Search Documents

By William Barrett

IN order properly to evaluate the data related to geomagnetic surveys, it is highly desirable to have all the available information concerning the magnetic properties of the, involved media. This is true of surface as well as subsurface formations and becomes of increasing importance as advancement in instrumental and interpretative technique permits the analysis of relatively slight magnetic reflections of buried masses. Since the magnitude and areal distribution of the usually complex resultant magnetic field at the surface of the earth is a function of the susceptibility1 of the involved matter, it necessarily follows that susceptibility determinations will afford valuable data for geophysical correlation. The present method was developed to meet the need for routine analysis of specimens in the geomagnetic laboratory where it was felt that general utility, ruggedness, ease of manipulation and reproducibility of results was of greater importance than extreme sensitivity.

Jan 1, 1931

By Ove Sandberg, Olav Bowitz

The operational characteristics of the Soderberg vertical spike anode are briefly discussed stressing the importance of the flow properties of paste in the fluid zone, the thermal shrinkage in the carbonizing zone, and the surface disintegration in the consumption zone. The requirements for paste recipe and binder quality are combined with design and operation of cell. A low temperature susceptibility of viscosity and low thermal shrinkage of paste together with a low microporosity of the binder coke are important properties. PRACTICAL application of Soderberg's idea of a selfbaking carbon electrode proved successful just before 1920. Shortly after, experimental work was started with the aim of developing a continuous electrode that could be adopted as anode in aluminium reduction cells. The intermittent operation of a large number of small prebaked anodes made the idea of developing a continuous anode for electrolytic production of aluminium especially tempting. Moreover, the electrode consumption in this process, even on a theoretical basis, is very high. Many installations were carried out in the 1930's and during the Second World War. During the tremendous post-war expansion of the aluminium industry, the Soderberg electrode has been steadily more widely adopted. Thus, today more than 60 pct of the Western World's output of aluminium is produced in cells with selfbaking anodes, see Big. 1. The quality of the anode paste of Sfiderberg elec- trodes is considered a major factor influencing the specific carbon consumption. The purpose of this paper is to survey the fundamental requirements which must be met in order to obtain good anode operation. We have limited this paper to a discussion of Elektrokemisk's research on the vertical spike type anode. I) FUNDAMEKI'TALS OF ANODE CARBON PERFORMANCE A) Brief Introduction. The only practical method for producing a conductive carbon anode of the size required is to form and carbonize a mixture of a carbonaceous binder and a precalcined dry aggregate coke. In the Soderberg electrode, the forming and carbonization take place in the electrolytic cell

Jan 1, 1962

By Frank C. Roberts

Neglecting the hydrogen and hydrocarbons, 1 will assume the following analysis as a fair average composition, by weight, of the waste gases escaping from a coke-burning blast-furnace: CO2............17.25 CO,............25.25 N,.............57.50 100.00 The 25.25 CO requires for combustion 62.6 of air, or 11.398 of oxygen, necessitating the passage of 48.202 nitrogen into the products of combustion. The latter, therefore, have the following composition: CO2,,............ 56.9 N,............105.7 Tile total specific heats of these quantities of the respective gases are 12.31 and 25.79, giving for the combined product, 38.1 approximately. That is, the product of combustion will absorb 38.1

Jan 1, 1889

By J. F. Smith, J. R. Ogren, N. J. Magnani

The uapor pressrcres of magnesium over binary alloys of magnesium with twelve of the yare-earth eletnetzts have been measured by the Knudsen effuion method in the temperature range 675° to 910°K. These vapor-pressure measurments were combined with data concerning the tevtrlitzul magnesium solubility and the vapor pressure of pure magnesinm to evaluale the standuvd free energies of pluase jormation. These free-etzergy values indicate that the CsCl structures of the heacy rave earths tend to be somewhat less stable than those of the light rare earths. This dif-]eying- behaviov covrelates with differences which have been obsevz~ed in other alloy systetns wherein a phuse appeurs, disappeavs, or changes crystal stvucture as the atomic number of the rare-earth com-ponent is changed. This behauior also appears to correlate with the struclurul rariations within the rare-earth elements themselves, and it is speculated that cariations in the spatial extent of the 4f orbitals are responsihle. STUDIES of the phase relationships and crystal structures in the binary systems between rare-earth metals (lanthanons) and magnesium are extensive but far from complete. However, the currently available information1-10 does produce a rather interesting pattern. This is illustrated in Table I. If one excludes europium and ytterbium from consideration because of their generally atypical behavior, it can be seen from the table that the phase relationships in the magnesium-rich regions show a distinctly different pattern for the lighter lanthanons as compared to the heavier lanthanons. For the lighter lanthanons, LnMg2 phases occur from lanthanum to gadolinium with the cubic MgCu2 structure, LnMg3 phases occur from lanthanum to terbium with the BiLi3 structure, and magnesium-rich phases occur from lanthanum to gadolinium with stoi-chiometries between Ln5Mg42 and LnMg12. In contrast, for the heavier lanthanons, those LnMg2 structures which have been examined have the hexagonal MgZn2 structure, LnMg3 phases have not been observed beyond terbium, and the magnesium-rich phases occur with the a manganese structure near a stoichiometry of Ln5MgZ4. The heavy lanthanon-magnesium systems thus appear to be analogous to the Y-Mg system""2 wherein YMg has the CsCl structure, YMg2 has the MgZn2 structure, and the region Y4Mgz5-Y5Mg24 has the a manganese structure, and no other intermediate phases are observed. Similarity in alloying behavior between yttrium and the heavy lanthanons occurs commonly, and on this basis it seems likely that LnMg2 phases will be found with the MgZn2 structure in the binary systems of dysprosium, thulium, and lutetium with magnesium when the appropriate investigations are made. In the case of the magnesium-rich phases of the lighter lanthanons, only the Ce-Mg phase relationships have been investigated thoroughly and in detail, and until similar investigations are made for the other systems there will remain questions as to which magnesium-rich stoichiometries represent equilibrium phases and what systematic variations occur in the sequence from lanthanum to gadolinium. Thus the data in Table I show that only the LnMg phases occur with the same crystallographic structure throughout the sequence from lanthanum to lutetium. It was speculated that the relative stability of these LnMg phases might vary from one lanthanon to the next in such a way as to presage the differences which occur among the more magnesium-rich lanthanon-magnesium phases. On this basis the present investigation of the thermodynamics of phase formation was Gndertaken for the LnMg phases. PROCEDURE AND RESULTS A generalized phase diagram for the lanthanon-rich portion of a lanthanon-magnesium alloy system is shown in Fig. 1 where ß represents a high-temperature bcc

Jan 1, 1968

By Rosewell H. Johnson

Discussion of the paper of ROSWELL H. JOHNSON, presented it the San Francisco meeting, September, 1915, And printed in Bulletin No. 102, June, 1915, pp. 1291 to 1294. WILLIAM A. WILLIAMS, San. Francisco, CaI.-A sliding. scale of royalties was proposed to the Department of the Interior in connection with the fixing of royalties to be charged upon oil leases made on the Osage Reservation in Oklahoma. The possibility of evasion and difficulty of enforcement required close inspection to satisfy all interests, particularly in connection with the exemption from royalty on oil to equal maintenance and interest on the junk. Mr. Johnson discusses the block method, the period method, and the cumulative method, and favors the adoption of the cumulative method with a proviso that the wells should be permitted to be pumped until the gross income is as low as the maintenance cost, which would mean exemption from royalty on the smallest wells. He recommends that depth be the variable factor upon which the sliding royalty is based and suggests that on partially developed territory in the Osage, the royalty be one-sixth for oil wells averaging less than 2,000 ft. in depth, one-eighth for wells from 2,000 to 3,000 ft., and one-twelfth above 3,000 ft.; for the rest of the Osage he suggests one-eighth above 2,800 ft. and one-twelfth below that depth. The net result, if Mr. Johnson's suggestions had been accepted in the Osage, would have been to reduce the then existing rate of royalty and considerably increase the cost of administration. The difficulties in determining the size of wells to be exempt and the possibility of obtaining oil at different depths in the same well might lead to complications which are avoided by charging a flat royalty as now universally charged throughout the United States. It is not uncommon to reduce the royalty when the production of the wells becomes unprofitable at an existing rate of royalty, accomplishing very much the same results as Mr. Johnson has attempted to accomplish by the cumulative royalties, and probably in a manner far more satisfactory to the operator and the lessor. A. C. MCLAUGHLIN, San Francisco, Cal.-The net revenue of the well depends, first, on the cost of production; second, on the amount of oil produced; therefore it would be impossible under Mr. Johnson's system to set a royalty which would be fair to all concerned. If it is impossible to set it at the beginning, it is certainly further impossible to do it from day to clay. I think it is entirely impracticable of application.

Jan 12, 1915

By P. D. Bush, E. H. Gates, M. D. Vijayaraghavan, L. F. Engle

The process developed over the last few years by Republic Steel Corporation in conjunction with Colorado School of Mines Research Institute has been used as a basis for the conceptual engineering of full size plants. The paper will cover the equipment design criteria, equipment design itself, and the integration of the complex unit operations. There are unique features of agitation and use of gas media through- out. The paper will provide an illustrative example of the process requirements for a variety of raw material feeds. It will discuss the materials of construction approach required.

Jan 1, 1973

By R. F. Hollis, C. K. McArthur

PRIOR to the application of anion exchange, all recovery of uranium from acid leach liquors precipitated an impure product requiring further upgrading before it could be refined. The ion exchange process, on the other hand, provides excellent selectivity for extracting soluble uranium from leach liquors, so that high grade concentrates can be produced directly. The discovery that uranium is readily adsorbed by anion exchange resins, together with the experience of resin and equipment manufacturers in water treatment, led to rapid development of ion exchange in a multiple column operation. Many processing plants using fixed bed ion exchange are in operation or under construction in Africa, Australia, and Canada. There are a limited number in the U. S. Although the fixed bed process has been highly successful, the feed to the ion exchange columns must be a clear solution, which is obtained by filtration or by countercurrent decantation of leached pulps. With some ores, poor filtration or settling characteristics make production of a clear solution difficult. Most processing plants in the U. S. receive their ores from a number of small mines, and there is considerable variation in the settling and filtering behavior of the ores. An ion exchange process was therefore desirable in which the uranium could be recovered directly for the leached pulp by adding ion exchange resin, which could be then separated from the pulp by a screening operation. The process would thus resemble the cyanide-charcoal process in which gold is adsorbed from cyanide pulp by means of activated charcoal. Preliminary tests in which leached pulps were directly contacted with resin beads led to the development of the RIP process.

Jan 4, 1957

By Betty M. Miller

INTRODUCTION In September 1974 the Resource Appraisal Group of the Branch of Oil and Gas Resources, U. S. Geological Survey, was asked to aid the Federal Energy Administration (FEA) in its legal responsibility to generate by June 1975 an independent appraisal of the undiscovered oil and gas resources of the United States, both onshore and offshore. As a result, the Resource Appraisal Group accelerated its ongoing efforts to develop sound appraisal methods and procedures that would permit the systematic collection and evaluation of basic data from petroleum provinces throughout the Nation. The results of this independent appraisal of the Nation's conventional oil and natural gas resources were published by the U. S. Geological Survey as Circular 725, June 1975 (1). The estimates in this report of undiscovered recoverable oil and gas resources for the United States were made: (1) by carefully re- viewing a large amount of geological and geophysical information gathered on more than 100 different provinces by over 70 geologists within the Survey; (2) by applying a variety of resource appraisal techniques to each potential petroleum province; and (3) by application of subjective probability procedures to group appraisals for each petroleum province. These methods provide a range of estimates which are summarized in terms of low, high and mean values for the various provinces and groups of provinces, or regions. The basic data and procedures used are documented and are being incorporated into a dynamic, data- intensive system that can be upgraded, updated and reevaluated periodically. These data are open to public inspection. In this study, the primary emphasis was placed on conventional crude oil and natural gas in the onshore provinces and the provinces on the continental shelf out to water depths of 200 metres; estimates

Jan 1, 1977

By C. A. Czako

INTRODUCTION In recent decades sintering and pelletizing of finely divided materials have become the primary tonnage producing modes of agglomeration. This statement is especially true in the iron and steel industry and, to a lesser degree, in the nonferrous, chemical and non-metallic minerals processing industries. In every industry the main objectives in agglomerating fines are essentially the same, namely to convert ores, minerals and chemicals of undesirable fineness into agglomerates characterized by a size consistency desirable for subsequent use or processing. Depending on the type of agglomeration process selected and the conditions maintained during agglomeration, the physical process of increasing size is complemented by a number of other unit processes. These processes can occur simultaneously, consecutively or in an overlapping manner. Some of these additional unit processes are incidental to the agglomeration operation, but at the same time can be critical, depending upon the subsequent use of the product. Accordingly, during processing, conditions have to be controlled to either suppress or enhance the extent of completion of these unit processes. The purpose of this report is to review laboratory testing as the basis for engineering modern sintering and pelletizing plants. Considering that most typical applications are for the iron and steel industry, agglomeration of ferrous materials is reviewed and discussed. When these total processes are adapted to suit non- ferrous materials, chemicals, or non-metallic substances, the over- all approach remains the same; only the processing parameters are affected as necessitated by the different nature of the materials.

Jan 1, 1977

By M. A. Mahtab, T. M. Yegulalp

This paper presents the development and application of an approach for clustering fracture orientation data. Data are projected on the surface of the unit upper hemisphere and the clustering approach is applied in three steps: (1) randomness test and identification of dense clusters, (2) estimation of cluster statistics, using Bingham distribution, and (3) rejection of extremal data based on Chauvenet's criterion.

Jan 1, 1982

By Henry M. Howe

The object of the present paper is to suggest injecting into the hearths of iron blast furnaces, whose temperature has become unduly lowered, some form of fuel whose calorific intensity, under the peculiar conditions existing there, is considerably higher than than of liquid petroleum, the rose of this substance for melting out chills having grievonsly disappointed the high hopes which were at first entertained of it. A chill being a fall of the temperature below that needed for the complete liquefaction of the slag, which requires, according to Plattner, about 1800' C., one would suppose that the chief thing to be accomplished in curing it would be to raise the temperature in the crucible of the furnace. The most obvious ways of doing this seem to be to raise the temperature of the blast, and to increase the amount of fuel in the crucible itself. Simply increasing the rate at which the blast enters the furnace, if carried beyond a certain point, should lower the temperature in the crucible. The existence of a chill shows that the fuel is arriving too slowly at the tuyeres. If air be introduced so rapidly as to he in excess of that required for the combustion of the fuel, all that excess will simply lower the temperature around the tuyeres, carrying the region of intense heat upwards, and weakening its intensity by increasing its size. Up to a certain point, increasing the rate of introducing the blast will increase practically pari passu the rate at which the fuel reaches the tuyeres. But when mechanical obstructions, which so often accompany chills, retard the descent of the fuel, there must be a point beyond which this does not hold good, and beyond which farther

Jan 1, 1883

By W. B. Daly, A. S. Richardson

The application of artificial refrigeration, or air-conditioning, to the ventilation of deep, hot mines has long been a subject of interest to the operators of such properties. Artificial cooling of the air in theaters, railroad coaches, and various industrial plants has been so successful within recent years that it has been natural to assume that the adoption of similar methods would afford a ready solution to the difficult problem of mine ventilation. It should however, be obvious, that although there may be nothing technically impossible in the application of this process to mine ventilation there is a great economic distinction between the maintenance of a high standard of comfort for a large number of people in a relatively small space such as a theater and the cooling of air to improve working conditions for miners scattered throughout the extensive workings of a large mine. Many methods of air-conditioning have been considered by the management of the Anaconda Copper Mining Co. at various times, but until the development of the process to be described in this paper none has seemed economically practicable. The Ventilating Problem at Butte The main obstacle to satisfactory ventilation in the Butte mines is the normally high temperature of the granite country rock. In the present operating zone, rock temperatures as high as 120' F. have been noted, and in some parts of the district the rate of increase of temperature with depth has ranged as high as 3.5" F. per 100 ft. Other factors, such as the decay of mine timber and the oxidation of sulfide minerals in the ore bodies, contribute to raise the temperature of the air in the working places but, particularly in the development of the mines to greater depth, the naturally high temperature of the rock is of predominant importance. In few other places, probably, are the ordinary ventilating measures more hindered than at Butte. At an operating depth now exceeding 3000 ft., all of the air required for ventilation must pass through timbered shafts which, because of heavy ground, are of small size and offer great resistance to the flow of air. Shaft compartments are rarely more than 4.5 X 5 ft., and the shaft area open to the flow of air usually does not exceed 65 sq. ft.; in only two shafts is the area as great as 85 sq. feet.

Jan 1, 1934

By Ove Rehnberg

Catalytic purifiers are widely used as exhaust treatment devices on diesel equipment in confined spaces. The paper summarizes some studies carried out at the University of Lulea on diesel exhaust purifiers. The main purpose has been to elucidate important chemical activities of catalysts useful for the improvement of their effect. The effects of platinum catalysts on exhaust constituents such as carbon monoxide, nitrogen oxides, unburned gaseous hydrocarbons, and polynuclear aromatic hydrocarbons are discussed. Also pointed out are the great differences in catalyst activity and advantages/disadvantages associated with the catalysts.

Jan 1, 1982

By Denis Yeung, B. H. G. Brady

A hybrid finite element-boundary element code with eight noded isoparametric finite elements and three noded boundary elements is described for plane strain and linear isotropic elasticity. In the direct formulation of the Boundary Flement Method, quadratic variation of geometry and displacements, and linear variation of tractions with respect to the element intrinsic coordinates are used. The boundary element region is treated as a "super-element" in the finite element sense.

Jan 1, 1982

By Walter H. Bucher

This symposium is designed to lay the basis for a general discussion of the place of geophysics in the training of geologists. As there is danger that in the ensuing debate individual interests may be given emphasis out of proportion to their place, we shall do well to view the whole field of geological inquiry in order to see the problem in true perspective. The Nature of Geological Inquiry "Basic" and "Complex" Sciences It is convenient to divide all science into two major divisions, the basic and the complex sciences. The basic sciences separate out from reality such entities as "substances" and "movements," describe their behavior in terms of arbitrary units of measurement and derive from them by progressive abstractions concepts and patterns of behavior that exist between them, so-called general "laws" and "properties" of nature. The complex sciences, on the other hand, deal, with little or no abstraction, with those objects of reality that are accessible to man in the atmosphere, the hydrosphere, the lithosphere and the biosphere. Their work comprises two types of inquiry. One is concerned with abstractions to the extent of dealing with types rather than individuals—that is, with such things as plants, animals, protoplasm; clouds, streams, gla- ciers; volcanoes and mountain ranges. It comprises the search for general properties and patterns of behavior or "laws" that characterize the objects and their reactions to each other. These properties and laws apply always, everywhere. They are independent of the stream of time. We may call the results of this sort of inquiry timeless knowledge. The other type of inquiry is concerned with the objects themselves—that is, with this animal and that plant; this river system and that mountain chain; this glacier and that valley. Like all concrete objects in nature, they are subject to change with the passage of time, especially when it is measured in years, centuries, eons. The characteristics by which we recognize them —indeed, their very existence—are dependent on their position at this point in the stream of time. This we may call time-bound kntowledge. The so-called descriptive sciences are all bound to the past of which the objects of their study are the product and through which alone their present properties call be understood. They are historical sciences. This obvious fact is easily overlooked, which leads to serious misunderstanding, as we shall see later. Dynamic Geology With this broad picture in mind, let us now examine the nature of geological inquiry, defining, for the purposes of this discussion, geology as the science of rocks. Air is not a rock; water is. Meteorology and climatology are, correspondingly, gen-

Jan 1, 1946

By Walter H. Bucher

This symposium is designed to lay the basis for a general discussion of the place of geophysics in the training of geologists. As there is danger that in the ensuing debate individual interests may be given emphasis out of proportion to their place, we shall do well to view the whole field of geological inquiry in order to see the problem in true perspective. The Nature of Geological Inquiry "Basic" and "Complex" Sciences It is convenient to divide all science into two major divisions, the basic and the complex sciences. The basic sciences separate out from reality such entities as "substances" and "movements," describe their behavior in terms of arbitrary units of measurement and derive from them by progressive abstractions concepts and patterns of behavior that exist between them, so-called general "laws" and "properties" of nature. The complex sciences, on the other hand, deal, with little or no abstraction, with those objects of reality that are accessible to man in the atmosphere, the hydrosphere, the lithosphere and the biosphere. Their work comprises two types of inquiry. One is concerned with abstractions to the extent of dealing with types rather than individuals—that is, with such things as plants, animals, protoplasm; clouds, streams, gla- ciers; volcanoes and mountain ranges. It comprises the search for general properties and patterns of behavior or "laws" that characterize the objects and their reactions to each other. These properties and laws apply always, everywhere. They are independent of the stream of time. We may call the results of this sort of inquiry timeless knowledge. The other type of inquiry is concerned with the objects themselves—that is, with this animal and that plant; this river system and that mountain chain; this glacier and that valley. Like all concrete objects in nature, they are subject to change with the passage of time, especially when it is measured in years, centuries, eons. The characteristics by which we recognize them —indeed, their very existence—are dependent on their position at this point in the stream of time. This we may call time-bound kntowledge. The so-called descriptive sciences are all bound to the past of which the objects of their study are the product and through which alone their present properties call be understood. They are historical sciences. This obvious fact is easily overlooked, which leads to serious misunderstanding, as we shall see later. Dynamic Geology With this broad picture in mind, let us now examine the nature of geological inquiry, defining, for the purposes of this discussion, geology as the science of rocks. Air is not a rock; water is. Meteorology and climatology are, correspondingly, gen-

Jan 1, 1946

By K. Hanumantha Rao, A. Nayak, . K. S. Narasimhan, S. N. Mahapatra

Selective flocculation studies carried out with iron ore tailings generated at Kudremukh iron ore plant indicate that a concentrate containing 63% iron can be obtained from the tailings containing 34% iron with around 60% recovery. This opens up the possibility of recovering most of the iron lost in the tailings generated at 2 kt/h (2200 stph) while processing 22 Mt (24 million st) ore per year. This would mean that the productivity could increase by around 50%. In these studies, it has been established that caustic degraded tapioca starch is a most effective agent for selective flocculation. While potato starch after caustic degradation can also be used, neither the parent starch nor the amylopectin compound is as effective.

Jan 1, 1986

By N. F. Dyson, T. R. Scott, M. R. Thornber, W. E. Ewers, M. Bussell

Leach liquors derived from the processing of nickel ores are generally highly contaminated and contain appreciable free acid. Methods are described for obtaining a commercial grade of concentrate from such solutions using pyrrhotite as the seed material to abstract nick- el, cobalt, etc. from solution. At temperatures in excess of 160° C., recoveries of 99% can be obtained from contaminated solutions where the free acidity is as high as 0.5 M in sulphuric acid. At lower temperatures down to 80° C., high recoveries can also be obtained either by adding H2S to the system with appropriate adjustment of the free acidity or by using "activated" pyrrhotite or artificial FeS in the system without prior addition of H2S. The methods are applicable to liquors derived from either oxide or sulphide ores, and the products are suitable for smelting or other known processes used to obtain pure metals. The mechanism of the reaction appears to vary with the operating temperature, and the results ye therefore discussed in the light of electron probe and optical microscopic studies.

Jan 1, 1973

By J. H. Nelson

An outline survey of the economic outlook for the United States export trade in petroleum products resolves itself broadly into two general divisions; first, a consideration of our present position in this trade, and second, a discussion of the visible factors which promise to affect appreciable changes in the immediate future in that trade. The United States PetRoleum Exports of majoR Petroleum Products 1925, 1926 and 1927

Jan 1, 1928

By R. W. Snyder, W. H. Guilinger, B. S. Gottfried

Two numerical methods are presented JOT solving the equations Jor one-dimensional, multiphase /low in porous media. The case oF variable physical properties is included in the Formulation, although gravity and capillarity are ignored. Both methods are analyzed mathematically, resulting in upper and lower bounds for the ratio of time step to mesh spacing. The methods are applied to two- and three-phase waterflooding problems in laboratory-size cores, and resulting saturation and pressure distributions and production histories are presented graphically. Results oJ the tuo-phase flow problem are in agreement with the predictions of the Buckley-Leuerett theory. Several three-phase flow problems are presented which consider variations in the water injection rate and changes in the initial oil-and ujater-saturation distributions. The results are different physically from the two- phase case; however, it is shown that the Buckley-Lez~erett theory can accurately predict fluid interlace velocities and displacing-fluid frontal snturations for three-phase flow, providing the correct assumptions are made. The above solutions are used as a basis JOT et~aluuting the numerical methods with respect to machine time requirements and allowable time step for a fixed mesh spacing. INTRODUCTION Considerable progress has been made in recent years in obtaining numerical solutions of the equations for two-phase flow in porous media. Douglas, Blair and Wagner2and McEwenll present different methods for solving the one-dimensional case for incompressible fluids with capillarity (the former using finite differences, the latter with an approach based upon characteristics). Fayers and Sheldon4 and Hovanesian and Fayers8 have extended these studies to include the effects of gravity. West, Garvin and Sheldon, l4 in a pioneer paper, treat linear and radial systems with both capillarity and gravity and they also include the effects of compressibility. Douglas, Peaceman and Rachford3 consider two-dimensional, two-phase, in compressible flow with gravity and capillarity and Blair and Peaceman1 have extended this method to allow for compressible fluids. No one, however, has examined the case of three-phase flow, even for the relatively simple case of one-dimensional flow of incompressible fluids in the absence of gravity and capillarity. In obtaining a numerical technique for simulating forward in situ combustion laboratory experiments, Gottfried5 has developed a method for solving the one-dimensional, compressible flow equations with any number of flowing phases. Gravity and capillarity are not included in the formulation. The method has been used successfully, however, for two- and three-phase problems in a variable-temperature field with sources and sinks. This paper examines the algorithm of Gottfried more critically. Two numerical methods are presented for solving the one-dimensional, multi-phase flow equations with variable physical properties. Both methods are analyzed mathematically, and are used to simulate two- and three-phase waterflooding problems. The numerical solutions are then taken as a basis for comparing the utility of the methods.

Jan 1, 1967