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By W. A. Klikoff, I. Fatt

The concept of fractional wet wattability is examined. Fractional water wettability of a reservoir rock is defined as the fraction of the internal surface urea that is in contact with water. Capillary pressure and relalive permeability of unconsolidated sand are shown to be functions of fractional wettability. INTRODUCTION The petroleum industry has long recognized that wettability of reservoir rock has an important effect on multiphase flow of oil, water and gas through reservoirs. As early as 1928 the American Petroleum Institute sponsored a study of wettability as part of API Project 27 at the U. of Michigan.' Despite 30 years of research, there is still little exact knowledge of the wettability of reservoir rocks. There are two parts to the wettability problem. After agreeing to a uniform nomenclature in regard to wettability,' the first question to be answered is, "What is the in situ wettability of a given reservoir rock?" If this can he answered the next question is, "What part does wettability play in determining the characteristics of multiphase fluid flow through the rock?" This paper represents an oblique attack on the problem of wettability. No attempt is made here to answer the basic question of wettability in situ. instead the consequences of the concept of fractional wettability are examined. Multiphase flow in sandpacks is shown to he highly influenced by fractional wettability. Jennings' has given 3 definition of wettability and the other terms used in discussing wettability. These terms must be applied to the physical situation existing In reservoir rock. A survey of the pertinent literature from 1928 to 1956 indicates that the concept of a contact angle was applied to reservoir rock in the same way it would be applied to a flat, homogeneous surface. Attempts were made to state quantitatively the wettability of a reservoir rock in terms of a contact angle which was presumably constant at all points on the very rough and heterogeneous interior surface of a porous rock. Calhoun, et al,3-6 prepared synthetic consolidated and un-consolidated porous media in which they claimed there was a known uniform contact angle. They then showed the effects on the capillary pressure and relative permeability characteristics of varying this angle. The API Project 47 at the U. of Texas' and others' have made extensive studies of an indirect approach to the contact angle through the use of heat of wetting data. Even if successful. however, this approach also states the wettability of porous rock in terms of a contact angle which is uniform over the entirc surface. If the angle varies from one part to another on the internal surface, there is no way of determining from the measurements the area distribution of contact angles. In 1956 Brown and Fatt5 suggested that the concept of a contact angle, as applied to reservoir rock, be abandoned. This suggestion was made because it is known that the internal surface of most reservoir rocks is composed of many different minerals, cach with a different surface chemistry and a different capacity to adsorh surface active materials from reservoir fluids. Furthermore, the operation of a contact angle in determining the form of a fluid-fluid interface is difficult to picture in the very complex geometry of a pore. Brown and Fatt proposed that the wettability of reservoir rock be stated in terms of the fractional internal surface area that is in contact with water or oil. All surfaces on which there is water are called water-wet; surfaces on which there is oil are called oil-wet. The fractional water wettability is then stated as a number which represents the fraction of the internal surface that is in contact with water. A symmetrical statement can be made for the fractional oil wettability. The concept of a fractional wettability as previously stated has in its favor the recognition of the heterogeneous mineral composition of most reservoir rocks. Another point in its favor is that fractional wettability can be measured quantitatively with relative ease. Hol-brook and Bernard10 se a simple dye adsorption test to obtain fractional wettability of reservoir rocks. Amott11 uses a combination of imbibition and displacement to arrive at a wettability index of reservoir rocks which seems related to fractional wettability in the range 0.25 to 0.75 fractional water wettability. Jennings" has shown the changes in relative permeability that take place when a porous material is changed from unity to zero fractional water wettability. He also shows that reservoir rocks in their natural state, but at room temperature and atmospheric pressure, have relative permeability characteristics which would indi-

E L. DEGOLYER, our new president, though a petroleum geologist by profession, has always s been associated with mining, for soon after his birth at Greensburg, Kan., on Oct. 9, 1886, his parents moved to Joplin, and when he went, in the course of time, to the University of Oklahoma, he intended to follow his course there with another at a mining school. He became a field assistant in the U. S. Geo-logical Survey, however, while still an undergradu-ate, and after field experi- ence in Montana, Wyoming, North Dakota, Colorado and Oklahoma, he went to Mexico as geologist for the Mexican Eagle Oil Co. This was in 1909, and as a result he was unable to complete his work for his degree until 1911. In Mexico, he located the Potrero de Llaño No. 4, one of the world's largest oil wells, and also the dis- covery well in the Naran- jos pool; and the Colorado School of Mines conferred the honorary degree of : Doctor of Science on him in 1925. On his return from Mexico, he engaged in the consulting business, specializing in financial ap- praisement, the Union and Marland companies being among his clients. In 1919, he organized the Amerada Petroleum Co., with the backing of Lord Cowdray. Last year, control of the company was purchased by an American group, headed by Dillon, Read and Co. Mr. DeGolyer is n o w president of the company. He is also vice-president and general manager of the Rycade Corp, the Rycade Oil Corp., and president of the Geophysical Re-search search Corp. The l a t t e r represents the practical appli-cation of his inter-est in the use of the torsion balance in the locating of salt domes, in which he has pioneered, the Nash dome being the first oil field in America actually brought into production by these methods.

Jan 3, 1927

By J. E. Castle

THE title of this article is descriptive, but not complete, for psychological evaluation is almost as important as rigid economic evaluation. This refers to those human traits that cause people to be too optimistic about the projects they are sponsoring, to overlook obvious weaknesses, to base decisions on incomplete and inaccurate data, and to gloss over embarrassing problems. Investment of capital in a new industrial mineral project is warranted only after rigorous economic analyses based on unquestionable facts. A plunge into production cannot be justified solely because these minerals have been deposited in the ground and are therefore free. There are no specially favorable economic laws that make the business of industrial minerals more attractive than any other. The factors of supply and demand, marketing, technological changes, taxes, competition, and fluctuating prices apply as much to industrial minerals as to other business enterprises. What is more, industrial minerals are subject to the higher risks that all mining enterprises face.

Jan 6, 1958

By N. J. Themelis, R. V. Flint

In a four-year period between 1973-76, the Metal Mining Division of Kennecott Copper Corp. conducted a company-wide program of operations improvement which involved line and staff personnel from all company functions. Specialist teams performed detailed studies of all operational aspects at Kennecott's four copper mines and concentrators, four smelters, and two electrore-fineries. The specific recommendations that resulted may transform the Metal Mining Division into the country's lowest cost producer of copper by the mid-1980s. In this article, N. J. Themelis and R. V. Flint describe the mechanics of MMD's integrated approach to operations improvement.

Jan 6, 1979

By C. W. Thompson

Paul D. Suloff (Goodyear Tire and Rubber Co., Inc., Akron, Ohio)—I would like first to comment on problems of the conveyor belt discussed in Mr. Thompson's excellent paper, since that is what we hope we know most about. Twists in relatively wide conveyor belt unavoidably produce a lateral maldistribution of tension, raising tension at belt edges and reducing it at the center. They also produce a lateral collapsing force on the belt at the center of the twist owing to the inherent tendency of all the longitudinal elements of the belt to try to pass through a point at the twist center. Calculation of the twist geometry by the methods shown in Mr. Thompson's paper keeps these extraordinary forces within limits which the belt designer can tolerate. No reduction in belt life due to twisting need be contemplated when this geometry is maintained. There is a minor exception that belts of extreme lateral flexibility will tend to curl laterally at the center of the twist. However, any ordinary fabric construction will perform satisfactorily in this respect. These twists are always made in regions of low tension in the conveyor so that even in the edges of the twist, belt tension does not exceed the average tension found in highly stressed regions of the conveyor. Offsetting these out-of-ordinary belt stresses is the advantage that Mr. Thompson has brought out of getting the return run up out of the dirt where it can be seen. This not only makes it easier to train, but also, in the event that it is not properly trained, frees it of the normal return run edge wear hazard. It is well known that return run edge wear is a prominent cause of belt mortality underground. An interesting aspect of this two-way conveyor is that the belt may be made what is known as a Mobius Strip. A Mobius Strip is obtained by splicing a belt after turning one end of it 180" about its longitudinal axis. In other words, one end is turned upside down before splicing. A belt spliced in this fashion turns itself upside down every time it comes around, but the twist which has been put in the splicing, of course, stays at one location on the conveyor, in this case one of the twist sections at the end. Turning the belt over every revolution might have advantages in some cases. Belts could be made with equal covers and the two sides worn equally and simultaneously. In this case there would be no problem of getting belts on upside down by mistake. However, the two-way conveyor does not have to be a Mobius Strip. It can be twisted in such fashion that the same side is up on both runs. It is simply a question of which way the final 90" twist is made before joining the ends. Another interesting aspect of the two-way conveyor is the problem of operating two-way conveyors in series. Here the sequencing of starting brings up some new problems. It will be recognized, although not always at first glance, that if the starting sequence is planned for one run of the conveyor the reverse will result on the other run. With the two runs carrying bulk material in both directions a reverse sequence on one run would be intolerable. In this situation the only solution appears to be a simultaneous starting of all conveyors in the series. However, with the coal in one direction and intermittent supplies in the other it would be entirely practical to sequence the conveyors for the coal run and accept a reverse sequence on the supply run. The two-way conveyor also lends itself to new driving possibilities. First, it is quite possible to drive at the head end of each run, which of course, means a drive at each end of the two-way conveyor. Driving in this way a given belt can be extended to substantially greater lengths than a conventional conveyor with drive at one end only. In addition to this, under certain conditions the conveyor can be extended to extreme length by driving at one end and at some intermediate point on the most heavily loaded run. As a particular case, a belt carrying coal downgrade and supplies back upgrade could be extended to extreme lengths by driving at the head of the coal run and at an intermediate point of the supply run. Mr. Thompson has been a pioneer in belt conveyor transportation underground and his accomplishment here with the first two-way conveyor of any consequence is another notable addition to the art.

Jan 1, 1954

By Eckley B. Coxe

IN the anthracite coal regions of Pennsylvania the custom has been to sight either at an open light (generally a mine-lamp), or at the string of a plumb-bob. If the station was intended to be a permanent one, a spud, as it is called, that is, a nail resembling a horseshoe nail with a hole in the head, is driven into the timbers over the station, or, if there be no timber, a hole is drilled in the coal or rock roof, into which a wooden plug is driven, which serves to hold the spud. The first operation in making a survey is to lay out the stations, that is, to mark the place where the holes are to be drilled for the plugs or the points on the timbers where the spuds are to be driven in. This should be done before any instrumental work is begun, as much labor can generally be spared, and the use of very short sights can often be avoided, by carefully laying out the stations beforehand. When the stations were laid out, a plumb-bob was hung from the innermost spud, which I will call No. 1, the instrument was put in position at No. 2, by plumbing down and putting a centre-pin under the spud, and then setting up over the centre-pin, and another plumb-bob was suspended from No. 3. If great accuracy was not required, a mine-lamp was set up under the plumb-bobs, at No. 1 and No. 3, and the engineer sighted at them. If great accuracy was required, a lamp or some white surface was held by an assistant behind the strings of the plumb-bobs. To work with any speed by the latter method (i. e., the accurate one), it was necessary for the engineer to have three assistants on whom he could rely even when the chaining was done afterwards; viz.: one to hold the light behind the string at No. 1, one at No. 3, and an assistant at the instrument to hold the light while levelling, reading the in-

Jan 1, 1873

By Ulick R. Evans

I Should like to commence by saying how much I appreciate the honor which the American Institute of Mining and Metallurgical Engineers has done me in inviting me to visit your country, and to deliver this lecture before you. In choosing a subject, and in deciding what to include and what to omit, I have endeavored to discuss as far as possible work carried out recently in Europe with which you may not be unduly familiar. It would be poor return for your hospitality, and a mistaken sort of compliment indeed, if I were to load the lecture with accounts of researches carried out in your own country—researches with which you are probably better acquainted than I. Not that I have in any way excluded work done on this side of the Atlantic from my survey; one would indeed find it difficult to write on this, or on any other branch of science, without mentioning American work. But I have endeavored as far as possible to concentrate on aspects of the case which will, I hope, be comparatively fresh to you, and I feel fairly certain that this will be in accordance with your own wishes. Films Produced at Elevated Temperatures If a strip of iron is heated strongly at one end, the other end remaining cold, there is produced over the heated portion a layer of oxide scale, the thickness of which diminishes steadily with the distance from the hot end. Somewhere in the middle of the strip, the thickness of the oxidized layer will become comparable to the wave length of light, and over this region the thin films give rise to a series of beautiful interference tints, commonly known as "temper colors." The colors are caused by the fact that two trains of light waves are reflected respectively from the outer and inner surfaces of the oxide film, and the possibility arises that the "crests" of one series of waves may coincide with the "troughs" of the other, thus diminishing the intensity of the light of some particular wave length. The state of affairs in this part of the strip is shown diagrammatically in Fig. 1, in which the film thickness is enormously exaggerated, of course, in comparison with the length of the strip; the

Jan 1, 1929

By Ulick R. Evans

I Should like to commence by saying how much I appreciate the honor which the American Institute of Mining and Metallurgical Engineers has done me in inviting me to visit your country, and to deliver this lecture before you. In choosing a subject, and in deciding what to include and what to omit, I have endeavored to discuss as far as possible work carried out recently in Europe with which you may not be unduly familiar. It would be poor return for your hospitality, and a mistaken sort of compliment indeed, if I were to load the lecture with accounts of researches carried out in your own country—researches with which you are probably better acquainted than I. Not that I have in any way excluded work done on this side of the Atlantic from my survey; one would indeed find it difficult to write on this, or on any other branch of science, without mentioning American work. But I have endeavored as far as possible to concentrate on aspects of the case which will, I hope, be comparatively fresh to you, and I feel fairly certain that this will be in accordance with your own wishes. Films Produced at Elevated Temperatures If a strip of iron is heated strongly at one end, the other end remaining cold, there is produced over the heated portion a layer of oxide scale, the thickness of which diminishes steadily with the distance from the hot end. Somewhere in the middle of the strip, the thickness of the oxidized layer will become comparable to the wave length of light, and over this region the thin films give rise to a series of beautiful interference tints, commonly known as "temper colors." The colors are caused by the fact that two trains of light waves are reflected respectively from the outer and inner surfaces of the oxide film, and the possibility arises that the "crests" of one series of waves may coincide with the "troughs" of the other, thus diminishing the intensity of the light of some particular wave length. The state of affairs in this part of the strip is shown diagrammatically in Fig. 1, in which the film thickness is enormously exaggerated, of course, in comparison with the length of the strip; the

Jan 1, 1929

By R. Hogg

INTRODUCTION The principal applications of the flocculation process in the coal industry lie in the area of waste water treatment. Consequently, the concern is more with the behavior of the associated minerals, clays for example, than with the coal itself. At the same time, however, the presence of even small amounts of fine coal can significantly influence the performance of the flocculation operation. Coal preparation waste water treatment is a substantial problem involving over 200 billion gallons of water annually. There can be no doubt that these quantities will continue to increase as coal production increases and environmental considerations dictate the increased use of closed circuit systems and tighter control of effluent quality. Furthermore, we can expect to find a continued increase in the amount of fines generated in the coal mining and processing operations. Modern mining techniques tend to yield a finer raw coal with a higher ash content. The greater emphasis on fine coal cleaning for improved sulfur and ash removal and increased coal recovery will also lead to greater demands being placed upon the wastewater treatment system. The costs of "blackwater" treatment have been shown to vary widely from plant to plant (1). Part of this variation can be attributed to differences in the coal being mined and the plant flowsheet but there are no doubt significant contributions from the improper design and operation of treatment facilities.

Jan 1, 1980

The Year Book of the Institute is mailed with this Bulletin. Its membership lists, both alphabetic and geographic, are corrected to Jan. 1, 1918, but its list of officers is revised inn accordance with the elections in February, 1918. The amendment to the Constitution, relating, to qualifications for membership, adopted at the same time, is also inserted in its proper place. We would call attention to the Honor Roll, heading the list of membership. This includes the names of those whom we know (in February, 1918) to be on active military duty, as well as those who are rendering emergency service to the Government in other branches. We are aware that the list is not complete, and shall be grateful for information as to any omissions or corrections. Because of the rapid movement of the military members, their addresses have been omitted from the alphabetic list. Mail addressed to such members, and sent to the office of the Institute, will be forwarded to the best of our information at the time.

Jan 3, 1918

By Willard P. Ward

IT is the object of the present paper to bring to the notice of members of this Institute, the results of experiments made during the past six months in the manufacture of the alloys of iron and manganese in the blast-furnace. The ores at hand and available for the purpose were brown hematites, containing but a very small percentage of manganese, and various manganese ores containing a small percentage of iron. It is hardly necessary here to call attention to the statements regarding the production of iron-manganese alloys from such ores, which are given by all the well-recognized authorities on metallurgy. Suffice it to say, in a few words, that they hold that the operation is practically impossible, and that in the use of oxides of iron and manganese, mechanically intermixed in the same ore, much difficulty has been found in producing spiegeleisen. Spathic ores, containing manganese chemically combined, are alone recommended for the production of spiegel, and even then it is said that well-managed furnaces produce only about 75 to 80 per cent. of spiegel, the balance of the production being white laminated pig or gray iron.

Jan 1, 1876

W. H. Blauvelt, New York, N. Y.—One thought lias been running through my mind during the wholc of this meeting and that is that the scientific and the practical men must recognize very clearly their interdependence. The value of scientific classification of coal is going to be of the very greatest importance to the users, the practical men. Is not the scientific investigation and the great amount of work that is being done in a measure at least lost to the world? Therefore the scientific investigations and the practical needs of the users should bo brought as close together, and the work should be done as closely together, as possible; that is, the scientific man should know what the practical man needs, and the practical man should not feel that the scientific man is merely a theorist. Scientific investigation is going to have a great effeet and be of great valuc to the practical man who is trying to solve his problems. In the subject which I discussed' for instance, we must look to the scientific man to tell us why coal cokes in one way and not In another and why certain coals will do certain things and others, which appear on the surfacc to be generally similar, do not act in the same way. Need or Physical Data on Coal H. J. Rose, Pittsburgh, Pa.—There is a subject which is a sort of hobby of mine; that is, the need for what might be called critical tables of constants for coal. The chemist has big volumes giving constants, such as the density, solubility, specific heat, thermal conductivity and all other physical and chemical data that have been determined for chemical compounds. Data arc also available on many common materials, for example, the density, hardness, modulus of rupture or maximum crushing strength of swamp white oak as compared with some other wood. In fact, physical data for practically cvery hype of wood commercially produced in the world can he found. In the same way the metallurgical man has handbooks giving the properties of alloys, etc., but we havc very little tabulated information about coal. Our principal reference works are the volumes published by the U. S. Bureau of Mines on the proximatc and ultimate analysis and calorific values of coals of the United States. That is 3 pioncer work of enormous value, but we have reached the point where we need more diversified information. Mr. Fulweiler raised the question of the relative strength of the different coals and cokes. Dr. Campbell and Dr. Ashley wanted to have some information on the resistance of coal to air slacking. It was brought out in the discussion that we want to know something about the coking properties of coal. There are any number of physical tests that we need, such as the thermal conductivity of certain coals, the coefficient of expansion, or the coefficient of friction; or other constants. A smattering of such information is scattered through the literature; for instance, a research worker in Wales will report a coefficient of expansion on Wclsh coals and one in South Africa will report something else for one or two kinds of African coals, hut it is difficult to find the information that is needed on our own coals. Would it not be worth while to consider collecting reliable critical

Jan 1, 1930

By F. C. Langenberg

It is the purpose of this paper to present a limited amount of experimental data obtained on the Charpy impact machine. Several concrete examples will be given showing the relation existing between the results obtained upon the Charpy impact machine and the behavior of the parts tested when in service. Although it is pointed out by G. Charpy and A. Cornu-Thenard1 that it is first necessary to determine a satisfactory working process before studying the correlation between the results of these tests and the behavior of the parts tested in service, this ideal course cannot be strictly adhered to. If a certain part repeatedly fails in service and the available tests give no indication of its cause, advantage must be taken of any possible means that will solve the problem; therefore, even though the reliability of the results obtained by the Charpy impact machine have been questioned by many, it was necessary to use this instrument without giving careful consideration to its possible sources of error. It would seem that the conclusions arrived at by Charpy -and Cornu-Thenard justify the assumption that the precision obtained by this machine is comparable to that obtained by the other more common forms of testing. The second general conclusion arrived at by them, namely, that the impact test upon notching does not offer any direct correlation to the ordinary tests, is also borne out by many hundred determinations made in the laboratories at Watertown Arsenal. This statement, however, should be qualified as follows: Other ordinary tests include the static tensile test from bars taken in a longitudinal direction and the Brinell hardness. The author agrees that no law is yet known for the computation of the energy absorbed in the rupture of bars of the same material but of different dimensions. Although Charpy and Cofnu-Thenard do not refer in their valuable article to the use of the Charpy machine in industrial practice, it should be stated that this instrument has been in constant use in the laboratory at Watertown Arsenal for several years, and is now employed for both routine and experimental testing.

Jan 1, 1920

By Strathmore R. B. Cooke

On the basis of experiments con- ducted on quartz using a bubble pick-up method, it was shown in an earlier paper1 that this mineral will preferentially adsorb hydrogen, calcium, or sodium ions, depending on the relative concentrations of those ions in the solution in which the quartz is immersed. For quartz particles ranging in size from 0.2 to 1 mm, it was demonstrated that the concentration of calcium in solution (assumed present as ions) necessary to completely activate quartz for flotation is given by the expression: In this expression, ionic concentrations are in mols per liter. It was further shown that the pick-up method is apparently more sensitive to changes in reagent concentration than the standard captive-bubble method, and that induction times are apparently much reduced. Since completing these earlier tests, a new type of cell has been constructed; this is shown in Fig 1 and 2. In Fig 1, A is a ground joint, B is a ceutral tube reaching to within a few millimeters of the bottom of the cell, and C is a stopper which may be removed for re- agent addition, and serves the further purpose of excluding carbon dioxide from the air during the test. The entire cell is constructed of Pyrex glass, and does not give the trouble experienced with the earlier cell, in which activating ions were released from the glass at high pH values. The only critical factor in the construction of the cell is the clearance between the central tube and

Jan 1, 1949

By Elmer R. Kaiser

Industry Adopts Research: Seventy-Ave years ago Thomas A. Edison began in a modest way and with limited funds to gather about him men of various talents to form the first industrial research laboratory. His laboratory at Menlo Park, N. J., became famous for many discoveries and inventions, but possibly the most important of all may yet be the industrial research laboratory itself. Today, private industry operates 2500 research laboratories in which 135,000 persons' are directly and indirectly creating new processes and products and improving old ones, as well as developing new information to help keep the fountain of knowledge from running dry. In this change-making function, the scientific personnel comprises 41 pct; the technical personnel 26 pct; and the balance, 33 pct, nontechnical. The term "industrial research" has become so broad as to include almost everything beginning with the search for and discovery of the laws governing the properties of matter and energy to the development and testing of processes, methods, and equipment. These classes of investigation commonly merge so that no sharp boundary can be traced between them. The National Research Council therefore defines industrial research as "the endeavor to learn how to apply scientific facts to the service of mankind."' Currently, expenditures for research by industry are variously estimated at between $450,000,000 to $700,000,000 a year,' or about twice the expenditure for 1940. The President's Scientific Research Board" estimated that the national research and development for 1947 (excluding atomic energy) was as follows: A few companies spend as much as 5 pct of their gross receipts for research, but 1% to 2 pct is considered a good proportion by many." Shortages: Commendable as is the record of growth and accomplishment of science in industry, it is only a beginning. America and the rest of the world have merely sampled the fruits of industrial research; most industries have yet to make research the key to their future. A top research consultant, T. A. Boyd, of General Motors, states ". . . perhaps 90 per cent of all companies still have no research laboratories."Y or example, of more than 17,000 manufacturing concerns whose gross sales exceed $500,000 a year, less than 2500 have research laboratories. A still smaller proportion of the 184,230 manufacturing establishments in 161 industriese have or could afford their own research facilities. Yet, the small and mediurn-sized com,panies with less than 250 employees each, produce one half of the dollar volume of manufactured products.' How are these companies to participate in and share the benefits of research? Boyd gives two reasons for the inadequate number of laboratories in industry: Many people still do not appreciate the importance of research, nor understand its tremendous potentiali-

Jan 1, 1951

By Elmer R. Kaiser

Industry Adopts Research: Seventy-Ave years ago Thomas A. Edison began in a modest way and with limited funds to gather about him men of various talents to form the first industrial research laboratory. His laboratory at Menlo Park, N. J., became famous for many discoveries and inventions, but possibly the most important of all may yet be the industrial research laboratory itself. Today, private industry operates 2500 research laboratories in which 135,000 persons' are directly and indirectly creating new processes and products and improving old ones, as well as developing new information to help keep the fountain of knowledge from running dry. In this change-making function, the scientific personnel comprises 41 pct; the technical personnel 26 pct; and the balance, 33 pct, nontechnical. The term "industrial research" has become so broad as to include almost everything beginning with the search for and discovery of the laws governing the properties of matter and energy to the development and testing of processes, methods, and equipment. These classes of investigation commonly merge so that no sharp boundary can be traced between them. The National Research Council therefore defines industrial research as "the endeavor to learn how to apply scientific facts to the service of mankind."' Currently, expenditures for research by industry are variously estimated at between $450,000,000 to $700,000,000 a year,' or about twice the expenditure for 1940. The President's Scientific Research Board" estimated that the national research and development for 1947 (excluding atomic energy) was as follows: A few companies spend as much as 5 pct of their gross receipts for research, but 1% to 2 pct is considered a good proportion by many." Shortages: Commendable as is the record of growth and accomplishment of science in industry, it is only a beginning. America and the rest of the world have merely sampled the fruits of industrial research; most industries have yet to make research the key to their future. A top research consultant, T. A. Boyd, of General Motors, states ". . . perhaps 90 per cent of all companies still have no research laboratories."Y or example, of more than 17,000 manufacturing concerns whose gross sales exceed $500,000 a year, less than 2500 have research laboratories. A still smaller proportion of the 184,230 manufacturing establishments in 161 industriese have or could afford their own research facilities. Yet, the small and mediurn-sized com,panies with less than 250 employees each, produce one half of the dollar volume of manufactured products.' How are these companies to participate in and share the benefits of research? Boyd gives two reasons for the inadequate number of laboratories in industry: Many people still do not appreciate the importance of research, nor understand its tremendous potentiali-

Jan 1, 1951

G. D. Kneip, Jr., and J. 0. Betterton, Jr. (Union Carbide & Carbon Corp., Oak Ridge, Tenn.)—The authors have contributed to the theory of zone melting by considering the effects of the solidification of the final zone on the distribution curves for the finite length bar. However, they do not consider in sufficient detail the restrictions imposed by the particular metals involved. Eq. 4 has the analytical solution which is equivalent to Pfann's' equation for normal solidification of the final zone. For distribution coefficients less than one, it is apparent from this form of the equation that, as the solidification approaches completion, the concentration attains extremely large values which are inconsistent with the density of physical materials. The necessary restrictions then are that the solute concentration cannot exceed the density of the alloy, or more frequently, the solubility limit in the solid phase. Secondly, the distribution coefficient cannot be constant from 0 to 100 pet solute unless the liquidus and solidus coincide over this whole region. It would thus be more correct to impose limits on the solubility such as would be indicated by a typical eutectic diagram. Furthermore, in this case the assumption that the distribution coefficient remains constant is more likely to be realized. Eq. 4 should then be replaced by the following C,,(x) =k/L-x [ ?11 3 C11 (x)Ddx - ?11 4 Cn(x)dx= k[Cn (L-l)/k] [ L-x/l]x-1 L-l = x = L-l [kCenterlie/Cn (L-l)]1/k-1 The typical shape for the distribution curve in the final zone is indicated schematically in Fig. 12 for the simple eutectic case. The solidification proceeds according to Pfann's' expression until the concentration reaches the maximum solubility in the solid phasc. At this point, the concentration changes abruptly to the eutectic composition and remains at this value for the duration of the solidification. The width of the flat region, and the back reflection of this effect into the concentration curve on subsequent passes, depends upon the ratio of the eutectic concentration to the original concentration, upon the distribution coefficient, and upon the number of passes. Similar effects on the concentration curves in the first zone length would be expected in many systems for which the distribution coefficient is greater than one, and where the maximum solubility is not too much larger than the original concentration. The discussers agree with the authors that the assumption that the liquid is uniform in concentration should be considered with caution. Kneip and Better-ton' have shown, however, that in floating zone refining of zirconium, using induction heating, the distribution of iron agrees with theory which assumes a uniform liquid composition. Hence, in this case, the experimentally realized distribution coefficient agrees with the present phase diagram within the experimental uncertainty. L. Burris, Jr., C. H. Stockman, and I. G. Dillon (authors' reply)—The authors are happy to have received the comments of G. D. Kneip, Jr., and J. 0. Betterton, Jr., which provide additional insight into the zone refining process. It is true that the equations developed are inapplicable if the solute solubility in the solid phase is exceeded. However, this restriction on the use of the equations was clearly stated in the paper. A closer approach to

Jan 1, 1957

By E. H. Lee, F. J. Fayers

Problems in reservoir analysis can usually he cupressed in terms of a system of nonlinear partial difjerential equations. A rnethod for .setting physically reasonable boundary conditions for these systerrls by ayplication of the theory of characteristics is discussed. A short description i.c. given of the technique for finding chnmcteristics of general first order and second orrler equations. Specific examples are quoted jrorn eqrrations occurring in theoretical reservoir studies. The princip1e. ossocicred wit11 the use of chnracteristic to set physically realistic boundary conditions me developed, and thr method is discussed in terms of boundary condition for the noncupillary, compressible, two-phase flow problen: jor the cupillary, ir~cowlpressible, two-phase flow problems for the tlrtergent flooding prohlenl; as for the compressible. noncapillary, two-phase flow pro11letn. INTRODUCTION In most problcms in reservoir analysis the physical situation is described by a system of nonlinear partial differential equations. The general solution to the set of equations usually comprises a wide range of functions ancl a particular solution is normally selectetl by applying suitable boundary conditions to the problem. In some cases it is clear from the physical situation what form the boundary conditions should take, but it is usually desirable to have an independent mathematical check of the suitability of the chosen conditions. From the mathematical standpoint, a system of partial differential equations with boundary conditions is said to be properly set if the combination determines a unique solution which is continuously dependent on the equation and the boundary conditions. Such a solution is sometimes termed "reasonable". In investigating the properties of the mathematical representation, it is useful to determine the structure of the system by the application of the theory of characteristics. This theory determines in the space of the independent variables, lines or surfaces which play a special role in thc system's behavior. The characteristics determine the possibility and nature of the propagation of discontinuities in the derivatives of the dependent variables. Along the characteristics certain differential relations hold which for some problems allow a so- lution to be obtained analytically. In the case of hyperbolic equations the characteristics can bc used as 3 basis for a numerical solution. If a complicated nonlinear system is to be solved, a study of behavior of the characteristics will indicate what boundary conditions should be chosen. By using the method of characteristics, several advances have rccently been made in solving reservoir engineering problems. Sheldon, Zondek and Cardwell' have discussed how the the method may be used grap-phically to solve the incompressible two-phase displaccmerit problem when the gravity term is included in the equations. Fayers and Perrine' have applied the method to study the equations representing detergent flooding. When compressibility and solution-gas effects are introduced into the two-phase flow problem, the equations and their characteristics become more complicated. It will be seen that in this problem the characteristics are useful for indicating a reasonable set of boundary conditions but cannot readily be used to compute a numerical solution. This problem has been solved on the IBM 701 using normal finite difference methods hy West, Garvin and Sheldon." The material to be prcscntcd in this report is divided into three sections. The first discusses the determination of the characteristics of first and second order partial differential equations; the second describes the selection of suitable boundary conditions by the application of the principle that the future cannot affect the past; the third discusses the use of characteristics for setting the boundary conditions of the two-phase solution-gas flow problem. A useful introduction to the method of characteristics has been given by Hildebrand.' A summary of the method will be given in this section of the paper. The First Order Equation The quasi-linear equation of first order is It is linear in the partial derivations of z. The properly linear equation has the form The characteristics of are curves along which the

QUICKSILVER is a body that consists of flowing and liquid materials, almost like water with a shining whiteness; it is composed by Nature of a viscous, subtle substance with an overflowing abundance of moistness and coldness together. This composition, in the opinion of the philosophic alchemists, is a thing that is very disposed to become metal-indeed they say that it is the original seed of all metals. When it lacks the warmness and dryness or the specific time that they require, it cannot congeal and so remains in the form that we see as an imperfect thing without becoming metal. These clever investigators have also called it mercury in consideration of its properties, perhaps because of its resemblance to the planet of him whose actions place him between gods and men, according to the poets in their stories. Thus these investigators think that this has a similar place among perfect metals, since it is the primary mineral matter. It might also be that they called it so because like the god Mercury it is winged and fugitive, and by virtue of its powerful subtlety penetrates all things and can issue forth from them at will. But let it be called by any name they wish-it does not matter to us. I, like them, shall sometimes call it mercury and sometimes [23 ] quicksilver as it has been named to me, and you will understand it as such. Now I shall leave aside the disputes on whether it is the primary matter of metals or not, since I have said enough concerning this question in the first chapter of the First Book. In order to approach what the philosophers say about it, I say that it may well be material about to be converted into metal, but since it is seen to be so ill-proportioned and so badly decocted, I cannot believe that it can be disposed to the generation of all kinds of metals. Indeed, if it is, I think that if its necessary processes had not been interrupted it would be more apt to generate lead, tin, iron, or even silver rather than copper or gold. And if we wish to consider it in relation to the natural complexions [of metals] or to the power of the, planets, I think that mercury is far distant from those of gold and from the power of the sun and of the moon. Therefore I say that if it is not what I have said, it is a thing that Nature has been pleased to make as it is. I am led to say this because all of it that I have seen has had the same

Jan 1, 1942

By S. LeFevre

THE solution of the housing and sanitation problem in mining communities, keeping in view both economic and humanitarian aspects, demands the best thought of the management of such enterprises. Upon the solution depend the health and comfort of the employee and his family, and as a consequence his contentment and efficiency. The following description covers briefly the methods installed for Witherbee, Sherman & Co. The operation of the system has been for about two years under the direct supervision of T. A. Hammond, Land Agent, and I am indebted to him for a compilation of the results.

Jan 2, 1915