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"The pumping of the underground water of the Butte mines is largely done from two central plants of the Anaconda Copper Mining Co. The mines of one part of the mining district are served by a modern and mechanically efficient underground plant at the High Ore mine, and the remaining part by a similar one at the Leonard mine. Properties not affiliated with the A. C. M. Co. have separate pumping plants, although in several instances that company handles the water of outside companies, under which arrangement costly single plants are dispensed with. An extensive system of underground crosscuts and drifts connects these mines to both the main pumping plants, so that either may receive the water from all the mines in case there should be a failure in the other to perform its designed service.Quintuple) vertical electric pumps, 7 inches by 12 inches each, of a capacity of 600 gals. per minute under a head of 1,203 feet, are installed at both the plants. Each pump is direct connected to two 150 h-p. motors using 2,300 volts, the motors being on top of the pumps.At the High Ore plant the power cable of 400,000 c. m. is placed in a nearby shaft, the cable at present being hung from the surface to the 2,200 level. From this cable feeders of 300,000 c. m. are laid in connecting crosscuts to the pumping station at the High Ore shaft.The Leonard motors use 440 volts. The practice of building the pumps with the motors on top requires stations with high roofs, but permits the operation of the pumps if they should be submerged by an unusual flow of water."

Jan 1, 1913

By H. Le Chatelier

An evident connection exists between chemical and calorific phenomena: the most important, of our sources of heat, the combustion of coal, is nothing else than a chemical reaction. Not satisfied with this indefinite statement, investigators have attempted to establish a more precise correlation between these two orders of phenomena, and have questioned whether there be not a necessary connection between the possibility of a chemical reaction and the algebraic sign of the quantity of heat which it would call into play (i.e., liberate or absorb). This question possesses the highest interest for metallurgical chemists. But the study of it by experimental methods only could not completely elucidate it. To arrive at a definite solution, it was necessary to appeal to a science much more general than chemistry,—namely, that of energetics, which embraces all the physical sciences. We can place absolute confidence in its conclusions, because they rest upon a proposition which can scarcely be denied, namely, the impossibility of The main facts in the history of the development o‡ this field of Triassic coals have been already set before the Institute in the papers of Mr. Oswald J. Heinrich, a former member of the Institute and the superintendent of the mines at Midlothian. † From these and other references to the field, it appears that coal was known to exist here as early as 1701; for on the 10th of May that year Colonel Byrd reported to the Colonial Council of Virginia the discovery of coal. Coal was mined from 1770 to 1780; but the amount shipped is unknown. It was much used in Richmond at this early date for gratefires. In 1789 shipments were made to northern ports. During the first half of the century just passed, mining operations attained in this field their greatest development, the number and extent of the collieries and the tonnage of coal raised per annum being greater for that period than for any similar period since. The maximum annual output exceeded 100,000 tons, while in two years only since the Civil War has the amount of coal raised exceeded 50,000 tons. This field covers about 150 sq. in. Its outline and the position of the strata in which the coal-outcrops occur are shown on the accompanying map, reproduced from the latest survey by the U. S. Geological Survey. Mining has been carried on along the margins of the area, often in the primitive manner in vogue at the beginning of operations, by means of shafts and slopes, usually too small in cross-section to permit the proper working of the beds. Most of the output has been won from

Jan 1, 1902

United Engineering Trustees, Inc James L Head, '55, E C Meagher, '56, Gail F Moul¬ton, '57 Advisory Committee to Real Estate Committee Cleveland Dodge, Herbert Hoover, Paul D Merica The Engineering Foundation W M Peirce, '56, A M Gaudin, '58 Research Procedure Committee A M Gaudin, March '54 Engineering Societies Library Board Frank T Sisco, '54, E M Wise, '56, James L Head, ex officio Engineering Societies Personnel Service Board of Directors E J Kennedy, Jr, E H Robie

Jan 1, 1954

By J. Chipman, N. J. Grant, J. C. Fulton

This paper contains data on the distribution of silicon between liquid iron-silicon-carbon alloys saturated with respect to graphite and CaO-SiO2-Al2O3 slags under 1 atm of CO at 1600°C. The ranges of slag compositions studied were extended from the dicalcium silicate saturated liquidus composition up to silica concentrations at which Sic appeared as a stable phase. IN blast furnace operation it is not to be expected that slag and metal reach equilibrium with one another. Nevertheless, the silicon content of the metal varies with slag composition and with temperature in a manner which would be predicted from equilibrium considerations. Similarly, the distribution of sulphur between slag and metal does not attain an equilibrium state, yet the influence of slag composition is strongly analogous to its effect on the distribution equilibrium. The desulphurizing power of metallurgical slags has been shown to be highly dependent upon the FeO content of the slag. Moreover, the rate of removal of sulphur from slags is influenced by the oxygen potential of the slag-metal system. Thus it was shown by Grant, Kalling, and Chipman1 that the presence of MnO in slags which are low in FeO causes a marked slowing down of the transfer of sulphur from metal to slag. This led to the hypothesis that the slow removal of sulphur by blast furnace slags of more acid composition might be due in part to the effect of SiO2 on the oxygen potential of the system. This was verified in the work of Grant, Troili, and Chipman,' who found that the desulphurizing power of the more acid blast furnace slags could be markedly improved by an increase in the silicon content of the underlying metal. Their explanation of this improvement was that the higher silicon content of the metal decreased the rate of transfer of more silicon and, along with it, of oxygen from the slag to the metal. The slowness of the transfer of sulphur from metal to slag was the result of the slow reduction of SiO2 from slag to metal. Attempts to study the rate of sulphur removal had in the past resulted in very slow rates corresponding to the rates of silica reduction. It has become evident on the basis of these studies that further experimental studies on the rate of removal of sulphur must take these factors into consideration if there is to be a clear understanding of the rate of sulphur transfer under conditions simulating those existing in the blast furnace. It will be necessary, at least in a part of such study, to employ combinations of slag and metal in which the disturbing effect of silica reduction has been eliminated; in other words, to employ slag-metal combinations which are already in equilibrium with respect to the transfer of silicon. In preparation for such studies of desulphuriza-tion, a preliminary program of research on the distribution of silicon between slag and metal has been undertaken. This will ultimately include a comprehensive survey of the effects of temperature and slag composition on the equilibrium distribution of silicon between slag and metal. The present paper is a report on experimental methods employed and on

Jan 1, 1954

By John W. Roberts

The Federal income tax law permits as a deduction in determining net income "in the case of mines,... a reasonable allowance for depletion and for depreciation of improvements, according to the peculiar conditions in each case, based upon cost, including cost of development not otherwise deducted: Provided, that in the case of such properties acquired prior to Mar. 1, 1913, the fair market value of the property (or the taxpayer's interest therein) on that date shall be taken in lieu of cost up to that date." The law provides for a reasonable allowance but the regulations provide for a definite method of computation that possesses more the virtue of simplicity than that of reasonableness. Article 210 of Regulations 45 reads: "When the cost or value as of Mar. 1, 1913, or within 30 days after the date of discovery of the property shall have been determined, and the number of mineral units in the property as of the date of acquisition or valuation shall have been estimated, the division of the former amount by the latter figure will give the unit value for purposes of depletion, and the depletion allowance for the taxable year may be computed by multiplying such unit value by the number of units of mineral extracted during the year." This is simple, but is it reasonable? The intent of the law is clearly that the cost of the ore in the ground shall be considered as part of the cost of the same ore when removed and sold. The regulations fail to carry out that intent, because of the unwarranted assumption that all the ore in the mine cost the same amount per ton. This is what gives the Treasury Department's method its simplicity, but at the same time robs it of its reasonableness because the assumption is contrary to fact. It is self-evident that a ton of ore near the surface or exposed by present workings is worth much more than a ton buried so far down in the earth that it cannot be removed for many years. If no improvements in mining methods were expected, the value of deeply buried ore would be further reduced by the greater expense that would be required to

Jan 1, 1922

By Bernard MacDonald

THE writing of this paper was prompted by the discussion by H. M. Chance, in the April Bulletin, of the paper written by Thomas M. Chance which appeared in the February Bulletin., and by the remarks of the Editor in which lie stated that while the matter contained in discussion did not refer to the original paper it "was presented as of interest to the operators of cyanide and other lixiviation processes dealing with fluid mixtures of varying specific gravity." For some years past the principle enunciated in the discussion referred to has been known to the writer and demonstrated by him to be an efficient and economical way of separating water or solution from solids in the cyanidation, lixiviation or acid leaching of ore pulps: In utilizing this principle in commercial practice he has invented a method whereby not only the separation of solution from solids may be effected in any given tank, but also the counter migration of the solids and solution may be effected continuously through a series of tanks in which the hydro-metallurgical treatment of ore pulps is being carried on. In effect this method is analogous to the counter-current system, but is different physically in that it is carried on throughout a series of tanks on practically the sane level, continuously and automatically, by hydrostatic pressure and gravity-flow, without the aid of intervening pumps or elevators, at the same time that agitation is being carried on in the same tanks. In the Parral system, agitation is effected in tanks by a number of air lifts of comparatively small diameter through which the pulp is continuously transferred from the bottom of the tank and spouted horizontally on top of the charge. The spouting force of the several streams thus discharged maintains a rotary flow in the pulp charge which extends from top to bottom of the tank. This continuous transfer of pulp and the spiral flow from top to bottom of the tank maintains the pulp constituents in uniform proportions and meets the requirements of efficient treatment in a most economical manner. The quantity of. compressed air required is very small, as the pulp is not lifted but simply trans-

Jan 7, 1918

By Freeman Bishop

The tight electric power supply is one of the most dramatic problems facing the mining industry in 1971. This is caused by rising demands for energy. Clean-fuel and air-pollution controls have contributed to the problems of producing energy from sulfur oil and coal. Coking coal has become scarce. One stimulating development is that coal is no longer the cinder in the mining industry's eye. In fact, it may be the favorite candidate as a base for fuel within a few years. Synthetic gas from coal is the watchword. In dedicating a multi-million- dollar project aimed at converting coal into oil and gas, Hollis M. Dole, Assistant Secretary of the Interior, recently made it clear that coal, which has been taking a back seat to nuclear fission research and study grants, is now coming into its own. Conversion pilot plants are being activated in all parts of the nation.

Jan 1, 1970

By Persifor Frazer

During the Centennial year some of our leading geologists in the United States and Canada conceived the happy thought of calling an International Congress of Geologists for the purpose of agreeing upon such important though subsidiary matters as the colors by means of which the different geological formations should be expressed ; the terms that should be applied respectively to these formations; and also upon the far more important problem of the limits and values of these different formations. The first session of this Congress was held in Paris in 1878, the second session in Bologna in 1881, and the third session in Berlin in 1884. The third session found the preliminary difficulties so far cleared away that some definite and tangible results could be attained. After a great deal of free discussion had taken place at Paris and Bologna, during which every one's views were listened to with attention; and a great deal more painstaking scientific work had been accomplished by the International Committees, having before them the objects of unifying the nomenclature of the science, and of preparing a scheme of colors between the second and third sessions of the Congress; and after the provisional results had been subjected to a searching criticism by the Congress in Berlin; it was decided to make an attempt to embody these provisional results in some work which should include as many as possible of the difficulties to

Jan 1, 1887

C. W. GOODALE,* Butte, Mont.-I notice Mr. Newton refers very briefly to the carbonate ores of manganese, rhodochrosite, but he does not go into any special description of the treatment of that material. In some of the veins in Butte, Mont., there is a large amount of rhodo-chrosite, and a large tonnage of that material has been shipped to the East for making ferromanganese. At the works of the Anaconda company at Great Falls they treated several thousand tons of this manganese ore, running about 37 to 38 per cent. manganese, in electric furnaces, giving a product of about 78 per cent. of manganese. But just at that time the demand for ferromanganese from the West was discontinued and the material, about 1000 tons of 78 per cent. manganese, is on hand at the works at Great Falls. With the higher-grade manganese ore, running, we will say, 37 or 38 per cent., there are large bodies of ore perhaps 20 or 25 per cent., but containing too much silica to be valuable in their present condition. Some efforts have been made for water concentration of that material, but owing to. there being only a difference of about 1 in the specific gravity of the quartz gangue and the manganese mineral, water concentration has offered some difficulties, I have been told, however, that some very satisfactory experiments have been made with magnetic concentration of this material. I think it is a new idea that this manganese ore can be treated successfully by magnetic concentration.

Jan 4, 1919

By H. T. Lundberg, J. H. Ratcliffe

In airborne gravity surveys effects of acceleration and irregular movements of the aircraft must be balanced out or overcome. The gradient of vertical gravity is recorded, therefore, by using two masses instead of one. As the amplitude variations are infinitesimal and difficult to measure accurately, at present it is enough to determine whether variation of gradient during flight is positive or negative. The positive portions of the pattern can then be indicated and contoured. Even with these simplifications, the source of energy must be exceptionally stable. General Principles: In the conventional gravi-meter the weight of a standard mass is determined at a number of selected points within the survey area. In most systems weight is determined by comparing the gravity pull with extension or torque

Jan 1, 1960

By John Randall

IT is a fair assumption that the main purpose of any diagram is to present facts to the eye in more convenient form than they could be tabulated in figures, and this implies that a screen diagram should set forth in a convenient and familiar form certain facts as to the character of the material screened regardless. of the screen standards used, and it seems particularly desirable on account of the well-known differences in the size of openings of different laboratory screens having the same nominal mesh. In making screen-sizing tests it has been customary to first consider the largest size, going progressively to the smallest, and this seems to have led to the practice of placing the smallest size at the right-hand side of the diagram and .measuring toward the left. This is not altogether convenient and might he changed to advantage, but for illustration I have preserved that feature and present the method just as I have used it for over 2 years. Direct plotting in which the intervals on the diagram are proportional to the sizes of the openings, or to the arithmetical difference between them, seems at first sight more natural and is extremely useful for certain purposes, but it makes the diagram very crowded in the smaller screen sizes while the larger ones occupy unnecessary space, snaking it less convenient for most purposes, and for that reason the method here discussed is the well-known one based oil the ratio between openings, and is plotted in logarithms instead of the direct values of the screen opening. Metric coordinate paper is convenient, although .not necessary; it is recommended, as the use of the metric scale gives a diagram of convenient size, but any scale of equal. parts may be used. In order to make any screen diagram translatable in terms of any standard screen size, it is necessary to have rioted on the size scale of the diagram all points corresponding to the openings of the various screens in question, instead of a single series 'of points as with a single screen. In drawing the diagram assume 0.001 in. (corresponding approximately to 0.025 mm.) to be the smallest size to be considered and fix this as the zero point at the lower right-hand corner of the diagram. This value is selected because the values are to be plotted in logarithms, and the logarithm of 1 is zero. Then lay off to the left for the position of each screen

Jan 9, 1917

The Office of Price Stabilization broke the copper price loggerhead between the U. S. and Chile when it permitted copper wire and brass mills to add to their ceiling prices 80 pct of the increase in cost of foreign copper above the 27 1/2 cents per pound specified in the agreement with Chile. Another step forward in the processing of taconite seems to have been made with the patenting of a process for the strengthening of taconite pellets. The patent was issued to Fred D. De Vaney and assigne to the Erie Mining Co., of Hibbing, Minn. Strength of the pellets is improved by adding from one to five pounds of starch or sodium silicate. A new iron ore deposit discovered on Vancouver Island will start producing soon, and is expected to yield 2 million tons of magnetite over its span of operation. A new mill will be built by the Argonaut Construction Co., of San Francisco, at the deposits of the Utah Construction Co., its parent organization. The Organization for European Economic Cooperation banned the use of nickel and nickel alloy in the manufacture of about 500 products in an attempt to conserve nonferrous metals in short supply. Some 18 members of the organization have already volunteered to restrict nickel consumption.

Jan 1, 1952

It appears that Utah is about to add another mining district to its already impressive roster. This time it is the Great Salt Lake, whose high-mineral content waters are being subjected to intensive study aimed toward the recovery of potassium, magnesium and lithium compounds by solar evaporation techniques. Among the firms conducting such experiments is Lithium Corporation of America, which, in a joint venture with West Germany's Salzdetfurth A.G., is operating evaporating ponds and running engineering tests at a site near Little Mountain, about ten miles west of Ogden. Here, on the clay flats along the northern portion of the lake, LCA holds leases and options totalling about 55,000 acres in the Bear River Basin.

Jan 7, 1966

SUCCESSFUL development of a new process for heat hardening of pellets made from taconite concentrates was announced by Arthur G. McKee & CO., steel plant engineering and construction firm of Cleveland, and Allis-Chalmers Mfg. Co. An order for the design, engineering, and materials for a plant incorporating the process, has been received by the McKee Co. from the Reserve Mining Co. for its new E. W. Davis Works at Silver Bay, Minn. It is estimated that this plant will cost around $19 million and when in full operation, will turn out 12,000 tons of pellets per day.

Jan 10, 1954

By R. W. Raymond

Alexander Brinton Coxe was born in Philadelphia, Pa., Jan. 19, 1838, the second of five sons of Hon. Charles Sidney Coxe and Ann Maria Brinton. A more extended history of his family and its important relations to the development of the United States will be found in my Biographical Notice of his younger brother, Eckley B. Coxe, published in 1895. It is therefore sufficient to say here that Dr. Daniel Coxe, a clis-

Jan 1, 1907

The U. S. Navy Department has perfected plans for the enrollment and training of considerable numbers of engineering officers. A school for this purpose, the U. S. Navy Steam Engineering School, has been established by the Department at Hoboken, N. J. The school is open to men between the ages of 21 and 40 who meet the physical requirements of the Navy, who are of thorough ability and officer-like character and who have completed the mechanical or electrical engineering course at certain recognized technical schools, or who possess an education and experience adjudged to be an equivalent thereof. Enrollment in the U. Naval Reserve Force of men properly qualified may be made at any Naval enrolling office, notation being made of the applicant's qualifications and desire to be detailed to this school. Applicants will be enrolled as Chief Machinist Mates, and during the course of instruction will draw the pay of this rating, $83 per month, plus $60 per month paid as subsistence. Upon graduation, men will be commissioned as Ensigns in the U. S. Naval Reserve, with a salary of $1700 per year. The duty to which a graduate of this school will be assigned will be that of an engineer officer in the auxiliary service of the Navy. Special provision has been made for the continuance of the school with proper material by a Navy regulation which permits undergraduates of the Freshman, Sophomore, and Junior Classes in recognized engineering schools to enroll in the Naval Reserve Force with the rating of Seaman 2d Class, and continue their courses at the institutions where they have matriculated. Such men will be called into active service after their graduation, and can at that time, if they are qualified to pass an officers' physical examination, apply for admission to the U. S. Navy Steam Engineering School. Men who are registered in the draft, either graduates or undergraduates, may enroll with the proper enrolling officer by securing from their draft board a letter of release, which in all probability can be obtained for this purpose. The aim of this school is not simply to produce engineers, but to produce naval engineering officers in the true sense of the word. The course of instruction covers a period of five months, arranged in four periods.

Jan 10, 1918

By V. R. Garfias, A. C. Fernandez

Despite artificial curtailment in all the fields of Mexico during 1937, owing to strikes and other disturbances, the production of crude petroleum aggregated approximately 46,738,000 bbl., showing a substantial increase of about 5,571,000 bbl. over the preceding year. Most of this increase occurred in the Poza Rica area, where, although only two wells were completed during the year, production increased from 14,162,000 bbl. in 1936 to 18,634,000 in 1937. While production in the South fields (Golden Lane) remained practically stationary, the output in the heavy-oil district of the Northern fields showed an increase of 1,930,000 bbl., because production had been considerably curtailed during 1936. Production in the Isthmus of Tehuantepec decreased about 596,000 bbl., owing to labor disturbances. Crude run to stills in local refineries increased from 34,000,000 bbl. in 1936 to 36,650,000 in 1937. Exports of crude and refined products were approximately 22,700,000 bbl., or 500,000 bbl. less than in 1936. Domestic consumption, excluding ships bunkers, reached a total of 20,000,000 bbl., which shows a small increase of 200,000 bbl. over the. previous year. Domestic demand for gasoline is estimated at 3,400,000 bbl. for the year, which represents an increase of 500,000 bbl. over 1936. In all, 60 wells were completed in Mexico during 1937, as compared to 70 in 1936 and 74 in 1935. In proven areas 52 completions resulted in 25 producers and 27 failures. In the Northeastern area near the United States border, five gas wells were drilled, all of which were producers; one of them, in Camargo, came in with a daily production of 20,000,000 cu. ft. of gas. One well, resulting in a failure, was drilled in Las Uvas, Coahuila, and three wells were completed in Quebrache, to the southeast of the heavy-oil district, resulting in two small producers and one failure. TWO more wells drilled in San SebastiBn, east of the Golden Lane, were failures. Fields Northern Fields (Heavy-oil District).—A total of 11 producers and 22 failures was completed in the proven areas of the Northern fields, as compared to 16 producers and 25 failures in 1936. In the Altamira

Jan 1, 1938

THE Joint Committee appointed to consider a Code of Ethics for Engineers recommends, after delib-erate consideration, that each participating Insti-tute or Society adopt the short simple Code of Ethics following this report. The Committee further recommends that the following method of interpreting and administering the Code be adopted by each participating Institute or Society after any necessary provisions have been, made in the Constitution and By-laws of the Organization. The President of each Society or Institute shall appoint a Standing Committee on Professional. Conduct, to administer the Code of Ethics. The duties of such a Committee shall be to interpret the Code and to render opinions on any cases of ques-tionable conduct on the part of members that may be submitted to the Committee. These interpretations shall be reported to the Executive Board of the Institute or Society who may approve these interpretations, or take such other action as may seem just and necessary. The reports of the Committee on Professional Conduct, when approved by the Executive Board, shall be printed in abstract and in anonymous form in the Institute's or Society's monthly journal for the instruction and guidance of fellow members. This Committee on Professional Conduct shall be appointed in each Institute or Society by the President holding office at the time of the adoption of this Code and shall consist of five member one appointed for five years, one for four years, a third for three years, a fourth for two years and a fifth member for one year only. Thereafter, the President then holding office shall appoint one member annually to serve for five years, and shall also fill any vacancies that may occur for the unexpired term of the member who has withdrawn. These appointments shall he made from among the older members of the Institute or. Society, so that advantage may be taken of their mature experi-ence and judgment. The Committee after appointment shall elect its own chairman and secretary. The Committee shall have power to secure evidence or other information in any particular case not only from the organization's own members, but if it should seem desirable, from men in other professions. The Committee may also appoint sub-committees to consider certain cases when deemed necessary.

Jan 3, 1922

By N. L. Britton

About two years ago Dr. Newberry referred to me for study a considerable collection of fossil plants sent him by Dr. Arthur F. Wendt, engineer of the silver mines " El Cerro Rico de Potosi" in Bolivia. As I had been interested in working up the extensive accumulations of existing plants made by Dr. H. H. Rusby in the Bolivian Andes further north, and in assisting Dr. Rusby in the study of those now being collected by Mr. Miguel Bang in other parts of that country, I was glad of an opportunity of ascertaining something of the Tertiary flora of the region. I was unable to take up the subject at that time, but have since been able to conclude the investigation, and the results are here presented. At a time when the mineral resources of the Southern States are attracting such widespread interest and attention, I have thought it appropriate to give a short general description of the iron-ore deposits of a territory concerning which little is as yet known and nothing published, so far as I am aware. The data used here are due to the preliminary examinations of the North Carolina Geological Survey, on which work I was engaged during the past summer, and my acknowledgments are due to Prof. J. A. Holmes, State Geologist, and Messrs. Harris, Ashe, and Lewis, of the survey, for their co-operation in the work; also to Messrs. A. S. McCreath and C. B. White for analyses which they Kindly furnished. Other analyses were made by Mr. Charles Baskerville, assistant chemist to the survey, and this may be understood where the name of the chemist is not mentioned. All samples for analysis were dried at 212' F. The accompanying map has been prepared from the revised sheets of the United States Geological Survey by Mr. H. L. Harris, and will be referred to throughout this paper. Ashe county lies in the extreme northwestern part of North Carolina, bordering on Tennessee and Virginia; it is drained principally by the north and south forks of New river and their tributaries, and is therefore on the eastern edge of the great Mississippi drainagebasin. The country is exceedingly rugged and mountainous, having an average elevation of about 2900 feet above sea-level. Jefferson, the county seat, near the center of the county, is 45 miles nearly due south from the Norfolk and Western R.R. at Marion, Va., and 30 miles northwest from the Richmond and Danville R.R. at Wilkesboro, N. C. Geologically the ore-deposits described in this paper are situated in the area of the crystalline rocks, consisting chiefly of gneiss, hornblende-schist, and micaceous schists.

Jan 1, 1893

By J. Jones-Parra, J. C. Calhoun

INTRODUCTION The purpose of this paper is to present the results obtained by solving the fractional flow' and frontal advance' equations to obtain oil recovery at water breakthrough as a function of the length of the system being flooded, the linear velocity of injection and the displacing phase viscosity. The method of solution makes use of the stabilized zone concept first presented by Terwilliger, et al3 when calculating saturation distributions in a gravity drainage system. In order to check the calculated results, the equations and method of solution were applied to the system on which Rapoport and Leas' reported experimental data. METHOD OF SOLUTION The solution of the fractional flow equation and the frontal advance equation is obtained by assuming that a water front forms to sweep the oil out ahead of it. There is ample evidence that under the proper conditions a water 'front does form. If this water front is not to dissipate, the water saturations which comprise it must have equal linear velocities. These water saturations are said to comprise the stabilized zone. Equation (2) indicates that for all these saturations and hence fw must plot as a straight line against saturation for those water saturations comprising the stabilized zone. The water saturations lying between the highest in the stabilized zone and the highest that can be achieved in the porous medium comprise the variable zone. Regardless of the numerical value of the length of the system, the variable zone must eventually span all of it, so that for long enough systems in Equation (1) will be small enough to be neglected. Hence, for the saturations in the variable zone Equation (1) can be simplified to In order to determine the composite fw function applicable to the entire range of saturations in the porous medium, it is necessary to find the water saturation which separates the stabilized zone from the variable zone. This dividing saturation must be on the curve defined by Equation (4), and a tangent curve at that point must pass through the initial water saturation to satisfy Equation (3). Hence, the valid fw curve is given by a straight line starting at the initial water saturation, tangent to the curve of Equation (4): and along the curve of Equation (4) from the point of tangency on. The point of tangency determines the water saturation dividing the zones. The length and shape of the stabilized zone can be found by solving Equation (1) for Integrating this expression numerically between any two saturations in the stabilized zone gives the distance separating these two saturations. By repeated integration, the saturation distribution of the stabilized zone can be determined. The total length of the stabilized zone is given by The integral appearing in Equation (5) is a function of the viscosity ratio, the capillary properties of the rockfluid system, the relative permeabilities, and the initial water saturation. Considering these variables fixed and designating the value of the integral by writing caw for and v/60 for q/A; Equation (5) becomes The saturation distribution of the stabilized zone can be integrated over its length and divided by the length to obtain the average water saturation The volume of water in the stabilized zone is then given by The average water saturation in the variable zone can be found by extending the straight line segment of (the segment joining Sw and Sw) until it intersects fw = 1.00. The saturation at the intersection is. This method of finding is nothing more than the graphical solution of the equation The volume of water in the variable zone at breakthrough is then given by Assuming no initial water saturation, the recovery at breakthrough expressed as percent pore volume is given by

Jan 1, 1953