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By R. J. Wagner, Jim Douglas Jr., P. M. Blair

The calculation of the behavior of an oil reservoir during a water flood has long been an important problem to reservoir engineers. Buckley and Leverett derived the differential equation which describes the displacement of oil from a linear porous medium by an immiscible fluid, but this equation could not be solved by the methods of classic mathematics. Consequently, in order to integrate the equation over the length of the reservoir, they neglected the effects of capillary pressure. In the present paper, a numerical method has been developed for determining the behavior of a linear wafer flood with the inclusion of capillary pressure. The differential equation which was derived for the case of incompressible fluids is second order and non-linear. This differential equation was approximated by an implicit form of difference equation which is second order correct in both time and distance. An electronic digital computer was used to perform the numerical solution of the difference equation. INTRODUCTION The problem of calculating the flow and distribution of fluids in an oil reservoir subjected to a water flood has long challenged the reservoir engineer. The ability to solve this problem would provide a valuable tool for the design and study of field waterflooding programs. One of the first contributions in this field was made by Buckley and Leverett,'.' who developed a method of calculating waterflood performance in a linear reservoir. Their technique was limited by the practical necessity of excluding quantitative consideration of capillary pressure. It is the purpose of this paper to describe a method for calculating the behavior of a linear water flood with capillary pressure considered. This method, although limited to the linear case, should serve as a step toward the solution of the two- or three-dimensional waterflooding problem which would better describe actual reservoirs. The treatment of the problem has assumed that the reservoir is linear and homogeneous, that both oil and water -are incompressible, and that gravitational forces may be neglected, and that water is injected into one end of the reservoir and oil and water are produced from the other. Though these assumptions may not be directly applied to natural reservoirs, they are closely approached in many laboratory core tests. The physical problem has been represented mathematically by means of a differential equation and suitable boundary conditions. The inclusion of capillary pressure effects causes the differential equation to be second order and non-linear, and it is not amenable to solution in terms of known functions. Nevertheless, the problem may be solved by numerical methods. The authors have successfully calculated several cases from the start of water injection through to depletion of the hypothetical reservoir using realistic capillary pressure and relative permeability characteristics that were chosen so as to put the method to a test. DIFFERENTIAL EQUATION In two- or three-dimensional problems involving the two-phase flow of incompressible fluids through a porous medium, the equations describing the flow can be combined until only two dependent variables remain, the pressure in one phase, and the saturation of one phase. These variables appear in two simultaneous partial differential equations which are derived on the basis of the conservation of mass and Darcy's law as applied to two-phase flow. For a linear reservoir, this system of differential equations can be reduced to a single, nonlinear, second order, parabolic differential equation for one dependent variable, the saturation of one phase. For incompressible water and oil, it can be shown that the conservation of mass for the two phases requires that Where q, and q, are the water end oil flow rates per unit cross-section, s, and so their saturations, +, the porosity, and [ and T, dimensional space and time variables. Darcy's law, as extended to two-phase flow including the effect of capillary pressure,' is as follows:

By W. W. Odell

Once it was believed that anthracite or coke were the only fuels generally available and suitable for the generation of water gas, particularly so when this gas was made in the generators of standard carburetted water-gas sets such as are commonly used in the manufacture of city gas. During the past 8 years, practice has changed considerably and it is now common to find gas plants operating without anthracite or coke and using bituminous coal in the generator. This change in fuel has appreciably increased the marketability and sales of certain coal producers' products; accordingly it is of interest to coal operators and others to know the reason for this change, the present trend in practice and the adaptability of various coals for generation of water gas. This paper briefly discusses these conditions and some of the factors relating thereto. Bituminous Coal not Ideal but Cheaper than Coke In spite of many changes which have been made in both process and generating apparatus for using bituminous coal as generator fuel more efficiently, in general it is not an ideal fuel for this purpose. It is supplanting coke because it costs less; it is so much cheaper per ton delivered at the gas works that water gas made therefrom costs less per unit-volume than that made from coke, even though the quantity of generator fuel consumed per therm (100,000 B. t. u.) of gas made is greater with coal. This is the reason why so many city gas plants, as well as others, are using bituminous coal instead of coke. Conditions Favoring Change from Coke to Coal The conditions which have made it possible and feasible, as well as economical, to supplant coke with coal may be summarized as follows: (1) Changes in methods of operating and alteration in generating apparatus; (2) lowering of the calorific standards for city gas, and (3) availability

Jan 1, 1927

By A. J. Weinig

NEED for some simple method of determining tonnages in mill circuits has always been felt by operators and consultants alike. To meet this demand the following method was evolved and has been found accurate and practical after considerable testing on various mill flows. The essence of the method is to add a chemical at a uniform rate to a mill flow, such as a launder conveying pulp, and then determine the concentration of the added chemical in a sample of the pulp. From this procedure the tonnage can be calculated. Common table salt has proved the most satisfactory chemical for ordinary conditions. It has many decided advantages for use in tonnage determinations, among them being the following:

Jan 1, 1933

By R. C. FLEMING

G OLD MINING is enjoying a real revival in the West, and a considerable portion of the production is coming from small properties. The large mining companies of the world get most of the publicity, but in the last year the small gold property has often proved a more attractive field for the mining engineer looking for something to do. Old mines have been re- opened, prospects have been more closely examined, and many properties that were out of the running with the high commodity and labor costs of two or three years ago, have recently been making money for their operators. An interesting phase of this activity is the operation of so-called one-man mines. The west is dotted with these small properties, without the resources or reserves to warrant large-scale operation, but which return a living and often something over to one or two men who under- stand mining and simple methods of treatment.

Jan 1, 1932

By AIME AIME

WHEN Russell B. Paul was born in Russell Gulch, Gilpin County, Colorado, that district was the state's leading gold producer. The son of Dr. Henry Paul, who had gone to Colorado from Missouri during the golden era following the Civil War, and had joined the Institute in 1889 when he was manager of the famous Aspen mine, young Paul's early life was steeped in a mining atmosphere from which developed his selection of mining engineering as a profes¬sion. After receiving his E.M. degree from the Colorado School of Mines in 1902, Mr. Paul worked in Colorado and Honduras. Returning from Central America he was married to Mary Ellen Gilmour, daughter of a prominent Central City mining man;

Jan 1, 1943

By PAUL M. Tyier

NOW that analytical chemistry has gone so far to debunk early misconceptions about minerals, the fact that the light of exact knowledge still fails to illuminate many dark corners is often overlooked. By combining the skills of the physicist with those of a chemist, the identification of minerals has become an exact science and the presence of even minute traces of impurities and extraneous elements is readily revealed by spectrographic means, Granted that we can learn all there is to know about the composition of a substance and even about its physical propertied (which latter assumption is somewhat far-reaching) it still does not follow that we clearly understood its commercial designation or utility.

Jan 1, 1941

By E. H. Crabtree

This paper traces the experimental and pilot plant work completed by the authors since 1939 including the various methods which have been developed in applying coarse activated carbon to cyanidation. The methods and results developed by the authors in desorbing gold and silver from carbons are given and the possibilities for the re-use of the desorbed carbons are discussed

Jan 1, 1950

Jan 1, 1925

By Luther Lennox

DURING the last few years, one of the great problems in the milling of all ores has been that of crushing. This subject involves not merely the cost of the operation, but also the selection of the proper degree and character of crushing to yield the best metallurgical results on the given ore. Considering the diversity of machinery, one is led to wonder at the variety of crushing methods employed, even when realizing that metallurgy demands varying products. In an attempt to investigate the relative crushing resistances of a number of ores now being milled in this country and Alaska, the management of the Portland mills requested samples of average mill-run of ore from various companies. The request met with a ready response, indicating the desire of all operators to gain information on the subject. The difficulties involved in this investigation were numerous, lack of time for outside problems during this strenuous period being a serious one. Also, we were unable, in the time, to obtain a correct 150-mesh . screen; in the screen analyses tabulated and plotted herewith, the 150 mesh screen was used merely to protect the 200-mesh screen, not to ascertain points on the curves.

Jan 8, 1918

By A. Springer

Chemists, physicists and others, whose occupations necessitate the use of fine scales, have heretofore regretted their inability to obtain any which would remain uniformly accurate. The difference between the theoretical and the actual results obtained in the ordinary balance (provided the pivot-distances are exact) is mainly due to the frictional resistance between the knifeedges and their bearings. This frictional resistance, although reduced to a minimum in the finest scales when new, constantly increases, thereby decreasing the sensitiveness proportionately. When examined under the microscope, neither the surface of the knife-edge nor that of' its hearings ever appears perfectly smooth. Soft kunife-edges are easily blunted, whereas hard ones are brittle and liable to crumble under the effects of over-load or shock. Prof. Frederick A. Roeder for many years attempted to discover some means by ,which the knife-edge could be replaced with some device free from the above-mentioned objections. His experiments convinced him that a torsion-joint was best suited for that purpose. After he had communicated his conclusion to me, we jointly developed the system to its present form. A torsion-wire had been used for the centre of rotation, prior to Prof. Roeder's invention, but it was found impossible to replace the terminal knife-edges with torsion-joints.

Jan 1, 1884

By Robert S. Shoemaker

Receiving the Richards Award is undoubtedly the most memorable event in my entire life. There should, however, be more names engraved on it. These are the names of men who were my teachers (but not all of the academic variety) and my friends, each of whom had a part in my ever continuing education and thus have a part of this award. There was Bill Caldwell who made me into a chemist, and Will Shorey who added a lot of ore dressing. There was Rush Spedden who put me to work in his minerals research lab, Joe Brennan who made me turn my research into plant practice, and Tom Meek who sent me all over the world on metallurgical jobs. Bob Cheatham and Abe Dor taught me to try to give the client what he needs rather than what he wants, while Ed Malouf and Casey Davis always gave their particular brand of advice at exactly the right time. And, lastly, there was Leo Abell and Frank McQuiston, both fine metallurgists and the best friends a man could have. In addition to those I have mentioned, there are literally scores of others I would like to acknowledge with my sincere appreciation.

Jan 6, 1974

For the first time, the attendance at the meetings of the Institute passed the thousand mark; as is shown by the following table: REGIS- AT BANQUET DID TOTAL TERED NOT REGISTER Men :..:... 703 76 806 Women 195 61 256 1062 The names of the members and guests who registered or attended the banquet but did not register are: A A. D. Beers C. A. Adams Hans Behr Thos. J. Adams Edgar G. Bell Lawrence Addicks Donald A. S. Bell H. T. Abrams W. de LeBenedict G. Aertsen G. B. Bertelli M. M. Albertson Charles P. Berkey James Aldrich Clinton Bernard D. C. Alexander, Jr. W. N. Best W. H. Alexander Robert M. Betts A. W. Allen Christopher H. Bierbaum F. D. Aller Paul Billingsley R. H. Allport R. A. Bingham F. C. Alsdorf R. M. Bird Capt. M. Altmayer John L. W. Birkinbine A.' W. Ambrose G. S. Bisey Henry M. Ami Charles W. Boise F. L. Antisell J. J. Blackmore R. S. Archer A. E. Blackwood Paul' Armitage Capt. C. K. Blatchly Andrew B. Armstrong E. L. Blossom Clifton T. Armstrong C. A. Bohn Ralph Arnold James M. Bonsall R. M. Atwater, Jr. E. E. Boon Joseph E. Aue Gail Borden A. M. Austin R. S. Botsford W. S. Ayres John M. Boutwell

Jan 4, 1919

By F. S. Crawford

IRON and copper are mined in the Lake Superior district. The iron mines of the district have the best safety record for that industry in the country as a whole, while the copper mines of the district rank second in two of the four years recorded (Table 1). In Utah copper comes mainly from open-pit mines, which enables that state to lead easily in safety. All of the Michigan production comes from deep underground workings. About 60 per cent of the iron miners in St. Louis County, Minnesota, are employed at open-pit mines; this favorably affects the combined open-pit and underground accident-frequency rate, as this county provides most of the Minnesota-mined iron ore. In Michigan, however, there are few open-pit mines, the bulk of the production coming from underground mines, while all of the Wisconsin production, just across the state line from Michigan, is from underground mines. In spite of the fact that fewer mines in Michigan use the safer open-pit method, the iron-mining industry of that state maintained a consistently low record from 1931 to 1934; however, it was many points behind its nearest competitor, Minnesota, with its much greater production from open-pit mines.

Jan 1, 1939

By F. S. Crawford

IRON and copper are mined in the Lake Superior district. The iron mines of the district have the best safety record for that industry in the country as a whole, while the copper mines of the district rank second in two of the four years recorded (Table 1). In Utah copper comes mainly from open-pit mines, which enables that state to lead easily in safety. All of the Michigan production comes from deep under-ground workings. About 60 per cent of the iron miners in St. Louis County, Minnesota, are employed at open-pit mines; this favorably affects the combined open-pit and underground accident-frequency rate, as this county pro-vides most of the Minnesota-mined iron ore. In Michigan, however, there are few open-pit mines, the bulk of the production coming from underground mines, while all of the Wisconsin production, just across the state line from Michigan, is from underground mines. In spite of the fact that fewer mines in Michigan use the safer open-pit method, the iron-mining industry of that state maintained a consistently low record from 1931 to 1934; however, it was many points behind its nearest com petitor, Minnesota, with its much greater production from open-pit mines.

Jan 1, 1939

By R. S. Shoemaker, D. L. Harris

Past investigations into the possibility of concentrating the low-grade iron ores of the Gogebic Range in Wisconsin have been hampered by the complex association of the constituent minerals. In part the problem arises from the fact that the iron occurs essentially as two minerals, hematite and goethite, having nearly the same chemical composition but exhibiting different physical properties. Individual grains of these minerals are usually so small that the ore must be ground to a size finer than 325 mesh if substantial liberation of the minerals is to be secured. Appraisal of beneficiation tests on this iron ore requires, therefore, some method of determining quantitatively the contents of constituent minerals in the various products of the beneficiation. Because of the chemical similarity of the two iron minerals, chemical analyses do not provide a means of differentiation. Although the minerals are different physically, they are both opaque and friable, and as the ore must be ground to a very fine size for liberation to be secured, quantitative microscopic methods of analysis are extremely difficult at best. In an effort to overcome these analytical problems, a quantitative X-ray diffraction analysis method has been developed at the University of Wisconsin for the research program on iron ore beneficiation.

Jan 5, 1955

By Herbert K. Kutter

This paper is concerned with the physical phenomena in the fracture process of presplitting and only indirectly with the establishment of the optimum presplitting parameters. Its nature is therefore qualitative, rather than quantitative.

Jan 1, 1968

By PAUL DYER MERICA

PAUL DYER MERICA, who has been awarded the James Douglas Gold Medal for his achievements in non-ferrous metallurgy, is a Hoosier, having been born at Warsaw, Ind., in 1889. His father, a clergyman and educator, was president of the University of Wyoming from 1908 to 1913. After graduating from the University of Wisconsin in 1908, young Merica (not yet twenty years of age) went to China, where he was professor of chemistry in Chekiang Provincial College, Hangchow, until 1911. He then went to Germany to s t u d y and was fortunate enough to receive his Ph.D. from the University of Berlin just a few months before the outbreak of the World War in 1914. Returning to America, his first position was as special investigator at the En¬gineering Experiment Station of the University of Illinois, but before the year was out he joined the staff of the U. S. Bureau of Standards as associate physicist. Since 1918, he has been superintendent of research for the International Nickel Co. His work during those years is excellently summarized in the following quotation from the statement of Zay Jeffries recommending him for the award.

Jan 1, 1929

By Hallan N. Marsh, Bruce H. Robinson

It is now generally recognized that to secure the greatest ultimate recovery of petroleum from a field it is necessary to maintain at all times the lowest possible ratio of gas to oil production. The numerous ways of securing low ratios are not so generally understood or practiced. To many operators, reduction of gas-oil ratio simply means "beaning back" wells, with resultant reduced production rate. This postponement of production is often considered and spoken of as "lost" production, with the result that control of gas-oil ratio is in disfavor with some operators. Various methods are herein discussed by which gas-oil ratio may be reduced, some of which invoLve no curtailment of current production, while others are accompanied by an actual increase of daily production. It is further shown that in cases where rate of production is reduced to conserve gas, the indicated ultimate recovery is generally increased. Principles involved are discussed, and conclusions are illustrated by data from the operation of wells. General Principles The rate and ratio in which oil and gas enter a well are solely dependent, so far as the operation of that well is concerned, upon the pressures maintained in the well opposite the producing strata at various times and at various depths. The method of getting the oil out of the hole, whether by natural flow, gas-lift, or pumping, has no effect upon either rate of production or ultimate recovery except through its effect upon pressures. Oil apparently enters wells according to some such equation as the following: R = KC(Pf - Pw)n Where R = rate of production. K = well coefficient, depending upon thickness of sand, and size and number of pores in the sand. C = fluid coefficient, depending upon viscosity, surface tension, etc.

Jan 1, 1929

By Alfred H. Brooks

LESS than a decade ago the consumption of coal in Alaska was practically limited to the salmon canneries and the few lode-mines and settlements along the Pacific coast of the Ter¬ritory. The sparse population of the interior depended on the forests, that of the shores of Bering Sea and the Arctic Ocean on driftwood for fuel. All this has changed. The thousands who have sought and mined gold on the Seward peninsula since 1898 have much impoverished the long-accumulated supply of driftwood, and at the same time the constantly increasing demand for fuel, on the part of the placer-camps and steamers, has resulted in heavy inroads being made on the accessible timber of the Yukon and its tributaries. While on the one hand the immediately available store of wood has decreased, on the other the consumption of fuel because of the rapid expansion of the mining and fishery industries and the attendant growth of population has much increased. Alaska, therefore, offers a constantly growing market for coal and other fuels. As the local coal-production has been insignificant, the demand has been met by importations from Washington, British Columbia, and even from Pennsylvania and Australia. Fuel-Consumption Mr. D. H. Jarvis, Collector for Alaska, has kept systematic records of the trade of the Territory since 1903. The statistics of the coal-importations of the past two years are shown in Table I. If data were available for a longer period of years, the increase of coal-importations would be much more striking.

Jul 1, 1905

By John D. Ridge, Robert C. Barwick

The amount of lead in concentrates that moved in international trade in 1952 was only 16 pct of the world mine production of lead and was less than 27 pct of the total of lead in concentrates and lead metal that traveled from one country to another. Because almost all lead is derived from galena, lead concentrates are high grade, with a theoretical maximum of 86 pct lead, and can be shipped as such without transporting a considerable weight of waste material. It would not be surprising, therefore, to find the large share of lead in international trade moves in concentrates (Rule 5). This is not, as has just been mentioned, actually the case. There is more than one explanation for the situation. Lead smelting is not a particularly difficult process and is one for which smelting equipment can readily be made of the best size for the tonnage to be handled. Another factor that encourages local smelting is the effort of many mining countries to see that a maximum of profit from their raw materials remains in the home country. Still another factor is the newness of large scale lead mining in two of the three largest exporters of lead in concentrates. In these countries, South West Africa and French Morocco, there has not yet been time to erect enough smelting capacity to process all of the concentrate output. Even in these countries, however, it will not be long, if present trends continue and plans are fulfilled, before most or all of the lead mined is domestically smelted.

Sep 1, 1955