Search Documents

Jan 1, 1900

By W. R. Clark, W. W. Cotter

Jan 1, 1946

By F. H. Deily, D. S. Rowley, R. J. Howe

By W. W. Cotter, W. R. Clark

Jan 1, 1946

Jan 1, 1907

By Luther W. Bahney

Jan 1, 1912

Jan 1, 1920

By C. E. Reistle, G. L. Nye

The East Texas field is in Smith, Rusk, Gregg, Upshur and Cherokee counties, Texas. The discovery well was completed Sept. 8, 1930, near the eastern limit of the field. Within less than one year the new field became the dominant factor in the world production of crude oil. On Aug. 16, 1931, eleven months after completion of the discovery well, there were 1644 wells in the field, and the average daily production was 584,475 bbl. Since that time the number of wells has increased to 8195 on Oct. 1, 1933, and the field has produced 385,979,691 bbl. of oil. The geology of the East Texas field has been discussed by Lahee,1 Levorsen,2 Minor and Hanna3 and others, and it will not be discussed in detail here. The field is a structure of the monocline type on the westward dipping homocline between the Sabine uplift and the East Texas geosyncline. Production is obtained from the Woodbine group, which has been truncated and then sealed by the Austin chalk, which rests unconformably upon it. The oil-saturated part of the sand lies bettween a sub-sea depth of 3050 ft. on the east side of the field, where the Woodbine sand stops and the Austin chalk rests directly upon older formations, and a sub-sea depth of 3320 ft., which was the average depth of the water table in the sand at the time the field was discovered. The field is about 40 miles long and has an average width of approximately 4 1/2 miles. The area within the proven limits of the field is close to 116,580 acres and the normal Woodbine water underlies nearly 62,000 acres on the western side of the field at the present time. The field is unusual in several respects: (1) the tremendous size of the reservoir system and the quantity of oil in place; (2) the large area of the oil and water contact, which makes water movement possible into the oil-bearing part of the structure; (3) the absence of free gas within the main producing sand of the field. Changes in the reservoir pressure during the production history of the field have been greatly affected by

Jan 1, 1934

By Archiblad MacMartin

The Kunigin-Marien-Hiitte is the only works in Germany where the Bessemer process is carried on by the direct method. The Besserner plant there, is arranged after the true English type, and the only resemblance to the Swedish mode of 'procedure is the dispensing with the use of spiegeleisen at the end of the "blow." In a new department of the establishment, started within three years, each of the converters is turned by means of a very neat and compact reversible engine, the steel shaft of which is an endless screw, which turns against the oblique cogs of a large wheel attached to the shaft of the vessel. An advantage which this arrangement possesses over the ordinary English hydraulic arrangement, is the fact that the endless screw suffices to turn the vessel, in either direction, any number of complete revolutions; while even the latest American improvements, so clearly explained to us by Mr. Holley at the opening session of this meeting, do not secure even one complete revolution without changing the angle of inclination of the hydraulic piston. In the endless screw arrangement, there being no limit to the working of the motor in either direction (no return-stroke necessary), the vessel can always, unless outside reasons demand the contrary, be turned around to any desired position by the shortest cut, whether backwards or forwards. Also, the diameter of the cogwheel attached to the vessel can be made sufficiently great to avoid all unevenness of motion. In the old department the motive-power still continues to be hydraulic. If reports be true, the new department produces spiegelized steel, for the manufacture of all-steel rails. But the old department is still, as from the beginning, devoted to the production by the direct method of steel for steel-headed rails. The most remarkable fact connected with this direct steel is the ease with which it welds to the iron 'of the rail-packets, although no borax or other fluxing agent is used to facilitate the welding. It is very rarely that an exception occurs, and an ingot or a charge is discarded by the rail-mill. The mixture of pig-iron used for the production of this steel is melted in cupolas of very interesting construction (not to be de-

By F. J. Fayers, J. W. Sheldon

A theoretical discussion is presented of the behavior of the interface between two fluids of different physical properties when displacement is occurring along a thin tilted bed. An approximate equation of motion is deduced for the motion of the interface, suitable boundary conditions are derived and the conditions necessary for the approximation to be valid are determined. Steady-state behavior and the circumstances under which a steady-state interface can develop are discussed. Finite-difference solutions of the equation of motion for two characteristic water-drive problems are presenled. The theory of displacement in a thin bed may be regarded as being the porous-medium-equivalent of the classical "shallow-water wave" theory of hydrodynamics. INTRODUCTION The solution of moving interface problems are important in predicting the behavior of oil reservoirs under various conditions of production. Kidder4,5 has obtained analytic solutions for the fingering problem and for another particular case of the motion of the interface between two immiscible fluids of unequal density in a porous medium. In the present analysis, we analyze the problem of the motion of an interface along a slightly dipping bed whose length is long compared with its thickness. The requirement of a thin bed is necessary in order to give a simple differential equation for the motion. The two fluids are of unequal density and mobility. In the derivation of the equation of motion, it is assumed that the lighter fluid is being injected at constant rate at the high end of the porous layer, while heavy fluid is produced at the low end of the layer. The analysis applies equally well, however, to the reverse procedure in which the heavier fluid is injected at the low end of the tilted layer. It will be shown that the behavior of the system is critically dependent on which fluid has the higher mobility and that the interface can in certain circumstances achieve a simple progressive steady-state shape. The fluids may be considered to be immiscible or miscible. It is assumed, however, that the thickness of the interface region is negligible in comparison with other dimensions of the system, and that the strength of the saturation or concentration discontinuity remains constant during the motion. In conjunction with Buckley-Leverett theory and areal sweep-out calculations, the tilted interface problem is one of the fundamental problems of reservoir engineering; it defines the very important underpassing and overpassing phenomena associated with water-drives, gas-drives and secondary recovery operations. The tilted interface problem has been dealt with previously by Dietz.2 In the present paper, we endeavor to derive the pertinent mathematical results more rigorously, and in doing so we obtain modifications in both the differential equation and boundary conditions for those given by Dietz. We also attempt to show the connection between these results and some of the recent work on the stability of interfaces. Finally, we attempt to demonstrate the practical importance of the thin bed theory by showing the difference in behavior of two characteristic waterflood problems. In the favorable mobility case recovery is improved by increasing production rate, while in the unfavorable case undercutting or overcutting is minimized by reducing the displacement rate. PROPERTIES OF THE EQUATION OF MOTION Fig. 1 illustrates a porous layer of constant thickness H and tilt 8 with Fluid 1 of mobility ?l and density pl below Fluid 2 of mobility ?2 and density p2. The fluids are incompressible and flowing with volumetric flux q along the layer. Both the slope a of the interface with respect to the bed and the curvature of the interface are assumed to be small. What is meant by "small" is indicated in the derivation given in Appendix A of an approximate equation of motion for the interface. Other symbols are defined in the "Nomen-

By Ralph J. Schilthuis, William Hurst

The nature of the forces that are important in producing the oil in the East Texas field and the manner in which these forces are affected by the rate of production have always been problems of outstanding interest. These questions are of great interest to the industry as a whole on account of the economic importance of the East Texas field and to the engineers in particular on account of the unique character and behavior of the field. Subsurface pressure data throughout the field have been collected systematically, so that a quite complete history of the reservoir pressures has been kept as the field has been developed and produced. Subsurface samples of the oil and gas have been taken and these have been examined to obtain data on the physical properties of the reservoir fluids under the actual conditions of temperature and pressure. All of these data have been valuable because they have afforded the basis for a careful study of the means by which the oil is produced. It is the purpose of this discussion first to point out several of the important facts revealed by the data mentioned and then to describe studies that have been made concerning the interpretation of these facts. Reservoir Pressure Data and Properties of Oil The reservoir pressure data on the East Texas field have shown conclusively that the pressures are readily affected by changes in the rate at which the field is produced. This can well be seen in Fig. 1, where the average reservoir pressures obtained from time to time are plotted with the daily production rates and the cumulative production of the field. It is noted that the average reservoir pressure has declined irregularly, depending upon the rate of production, from the estimated original value of 1625 Ib. per sq. in. to the value of 1228 lb. per sq. in. observed for Aug. 11,1934. The decline in pressure has been more rapid at the higher rates of production than at the lower rates. In contrast, the average reservoir pressure has increased, on several occasions, upon reduction of the withdrawal rate from a high value to a lower value. The reservoir pressure data have also shown that a definite gradient in pressure has existed across the field from west to east since the begin-

Jan 1, 1935

By Charles E. Lees

The Globe Mining District is in the southeast central part of Arizona, in Gila County. Globe, with a population of about 7000, is the terminus of the Arizona Eastern R.R., a branch line 130 miles long that connects with the Southern Pacific R.R. at Bowie. In 1874, prospectors crossing the Pinal Mountains from the west located what is generally known as the Old Dominion mine. For several years, it attracted little attention, because of the greater interest aroused by the discovery of high-grade silver ores in some of the foothills northeast of Globe. About six years later, the prospector turned his attention to the abundant copper ore revealed by surface workings along the Old Dominion vein, and, in 1884, the Old Dominion company erected two 30-ton furnaces. From 1888 to 1893, the Old Dominion company is said to have maintained an average annual production of about 8,000,000 Ib. of copper. Until Dec. 1, 1898, all supplies had to be freighted into Globe by wagons and the mines of the district operated intermittently because of high expenses, but with the advent of the railroad the Old Dominion company continued to be a large and steady producer. In the Globe district, the production of copper far exceeds in importance that of any other metal. There are four operating companies along the Old Dominion vein and the total annual product of these properties for 1923 was about 45,000,000 lb. of copper. The unit size of the mineral tracts in the district is the regulation mining claim, 600 ft. wide by 1500 ft. long, and all ownerships are held in fee. Globe is 3600 ft. above sea level, and lies between the Apache MOUntains to the east and the Pinal Mountains to the west. The principal drainage of the district is northward through Pinal creek into the Salt River. The general slope from the high point along the vein, where the Superior & Boston mine is, to Pinal creek, where the Old Dominion mines are, is about 250 ft. to the mile. Geology The oldest rocks in the district are pre-Cambrian crystalline schists known as the Pinal schist, which are the basement upon which all the later rocks were deposited. These latter rocks comprise shale, con-

Jan 1, 1925

By C. K. Leith

GENERAL GEOLOGY OF THE LAKE SUPERIOR IRON-BEARING AND COPPER-BEARING SERIES. THE geology of the Lake Superior region is of general interest, both from an economic and a scientific standpoint. The presence of large and rich iron- and copper-deposits has made a knowledge of the geology of the region necessary for purposes of exploitation and exploration. The ores of the region are contained in rocks of pre-Cambrian age, 'pith for most of the country up to recent years have usually been referred to as « crystalline schists " or " crystalline complex;" and regarded principally as metamorphosed basement-unit upon which the sedimentary rocks, beginning with the Paleozoic, were laid down. In the Lake Superior re¬gion this pre-Cambrian complex presents an unusual variety of rocks with determinable relations. It has been possible, with the large expenditures which-the magnitude of the iron-mining industry warrants, to work out their stratigraphy to a larger extent than has been possible in almost any other area of pre-Cambrian rocks. The real complexity of Lake Superior geology, the confusion of names and the multiplicity of reports covering small parts of the region, are such that interested persons, other than. geologists directly engaged in the work, may well hesitate to attempt to comprehend the geology of the region as a whole. The following paper is a somewhat elementary outline of the geology of the Lake Superior region with special reference to new developments not yet covered in published reports. Geological information concerning the region has been gath¬ered by mining companies, and by the geological surveys of Michigan, Wisconsin, Minnesota, Ontario, Canada, and the United States.. Perhaps in no other part of the country have the mining men themselves spent such large sums in purely geological work. This has made possible the publication of ,reports and maps by the State and Government surveys in much less time and at far less cost than would have been otherwise possible. The. U. S. Geological Survey is the only organization which has covered all of the region on the United 'States side of the boundary, and as its reports include the in¬formation gathered by the mining companies and State organi

Mar 1, 1905

By T. F. Witherbee

It is proposed to give, first, a description of the works; second, a report of the first six months of the present blast; and third, such improvements as have been suggested by the practical working. The site selected for this furnace was, at the time of commencing work, October, 1872, entirely covered by the navigable waters of Lake Champlain. A coffer-dam was first built of cribs of round timber filled with stone, forming three sides, while the shore answered for the fourth. Considerable excavating was done with a steam-dredge, a hole being left for it to pass out. The opening was then built up, and the cribbing banked up with blue clay from the bottom of the lake, to render it water-tight and the dam pumped out; the remainder of the excavating being done by hand. All of the foundations, with the exception of the elevator-tower, and fifteen feet of the east side of hot blast, rest on the Potsdam sandstone, which forms the shore line, dipping into the lake at an angle of fifteen degrees. Owing to jogs in the formation, a much greater depth was found necessary than was at first anticipated, the foundation under the stack

By F. E. Pawlek, J. K. Gerlach

The chloridizing roasting of ores is applied when metal sulfides and oxides are to be converted into soluble or volatile compounds. The chlorine required is either obtained from the admixed chlorides of sodium or calcium or added in the gaseous state. In the first part of the investigations the reaction rate of the chlorides of sodium or calcium with gas mixtures of SO,-0, or SO ,-O2 ,-SO , was measured. The rate for reactions with gas mixtures SO2-O2 is ThE chloridizing roasting of ores is applied when metal sulfides and oxides are to be converted into soluble or volatile compounds. At present the process is mainly applied to produce nonferrous metals which occur in pyrite cinders in small concentrations. Thereby the nonferrous metals are converted into water-soluble, acid-soluble, or volatile compounds whereas all the iron remains as insoluble oxide. The chlorine required is either obtained from the admixed chlorides of sodium or calcium or added in the gaseous state. The reactions occurring during the roasting process can be divided into two groups: solid-solid reaction and gas-solid reaction. The reactions between solids proceed by means of solid-state diffusion and are therefore of low velocity. The heterogeneous reactions between solids and gases of the roasting atmosphere5 are high-velocity processes and determine the velocity of the chloridizing roasting. These gas-solid reactions shall be the subject of the paper presented. In order to investigate the still little-known processes which occur during the chloridizing roasting 6-' the complex reaction is split into several partial steps. First the reactions of NaCl and CaCl, with gas mixtures of SO2 and 0, have been investigated at temperatures between 500" and 600°C by measuring the weight increase of the samples. The gas mixtures used in this series of experiments had first variable compositions, then the amount of SO 2 had been increased. Furthermore the influence of Fe 2 O3 admixtures upon these reactions, the behavior of pure Fe 2 O3 with the gaseous reactants, and the chlorination of the sulfides of lead, copper, nickel, and zinc have been investigated. FORMATION OF GASEOUS CHLORINE Pyrite cinders are never completely roasted and therefore contain still a small amount of sulfide sulfur. When heated again in air, this sulfur is converted into SO,. Accordingly the formation of chlorine can first be described by the reactions: dependent on the composition of the gas phase. If more than 1 pct SO 3 is added to the roasting gas, the reaction rate is determined only by the concentrations of the SO,. In the second part the reactions between chlorine and metal sulfides are discussed. The rate of formation of gaseous chlorine is higher by me order of magnitude than is the reaction rate between ZnS and chlorine. The reaction rate of NiS and PbS lies considerably below that of ZnS. The conversion rate of both pure Fe 2 O 3 and Fe 2 O 3 containing NaCl or CaCl2 when reacting with SO2-O2, mixtures with and without SO3 portions was measured at temperatures of 500", 550°, and 600°C. The weight increase of pressings was determined by means of a spiral balanceg and the reaction rate calculated therefrom according to Eqs. [ll to [31 and [5] to [7]. The prepared samples were suspended on a platinum filament in a vertically mounted tube of mullite (ID 4 cm, length 110 cm) which could be heated by a resistance tube furnace. The platinum filament was tied to the lower end of the spiral balance. A supremax glass tube (length 70 cm) was mounted gas-tight on top of the reaction tube. The unit was sealed up at its top by a ground-in stopper which was holding the spiral balance with the sample. The spiral balance therefore hung outside the high-temperature region of the furnace. Fig. 2 shows the experimental arrangement schematically. While lowering the sample into the reaction tube pure nitrogen was flowing through the reaction zone providing a protective atmosphere. After the sample had reached the reaction temperature within approximately 1 min, the protective gas was replaced by the sulfur dioxide-oxygen reaction mixture. It took about 30 sec until the mixture filled the tube homogeneously. A Ni/NiCr thermocouple placed in the center of the furnace where the sample hung during the measure-

Jan 1, 1968

By Fred R. Ingram

FOR the purpose of this discussion, let us consider that the Rocky Mountain region covers the area in the seven Mountain States, Idaho, Montana, Wyoming, Utah, Colorado, New Mexico, and Arizona, and before we discuss the needs of these states, let us define Industrial Hygiene. Industrial Hygiene is that branch of preventive medicine concerned with the protection of health, improvement of efficiency, and prolongation of life of the industrial worker; in short, adult health conservation. It includes in its broad meaning not only the prevention of occupational diseases, such as silicosis, lead poisoning, cadmium poisoning, and many others, but such relative problems as overcrowding, fatigue, and personal and mental hygiene; exposure to abnormal temperatures, pressures, and humidities; ventilation, heating, and lighting. It is a science which requires the combined activity of medical personnel (doctors and nurses), engineers, and chemists to evaluate the exposures and determine the means of eliminating the hazard. The engineer surveys the workplace, takes air samples at the breathing level of the workman, and analyzes the work exposure. The chemist determines in his laboratory the exact amount of toxic material collected in the sample, which represents the exposure of the workman. The doctor must diagnose the occupational disease, recognize its cause, and evaluate the disability. Together, all three must correlate the data obtained and devise efficient methods, medical or engineering or process changes, for controlling or minimizing the dangerous condition and for studying the effectiveness of these measures. The plant doctor, in addition, must aid in the readjustment of the incapacitated worker and provide facilities for prevention. Industrial hygiene, however, is of no avail without the understanding co-operation of management.

Jan 1, 1945

By J. R. Martson

The arrangement of the larger furnace at the United Verde smelter, together with the boiler layout and connecting flues, is shown in Fig. 1. The important dimensions are given in the figure, and cross-sectional areas of combustion space, flues, etc., are recorded. The location and extent of the baffling in the boilers also are shown because of their importance in the interpretation of the data. Two boilers serve each reverberatory furnace. They are of the class M-26 Stirling type (rated at 713 boiler hp. each). Steam is generated at 178-lb. gage pressure at a total temperature of 528" F., from feed water at a temperature of 113" F. The feed water is condensate from turbogenerators plus make-up softened by the lime-soda process. The make-up is rather large in amount as it must match the amount of steam consumed in reciprocating blowing engines and the like, which are not served by surface condensers. As a result the boiler feed water has a hardness of 1.5 to 3.0 grains per gallon, but this results in the formation, during six months to one year of boiler operation, of scale only of "eggshell " thickness or less. The boilers are set at the same elevation as the tapping floor of the furnace, which results in the introduction of the waste-heat gases at the top of the front bank of tubes and necessitates the inversion of the usual baffling arrangements. The boilers are equipped with valve-in-the-head soot blowers, which keep most of the dust blown off the surface of the tubes, but it is necessary to supplement the soot blowers by high-pressure air lances, inserted by an attendant through side doors in the boiler setting. Deposits of coal ash and of dust from the furnace charge accumulate in the flues between the reverberatory furnaces and the boilers and this necessitates cleaning of these connecting flues by hand during the greater part of one of the three 8-hr. shifts during each 24 hr. This cleaning operation requires the opening of clean-out doors, which, of course, has some effect on the yield of steam. Revebberatory Furnace Practice The United Verde furnaces are fired with pulverized coal of sub-bituminous type of which the screen and chemical analyses are given in Table 1.

Jan 1, 1934

By W. C. T. Yeh, T. G. Oakwood, A. A. Hendrickson, R. H. Hammar

The objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for by the influence of the solute addition on the dislocation structure oj- the crystals. The additions of both tin and indium produced only small changes in the dislocation densities and arrangements in silver crystals. However, as found previously, small solute additions have large effects on the tensile properties; the inj-luence of the tin and indium additions on the temperature dependence of the flow stress and the easy-glide range is especially strong; It is concluded that the indirect strengthening effect of the solute due to variations in the dislocation density as proposed by Seeger is of minor importance and that solute atom-dislocation interactions are responsible for the observed strengthenirzg effects. The experimental results were combined with those of Rogausch to test the concenlvatiorz dependence of solute strengthening. Both the first and one-half power dependences of the critical resoleed shear stress on concentratiorz fail in very dilute solutions. THE objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for, at least in part, by the influence of the solute addition on the dislocation structure of the crystals. It is recognized that the addition of solute atoms may influence the strength properties of a metal through both "direct" and "indirect" effects. The former refer to the strengthening mechanisms that result from the interaction of solute atoms with dislocations; in the latter case, the strengthening effects arise as a result of solute's influence on quantities such as dislocation density, dislocation arrangement, stacking-fault energy, diffusivities, the elastic constants, and so forth. It is clear that the correct interpretation of solid-solution strengthening phenomena cannot be given until the importance of indirect strengthening effects is properly evaluated. In the particular case of close-packed metal crystals, Seeger showed that solute strengthening effects in dilute solutions of copper and silver might be accounted for by an increase in dislocation density due to the addition of the solute. Seeger's argument was that the strengthening effects extrapolated from more concentrated solutions indicate that small concentrations of impurities raise the critical resolved shear stress much more than is predicted by a concentration-independent dislocation density. The above idea was a very reasonable one. The dislocation theories of work hardening of Taylor,2 Cot-trell, 3 Mott, 4 and seeger5 had already associated the increased flow stresses with increased dislocation densities in deformed metals; investigations of the dislocation structure of metal crystals had provided a logical basis for expecting an increased dislocation density in crystals containing impurities (see for example, Ref. 6). The numbers involved seem reasonable, too. It can be expected that the flow stress of the crystal would increase as the one-half power of the dislocation density.' Solute additions of 1 at. pct to metal crystals result in strength increases by factors in the range of three to ten. If one assumes that the strengths of the pure metal crystals are determined by their dislocation densities, then dislocation-density increases of one to two orders of magnitude as a result of solute addition would be required to account for the observed strengthening—not an unreasonable expectation. In addition to the effect of the solute addition on dislocation density, one might also anticipate important strengthening contributions to result from the solute's influence on the dislocation arrangement. Parker and washburns have reviewed a number of experimental evidences which show important strengthening effects due to the presence of subboundaries. Further, lattice strains due to impurity segregation would be expected to influence the distribution as well as the dislocation density of the as-grown crystal. As pointed out in the reviews of Chalmers,6 Elbaum,9 and winegard,lo micro segregation of impurities occurs at all interfaces of crystals in cellular growth; the impurity gradient results in lattice strains which can be reduced with the presence of dislocation arrays in the region of the impurity gradient. Hence, one would expect the presence of a solute to favor the formation of dislocation subgrain structures and that the subgrains would have an important influence on the strength of the crystal. The experimental observations that concern the possibility of an important strengthening contribution through the influence of the solute on the dislocation density or arrangement are not in agreement. Haasen has reviewed the observations of Meakin and Wils-dorf,12 Howie,13 and Bocek 36 and concluded that the solute's influence on dislocation density is not sufficient to account for strengthening effects in concentrated solutions but might, as seegerl suggested, make an important contribution in very dilute solutions. On the other hand, Hendrickson and Fine 14 concluded that changes in the dislocation density and dislocation width accounted for the solid-solution strengthening effects observed in silver-based aluminum solid solutions. Goss et a 1.I5 observed dislocation arrays in Ge-6 at. pct Si, Ge-0.2 at. pct Sn, and Ge-0.2 at. pct B crystals that were not observed in germanium crystals of

Jan 1, 1968

By John G. Simmons

A tutorial account of the tunnel effect between metal electrodes separated by a thin insulating film is presented. Energy diagrams of metal-insulator -metal sandwiches are briefly discussed, and the isothermal and thermal J-V characteristics for symmetric and asymmetric tunnel junctions are derived from a generalized expression. Experimental data from tunnel junctions are presented, and it is shown how, correlation between theory and experiment permits a determination of some of the oxide properties. Finally, the barrier heights in AT-Al2O3-A1 junctions determined by various inr3estigators are discussed. The object of this paper is to give a tutorial account of the electric-tunnel effect between metal electrodes separated by a thin insulating film and to illustrate its utility in the study of metal-oxide interfaces. This paper will emphasize the theoretical aspects of the electric-tunnel effect: however, a brief account of the more recent experimental work will be presented. A more comprehensive experimental study of the tunnel effect will be presented in the following paper by Drs. Pollack and Morris, see p. 497. We will open with a discussion of the energy diagrams for metal-insulator-metal junctions and what we mean by the electric-tunnel effect. Following this is an account of the theoretical studies of Sommerfeld and Bethe, and Holm, and the recently reported calculations on symmetric and asymmetric junctions using the generalized formula. The theoretical presentation is concluded with calculations on the temperature dependence of the tunnel J-V characteristic. In the experimental section, it is shown how barrier heights and thicknesses are determined by comparing the experimental data with the theory. Finally, the results of various investigators on the determination of the barrier heights in Al-Al2O,-A1 systems are discussed. I) POTENTIAL BARRIERS BETWEEN CLOSELY SPACED ELECTRODES Since it is necessary to supply energy to a metal in order to observe electron emission from its surface, it is evident that the potential energy of an electron within a metal is lower than that of an electron at rest outside the metal. It follows, then, that the electron must undergo a change in potential as it crosses the metal-vacuum interface. In the Sommerfeld1 free-electron theory of metals it is assumed that the free electrons, the electrons responsible for the electrical characteristics of metals, move in a constant potential environment in the metal, and are contained within the metal by a potential barrier at the metal-vacuum interface. It will be evident that the idea of a constant potential environment is a very idealized model, since the potential energy of an electron is influenced by all of the atoms and the other electrons within the metal; however, its use is justified by the many excellent results it gives.2 Fig. l (a) is the energy diagram of the model envisaged by Sommerfeld; the metal is represented by a potential-energy well of depth V,; the vacuum level represents the energy of an electron at rest outside the metal. At 0°K the electrons, which exist in pairs in discrete energy levels, fill up the well to an energy ?, the Fermi level. The distance, Vo - ?, from the Fermi level to the vacuum level is known as the work function of the metal, and represents the minimum energy required to free electrons from the interior of the metal at 0°K.

Jan 1, 1965

By G. D. Monk, W. C. Krumbein

The relation between permeability and the size parameters of unconsolidated sand is approached by considering sands as logarithmic frequency distributions having the basic parameters mean size and standard deviation. Sieve separates were mixed in accordance with the normal logarithmic probability law, so that the mean and standard deviation could be varied at will. Experiments were conducted in which one parameter was kept fixed and the other varied; in this manner the dependence of permeability on the individual parameters was evaluated. It was found that permeability can he expressed as the product of a power function of the mean size and an exponential function of the standard deviation. Earlier studies of the effect of size of particles on the permeability of uncon-solidated sand have shown that the permeability varies with the square of some average diameter. This was first pointed out by Hazenl in 1892 and verified by Slichter2 in 1898. Hazen's mean size was defined as the 10 percentile of the cumulative curve (i.e., size that is smaller than 90 pel cent of the distribution and larger than 10 per cent). Slichter's effective size, on the other hand, was found by Wilsey3,4 to agree with the 31 percentile. Fair and Hatch6 found that the geometric mean size of sieve separates yielded the same power function; Hulbert and Feben6 found that the permeability of sieve separates varied as the 1.89 power of the median diameter (i.e., the size associated with the 50 percentile of the cumulative curve). Relatively few studies included the effect of the "sorting" of the sediment on the permeability. It was recognized that the nature of the size distribution, in terms of the spread of the particles about the mean, affects the permeability, but no systematic investigations of this effect are known to the writers. Cloud7 demonstrated that the effect of the grain-size distribution on permeability is definitely measurable. In the present paper the authors investigate this relation analytically, and show that the effects of the size parameters on permeability may be predicted for at least a restricted set of conditions. Properties OF Sediments Recent investigations have shown that essentially all the geologically important characteristics of sediments may be expressed in terms of six measurable quanti-tities possessed by each clastic sedimentary particle. These attributes are: (I) size, (2) shape (sphericity), (3) roundness (angularity) , (4) mineralogical composition (density), (5) surface texture, (6) orientation. Each of these characteristics may be defined in several manners. Size may be expressed in terms of sieve mesh, settling velocity, volume, etc. Sphericity is a shape concept introduced by Wadell;8 it is essentially a measure of the ratio of the surface area of an equivalent sphere to the surface area of the particle. The same

Jan 1, 1943