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Organization Place 1917 National Association of Stationary Engineers .... Evansville, Ind. Sept. 10-15 National Safety Council New York City. Sept. 10-15 National Exposition of Safety and Sanitation.... New York City. Sept. 10-15 American Iron, Steel & Electrical Engineers Philadelphia, Pa. Sept. 10-14 American Association of Port Authorities Cleveland, Ohio. Sept. 11-14 American Institute of Metals Boston, Mass. - Sept. 24-29 American Foundrymen's Association Boston, Mass. Sept. 24-29 Chemical Industries, Third National Exhibition.. New York City. Sept. 24-29 American Electrochemical Society Pittsburgh, Pa. Oct. 3-6

Jan 9, 1917

Organization Place Date 1918 American Institute of Architects Washington, D. C. April American Iron and Steel Institute New York, N. Y. May American Institute of Chemical Engineers : Berlin, N. H. June 19-22 American Society for Testing Materials Atlantic City, N. J. June 25-28 New York Electrical Society New York, N. Y. June National Association of Stationary Engineers Cincinnati, 0. Sept. 9-13 National Exposition of Chemical Industries New York, N. Y. Sept. 23-28 American Chemical Society Cleveland, 0. Sept. National Petroleum Association Atlantic City, N.. J. Sept.

Jan 4, 1918

By J. C. Van de Water

THE original trucks at Castle Dome were 30-ton Knuckeys with 150 hp, H-series Cummins engines and 15-ton Euclids with the same engines. The Euclids were used early in the operation, working with 2 1/2-yd Diesel shovels on stripping and later in opening new benches where the lack of room favored the smaller trucks because of their shorter turning radius. They have also been used on road building and similar jobs. On regular production, where the 30-ton trucks can be used, they are not economical.

Jan 11, 1951

By Robert B. Kistler, Ward C. Smith

The borate industry is one of the few sectors of the mining and mineral-processing industry which the United States still dominates. Since about 1927, the United States has supplied over half of the world's total boron and borate raw materials, and many of the chemical derivatives as well. Chiefly responsible for this record are companies producing sodium borates from two large deposits in southern California, at Boron (Kramer) and Searles Lake. The sodium borates, or products derived from borax and borax-containing brines, are the preferred borates for industry because they are soluble in water and combine readily with most other chemicals. Calcium borates (or sodium-free compounds) are required for certain end uses, but in general, nonsodium borates are used only where borax is not avail- able. During the past hundred years, the use of boron compounds throughout the world has risen from a few tons per year to the equivalent of about a million tons of B2O3. Leadership in supplying borates has shifted from country to country and from region to region during this period, generally as the result of the development of newly discovered deposits that were better in quality, more accessible, or more economically exploitable than previous sources (Table 1). Primary Products and End Uses The principal borate products offered by primary producers in the United States are listed in Table 2. In general, these products are utilized worldwide by almost all consumers, regardless of the original source of the primary borates. In the United States, the primary borates all originate in southern California. Colemanite is produced as crude or processed crude ore from the Death Valley area and is utilized by the fiber glass and ceramic industries without further treatment. Production from Searles Lake, Calif., is from brines that are processed in chemical plants where borax and other compounds are recovered and the principal borate products are produced. At Boron, Calif., the world's leading producer is mining a deposit of mineral borax and operating a chemical refinery. The mineral borax is mined together with included clay, and refined borax or "lo-mol" is one of the refinery products. The mineral and the chemical compound are identical, Na2B4O7- lOH2O. In addition to ship- ping all major refined borate products from Boron, the company ships semiprocessed ore concentrates to treatment plants elsewhere.

Jan 1, 1975

By AIME AIME

MANY interesting papers, opportunity of seeing o1d friends, and an exposition showing all that is latest in equipment, all were factors in bringing a large crowd to Detroit during "Metal Week," October 2-6. The Institute's Iron and Steel and Institute of Metals Divisions held technical sessions at the Statler Hotel on October 4 and 5, and that hotel was also headquarters for the American Society for Steel Treating and the American Society of Mechanical Engineers, both of which also had technical sessions. The American Welding Society and the Wire Association met at the Book-Cadillac Hotel, and the exposition was staged at Convention Hall, out Woodward Avenue. All in all it was a big week for men interested in metal working. One of them stated to your reporter on the train en route to Detroit that this was the one convention that he never missed, and doubtless others felt the same way about it.

Jan 1, 1933

By AIME

A present the colleges and universities are struggling to meet the responsibilities placed upon them by the return of the veterans from the armed forces to the educational institutions as well as the youth graduating from the high schools. The problems of meeting these responsibilities are complex and upon the shoulders of the educational administrators lies much of the burden. One of those educators who is in the midst of this situation is James Rowland Cudworth, dean of the College of Engineering of the University of Alabama and Chairman of the Mineral Industry Education Division, AIME, both for 1946 and 1947. He was born at Norwich, Conn., on Sept. 23, 1897, and like his father before him went to the Massachusetts Institute of Technology where he received his Bachelor's degree in 1921. His studies at MIT were mainly in the fields of geological and mining engineering. Why a New Englander studies mining is anybody's guess, but it may be due to a love of traveling to far places which so many New Englanders do. After graduating tinder the famed Waldemar Lindgren. Jim trekked to Mexico where he worked at Pachuca for the Cia. Real del Monte and at Charcas with the American Smelting and Refining Co.

Jan 1, 1946

By E. W. Rouse

THE year 1936 has seen rehabilitation of many plants which had been closed or severely curtailed. The Steptoe smelter of the Nevada Consolidated Copper Co. has been transformed by a rearrangement of the flow of material and utilization of mechanical handling to a maximum. The Phelps Dodge Corp. reports the construction of newer and better reverberatories at the Copper Queen smelter, and of particular interest, a single high-pressure waste-heat boiler placed directly over the uptake. There has also been a complete reconstruction of the smelter at the Laurel Hill plant of the Nichols Copper Co.

Jan 1, 1937

By Horace Winchell

IT IS OFTEN interesting to look backward and review the world's progress in any line of human endeavor. Our pride is flattered by our achieve-ments and our imagination stimulated by the compari-son between our present productivity and prosperity and those of the relatively unenlightened days of our recent ancestors. We love to reflect on the progress of the last quarter of a century in the art of metallurgy, in. the production and consumption of the various metals and minerals which constitute the basis of our industrial and commercial supremacy. We dwell complacently on the figures which prove that we are the world's leader in nearly all departments of mining and that our production of necessary minerals over-shadows that of other countries. We recall the days when it was considered the proper thing, if not indeed indispensable, to go abroad for the rounding out of a mining engineer's education. We had no mining schools equal to those of Germany. Our schools of technology were elementary and their equipment limited. RISE OF AMERICAN MINING SCHOOLS Now we point with true American pride to institutions which, are unsurpassed in all the world in their standard of efficiency. We know full well that the American engineer is in demand in many foreign parts and when we read recent scientific treatises published abroad we are amazed to find them unfamiliar with many of the more advanced ideas which have here already come to be an everyday part of our professional knowledge and equipment. Blessed with a country of unrivalled natural resources, dwelling in a latitude whose climate is most conducive to enterprise, peopled with races of inventive and organizing genius with equality of individual opportunity, our industries have grown and expanded until our output has reached staggering proportions and the draft upon our mineral reserves is appalling. Coupled with this development has arisen a demand for engineers which has brought into our schools of technical science larger and larger numbers of young men whose imagination has been stimulated by the success of their predecessors who happened to be contemporary elements in the recent industrial expansion and prosperity.

Jan 1, 1923

By Edward Adarns Richardson

As developed up to the end of the Great War, an airplane was essentially a mechanism of wood and fabric, joined and held together by metal fittings and fastening. The engine and accessories, wire for wheel spokes and other tension members, and the occasional use of metal for inter-plane struts and the shafts of surface controls required some metal, but essentially it was a wood and fabric structure. Attempts had been made to use metal for other purposes, such as struts in the drag-trussing of wing panels and for short interplane struts, and Junkers had produced an airplane of iron in 1915. By 1917 he was using steel tubes and duralumin sheets, securing noteworthy advantages aerodynamically and from the standpoint of weight and upkeep. He was a pioneer along lines in which progress is still being made. Principles of Airplane Construction The loaded weight of airplanes ranges from 500 lb. for the light plane of which we heard so much a short time ago, to about 40,000 Ib. The great majority of planes range from 2000 to 10,000 Ib. Of this weight from 15 to 30 per cent. is for the dividend-earning load. This percentage is so low that every per cent. saved on the rest of the weight increases the pay load from 3 to 6 per cent,. The economic value of every pound that can be saved in designing or constructing a plane is sufficiently great to warrant spending money on refined methods of structural analysis, materials of superior strength properties for a given weight, methods of manufacture which may make possible the use of refinements in structural design, and the like, to an extent unknown heretofore. The weight of the airplane, without fuel, oil and crew, and pay load, ranges from 50 to 65 per cent. of the total weight loaded for planes suitable for commercial use. It is doubtful if the structural weight will ever be brought down to as low as 40 per cent. for commercial planes. The airplane may be roughly divided into: (1) Power plant, which includes engines, radiators, cooling water, oil and fuel tanks, piping, propellers, engine-starting systems, pumps, super-

By G. J. Ballmer

Drilling and blasting 12-in. blastholes started about the middle of 1946 and has worked out so well that about one half of the blasting, formerly done with 9-in. holes, is now done with 12-in. holes. In most of this work the harder benches were chosen for the 12-in. size because these were the areas where the greatest difficulty was encountered in thorough fragmentation. At the start of this experimental work a 42-T Bucyrus- Erie churn drill was available whereas all other blasthole drilling was being done with 29-T rigs. The large drill was first equipped with a standard 9-in. string of tools but it could not drill quite as fast as the 29-T drills. How- ever, when the weight of the string was increased about 700 lb, or to a total weight of about 3500 lb, it was found that the 42-T exceeded the drilling speed of the 29-T by about 25 per cent. When a 12-in. bit was substituted for the 9-in. bit the 42-T rig again dropped behind the drill- ing rate of the 29-T rigs. At this stage of the experiment the 42-T was using a 12-in. bit with detachable points and the total weight of the string of tools was about 3800 lb. It took longer to change the drill points than it did the regulation bit and this accounted for some of the slower drilling rate. When a heavier stem and standard construction 12-in. bits were used it was found that the 42-T could drill a 12-in. hole slightly faster than a 29-T could drill a 9-in. hole even in the hardest rock in the pit.

Jan 1, 1949

Minute of the Board of Directors, Jan. 26, 1917 In the name of all the members of the American Institute of Mining Engineers, this Board extends to. Mr. Herbert C. Hoover, an honored Vice-President of the Institute, on the occasion of his present temporary return to his native land, the cordial welcome of his colleagues, and their congratulations upon the noble work splendidly done by the Commission for Relief in Belgium of which he is the head. It is understood that a leading purpose of Mr. Hoover's visit to America at this time is the collection of additional funds, to be administered by his Commission in the care of the destitute children of Belgium. To this enterprise endorsed by both the belligerent parties, as well as inspired by the purest and tenderest sentiments of humanity, contributions are solicited from engineers, especially through an organization known as the "Belgian Kiddies Limited," which this Board, heartily approving its object and method, recommends to the consideration of the members of the Institute. On motion duly seconded it was unanimously VOTED.-That this minute be spread upon the record of the Board, and published in the Bulletin, and that a copy thereof be transmitted to Mr. Hoover, and to the San Francisco Section of the Institute.

Jan 3, 1917

By Philip Kraft

WHEN it came time to write a biography of Philip Kraft, we got out a copy of Bartlett's "Familiar Quotations" and looked through the references to Travel, Traveled, Traveler, and Traveling, feeling sure there would be some reference to Mr. Kraft. Sure enough, we found: "Travel, in the younger sort, is a part of education; in the elder, a part of experience." Had Francis Bacon done his writing three and a half centuries later, Mr. Kraft might well have served as the inspiration for that sentence. New Yorker born, he received his B.S. and E. M. degrees from Columbia. In 1912, then 22 years old, he took off for Germany where he spent two years studying at the Royal School of Mines, Berlin, for his Doctor of Engineering degree. Contrary to the Greeley-Soule precept, Mr. Kraft, on his return from Europe, went north to South Porcupine. Ont., working as geologist and mining engineer for the Dome Mine. From South Porcupine his next stop was Washington, D. C., where, during the years the country was in the first World War, he was engaged in war work.

Jan 1, 1947

By Walter F. Bradley

CLOSE to 300 members and guests were registered at the Regional Meeting of the Institute in San Francisco. Oct. 3-6, and many other mining men were present at some of the sessions, but failed to register. Headquarters were at the Palace Hotel. Technical papers for the Metals Session were sponsored by the San Francisco Section, whereas the program for the Industrial Minerals Session was arranged by the Southern California Section. Walter W. Bradley, Chairman of the San Francisco Section, opened the General and Metals Session, introducing President Buehler, who gave a hearty welcome to those present. Clyde M. Eye, of the. Benguet Consolidated Mining Co., presented the first paper, entitled "The Economic and Strategic Value of Philippine Metals to the United States." In closing, he urged. that this country retain and control the Philippines because their large

Jan 1, 1935

By W. A. Backofen, G. Y. Chin, W. F. Hosford

The ductile fracturing process was studied in single-crystal and poly cvystalline aluminum deformed in tension over a temperature range from 295° to 4.2°K. At temperatures as low as 77°K, the fracture of "inclusion-free" material, including zone-refined aluminum, was by rupture (-100 pct RA). At 4.2 OK, fracture was brought on by adia-batic shear. Metallographic examination did not disclose any voids or slip-band microcracks, thus negating for inherently ductile metals any mechanism of void nucleation by vacancy condensation or of cracking due to dislocation pile-ups. In Izigh-purity aluminum not treated to be inclusion-free, fracture at temperatures as low as 45°K was of the double-cup type and a result of void formation. The reduction-of-area decreased as temperature was lowered, corresponding to the earlier appearance of voids. Such behavior was rationalized in terms of a larger increase, with decreasing temperature, in the .flow stress relative to the strength of the inclusion-matrix interface. Evidence for low-temperature adiabatic shear was found in discontinuous flow at 4.2"K, in the transition to a localized shear fracture at low temperatures, and in the suppression of shear fracture with an elastically hard pulling device. A simple analysis for the initiation of adiabatic shew permitted a general correlation of the various contributing factors. It has been pointed out that the duration of shear depends upon effective mass and elastic stiffness of the deformation system. IT has long been recognized that fracture* may Throughout this paper, the term "fracture" is taken to mean any process that results in the separation of a material into two (or more) parts. Thus rupture as it may be encountered in a tension test leading to 100 pct reduction-of-area is included in this category. occur in a ductile mode, and that the process can be of great practical as well as general interest. Much information about ductile fracture has also been accumulated over this period, but only recently has an understanding of mechanism begun to appear. Ludwik,' in 1926, first reported fracture in a tensile specimen starting with a central crack in the necked section. Since then, other studies have disclosed that such cracks may form by the coalescence of voids nucleated in this region where hydrostatic tension is highest.2-4 Rogers and Crussard et al.' have emphasized void formation and reori-entation along localized shear bands as a mode of crack propagation. pines6 has considered the tensile rod as a bundle of fibers joined by weak interfaces, which subsequently separate to allow individual fiber contraction. The notion of cavity growth and coalescence by purely plastic processes was discussed by Cottrell: who added that the tensile reduction-of-area ought not to be sensitive to temperature. On the other hand, it has been observed that the reduction-of-area is greatly increased if tests are carried out at high temperaturesa or under high hydrostatic pressure.' Fracturing anisotropy in wrought products lends support to the idea of void formation from preexisting flaws strongly aligned by earlier processing.''-l2 There is evidence that many voids result from the fracturing of inclusions or separation at the inclusion-matrix interface Another possibility is that voids grow out of pore volume produced in the initial solidification and never fully removed in later working. In general, a structure 3f particles, pores, and weak interfaces can be expected, at least in materials of engineering interest. Vacancy condensation has been suggested as an alternative mechanism of void formation for materials considered to be inclusion-free.13 Yet experience has shown that tensile reduction-of-area increases with purity, to the extreme of rupture as so often observed in single crystals. Adiabatic shear has an important bearing on ductile fracture. It occurs when the decrease of flow stress, as a result of local temperature rise from heat generated during straining, becomes larger than the increase due to strain and strain-rate hardening. As demonstrated by experiments on punching of plates,14 a large temperature rise may be brought about by rapid straining. Adiabatic flow as a result of the high strain rate reached in an ordinary tensile specimen just prior to separation may account for the cone formation in cup-and-cone fracture;14 evidence of such local heating has been presented.15 For geometrical reasons, however, pure sliding along the conical surfaces is unlikely, and separation under tensile forces is probably an important accompanying feature of the shear.7 In deformation processing operations, a high shear-strain rate may exist at boundaries between plas-

Jan 1, 1964

By George T. Bator

If confronted with the problem of pumping a mixture of slime-free sand, gravel and boulders up to six in. in diameter, at the rate of 175 tons per hr in one single-stage pump against a static head of 90 ft and a total head of 140 ft, of which 20 is on the suction side, an engineer might be forgiven for backing away from the job, especially if he were also told that the pump wearing parts must have a minimum hardness of 550 Brinell for the sake of abrasion resistance.

Jan 1, 1950

By T. F. Mueller, P. A. Witherspoon

For the case of an infinite radial system operating at constant terminal rate, the reservoir engineer often uses the "point source" solution of the diffiusivity equation to study pressure interference effects. At early times and at short distances from the inner boundary these solutions are invalid. The amount of error is often not precisely defined because of mathematical difficulties. Work presented here shows that, if dimensionless time is defined appropriately, previous solutions of the pressure equation can be displayed .as a family of curves on one chart. These solutions include the point source solution (referred to in the field of hydrology as the Theis solution) and other solutions obtained with digital computer methods. With these curves, an exact evaluation of the pressure drop within a reservoir or an aquifer can be made by the engineer. Examples of field problem solutions are presented. In most reservoirs the error involved when the Theis solution is employed is often negligible; whereas, in the calculation of interference effects in an aquifer, a substantial error can occur through such an approach. INTRODUCTION Flow equations are used in petroleum engineering to study the behavior of individual wells and reservoirs. In the case of wells, the pressure response at the wellbore face is the major point of interest; whereas, in the case of reservoirs, the pressure response at the interface of the aquifer boundary is sought. To aid in such studies, the flow equations have been solved in terms of the behavior at these two inner boundaries. Only limited work has been published in regard to the pressure conditions away from these points, i.e., within the reservoir or aquifer. Theis and Mortada are among the few who have reported on this problem. The Theis approach employs the exponential integral and is valid for pressure conditions that occur some distance away from the flow disturbance. It is derived from the concept of a point source, as opposed to a flow across some finite area. The Mortada results, on the other hand, are valid at all points within the reservoir or aquifer. They are presented in terms of dimension less ratios of the radius where the pressure is desired to the radius where the flow rate is measured. Their main use, in the past, has been in aquifer studies. The published results are presented in the form of graphs that are limited to a maximum radius ratio of 64. These graphical results are cumbersome to interpolate at non-integral radius ratios, so that one may be forced to utilize a rather involved analytical expression presented by Mortada. BASIC EQUATIONS The solutions of Mortada and Theis are both based on the diffusivity equation as applied to the case of an infinite radial system subject to a constant terminal rate. The equation is obtained by combining the material balance equation with Darcy's flow equation. The assumptions implicit in the use of this equation are as follows: (1) a single fluid is present that occupies the entire pore volume; (2) the reservoir is horizontal, homogeneous, uniform in thickness, and of infinite radial extent; (3) compressibility and viscosity of the fluid remain constant at all pressures; and (4) fluid density obeys the equation Using the diffusivity equation in situations where the above conditions do not hold will result in errors. These errors (not discussed here) but only the errors which arise in the solution of the equation itself. The diffusivity equation for the homogeneous reservoir conditions cited above can be written in cylindrical coordinates, as To obtain a dimensionless equation, so a single solution can be used for applications of different porosity, permeability and fluid properties, the following transformations are usually made: After these transformations are made, Eq. 3 .can be written in dimensionless form, as MORTADA SOLUTION One solution of Eq. 6 has been given by Mortada.

Jan 1, 1966

By R. J. Woody

Design of the most economic continuous counter-current decantation (CCD) circuit is based on selection of the number of stages and the wash volume that will give the minimum summation of the following items: 1) Capital and operating costs of the CCD circuit. 2) Capital and operating costs of the precipitation circuit. 3) Value of the dissolved product lost.

Jan 1, 1959

By T. MacDONALD

ATHOUGH flotation has been a commercial process for over twenty years, the last two years have witnessed a sudden and phenomenal increase in our knowledge of how to separate minerals heretofore not considered amenable to flotation at all. As remarked by Professor Locke in the January issue. "Either commercial or laboratory flotation is reported on zircon, ilmenite, carnotite, kyanite, scheelite, chromite, fluorite, feldspar, cassiterite, wolframite, barite, and clay. Attractive patents on soap flotation are U. S. Nos. 2,000,656 and 2,040.187. A survey by Ralston in the February E. & M. J. adds many other minerals to this impressive list. The simple but pregnant fact is that any mineral can be coated, directly or indirectly, with a water-repellent coating, and since this is true, it follows that any mineral can be floated. Fundamentally, this is no new discovery, where, for instance, is the mineral that cannot he washed from a pair of dirty hands by means of soap and water, given the absence of refractory greases or oils which would have no proper place in flotation ?

Jan 1, 1937

By M. A. Roche

AST fall over half a million tons of ore and rock were broken in one blast at the open pit of the Hudson Bay Mining & Smelting Company's operation, at Flin Flon, Manitoba. The following particulars of the blast, and details of the preparatory work, indicate how an operation of this scope is carried out. The data given, in essentially the present form, were first published by The Canadian Mining Journal. The area blasted was 150 ft. wide and about 700 ft. long. A total of 123 tons of 50 per cent forcite gelatin, in 5 by 16-in. cartridges, was used for the charge. Drilling for the blast was started on May 29, and was completed late in August, requiring 1297 machine shifts for drilling only. Total footage drilled for the shot was over 5 miles of 6-in. hole. The main blast consisted of 232 holes spaced on 17.5-ft.

Jan 1, 1934

By R. V. Higgins, A. J. Leighton

Interest by petroleum engineers in the flow of three phases—oil, gas and water—in irregularly bounded porous media lies mostly in the performance calculation of water floods of reservoirs that have been partially depleted as the result of expansion of much of the originally dissolved gas. The authors present a method to forecast three-phase flow in complex geometry and explain the details by the use of a specific example of a five-spot water flood of a partially depleted stratified reservoir. In this example, the fluid and rock properties of a field given by Prats, et al,' were used. The computed results fit the field performance more accurately than Prats, et al, and Slider.' The time required for the high-speed digital computer to make the calculations, including the contributions from the different layered zones, is about one minute. INTRODUCTION The declining rate of discoveries of new oil fields in the United States makes the recovery of more oil from known reservoirs more attractive than previously. Water flooding has an excellent proved background for recovering additional oil economically. Accordingly, the main interest of this paper is in this type of recovery. In petroleum engineering studies, commercial interest in three-phase flow is mostly in the water flooding of reservoirs in which the oil has been partially produced by the expansion of dissolved gas. When water is pumped into these reservoirs, three-phase flow takes place. Although this paper is concerned with these conditions, the principles involved could be used for other conditions when and where they come to the fore. Many investigators have made contributions to non-empirical forecast methods using basic scientific engineering principles. Several of these used the oil in place at the start of the water flood and the oil remaining after a large quantity of water has passed through a core for key values in their calculations. Recently, Prats, et al,' and Slider have reduced assumptions by adding the third phase—gas—in their forecasting methods. Slider uses the mobilities in the immediate vicinity of inlet and outlet wells as an aid to simulate the resistance effect in the five-spat pattern of the flow of oil, gas and water. Prats, et al. minimize assumptions by using previously determined laboratory data for determining sweep efficiency in the five-spot pattern. In neither of these papers is the saturation profile continuously affected by permeability-saturation curves. Sheldon and Dougherty- recently described a method that employs continuously changing saturation profiles using permeability curves, has a minimum of assumptions and needs no prior sweep efficiency. The Higgins-Leighton method, described in this paper, has all of these features; however, many of the techniques are different from those of Sheldon and Dougherty. The Higgins-Leighton method, tested in May, 1961, is direct and easy to apply and requires very little computer time to calculate a forecast. The short computer time is especially helpful in the study of a reservoir containing many layers of different relative permeabilities. In the Higgins-Leighton method, the individual pressures do not have to be calculated, as the resistance to flow in each cell in the flow pattern is readily determined without the use of any iterative techniques. The saturation and permeability distributions are readily determined. These data and the shape factor, which is measured only once from the potentiometric model when mobility ratio is one, determine the resistance to flow in each cell. THEORY The authors showed in a previous paper4 that, as an aid to calculating performance, the reservoir can be divided into channels using the streamlines of a potentiometric model as a guide. See Fig. 1. This procedure also was used in this paper. The authors also showed that, by treating conduits as approximately one-dimensional and neglecting pressure gradients transverse to the main flow, the Buckley-Leverett equation may be expressed as The principles expressed by this equation are employed extensively in the three-phase flow, as they were in two-phase flow. In the three-phase flow, the channels (the size and shape of which are taken from a potentiometric model)