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By John W. Cloud

In 1877 the Pennsylvania Railroad Company removed an old bridge from its line at Duncannon, Pa., built intermediate piers and erected shorter spans of the Pratt truss type, which had previously been in use on another portion of the road. The design of this truss would not admit of diagonals larger than 19 inches diameter, and in order to stiffen the bridge somewhat steel rods were introduced for the main diagonals in the first and second panels, 19 inches and 18/8 inches diameter respectively. These rods were threaded without upsetting, and by the ordinary formulae the strains were of the same intensity upon both, viz., 16,000 pounds per square inch with the maximum loading. The other main diagonals in the truss are 19 inches diameter, and of iron. It was specified for the steel rods: Elastic limit,.......46,000 Ibs. Tensile strength,. .. ,. .. 80,000 lbs. Elongation,,.,.,. 20 per cent. The steel was procured without difficulty, and it allowed a factor of safety of 23/4 at elastic limit, while a similar factor of 2½ had for a long time been successfully used for iron. In the course of three years, from time to time, six of these steel rods broke, three of them being 18 inches in diameter, and three 19 inches in diameter. The broken rods were tested, and three of them analyzed at Altoona to ascertain the cause of failure, and what modifications should be made in the steel for such service. Examination showed that all the rods were broken in detail close under the nut. The threads were well cut and properly rounded at the root. testing the rods micrometer screws, reading to .0001" with c bell to signal the contact, were attached to the test pieces, and by this means the modulus of elasticity and elastic limit accurately obtained.

Jan 1, 1881

All the TECHNICAL PUBLICATIONS and CONTRIBUTIONS published in 1933 are available at Institute headquarters, unless otherwise noted. They are also on file in many public, university and technical libraries and, when so indicated in the list, may be found in the TRANSACTIONS. Copies of the TECHNICAL PUBLICATIONS have been mailed to those members of the Institute who are registered in the different classes: A-Metal Mining; B-Milling and Concentration; C-Iron and Steel Division; D-Nonferrous Metallurgy;. E-Insti¬ tute of Metals Division; F-Coal Division; G-Petroleum Division; H-Nonmetallic Minerals; I-Mining Geology; J-Mineral Industry Education Division; K-Mining Administration; L-Geophysical Prospecting. Other members may obtain copies by writing to the Secretary. Copies of CONTRIBUTIONS may also be obtained from the Secretary's office. Additional copies are sold at the rate of 1 cent per page; minimum charge, 25 cents. Nonmembers may purchase the papers at the prices mentioned. METAL MINING TECH- NICAL PUBLI- TITLE AUTHOR MEETING TRANS. CATION VOLUME No. AND PAGE* 499-A.47 Red Ore Mines of the Woodward T. C. DeSollar New York, Iron Company at Bessemer, Feb., 1933 Alabama (11) CONTRI¬ BUTION No. 1-A The Owyhee Tunnels (16) P. R. Hines New York, Feb., 1933 2-A Sinking and Equipment of the No. D. D. Homer New York, 2 Shaft at Minas de Mata- R. H. Cromwell Feb., 1933 hambre (25) 3-A Subsidence Resulting from the Charles W. Allen New York, Athens System of Mining at Feb., 1933 Negaunee, Michigan (8) 4-A Effect of Approximately Vertical P. B. Bucky New York, Cracks on the Behavior of Hori- Feb., 1933 zontally. Lying Roof Strata (16) 21-A Selection of a Mining System (11) R. K. Warner New York, Feb., 1933

Jan 1, 1933

WHAT was certainly the greatest event of January, and perhaps it will prove to be the greatest of 1923, or even of the next decade, was the meeting of the premiers of the principal Euro-pean powers in Paris on Jan. 2, to consider what should be done with respect to German reparations. The French and British were unable to come to any agree-ment, and the conference broke up on Jan. 4. The French and British parted friends, but each with the determination henceforth to pursue its own economic and political way. This event was profound in its significance and perhaps will be calamitous) in its consequences. Following the disruption of the Conference at Paris, the French immediately began preparations to occupy the Ruhr district on the ground that Germany was in default on coal deliveries, without waiting. for Jan. 15, the next due date for reparation payment. This action by the French led to orders being issued by President Harding on Jan. 10 for the withdrawal of the remainder of the American troops on the Rhine. Thus ended the physical participation in. European affairs by the American army, whose vanguard landed in France in June, 1917. The French occupation of the Ruhr Valley, i.e., the great industrial region of western Westphalia, was made with a large military force. The Germans offered no physical resistance, and passed under French control with sullen resentment. The coal miners to a con-siderable extent refused to work and there was more or less disorganization of railway service. Before the end of the month the opinion was expressed that the French occupation was an economic failure and there were reports of French blast furnaces being blown out for lack of coke.

Jan 2, 1923

By R. W. Heckel, R. E. Trabocco

The recovery process in 400 Monel filings was followed, principally, by using the Warren-Averbach technique of X-ray peak profile analysis. The deformation fault probability, a, was 0.006 in samples of unannealed filings. a , the twin fault Probability , was approximately 0.002 in samples of unannealed filings. Both a and 0 were found to "anneal out" at 600°F. The effective particle size and mzs strain increased and decreased in the (111) direction, respectively, with increasing annealing temperature. The actual particle size was found to be almost equivalent to the effective particle size. Tile small values of deformation and twin fault probabilities accounted for the similarity in values of the effective and actual particle sizes. Stored strain energy and dislocation density calculations based on rms strain decreased with increasing annealing temperature. The dislocation density decreased from 10" per sq cm in the unannealed filings to 10' per sq cm in the partially re-crystallized filings. The square root of the dislocation density based on strain to that based on particle size indicated a random dislocation distribution in the unannealed filings. The dislocation arrangement changed to one with dislocations in cell walls with increasing annealing temperature. THE recovery processes which occur in metals are generally thought to be a redistribution and/or annihilation of defects.' Investigators' have shown that recovery processes can be characterized by X-ray line-broadening analyses. Michell and Haig4 measured the stored energy of nickel powder by calori-metry and found the value to be greater by a factor of 2.5 than that from X-ray data obtained by the Warren-Averbach technique.= Minor increases in particle size occurred up to 752°F (recovery), while above 752°F the particle size increased greatly due to recrystalliza-tion. X-ray microstrain values decreased between room temperature and 392"F, remained constant from 392" to 752"F, and decreased from 752°F to a negligible value at 1112°F. Faulkner developed an equation for calculating stored strain energy based on X-ray line-broadening data which gave a closer correlation of measured and calculated stored strain energy based on the data of Michell and Haig. The stored strain energy released during recovery is predominately dependent on the decrease in dislocation density which was p-enerated from cold work.7 Stored energy has been measured8 in alkali halides during recovery and recrystallization and 80 pct of the stored energy was found to be released during recovery. Dislocation distributions have been studiedg in a number of fcc metals by thin-film electron microscopy. Howie and Swann" found the stacking fault energy of copper and nickel to be 40 and 150 ergs per sq cm, respectively. ~rown" has pointed out that these stacking fault energy values should be corrected to 92 and 345 ergs per sq cm, respectively. The dislocation distribution of a metal is directly dependent on the stacking fault energy of the system. Metals of high stacking fault energy such as aluminum cross-slip readily and do not form planar arrays of dislocations. Metals of lower stacking fault energy such as stainless steels" do not cross-slip readily. Cold-worked nickel has been found to form a cellular dislocation structure after annealing.13 The relatively high stacking fault energy of nickel and copperlo to a lesser extent favor cellular structures of dislocations rather than planar arrays after deformation. The present study of recovery was carried out on a Ni-Cu alloy (Monel 400) to compare with prior studies for pure nickel and pure copper. X-ray line-broadening techniques were used to measure the effect of recovery temperature on rms strain and particle size and the results were compared with previous studies on copper'4-'7 and nickel., Calculations were also made on stacking fault probabilities, dislocation density, dislocation distribution, and stored strain energy as affected by temperature. EXPERIMENTAL PROCEDURE The nominal analysis of the Monel 400 used in this investigation was: 66.0 pct Ni, 31.5 pct Cu, 0.12 pct C, 0.90 pct Mn, 1.35 pct Fe, 0.005 pct S, 0.15 pct Si. The annealed material was cold-reduced in two batches, one 50 pct and the other 80 pct. It was originally planned to conduct line-broadening studies of these bulk samples; however, rolling textures that developed produced low-intensity peaks which were not suitable for line-broadening analysis. Filings were prepared at room temperature from both the 50 and 80 pct cold-reduced specimens, series A and series B, respectively, and were not screened prior to heat treatment or X-ray studies. Heating to the annealing temperature, 200" to 120O°F, was accomplished in a matter of minutes in a hydrogen atmosphere. Following heat treatment, some of the filings were mounted and polished for microhardness measurements with a Bergsman microhardness tester, using a 10-g load. A G.E. XRD-5 diffractometer using nickel-filtered Cum radiation was used to obtain all diffraction patterns. Only (111)- (222) line-broadenin data were used in the present study since the {400f peaks were too weak to use. The Fourier analysis of the (111) and (222) peak

Jan 1, 1969

By Charles E. Lundin

The character of the Er-D system was established by determining pressure-temperature-composition relationships. A Sieuerts&apos; apparatus was employed to make measurements in the temperature range, 473" to 1223"K, the composition range of erbium to ErD3, and the pressure range of 10~s to 760 Torr. The system is characterized by three homogeneous phase regions: the nzetal-rich, the dideuteride, and the trideuteride phases. These phases and their solubility boundaries were deduced from the family of isotherms of the system zchich relate the pressure-temperature-composition variables. The equilibrium plateau decomposition relationships in the two-phase regions were determined from can&apos;t Hoff plots to be: The differential heats of reaction in these two regions are AH = - 53.0 * 0.2 and -20.0 *0.1 kcal per mole of D2, respecticely. The differential entropies of reaction are AS = - 36.3 * 0.2 and - 31.0 * 0.2 cal per mole D2. deg, respectively. Relative partial molal and intepal thermodynamic quantities were calculated from the pure metal to the dideuteride phase. The study of the Er-D system was undertaken as a logical complement to an earlier study of the Er-H system.&apos; The primary interest was to compare the characteristics of the two systems and relate the difference to the isotopic effect. Studies of rare earth-deuterium systems by other investigators have been very limited in number and scope. Furthermore, there is even less information available wherein an investigator has systematically compared a binary rare earth-hydrogen system with the corresponding rare earth-deuterium system. The available information consists primarily of dissociation pressure measurements in the plateau pressure region of a few rare earths. Warf and Korst&apos; determined dissociation pressure relationships for the La- and Ce-D systems in the plateau region and several isotherms for each system in the dideuteride region. They compared these data with those of the corresponding hydrided systems. The study of these systems as a whole was very cursory and did not give sufficient data for a thorough comparison of the effect of the hydrogen vs the deuterium in the respective rare earths. The heat capacities and related thermodynamic functions of the intermediate phases, YH, and YD2, were determined by Flotow, Osborne, and Otto,~ and the investigation was again repeated for YH3 and YD3 by Flotow, Osborne, Otto, and Abraham.4 This investigation studied only these specific phases. Jones, Southall, and Goodhead5 surveyed the hydrides and deu-terides of a series of rare earths for thermal stability including erbium. They experimentally determined isotherms of selected hydrides and plateau dissociation pressures for deuterides. These data allowed comparison of the enthalpy and entropies of formation of the dihydrides and dideuterides. To date, no one rare earth has been selected to thoroughly establish the complete pressure-temperature-composition (PTC) relationships of binary solute additions of hydrogen and deuterium, respectively. The objective in this investigation was to provide the first comparison of a complete family of isotherms of a rare earth-deuterium system with those of a rare earth-hydrogen system. This would allow one to determine what differences exist, if any, in the various phase boundaries and the thermodynamic relationships in various regions of the systems. I) EXPERIMENTAL PROCEDURE A Sieverts&apos; apparatus was employed to conduct the experimental measurements. Briefly, it consisted of a source of pure deuterium, a precision gas-measuring buret, a heated reaction chamber, a mercury manometer, and two McLeod gages (a CVC, GMl00A and a CVC, GM110). Pure deuterium was obtained by passing deuterium through a heated Pd-Ag thimble. A 100-ml precision gas buret graduated to 0.1-ml divisions was used to measure and admit deuterium to the reaction chamber. The reaction unit consisted of a quartz tube surrounded by a nichrome-wound furnace. The furnace temperature was controlled by a recorder-controller to . An independent measurement of the sample temperature in the quartz tube was made by means of a chromel-alumel thermocouple situated outside, but adjacent to, the quartz tube near the specimen. Pressure in the manometer range was measured to k0.5 Torr and in the McLeod range (10~4 to 10 Torr) to *3 pct. The deuterium compositions in erbium were calculated in terms of deuterium-to-erbium atomic ratio. These compositions were estimated to be *0.01 D/Er ratio. The erbium metal was obtained from the Lunex Co. in the form of sponge. The metal was nuclear grade with a purity of 99.9+ pct. The oxygen content was reported to be 340 ppm and the nitrogen not detectable. Metallographically the structure was almost free of second phase (<i vol pct). A quantity of sponge was arc-melted for use as charge material. The solid material was compared with the sponge in the PTC relationships. They were found to be identical. Therefore, sponge material was used henceforth, so that equilibrium could be attained more rapidly. The specimen size was about 0.2 gr for each loading of the reaction chamber. The procedure employed to obtain the PTC data was to develop experimentally a family of isothermal curves of composition vs pressure. First, a specimen

Jan 1, 1969

By W. Vickers

Single-point rotating cantilever fatigue tests have been carried out at 550" to 650°C on beryllium produced by a variety of fabrication routes. All the specimens gave similar plots of stress against number of cycles to failure but failure occurred at a lower stress range in the hot-pressed material than in the extruded material. A discontinuity or "kink" appears to exist in the curves and this is considered. A true endurance limit was not evident up to 10 cycles. When Brush hot-pressed warm-extruded beryllium was tested at 600oC a relationship where Nf = number of cycles to failure, ?ep = plastic strain range, and c = constant, was shown to be applicable for values of ?ep > 6.3 x 10-4. Further for this moterial and temperature and for frequencies between 150 and 4500 cycles per min, the variation of number of cycles to failure with frequency obeyed the expression N = Af0.44 where N =number of cycles to failure, f = frequency, and A = constant. Examination of the fracture surfaces indicated that they were generally intergranular and in all cases the higher the stress the more irregular was the fracture. Microexamination has shown that grain boundary cavities and fine intergranular cracks were associated with the fractures. REVERSING or cyclic stresses set up in fuel elements can lead to failure by fatigue. Fatigue stresses may be developed by instability of the fuel element in the coolant flow leading to rattling against the channel wall or fin vibration. Thermal cycling also sets up reversing stresses due to differential expansion of fuel and can. Fatigue resistance is of some importance therefore in the evaluation of canning materials. At the time the work described in this paper was initiated, beryllium was being considered for the can and endcaps of an advanced gas-cooled reactor fuel element. With this in mind, beryllium obtained from different manufacturing routes was tested on single-point rotating cantilever fatigue machines at temperatures the same as those envisaged in the reactor to obtain appropriate fatigue data. The results obtained indicated a discontinuity in the S-N curves coinciding with the yield stress in the specimens. Although in some cases the data is insufficient to warrant a detailed quantitative analysis, a qualitative analysis of this effect was thought to be justified. 1) EXPERIMENTAL DETAILS The materials used are given in Table I together with the production route and available analyses. The specimen shape is shown in Fig. 1. The fatigue specimens were machined slightly oversize, after which they were given a stress-relieving anneal of 1 hr at &apos;750° C in vacuum. This was followed by an etch in sulfuric-phosphoric-chromic acid mixture down to the finished dimensions given in Fig. 1. Etching served to remove the interference colored oxide film formed on the surface during annealing and very small recrystallized surface grains too. The specimen was mounted in the grips of a cantilever machine and rotated inside a furnace controlled at the testing temperature. The specimen was loaded in increments as the speed was increased until the required load was applied at 5000 cycles per min. A revolution counter was used to record the total number of cycles.

Jan 1, 1964

By I. S. Servi, N. W. Marr

TIN markedly increases the softening temperature of pure copper with only a moderate effect on conductivity. Smart and smith&apos; indicated a substantial increase in softening temperature upon addition of different levels of tin up to 0.05 pct in oxygen-free copper. However, after finding no effect of tin in copper containing about 0.025 pct O, they concluded that "the presence of oxygen completely nullifies these changes in properties by precipitation of SnO2.&apos;&apos; Since preliminary tests on Cu-Sn-0 alloys indicated that this conclusion is not valid outside the extremely limited tin range investigated by Smart and Smith, research was primarily directed toward the partition of tin between the copper-base matrix and the oxide phases. Experimental. Material was prepared by sealing an 80 to 100-g charge consisting of oxygen-free copper, tin, and copper oxide into a y-in.-ID quartz capsule which was evacuated and back-filled with tank-grade argon to 3 atm. The sealed vials were heated to 1125ºC, kept at temperature for 30 min, occasionally agitated, and then allowed to air-cool outside the furnace ("as-cast"). The castings were cold-swaged to 0.370 in., annealed 1 hr at 600°C ("as-annealed"), and cold-swaged 16.5 pct ("as-swaged"). Cross sectional wafers were annealed for 1 hr at various temperatures and Rockwell F hardness measured. The "softening temperature" was defined as the interpolated temperature at which the hardness was 50 Rockwell F. Electrical resistance was measured by an ac poten-tiometric method on 0.040-in.-diam wires after a 1 hr anneal at 600°C. Relative accuracy was of the order of 1 pct. Chemical analyses for tin were performed by two methods, identified as "Acid flux" and "HN03 dissolution". The first consisted of fusing the sample with potassium pyrosulfate and leaching the resulting melt with 10 pct sulfuric acid. The spectrophotometric procedure which followed is described in Ref. 2. Oxygen analyses were performed by the vacuum-fusion method with a bath temperature of 1650°C. Tin content of oxides and copper phases was measured with the X-ray microprobe, using a calibration curve based on a series of oxygen-free Cu-Sn alloys. Results. In Fig. 1, the nominal tin composition for alloys containing nominally 400 ppm O was plotted vs the analyzed or the computed tin content—the latter derived from one of the following: 1) "acid flux" chemical analysis; 2) "HN03 dissolution" chemical analysis; 3) X-ray microprobe analysis of the copper matrix; 4) equivalent tin content, based on the measured increase in electrical resistivity (an increase in resistivity of 1.6 microhm-cm is approximately equivalent to 1 wt pct of sn1,3). It is evident from Fig. 1 that the results of the acid flux analysis are consistent with the nominal composition while the HNO3 dissolution method generally yields lower values, consistent with those obtained from electrical resistivity measurements and somewhat higher than those obtained by microprobe analysis. Microprobe and resistivity values are affected only by the tin in solid solution; hence the HN03 method

Jan 1, 1970

By C. W. Spencer, Che-Yu Li, R. J. Knight

The usual reaction product for the monotectic reaction in the Bi-Se system consists of rod -shaped particles of selenium-rich liquid embedded in a single crystal matrix of At certain crystallo-graphic orientations of the matrix with respect to the reaction interface, more complex shapes are as -sumed by the liquid particles. This reaction has been examined at different growth rates and relative crystallographic orientations of the matrix with respect to the reaction interface. The uhriation in auerage particle size of the liquid phase with reaction rate has been determined at one crystallograpIzic orientation of the matrix. On a plot of logarithm of average particle diameter vs logarithm of reaction rate, data points for crystals grown at rates of 10- to 1.0 cm per hr fall near a curve of slobe -0.4. MONOTECTIC reactions in binary alloy systems are reactions of the eutectic class in which, as the system is cooled through the three-phase reaction isotherm, one liquid phase (L) decomposes to a solid phase and another liquid phase (LII).&apos; A partial phase diagram, as taken from Hansen, showing the monotectic reaction in the Bi-Se system is given in Fig. 1. This diagram specifies the monotectic point at 618°C and 72 at. pct Se, and the monotectic reaction products as the intermetallic Bi Se3 and a liquid (LII) which contains approximately 98 at. pct Se. At a lower temperature, 217°C, this liquid may undergo a eutectic reaction in which the reaction products are BizSe3 and crystalline selenium. However, under conditions of rapid cooling, or quenching, from above 217°C, this selenium-rich liquid may be partially retained to room temperature in an amorphous or glassy state. The intermetallic BizSe3 is rhombohedral, of the space group jm;&apos; however, for convenience it is usually represented by a hexagonal struture. A pronounced plane of cleavage, which lies perpendicular to the main axis of the rhombohedral unit cell or parallel to the basal plane of the hexagonal cell, exists in the structure. The usual monotectic reaction product consists of rod-like particles of LII embedded in a single-crystal matrix of BizSe3, although at certain crystallographic orientations of the matrix BizSe3 other more complex shapes are assumed by LII. A similar rod-like, or cylindrical, morphology for the carbide phase has been reported by westbrook7 in the a Cr-Crz3Ce eutectic structure. In this paper the morphological characteristics of the LII particles, as retained to room temperature, have been examined under conditions of varying growth rate and crystallographic orientation of the matrix BizSe3 with respect to the growth direction. EXPERIMENTAL PROCEDURE Alloy specimens corresponding to the monotectic composition, 72 at. pct, or 50 w pct Se, were prepared from 99.999 pct pure bismuth and selenium obtained from the American Smelting and Refining Co. The two elements, corresponding to a total specimen weight of approximately 30 g, were encapsulated in 13 mm OD Vycor tubing under a vacuum of 5 x X mm of Hg. The capsules were suspended on a fine platinum wire in a Bridgman-type furnace which exhibited a temperature gradient of

Jan 1, 1963

By C. H. Samans, G. F. Tisinai, J. K. Stanley

The times at which the first detectable amount of a phase forms at temperatures between 900° and 1800°F were determined. Both X-ray diffraction and metallography were used to detect a in highly strained filings; metallography alone to detect it in annealed bulk samples of six different types of stainless steels. The a phase was found to form in accordance with the C-type reaction curve in both austenitic and ferritic alloys. In filings of types 304, 347, and 446, a formed in a few hours, and in types 316, 309, and 310, it formed in a matter of minutes at temperatures corresponding to the knee of the C-curve. Only in the bulk type 309 steel, after 500 hr, and in the bulk type 310 steel, after as short a time as 25 hr at temperature, was n detected; in both instances at approximately the same optimum temperature as in the filings. The annealing temperature affected a phase nucleation only for the filings of type 304 and 347 steels, and for the bulk samples of type 309 and 310 steels. KNOWLEDGE of both the rate of nucleation and the rate of growth of the new phase is required for a complete description of metallurgical rate phenomena. However, data on the time for nucleation alone may frequently be useful in evaluating the tendency of commercial stainlcss steels to form s under various conditions. Very little correlated information of this type is available in the literature. Shortsleeve and Nicholson&apos; indicate that s forms in ferritic 24, 27 and 30 pet Cr steels according to a C-type of reaction curve, and Emmanuel&apos;s&apos; data for austenitic type 310 steel also suggest this type of solid state reaction. In addition, significant, though fragmentary, information has been given by Binder, Dulis and Smith,4 Payson and Savage,.; Guarneri, Miller, and Vawter,8 rerichs and Clark,7 Wilder,5 Lismer, Pryce, and Andrews,&apos; Smith, Dulis, and Link,10 Dulis, Smith, and Houston," and Henry, Cordovi, and Fischer." The bearing of these data on this work is covered in the discussion. The purpose of this paper is to present such correlated data on s formation in AISI type 304 (18 pct Cr-8 pet Ni), 347 (18 pet Cr-10 pet Ni-Cb), 316 (18 pet Cr-12 pet Ni-2 pet Mo), 309 (25 pet Cr-12 pet Ni), 310 (25 pet Cr-20 pet Ni), and 446 (27 pet Cr) stainless steels. Materials and Test Methods X-ray diffraction and metallographic methods were used to determine the first appearance of the s phase in cold worked filings and in annealed bulk samples of seven steels, under various combinations of time and temperature. The rate of growth of the s particles was not determined. Commercial heats of six AISI steels and a low carbon laboratory experimental heat containing about 28 pet Cr were studied. Analyses are given in Table I. Because cold work greatly accelerates the nucleation of s particles, the relative rates of s nucleation in mechanically strained samples, i.e., filings through 120 mesh, were determined for direct comparison with those in annealed bulk alloys of the same composition.

Jan 1, 1957

By J. W. Halley

THE effects of tin on steel have become increasingly important because of the necessity of using poorly detinned scrap, tin cans, and terne plate, in the open hearth. Since a tin can contains about 1.5 per cent tin, it would be possible to have up to 0.75 per cent tin in steel made with a 50 per cent scrap charge. In order to use tin-containing scrap, it is necessary to know the effect of tin on various grades of steel. The following investigation is by no means comprehensive but covers a number of steels in which tin content is important. PUBLISHED WORK A number of investigations of the effects of tin on rolling quality and physical properties have been published. It has been found that tin increases strength and hardness and reduces ductility and notched impact resistance. The decrease in ductility and notched impact resistance becomes more marked as the carbon decreases. McKimm1 found no change in Olsen ductility, Rockwell hardness, yield strength, tensile strength or elongation in cold-reduced strip containing up to 0.124 per cent tin. A tin content of 0.15 per cent gave difficulties in rolling and increased the hardness but 0.21 per cent tin showed no change in properties from material containing very little tin. No explanation of this contradiction is offered. Andrew and Peile2 investigated steels containing 0.10 to 0.25 per cent carbon and up to 0.63 per cent tin. They found an increase in tensile strength 0f from 100 t0 200 lb. per sq. in. for each 0.01 per cent tin on normalized samples. The elongation and reduction of area were decreased and the notched impact resistance was reduced markedly. Quenched and drawn samples did not show embrittling if water-quenched from the draw temperature of 1148°F. (620°C.). They could find no evidence of tin under the microscope. Whitely and Braithwaite3 investigated the effect of tin on rail steel containing 0.55 to 0.60 per cent carbon. They found that 0.08 per cent tin caused a marked decrease in elongation, notched impact resistance and the degree of bend. The tensile strength was increased in some tests and not in others. Bolsover and Barraclough4 investigated the effect of tin up to 0.50 per cent on a 0.35 per cent carbon steel and on several alloy steels with from 0.30 to 0.40 per cent carbon. They found a comparatively uniform decrease in notched impact resistance with increasing tin on quenched and drawn samples. If the samples were quenched from the drawing temperature or reheated to the drawing temperature and quenched, the embrittling was much less severe. Steels containing molybdenum suffered much less embrittlement than other steels. EXPERIMENTAL WORK Effect of Tin on Low-carbon Rimmed Steel Increasing quantities of tin were added to four ingots of a heat of the following ladle analysis: carbon, 0.08 per cent; manganese, 0.39; phosphorus, 0.009; sulphur, 0.025.

Jan 1, 1942

By O. D. Gonzalez

ThIS communication presents the results of a determination of the permeabilities of hydrogen and deuterium in a iron from 360° to 560°C. Recently Heu-mann and primas&apos; have given values of the diffusivity and solubility in a iron of the two isotopes from which the permeability can be calculated. The work reported in the present communication, however, is a direct measurement of the rate of permeation of the isotopes through an identical iron specimen under the same conditions, so that systematic errors can be minimized in the calculation of the ratio of the permeabilities—the value which is usually of main importance in establishing limits for isotopic differences in diffusive processes. Experimentally the procedure used was the usual one: a steady-state flow of gas produced by a pressure difference across an iron membrane was observed as the pressure rise with time in a previously evacuated, calibrated volume connected to the outlet side of the membrane, while a constant pressure of gas was maintained on the opposite inlet side. The membrane was a cylindrical tube 9.38 cm long, 0.730 cm inside diam, 0.187 cm wall thickness, fabricated of 99.95 pct vacuum-melted National Research Corp. iron (less than 0.003 pct C). One end was sealed by a heliarc-welded iron (99.95 pctj lid of 0.147 cm thickness; the other end of the tube was welded to a 304 stainless-steel tube (0.318 cm ID and 0.318 cm wall) which connects to a vacuum system and to the calibrated volume including a dibutylphthalate manometer. The temperature of the iron membrane was maintained constant to ±0.l°C and was measured with an iron-constantan thermocouple which was calibrated against a standard Pt/Pt-Rh thermocouple: the temperature variation along the length of the membrane did not exceed ±0.5°C. Hydrogen was allowed to pass through the membrane assembly for 72 hr at 615°C before permeability measurements were begun. The system was tested at temperature before and after the experiments by a substitution of helium for hydrogen in the inlet side; under these conditions the pressure rise observed in the outlet side was negligible at all times. The gases used for the permeability measurements were 99.95 pct Matheson prepurified H2 and 99.7 pct D2 (0.3 pct HD) from the Isomet Corp. The gases were dried with liquid N2 before use. In Fig. 1 the logarithms of observed flows, jt, for a pressure difference of 73.4 cm Hg are plotted against T-1 Each point in Fig. 1 represents the slope determined by a least-square evaluation of a plot of the pressure in the outlet side of the membrane against time, including at least two separate sets of observations. Each point in the figure has an uncertainty of ±0.6 pct arising from the experimental uncertainty in the pressure and time measurements. The standard deviation of the observed pressures from the straight lines in all cases is less than the experimental precision of the measurements. The observed flow, jt, includes a small but not negligible flow through the stainless-steel connection.

Jan 1, 1968

By J.W. Halley

The effects of tin on steel have become increasingly important because of the necessity of using poorly detinned scrap, tin cans, and terne plate, in the open hearth. Since a tin can contains about 1.5 per cent tin, it would be possible to have up to 0.75 per cent tin in steel made with a 50 per cent scrap charge. In order to use tin-containing scrap, it is necessary to know the effect of tin on various grades of steel. The following investigation is by no means comprehensive but covers a number of steels in which tin content is important. Published Work A number of investigations of the effects of tin on rolling quality and physical properties have been published. It has been found that tin increases strength and hardness and reduces ductility and notched impact resistance. The decrease&apos; in ductility and notched impact resistance becomes more marked as the carbon decreases. McKimml found no change in Olsen ductility, Kockwell hardness, yield strength, tensile strength or elongation in cold-reduced strip containing up to 0.124 per cent tin. A tin content of 0.1j per cent gave difficulties in rolling and increased the hardness but 0.21 per cent tin showed no change in properties from material containing very little tin. No explanation of this contradiction is offered. Andrew and Peile2 investigated steels containing 0.10 to 0.25 per cent carbon and up to 0.63 per cent tin. They found an increase in tensile strength of from 100 to 200 lb. per sq. in. for each 0.01 per cent tin on normalized samples. The elongation and reduction of area were decreased and the notched impact resistance was reduced markedly. Quenched and drawn samples did not show embrittling if water-quenched from the draw temperature of 1148°F. (620°C.). They could find no evidence of tin under the microscope. Whitely and Braithwaite3 investigated the effect of tin on rail steel containing 0.55 to 0.60 per cent carbon. They found that 0.08 per cent tin caused a marked decrease in elongation, notched impact resistance and the degree of bend. The tensile strength was increased in some tests and not in others. Bolsover and Barraclough4 investigated the effect of tin up to 0. 50 per cent on a 0.35 per cent carbon steel and on several alloy steels with from 0.30 to 0.40 per cent carbon. They found a comparatively uniform decrease in notched impact resistance with increasing tin on quenched and drawn samples. If the samples were quenched from the drawing temperature or reheated to the drawing temperature and quenched, the embrittling was much less severe. Steels containing molybdenum suffered much less embrittlement than other steels. Experimental WoRk Effect of Tin on Low-carbon Rimmed Steel Increasing quantities of tin were added to four ingots of a heat of the following ladle analysis: carbon, 0.08 per cent; manganese, 0.39; phosphorus, 0.009; sulphur, 0.025.

Jan 1, 1943

By J. W. Halley

The effects of tin on steel have become increasingly important because of the necessity of using poorly detinned scrap, tin cans, and terne plate, in the open hearth. Since a tin can contains about 1.5 per cent tin, it would be possible to have up to 0.75 per cent tin in steel made with a 50 per cent scrap charge. In order to use tin-containing scrap, it is necessary to know the effect of tin on various grades of steel. The following investigation is by no means comprehensive but covers a number of steels in which tin content is important. Published Work A number of investigations of the effects of tin on rolling quality and physical properties have been published. It has been found that tin increases strength and hardness and reduces ductility and notched impact resistance. The decrease&apos; in ductility and notched impact resistance becomes more marked as the carbon decreases. McKimml found no change in Olsen ductility, Kockwell hardness, yield strength, tensile strength or elongation in cold-reduced strip containing up to 0.124 per cent tin. A tin content of 0.1j per cent gave difficulties in rolling and increased the hardness but 0.21 per cent tin showed no change in properties from material containing very little tin. No explanation of this contradiction is offered. Andrew and Peile2 investigated steels containing 0.10 to 0.25 per cent carbon and up to 0.63 per cent tin. They found an increase in tensile strength of from 100 to 200 lb. per sq. in. for each 0.01 per cent tin on normalized samples. The elongation and reduction of area were decreased and the notched impact resistance was reduced markedly. Quenched and drawn samples did not show embrittling if water-quenched from the draw temperature of 1148°F. (620°C.). They could find no evidence of tin under the microscope. Whitely and Braithwaite3 investigated the effect of tin on rail steel containing 0.55 to 0.60 per cent carbon. They found that 0.08 per cent tin caused a marked decrease in elongation, notched impact resistance and the degree of bend. The tensile strength was increased in some tests and not in others. Bolsover and Barraclough4 investigated the effect of tin up to 0. 50 per cent on a 0.35 per cent carbon steel and on several alloy steels with from 0.30 to 0.40 per cent carbon. They found a comparatively uniform decrease in notched impact resistance with increasing tin on quenched and drawn samples. If the samples were quenched from the drawing temperature or reheated to the drawing temperature and quenched, the embrittling was much less severe. Steels containing molybdenum suffered much less embrittlement than other steels. Experimental WoRk Effect of Tin on Low-carbon Rimmed Steel Increasing quantities of tin were added to four ingots of a heat of the following ladle analysis: carbon, 0.08 per cent; manganese, 0.39; phosphorus, 0.009; sulphur, 0.025.

Jan 1, 1943

By H. L. Gilbert, H. A. Johansen, R. G. Nelson

High purity electrolytic chromium plate has been hydrogen-reduced and arc-melted under inert atmosphere to give sound ingots. These ingots may be hot forged to break the as-cast structure and then worked at 500°C to finished form. An intermediate and final high temperature anneal gives best ductility and grain refinement. HE increasing interest in refractory metals for I use in high temperature gas turbines, jets, and rockets has led to great efforts in exploiting the fifth and sixth groups of transition elements. Much of the interest has centered upon production of metals that can be worked and fabricated by normal means to produce various engine parts or components having the high temperature characteristics of oxidation resistance and high creep strength required for such uses. If these pure elements do not exhibit all of the desired characteristics, it may be possible to obtain a high purity alloy that will. Since, in all cases, development of these transition elements has depended to a large extent upon removal of oxygen and nitrogen as a means for producing ductile metal, the hypothesis has been accepted that oxygen is the normal embrittling material in a high grade electrolytic chromium metal. Various methods have been employed in an effort to remove this oxygen by direct or indirect attack.&apos; Many workers have endeavored to produce pure chromium through reduction of the oxide by carbon or active metals, while others have recommended fusion electrolysis of chromium salts or reduction of these salts by active metals, such as sodium or calcium. Hydrogen reduction of the oxide or chloride and thermal dissociation of the iodide have been reported to give high purity metal. Experimental Work The U. S. Bureau of Mines, Northwest Electro-development Laboratory, has systematically re-examined the more promising methods and developed two which produce metal having ductility at temperatures lower than heretofore described. It has been found&apos; that oxide-free chromium chlorides in a NaCl-KCl carrier salt may be mag- nesium-reduced and the byproduct salts distilled off in vacuo to give a high purity chromium sponge. Fusion analysis conducted under the supervision of W. W. Horton of Knolls Atomic Power Laboratory showed the oxygen and nitrogen both to be below 10 parts per million on a selected sample. A small amount of carbon is carried over in the final metal from the chlorination and reduction steps which are carried out in graphite crucibles. This trace of carbon is not detrimental to hot ductility. A more practical method for producing ductile metal is through hydrogen reduction of high purity electrolytic chromium. Normal electrolytic chromium will, if "developed" for a few minutes at 1100°C in high vacuum, be found by the method of Adcock:; to contain about 1 pct chromium sesquioxide (Cr2O3). This small amount of oxygen may be effectively reduced by hydrogen.2, 4 The method employed was to crush electrolytic chromium plate in a gyratory crusher to pass 60-mesh; finer crushing appears to offer no advantage. A nitric acid leach removed the iron picked up during crushing. The leached powder was rinsed until neutral with distilled water and vacuum-dried.

Jan 1, 1954

By J. W. Halley

THE effects of tin on steel have become increasingly important because of the necessity of using poorly detinned scrap, tin cans, and terne plate, in the open hearth. Since a tin can contains about 1.5 per cent tin, it would be possible to have up to 0.75 per cent tin in steel made with a 50 per cent scrap charge. In order to use tin-containing scrap, it is necessary to know the effect of tin on various grades of steel. The following investigation is by no means comprehensive but covers a number of steels in which tin content is important. PUBLISHED WORK A number of investigations of the effects of tin on rolling quality and physical properties have been published. It has been found that tin increases strength and hardness and reduces ductility and notched impact resistance. The decrease in ductility and notched impact resistance becomes more marked as the carbon decreases. McKimm1 found no change in Olsen ductility, Rockwell hardness, yield strength, tensile strength or elongation in cold-reduced strip containing up to 0.124 per cent tin. A tin content of 0.15 per cent gave difficulties in rolling and increased the hardness but 0.21 per cent tin showed no change in properties from material containing very little tin. No explanation of this contradiction is offered. Andrew and Peile2 investigated steels containing 0.01 to 0.25 per cent carbon and up to 0.63 per cent tin. They found an increase in tensile strength of from 100 to 200 lb. per sq. in. for each 0.01 per cent tin on normalized samples. The elongation and reduction of area were decreased and the notched impact resistance was reduced markedly. Quenched and drawn samples did not show embrittling if water-quenched from the draw temperature of 1148°F. (620°C.). They could find no evidence of tin under the microscope. Whitely and Braithwaite3 investigated the effect of tin on rail steel containing 0.55 to 0.06 per cent carbon. They found that 0.08 per cent tin caused a marked decrease in elongation, notched impact resistance and the degree of bend. The tensile strength was increased in some tests and not in others. Bolsover and Barraclough4 investigated the effect of tin up to 0.50 per cent on a 0.35 per cent carbon steel and on several alloy steels with from 0.30 to 0.40 per cent carbon. They found a comparatively uniform decrease in notched impact resistance with increasing tin on quenched and drawn samples. If the samples were quenched from the drawing temperature or reheated to the drawing temperature and quenched, the embrittling was much less severe. Steels containing molybdenum suffered much less embrittlement than other steels. EXPERIMENTAL WORK Effect of Tin on Low-carbon Rimmed Steel Increasing quantities of tin were added to four ingots of a heat of the following ladle analysis: carbon, 0.08 per cent; manganese, 0.39; phosphorus, 0.009; sulphur, 0.025.

Jan 1, 1942

By R. C. Buehl, M. B. Royer

A three ton per day blast furnace using blast temperatures up to 2200°F was operated to recover manganese from open-hearth slag and manganiferous iron ore. The spiegel product containing 12 to 24 pct Mn was blown in a basic converter to high manganese oxide slag as described in the paper which follows this one. HE steel industry, which uses over 900,000 short tons of contained manganese yearly, depends on the maintenance of supplies of manganese from foreign sources such as India, Gold Coast, and Union of South Africa. Domestic ores furnish less than 10 pct of the yearly requirements of metallurgical ores and, unfortunately, the United States has no large, or even moderate, grade deposits that could supply a major portion of the requirements for many years. It may be necessary to obtain manganese from low grade materials, even though the cost is appreciably higher than when imported ores are used. An American Iron and Steel Institute questionnaire prepared in 1949 revealed the startling fact that open-hearth slags contained about as much manganese as is imported annually. The quantity of slag produced each year by integrated steel plants (not including cold-melt shops) and the manganese contained in the slag follows: Flush slag, 4,500,000 net tons a year containing 408,000 net tons Mn; tap slag, 7,230,000 net tons a year containing 364,000 net tons Mn; for a total of 772,000 net tons Mn. Some of this slag is returned to blast furnaces but about 75 pct would be available for the recovery of manganese. In several decades, when many of the present sources of high manganese ores have been depleted, open-hearth slag and manganiferous iron ore may become the major source of the manganese required for steel production. In 1948, manganese-ore imports from the U.S.S.R. were 427,000 net tons or 34 pct of the foreign ore. Imports from this source were only 81,000 tons in 1949. It became evident that adequate stockpiles of manganese could not be accumulated for many years. The Bureau of Mines initiated an extensive research program on methods for increasing domestic production of manganese and entered into a cooperative agreement with the American Iron and Steel Institute for recovering manganese from open-hearth slags whereby the Institute provided additional research funds and trained operating personnel. Description of Process and Equipment Numerous pyrometallurgical and hydrometallur-gical processes and combinations of the two can be applied to the recovery of manganese from open-hearth slag and manganiferous iron ore. The process being developed at the Pittsburgh Station of the Bureau of Mines consists of: 1—Reduction of open-hearth slag in a blast furnace to recover the iron and manganese as spiegel-eisen with 12 to 24 pct Mn. 2—Selective oxidation of the manganese from the blast-furnace metal in a basic-lined converter to produce a high manganese slag with up to 60 pct Mn content, which is a synthetic ore for the production of ferromanganese. This process has the advantage over other processes in that the equipment which would be used, such as blast furnaces and converters, has been highly

Jan 1, 1953

By J. Wade Watkins, E. S. Mardock

The accurate evaluation of reservoir-performance characteristics in the secondary recovery of petroleum by water flooding requires use of a water tracer that may be injected into water-input wells and detected at oil-production wells to supplement data obtained from core analyses, wellhead tests, and subsurface measurements. Radioactive iodine has been used successfully as a water tracer in field tests to determine: (I) relative rates and patterns of flow of injected water between water-input and oil-production wells and (2) zones of excessive water entry into oil-production wells. Laboratory evaluations of potential water tracers, previous tracer studies, the value of using a radioactive tracer, general field procedures, and the use of surface and subsurface instruments for the detection of the emitted gamma radiation, are summarized. Data from the field tests are presented graphically and discussed in detail. It is concluded that the radioactive-tracer method, using radioactive iodine, may be used successfully to measure either the relative rates and patterns of flow or zones of excessive water entry into wells under conditions of comparatively rapid transit time between wells. INTRODUCTION Extensive use is made of data obtained from core analyses, wellhead tests, fluid characteristics, and subsurface measurements in evaluating the sweep efficiency of water injected into oil sands for the recovery of oil. Theoretical flow rates and patterns may be calculated from those data using radial-flow formulas, if it is assumed that the physical conditions in the productive formation are homogeneous. Unfortunately, homogeneous conditions rarely, if ever, exist in oil-productive formations. The use of a tracer that may be injected into an oil sand and detected quantitatively, or even qualitatively, at offsetting oil-production wells provides basic data that may be used in determining more accurately the subsurface rates and patterns of flow of injected water between wells than is possible by theoretical calculations based on assumed conditions. Consideration of the data obtained by using a water tracer assists in the application of remedial measures to water-input wells, such as plugging of channels, or selective plugging of highly permeable zones, thereby effecting a more uniform flood and a greater ultimate oil recovery. A water tracer should have the following characteristics: (1) low adsorption on solid reservoir material; (2) high solubility in water; (3) low or negligible solubility in crude petroleum; (4) a wide range of solubility of compounds that may be formed by chemical reactions with ions present in reservoir rocks or waters; (5) high detectability in low concentrations by portable apparatus; and (6) general availability at low cost. Additional desirable characteristics are that the tracer should be nonhazardous in nature under normal working conditions and quantitatively detectable in the well bore, as well as at the surface. Review of Previous Tracer Studies The need for a water tracer has been recognized for many years. As far back as 1906, Dole1 described the use of fluorescein in flow-rate studies made in France in 1901. In 1921, Ambrose" discussed in detail the use of organic and inorganic dyes, chlorides, nitrates, and other anions, lithium salts, and the Slichter electrical

Jan 1, 1955

By D. J. Carney, E. C. Rudolphy

Large macroscopic nonmetallic inclusions were related to altered fireclay refractories by chemical and microscopic means. Pouring refractories are discussed as a source of these large inclusions. Nozzles and wells are major contributors. Use of alkali and titania contents as tracers is described. Recommendations are offered to minimize the sources of inclusions from pouring refractories. IN any attempt to improve the cleanliness of plain carbon and alloy steels, consideration must be given not only to the proper deoxidation practice to minimize inclusions, but also to sources of inclusions from pouring refractories. In some cases, the inclusions resulting from deoxidation may be minor in amount, yet a relatively dirty steel may be produced as a result of improper care in the pouring practices for the steel. The number of studies of inclusions resulting from pouring refractories has increased recently and some excellent reports on this subject have already been published.&apos;4 Some of these reports were reviewed briefly in a companion paper by M. P. Fedock.5 Mr. Fedock&apos;s contribution is a fine addition to the studies necessary to improve steel cleanliness for the ultimate benefit of all steel producers and consumers. In the interest of constantly improving cleanliness, the authors have been actively engaged for the past two years in experimentation to determine more closely the sources of inclusions in steel. One phase of this work was associated with efforts to define more closely the sources of macroscopic inclusions which have been experienced on occasional heats. The term "macroscopic inclusions" is defined in general as those inclusions which are visible to the naked eye or at low magnifications of the order of less than X25. These inclusions sometimes can be seen in the macro-etch tests of billets and slabs. This report summarizes a few of the field experiments and laboratory studies conducted at the South Works of the United States Steel Corp., which were made regarding nozzles, wells, and ingot scums, as well as inclusions occurring in steel products. The data in the present study, together with the data of Mr. Fedock concerning ladle erosion, should be of value in regard to future studies of inclusions arising from pouring refractories. The knowledge gained as a result of data collected thus far at South Works has been helpful in improving the cleanliness of the products and in pointing the way toward further improvements. Similarity of Large Inclusions to Refractories and Altered Refractories In the routine inspection of billet etch tests, occasional inclusions visible to the naked eye have been observed. These large inclusions most frequently occur near the top of the ingot and near the billet surface. When such material was encountered, careful examinations were made in an attempt to determine the origin of these inclusions. In a relatively few cases, examination revealed that the material was unaltered fireclay refractory of a type similar to that used for hot-top material, with only the surface of the inclusions having an altered appearance under the microscope. However, the great majority of these inclusions were completely altered-refractory material. The term "altered refractory" is defined

Jan 1, 1955

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

By H. H. Rachford

Numerical solutions of immiscible flow problems in which dispersive effects of capillarity are dominated by convection require excessively fine grid spacing with attendant high computing costs. The use of coarser spacing reduces cost but often produces oscillation or undue dispersion associated with displacement fronts, A numerical formulation is proposed here which should be applicable to two-dimensional flow problems. it is in part analogous to an approach previously tested for miscible systems. The convective transport is approximated using a change of variables to yield a coordinate system moving approximately with the local characteristic velocity. The capillarity-induced dispersive terms in the differential system describing the process are approximated with respect to a fixed coordinate system by the usual implicit formulation. One-dimensional tests of the procedure yielded results in which the saturation profiles tended smoothly to the zero-capillary pressure solution as the ratio of viscous to capillary forces was successively increased in a sequence of calculations. This contrasted favorably with solutions by other numerical procedures which would require attendant grid refinements to approach the zero capillary pressure results. INTRODUCTION Numerical solution of displacement problems has until recently relied on applying methods developed primarily for transient heat-flow problems. Such problems are classified as parabolic in type, and where the heat transport is purely by diffusion their solutions are characterized by a high degree of smoothness. It is not surprising, therefore, that for approximating these solutions available finite difference methods are quite adequate. In flow problems the transport is partly by diffusion, partly by convection or flow. Although the problem remains of parabolic type because the dispersive effects of capillary forces or diffusion play some role in every displacement, at high flow rates the problem is dominated by convection, and solutions tend toward those of equations of the hyperbolic type. Solutions of hyperbolic problems are characterized by the translation of fronts, or discontinuities, that may progressively increase in sharpness. Numerical methods for treating parabolic problems become less and less satisfactory as displacement rates increase and the role of dispersion due to concentration or capillary pressure gradients becomes small relative to transport due to flow. In computation the difficulty manifests itself as an error associated with the grid size chosen. 1-6 In summary, if the heat-flow type approximations are to include the terms arising due to convection, one of several choices may be made: (1) an upstream (to the direction of flow) approximation for the convection terms may be used; (2) a centered-in-distance (CID) approximation may be used; or (3) a recently developed approximation based on the theory of oscillation matrices may be chosen.6 The last appears to have significant promise for one-dimensional flow problems; its extendibility to two or three dimensions is an open question. In either of the first two approaches, a suitably small ratio of v&/D must be maintained, where v is the velocity, & is the grid spacing and D the effective dispersivity in the direction of flow. In the first choice, the approximation of the convective part is only first-order correct and errors introduced appear as a numerically induced dispersivity of magnitude proportional to v?x. In the CID choice, the approximation can be second-order correct, but the difference formulation fails to satisfy the maximum principle unless a condition on v?x/D is met. Practically, this means that for high flow rates oscillatory solutions may result in the neighborhood of a front unless exceedingly small grid intervals are taken. While the procedure proposed by Stone and Brian4 permits a less severe limitation to be placed on this ratio, ultimately the flow rates increase relative to the dispersivity the oscillation obtains. Further, extensions of their approach to higher dimensional systems may be attended by considerable

Jan 1, 1967