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By L. F. Stutzman, George Thodos

A new graphical method, which is a modification of that proposed by Buckley and Leverett', is presented for the determination of the displacing fluid saturation at breakthrough for frontal drive mechanisms. This method is applicable to all types of fluids, which may be either soluble or insoluble in the oil at reservoir and injection conditions. This adaptation has unique advantages in handling problems in which either liquids or gases are the displacing fluids. INTRODUCTION In the displacement of oil from a reservoir with water or gas injected into the formation or by the expansion of a gas cap, the determination of breakthrough or flood advance is important to define the initial and subordinate phases of the operation. Thus, the determination of the displacing fluid saturation at breakthrough is fundamental to the establishment of over-all reservoir production. Methods for analyzing this saturation and for calculating production rates have been previously reported1,'*".". All of these methods utilize the rate equation for linear flow developed by Buckley and Leverett1. xs = QT - Qn/A? (?fu/?Su) .....(1) Sp where f, represents the volumetric fraction of displacing fluid in the total flowing fluid within the reservoir as is defined by: fo = 1/1+ ku/kd µn/µn .......(2) Since the time, ?, necessary for the flood front to travel distance ?X is unknown, Eq. 1 cannot be solved directly for the determination of the breakthrough point. Therefore, it becomes necessary to solve Eq. 1 simultaneously with an equation representing a fluid bal-ance on the reservoir behind the flood front. To develop such a fluid balance equation, it has been assumed that the fluid composition is uniform in the reservoir behind the flood front. Based upon this assumption, the follow-ing equation can be derived from a material balance on the displacing fluid: x = (?X) s Dx ? x=0 [ Snx - Sn1 ] dx = QT - Qn/A? It is readily observed that the displacing fluid satura-tion behind the flood front, Snx, may be determined through the simultaneous application of Eqs. 1 and 3. Although the approach may vary, this objective re-mains the same for all of the previously mentioned graphical or analytical methods. After Sox is determined, it is then possible to calculate the gas-oil and/or water-oil ratios and the rates during the initial and subordinate phases of production, and thereby define the production history of the reservoir. In this presentation only the de-termination of Snx is considered, and the reader is re-ferred to the several texts in reservoir engineering2,4,5 for a complete discussion on the methods for establish-ing the production history of a reservoir. PROPOSED METHOD FOR DETERMINING Snx Since at any time the quantity, QT - Qn/A? is a constant, Eq. 1 may be expressed in differential form as follows: dxsn = QT - Qn/A? d (? fn/? Sn) sn .....(4) Eq. 4 may be substituted directly into Eq. 3 to obtain: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = QT - Qn/A? ...............(5) Eq. 5 simplifies to the expression: ? fn/? Sn ? [ Snz - Sn] QT - Qn/A? d ( ? fn/? Sn) = 1 ....(6)

Jan 1, 1958

By A. L., Bailey

All who are even generally aware of the tremendous rate of increase in coal washing operations must realize the growing importance of the float-and-sink test. I believe it is conservative to estimate that, in the past decade, the dollar volume of float-and-sink testing has increased tenfold. It is a simple matter of economy, then, to examine the factors that determine the cost of adequate float-and-sink testing. When the Coal Preparation Section of the Bureau of Mines entered upon a greatly expanded program of such work in connection with the synthetic liquid fuels investigations, it seemed advisable to examine these factors experimentally. The principal consideration that differentiates float-and-sink test sampling from general purpose sampling, is that the original particle size must be preserved. Therefore, the total cost of the test will be directly affected by any standard that might be proposed to limit sample bulk reduction at any given particle size. For this reason, the relationship of sample size to variability of results was the first factor to be studied experimentally.

Jan 1, 1949

RICHARD R. HICE, Beaver, Pa. (written discussion *).-The matter of selective. mining is probably of more importance in Pennsylvania than is washing, and perhaps washing would not be necessary at some plants where now practised if proper care were taken in the mining. I have in mind one plant where the sulfur content of the entire bed is more than 2 per cent., yet if the bottom 12 in. and the top 12 or 15 in. are separated, the main portion of the bed, some 6 ft., will not contain more than 1.25 per cent. sulfur; and yet in this mine the entire bed .is worked together, the resultant coke, as a matter of course, not being fit for use in iron smelting. Not sufficient notice is taken of the "Double-thick" Upper Freeport coal in Allegheny and Butler counties. This is a very valuable deposit. Other areas where there is a, top member of the Upper Freeport coal are also known, which add to the value of this bed as a coking coal. This double Freeport coal is especially suited for byproduct coking. I cannot be as optimistic as regards the "low-sulfur" Pittsburgh coal in Greene county as the authors. If the term low-sulfur is to he confined to coal with not exceeding 1.25 per cent. sulfur, there is probably little

Jan 10, 1919

By AIME AIME

ADDRESSING the Ohio Section at a recent meeting in Columbus, Ohio, R. C. Allen, executive vice-president for Oglebay, Norton & Co., Cleveland, spoke on "The Iron-Ore Industry of the Lake Superior Region in Prosperity and Depression." The speaker considered this region in connection with the problem of national security. This is the age of minerals; progress depends on them; and next to agriculture, the mineral industry is of prime importance. The United States has no shortage of minerals rather an over-supply; but many mines have been and are being exhausted. The shifting of the sources of supplies of minerals so important as copper, petroleum, and iron to other countries would create internal strains and affect international relations. There will be no early decline of ore mining in the Lake Superior region unless it is forced by unwise public policies. Iron ore is industrial strength and self-sufficiency. A study of economic geography is important for statesmen and mining men, because the minerals essential for peace and war are haphazardly or irregularly distributed throughout the world. Of these minerals, 75 per cent are owned by 10 per cent of the population, mainly peoples of Anglo-Saxon origin.

Jan 1, 1934

By F. R. Koeberlin

ABOUT thirty miles south of the port of Coquimbo, Chile, nestling in one of the western outliers of the main Andes range, lies the little mining town of Andacollo, a place whose history and traditions make up one of the most romantic pages in the life story of this southern republic. The beginning of Andacollo is shrouded in the penumbra of the pre-Columbian era, but its first mining activity probably dates from about the years 1440 to 1460. It was in the middle of the fifteenth century that the Inca Tupac-Yupanqui, grandfather of Atahualpa, conquered this part of Chile. His domain extended even as far south as the present site of Santiago, and perhaps farther, but was maintained with increasing difficulty against the fiercely independent and indomitable tribes of Araucanian Indians of the South.

Jan 1, 1938

By A. Gatti

Studies were made on the system iron plus alumina. Various methods of dispersing and various amounts of alumina were used. Powder metallurgy techniques were used to produce the final product. Microstructures and some mechanical properties are presented. Alloys containing up to 16 pct alumina by weight are ductile at all temperatures tested. The ivon-alumina materials have a higher yield stress and improved creep resistance over that of pure iron. SINCE the development of SAP' an A1- Al2O3 powder metallurgy product, great interest has been shown in the development of a SAP-like structure in metals and alloys other than aluminum. The outstanding properties of this class of materials are: 1) Good creep resistance at high temperature. 2) High yield strengths and high hardness at high temperatures. 3) High recrystallization temperature. However, the lack of ductility and formability has thus far limited the applications of SAP-like materials. The following report deals with methods of dispersing A12O3 in Fe, processing of powders into rod, structures produced after processing, and mechanical properties of the iron-alumina material produced. Methods of dispersing the alumina and also the volume fraction of alumina added were varied. MATERIAL Powder Processing— Four methods of obtaining dispersions of alumina in iron were studied. 1) Oxidation-reduction of a Fe + 8 pct Al alloy. .2) Coprecipitation of Fe(OH)3 + Al(OH)3 from aqueous solution. 3) Colloidal mixing of Fe,O3 and Al2O3. 4) Colloidal mixing of Fe powder and A1,O3. Fig. 1 is a processing flowsheet which outlines the processing steps taken to produce a final extruded bar 1/4 in. in diameter and about 30 in. long. The - 100 mesh iron-aluminum alloy was oxidized by placing a thin layer of powder on an alumina plaque. The reduction step was modified to include 1/2 hr at 1000°C since the powders tended to become pyro-phoric unless sintered slightly after low-temperature reduction. Compacting was done in a 1-1/8-in.-diam pressing die. The slugs produced averaged 1 in. in length. The billets were encased in low-carbon steel cans shown schematically in Fig. 2. The blank is included for structure and property comparison purposes. TESTING PROCEDURE All tests were made on as-extruded material.

Jan 1, 1960

Bailey, Lewis Newton, Master Engineer, Senior Grade, 4th Regiment, U. S. Engineers, Headquarters Company, died of pneumonia at Camp Merritt, N. J., on April 30, 1918. Baird, Louis, Lieut., Royal Field Artillery, British Army, died on the battlefield in 1915. Cobeldick, William Morley, Royal Engineers, died from gas poisoning on October 7, 1915. Dougall, Ralph, killed in action. Evans, Alfred Winter, Lieut.-Col., New Zealand Rifle Brigade, D. S. 0., D. C. M., killed in action on October 12, 1917. Gorman, Thomas C., Lieut., Canadian Engineers, killed in France, Mar. 18, 1918. Hague, William, 1st Lieut., Engineer Officers' Reserve Corps, died in active service. Hall, William T., Capt., Royal Flying Corps, killed in action. Heine, Bernhardt E., Lieut., Aviation Service, killed at Fort Sill, Okla., Aug. 10, 1918. Irving, John Duer, Capt., 11th Engineers, A. E. F., died while on active service in France on July 26, 1918.

Jan 9, 1918

By George W. Sargent

For the experiments here described a rod was used, 0.75 in. in diameter, and rolled from one ingot. Analyses of the ingot and rod showed them to have the following composition respectively: C. Mu. Si. P. 8. Percent. Percent. Percent. Percent. Percent. Ingot,. .. 1.150 0.328 0.223 0.020 0.016 Rod,. .. 1.033 0.327 0.223 0.020 0.016 Pieces 4 in. long were heated to various temperatures in a closed porcelain tube, within a gas furnace, and allowed to cool with the same; they were then turned, threaded, and subjected to physical tests in a Riehlé testing-machine. The elastic limit was determined by the drop of the beam. The elongation was measured in two inches. From the threaded ends of the testrpieces, disks were cut, and prepared by combined polishing and etching, using parchment stretched over a wooden block and moistened with a 2-per cent. solution of ammonium nitrate. The structure, as thus developed, and the fractures, were magnified and photographed. A cooling-curve was constructed, and the critical point was located at 675º-680º C. A thermo-electric pyrometer was used to make the measurements of temperature. The micro-constituents of steel have been so frequently and thoroughly described by others that I need only say here that the theoretical micro-structural constituents of this steel were : pearlite, 95 ; ferrite, 0 ; cementite, 5 per cent. The quenched metal would be expected to consist almost entirely of martensite—provided, however, the quenching be done at or near the proper temperature. Rapid quenching from a high temperature would give rise to austenite.

Jan 1, 1902

By John B. Hastings

THE origin of the watery vapors of vulcanism has always been an object of interest and speculation to the seismologist, and as theories of the genetic origin of ore-deposits have of late years been pretty well narrowed down to the expiring forces of plutonic action, the same question has had a lively interest for mining engineers and geologists, as is well shown by the discussions of the subject in our Transactions. The important part taken by volcanic emanations in the origin of pegmatites and quartz-veins, described in my paper, Origin of Pegmatite,1 and their latent power to concentrate into useful deposits such scattered gold as occurs in the Hartsel granite, make a discussion of their derivation but a natural third and final step. It is conceded that enormous amounts of vapor accompany volcanism, though perhaps we are apt to forget that steam has 1,700 times the volume of water, besides which the column seen over Vesuvius and other volcanoes is greatly mixed with air; the immensity of such volumes compared with solids and liquids is shown by the experiment of Gautier, who, by heating dessicated granite to 100° C., evolved from it uses 20 times, and steam 90 times, its own volume. Dana appraised the average amount of water left in ordinary rocks as 2.5 per cent. T. M. Read estimated that the Mississippi river carries to the sea annually 150,000,000 tons of rock material. If these Mississippi sediments, as deposited, contained 20 per cent. of water, it would be 600,000,000 cu. ft., or 4,500,000,000 American gallons, annually. Allowing the vapor suspended over a volcanic cone to be mixed with 80 per cent. of air, this amount of water converted into steam would replenish anew, every 9 min., a column 15,000 ft. high, 2,000 ft. in diameter at the base, and 10,000 ft. at the top. Read's estimate is only half of the amount given in a more recent and probably correct one .2

Jan 5, 1908

By Neville J. Price

In order that the reader may not be misled, I feel it necessary to comment upon the title of this paper. "Laws of Rock Behavior," one may take as being part of the all-embracing "Law of Nature" and this, according to the Oxford Dictionary, relates to the principles of conduct recognized as being pleasing to God. I feel it would be presumptuous to erect a code of rock behavior on this basis, so turn to a secondary definition, namely that a "Law" is that which is intrinsically reasonable. It is extremely unlikely that any group of geologists, or workers in rock mechanics would be in complete agreement about what could be taken to be "intrinsically reasonable." Therefore, this paper does not present any deified utterances, but rather deals with a few aspects of rock behavior which I consider to be intrinsically reasonable and with which I hope the reader will concur. The mode of behavior of rocks in the Earth's crust covers the range from wholly brittle to completely ductile ; with a deformation time scale which may be measured in milliseconds, for some events such as meteoritic impact, or in millions of years for the tectonic deformation involved in mountain building. A complete survey is, of course, outside the scope of an introductory paper, so I must be both brief and selective in my treatment. Any attempt to establish the mode of rock behavior in the Earth's crust should take into account data and relationships established in laboratory experiments and correlate these with field evidence. Consequently, the first section of this paper presents a brief discussion of the experimental aspects of rock mechanics which are pertinent to the subsequent discussion.

Jan 1, 1970

By AIME AIME

UNTIL recently, practically all geophysical prospecting in Australia was conducted by government departments, either by the Aerial, Geological and Geophysical Survey of Northern Australia or the New South Wales Department of Mines. At present, in addition, the Shell company is carrying out an extensive geophysical campaign in South West Queensland. The Northern Australia Survey has now been in operation for over six years, its work being carried out principally in the northern and central parts of Australia over an area of about a million square miles. At present this Survey is being brought to a conclusion but it appears certain that the geophysical section will be transferred to a Commonwealth Government department on a permanent basis. At present the officers of the Geophysical Section are preparing or have issued some 150 reports on their field work and also a special technical report on the geophysical practice of the Survey.

Jan 1, 1942

By AIME AIME

A METALLURGICAL research building is to be erected for the Armour Research Foundation at the Illinois Institute of Technology. It will be located at the corner of Federal and 34th Sts., Chicago, and fully equipped will cost $250,000. It will provide the Middle West with the largest and most complete of facilities for the conduct of developmental and industrial research in this field. The new building will be constructed around an existing foundry and metallurgical research building which has become too small to carry on and service the many research projects contracted for by the Foundation, having to do with steel, alloys, and nonferrous metals. After two bays of the new unit have been completed, the old unit will be torn down and the new one completed.

Jan 1, 1942

By Bernard MacDonald

The writing of this paper was prompted by the discussion by H. M. Chance of the paper written by Thomas M. Chance,l and by the remarks of the editor in which he stated that while the matter contained in discussion did not refer to the original paper it " was presented as of interest to the operators of cyanide and other lixiviation processes dealing with fluid mixtures of varying specific gravity." For some years past the principle enunciated in the discussion referred to has been known to the writer and demonstrated by him to be an efficient and economical way of separating water or solution from solids in the cyanidation, lixiviation or acid leaching of ore pulps. In utilizing this principle in commercial practice he has invented a method whereby not only the separation of solution from solids may be effected in any given tank, but also the counter migration of the solids and solution may be effected continuously through a series of tanks in which the hydro-metallurgical treatment of ore pulps is being carried on. In effect this method is analogous to the counter-current system, but is different physically in that it is carried on throughout a series of tanks on practically the same level, continuously and automatically, by hydrostatic pressure and gravity-flow, without the aid of intervening pumps or elevators, at the same time that agitation is being carried on in the same tanks. In the Parral system, agitation is effected in tanks by a number of air lifts of comparatively small diameter through which the pulp is continuously transferred from the bottom of the tank and spouted horizontally on top of the charge. The spouting force of the several streams thus discharged maintains a rotary flow in the pulp charge which extends from top to bottom of the tank. This continuous transfer of pulp and the spiral flow from top to bottom of the tank maintains the pulp constituents in uniform proportions and meets the requirements of efficient treatment in a most economical manner. The quantity of compressed air required is very small, as the pulp is not lifted but simply transferred from the bottom to the top of the tank charge under hydrostatic balance. Fig. 1 gives a bird's-eye view of two adjoining tanks in any series equipped with the apparatus for producing the separation of

Jan 1, 1919

By R. K. Buhr, H. Thresh, M. Bergeron, F. Weinberg

The microsegregation of nickel and chromium in directionally solidified AISI 4340 steel castings has been measured using electron probe microanalysis. Minimum concentrations were observed to occur at the center of the dendrite stalks, as reported previously. However, the position of the maximum concentrations could not be determined from the dendrite configuration. An etching technique has been developed which shows the position of maximum concentration. Measurements were made of the distribution of nickel and chromium in the dendritic structure. The ratio of maximum to minimum concentration was determined as a function of primary dendrite arm spacing for both as-cast and partially homogenized materials. The results are compared with observations reported in the literatuve. A S part of an investigation of solute segregation in directionally solidified AISI 4340 steel casting, electron probe microanalysis was used to measure the distribution of nickel and chromium in the dendritically segregated material. This complemented the observations on the segregation of radioactive phosphorus obtained by autoradiographic techniques in the same castings.' Kattamis and I?lemings2 have reported similar measurements, using electron probe microanalysis, on dendritically segregated AISI 4340 steels. They found minimum solute concentrations occurred at the center of dendrites, maximum concentrations occurred in the center of interdendritic regions, for symmetrically oriented dendrites, and a regular variation of concentration within dendrite arms. The ratio of maximum to minimum concentration was found to be essentially independent of position in the castings, except near the chill surface where it was somewhat higher. Assuming complete diffusion in the liquid and no diffusion in the solid during freezing, they considered that isoconcentration curves in the steel were homothetic. As a result, isoconcentration curves of the various elements, contour surfaces of dendrites produced by isothermal-transformation studies, and the contour of the solid-liquid interface would all be similar, and could be superimposed by a uniform expansion or contraction of the contours. Preliminary results of the present investigation suggested that isoconcentration curves were not homothetic. It was also evident that points of maximum concentration could not be predicted from the dendrite configuration. Since the ratio of maximum to minimum concentration appeared to be an important parameter in defining the overall segregation in a casting, other techniques for determining the point of maximum concentration were investigated. In addition the overall solute distribution associated with the dendritic structure was examined for both nickel and chromium, and the consistency of the distribution for neighboring dendrites was determined. METHOD Fifty-pound heats of AISI 4340 steel were cast in a manner similar to that used by Flemings et al3 with a water-cooled copper base plate and exothermic sides and top. The nominal composition of the material was C, 0.41 pct; Mn, 0.66; Si, 0.35; S, 0.012; P, 0.010; Ni, 1.88; Cr, 0.95; Mo, 0.28. The steel solidified directionally from the chill surface, with a dendritic structure which increased in dendrite arm spacing with increased distance from the chill. Results of the general investigation of the cast structure and segregation of radioactive phosphorus in these castings have been reported elsewhere.' For the present measurements, sections were cut from the casting at several distances from the chill surface. The sections were subsequently heat-treated, mounted, and then polished on a plane perpendicular to the general freezing direction of the casting. Electron probe microanalysis was carried out with the JEOL-JXA3 microprobe using a voltage of 25 kev and beam current of 0.15 µa. The take-off angle is 22 deg. Quartz crystals were used in the spectrometers and measurements made for Ka radiation from both nickel and chromium simultaneously. A thin layer of carbon was deposited on all specimen surfaces prior to examination in the microprobe. Early measurements were made on polished surfaces, with indentation marks produced by a hardness tester to indicate the area of interest. It was found desirable to use etched surfaces, as opposed to polished surfaces, to reduce sample preparation time and more readily relate the microprobe scan to the structure. To determine if this could be done, without introducing significant errors, a series of measurements were made on polished and etched surfaces of the same specimen. Both polished and etched surfaces produced similar results within normal scatter as shown in the observations. Subsequent measurements were then made on etched surfaces. Measurements with the microprobe analyzer were made by point counting, for periods of 100 sec, at 10-µ intervals. Ten-second counts were made on pure nickel and chromium standards, incorporated in the specimen mount before and after each set of measurements. The results were adjusted for background, then corrected for dead time using the expression:

Jan 1, 1969

By WILLIAM BOWIE

IN most human endeavors a knowledge of the terrain is essential to the effective carrying out of projects, but no line of work is more dependent on maps than theoretical and applied geology. Maps of a kind do exist for all of the area of the United States, but most of them are crude affairs and of little use in engineering, planning, and scientific research. Topographic mapping in the United States was initiated on a national scale by the U. S. Geological Survey and the organizations that were merged in its creation to make base maps for geologists. Their work could not be effectively done then and cannot be effectively done now without maps that accurately delineate the earth's surface. The distribution of the rock masses that contain valuable mineral bodies, or that by their intrusion brought them into existence, is the first step in a study of the mineral resources of the nation. This work requires three-dimensional maps, that is, topographic maps on which the land forms are shown by contours.

Jan 1, 1938

By PERCY E. BARBOUR

SECONDARY copper1 has &come more or less of a bugbear generally. What is its influence is often the subject of heated argument. The inedapable fact usually quoted is that since in 1929 primary production of copper in the United States was 1,026,348 tons and secondary production was 626,550 tons, there- fore, 0.6 lb. of secondary is produced for every pound of primary, and "How can you get around that?" The matter seems very plain, now that I have reached my conclusions, but they are the result of much laborious study and research. I shall show that' the production of secondary copper is not 0.6 per lb. of primary, in spite of statistical appearances; that the production of secondary is a function of primary production rather than of price; that secondary production has 'only a sub-. ordinate influence on the price of copper and then only in abnormal times; that there is not an accumulating reservoir of secondary from which the country is some- time to be drowned in copper, as is believed by some, or a reservoir from which we are going to draw much needed and more or less inexhaustible stores in the future, as is believed by others; and finally, that the United States always produces more copper than it uses and exports the surplus. These are all controversial points, and for that reason and to anticipate argument I have set forth my reasoning in considerable detail.

Jan 1, 1931

By J. P. Hirth, A. H. Clauer

A simple graphical method is presented for the determination of climb forces on dislocations exerted by uniaxial stresses. In conjunction with standard stereographic projections, the technique is applicable for any crystal system. Climb forces on glide dislocations in bcc crystals are determined as an application. In connection with a study1 of elevated temperature creep of molybdenum single crystals, a detailed analysis of the climb force on a dislocation was necessary. In general, such forces can be calculated for an arbitrary dislocation segment from the Peach-Koehler equation2 (or one of its variants3"6) where Fk are the components of the force per unit length of dislocation line, ?i of the unit sense vector tangent to the line, ojl of the stress tensor, bl of the dislocation Burgers vector, and is the Einstein permutation operator with components ?123 = ?231 = ?321 = —?132 = — ?321 = —?—213 = unity, and all other components zero. It is understood in the suffix notation of Eq. [I.] that repeated indices are to be summed over 1, 2, and 3. For the most general coordinate system, the matrix manipulations required to solve Eq. [I] are fairly complex. However, a simplification can be achieved by specifying a coordinate system based on the dislocation in question. The pertinent system involves cartesian coordinates xi, x;, xi, with attendant unit vectors e'i; ei being parallel to the Burgers vector b, and e'3; being parallel to the climb directions (b x ?), i.e., normal to the slip plane. In this coordnate system b = (bi, 0, 0) and ? = (?'1,?'2, 0). Hence, Eq. [I] yields for the climb force per unit length F3 = ?'2s'11b'1—?'1s'12b'1 [2] The first term on the right side of Eq. [2] is the climb force on the edge component of the dislocation, while the second is the (cross-slip) force normal to the glide plane acting on the screw component. Thus, the problem of determining the climb force reduces to that of resolving the stress components —il and s'12 in the xi coordinate system. Several authors7- l0 have shown, for the glide case, that such stress resolution can be performed most readily by graphical methods. Therefore, we present a similar method for the climb case. Of the suggested methods, we follow that of Hartley and Hirth,9 which can be performed directly with a standard stereographic projection for the crystal system in question. We treat the case of simple tension, or compression, this being the most common creep test in which climb is important. A set of cartesian coordinates (x1, x2, x3) is fixed with x3 parallel to the specimen axis. This set is connected to the x'i set by the factors defined in Table I. A perspective view of the coordinate systems relating them to the glide ellipse, is given in Fig. 1, while a stereographic projection of the coordinate systems is presented in Fig. 2. The transformation matrix connecting the xi and xi coordinates is x'i =aijXj [3] where an a11 a13 aij = a21 a22 a23 a31 a23 [4] s The corresponding transformation for the stresses is i [5] The only nonzero component of okl for the simple tension case is s33,. Hence, using Eqs. [4] and 151, we find that Eq. [2] becomes F3 = b'1s33 sin2 cos ?[cos ? sin a - sin ? cos a] [6] = m1b'1s033 sin a- rn2b's33 cos a where sin a = 5: and cos a = ?i, with a the angle measured from b to ?, i.e., a polar angle in the x1, x2 plane. The same equation with a sign change applies for compression. A graphical plot of the "Schmid" factor m1, relating to the climb force on the edge component, is presented in the stereographic projection of Fig. 3. In this projection the glide plane normal points toward the top of the page and the glide direction points normal to the plane of the page. To use the graph, one

Jan 1, 1970

By Gerhard Derge

A SERIES of studies of the corrosion of tin is under way in the Metals Research Laboratory at the Carnegie Institute of Technology. The complete program includes examination of the corrosion properties of high-purity tin and the changes produced in these properties by the addition of varying amounts of alloying elements. Other studies of this subject have been made recently under the sponsorship of the International Tin Research and Development Council, but these researches have been confined largely to the weakly acid environments commonly encountered in the canning industry.1 There is little information available regarding the corrosion of tin under alkaline conditions, but such data would be of value, for a large amount of the metal is used under such conditions. The potential measurements to be described were made because they seemed to offer the most rapid method for obtaining a general view of the conditions to be encountered in such service. These experiments will also serve to establish a technique that will be of value in further studies. It must be emphasized that the results reported are those of controlled laboratory experiments and that the conclusions drawn cannot yet be applied to service conditions; rather, they point to the directions in which more exhaustive experimental work may be done to best advantage. EXPERIMENTAL PROCEDURE The first work was devoted entirely to the problem of obtaining reproducible results from a series of potential measurements. Only the methods finally adopted as standard will be described here, except when the variations from these have furnished results of interest. The cell used is shown schematically in Fig. 1. The electrolyte is contained in the vessel A (an inverted bell jar), whose ground top is fitted to the transite-board lid B. The controlled atmosphere can be admitted

Jan 1, 1938

Jan 1, 1886

By H. I. Meyer, D. F. Searcy

INTRODUCTION The analysls of our previous paper' on the behavior at two immiscible fluids separated by gravity into two dlstinct saturated zones in the porous medium was shown to be theoretically valid only if one of the two fluids was immobile. The practical problems associated with flow of both phases have so far been impossible of solution by these analytic methods. We, therefore, decided to resort to a simulator study to answer the following pertinent questions: 1. If the lighter fluid is produced from a point above the fluid-fluid interface, how long will it take for the heavier fluid to come up to the point where production of both fluids is taking place? 2. After steady-state two-phase production is established, what is the relative production rate of each phase, on what physical variables does this depend, and what are the boundary conditions at the outflow face? 3. A third question was at least partially answered in the course of this investigation: that of the shape of the interface under flow conditions. These questions are of fundamental importance in the fields of hydrology and the reservoir mechanics of oil and gas production. In order to simplify equipment used and still retain a fair physical representation of these phenomena, it was decided to use a Hele-Shaw type of analogy in which the flow took place between two vertically mounted pieces of plate glass. The advantage of this system is that it eliminates any surface effects between the matrix of the porous medium (e.g. packed sand) and also allows equilibrium conditions to be established more quickly. The principle disadvantage (apart from the obvious one of being one more step removed from the prototype) is that our equipment limited us to two dimensional flow studies. In spite of these limitations answers to the questions were obtained which seem adequate for our purposes. We would like to see more work of this nature done to verify and to improve our conclusions. DESCRIPTION OF EQUIPMENT AND PROCEDURE A drawing of the equipment used in this study is shown in Fig. 1. Fluid flow takes place between the two 36 in. x 12 in. pieces of plate glass held apart at the long edges by two spacers of cellulose acetate sheet (Kodapac IV) which is available in several thicknesses. This sandwich was clamped together by small c-clamps whose stress was distributed by long pieces of 3/8-in. keystock. Accurate spacing was obtained by tightening these clamps as indicated by micrometer measurements on the outside of the glass. At the upstream end of the plates a piece of 6-in. diameter pipe simulated an infinite reservoir, while at the downstream end a 2-in. Lucite cylinder with a small hole near the top of the flow region served to drain the fluid. Sealing was achieved by O-rings, the whole system being tightened by pressure on the Lucite tube provided by set screws (not shown in the drawing). The total head

Jan 1, 1957