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By H. O. Jahns, R. A. Greenkorn, R. E. Haring, L. K. Shallenbarger

This paper is a study of the effects of heterogeneity on flow in an analog of porous media, the Hele-Shaw model. l-3 A set of experiments in heterogeneous Hele-Shaw models showed streamlines through and around heterogeneities of various sizes, shapes and levels. (A level, we define as the ratio between the transmissibility of the heterogeneity and that of the rest of the model.) The heterogeneities were restrictions or expansions of the flow stream analogous to variations in the transmissibility of porous media. The experimental data agreed well with numerical results and with an analytical solution, which we derived for a circular heterogeneity in an infinite field. This study considers the flow-stream distortion due to the shape, size and level of heterogeneities. Size and level are much more important than shape provided the heterogeneity is not long and narrow. Our analytical solution shows that a circular heterogeneity in a large field can be replaced by an equivalent circle of either zero or infinite permeability. The radius of the. equivalent circle is a simple function of size and level of the actual circle. INTRODUCTION With the availability of high-speed computers and numerical procedures to predict reservoir behavior, we are faced with an important question. How much information about the reservoir do we need to justify the cost of the computer in any given case? To answer this question, we have to know how various reservoir parameters affect flow behavior. Reservoir heterogeneity is one of these parameters. In this study, we used a simple, two-dimensional model of porous media, the hele-shaw model, to investigate the effect of heterogeneity on flow behavior. We restricted ourselves to linear, single-phase, steady-state flow in a rectangular field with a single heterogeneity at its center. The analogy between flow in Hele-Shaw models and in porous media is easily verified. Let us first consider a homogeneous Hele-Shaw model with constant plate separation h. (The Hele-Shaw model is constructed by placing two plates, usually glass, very close together and allowing liquid to flow between them. Streamlines are made visible by introducing colored fluid into the space between the plates at a number of points across the model.) We assume a cartesian coordinate system with its origin in the middle between the plates and the z axis directed perpendicular to the glass plates (Fig. 1). The fluid flow is always in a direction parallel to the glass plates and varies from a maximum value to zero in the very small distance from the middle (z = 0) to either plate (z = h/2). For slow motion of an incompressible fluid, neglecting inertia and body forces, we have the viscous flow equation: where p is the fluid pressure, p the viscosity, and v the velocity vector with components u, v and w in the x, y and z directions, respectively. In our rase. and the derivatives of 3 with respect to x and y are small as compared with the derivative in the z direction. Therefore, approximately, with Vp and v being two-dimensional vectors in the x-y plane. Two integrations with respect to z give

Jan 1, 1965

By H. G. HYMER

B ECAUSE of its remote geographical position and inaccessibility, little is generally known of the mining and prospecting in Northern Rhodesia. In this rather new and promising region, the development of mines presents many difficulties. Although many mineral discoveries have been made, progress in .prospecting the huge mining concessions has been handicapped by the lack of roads, communication, transportation, native population and incomplete knowledge of geology.

Jan 1, 1929

By T. S. Lovering

An economic geologist is concerned primarily with finding deposits of economic value, estimating their tenor and quantity, their shape and position. Thus the primary problems can largely be lumped under three headings: position, character and quantity; and all three are phases of the broader problem of genesis. Distribution, tenor and quantity are of immediate practical importance and are studied constantly by all who exploit mineral deposits. Although the emphasis changes from year to year, the problems of genesis seem more remote and rarely get the serious consideration from the field man that the other three do. Our understanding of the problems of the genesis of mineral deposits has come largely as a by-product of more evidently utilitarian work in the past, and probably will continue to grow in the same manner lor many years to come. However, it might be economically fruitful for the producers to have many competent investigators spending their time chiefly on the problems of genesis of mineral deposits. Many years ago, when first engaged in work for the United States Geological Survey in Colorado, I expressed a conviction which was just then dawning on me by saying that economic geology was turning out to be 80 per cent structural geology, to which Mr. B. S. Butler replied, "Yes, and more than 80 per cent of structural geology is lithology." At the present time there seems to be a widespread feeling among economic geologists that the problems of position or distribution are largely problems of structure and rock types. Types of Research Ptesearch in any branch of geology can be conveniently divided into two types: field research and laboratory research. Ideas are usually dug up in the field, pruned or developed in the laboratory, and taken back to the field for proving. For either the first or last step the field data should he as complete as possible, and the structural geology of nearly all our mineral deposits still needs more detailed delineation. In general, this means mapping on larger seales. Ideally the structural map should give a factual picture of a11 visible effects of stress; there is still room for vast improvement in the technique of presentation. Information that is much

Jan 1, 1940

By T. S. Lovering

An economic geologist is concerned primarily with finding deposits of economic value, estimating their tenor and quantity, their shape and position. Thus the primary problems can largely be lumped under three headings: position, character and quantity; and all three are phases of the broader problem of genesis. Distribution, tenor and quantity are of immediate practical importance and are studied constantly by all who exploit mineral deposits. Although the emphasis changes from year to year, the problems of genesis seem more remote and rarely get the serious consideration from the field man that the other three do. Our understanding of the problems of the genesis of mineral deposits has come largely as a by-product of more evidently utilitarian work in the past, and probably will continue to grow in the same manner lor many years to come. However, it might be economically fruitful for the producers to have many competent investigators spending their time chiefly on the problems of genesis of mineral deposits. Many years ago, when first engaged in work for the United States Geological Survey in Colorado, I expressed a conviction which was just then dawning on me by saying that economic geology was turning out to be 80 per cent structural geology, to which Mr. B. S. Butler replied, "Yes, and more than 80 per cent of structural geology is lithology." At the present time there seems to be a widespread feeling among economic geologists that the problems of position or distribution are largely problems of structure and rock types. Types of Research Ptesearch in any branch of geology can be conveniently divided into two types: field research and laboratory research. Ideas are usually dug up in the field, pruned or developed in the laboratory, and taken back to the field for proving. For either the first or last step the field data should he as complete as possible, and the structural geology of nearly all our mineral deposits still needs more detailed delineation. In general, this means mapping on larger seales. Ideally the structural map should give a factual picture of a11 visible effects of stress; there is still room for vast improvement in the technique of presentation. Information that is much

Jan 1, 1940

By D. B. Williams

For the first time in the history of the Venezuelan petroleum industry production exceeded 200 million barrels. The total production for all fields amounted to 205,430,869 bbl., which is more than 9 per cent of the world's 1939 total. This is an increase of over 15 million barrels or 8.0 per cent above the 1938 figure, which, compared with the slightly less than 2 per cent increase of the 1938 figure over 1937, shows the marked activity in Venezuela during the past year. The Maracaibo Lake fields are still the predominating factor in Venezuelan production, showing an increase of approximately 9½ million barrels over last year's figure and accounting for 71.8 per cent of Venezuela's total. Lagunillas continues to hold precedence as a single field, having yielded 47.1 per cent of the accumulative total and 39.4 per cent of 1939's total. This field showed an increase of slightly more than 3½ million barrels over 1938. Tia Juana, the second largest field, attained a record production, increasing its percentage of the Venezuelan total from 23.4 in 1938 to 23.7 in 1939. The La Rosa field, which includes Punta Benitez and Ambrosio, declined from 13.7 to 12.0 per cent; Bachaquero, the southernmost Lake field, which came into regular production at the end of 1938, contributed over 31/3 million barrels. Quiriquire, in eastern Venezuela, ousted La Rosa as the third largest producing field, and, although production increased by 11/3 milliorl barrels, percentage of the total declined from 13.2 to 12.9. Mene Grande, the oldest field, declined from 6.6 per cent in 1938 to 5.9 in 1939. Tem-blador produced for a whole year for the first time and yielded 3,647,867 bbl. The Colon district, in the Maracaibo Lake area, comprising the Tarra-Los Manueles fields, showed slight increases, as also did Cumarebo and Pedernales. Construction of the 16-in. pipe line from Oficina to Puerto La Cruz (Guanta), the longest line of this size in the world, was completed toward the end of the year and this new field in eastern Venezuela started shipping oil in December. This field is operated by the Mene Grande Oil Co. and was credited with a production of 2,347,625 bbl. in 1939. Jusepin field, some 25 miles southwest of Quiriquire in eastern Venezuela,

Jan 1, 1940

By D. B. Williams

For the first time in the history of the Venezuelan petroleum industry production exceeded 200 million barrels. The total production for all fields amounted to 205,430,869 bbl., which is more than 9 per cent of the world's 1939 total. This is an increase of over 15 million barrels or 8.0 per cent above the 1938 figure, which, compared with the slightly less than 2 per cent increase of the 1938 figure over 1937, shows the marked activity in Venezuela during the past year. The Maracaibo Lake fields are still the predominating factor in Venezuelan production, showing an increase of approximately 9½ million barrels over last year's figure and accounting for 71.8 per cent of Venezuela's total. Lagunillas continues to hold precedence as a single field, having yielded 47.1 per cent of the accumulative total and 39.4 per cent of 1939's total. This field showed an increase of slightly more than 3½ million barrels over 1938. Tia Juana, the second largest field, attained a record production, increasing its percentage of the Venezuelan total from 23.4 in 1938 to 23.7 in 1939. The La Rosa field, which includes Punta Benitez and Ambrosio, declined from 13.7 to 12.0 per cent; Bachaquero, the southernmost Lake field, which came into regular production at the end of 1938, contributed over 31/3 million barrels. Quiriquire, in eastern Venezuela, ousted La Rosa as the third largest producing field, and, although production increased by 11/3 milliorl barrels, percentage of the total declined from 13.2 to 12.9. Mene Grande, the oldest field, declined from 6.6 per cent in 1938 to 5.9 in 1939. Tem-blador produced for a whole year for the first time and yielded 3,647,867 bbl. The Colon district, in the Maracaibo Lake area, comprising the Tarra-Los Manueles fields, showed slight increases, as also did Cumarebo and Pedernales. Construction of the 16-in. pipe line from Oficina to Puerto La Cruz (Guanta), the longest line of this size in the world, was completed toward the end of the year and this new field in eastern Venezuela started shipping oil in December. This field is operated by the Mene Grande Oil Co. and was credited with a production of 2,347,625 bbl. in 1939. Jusepin field, some 25 miles southwest of Quiriquire in eastern Venezuela,

Jan 1, 1940

By J. P. Smith

Permian salt measures carry extensive lenses of soluble potash salts in north central Germany. Potash deposits of Oligocene age are found in the Upper Rhine Graben of Alsace (France), and in the Catalonian Basin of Spain. These deposits are found in a wide range of structural settings. Reserves are large, and the production of potash salts is an important phase in the economy of each of these countries.

Jan 1, 1950

By Persifor Frazer

The subject of Egypt, to use the words of perhaps the second of modern writers on the subject [Deodat. de Dolomieu, in Observations sur la Physique, etc., January, 1793, vol. xlii., pp. 41+, 108+; Abbe Rozier, J. A. Mongez, and J. C. Delametherie, Paris], is one which strongly excites our interest, and everything relating to it demands our respect. "Thus," he continues, "the Greeks appeared to the Romans," ..." thus Egypt appeared to the Greeks, and thus all three appear to us." This writer, in the three parts of the memoire given above, speaks of Norden as the modern pioneer of Egypt, and does not seem to have made original observations himself; nevertheless he seems to have rendered the same service to his authority that Playfair not very long afterward rendered Hutton. The limitations of a paper will permit little else than citations, but these are so numerous that, unless much compressed, they would supply a chapter of moderate size. A great deal of the very interesting memoire of Dolomieu is taken up with Quixotic tilts

Jan 1, 1883

By John T. Galey

In all, 210 wellst were completed in southwestern Pennsylvania during 1939, which is 59 more than were drilled during the preceding year. Of this number, 137 were gas wells, which is a considerable increase from the 81 completed during 1938. Only 25 oil wells were completed, as against 28 in the previous year, and 28 dry holes, 6 more than last year. Shallow Development—Gas The increase in the number of gas wells is largely the result of a search for additional gas in Armstrong and Indiana Counties. Although a considerable number of wells were drilled in the latter county, the majority of them produced less than 100 M cu. ft. initial open flow. In Armstrong County, a new pool was opened in Cowanshannock township, producing from the third Bradford sand. Several large wells were obtained there, one of which produced an initial of nearly 12 million cu. ft., with a reservoir pressure of 1100 Ib. However, the productive area has been fairly well outlined by further drilling and shows that the pool covers only about 800 acres. The sand is 20 to 30 ft. thick, and probably has 5 to 6 ft. of pay. Thus this reserve is not an important one. Several wells were found in Menallen township, Fayette County, where the Big Injun sand has been having a play for the past three years, but the activity there is much less than a year ago. Oil On the west side of the Bradford sand gas pool, Cowanshannock township, Armstrong County, a well was drilled which flowed 100 bbl. the first day from the Tiona sand. The probability is that this well is a freak, as the Tiona has been drilled within a fairly close distance on every

Jan 1, 1940

By John T. Galey

In all, 210 wellst were completed in southwestern Pennsylvania during 1939, which is 59 more than were drilled during the preceding year. Of this number, 137 were gas wells, which is a considerable increase from the 81 completed during 1938. Only 25 oil wells were completed, as against 28 in the previous year, and 28 dry holes, 6 more than last year. Shallow Development—Gas The increase in the number of gas wells is largely the result of a search for additional gas in Armstrong and Indiana Counties. Although a considerable number of wells were drilled in the latter county, the majority of them produced less than 100 M cu. ft. initial open flow. In Armstrong County, a new pool was opened in Cowanshannock township, producing from the third Bradford sand. Several large wells were obtained there, one of which produced an initial of nearly 12 million cu. ft., with a reservoir pressure of 1100 Ib. However, the productive area has been fairly well outlined by further drilling and shows that the pool covers only about 800 acres. The sand is 20 to 30 ft. thick, and probably has 5 to 6 ft. of pay. Thus this reserve is not an important one. Several wells were found in Menallen township, Fayette County, where the Big Injun sand has been having a play for the past three years, but the activity there is much less than a year ago. Oil On the west side of the Bradford sand gas pool, Cowanshannock township, Armstrong County, a well was drilled which flowed 100 bbl. the first day from the Tiona sand. The probability is that this well is a freak, as the Tiona has been drilled within a fairly close distance on every

Jan 1, 1940

By Walter Kauzmann

All viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.† Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem —i.e., the dependence of shear rates on temperature, stress, etc.—from the standpoint of .recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of app1ications.l Resolution of Macroscopic Shear into Microscopic Movements; Resemblance to Chemical Reactions Just as any large body is made up of many small units, or atoms, so macro-scopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for non-turbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove' In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker14 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the plastic flow of crystalline solids from this

Jan 1, 1941

By Walter Kauzmann

All viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.† Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem —i.e., the dependence of shear rates on temperature, stress, etc.—from the standpoint of .recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of app1ications.l Resolution of Macroscopic Shear into Microscopic Movements; Resemblance to Chemical Reactions Just as any large body is made up of many small units, or atoms, so macro-scopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for non-turbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove' In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker14 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the plastic flow of crystalline solids from this

Jan 1, 1941

By F. C. Blake

THE test of the English Cupellation furnace should be so supported that the cupeller can change readily the elevation of the test, and at the same time watch the litharge channel. It is also important to raise or lower either side, independently of the other, in case of uneven wear of the side walls or of the breast. If the refined silver is poured from the test, it is much better to control the lowering of the test from the front than to raise the back by screws or a lever. In order to. enable the cupeller to manipulate the test with one hand, when the litharge is running, and to pour the refined silver from the test without aid, I have altered the common support to the .test, as shown in the accompanying drawing. The common method of supporting the test is by four screws, working in cross-bar nuts beneath the test. The points of the screws set into the test plate upon which the test rests. These screws are usually worked by pounding or pulling upon the heads, which may be either small pulleys or straight bars, as shown on the back screws in the drawing. The screws are also worked by turning a crank, which is

Jan 1, 1882

By R. Schumann

THE expression "unit process " comes up with increasing frequency in discussions among metallurgists and mineral engineers, especially among those concerned with training the next generation. The unit process approach characterizes a significant advance along the road from metallurgy as an empirical art to metallurgy as a branch of engineering. The purposes of this paper are to define and list the unit processes in specific terms, to indicate the scientific and engineering principles basic to all the unit processes, and finally to show how these ideas have been applied to a reorganization of instruction in chemical metallurgy. UNIT OPERATIONS AND UNIT PROCESSES Metals are extracted from ores and other raw materials by stepwise procedures. In general, each metallic element is extracted by a different procedure. For many of the metals there is a choice of several flowsheets. However, the procedures all have steps in common. In fact, the many different flowsheets are all made up of a relatively small number of steps which are combined in different groups and sequences. For example, crushing, screening, roasting, sintering, melting, and gaseous reduction are steps which each appear in the flowsheets for extracting the majority of the metals. The individual steps or flowsheet units can be designated as unit operations or unit processes. These terms are well established in the field of chemical engineering, as the American Institute of Chemical Engineers' definition of chemical engineering shows: " Chemical engineering is that branch of engineering concerned with the development and application of manufacturing processes in which chemical or certain physical changes of materials are involved. These processes may usually be resolved into a coordinated series of unit physical operations and unit chemical processes. The work of the chemical engineer is concerned primarily with the design, construction, and operation of equipment and plants in which these unit operations and processes are applied. Chemistry, physics, and mathematics are the underlying sciences of chemical engineering, and economics its guide in practice."1a In this definition, the distinction between unit operations and unit processes is that the unit operations are physical while the unit processes are chemical. Table I gives a list of the principal unit operations and unit processes of chemical engineering, taken from Shreve. lb Table 2 lists the principal unit operations and unit processes used for metal extraction. The division between unit operations and unit processes is similar to the chemical engineers' distinction and also corresponds approximately to the division of labor between mineral dressing and chemical metallurgy which has been customary in the past. Furthermore, it will be noted that in the proposed classification the unit processes primarily involve chemical reactions and/or changes in state of aggregation; the unit operations, primarily do not involve either bulk

Jan 1, 1948

By E. C. Pechin

At the September meeting of the Iron and Steel Institute of Great Britain, Mr. Charles Wood, of the Tees Iron-works, read an interesting paper on "Further Improvements in Blast-Furnace Hearths," which was followed by an animated and instructive discussion. If the durability of hearths and in-walls is a matter of interest in England, where furnaces stay in blast from eight to twenty years, it

By William F. Harris, Joseph Easha

FOR many years basic control of refinery operations depended on visual observation of small chill specimens poured at various intervals during processing. The oseto of these samples was related to the physical and chemical properties of the metal. Since the =setn is dependent on many factors other than oxygen content, this method, while giving a general indication of the condition of the copper, does not accurately measure the oxygen content. For the last 3 years a modified vacuum fusion procedure which enables the operator to determine the oxygen content of the copper within 1 5 min of sampling has been in use at the Westinghouse Copper Mill. For use with this apparatus a sampling technique has been developed which gives oxygen values representative of the oxygen content of the wire bar. The sampling technique is based on a statistical study, which compared the oxygen content of the laboratory sample of copper poured at the same time a wire bar was being poured, with the oxygen content of the wire bar. The apparatus used for the determination of oxygen in copper is shown in Fig. 1 and is essentially the same as previously described but with one important modification. A very porous fritted glass disc has been inserted in the tubing between the manom- eter and 40/50 ground glass joint. The fritted disc retains the copper vapor and copper particles in the furnace section and prevents contamination of the mercury in the manometer. Without the disc the manometer became difficult to read after a few weeks of operation. In earlier work1 it had been established that the simplified vacuum fusion apparatus used at the Copper Mill gave essentially the same results as a con-vential vacuum fusion apparatus. However, for this study it was necessary to determine the difference, if any, between the oxygen content of the wire bar and the oxygen content of the small chill sample used for the oxygen analysis. This correlation was established by taking a chill sample at the same time wire bars were being poured. The wire bar being poured at the time the chill sample was taken was marked and removed for further analysis. The copper is sampled at various times during refining and cast into laboratory size samples with the mold shown in Fig. 2. The mold is made of cold rolled steel and is 2 in. high and 2 1/2 in. in diam. The large upper portion of the cast sample is used for measurement of the conductivity of the copper, The lower portion which is a rod about 1/4 in. diam by 3/4 in. long is used for determination of the oxygen content. This portion of the sample weighs about 5 g which is approximately the size sample used for the analysis. The only preparation neces-

Jan 1, 1962

By R. W. Borio, T. S. Spicer

Inflammability and crossing point apparatus were used to study the influence of increasing amounts oi such inerts as ash, fly-ash, pyrite, limestone and Portland cement with several pulverized bituminous coals. The results indicate that it requires large proportions of inerts to substantially suppress the ease of ignition. The ignition phase of the combustion of solid fuels has been under study periodically since 1900. With the advent of pulverized coal firing some 60 years ago, a technique now dominating the coal utilization field, the ignitibility characteristics have become increasingly important. Much of the early work was directed toward the prevention of coal dust explosions and improved mine safety rather than combustion. Many factors affecting ignitibility have been studied and numerous methods devised in an effort to measure the ignition temperature and these have been reviewed by other authors. A recent survey was made by Finney and Spicerl in 1959, so a discussion of previous work will be omitted. Despite these efforts, the initial stage of combustion, termed ignitibility, is still a little understood phenomenon. In fact, no ASTM method has been adopted for the calibration of this illusive property. However, a D-5 Subcommittee XVI on Ignitibility of Coal and Coke of ASTM (now inactive) defined ignitibility:' "The ignitibility of a fuel is that char-

Jan 1, 1963

By J. W. Harden

APART from the merits of the respective systems of mining under conditions alike, there is much in the nature of the coal and the measures with which it is associated, to make that system which is successfully practiced in one locality ill adapted to that of another ; the structure of the coal itself, the roof, the floor, the depth and character of the overlying strata, each exercising more or less controlling influence. Again, in the highly bituminous districts, and with such as have caking coals, where the size of the coal as it comes off the face does not affect its value, as the very smallest of it may be utilized, and in the hard, the open and free-burning coals, in some of which the round only (large coal) is merchantable,

By Aaron Miles

THE pressure distribution in a producing oil or gas reservoir has been obtained mathematically in a limited number of special cases where the boundary of the reservoirs are simple geometric figures with the wells conveniently located within them. Using some of the previous work as a basis, it can be proved that a number of additional problems of pressure distribution can be solved by use of soap film. This method is particu-larly applicable to a reservoir drained by a number of wells, or to a reservoir of irregular shape, or to both. Since this method obtains the pressure distribution, it also establishes the drainage boundaries of the wells. This paper derives the analogy between the equation representing the pressure distribution in a reservoir and the equation of the deflected membrane. It also describes the apparatus and the method of operation. The experimental method is employed to solve a problem whose mathe-matical solution is known and the results compared. These are found to be in good agreement. The method is applicable to any homogeneous liquid, compressible or incompressible, or to a gas, flowing in a reservoir of uniform thickness, permeability and porosity. The flow state may be either the steady state or the transient state wherein the density or pressure of the fluid in the reservoir declines at a constant rate.

Jan 1, 1938

By Bailey Willis, George Otis Smith

I. Summary of General Features. Location.—The Clealum iron-ore deposits occur on Clealum river, a tributary of the Yakima river; in the eastern spurs of the Cascade range, Washington.† Mount Stuart, 9470 feet in altitude, is a dominant peak of the district, which will therefore be referred to as the Mount Stuart district. By way of the valley and cañon of the Clealum, the ores are 18 miles from Roslyn, the colliery-town, which is reached by a short branch from the Northern Pacific Railroad. Where they occur the valley has an elevation of 2900 to 8000 feet above sea; that of the end of the branch railroad at Ronald is 2345 feet. The grade of the valley from near Ronald to the junction of the Clealum and Salmon Lasac rivers, 144 miles, is 20 feet per mile; thence to the iron-ores it is 130 feet per mile, through a cañon 241/2 miles long. Abreast of the deposits the western wall of the valley is formed by precipices of sandstone; the eastern slope is comparatively gentle, being cut in easily eroded

Jan 1, 1901