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By S. A. Hovanessian

The method of characteristics which reduces the Buckley-Leverett mnlineur, partial differential equation to two first-order, linear differential equations is applied to the solution of a waterffood recovery problem for multiple lines of producing wells and one line of injection wells. The application of the method is described by a numerical example, and a brief theoretical background is given. From the results of this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple sets of producing wells. INTRODUCTION In this paper, the method of characteristics is applied to the solution of a waterflood recovery problem with multiple lines of producing wells and one line of injection wells. The application of the method to this type of recovery problem considerably simplifies the procedure of obtaining a numerical solution. It differs from the method described by Kern1 because it eliminates the need for integration in obtaining saturation fronts. In addition, the saturation history at any location within the field is obtained from a single diagram (time vs distance with saturation as a parameter)'. The paper includes a brief theory of the method of characteristics and its application to the solution of oil recovery problems. A numerical example is worked out, and the cumulative oil recovery-vs-time curve for a system with multiple sets of producing wells is obtained. This curve is then compared with the recovery curve of a system with only one set of producing wells. From this study, it is concluded that the cumulative water injected and oil produced are the same for single and multiple lines of producing wells. However, the recovery time is considerably longer for multiple sets of producing wells.

By Robert Adams

Secondary or scrap materials appear at all stages in the industrial process and in a bewildering variety of forms, grades, and values. It is useful to begin analyzing them by dividing the broad concept of "Secondary Supply" into three parts First, the concept must encompass the stock, or pool, of secondary materials. In the process of satisfying his wants, man produces desired products from the materials and natural resources found around him. As long as the rate of production is greater than the rate of obsolescence of a given product, the total stock or pool of materials embodied in that product will increase in size This stock concept relating to secondary materials is directly analogous to the "resource" concept used for primary raw materials in the preceding chapter, and includes all materials embodied in existing products (Obviously, this excludes those materials which are destroyed in the consumption process, viz , fuel oil burned to provide heat.) Consumption of a primary material in a productive process tends to reduce the resource base of that primary material In direct contrast, however, the production or use of products increases the resource base of the secondary material. Thus, we find that a country which has no resource of a primary material can, by importing products that contain the material, build up a large enough stock to provide a basis for secondary recovery. The estimated growth of the pool of copper in use in the United States through 1967 is shown in Table 5.B.1.a The estimate of 39 3 million tons at the end of 1967 includes only technologically recoverable copper and is, therefore, somewhat less than the stock concept described previously, which does not distinguish between recoverable and unrecoverable material. Nevertheless, Table 5 B.1 does give an idea of how a nation's secondary resource of a material can grow over the years. A second aspect of the concept of secondary supply is the generation of secondary materials. This includes materials generated as scrap in production as well as the movement of a material out of the stock of existing products via wear, damage, or obsolescence The quantity of materials generated is usually either nearly or completely independent of the technologic capabilities and economic forces which prevail in the secondary recovery market.b The justifications for and the qualifications to this statement are considered later. The final aspect of the concept of secondary supply consists in the secondary recovery process It is at this point that the technologic and economic forces of the secondary recovery market become the controlling fac-

Jan 1, 1976

By James Douglas

THOUGH liberality is not supposed to be a prominent trait of the Scottish character, Canada owes to a Scotchman, Sir Wm. Macdonald, more than to any other of its people, not only wise ideas, but pecuniary help towards extending education: and another Scotchman, in New York, has sumptuously housed under one roof three branches of the engineering fraternity, of which we are one. Having thus created us members of the same family-for the metaphorical meaning of house and kinship is identical-Mr. Carnegie expresses more emphatically than even he could in words, that, by affording facilities for closest intercourse, he in¬vites the mechanical, electrical and mining engineers to par¬ticipate in the freest interchange of idea and experience, and to correlate and combine the results of their studies and activi¬ties; and, being members of the same household, to banish re¬serve and secrecy. And now we, the members of the - American Institute of Mining Engineers, meet as though we were at home in a neighboring country. For whether we meet in Canada, in England, or elsewhere, the Institute is always received as though no political or geographical divisions separated its members from those of congenial associations in the land of its host. In truth, the title which we have assumed claims for the sphere of our activities the whole American continent, regardless of such trifling details as boundary-lines. The fact that we meet to communicate each other's experience, to discuss our difficulties, and to seek each other's aid in solving the intricate problems that so often present themselves in the course of our profes¬sional life, is an acknowledgment of our individual helpless¬ness; and therefore an argument for united effort. But no effort can be of any value if there is an underlying suspicion

Jan 9, 1907

By DR. DOUGLAS

Discussion of the Paper of Dr. Douglas, presented at the Toronto Meeting of the Institute, July, 1907 (Trans., xxxviii., 455 to 471). EDGAR HALL, Silverspur, Queensland, Australia (communication to the Secretary*) :-Dr. Douglas has written on this subject before, and his influence has had a powerful effect on the side of freedom among the younger generation of engineers. Moreover, it is not the first time that he has attributed the decline of the copper-smelting industry in Swansea to the secrecy maintained by the firms there engaged in smelting-operations. In this latter statement I think his conclusions are open to criticism. Whether the firms referred to have suffered by their secrecy is their own business-I. bold no brief for them ; but that the decline of the copper-industry at Swansea was inevitable seems to me to be proved conclusively by Dr. Douglas's own writings. In his paper on The Copper Situation,1 Dr. Douglas says "In comparing iron and copper mining, . . . it must be remembered that 2 tons of average iron ore from the most prolific source now available will make 1 ton of metal; whereas from 33 to 75 tons (say an average of 50 tons) of copper ore must be mined to produce 1 ton of copper." And further: "Last year's production of iron was made from approximately 50,000,000 tons of ore. Our copper mines, to yield a production of 900,000,000 pounds, must have handled approximately 22,000,000 tons of ore, or nearly half the quantity raised from our iron mines." Is not this the key to the whole situation ? In transporting the 50,000,000 tons of iron-ore, 25,000,000 tons of the metal iron were carried so much nearer to the market, but the transportation of 22,000,000 tons of copper-ore would have carried only 450,000 tons of the metal copper nearer to its ultimate destination. The small percentage of copper available in its ores makes

Sep 1, 1908

H. M. BOYLSTON E. B. YOUNG SECRETARY-TREASURER OF SECRETARY-TREASURER OF BOSTON SECTION MONTANA SECTION R. M. KEENEY F. G. MOSES SECRETARY-TREASURER OF SECRETARY-TREASURER OF COLORADO SECTION UTAH SECTION

Jan 7, 1919

IN the footnote on the first page of Prof. Stoek's paper, as printed in vol. xxviii. of the Transactions, I alluded to him, under an erroneous impression, for which he was in no way responsible, as " the present Director of the Scranton Schools." This incorrect statement placed him in a false position, as possibly having authorized the use of a title to which he had no claim. In fact, Prof. Stoek has never had any official connec-

Jan 1, 1900

L. K. ARMSTRONG H. L. NORTON SECRETARY-TREASURER of SECRETARY-TREASURER Of COLUMBIA SECTION ARIZONA SECTION PERCY E. WRIGHT A. B. CARPENTER SECRETARY-TREASURER Of SECRETARY-TREASURER Of PUGET SOUND SECTION SOUTHERN CALIFORNIA SECTION

Jan 8, 1919

Jan 1, 1901

By AIME AIME

This section contains announcements of general interest to the members of the Institute, but not always of sufficient permanent value to warrant republication in the volumes of the Transactions.

Sep 1, 1906

By Francis A Thomson

Montana Bureau of Mines and Geology, Montana School of Mines, Butte, Mont Francis A Thomson, President. The Bureau of Mines and Geology was formerly known as the Bureau of Mines and Metallurgy. A list of publications will be sent upon request¬ A series of six Bulletins and five Memoirs liave been issued by tlie Bureau, as well as several miscellaneous contributions Where the price is not indicated in tlie following selected list of those publications which are now available, the publications are presumably distributed gratis: Bulletin 3, Mechanical ore sampling in Montana, by H B Pulsifer (1920); 6, Geology and ore deposits of Bannack and Argenta, Montana, by P. J Slienon, 50 cents, Memoir 1, The Kevin-Sunburst and otlier oil and gas fields of the Sweetgrass Arcli, by E S Perry (1929), 2, Natural gas in Montana, by E S Perry (in preparation), 4, Tlie geologic structures of western Montana, by C H Clapp and others (in preparation), 5, Placer mining possibilities in Montana, by O A Dingman (1932).

Jan 1, 1933

By AIME AIME

ALL 32 of the Local Sections of the Institute in the continental United States and practically all of the Divisions as well, had representatives present at the Conferences of Local Section and Division Delegates at the Annual Meeting. Three sessions were held, two on Monday and one on Thursday, both the incoming and outgoing Presidents of the Institute being on hand to con- duct the meetings. H. J. Brown was called to the chair during a portion of the last session, President Fulton having to leave early. Complete minutes of the meetings have ,been sent to all delegates. In general, the Local Sections appeared, from their reports, to have risen to the wartime demands made upon them with their usual resourcefulness. Apparently more difficulty has arisen in the last year in arranging attractive programs and securing acceptable speakers, this being perhaps attributable to the fact that most technical men have been extremely busy. Careful planning ahead .has usually brought good results, however. Another wartime difficulty has been the matter of transportation to meetings, gasoline rationing and congestion on the railroads and buses being a handicap to attendance. Sharing cars has proved practical as a method of meeting this issue, this again requiring planning. Suitable meeting places and a supply of food have been another difficulty for some local groups.

Jan 1, 1944

By AIME AIME

THE time of the Section delegates was economized this year by providing the section reports in mimeo- graphed form, together with the reports of the officers and committees of the Institute, for their consideration on arrival. The meeting was called for Thursday forenoon and despite a certain amount of oratory managed to get through before all the luncheon was gone. In all, nine section delegates and one from the Iron and Steel Division attended and took part. One delegate, who had come many miles, got lost in the complication of the program and failed to attend. Six appointed dele- gates failed to attend and two sections neglected to make appointments.

Jan 1, 1929

By AIME AIME

TWENTY-TWO sections and all four of the divisions sent delegates to the annual meeting. They became so interested in the wide ranging dis6ussion of old and yet ever-new problems of Institute affairs that three instead of two sessions scheduled were necessary. Monday morning the meeting assembled with President Bassett presiding in the absence of President-elect Tally, who had been called to Baltimore by the serious illness of a brother. Thursday morning Vice-president Turner presided until Mr. Tally appeared after which the latter guided the sessions. Since reports from all of the active sections save one had been mimeographed and sent in advance to the delegates, detailed reports from each were dispensed with. The discussions dealt largely with membership problems, both local and national, with financing, speakers and programs, visits from national officers, and the conduct of the annual meeting. Many interesting and constructive suggestions were made and will be reported back to the sections by the delegates.

Jan 1, 1931

By AIME AIME

SECTION DELEGATES were given an opportunity to see how the machinery of Institute administration functions, on Tuesday evening, Feb. 16, when they were the' guests at the regular monthly meeting of the Directors. Of the new board of 25 members, 19 were present at the meeting, including directors from Seattle, Los Angeles, Wyoming, Oklahoma, Chicago and Pitts-burgh, the new junior past-president from Jerome, Ariz., and the new president from .Washington, D. C. The complete list of the 72 in attendance at the dinner,: held in the main dining room of the Engineers' Club, which pre-ceded the general session of the Directors'. meeting, follows:

Jan 1, 1932

By John Johnston

ONLY two of the Institute's 26 Local Sections were unrepresented at the delegates' three sessions, held on Monday morning and afternoon and Thursday afternoon of the annual meeting. The Philadelphia and Wyoming Sections alone sent no delegates. In all, seven hours were spent most profitably in reviewing the work done by the Institute at headquarters and in the field, comparing ideas and practices in varied activities, and in establishing personal contacts. Cordiality and the co¬operative spirit marked the meeting and apparently no one had any serious grievances to air. Four motions were introduced and unanimously passed. The first, which was introduced by B. L. Sackett, was a recommendation by the delegates that a national committee be appointed to cooperate with Local Sections in the matter of student activities, to promote Institute welfare. It was agreed that this recommendation be made simultaneously to the Board of Directors and to the Mineral Industry Education Division. A subsequent resolution by A. M. Smith was passed asking that a part of the duties of this committee be to secure the opinions of Local Sections as to the most desirable methods of interesting students in the preparation of technical papers, by giving prizes or otherwise, and to report their findings at the Section Delegates' meeting next year.

Jan 1, 1933

By C. M. Smith

DELEGATES from 26 Local Sections and- Divisions of the Institute had three stimulating sessions during the Annual Meeting, a few topics still remaining to be discussed after the two Monday sessions.. The final session was held on Thursday morning. An abstract of the discussion will be transmitted to each delegate present. The topics included: Student relations. Section operation, membership, employment, MINING AND METALLURGY, a new nonmetallic minerals Division. licensing of engineers, and increased allotments of money to Local Sections. Some of the Sections felt that the present limit of $250 allotted to them - from the national treasury was insufficient to carry on their activities, and that this maximum should he increased. A resolution to this effect was passed for transmission to the Board of Directors.

Jan 1, 1935

By AIME AIME

APPARENTLY unperturbed by any misgiving as to ill luck connected with the mystic number thirteen -for there were exactly that number of Directors on deck-the Board held two sessions on Tuesday, Feb. 21. , . Between the executive session at 5:15 p. m. and the general session at 8:30 p. m., 28 Section and Division delegates were wests of the Directors at dinner. Committee chair- " men and past officers brought the attendance to 75. Messrs. McAuliffe, Merica, Mudd and Tally had expressed their intention to be at the Directors' meeting, but each was prevented unavoidably at the last minute. At the executive session of the Board, J. V. W. Reynders was unanimously chosen to fill the unexpired term of Dr. Becket as Director: and Eugene McAuliffe in like " manner was selected to become Vice-president to fill the vacancy created hy Dr. Becket's assumption of the Presidency. Upon nomination of President Becket the following Executive Committee was appointed: Frederick M. Becket, chairman; Howard N. Eavenson, H. A. Guess, J. V. W. Reynders and William Wraith; and the Finance Committee was appointed as follows: Henry Krumb, chairman; Paul D. Merica and H. G. Moulton. Karl Eilers was reelected Treasurer and A. B. Parsons was re- elected Secretary to serve for the ensuing year, whereupon the executive session was adjourned.

Jan 1, 1933

By AIME AIME

THE section delegates assembled Monday morning with the incoming president, W. H. Bassett, in the chair and F. W. Bradley as vice-chairman. The secretary called the roll and urged the delegates to become familiar with the activities of the Institute. He explained the allotment of funds to local sections and the uses to which these funds may be put. He also announced plans for travel by Mr. Bassett and asked the delegates to confer with him as to meetings en route. An invitation was extended for all section delegates to attend the Directors' dinner Wednesday evening. He suggested that local sections hold a meeting once a year under the auspices of each division of the Institute. He further explained the system of choice of publications by members. The question of licensing of engineers was brought up, and the consensus of opinion among the membership was asked for. Because the matter is controversial, no official action has been taken and it was suggested that the' local and State sections act separately in this regard. A. B. Parsons, the assistant secretary, next spoke. In his remarks he indicated surprise that many prominent mining men still did not belong to the Institute, and urged that section delegates make up a list of such prospective members and send it in to the office for study by the New York staff. He also asked that re- ports of all meetings be turned in for publication in MINING AND METALLURGY, and said that the reports

Jan 1, 1930

TWENTY-FOUR of the 28 local sections and the two divisions of the Institute were represented at the meeting. Three sections failed to appoint delegates and two of those appointed failed to attend the delegates' meeting proper. Four sessions were held, two on Monday and two shorter adjourned ses-sions on Tuesday and Wednesday. Even at the end many things remained to be said and, in view of the amount of time the delegates lost from technical ses-sions the feeling was general that next year it would be advisable to hold their meeting the day before or day after the general meeting. Every part of the country was represented from Boston to Los Angeles and Seattle to Washington. All phases of Institute work and policy were taken up in the most informal way and the delegates will carry back to the sections, as they brought to headquarters, many ideas that will prove useful and stimulating. The time was divided between reports by the delegates on section activities and reports by officers of the In-stitute and of the various joint activities on the work at headquarters : A. D. Flinn told of the work of Engi-neering Foundation; W. V. Brown discussed the Em-ployment Service; J. A. Sohon explained what the Library is doing; T. T. Read told how the sections could help MINING AND METALLURGY ; H. Foster Bain discussed Institute affairs in general and asked and answered questions. An interesting new feature of the meeting was the appearance by request of Directors Turner and Smith of the U. S. Bureau of Mines and U. S. Geological Survey to answer inquiries as to the needs and work of their Bureaus. So much attention had been paid this year by the western sections to the diminished funds made available at Washington for research on mining problems that many questions came up. The accom-panying figures epitomize the answers.

Jan 3, 1928

By AIME AIME

NO FEATURE of the annual meeting is considered more important at Institute headquarters than the assembly of delegates from the various local sections and divisions. There the president of the Institute and other officials may learn at first hand what the members are thinking and doing in every part of the country, and the delegates, in turn, may find that head- quarters is not a group of more or less cold-blooded New Yorkers whose primary function is to send out annual bills for $15. This year, the section and division delegates required three sessions to thresh out the matters of common interest: Monday morning and afternoon and Thursday afternoon. They were also guests of the Institute at the Directors' dinner on Tuesday night, and at the Directors' meeting afterward.

Jan 1, 1932