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By Albert S. Trube

The purpose of this paper is to clarify the definition of compressibility and to present a uniform basis upon which instantaneous compressibilities of liquids and gases can be compared. The equations gaverning the instantaneous compressibilities of imperfect gases are derived and the concept of pseudo-reduced compressibility is introduced. Part of the data presented by Brown, Katz et a1 on compressibility factors for natural gases has been rearranged. A graph of pseudo-reduced compressibility vs pseudo-reduced pressure for various pseudo-reduced temperatures is presented. The need for additional work in relating the compressibilities of liquids and gases is discussed. This information should be of value to reservoir engineers in making non-steady state performance calculations in gas reservoirs. It should be of further use irz pointing the direction for additional research in the nature of liquid and gas compressibilities. INTRODUCTION With the increasing use of steady and non-steady state well and reservoir data, there is a corresponding increase in the importance of the various factors entering into such calculations. Increasing emphasis is being placed on the necessity for obtaining reasonably accurate estimates of the physical properties of the reservoir fluids well in advance of the more accurate laboratory data. One such factor is the isothermal coefficient of expansion of the media which are transmitting and attenuating the non-steady state pressure waves. The average isothermal coefficient of expansion, or "compressibility" is a complex function controlled by the physical properties of the formation and the fluids contained therein. The isothermal expansion coefficients for reservoir gases are usually quite variable, in many cases being highly-pressure sensitive. The coefficients for reservoir liquids tend to be pressure sensitive, but not nearly so much as reservoir gases. The coefficients for solids, usually expressed in terms of a "modulus of elasticity" are relatively insensitive to pressure variations within their elastic limits. For this reason, and also because many previous applications have been limited to rel- atively small pressure ranges, there has been a tendency to ignore the variable nature of isothermal expansion coefficients and treat them as constants. Also, the term "compressibility" by which these coefficients are generally designated is commonly confused with a similar term, z, used to define the deviation of an imperfect natural gas from the perfect gas laws. A clear distinction should be made at the outset between the term "compressibility", which is an isothermal coefficient of expansion of a substance, and the term "compressibility factor", z, which refers to the deviation of a gas from the perfect gas laws. Although the scope of this paper is limited to the compressibility of single phase natural gases, it is definitely related to the problem of accurately estimating the compressibilities of single phase hydrocarbon reservoir liquids, which will form the basis of a future presentation. BASIC PRINCIPLES The coefficient of isothermal compressibility of a substance, c, is usually determined from pressure-volume or pressure-length -measurements depending upon whether the substance is single phase gas, liquid, or solid. A convenient method for making such estimates for a finite change in pressure and volume at constant temperature is to use the well known equation V1-V2/V1 (p2 - p1) .....(1) Eq. 1 is negative because the volume of a confined substance decreases as the pressure is increased. In this case V1 > V2 and p2 > p1. This equation is useful in approximating the compressibilities of single phase gases and liquids undergoing small pressure changes. It is evident, however, that this equation is almost identical with the determination of Young's modulus of elasticity for solids. If the assumption is made that change in length is directly proportional to change in volume, as would very nearly be the case for a steel rod in tension within its elastic limit, then E5=-L1 (p2 - p1)/L1 - L2 .......(2) in which E. is the isothermal expansion coefficient, or Young's modulus of elasticity, for a solid. And further, for this special case L1 (p2 - p1)/L1 - L2 .......(3)

Jan 1, 1958

By A. O. Drysdale

In Canada, the market for cement is not a national one but rather a collection of local or regional markets. Excess capacity on a national basis does not necessarily preclude a shortage on a regional basis. with portland cement selling for less than a cent a pound, the low price-to-weight factor makes transportation to the market a major cost item and thus a small plant can be justified to serve a limited regional market. The Brookfield plant of the Canada Cement Co. is designed to supply the Province of Nova Scotia, a regional market that shows promise of growing to a point where it will support a one-kiln plant. The market is presently being served by boat shipments from the Canada Cement Co. plant at Montreal East, Quebec, and from the North Star Cement Ltd. plant at Corner Brook, Newfoundland, and by rail and road shipments from the Canada Cement Co. plant at Havelock, N. B.

Jan 4, 1965

By M. R. Geer, J. D. Davis, H. F. Yancey

ALTHOUGH the mechanical cleaning of coal is carried out at plants on the surface, preparation is actually begun at the face in the mine. Here the character of the coal and the amount, character, and distribution of the impurities within the bed may be seen. Blasting methods, dust-allaying procedures, location of mining cut with respect to bands of impurity, and the practice of discarding segregated impurities underground, all have an important bearing on the successful operation of surface cleaning units. The most important single characteristic of both coal and its associated impurities from the standpoint of cleaning is specific gravity. Other characteristics related in one way or another to the preparation of coal are rank, petrographic composition, structure and hardness, and friability. These and still other coal properties are discussed in the first section of this chapter and impurity characteristics in the second. COAL CHARACTERISTICS RELATED TO PREPARATION Rank As a result of work done over a period of several years by committees of the American Society for Testing Materials and the American Standards Association, standard specifications are now available showing the classification of coals according to rank and quality of grade. The term "rank" expresses the degree to which the original coal-forming material has been changed by metamorphism through successive stages from peat to anthracite. Table 1 shows the classification of coals according to rank as devised by the committees of the organizations mentioned. The basic scheme of classification for the higher-rank coals is according to fixed carbon content, calculated to the dry, mineral-matter-free basis. Groups of lower rank are divided

Jan 1, 1950

By Tenney, J. B.

DEVELOPMENT of complex ores in the south- western part of the Rocky Mountain region has been retarded by the prohibitive distance to the nearest suitable zinc treatment plants. In the north- western and central Rocky Mountains the building, cluring tlie past decade, of electrolytic zinc plants at Anaconda, Great Falls, Trail, and Burke has tremendously stimulated the mining and exploiting of such .ores, greatly increasing the production of lead, zinc, copper, gold, and silver. Selective flotation permits the making of high-grade led, copper, and zinc concentrates. If the zinc concentrates could be made free from lead, copper, gold, and silver, they could be shipped economically to Mid- Western retort plants designed for such concentrates. Unfortunately a considerable proportion of the precious metal content accompanies the zinc blende in the ores of this region. Although some of it is saved in 'retort residues, the treatment cost is thereby increased so materially and the proportion saved so small, that .concentrates of ordinary grade cannot stand treatment charges and freight.

Sep 1, 1928

By T. R. Armstrong

Total crude oil production in Mexico in the year 1941 is estimated at approxi- mately 41,000,000 bbl.; a daily average of 112,700 bbl. and a decrease of about 5 per cent as compared with the daily average of 120,000 bbl. produced in the year 1940, and nearly 11 per cent decrease as com-

Jan 1, 1942

By T. R. Armstrong

Total crude oil production in Mexico in the year 1941 is estimated at approxi- mately 41,000,000 bbl.; a daily average of 112,700 bbl. and a decrease of about 5 per cent as compared with the daily average of 120,000 bbl. produced in the year 1940, and nearly 11 per cent decrease as com-

Jan 1, 1942

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Jan 1, 1938

Jan 1, 1885

By E. J. MCOAUSTLAND

THE behavior of steel after overstrain and at moderate temperatures is fairly well known. It has been made the subject of much investigation, and our knowledge is clear and definite on many points. The ultimate raising of the elastic limit, after moderate overstrain, and the consequent lowering of the ductility, seem to be well established. It is also well understood that the immediate effect of overstrain is to lower the elastic limit, possibly to zero, but that if not interfered with, this limit will subsequently rise higher than before. The "tests after moderate temperature," reported in this paper, were undertaken to verify the above statements for the particular steel under investigation, and also to determine, if possible, the total time required for complete recovery from this state of overstrain. The behavior of overstrained steel at temperatures at or below 32° F. is not so well known. Tests made by Prof E. G. Coker, at McGill University,' show that steel, overstrained and subjected to cold, will remain in a state of overstrain for an indefinite period. I am not aware of any other published results of tests along this particular line. The effect of time and temperature on the recovery of steel from overstrain was made in 1902-3 the subject of sortie investigation in the laboratories of the College of Civil Engineering of Cornell University. A general plan was outlined in connection with the regular courses of instruction in testing of materials; but the press of routine work and the demands of the schedules on the time of the students were so great as to presage long delay in the completion of the work. Not much had been accomplished up to 1904-05, when Messrs. E. C.

May 1, 1906

By R. V. Wheeler, F. V. Tideswell

The suggestion, which appears to find increasing favor, that the elementary composition of coals should be used as the basis of their classification, makes it important that our methods of expressing this elementary composition should be refined. It is doubtful whether many published ultimate analyses of coals are accurate within 1 per cent. carbon. Many are probably as much as 3 or 2 per cent. in error in carbon. It is, perhaps, not always realized that the extreme variation in carbon content over the range of bituminous coals is but 16 per cent. An error of 1 per cent. in carbon on analysis corresponds therefore with one-sixteenth of the whole range, an amount which is unjustifiable even for the application to commercial needs of a system of classification based on ultimate analysis. For the purposes of scientific research such limited accuracy is of little value. The object of this paper is to examine one important source of error in ultimate analysis, that due to the occurrence in coal of inorganic material, and to emphasize the need for the quantitative measurements (of carbon more particularly) on coals to be rendered independent of their contents of such material. Adventitious Mineral Matter When a determination of calorific value, for example, is made upon a coal, it is customary to correct the measured value with respect to the ash left by the coal on incineration, recording the result as being on an "ash-free basis." It is desirable, before discussing the adequacy of the correction thus made, to demonstrate its validity, which turns on whether the ash is present as an adventitious impurity in the coal and forms no part of the coal substance itself. The inorganic matter associated with coal has originated in several ways1: 1. The "inherent" inorganic materials, occurring as constituents of the plants from which the coal-forming deposits were derived.

Jan 1, 1928

By C. B. Foraker

THE Magma mine, of the Magma Copper Co., at Superior, Pinal County, Arizona, is 68 miles east of Phoenix and 21 miles west of Miami, Arizona, on highway U. S. 180. TEMPERATURES AND UNDERGROUND WATERS Surface Temperatures.-The average surface dry-bulb temperature at Superior is 72.4º; wet-bulb, 57.4º; with an indicated relative humidity of 38 per cent. The average yearly rainfall from 1921 to 1936, inclusive, was 18.74 in. The maximum condition of the atmosphere is in June, July and August, and the minimum is in January and February. The surface temperatures, of course, influence the temperatures of the down- cast shafts; however, the variation between winter and summer causes a difference of only 2º to 3º in the stopes and working places that are not close to the intake shafts. Average atmospheric conditions are shown in Fig. 1. Rock Temperatures.-Rock temperatures on the deeper levels of the mine are as follows: [ ] There appears to be no difference in rock temperature for any particular horizon of the various formations or in the vein. Water encountered is always the same temperature as the rock from which it flows, and for this reason it is thought that the water is heated by the rock; not the rock by the water. The country rock apparently has been heated by the various intrusions, perhaps the vein itself, and has not yet had time to cool off. The geothermal gradient (Fig. 2) as indicated by the rock temperatures given above is 1 ½ º per 100 feet. Underground Waters.-The underground water varies from 350 to 565 gal. per min., depending on the rainfall. The limestone and other

Jan 1, 1938

By AIME AIME

INSTITUTE HEADQUARTERS, Hotel Statler. On Monday evening, Oct. 28, 1912, the visiting members and guests were informally received by the Local Committee at the Headquarters of the Institute at. the Hotel Statler. The evening was very pleasantly spent in renewing old acquaintances and friendships and in forming new ones. The first session, held Tuesday morning, Oct. 29, 1912, in the impressive Assembly-Room of the hotel, was called to order by David T. Croxton, Chairman of the Local Committee. Mr. Croxton introduced the Hon. Newton D. Baker, Mayor of Cleveland, who extended a cordial welcome to the members and guests present. James F. Kemp, President of the Institute, who subsequently presided at the meeting, responded in behalf of the Institute.

Nov 1, 1912

By William E. Hughes, Roderick K. Davey

The objective of this chapter is to review and discuss interpolation techniques commonly in use in the mining Industry today, including simple examples. This chapter will not attempt to compare the relative accuracy of each technique as this subject has adequately been covered by several authors (Knudsen and Kim, 1967; David, 1974; and Barnes, 1979) When appropriate, methods will be compared relative to the results of simple examples and computational ease. The examples presented are based on metallic deposits. The techniques, however, are not restricted to metallic deposits and can generally be applied to nonmetallic ones. The purpose of interpolation, as applied to a mineralized deposit, 1s to extend the knowledge of the grade and geology of localized samples to an estimate of the grade and mineralogy of a larger block of ground or even an entire deposit. The word interpolation means to compute values between given values and is limited to that region between the known values. The distinction between interpolation and extrapolation is important and must be adhered to in the application of these techniques in general, the interpolation must be limited to the area enclosed by verified samples. The methods being discussed can be broadly broken into three categories. ( 1 ) geometrical methods, (2) distance weighting methods, and (3) geostatistical techniques.

Jan 1, 1979

Feb. 18 to. 21, 1918 Committee on Arrangements J. E. JOHNSON, JR., Chairman BRADLEY STOUGHTON, Vice-Chairman A. R. LEDOUX RALPH W. DEACON F. T. RUBIDGE L. W. FRANCIS E. M. SHIPP MRS. S J. JENNINGS J. V. N. DORR A. L. WALKER G. D. VAN ARSDALE R. M. RAYMOND Finance Committee ALBERT R. LEDOUX, Chairman WALTER H. ALDRIDGE J. H. JANEWAY GEORGE D. BARRON CHARLES F. RAND WALTER DOUGLAS BENJAMIN B. THAYER

Jan 4, 1918

United Engineering Society WILLIAM L SAUNDERS,, President GEORGE H PEGRAM, 1st Vie-president ALFRED D FLINN, Secretary J V W REYNDERS, 2d Vice-president JACOB S LANGTHORN, Treasurer HENRY A LARDNER Assistant treasurer Finance Committee House Committee GEORGE H PEGRAM, Chairman ALFRED D FLINN, Chairman J 'VIPOND DAVIES FREDERICK F SHARPLESS BANCROFT GHERARDI . JOHN H DUNLAP WILLIAM L SAUNDERS CALVIN W RICE W F M GOSS, ex-officio F L HUTCHINSON

Jan 1, 1923

Established as a Division March 13, 1935 R H Feierabend, Chairman T E Gillingham, Jr, Northeast Vice-Chairman W A Riggs, Southeast Vice-Chairman C F Clausen, Mid-Continent Vice-Chairman R H Wilpolt, Rocky Mountain Vice-Chairman J K Brooke, Pacific Southwest Vice-Chairman Leslie C Richards, Pacific Northwest Chairman V A Haw, Canadian Vice-Chairman J S Holland, Sec'y -Treas National Lead Company Mining Department 111 Broadway New York 6, New York

Jan 1, 1960

The Nominating Committee desire to submit the following nominations. President and Director: SIDNEY J. JENNINGS District 0 Vice-President and Director: H. S. DRINKER District 2 R. M. RAYMOND District 0 Directors: G. C. STONE District 0 HENNEN JENNINGS District 9 S. A. TAYLOR District 2 F. G. COTTRELL District 6 ARTHUR THACHER District 3 These nominations were unanimous. By order of the Committee J. V. N. DORR, Chairman. Oct. 10. 1917.

Jan 12, 1917

PRESIDENT AND DIRECTOR EUGENE MCAULIFFE OMAHA, NEBR. PAST PRESIDENTS AND DIRECTORS HERBERT G. MOULTON NEW YORK, N. Y. JOHN R. SUMAN HOUSTON, TEXAS TREASURER AND DIRECTOR H. T. HAMILTON NEW YORK, N. Y. VICE PRESIDENTS AND DIRECTORS ERLE V. DAVELER NEW YORK, N. Y. W. M. PEIRCE PALMERTON, PA. PAUL D. MERICA NEW YORK. N. Y. LEROY SALSICH DULUTH, MINN. CHESTER A. FULTON NEW YORK, N. Y. L. E. YOUNG PITTSBURGH, PA.

Jan 1, 1942

By M. J. Virnig, G. A. Kordosky, K. D. MacKay

LIX 34 liquid ion exchange reagent, one of a totally new class of metal extractants, is discussed in terms of its properties. Specifically, these properties include improved selectivity for copper and greater recovery. Some comparisons to the well known General Mill's LIX 64N have been made. Particular emphasis is given to treating solutions containing very low copper values and high impurity levels.

Jan 1, 1978

By T. Turner, C. L. Zimmerman, U. Kappus

The purpose of the project is to divert flood flows of North Potato Creek. The project is located in the southeast corner of Tennessee near Copperhill, approximately 160 km north of Atlanta, GA. The project consists of: a 28-m high dam, a 0.9-m diam outlet conduit, an emergency spillway, and a 4.0-m diam hard rock transbasin diversion tunnel. This flood-water management system was part of Cities Service Co. mine safety program for the Cherokee ore body, which is partially located within the creek channel. The following paper describes the entire project development from feasibility studies to design and construction management.

Jan 1, 1981