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By Tell Ertl, Ernest E. Burgh

INTRODUCTION THE Bureau of Mines is operating an oil-shale mine 10 miles west of Rifle, Colo., as part of its Synthetic Liquid Fuels program. The purpose of operating this mine is twofold: First, to supply oil shale to an experimental processing plant; and second, to develop practices and select methods for mining oil shale on a commercial scale at the lowest practicable cost. The second purpose-that of finding out how to mine oil shale most cheaply-entails considerable mining research. Since the drilling of oil shale probably will be one of the major items of the mining cost, factors that influence drilling speeds were investigated. One phase of the drilling program was the development of a successful hard-surfaced rock-drill bit1 that can be used for drilling long holes in oil shale without changing bits. During that phase, drilling speeds were measured and drill cuttings were collected for assay and for screen sizing. When the cuttings from the individual tests were compared, a definite relationship was shown to exist between the drilling speed and the coarseness of the drill cuttings. PROCEDURE Measurement of Drilling Speeds All drilling in the tests was done with a Model UMB-D-99W Gardner-Denver wagon drill. Round-lugged drill steel, 1 ¼ in. in diameter was used in 6, 12, and 18 ft lengths with 2 1/8 -in. Timken H-type bits hard-faced with acetylene tube borium. The tests were made in the lower adit of the Bureau of Mines oil-shale mine; the grade of the oil shale drilled ranged from 18.6 to 42.7 gal per ton. During the experiments air pressure varied between 75 and 90 psi while water pressure remained fairly constant at 75 psi. All holes were drilled almost horizontally. Each drill hole was thoroughly cleaned of cuttings after being collared. The advance of the drill along the carriage was measured and recorded as the drilling speed in inches per minute. Method of Collecting Cuttings To facilitate the collection of cuttings, each drill hole was collared in a smooth, vertical portion of the oil-shale breast (Fig 1). A galvanized-steel sheet was fastened to the breast below the area in which the hole was to be drilled. The cuttings washed out of the drill hole by the drilling water were guided by the steel sheet into a wooden box. The cuttings that remained in the drill hole after the drill was withdrawn were scraped out and placed in the same box as the cuttings washed out of the hole. After the cuttings from a 1-min. drilling interval were collected, they were placed in flat metal pans. The fines were allowed to settle and the clear water was decanted. The cuttings then were dried in the sun.

Jan 1, 1947

By Thomas Fraser, H. F. Yancey

BefoRe a new coal-washing plant is installed, or an existing washery is remodelled and improved, considerable experimental work on the coal to be washed should be done. A thorough examination of a coal, to determine whether it can be washed successfully and the best and most economical process for securing a satisfactory grade of washed coal, calls for mine sampling, analytical work, and experimental coal-washing tests which may require several months' time and the expenditure of considerable money. Having collected the required data on the characteristics of the coal and the results secured with different types of machines under different sets of conditions, it is necessary to decide what method of treatment should be used. The interpretation of the experimental data is no small part of the problem. The first step in the investigative work is to determine from the characteristics of the coal and the manner of occurrence of the impurities whether it is possible to separate the dirt from the coal and produce a washed coal of the required quality. Then it is necessary to select the type of washer or the system of treatment that will produce the greatest amount of washed coal of this grade for the least cost. To secure this information, tests may be made at laboratories operated by consulting or contracting engineers, at the testing plants of machinery manufacturers, at commercial washeries, or in an experimental washery erected on the site of the proposed plant. Such tests will produce figures in which every factor, including analyses of raw coal and washed coal and yield of washed coal, may vary widely. To reduce these results to a common basis for comparison is very difficult. A number of plans

Jan 1, 1923

By Thomas Fraser, H. F. Yancey

BefoRe a new coal-washing plant is installed, or an existing washery is remodelled and improved, considerable experimental work on the coal to be washed should be done. A thorough examination of a coal, to determine whether it can be washed successfully and the best and most economical process for securing a satisfactory grade of washed coal, calls for mine sampling, analytical work, and experimental coal-washing tests which may require several months' time and the expenditure of considerable money. Having collected the required data on the characteristics of the coal and the results secured with different types of machines under different sets of conditions, it is necessary to decide what method of treatment should be used. The interpretation of the experimental data is no small part of the problem. The first step in the investigative work is to determine from the characteristics of the coal and the manner of occurrence of the impurities whether it is possible to separate the dirt from the coal and produce a washed coal of the required quality. Then it is necessary to select the type of washer or the system of treatment that will produce the greatest amount of washed coal of this grade for the least cost. To secure this information, tests may be made at laboratories operated by consulting or contracting engineers, at the testing plants of machinery manufacturers, at commercial washeries, or in an experimental washery erected on the site of the proposed plant. Such tests will produce figures in which every factor, including analyses of raw coal and washed coal and yield of washed coal, may vary widely. To reduce these results to a common basis for comparison is very difficult. A number of plans

Jan 1, 1923

W. H. BASSETT, * Waterbury, Conn.-Manganese should not be expected to remedy all the defects that are due to poor melting practice. It is undoubtedly valuable in helping to eliminate porosity in many of the alloys. In the copper-nickel alloys, its use is becoming almost universal, for, beside helping to make sound castings, it tends to hold the carbon in solution in the solidified alloy. GWILLIAM H. CLAMER,? Philadelphia, Pa.-I have found that manganese copper is satisfactory for eliminating sulfur and that it works very well in the crucible and when you have reducing conditions; but in a large reverberatory charge, where the conditions are oxidizing, we were not able to eliminate the sulfur.

Jan 1, 1919

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc , the Proceedings, and the papers revised for final publication (In this revision, after the prelimi¬nary publication, authors are permitted to use the largest liberty , and the changes and additions made in papers are sometimes important It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views It should be added, however, that in the majority of cases there are no important changes) These volumes are for sale as follows, in paper covers

Jan 1, 1910

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc., the Proceedings, and the papers revised for final publication. (In this revision, after the preliminary publication, authors are permitted to use the largest liberty; and the changes and additions made in papers are sometimes important. It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views. It should be added, however, that in the majority of cases there are no important changes.) These volumes are for sale as follows, in paper covers:

Jan 1, 1917

By C. C. Furnas

IT is well known that particles of different sizes are not distributed evenly throughout the average charge in an iron blast furnace. Just how great the disparity in particle size in different parts of a single plane in a furnace may be is indicated by the results of some recent investigations1 conducted by the Bureau of Mines on a furnace operating on Lake ores. The wide variations found in gas velocity, gas composition, and temperature from the periphery to the center of the upper charge column were caused by the great variation in particle size of the raw materials used and were also greatly influenced by the methods of charging. This paper summarizes the results of an investigation of the influence of different methods of charging and of the treatment of raw materials upon the size distribution of the solid particles in the blast furnace. A more complete report will appear later as a Bureau of Mines technical paper.

Jan 1, 1929

By W. H. Meyer

During the seventeen years Fairchild has been making aerial surveys and aerial photographic equipment many changes and improvements have been made in the equipment and in the technique of using it. Aerial photographic operations have been developed from the crude methods and apparatus of wartime to a science upon which exact engineering calculations can be based. In the early days there was no airplane specially designed to meet aerial photographic requirements. One type of camera was used in all types of operations. Projects were made to conform to the products we could make and deliver. Obviously this entailed definite limitations. We now have airplanes designed specially for aerial photographic operations in accordance with the conditions encountered in actual service experience. We have cameras for every photographic purpose and our laboratory technique and equipment have been developed to the point where it is possible to make contour maps from vertical aerial photographs with contour intervals as close as five feet. Therefore, the selection of equipment now can be made in accordance with the time at our disposal, the justifiable cost, the scale desired, and the general requirements of the client. This does not mean, however, that arbitrary deliveries can be set for aerial photographic products. The factors in each project vary and each job must be considered in accordance with the factors involved. This accounts for the fact that products of aerial surveys may readily vary from $1.25 to $200 a square mile. Sherman M. Fairchild became interested in the design of a radically different aerial camera during the war. At its close he was about ready to demonstrate his design to the War Department. By 1920, he was able to bring out his first completed model. It had a number of radical features, one of which was the first dependable high-speed between-the-lens shutter, which makes for accuracy in aerial photographic work. Another feature was the use of metal throughout, eliminating the wooden parts that had been employed in wartime cameras. Another feature was the interchangeability of parts.

Jan 1, 1937

By Milton E. Wadsworth, J. Brent Hiskey

Galvanic interaction between particulate chalcopyrite (CuFeS2) and copper results in the rapid conversion of chalcopyrite to chalcocite. The effects of temperature, surface area, concentration of sulfuric acid and agitation were systematically evaluated. The kinetics were found to be controlled by a steady-state current flow controlled by the effective anodic and cathodic surface areas involved in the galvanic couple. The experimental activation energy was 11.5 and stoichiometric data and reaction products have been characterized. The overall kinetic system has been evaluated based upon an electrochemical model.

Jan 1, 1974

By Charles P. Williams

The lead-bearing area of Missouri has been subdivided, geographically, into the Southeastern, the Central, and the Southwestern

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3

Jan 1, 1923

Jan 1, 1951

COUNCIL OF SECTION DELEGATES Nicholas A D'Arcy, Jr, Chairman (Southern California Section) Charles Chapman, Vice-Chairman (Florida Section) Ben H Parker, Secretary (Colorado Section) Frontier Refining Co Boston Bldg Denver 2, Colorado

Jan 1, 1956

By C. O. Swanson

In the iron ranges of northern Michigan, magnetic data have been used as an aid in geologic field work since the time of the earliest surveys. The presence of complex structures containing magnetic formations, and the general scarcity of exposures, guided the early work into this line of attack, and later field studies tended to place more and more emphasis upon this geophysical relationship, until, at present, the collection of magnetic data is a matter of routine in any areal survey. At first, horizontal deflections of the compass needle were the only data collected. In subsequent surveys, greater dependence was placed on dip-needle readings, which record variations in the intensity and inclination of the earth's magnetic field. Recently the trend has been toward adjusting the instrument so as to reduce the influence of changes in inclination, and using a more sensitive modification, called the Superdip,' in weakly magnetic areas. To a minor extent, the magnetometer has also been employed. The object of this paper is to present the writer's experience with magnetic data in this region. The conclusions are based on work covering a period of 10 years, and spread over nearly all of the iron ranges and a large part of the intervening areas. The viewpoints expressed are purely geological ones. In other words, any opinion as to the usefulness of a certain relationship is based upon the writer's experience with it as a guide in interpreting the structures of this region, and not upon its soundness theoretically, nor its usefulness under other conditions. A very brief summary of the conclusions is as follows. The most important step is that of collecting the magnetic data. This requires a suitable adjustment of the dip needle, and sufficient readings to accurately portray the variations in the magnetic field, which are apt to be irregular. Once the readings are taken and plotted in some clear fashion, the interpretation of them is usually merely a matter of observing their relation-

Jan 1, 1934

By B. H. Caudle, W. J. Bernard

Factors which influence the success or failure of a waterflood can seldom be determined in the laboratory. For this reason pilot waterfloods are initiated in a repreventative portion of the oil reservoir in question. For a pilot flood to predict quantitatively the recovery to be expected in a field-wide waterflood operation, the pilot area must behave as though it were confined (surrounded by similar areas). In this study, laboratory fluid-flow models were used to determine the simplest pilot pattern, for particular conditions of mobility ratio and initial gas saturation, that would behave as though it were confined. Pilot patterns studied ranged in complexity from a single inverted five-spot to a grouping of nine regular five-spots. Only the innermost producing well in each pattern was studied. Model results showed that the optimum number of wells in the pattern depends upon the oil-water mobility ratio and the expected oil-bank size. Unfavorable mobility ratios will, in general, require more wells in the pilot pattern than will favorable mobility ratios. Pilot patterns in reservoirs which contain a dispersed, flowable, free gas saturation will require fewer wells than for the under-saturated case. The single inverted five-spot pattern was found to be unsatisfactory for predicting behavior of fully developed waterfloods. In particular, it is possible that, in reservoirs which contain a flowable, dispersed gas phase, the oil bank will never be observed at the producers due to the large amounts of free gas which continue to be produced with the oil. INTRODUCTION One method which has been used to predict the performance of a waterflood is the pilot flood. The pilot waterflood is a flood which involves only a small cluster of the reservoir wells and is located in a small, representative portion of the reservoir. The object is that oil produced from the pilot can, in some way, be related to the oil recovery to be expected from a field-wide expansion of the waterflood. However, these field pilot waterfloods have often been unreliable in the prediction of oil recovery in a fully developed waterflood. This unreliability has also been demonstrated in several laboratory studies of pilot floods. Some of the investigators have shown that there are situations in which the pilot flood oil production is far too optimistic with respect to the oil recovery in the fully de- veloped flood. Others4-G have shown that the pilot results can also be pessimistic, especially if the pilot waterflood is initiated in an oil reservoir which has been depleted by primary recovery and is at very low pressure. The major reason for this unreliability of pilot water-floods is the migration of fluids into or out of the pilot area. By the well-known method of images, if straight lines can be drawn to represent vertical planes of symmetry in a porous medium which contains pressure sources and sinks (injectors and producers), then these lines are invariant streamlines, or lines across which there is no potential gradient, and therefore no flow. In an actual reservoir, these lines of symmetry can never be established exactly because of reservoir inhomogeneities and irregular reservoir boundaries. However, if the reservoir is relatively large and contains wells in repetitive patterns, these lines of symmetry are commonly assumed to exist for the pattern units sufficiently far removed from the reservoir boundary. Lines of symmetry for the five-spot injection pattern are shown in Fig. 1. Each five-spot unit in this figure can be considered confined with respect to flow across its boundary. In pilot floods this is not the case. The lines of symmetry for the pilot patterns investigated in this study are shown in Fig. 2. It is obvious that the fluid within these pilots is not confined and is therefore able to migrate into or out of the pilot area. Intuitively, one can see that, if more wells are added to the pilot, the innermost unit tends to behave more and more like the confined pattern. However, there is a practical limit to the number of wells which should be placed in the pilot. This limit is usually determined by economic factors. It was the purpose of this study to use laboratory fluid-flow models to determine which of the previously mentioned pilot patterns will force the innermost producing well to behave as it would in a fully developed waterflood. Since fluid migration is influenced by initial saturation conditions and the mobility ratio, these factors were included in the study. The ultimate objective of this study was to develop data which would allow the operator to choose a pilot pattern and operating conditions that will yield a production history which can be applied directly as an estimate of the performance of each production well of the fully developed waterflood. BASIS FOR THE STUDY The basic problem of field pilot floods is the migration of the reservoir fluids into or out of the pilot area. This problem has been the subject of previously reported model studies on pilot floods. These studies have been concerned mainly with the development of arbitrary "correction factors" to be applied to the simple, unconfined pilot systems such as the single five-spot. The correction factors were intended to adjust the production history of the un-

By H. M. St. John

MAINTAINING a satisfactory structure in brass and bronze castings has always been a foundry problem of great practical importance. While metallurgists and scientific investigators have not entirely ignored this matter, it has received less of their attention than has been given to iron, steel and the wrought copper and aluminum alloys. Investigation in this field has probably been discouraged to some extent by the complicated nature of the alloys involved. Hundreds of alloys are in more or less common use, most of them containing copper, zinc, lead and tin in-widely varying proportions. They also contain appreciable percentages of iron and antimony as impurities, and often phosphorus, which has been added as a deoxidizer and fluidifier. Small amounts of sulfur are usually present. It is not uncommon to find nickel, sometimes in rather substantial quantities. Traces of other metals are frequently present. So complicated and variable a mixture obviously offers difficulties in. any investigation of the various factors that influence the structure and other properties of the casting.

Jan 1, 1930

By J. O. Nelson, C. J. Altstetter

Single crystals of hcp cobalt, 3 mm in diameter and up to 35 cm long, were grown using an electron-beam, zone-melting technique. The martensitic-phase transformation was studied in single-crystalline and polycrystalline specimens by making length-change measurements as a function of temperature under various elastic compressive stresses. Upon thermal cycling, single-crystalline or polycrystalline specimens repeatedly transformed almost entirely on the same variant of close-packed plane provided the maximum temperature did not exceed 600°C. Cycling to 1000°C resulted in transformation on more than one {111} variant. This behavior is termed multivariance. The multivariant transformation occurred very rapidly at an M, temperature 2° to 6°C lower than the M, of a transformation which would result in a single-crystal product. Elastic compressive stresses (up to 253 g per sq mm) tended to lower the A, and raise the M, temperatures, decreasing the width of the temperature vs dilatation hysteresis loop. The transformation habit plane and transformation shear direction of an as-grown single crystal were not grossly affected by elastic compressi?ie stress. This was evidenced by similar dilatations on the temperature us dilatation loops joy specimens with and without compressive stress. A dislocation mechanism is proposed to explain the observed results. IT has been shown that, on heating, cobalt transforms martensitically from the hcp to the fcc phase.' The transformation habit plane is (0001)hcp || (lll)fcc and the transformation shear direction is (1010)hcp || (112)fcc. The transformation involves a shear of 1g°28', which may be achieved by a shearing of a/6(112) of every two planes with respect to the plane beneath, thus changing the ABABAB stacking of hcp to the ABCABC stacking of fcc. Associated with the phase change is a 0.3 x 10"3 contraction in the habit plane and a 4.2 X 10"3 expansion perpendicular to the habit plane resulting in a 3.6 x X volume increase on heating.' On cooling, an identical volume decrease takes place. The temperature at which the fcc phase begins to form on heating (A,) is reported as 430°C, and the temperature at which the hcp phase begins to form on cooling from an elevated temperature (A&) is reported as 390oC1,3 Consequently, temperature vs dilatation plots have the form of a hysteresis loop. If heating or cooling is reversed during a transformation, a smaller hysteresis loop results. Upon heating, the transformation is always complete; whereas, fcc is often retained at room temperature as a metastable phase entrapped in the polycrystal-line hexagonal matrix.1,4,5 Two obstacles in the theory of the allotropic-phase transformation of cobalt have been: 1) a detailed knowledge of the product nucleus, and 2) a plausible method of propagation of the transformation. Bilby,8 christian, 7 and seeger 8,9 have suggested a "pole mechanism" as a means of propagation of partiai dislocations from plane to plane. A pole dislocation and a Shockley partial come together at a node. The a/6(112) Shockley partial rotates about the pole dislocation effecting the transformation shear. The pole dislocation must have a 2a/3(111) screw component which causes extension of the transformed region by two atomic planes with each full rotation of the Shockley partial. Bollmannl0 suggested, on the other hand, that transformation propagation occurs due to the stress fields of intersecting (111)-type stacking faults. As faults intersect, a stress distribution is set up about their intersection which is in turn reduced by the emergence of another fault on the second nearest plane. This process continues with the final result of a complete phase transformation. In view of the similarities between deformation and transformation in cobalt, the effect of stress on the transformation would, hopefully, yield valuable information concerning nucleation and propagation. In the present work single-crystalline and polycrystalline specimen length changes were measured as a function of temperature at various compressive loads. PROCEDURE Several orientations of single crystals of hcp cobalt in lengths up to 25 cm were grown by electron-beam floating zone melting from 99.95 and 99.999 pct, 3-mm-diam cobalt rod as supplied by Johnson

Jan 1, 1964

By R. M. Hudson

Equilibrium constants have been determined for the jeaction C (in steel) + H2O = CO + H2 as a function of carbon content (0.013 to 0.74 ujt pct) and temperature (1200° to 1800°F) by using a flow system in which the water-vapor content of various gas mixtures containing hydrogen, carbon monoxide, and nitrogen was systematically controlled. The equilibrium partial-pressure ratio K1 = PcoPH2/PH2O was obtained for two low-carbon steels and four Fe-C binaries from a series of runs made at each temperature. By comparison of Ki with the analogous ratio for the reaction C (graphite) + H2O = CO + H2, the activity of carbon in steel (ac) was comDuted for each temperature and carbon content studied. From these data values of the equilibrium constants for two other carburization-decarburiza-tion reactions of importance were estimated. The chemical compositions of the two steels and four Fe-C binaries used are given in Table I. Specimens of Steel E were cut from a 0.035-in.-thick commercially box-annealed and temper-rolled lot of a low-carbon low-metalloid steel. Steel F was a commercially hot-rolled rimmed steel that was cold-reduced at the Laboratory to a 0.059-in. thickness. Fe-C binaries A, B, C, and D were vacuum-melted and poured, hot-rolled, pickled, and cold-reduced at the Laboratory to furnish specimens 0.035 in. thick. Sheet specimens were cut from all lots to approximately 3/4 by 3 in. by gage and were vapor-degreased with trichlo-roethylene and weighed before heat treatment. Heat treatments were carried out in a hinged-top Hevi-Duty electric furnace with a Vycor-glass tube. When the furnace was at the desired

Jan 1, 1965

By I. Javandel, P. A. Witherspoon

The finite element method was originally developed in the aircraft industry to handle problems of stress distribution in complex airframe configurations. This paper describes how the method can be extended to problems of transient flow in porous media. In this approach, the continuum is replaced by a system of finite elements. By employing the variational principle, one can obtain time dependent solutions for the potential at every point in the system by minimizing a potential energy functional. The theory of the method is reviewed. To demonstrate its validity, nonsteady-state results obtained by the finite clement method are compared with those of typical boundary value problems for which rigorous analytical solutions are available. To demonstrate the power of this approach, solutions for the more complex problem of transient flow in layered systems with crossflow are also presented. The generality of this approach with respect to arbitrary boundary conditions and changes in rock properties provides a new method of handling problems of fluid flow in complex systems. INTRODUCTION Problems of transient flow in porous media often can be handled by the methods of analytical mathematics as long as the geometry or properties of the flow system do not become too complex. When the analytical approach becomes intractable, it is customary to resort to numerical methods, and a great variety of problems have been handled in this manner. One such method relies on the finite difference approach wherein the system is divided into a network of elements, and a finite difference equation for the flow into and out of each element is developed. The solution of the resulting set of equations usually requires a high speed computer. When heterogeneous systems of arbitrary geometry must be considered, however, this approach is sometimes difficult to apply and may require large amounts of computer time. The finite element method is a new approach that avoids these difficulties. It was developed originally in the aircraft industry to provide a refined solution for stress distributions in extremely complex airframe configurations. 27 Clough has recently reviewed the application of the finite element method in the field of structural mechanics.6 The technique has been applied successfully in the stress analysis of many complex structures.l, 27, 28 Recognition that this procedure can be interpreted in terms of variational procedures involving minimizing a potential energy functional7 leads naturally to its extension to other boundary value problems. In the field of heat flow, there recently have been introduced several approximate methods of solution that are based on variational principles.2-4, 17 By employing the variational principle in conjunction with the finite element idealization, a powerful solution technique is now available for determining the potential distribution within complex bodies of arbitrary geometry. In the finite element approximation of solids, the continuum is replaced by a system of elements. An approximate solution for the potential field within each element is assumed, and flux equilibrium equations are developed at a discrete number of points within the network of finite elements. For the case of steady-state heat flow, the technique is completely described by Zienkiewicz and Cheung.33 Since the flow of fluids in porous media is analogous to the flow of heat, Zienkiewicz et al. have employed the finite element method in obtaining steady-state solutions to heterogeneous and anisotropic seepage problems. 34 Taylor and Brown have used this method to investigate steady-state flow problems involving a free surface.25 The work of Gurtin has been instrumental in laying the groundwork for the application of finite element methods to linear initial-value problems.12 As a result, Wilson and Nickell have recently

Jan 1, 1969

Jan 1, 1947