. The original manuscript of this guide was written in April 1943 at the peak of war emergency. It was not used be- cause shortly thereafter a decision was made to buy on a one price basis eliminating differentials for both quality and size. This is now presented with the thought that from the standpoint of preparedness we can only consider an- other war imminent and every effort should he made to set up in usable form the experience gained during the Second World War. Colonial Mica Corp. was set up by Metals Reserve Co. as a wholly owned government agency to encourage production of domestic mica and to purchase it. It soon became the exclusive buying agency for such mica. The writer as Southern Manager called on all the private agencies buying mica to assist in formulating buying policies, methods, and prices.

Jan 1, 1949

Jan 1, 1881

By R. D. Pehke, J. F. Elliott

The solubility of nitrogen in liquid pure iron has been measured as a function of pressure and temperature. Sieverts' Law is obeyed at all pressures up to 1 atm and the temperature coefficient of solubility is 8 x 106 %/°C. The solubility of nitrogen in liquid iron alloys has been studied by the Sieverts' method and by the sampling method. The solubility is decreased by Al, C, Co Cu, Ni, 0. Si atzd Sn, and it is increased by Cr, Cb, Mn, Mo, Ta, W, and V. Interaction coefficients eN, for the effect of these elements on nitrogen dissolved in liquid iron, are reported. 1 HE effect of nitrogen upon the properties of steel may be desirable or not, depending upon the composition, processing treatment, and the use of the product. To understand the behavior of nitrogen in the various steelmaking processes, it is necessary to have reliable fundamental data pertaining to the solubilities, rates of solution, and chemical reactions of nitrogen in steel, particularly in the liquid state. In an effort to extend our knowledge in these areas, an investigation of the thermodynamics and kinetics of the solubility of nitrogen in liquid iron alloys was undertaken. The thermodynamic aspects of the study are presented in this paper. The solubility of nitrogen in liquid pure iron has received the attention of several investigators whose results are summarized in Table I. Reasonable agreement among the more recent researches1-l8 is found for the solubility of approximately 0.044 wt pct at 1600°C and 1-atm pressure of N,, for the temperature coefficient of solubility being small but positive, and for adherence to Sieverts' law for pressures up to 1 atm. The solubility of nitrogen in a number of binary liquid iron alloys has been studied: Fe-A1,3 Fe-As,16 Fe-C,3, 71 18, 19, 20 Fe-Cr ,5,7, 10, 11, 15 21 Fe-Co,'4, '6 Fe-Cu,'6 Fe-Mn,10, 11, 18 Fe-Mo,13, 16 Fe-Ni,10, 11, 13, 15, 16 Fe-O,16, 17, l9 Fe-p,7 Fe-S,l6 Fe-Sb,16 Fe-Se,lg Fe-Si,4) 97 '77 187 19>2° Fe-Sn,16 and Fe-v.51 '3 A few ternary systems have been studied, most of which were reviewed by ~angenberg" who applied the methods suggested by WagnerPz3 Chipman,24 Darken and G~rry, and Morris and Buehl26 for predicting solubilities in multicomponent alloys. Langenberg22 and Humbert and Elliott15 compared the solubilities computed from simple binary alloy systems with experimental measurements of nitrogen solubilities in liquid iron containing two or more alloying elements. The interaction coefficients for nitrogen in

Jan 1, 1961

By C. M. EYE

IN the spring of 1905 I was employed by Messrs. Bradley and Requa, under our fellow member, Thomas Cox, on the mill plans for the Nevada Consolidated, when an opportunity came to go to the Philippines to erect a small mill on the property of the Benguet Consolidated. This I accepted, expecting to be away eight months or so, but it was seven years before I got back. .I sailed in May, on the Coptic, having as room-mate as far as Kobe, A. E. Drucker, who was going out to Korea for the Oriental Consolidated. It was the first trans-ocean trip for either of us, and we had some rather unusual experiences. This was toward the close of the Russo-Japanese war and the Russian fleet was known to be on the way from Suez to Asiatic waters, but it was a matter of doubt whether they would risk a passage between Japan and the mainland, or take the longer but obviously safer route outside of Japan. The Coptic carried much contraband of war for Japan, so naturally did not care to meet this fleet. No definite word being available at Honolulu, we went to the Midway Islands, but the cable station there had very little information to offer, so we proceeded cautiously toward Japan. On the last afternoon out, we steamed due north at half speed for several hours, and finally sneaked into Yokohama at night, to learn that ' the Russian fleet had met the Japanese the day before and had been annihilated. We sailed over the spot in the Sea of Japan a week later, and when we got to Manila we found three of the Russian boats interned and being guarded by the monitor Monadnock and a cruiser. This was only a matter of form, as the Russians were only too glad to be there for the rest of the war, and the boats could not have gone far anyway, for they were literally shot to pieces. The Admiral's flagship had a hole within 3 ft. of the water line, for ward, through which a man could enter by stooping.

Jan 1, 1929

By F. E. Bedale

STUDY of several severe mine explosions that occurred during the winter of 1907 led to the belief that coal dust was a definite explosion hazard. The Consolidation Coal Co. was a pioneer in the early work to' eliminate this hazard and to combat the dangers incident to poor ventilation and the presence of methane. Maintenance of high humidity throughout the mines was one of the first measures adopted, later to be superseded by rock-dusting. In the twenty years from 1907 on, many safety measures were developed and adopted, and several prizes were won, though the practice was crude by present-day standards. But in 1927, the company went to work in earnest, and organized a Department of Safety with adequate personnel and with authority to enforce all approved rules for the prevention of accidents and the preservation of company property. All plans for new construction work, changes in mining systems, and proposals for the purchase of new mining equipment had to receive the approval of this Department. A set of operating- and safety standards was written to govern the activities of all employees, and physical examinations for them were required.

Jan 1, 1938

By David Sinclair, Philip B. Bucky

THE dimensions and shapes of mine structures may at present be determined by (1) field experience, (2) structural calculations, and (3) barodynamic tests.§ None of these, however, provide information as to the stresses, their direction and distribution in a mine structure. For the design of pillars, the placing of openings relative to working places such as gangways, haulage levels, etc., this information is desirable. Photoelastic methods provide this and, while relatively new, their application in all engineering fields is assuming increasing importance. This paper, therefore, will present the method with a few applications to mining, and with sufficient reference for further study by the reader. PART I THE PHOTOELASTIC METHOD The photoelastic method of stress measurement determines the stress distribution in a two-dimensional model by optical means. It makes use of the fact that when a piece of isotropic transparent material, such as glass, celluloid, or Bakelite, is stressed and viewed in polarized** light a picture is seen which indicates by its color bands of light, or fringes, the magnitude of the stresses, their direction and their distribution. GENERAL EXPLANATION The stress at any point 0 in a structure (Fig. 1), may be resolved into two components, P and Q, each a pure tension or compression, at right angles to each other, called principal stresses.1 To fully identify the stress, the values of P and Q and their directions or angle [0] must be known.

Jan 1, 1940

By Chikao Nishiwaki

INTRODUCTION The Japanese dependency for mineral raw materials from foreign sources increased rapidly within the 20 years since the Korean war. During this 20 year period Japan has attempted to industrialize and develop her economy while depending mostly on heavy import of nearly all kinds of mineral raw materials. She has fabricated them using energy generated mostly by mineral fuel that are also imported. Fabricated goods are either used domestically to accelerate more fabrication industry or exported after adding more refinement or fabrication. In this paper iron ore as a major raw material for the Iron and Steel industry, three major base metals, copper, zinc and lead, and petroleum as a major energy source have been selected as examples to represent the general features of various kinds of mineral raw materials that are imported. Among other important mineral commodities for which Japan dependa upon foreign sources are: Aluminium, nickel and cobalt, potash and phosphorous 100 percent dependent and tin, tungusten, chromium and molybdenum over 95 percent dependent. IRON ORE Statistics for the important iron and steel raw materials, namely iron ore, coal and scrap iron are shown in Tables 1, 2 and Fig. 1. Iron ore is by far the most important and basic among these three commodities. There has been practically no steel or iron imported as a metal into Japan during this period. Iron ore, including aggregate such as pellets, and metallurgical coal are mostly transported in large ore cargo boats to the port where very efficient port facilities unload them directly at the steel mill site. As a result

Jan 1, 1976

By O. G. Lellep

IN every country economic circumstances prescribe the method used to produce a commodity at lowest cost. In Pennsylvania a man's wages for working 4 hr buys a ton of coal wholesale; in Germany a laborer must work 40 hr, or ten times as long. In western Europe, therefore, conservation of fuel is of primary importance, and recent practices of burning lime and cement differ from those employed in the United States. This paper presents data collected during a trip through western Europe in 1953. Considered uneconomical, shaft kilns for burning cement disappeared in the United States two generations ago. But because required capital investment is low and operation greatly improved, shaft kilns are still used to some extent in Europe, where fuel costs are high, and are even included in designs for plants under construction. During the last 50 years shaft kilns have been maintained at the same physical size, while their output has been increased at least four times.

Jan 7, 1954

By Charles B. Henderson

DESPITE the loss, by enemy conquest, of a high percentage of our normal sources of supply for tin, the position of this important metal is easier today than that of rubber and a long list of other strategic materials, many of which are produced in this country. Actually, there is no shortage of tin for essential war purposes, owing to a strict control of its use, to increasing considerably the amount of secondary tin available, and to the foresight of the Government in authorizing the Reconstruction Finance Corp., as early as June, 1940, to acquire and produce certain critical and strategic materials of which tin was one of the most important. The construction of the Longhorn Smelter on the Gulf Coast in Texas is an important part of this program.

Jan 1, 1943

By Persifor Frazer

CONTENTS. PAGE 1. Committee House of Commons Report (1843).......521 2. Clark (1880).............521 3. Schröder and Schertel (1884).... . 521 4. Committee House of Lords Report (1887).......523 5. Vita (1890).............524 6. Irvine (1890-1)............524 i. Cramer (1891)............525 8. Bailey. Cohen. Tatham and Hartog (1891))......525 9. Morrison (1891)............525 10. Brunner (1891)............525 11. Bell (1892).............585 12. Oades (1892).............526 12a. Purcell (1892)............526 13. Sennett (1892)............526 14. Bulier (1892).............526 1.7. Wiesner (1892))...........526 16. Thomson (1892)............530 17. Fletcher (1892)............530 18. Committee Engineers' Club Report (1892).......530 19. Cohen and Hefford (1892)..........531 20. Discussion Soc. Chem. Ind. (1893). ..532 21. Reuss (1893).............532 22. Thomson (1894—5) ...........535 23. Clowes and Feilmann (1895). ...536 24. Callan (1895)...........536 2.5. Wright (1895)............536 25A. Mabery (1895)............536 26. Re- (1896). ..........536 27. Herman (1896)............ 537 28. Cohen and Russell (1896).......... 537 29. Dennstedt and A hrens (1896). ..537 30. Cohen (1897). ...........537 31. Drehschmidt (1897)........... 538 32. Pfeiffer (1898). .........538 33. Fritzche (1898)............ 540 34. Ost and Wehmer (1899)........... 540 35. Donkin (1899). .........541 36. Beilby (1899)............. 643 37. Berthelot (1900)............ 544

Jan 1, 1908

By AIME AIME

AMERICAN participation in the World Engineering Congress in Japan will be generous. Nearly seventy papers have been prepared and for- warded for printing and the A. I. M. E. is well represented in the list. At our San Francisco meeting four of these will be briefly reviewed by the authors for the benefit of those who are unable to go on to Tokyo. They constitute a group dealing with the present economic status as seen by engineers of the world's iron, coal, petroleum and non-ferrous metals. Messrs. Leith, Smith and Tryon, Requa, and Probert have written papers that constitute a notable series. Messrs. Jeffries, Sweetser and Kinney, and other Institute members have written papers dealing more closely with technologic progress. The latest list of delegates and members is printed below, names of A. I. M. E. members being set in italics.

Jan 1, 1929

By K. D. Jacob

MONTANA Phosphate Produucts Co., a subsidiary of The Consolidated Mining and Smelting Co. of Canada Ltd., operates three properties near Garrison, Mont., known as the Anderson, Graveley, and Luke mines. All three are underground operations, mining the same narrow bed at points several miles apart. The Anderson, the oldest and largest of the three, has produced about 700,000 long tons since 1929. The Graveley has produced slightly over 100,000 long tons since 1940, and the Luke, acquired in 1943, is still in an early stage of development. The great bulk of the output has been shipped to the Trail, B. C., plant of Consolidated Mining and Smelting Co. for use in the manufacture of fertilizers. The phosphate seam is the basal member of the Permian Phosphoria formation. In all three mines it has a uniform thickness of 3 to 4 ft. of oulitic phosphate, with a few shaly partings. The overlying part of the formation comprises about 50 ft. of chert and the immediate footwall consists of a few feet of shale and sandstone. underlain by the Quadrant quartzite.

Jan 1, 1944

By Robert J. Ramsey, Robert D. Jeppson

Introduction The Utah Copper Division of Kennecott Copper Corporation will present its contribution to the A. M. Gaudin Flotation Symposium in four parts. The first two segments will discuss briefly the historical development of the Utah Copper Division and describe the ore body. The third segment will review the facilities and operating procedures for the Utah Copper division's newest plant, the Bonneville Concentrator. The fourth segment describes flotation process circuitry, including molybdenite recovery procedures, at the Arthur and Magna concentrators. (The Bonneville concentrator is a crushing and grinding unit and does not have its own flotation plant). I. Historical Development Progress through change has been the key to the successful operation of the Utah Copper Division for more than 70 years. As the original low-grade copper operation, the pressures to remain competitive and profitable have dictated the timing and extent of each change. Much of the change has occurred through technological and economic advancements in the area of ore concentration. The Utah Copper Division of Kennecott Copper Corporation had its origin June 4, 1903, when the Utah Copper Company was organized. The initial mill of 300 tpd (tons per day) capacity was built at Copperton a few miles below the present Bingham Canyon mine site. From 1904 to 1910, the Copperton mill was expanded to a capacity of 1,000 tpd, and all of the known apparatus for gravity concentration were evaluated.

Jan 1, 1976

By Robert H. Richards

(Pittsburg Meeting, March, 1910.) 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 way 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 recrushing as the only means of severing the values from the waste. This last case is the only one requiring special treatment at our hands. We will therefore consider that next. * By mutual consent, this paper has been presented also before the Colorado Scientific Society, and the Canadian Mining Institute, Montreal.

Feb 1, 1911