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By R. H. Gautschi, F. C. Langenberg

Rare-earth additions were made to laboratory heats of Type 310 stainless to observe their effect on as-cast ingot structure, nitrogen and sulfur contents, and nonmetallic inclusions. Lanthanum had a grain-refining effect in 30-lb ingots, but results with 200-lb ingots were inconsistent. Cerium, lanthanum, and misch metal lowered the sulfur content when the sulfur exceeded 0.015 pct and the rare-earth addition was greater than 0.1 pct. The rare-eardh content in the metal dropped very rapidly within the first few minutes after the addition. The size, shape, and distribution of nonmetallic inclusions was not changed in 30-lb ingots, but changes were noticed in larger ingots. RARE-earth* additions have been made to austenitic Cr-Ni and Cr-Mn steels to improve their hot workability. The high alloy content of these steels often results in a considerable resistance to deformation and inherent hot shortness at rolling temperatures, particularly in larger ingots. Rare earths in the metallic, oxide, or halide form are usually added to the steel in the ladle after deoxidation although they can be added in the furnace prior to tap or in the molds during teeming. The literature- indicates that the effects of rare-earth treatments on these stainless steels are not consistent, and sometimes even contradictory. Since no mechanism has been presented which satisfactorily accounts for the claimed improvements, the effects of rare earths are a qualitative matter. The work described in this paper was initiated to expand the knowledge of the effects of rare-earth additions on melting variables such as ingot structure, chemical analysis, and nonmetallic inclusions. REVIEW OF LITERATURE Ingot Structure—Rare-earth additions to stainless steels have been reported to cause a change in primary ingot structure in that there are fewer coarse columnar grains. However, the results are inconsistent. While one investigation1 has shown a large reduction in coarse columnar crystals, another2 has been unable to observe this effect, particularly when small ingots were poured. Post and coworkers3 observed ingot structures for a number of years and found that the columnar type of structure is not definitely a cause of any particular trouble in rolling or hammering, provided the alloy is ductile. Knapp and Bolkcom4 found rare-earth additions to be quite effective in preventing grain coarsening in Type 310 stainless steel. Chemical Analysis—Many effects of rare-earth treatment on chemical analysis have been claimed in the literature. Russell5 observed that some sulfur is removed by rare-earth metals, and that a high initial sulfur content improved the efficiency of sulfur removal. Lillieqvist and Mickelson6 report that rare-earth treatment causes sulfur removal in basic open-hearth furnaces, but not in basic lined induction furnaces. Knapp and Bolkcom found no sulfur removal in acid open-hearth and acid electric furnaces, probably because the acid slag can not retain sul-fides. snellmann7 showed that sulfur could be lowered apprecfably with rare-earth additions; however, a sulfur reversion occurred with time. Langenberg and chipman8 studied the reaction CeS(s) = Ce(in Fe) + S(in Fe), and found the solubilit product [%Ce] [%S] equal to (1.5 + 0.5) X 10-3'at 1600°C. Results in 17 Cr-9 Ni stainless were about the same as those in iron. Beaver2 treated chromium-nickel steels with 0.3 pct misch metal and observed some reduction in the oxygen content. He also noted an inconsistent but beneficial effect of rare earths when tramp elements were present in amounts sufficient to cause difficulty in hot working. It is not known whether rare earths reduce the content of the tramp elements or change the form in which these elements appear in the final structure. No quantitative data are available concerning a possible effect of rare-earth treatment on hydrogen and nitrogen contents. However, Schwartzbart and sheehan9 stated that additions of rare earths had no effect on impact properties when the nitrogen content was low (0.006 pct), but served to counteract the adverse effects of high nitrogen content (0.030 pct) on these properties. Knapp and Bolkcom4 analyzed open-hearth heats in the treated and untreated conditions and found the nitrogen content (0.006 pct) to be unaffected. These two results lead to the speculation that rare-earth additions can reduce the nitrogen content to a certain level. Decker and coworkers10 have observed that small amounts of boron or zirconium, picked up from magnesia or zirconia crucibles, increased high-tem-

Jan 1, 1961

By E. A. Steigerwald, G. L. Hanna

The influence of work-hardening exponent on the variation of fracture toughness with material thickness was studied for high-strength steel, aluminum, and titanium alloys. The results indicate that, when materials are compared at similar fracture toughness to yield strength ratios, the material with the lower work-hardening exponent undergoes the transition from flat to slant fracture at a larger thickness than material with a high work-hardening exponent. In the thickness range where complete slant fracture is obtained the reverse is true and a lower work-hardening exponent results in a lower fracture toughness. The influence of work-hardening exponent on fracture toughness is, therefore, dependent on the particular fracture mode. In the transition region a low work-hardening exponent is beneficial for fracture toughness while in the 100 pct slant region it is detrimental. THROUGH the use of fracture mechanics analyses, the influence of geometric variables on the crack propagation resistance of structures can be interpreted with reasonable consistency. However, in order to gain a more complete understanding of the fracture process, the influence of material parameters on crack propagation must be defined and coupled to the macroscopic fracture mechanics approach. The work-hardening exponent, which characterizes specific material behavior, may serve as an effective parameter to allow some degree of coupling to be accomplished. In the extension of a crack in a specimen of suitable dimensions the propagation process occurs in a stable manner when the crack extension force is balanced by the resistance to crack extension, which exists in the material at the crack tip. As the applied stress, and therefore the crack extension force, on the specimen increases, the resistance also increases primarily because the effective plastic zone at the crack tip, which is the main energy absorption process, becomes larger. Since the work-hardening rate of a material influences the stress-strain relationship, it will also influence the energy absorption process in the plastic enclave at the crack tip and hence should have an effect on crack propagation. A number of studies have been made correlating the strain-hardening exponent or the strain to tensile instability with the ability of a material to resist fracture. Gensamer1 concluded that a low-strain-hardening exponent would result in a steep strain gradient at the base of a notch. He reasoned that a large work-hardening coefficient would result in high-energy ab- sorption due to the increased area under the stress-strain curve. Larson and Nunes2 experimentally observed in Charpy tests on steels heat-treated to below 200,000 psi yield strength that the energy to failure in the fibrous mode, i.e., above the brittle-to-ductile transition temperature, was logarithmically related to the strain-hardening exponent. In order to avoid the complicating effects present in studying materials which undergo a brittle-to-ductile transition, Ripling evaluated the notch sensitivity of a variety of fcc metals with varying work-hardening exponents.3 The results indicated that the relative notch sensitivity, as determined from tests on specimens with a sharp notch, decreased with increasing values of strain hardening. Although the energy required for ductile or fibrous fracture increases with increasing work hardening, high-strength steels often exhibit improved crack propagation resistance when heat-treated to obtain low values of strain hardening.4,5 An analysis of whether low strain hardening is beneficial or detrimental to crack propagation resistance must depend on the particular fracture criterion involved. At temperatures where the material is relatively ductile and the development of a critical strain is required for fracture, high strain hardening increases the energy required to produce failure. In the transition region and below, however, a critical stress law appears to be valid6 and a low rate of work hardening may produce superior resistance to semibrittle crack propagation. The experimental program is aimed at studying these possibilities and determining the specific influence of strain hardening on the crack propagation resistance of several high-strength materials. MATERIALS AND PROCEDURE The alloys, chosen as representative of various classes of high-strength materials, are summarized in Table I. The heat treatments evaluated along with the smooth tensile properties are presented in Table 11. Pin-loaded sheet tensile specimens were employed to determine the smooth tensile properties. A strain gage extensometer (measuring range 0.200 in.) was used at a strain rate of 0.02 in. per in. per min. The work-hardening exponents were determined from the stress-strain curves generated in the smooth tensile tests and the assumption that the portion of the stress-strain curve beyond the yield point can be described by the power relationship: where a is the true stress, P is the true plastic strain,

Jan 1, 1969

By T. S. Lovering

The use of geothermal energy is expanding very rapidly. This type of energy has proven commercially profitable for generation of electricity, for space heating, process heating, auxiliary heating of water in conventional steam power plants and for recovery of chemicals contained in natural hot water and steam. Two types of geothermal energy sources are recognized: 1) hot springs in regions of nearly normal heat flow that tap a deep reservoir through which water moves slowly to a hot springs conduit and then rapidly to the surface; 2) hyperthermal areas in which the water is heated by a relatively concentrated heat source related to volcanicity. If there is a geologic trap that provides a geologic analog to a steam boiler, as at Larderello, Italy, the hyperthermal area will have a convecting system that develops superheated water at relatively shallow depth and may provide natural steam in large quantities. If a hyperthermal area is to be productive for a long time, the underflow into the reservoir should be slow enough to allow the heat source and convective system to heat the underflow to the working temperature, and the production rate must not exceed this rate of underflow. A model based on a typical aquifer suggests that the rate of movement of water through the reservoir be such that a few years are spent in transit between isotherms that are spaced about 2°F apart. The possibility of finding blind geothermal areas is illustrated by discussion of the techniques developed in evaluating the subsurface temperatures in the East Tintic district of Utah where a map of isotherms at water level (2000 to 2000 ft below the surface) shows that a hyperthermal area may exist a short distance southeast of the mining district. Very nearly all of the energy that man currently uses comes ultimately from the sun's radiation. This includes water power, fuels such as wood, peat, coal and petroleum, the wind and all our animal power. In the paper summarizing a conference on solar energyl6 the average amount of solar energy received daily on the earth is taken at about 1 cal per m2 per min or slightly less than 2 pcal per cm2 per sec; this is almost exactly the amount of energy on the average that the earth liberates in regions of normal geothermal gradient due to its own internal heating. In many places, however, the energy released is many times the average and in some of these hyperthermal areas, geothermal steam is used for generation of electricity, and hot springs are used for heating buildings and private dwellings, process heating, auxiliary heating of water in conventional steam power plants, and chemicals may be recoverable from both hot water and steam. The use of hot springs waters for heating houses goes back hundreds of years but until recently was confined to a few dwellings close to the hot springs. In Korea, some houses had hot spring water channeled through conduits in the floor centuries ago and thus the Koreans can be credited with pioneer development of radiant heating. In Iceland at present nearly a third of the population uses natural thermal water for domestic heating." The Reykjavik system pipes hot spring water at about 94°C throughout the city and has devised insulated double pipes that allow the water to be piped for some 25 km with a drop of only 1°C for every 5 km. The actual cost to the Icelandic consumer is only one-third the cost of heating by imported coal and yet the industry is one of the most profitable in Iceland. The most profitable use of geothermal energy has been its conversion into electricity which can be transmitted economically much greater distances than hot water. The largest installation at the present time is that at Larderello, Italy, where the Count of Larderello began to experiment in the production of electricity from geothermal steam 60 years ago — in 1904. He installed his first steam turbine, with a capacity of only 250 kw, in 1912 as the result of a local quarrel with the power company which furnished the current required in the Larderello chemical industry - an industry that then dated back nearly a century. As experience was gained in drilling deep holes to tap geothermal steam and in converting it to electric power, the capacity of the installation of Larderello gradually increased, but was all destroyed by the Germans during their retreat from Italy in the closing

Jan 1, 1965

By M. J. Marcinkowski, A. S. Sastri

A detailed compressive stress-strain analysis and transmission electron microscopy investigation has been made of the deformation behavior occurring in a 50 at. pct Ni-Ti (hypoeutectoid) alloy and a 54.5 at. pct Ni-Ti (hypereutectoid) alloy. In the case of the hypoeutectoid alloy, three stages of work hardening are observed. Stage I occurs at a very low stress and is associated with plastic deformation via martensite formation. Stage 11 is characterized by very rapid work hardening and is due to difficulties in causing further deformation in the fine martensite aggregate produced in Stage I. Stage III which occurs at very high stress levels is characterized by smaller work hardening rates and is due to the plastic deformation arising from alternate reconversions of the original martensites to martensites of varying orientation. Rapid quenching of the hypereutectoid alloy leads to very high yield strengths and is related to a fine precipitate dispersion that such treatment brings about. The present investigation represents the final phase of a three-part study directed toward an understanding of the solid-state transformations in near equi-atomic Ni-Ti alloys as well as the deformation mechanisms associated with these alloys. In the first part,"2 to be henceforth referred to as I, it was found that alternate simple shears on {112} planes and in (111) directions convert the parent B2 structure in the equiatomic NiTi alloy into two distinct close-packed monoclinic martensites. All of the marten-sites were of this type, whether they were formed by cooling or by plastic deformation, whether induced to form in bulk samples or in thin foils, or whether examined in the electron microscope at room temperature or below. On the other hand, in the second part of this investigation,3 to be reffered to as 11, it was shown that upon slow cooling to about 640°C. alloys in the neighborhood of NiTi which possess the B2 structure transform eutectoidally into their equilibrium phases Ti2Ni and TiNi3. However, preceding the formation of these equilibrium phases a series of metastable intermediate phases are formed. This paper will set as its goal the elucidation of the remarkable deformation behavior exhibited by NiTi. In particular, Buehler and Wiley4 have found equiatomic NiTi to be surprisingly soft, while Buehler et al.5 have shown this alloy to possess a memory effect: i.e., upon bending at room temperature it will revert to its original shape when heated to above about 50°C. In I it was shown that NiTi was soft in the sense that the yield stress was low; nevertheless, the alloy work-hardened at an extremely rapid rate to very high stress levels. On the other hand, the hypereutectoid alloys with somewhat higher nickel, say 54.5 at. pct (60 wt pct) have enormously increased yield strengths compared to those of the equiatomic alloys. In order to determine the atomistic processes giving rise to the above behavior, it was decided to examine samples that were wafered from bulk specimens deformed in compression to various strains using the techniques of transmission electron microscopy. EXPERIMENTAL TECHNIQUE All of the alloys used in the present investigation contained either 50 at. pct Ni (55.06 wt pct) or 54.5 at. pct Ni (60 wt pct) and were arc-melted in the form of a finger using the same techniques described in I and II. The finger was capsulated in a stainless-steel jacket and swaged at 850°C into rods. Compression specimens 0.300 in, long and 0.200 in. in diam were machined from these rods. In order to completely re-crystallize the samples and remove residual stresses, all of them were capsulated in evacuated quartz, annealed for 1/2 at 1050°C. and then furnace-cooled. Compression tests were carried out in an Instron tensile testing machine covering a range of temperatures from —196° to 200°C using procedures described previously.6'7 In all cases crosshead speed was 0.02 in. per min. Wafers 0.015 in. thick were spark-cut from the cylindrical samples at 45 deg to the compression axes after they had been deformed to the desired strain. These specimens were then spark-planed to about 0.005 in. and then electrochemically thinned for examination by transmission electron microscopy as described in I.

Jan 1, 1969

By D. Atkinson, C. Bodsworth, I. M. Davidson

A geometric model of interstitial solid solutions, which has been used previously as a basis for the prediction of carbon activities in Fe-C austenite, is shown to serve also for the calculation of nitrogen activities in Fe-N austenite. The model has been developed to enable predictions to be made of the activities of an interstitial element in the presence of two host atom species. The activities calculated via the model are shown to be in satisfactory agreement with the measured values in the austenite phase for carbon in Fe-C-Co, Fe-C-Cr, Fe-C-Ni, Fe-C-~n, Fe-C-Si, and Fe-C-V alloys and for nitrogen in Fe-N-Ni alloys. The effect of the second substitu-tional solute on the logarithm of the activity of the interstitial element is expressed as the product of a constant mad the atomic concentration of that solute. The constants so derived we related to the thermo-dynamic interaction coefficients which describe the effect on the activity coefficient of carbon of an added solute element. In recent years the thermodynamic activities of carbon and nitrogen in the single-phase austenite field have been determined for iron binary alloys and for several iron-base ternary alloys. In order to extend the use of these measurements, it is desirable to be able to predict with reasonable accuracy the activities of the interstitials at compositions and temperatures other than those which have been measured experimentally. In all the systems studied to date, the interstitial elements do not conform to ideal behavior. Hence, the available data cannot be extrapolated or interpolated using the simple thermodynamic concepts of solutions. Several models have, therefore, been formulated for the purpose of predicting the activity of an interstitial element in the presence of one species of host atom. These models can be divided into the geometric1"5 and energetic6-' types. The former group is based on the assumption that at low concentrations the activity of the interstitial species is determined by a composition-dependent configurational entropy term and an excess free-energy term which is temperature-dependent but independent of composition. The purpose of this paper is to show that the treatment, based on a geometric model, can be extended to enable predictions to be made of interstitial activities in the presence of two substitutional host atom species. THE CONFIGURATIONAL ENTROPY OF MIXING ICaufman5 has shown that the configurational entropy, S,, for a binary solution comprising of a host atom species, A, and an interstitial species, I, can be expressed as: where NI is the atom fraction of the interstitial species, R is the gas constant, and (2 - 1) is the number of interstitial sites excluded from occupancy by the strain field around each added interstitial atom. The number of interstitial sites per host atom, p, is unityg for the fcc austenite solutions considered here. The configurational entropy of mixing for a ternary solution comprising two substitutional atom species, A and B, and one interstitial species, I, can be derived similarly. Let the number of atoms per mole of each of these species in the solution be represented by «a, ng, and nI. From geometric considerations, it is improbable that the addition of a few atom percent of a second host atom species will change the type of sites (i.e., octahedral) in which the interstitial atom can be accommodated in the austenite lattice. At higher concentrations (determined largely by the relative atomic radii of the atomic species present and any tendency to nonrandom occupancy of the host lattice sites) other types of interstitial sites may become energetically favorable. Restricting consideration to compositions below this limit, for 1 = 1 the number of suitable interstitial sites is given by (n + nB). However, if each interstitial atom excludes from occupancy (Z - 1) additional sites, the total number of sites available for occupation is reduced to (n + ng)/Z. The number of vacant interstitial sites is given by: The total number of recognizable permutations of the atoms must include the recognizable, different configurations of the A and B atoms on the host lattice. Assuming that these arrangements are purely random, and are not affected by the presence of the interstitial species, the total number of recognizable permutations in the ternary alloy is given by: The configurational entropy is obtained by expanding, using Stirling's approximation, and collecting like items, as:

Jan 1, 1969

By F. W. Jessen, John C. Miller

In many areas where carbonate rocks form important parts of the stratigraphic sequence, stratigraphers have experienced varying degrees of difficulty in differentiating and correlating limestone and dolomite units in both surface and subsurface work. With early Paleozoic rocks of the Mid-Continent, insoluble residues yield a remarkable amount of strati-graphic data and relatively good correlations may be carried over broad distances.' Unfortunately, neither such information nor electric logs and radioactive logs have been particularly helpful in interpreting the limestone sections of the Permian Basin of West Texas. This is because: (1) the variations in the sections may be very slight; (2) no completely satisfactory method of interpretation has been developed; and (3) the measurements themselves are not sensitive enough for small variations. Also, such logs are influenced by the fluid content. Paleontology and micro-paleontology remain the ultimate arbiters. As a routine tool, however, paleontol-ogical examination is slow and tedious. Chemical analysis may be used, but this, too, is extremely slow. Although rocks are not classified according to chemical composition, there is considerable variation with rock types. Correlation by chemical composition has two advantages, first, the characteristics determined are subject to minimum human error and interpretation, and secondly, the lithologic changes are not masked by fluid content as in the case of electric and radioactive logs. Some fossils concentrate certain elements which tentatively might be used to date rock units.' Rapid chemical analysis by spec-trographic means could be used as an adjunct to other means employed in correlation work, or might, in itself, present a suitable method. PURPOSE OF THIS INVESTIGATION Sloss and Cooke' have published data concerning spectrographic analysis of limestone rocks specifically for purposes of direct correlation of a single formation. These authors found satisfactory evidence that differences in percentage of four elements (Mg, Fe, Al, and Sr) in the Mississippian limestones of northern Montana were useful in carrying out correlation of this formation over a distance of approximately 50 miles. It was concluded from the preliminary work that the spectrochemical method offered possibilities of solution of some problems of correlation heretofore not possible. Since the work of Sloss and Cooke' was confined to one particular limestone zone, extension of the use of the method to examine two or more geologic formations would aid materially in the over-all problem of correlation of such rocks. Equipment is now available commercially with which very rapid spectrographic analyses may be made, and hence the problem was to determine whether the variations existing in the minor constituents of limestones were sufficient for use in possible correlation. Qualitative and semi-quantitative investigations were made to determine whether significant changes in the chemical condition occurred. It was a further purpose to investigate the geologic time-boundaries to see whether significant chemical variation could be found corresponding to the paleontological breaks. It was desirable to attempt correlation of a thick section of limestone or dolomite rock and to have as much information as possible on the section. Furthermore, it was felt that examination of formations more difficult to correlate by other means would enhance the value of the method should definite points of correlation be found. Samples were chosen from the Chapman-McFarlin Cogdell No. 25 well in the Cogdell field, Kent County, Tex., and from the General Crude Oil Co., Coleman No. 193-2 well in the Salt Creek field, Kent County, Tex. These fields belong to the famous series of "Canyon" reef fields of West Texas. Cores from the above wells were available from the United States Geological Survey, Austin, Tex. THE SPECTROGRAPHIC METHOD The choice of procedure to be followed in this investigation was based on the anticipated requirements peculiar to the problem. Since the problem was primarily to investigate the possibilities of applying the spec-trograph to problems of correlation in thick carbonate sections, a precise quantitative analysis did not appear necessary. A qualitative analysis to show the possible absence of presence of any element, or a semi-quantitative analysis of the elements present to show the relative changes in magnitude of selected elements was required. Both types of analysis were employed. The two most widely applied methods of semi-quantitative estimates are those of Harvey and of Slavin4,5 though various other procedures have been described.6 while the Harvey method has been modified by Addink,7 this refinement did not seem necessary to the present problem. Essentially, the procedure employed is a variation of the total energy method of Slavin with two exceptions: (1) stressing matrix effect, and (2) using densitometer measurements. As measured by a densito-

Jan 1, 1956

By A. B. Cook

Gas cycling is generally considered a much less efficient oil recovery mechanism than water flooding. HOWever, recoveries from some fields have been exceptionally high as a result of gas cycling. Recovery from the Pick-ton field, for example, was calculated to be 73.5 perceni of the stock-tank oil originally in place. In evaluating pressure maintenance projects, determining how much of the recovery is due to displacement by gas and determining how much is due to vaporization of the imrnohile oil in the flow path of the cycled gas is very difficrilt. Even though most of the oil is recovered by displacetr~ent, the success of a project may depend on the amount of oil vaporized. A limited number of experiments have heen performed with a rotating model oil reservoir that simulates gas cycling operations and allows a separation of the oil from, tile free gas flowing into the laboratory wellbore at reservoir conditions, thus revealing which is displaced oil and which is vaporized oil. It Iras been determined that the amount of varporizatio'n is .significant if proper conditions exist These experiments show that oil vaporization depends on pressure, temperature, volatility of the oil and amount of gas cycled. Increases in each of these conditions increase the volume of oil vaporized. Data from six experiments affecting vaporization are presented to illustrate reservoir condition that range from favorable to unfavorable. 111 these eaperitnenis recovery by vaporization ranged from 73.6 to 15.3 percent of /he immobile oil (oil not produced by gas displacerrlt). INTRODUCTION Between 1930 and 1950, gas cycling was a popular. oil recovery practice. especially for the deeper reservoirs. Later, with many case history-type studies published for both gas cycling and waterflooding, it was generally believed that waterflooding was far superior to gas cycling, even when gas cycling was conducted as a primary production procedure by complete pressure maintenance. A good example illustrating the advantage of water-flooding over gas cycling is given in a paper by Matthews' on the South Burbank unit where gas injection was followed by waterflooding. The author concluded in part that "Early application of water injection, without the intervening period of gas injection, would have recovered as much total oil as ultimately will be recovered by waterflooding following the gas injection, and total operating life would have been shortened". This appears to be a logical conclusion. However, it should not be applied to all fields. Pressure maintenance with gas in the Pickton field, as reported by McGraw and Lohec;' will result in a much larger percentage of oil recovery than was obtained in the South Burbank unit. The great success in the Pickton field resulted partly from vaporization of the immobile oil in the flow path of the cycled gas. The amount of vaporization is related to the following conditions: volatility of the oil as reflected by the APT gravity of the stock-tank oil; reservoir temperature; reservoir pressure during gas cycling; and the amount of gas cycled. Therefore, the U. S. Bureau of Mines is investigating these effects on vaporization in a research project using a model oil reservoir. Three different stock-tank oils having 22, 35 and 45" API gravities are being used as base stock to synthesize reservoir oils. Experiments are being performcd to determine vaporization at 100, 175 and 250F and at 1,100, 2,600 and 4,100 psia. This is a progress report showing the results from six experiments. Other Bureau of Mines reports"- concerning vaporization are listed. LABORATORY EQUIPMENT AND PROCEDURES The equipment ' consists of an internally chromium-plated steel tube packed with finely sifted Wilcox sand. The tube is approximately 44 in. long and has an ID of 13/4 in. The sand section contains approximately 570 ml of voids, has a porosity of 32 percent, and a permeability to air of 4.3 darcies. A unique feature of the laboratory reservoir (Fig. 1) permits the tube part to rotate at 1 rpm while the outlet and inlet heads are held stationary. The outlet end contains diametrically opposed windows to permit observatlon of the flowing fluids, and two valves, one on the top and the other at the bottom. Oil and free gas. when being produced simultaneously, can be separated by manipulating the two valves to keep a gas-oil interface in view through the windows. Thus, only gas is produced through the top valve and only oil flows through the bottom valve. The laboratory equipment was designed to study vaporization. Therefore, a uniform reservoir was made using dry sifted sand as opposcd to using a consolidated sand core with interstitial water. Furthermore. the reservoir was tilted to minimize fingering of gas. This tilting also in-

By F. W. Bloecher, A. M. Gaudin

H. H. Kellogg—There is one point that the author has failed to emphasize sufficiently in his paper. What is commonly called the equilibrium contact-angle (the author's "maximum contact-angle") can have only one value on a smooth, flat, homogeneous surface under a given set of conditions. The equilibrium contact-angle is defined, for such a system, as the angle between the solid-liquid and liquid-gas interfaces, measured through the liquid. The value of the equilibrium contact-angle is uniquely determined by the value of the interfacial energies of the three intersecting interfaces and is independent of other forces in the system. When the liquid-gas interface intersects the solid at an edge—as was the case for all the experiments reported in this paper—the orientation of the solid-liquid interface is indeterminate or varies through 90" for a right-angle edge. Mr. Morris has called the angle between the horizontal and the liquid-gas interface for this edge condition a "static contact-angle." I feel that this term is unnecessarily misleading. In the first place, "static contact-angle" sounds too much like "equilibrium contact-angle." In the second place, the magnitude of the "static contact-angle," which I would prefer to call the "supporting angle," is determined by the forces in the system other than those derived from the interfacial energies, hence "contact angle" is misleading. If Mr. Morris had said that the "supporting-angle" is variable and depends on the weight of the particle and size of the bubble and that it has a maximum possible value equal to the equilibrium contact-angle, his discussion would have been more accurate. T. M. Morris (author's reply)—Mr. Kellogg puts forth a reasonable criticism of some of the terminology used in the paper. I agree that the term "static contact angle" may be misleading. Substitution of the term "supporting angle" or "vector angle" may be more suitable. F. X. Tartaron—In this paper the author presents a very interesting mathematical development of the forces present when a mineral particle adheres to an air bubble. Excellent concordance is obtained between mathematical formulation and experimental results. It is the writer's understanding that when the mineral surface presented to an air bubble is greater than the area of contact, the maximum contact angle is obtained. However, this contact angle represents distortion of the bubble, the normal shape of which is spherical or in cross-section, circular. This distortion produces a force that acts in opposition to the force of adhesion between the bubble and particle. Hence, at maximum contact angle, the force of adhesion between bubble and particle is at a minimum for static conditions. However, when the size of bubble is increased, the size of particle remaining the same (and all other conditions remaining the same), the contact angle decreases, the distortion of the bubble decreases and the force in opposition to adherence of bubble and particle also decreases. Thus, there is stronger attachment between bubble and particle. When this situation is applied to actual flotation conditions, it is doubtful that it has any significance. The reason is that the bubbles are normally so much larger than the particles, that in substantially all cases, it is probable that negligible distortion of the bubble takes place. In table IV, the author makes computations for bubbles from 0.50 to 2 mm diam. This is from 0.02 in. to 0.08 in. Certainly the bubbles generated in a flotation machine are far larger than this. The surfaces of the author's bubbles range from 0.79 to 12.6 sq mm. The area of contact of the glass rod (0.15 mm diam) is 0.017 sq mm. Thus, ratio of bubble surface to mineral area of contact ranges from 47 to 741 in round numbers. If we take a %-in. diam bubble and a 65-mesh (0.208 mm) particle of cubical shape, the ratio of bubble surface to mineral area of contact is 2931. Mineral particles do not readily become attached to air bubbles. Taggart has shown that in pneumatic flotation machines collector-coated particles are only temporarily attached to bubbles. They keep falling off and down in the froth but at a delayed rate as compared with gangue. Spedden and Hannan's motion pictures confirm the difficulty of attaching particles to air bubbles. In the agitation froth process, according to Taggart, air is precipitated from the water selectively on to the collector-coated particles and these

Jan 1, 1951

By F. W. Bloecher, A. M. Gaudin

H. H. Kellogg—There is one point that the author has failed to emphasize sufficiently in his paper. What is commonly called the equilibrium contact-angle (the author's "maximum contact-angle") can have only one value on a smooth, flat, homogeneous surface under a given set of conditions. The equilibrium contact-angle is defined, for such a system, as the angle between the solid-liquid and liquid-gas interfaces, measured through the liquid. The value of the equilibrium contact-angle is uniquely determined by the value of the interfacial energies of the three intersecting interfaces and is independent of other forces in the system. When the liquid-gas interface intersects the solid at an edge—as was the case for all the experiments reported in this paper—the orientation of the solid-liquid interface is indeterminate or varies through 90" for a right-angle edge. Mr. Morris has called the angle between the horizontal and the liquid-gas interface for this edge condition a "static contact-angle." I feel that this term is unnecessarily misleading. In the first place, "static contact-angle" sounds too much like "equilibrium contact-angle." In the second place, the magnitude of the "static contact-angle," which I would prefer to call the "supporting angle," is determined by the forces in the system other than those derived from the interfacial energies, hence "contact angle" is misleading. If Mr. Morris had said that the "supporting-angle" is variable and depends on the weight of the particle and size of the bubble and that it has a maximum possible value equal to the equilibrium contact-angle, his discussion would have been more accurate. T. M. Morris (author's reply)—Mr. Kellogg puts forth a reasonable criticism of some of the terminology used in the paper. I agree that the term "static contact angle" may be misleading. Substitution of the term "supporting angle" or "vector angle" may be more suitable. F. X. Tartaron—In this paper the author presents a very interesting mathematical development of the forces present when a mineral particle adheres to an air bubble. Excellent concordance is obtained between mathematical formulation and experimental results. It is the writer's understanding that when the mineral surface presented to an air bubble is greater than the area of contact, the maximum contact angle is obtained. However, this contact angle represents distortion of the bubble, the normal shape of which is spherical or in cross-section, circular. This distortion produces a force that acts in opposition to the force of adhesion between the bubble and particle. Hence, at maximum contact angle, the force of adhesion between bubble and particle is at a minimum for static conditions. However, when the size of bubble is increased, the size of particle remaining the same (and all other conditions remaining the same), the contact angle decreases, the distortion of the bubble decreases and the force in opposition to adherence of bubble and particle also decreases. Thus, there is stronger attachment between bubble and particle. When this situation is applied to actual flotation conditions, it is doubtful that it has any significance. The reason is that the bubbles are normally so much larger than the particles, that in substantially all cases, it is probable that negligible distortion of the bubble takes place. In table IV, the author makes computations for bubbles from 0.50 to 2 mm diam. This is from 0.02 in. to 0.08 in. Certainly the bubbles generated in a flotation machine are far larger than this. The surfaces of the author's bubbles range from 0.79 to 12.6 sq mm. The area of contact of the glass rod (0.15 mm diam) is 0.017 sq mm. Thus, ratio of bubble surface to mineral area of contact ranges from 47 to 741 in round numbers. If we take a %-in. diam bubble and a 65-mesh (0.208 mm) particle of cubical shape, the ratio of bubble surface to mineral area of contact is 2931. Mineral particles do not readily become attached to air bubbles. Taggart has shown that in pneumatic flotation machines collector-coated particles are only temporarily attached to bubbles. They keep falling off and down in the froth but at a delayed rate as compared with gangue. Spedden and Hannan's motion pictures confirm the difficulty of attaching particles to air bubbles. In the agitation froth process, according to Taggart, air is precipitated from the water selectively on to the collector-coated particles and these

Jan 1, 1951

By Thomas R. Mager

An in.t!estigation has been made of the equilibrium conditions at 1200°C in the reaction between hydrogen sulfide gas and sulfur dissolved in Fe-Si alloys From this the equilibrium constant, activity coefficient, and activity of sulfur in solution were calculated. A number of studies of the equilibrium of sulfur with iron and iron alloys have given closely agreeing results from which the activity and free energy of the dissolved sulfur may be found. Sherman, El-vander, and chipman1 discussed the significant researches of dilute solutions of sulfur in liquid iron prior to 1950, and the results of this study indicated that the relationship between the ratio of PH2S/PH2 in the environment and the percentage of sulfur in solution is not a linear one. Morris and williams2 studied the equilibrium conditions in the reaction between hydrogen sulfide gas and sulfur dissolved in liquid iron and Fe-Si alloys, and reported that silicon dissolved in iron has a pronounced effect on the equilibrium conditions. They found that the activity of sulfur in iron is increased by the addition of silicon. At a silicon content of 4 pet the activity coefficient of sulfur was about twice that for sulfur dissolved in pure iron. Sherman and chipman3 investigated the chemical behavior of sulfur in liquid iron at 1600°C through the study of the equilibrium: H2 + S = H2S; K = PH2S/PH2 . 1/as [1] From the known equilibrium constant of the reaction between H2, H2S, and S and the experimental data, the activity of sulfur in the melt was determined. They found that the activity coefficient of sulfur defined as fs = as/%s is increased by silicon and decreased by manganese. Morris4 and Turkdogan5 also reported that manganese decreases the activity coefficient of sulfur in liquid iron and iron-base alloys. A recent technique of sulfur analysis developed by Kriege and wolfe6 of the Westinghouse Research Laboratories permits an accurate sulfur analysis of 0.5 * 0.2 ppm in the range of 0.1 to 3 ppm, whereas in the range of 3 to 50 ppm the accuracy is ±1 ppm. This technique of sulfur analysis was utilized in this experiment. Previous unpublished data reported that sulfur analysis by the combustion technique was not accurate below 20 ppm. EXPERIMENTAL PROCEDURE Five 5-lb ingots of high-purity Fe-Si were prepared. Three of these ingots were prepared without the addition of manganese but with a variation of silicon contents from 2 to 4 pet. The remaining two ingots contained 3 pet Si with the addition of manganese. Ingots were made at each of three silicon levels: 2, 3, and 4 pet. No alloys were made with less than 2 pet Si since below approximately 1.8 pet Si the binary alloy exhibits a to ? transformation. The two additional ingots of 3 pet Si-Fe were made at each of two manganese levels: 0.20 and 0.50 pet. To minimize the effects, if any, of impurities on the activity of sulfur on Si-Fe, the best metals available were used for melting. All ingots were vacuum-melted in magnesium oxide crucibles. After obtaining samples for chemical analyses, the ingots were processed. This consisted of hot rolling and subsequently cold rolling the alloys. Each ingot was hot-rolled at 1000°C, reheating between every pass to minimize grain growth. All heating was done in a protective argon atmosphere. The slabs were hot-rolled to strips 50 mils thick. After hot rolling, all the material was pickled to remove the scale formed on the surface of the strip during hot rolling. The material was then cold-rolled to 12-mil strips. Single strips of the material used in this experiment were hydrogen-annealed at 1200°C for 16 hr in an alumina tube. Chemical analyses of strips M-1, M-3, M-4, M-7, and M-8 are given in Table I. Sulfur, silicon, and manganese analyses were made from the millings from the cold-rolled 12-mil strips. The oxygen analyses were made from slugs of the as-cast material. The hydrogen sulfide used in these experiments was supplied from cylinders containing a mixture of argon and 1 pet hydrogen sulfide. The parts per million of hydrogen sulfide were determined from the analysis of the exit gas of the annealing furnace during each anneal. The flow rate of hydrogen was approximately 1 liter per min in all anneals. The

Jan 1, 1964

By R. D. Daniels, T. W. Wood

The tensile properties of columbium and Cb-H alloys containing up to 455 ppm H were studied as a function of temperature and strain rate. Hydrogen, introduced into columbium at elevated temperatures, using a thermal -equilibrium technique, embrittled columbium most severely at about —77°C. This elnbrittle ment occurred even at hydrogen concentrations of an order of 20 ppm. At higher temperatures, the hydrogen tolerance of columbium increased in relation to the increased solubility of hydrogen in tile metal. Below this temperature hydrogen tolerance, as determined by ductility and fracture stress, increased slightly. Strain rate had little effect on the tensile results for cross-head speeds over the range 0.002 to 2.0 in. per min. Strain aging during the tensile test appears to explain the ductility mininmum at —77°C. The apparent increase in hydrogen tolerance at lower temperatures is attributed to the low mobility of hyhogen. Experiments were performed in which samples were prestrained in tension at room temperature and tested to failure at —196°C. Results suggest that hydrogetz segregation to preformed crack nuclei can cause subsequent embrittlement even at temperatures where hydrogen mobility is too low to cause embrittlement in a normal tensile test. COLUMBIUM is an example of the class of bcc metals with ductile-brittle transition temperatures sensitive to the presence of interstitial atom contaminants. Hydrogen is one of these embrittling contaminants. The embrittling effect of hydrogen is less potent, perhaps, in columbium than in some of the other bcc refractory metals, but it is still a problem of both theoretical and practical interest. Unlike hydrogen in iron and steels, hydrogen in columbium is exothermically rather than endo-thermically occluded. The embrittlement process in exothermic systems has not been studied as extensively as that in endothermic systems, especially at hydrogen concentrations below the limit of solubility. The purpose of this investigation was to evaluate the embrittlement process in initially pure columbium as a function of hydrogen content, temperature, and strain rate. The Cb-H phase diagram, according to Albrecht et al.,1 is shown in Fig. 1. Columbium reacts exothermically with hydrogen producing a solid solution at concentrations of less than about 250 ppm (parts per million by weight) H at room temperature. At concentrations above the highly temperature-dependent solvus a second phase is formed. Like many similar hydrogen-metal systems,2 his system exhibits a miscibility gap with respect to hydrogen solution. Albrecht found the critical temperature of the miscibility gap to be about 140°C, the critical concentration to be 0.23 atom fraction hydrogen, and the critical pressure to be 0.01 mm Hg. Above 140°C there is a solid solution of increasing lattice constant extending across the phase diagram. Hydrogen concentrations of particular interest in this investigation were those below the limit of solubility in columbium. At hydrogen concentrations above the limit of solubility, columbium will contain the hydrogen-rich second phase and will be brittle under most testing conditions because the hydride generally precipitates as platelets with coincident matrix lattice strains.1'3 At hydrogen concentrations below the limit of solubility, the tensile behavior of columbium is expected to be more sensitive to the interrelationships between hydrogen concentration and mobility and the testing variables such as temperature and strain rate. Literature references to the hydrogen embrittlement of metals, especially ferrous alloys and titanium alloys, are too voluminous to mention. It is only recently, however, that detailed studies of the hydrogen embrittlement of columbium have been undertaken. Wilcox et a1.4 studied the strain rate and temperature dependences of the low-temperature deformation behavior of fine-grained are-melted columbium (1 ppm H) and the effect of hydrogen content (1,9, and 30 ppm H) on the mechanical behavior of columbium at a series of temperatures for a single strain rate. A strain-aging peak was ob-served at about -50°C which was attributed to the presence of hydrogen in the metal. Eustice and carlson5 studied the effect of hydrogen on the ductility of V-Cb alloys at a series of temperatures over the range -196° to 25°C. Pure columbium was embrittled by 20 ppm H which produced a ductility transition at approximately -70°C. Ingram et al.6 studied the effect of oxygen and hydrogen on the tensile properties of columbium and tantalum. A minimum in the notched-to-unnotched tensile ratio of hydrogenated columbium was obtained at about -75°C, but because of the relatively large hydrogen content employed (200 and 390 ppm) the ductility

Jan 1, 1965

By T. E. Watkins, M. D. Nelson

INTRODUCTION Deeper drilling for oil is becoming more and more the rule rather than the exception. With deeper drilling come additional problems, perhaps the greatest being those brought on by the higher temperatures encountered down the hole. particularly in the Gulf Coast region of Texas and Louisiana. Temperature gradients of the order of 1.8° to 2.0°F/100 ft are not unusual, and a gradient of 2.3"F.'100 ft is found in some areas of Texas. With a mean surface temperature of 74oF, the following temperatures could be expected for a geothermal gradient of 2.0°F; 100 ft: at 10,000 it. 271°F. 12,000 ft, 314°F: 14,000 ft, 354,oF; and 16.000 ft. 394°F. Severe gelation of lime-base drilling fluid in wells that have high bottom hole temperatures has become perhaps the most serious difficulty enconntered in drilling under such conditions. Lime-base drilling fluids have been very succesefully and widely used in the drilling of wells in the Gulf Coast region because of their inherent stability toward contaminants. their ability to suppress the swelling dispersion of bentonitic shales, and their ease of maintainance. The gradual recognition: during the past few years, that these muds were. in themselve. the cause of many difficulties experienced in drilling has led to wide-pread efforts by the drilling industry. to determine the reasons for the failure of these mud systems and to develop mud systems capable of performing satisfactorily under high-temperature conditios. MANIFESTATIONS OF HIGH-TEMPERATURE GELATION it is generally possible to recognize the symptons of high-temperature gelation early enough that advance predictions can be made of serious difficulties. in mud control, and the useful life of the drilling fluids can be extended by proper treatment. Following i.; a list of the manifestations of high-temperature gelation: (1) The drill string 'takes weight' while going in the hole after a trip. In early stages of high-temperature gelation it is possible to notice a slight reduction in drill string weight as the drill pipe is lowred near the bottom of the hole. (2) Excessive pump pressure is required to .tart the circulation of drilling fluid at or near the bottom of the hole when going hack to bottom after a trip. As the severity of the gelation increases it may be necessary to break circulation a number of times when going in the hole. (3) The drilling fluid from the bottom of the hole is thick and often granular or lumpy when pumped up after making a round trip. In a severely gelled drilling fluid system such a condition may be irreversible; that is, it cannot be stirred or chemically treated to produce a satisfactory drilling fluid. (4) Completion tool.. such as logging tools or perforating guns will not sink to the bottom of the hole. On some occasions completion tools will become stuck and require a fishing job to retrieve them if the wire line attached to them is broken. It is often difficult to determine whether the condition of the drilling fluid is responsible for sticking the tool or whether the wire line becomes key seated in a crooked hole and causes the allow difficulty. When there are 110 other symptoms of high-temperature gelation. then the difficulty may usually be attributed to the latter cause. (5) In extreme cases of high-temperature gelation it is necessary to "wash" and "ream" when going back to bottom after coming out of the hole. (6) In many -instance. it has been found to be extremely difficult and expensive to 1111 production packers 2nd tubing in moderately deep oil wells which had been drilled with a lime-base drilling fluid. In such instances-the original mud had apparently "set" to a consistency approaching that of a weak cement. CAUSES OF HIGH-TEMPERATURE GELATION Extensive test; have indicated that a lime-base mud does not develop a highly gelled condition at temperatures below 250°F. whereas above that temperature such condition often develops rapidly. (Fig. 1) concurrently. the following changes are evident ill the mud: (1) The alkalinity of the mud decreases to a very low value. with both caustic soda and lime being consumed. (2) The quartz content of the mud decreases sharply. (3) The bentonitic content of the mud decreases or di-appears, with concurrent decrease or loss of base exchange capacity of mud solids. (4) New compounds formed in the mud have been found to be cal-cium silicate, calcium aluminum silicate, and calcium sodium aluminum silicate. (5) The mud loses the ability to form a filter cake of low permeability. The above characteristics have been discussed, in part. by other authors

Jan 1, 1953

By F. E. Werner, B. L. Averbach, Morris Cohen

THAT bainite formed near the M, temperature bears a striking r esemblance to martensite tempered at the same temperature has been shown by the electron microscope.' By means of electron diffraction,' it has been established that carbide and cementite are present in bainite formed at 500°F (260°C); these carbides are also found in martensite tempered at 500°F (260°C).' The investigation reported here is concerned with an X-ray study of the matrix phases in lower bainite and tempered martensite. These phases have turned out to be dissimilar in structure; the matrix of bainite is body-centered-cubic while that of tempered martensite is body-centered-tetragonal. A vacuum-melted Fe-C alloy containing 1.43 pct C was studied. Specimens of 16 in. diam were sealed in evacuated silica tubing and austenitized at 2300°F (1260°C) for 24 hr. One specimen was quenched into a salt bath at 410°+7 °F (210°+4°C), held for 16 hr, and cooled to room temperature. The structure consisted of about 90 to 95 pct bainite, the re: mainder being martensite and retained austenite. A second specimen was quenched from the austen-itizing temperature into iced brine and then into liquid nitrogen. It consisted of about 90 pct martensite and 10 pct retained austenite. The latter specimen was tempered for 10 hr at 410°+2°F (210°+1°C). The specimens were then fractured along prior austenite grain boundaries (grain size about 2 mm diam) by light tapping with a hammer. Single aus-tenite grains, mostly transformed, were etched to about 0.5 mm diam and mounted in a Unicam single crystal goniometer, which allowed both rotation and oscillation of the sample. Lattice parameters were measured by the technique of Kurdjumov and Lyssak. This method takes advantage of the fact that martensite and lower bainite are related to austenite by the Kurdjumov-sachs orientation relationships Thus, the (002) and the (200) (020) reflections can be recorded separately, permitting the c and a parameters to be determined without interference from overlapping reflections. According to these findings, the matrix phase in bainite is body-centered-cubic and, within experimental error, has the same lattice parameter as ferrite (2.866A). On the other hand, martensite, tempered as above, retains some tetragonality, with a c/a ratio of 1.005t0.002. Most workers in the past have assumed that bainite is generated from austenite as a supersaturated phase, but the nature of this product has not been established. The question arises as to whether bainite initially has a tetragonal structure and then tempers to cubic, or if it forms directly as a cubic structure. If it forms with a tetragonal lattice, it might well be expected to temper to the cubic phase at about the same rate as tetragonal martensite. The martensitic specimen used here was given approximately the same tempering exposure, 10 hr at 410°F, as suffered by the greater part of the bainite during the isothermal transformation. About 50 pct bainite was formed in 6 hr at 410°F. On tempering at this temperature, martensite reduces its tetragonality within a few minutes to a value corresponding to 0.30 pct C.' Further decomposition proceeds slowly, and after 10 hr the c/a ratio is still appreciable, i.e., 1.005. Thus, even if the bainite were to form as a tetragonal phase with a tetragonality corresponding to only 0.30 pct C, which might be assumed to coexist with e carbide, it would not be expected to become cubic in this time. It seems very likely, therefore, that bainite forms irom austenite as a body-centered-cubic phase and does not pass through a tetragonal transition. The carbon content of the cubic phase has not been determined, but it could easily be as high as 0.1 pct, within the experimental uncertainty of the lattice-parameter measurements. It has been postulated that retained austenite decomposes on tempering into the same product as martensite tempered at the same temperature. There is now considerable doubt on this point. The isothermal transformation product of both primary and retained austenite at the temperature in question here is bainite," and the present findings show that bainite and tempered martensite do not have the same matrix. Acknowledgments The authors would like to acknowledge the financial support of the Instrumentation Laboratory, Massachusetts Institute of Technology, and the United States Air Force.

Jan 1, 1957

By P. G. Shewmon

A novel technique for determining the surface energy (?) and its derivative with respect to orientation, (?') is described. Essentially it involves the 'floating" of a wedge on the substrate, said wedge being made of a material which is not wet or only slightly wet by the substrate, i. e., as a greased needle "floats" on water. A thermodynamic analysis of a system in which the wedge is supported entirely by surface energy is given. If the original suyface is not at a cusp orientation, the surface tension is directly measurable from the groove angle formed. If the original surface is at a cusp orientation, there may or may not be a groove depending on the relative value of ?' and the weight of the wedge. Experiments primarily on copper and silver showed that sapphire, quartz and refractory metal wedges were wet while graphite wedges were not. The technique was demonstrated to work using graphite wedges, but the results obtained were not as eccurate as those obtained by other workers using the wire-creep experiments. It is concluded that the technique might prove most useful with non-metals where ?' is large and filament creep experiments would be quite difficult. If an absolute value of the surface free energy (?) of a metal is to be determined, the most reliable methods used to date measure an average over the various orientations exposed on a polycrystalline sample. For example, ? for silver, gold, and copper have been measured by determining the force required to just keep a thin wire,' or foil,' specimen from contracting under the influence of ?. Herring 3 has predicted and experiment confirms, that the sensitivity of this method is inversely proportional to the grain size.' Thus it cannot be used to measure ? for a particular orientation by using a foil single crystal or a very coarse-grained specimen. An accurate value if ? for tungsten averaged over a range of orientations has been determined using a field emission technique. The same techniques cannot or have not been used to measure ? for non-metallic solids, and as a result the values available are much less accurate.4 This Paper resents a means of making an absolute determination of ? for a particular surface orientation on any solid, as long as the given surface orientation does not break up into other orientations during an anneal. Experimentally ? is found to vary with orientation and at a few low index orientations it is found to have a cusped minimum, i.e., the derivative of ? with respect to the orientation of the surface changes discontinuously at the low index orientation, see Fig. 1. The slope of a plot of ? vs orientation (herein designated ?') is called the torque on the surface, since it tends to rotate the exposed surface toward the low index orientation, or if the surface is at the cusp orientation it opposes any force tending to rotate the surface out of the low index orientation. The ratio ?'/? has been determined for a few metals, but in cases where this ratio is high there is presently no means of determining either ?'/? or the absolute value of ?' for the orientations present on an annealed surface. The technique discussed herein also provides a means of determining an absolute value of ?' for those orientations which deviate only infinitesimally from a cusp orientation. It should work best on surfaces where ?'/? is large; that is, for cases where no other technique is available for measuring ?'. Aside from trying to learn more about surfaces through measuring ? and ?', the primary reason for wanting values of ? or ?' is to study adsorption. From measurements of the variation of ? for a particular orientation with the concentration of an impurity, one can obtain the number of impurity atoms adsorbed per unit area (Ti) on that orientation using the Gibbs adsorption equation.' where µi is the chemical potential of the adsorbed impurity. Thus, if absolute values of ? could be obtained for the free surface of a given surface orientation as a function of µi, ri could be determined for the given orientation. Furthermore, by equilibrating a grain boundary with the given surface at various values of ki, one could also determine ri for the grain boundary. Similarly Robertson 6 has pointed out that if y is taken to be a continuous function of and µi, then a2 ?/a @a µ2 = a2 ?/a pi a +. Thus, at all orientations away from cusps the following equation holds From a measurement of ?' vs ki, it is thus possible

Jan 1, 1963

By Ralph Hultgren

IN solid solutions atoms of differing sizes occupy the same crystalline lattice, requiring that some of them be compressed and others expanded. The energy involved has been called misfit strain energy and is an important concept of crystal chemistry. If the atomic sizes and elastic constants of interatomic bonds are known, the misfit energy may be calculated,' provided certain simplifying assumptions are allowable. Usually, isotropic crystals are assumed and interatomic distances are taken to be the statistical average determined from X-ray diffraction. Such calculations yield values of the misfit energy of the order of 1 or 2 kcal per atom in alloys such as Au-Cu at compositions of 50 atomic pct. However, evidence has accumulated in recent times that atoms change their sizes with composition of alloys, implying electronic rearrangement of the bonds. The size changes have been found particularly by application of the X-ray method developed by Warren, Averbach, and Roberts.' Thus, Averbach, Flinn, and Cohen3 determined radii in Au-Cu alloys. Oriani4 showed that these new radii led to a calculated misfit energy in disordered AuCu, which was decreased from the values calculated by the usual theory more than twenty-fold, to only 80 cal per g atom. Thermodynamic calculations from the phase diagram5 also show misfit energy to be no more than a few hundred calories per g atom in this alloy. The question of what electronic rearrangements are possible therefore becomes compelling in estimating misfit energy. In the following pages the results of certain calculations on the AuCu tetragonal superlattice are submitted. Conclusions drawn from these should be applicable in large degree to disordered solid solutions. As in all ordered states, bonding distances in the superlattice are individually known, rather than being merely average distances as found from lattice constants of disordered states. Moreover, only the Au-Au and Cu-Cu distances are strained; the elastic constants of these are known in the elementary state. In the usual calculation it is necessary to assume elastic constants for Au-Cu bonds. Misfit energy has thus been calculable without the need of many simplifying assumptions usually made. It is still assumed that equilibrium bond lengths and elastic properties of the bonds are the same in the alloy as in the pure metals. As previously discussed, this is probably not correct. Also assumed is that the bonds are not affected by strain of neighboring bonds. A calculation of Young's modulus from compressibility data shows this to be far from true; extensive electronic rearrangements take place. It would seem that misfit energy cannot be calculated from elasticity data for the elements. The usual methods may, however, give an upper limit which is often much higher than the true value. The question of electronic rearrangement is, of course, a complex one. Pauling's theory gives a simple, approximate treatment of the relation between type of bond and bond distance. This has been applied with some success to the Au-Cu system, as will be shown in a later section. Misfit Energy in Au-Cu Alloys Hume-Rothery and Raynor6 discuss the Au-CU system as a type example of strain energy. The gold atom is 12.8 pct larger in diameter than the copper atom, near the size factor limit beyond which solid solubility is severely restricted. They therefore consider the misfit energy to be large, a conclusion for which they believe they find evidence in the phase diagram. Gold and copper are completely miscible in the solid state, but the alloy has a minimum melting point at an intermediate composition. From this Hume-Rothery and Raynor conclude that the strain energy is nearly large enough to prevent miscibility; the phase diagram tends toward a eutec-tic type. In Ag-Cu, which has almost identical size relationships, solid miscibility is quite limited; whereas in Au-Ag, where atomic sizes are nearly the same, there is complete miscibility without a minimum in the melting point. From their arguments the heat of formation of Au-Cu would be expected to be endothermic or only slightly exothermic, that of Ag-Cu to be endothermic, and that of Au-Ag to be exothermic. Deviations, from Ve-gard's law of additivity of atomic radii support these conclusions, since Au-Cu and Ag-Cu both have pronounced positive deviations, and Au-Ag has a negative deviation. Nevertheless, Au-Cu alloys form exothermically; indeed, considerably more exothermically than Au-Ag, Table I. Hence, strain energy must be much less important in this case than Hume-Rothery and Raynor have supposed.

Jan 1, 1958

By P. L. Allsman

Butte mining district contains extensive manganese vein deposits forming a peripheral zone. Oxidation in the veins studied usually extends to a depth of about 75 ft. Secondary minerals formed by oxidation were found to be ramsdellite—always accompanied by intermixed pyrolusite—and cryptomelane. Enrichment of the gossan is accomplished by reduction of weight upon oxidation; theoretical enrichment is 32.2 pct. Additional enrichment is caused by leaching of soluble minerals, particularly calcium and magnesium carbonates. BUTTE mining district contains extensive manganese vein deposits in the outer zone, surrounding the copper and zinc deposits and corresponding to the well known silver zone. This article describes the mineralogy of the manganese veins, the oxidation and enrichment processes, and the use of this information in prospecting. Information was derived from a study of the Emma, Star West, Tzarena, and Norwich mines, selected as representative of the district. Vein exposures at these mines were mapped, studied, and sampled on the outcrops and throughout the oxidized zone. Specimens were cut and polished for minera-graphic examination, identification, and textural studies. Knowledge of the manganese oxide minerals is scanty, previous information having been rendered obsolete by publication of the first correctly identified list of manganese oxide minerals by Fleischer and Richmond in 1943. Positive identification of the manganese oxides is possible only by X-ray analysis. Identifications for this study were made by the author with a Phillip's Diffractometer at the Montana School of Mines and confirmed by Lester Zeihen of The Anaconda Co., using a Norelco X-ray camera. It was necessiary to re-evaluate some X-ray data, as published patterns of several manganese oxides proved to be of mixtures, mostly showing pyrolusite as a contaminant. Perhaps the most useful information on oxidation and enrichment of manganese is presented in recent books by Goldschmidt1 and Rankama and Sahama.2 While their hypotheses are not conclusively proved, all laboratory and field evidence has served to substantiate them. This information was very useful in this study. Mineralogy: The primary minerals of the manganese veins are chiefly rhodochrosite and quartz. Rhodonite is abundant in the northern part of the district and in places has been found to comprise over a third of the vein matter. A variable but generally small amount of sulfides may be present, principally pyrite and silver minerals. Sphalerite is progressively more abundant near the zinc zone. Rhodochrosite is believed to form complete iso-morphous series with siderite, ankerite, and calcite. Some variation into these compositions is common, and the intermediate forms are termed manganosid-erite, manganankerite, and rnanganocalcite. Much of the rhodochrosite is remarkably pure. Other manganese minerals in the district include huebner-ite, alabandite, and helvite. Ramsdellite (MnO2, orthorhnmbic) is the principal manganese oxide mineral, comprising perhaps two-thirds of the total oxides. It is dull to iron black, and generally massive or platy in structure. A prominent platy cleavage is the only distinguishing megascopic characteristic. Pyrolusite (MnO2, tetragonal) is next most abundant to ramsdellite, with which it is usually intimately mixed. The luster is often brighter or more metallic than in ramsdellite, and needle-like crystals are diagnostic. Pyrolusite is common in small cavities formed by oxidation of pyrite grains. It is relatively abundant in zones of high limonite content. Cryptomelane (KMnO16 tetragonal ?) is rare in the outcrop, but becomes more abundant with depth. At depths of several hundred feet it is the principal oxide. Although its appearance varies, a blue-black flinty luster and blocky to conchoidal fracture are most common. A potassium flame test will identify this mineral. Hardness of all three oxides varies from 2 to 6. The three are quite commonly intermixed, and their textures can vary greatly. The commonest textures are massive or colloform, representative of colloidal deposition, or vuggy and boxwork textures, formed by partial leaching and oxidation in place. A box-work of either ramsdellite or chalcedony is formed after rhodochrosite rhombs and is indicative of ore shoots in this district. Some replacement of both quartz and the granitic wallrock by ramsdellite has been noted, but most of the oxide was deposited as a fissure filling by fine particles. No trace of manganite, hausmannite, braunite, or manganosite was found. No minerals of the psilome-lane group were detected besides cryptomelane. Amorphous MnO, was found at several spots. A specimen of oxide coated with yellow barite crystals was amorphous and not psilomelane (BaMn9O18. 2H2O). Voids formed by the leaching of sphalerite were coated with cryptomelane, not hetaerolite (ZnMn2O4) as might be expected. No manganese sulfate minerals were found in the gossans; however manganese alum (apjohnite ?) has been re-

Jan 1, 1957

By D. L. Feucht, R. L. Longini

The semiconductor heterojunction is considered in terms of simple models which may lead to an understanding of move complex heterojunctions. Metallurgical and electrical properties of hetero-junctions aye discussed including the interface structure, energy -band diagram, and carrier transbovt across the interface. It is found that in a heterojunction all mechanisms such as injection, tunneling, and junction recombination found in simple junctions play modified voles. INTERFACES between materials (grain boundaries, the electrical junction between two differently doped materials in a single crystal, the oxide-metal interface, or metal-metal junctions) are of considerable importance in many situations. These various interfaces all have one very fundamental thing in common. Quantum mechanically speaking, the wave functions of the electrons in one material may penetrate the other material but, in general, only to the extent of angstroms. From an electrical point of view the conduction mechanism changes as a current passes through such junctions. In some cases the change is tremendous, in others almost negligible. The interface, then, is the locus of a change of conduction mechanisms. Some of these, particularly in semiconductors, are well-understood. The ordinary p-n junction in a single crystal can be the locus of an injection mechanism or a tunneling process, depending on conditions. The mechanisms are probably best understood in semiconductors because of the possible simplified view of particlelike conduction. The bands are either nearly filled or nearly empty and band overlap is seldom involved. The same fundamentals are probably important in other situations too but they are very difficult to look at naively. Although the simple look at the semiconductor case only gives us a relatively rough picture which must then be refined, the other systems, which involve a more complex situation, immediately are in many ways too difficult. There are too many initial choices of complex systems and therefore it is not possible to be even reasonably certain of any one model. Because of the relative simplicity of semiconductors, their good and controllable structure, and because of the ability to make many measurements on them not normally available to either metals or insulators! they are probably the best understood materials. It is therefore desirable to use them as a tool to further the understanding of interfaces in general. Semiconductor-heterojunction concepts were first proposed by kroemer1 in 1957. This was followed several years later by reports on the fabrication and experimental characteristics of heterojunction structures by Anderson2 and Diedrich and jotten.3 I) THE HETEROJUNCTION STRUCTURE To get down to hardware, when we refer to a semiconductor heterojunction we imply that there exists an intimate contact between different semiconductor materials. We could put two pieces of material together, complete with oxide layers, we could remove the oxides, or we could even melt the interface and hopefully get wetting and a good "bond" on solidifying. In fact we could by some means grow a crystal of one material using the other as a seed. Essentially we are interested only in the last two because they are the simplest to look at analytically. The degree of perfection of fit varies greatly and is reflected somewhat in the arc welder's joint strength. The lattice match of the two materials, their orientation, and so forth. is obviously necessary for a good bond but so is the continuity of any polar bonds which are involved such as in the III-V semiconductors. The mechanical misfit between two similar lattices can be described in terms of edge dislocations. The edge-type dislocations must be very close together for the usual misfit and there must be dislocations for each of several different Burger's vectors in order to produce a lattice match. The .'dangling bonds'' resulting will be involved in producing interface charge. Order of magnitude estimates of the charge density extrapolated from low densities of dislocations in homogeneous materials give 5 x 1013 cm-2 Ge-Si and 1 X 1012 cm-2 Ge-GaAs electronic charges. Edge dislocations also act as very active recombination centers between holes and electrons. One lattice "matching" difficulty usually exists even if two structures have essentially the same lattice constants as they will have different coefficients of therma1 expansion. Thus, on cooling from the usually high temperature of fabrication to room temperature, dislocations are produced, a good fit not existing at both temperatures. In brittle materials this shrinkage may even result in cracking. For the Ge-Si interface the mismatch is about 2 x 10 -6 per degree whereas it is less than 10"7 per degree between germanium and GaAs. The exact effect of the misfit is dependent on the thickness of the materials involved. For a very

Jan 1, 1965

By G. W. Thomas

A mathematical tnodel of forward combustion in an oil reservoir is treated in this paper. The model describes a radial system having a vertical section of essentially infinite thickness, all of which is permeable to gas flow. Combustion, however, is presumed initiated over a limited thickness of the total vertical section. In the interval supporting cotnbustion, the mechanisms of radial conduction, convection and heat generation are taken into account. Above and below the burning interval, heat transport in the radial direction is by cottduction and convection. Vertical heat losses from the ignited interval are accounted for by conduction alone. A general solution is presented for the temperature distribution caused by radial movement of the combustion front. The results show that no feedback of heat occurs into the ignited interval when convection and conduction are acting in the bounding media. Peak temperatures are also 5 to 10 per cent higher than in the case where heat transport in the bounding media is by conduction alone. We arbitrarily define vertical coverage to be that fraction of the total ignited interval which is at 600F above atnbient, or greater, at any given time. The radial distance at which the vertical coverage becomes zero is the propagation range of the combustion front. It was found that an increase in vertical coverage results when the oxygen concentration, fuel concentration or gas-injection rate is increased. Moreover, the combustion front can be propagated 10 to 15 per cent further than in the case where only conduction is acting above and below the ignited interval. INTRODUCTION In the theoretical treatment of forward combustion in a radial system, one of the problems encountered is the determination of the transient temperature distributions caused by an expanding cylindrical heat source. Bailey and Larkin' and Ramey' simultaneously presented analytical solutions to the problem assuming heat transport by conduction alone. In a subsequent publication, Bailey and Larkin3 included the effects of both conduction and convection while treating linear and radial models. In this latter work, however, vertical heat losses were largely neglected. Selig and Couch' dealt with a radial model in which both conduction and convection were acting. Only a limiting case involving vertical heat losses was considered, however. Namely, temperatures on the boundary of the bed of interest were set equal to zero. Solutions thus obtained were representative of a system having a maximum vertical heat flux. Chu5 recently treated a more general case in which a permeable bed was considered bounded by impermeable media. Conduction and convection took place within the bed, and only conduction outside of the bed. The effects of vertical heat losses were included in his study. Solutions were obtained by numerical techniques. This paper is an extension of the theoretical work of other authors pertaining to forward combustion in a radial system. In particular, a mathematical model of the process is treated in which heat generation occurs over a small vertical interval of a larger permeable section. In the interval supporting heat generation, and above and below this interval, the mechanisms of radial conduction and convection are also presumed acting. Heat losses from the ignited interval are accounted for by vertical conduction. An analytical solution for the temperature distribution caused by radial movement of the burning front is presented. The effects of certain process variables are indicated and comparisons with Chu's results are made. THEORY To render the mechanism of forward combustion tractable to mathematical treatment, we idealize the problem to the extent of assuming continuous reservoir media possessing homogeneous and isotropic properties. The following additional assumptions are implicit in this analysis. 1. The thermal parameters, i.e., heat capacities, thermal conductivities and thermal diffusivities are invariant with temperature and pressure. Moreover, the bounding media possess the same thermal properties as the bed of interest. 2. The temperatures of the porous media and its contained fluids at any point and at any time are equal. 3. The reaction rate between the oxidant gas and the fuel is infinite. This assumption implies that the incoming oxygen concentration instantaneously goes to zero within an infinitesimal distance, i.e., the width of the combustion zone is negligible. 4. The rate of gas injection is constant and corresponds to the average rate throughout the lifetime of the project. 5. The fuel concentration is constant throughout the volume of rock swept out by the burning zone. 6. There is complete burnoff of fuel. This assumption demands that the rate of propagation of the burning front equals the rate of fuel burnoff. In a radial system, with a

By W. C. Hauber

Techniques previously published to predict the production performance of a water flood when the mobility ratio is not unity have been primarily restricted to a five-spot well pattern. When other types of well patterns are considered, the prediction of performance has required either a model study or a complex numerical solution of a multiple-fluid system with a high-speed digital computer. Simple methods are developed in this report for predicting the areal sweep efficiency and injectivity history of a water flood for arbitrary well patterns and mobility ratios. The effect of an initial gas saturation can be incorporated into this method of prediction. With the layer superposition concepts published by Prats, et al.,1 these methods can be used to predict the production performance of a water flood in a reservoir having a wide range in permeability. A reasonably good agreement is shown by comparisons of the results calculated by this method with those obtained either by model studies or by complex numerical solution of multiple-fluid systems. Therefore, it has been concluded that a reasonably accurate method has been developed for predicting the production performance of a water flood employing an arbitrary type of well pattern for any given mobility ratio. A medium-speed digital computer can be used in applying this method. INTRODUCTION Production performance of multi-fluid five-spot water floods can be predicted by the techniques published by Prats, et al.1 This technique takes into account the effects of initial gas saturation, mobility ratio and vertical variations in horizontal permeability. A basic assumption in applying this technique is that unit displacement efficiency does not vary with time after the passage of the flood front. Prats, et al. demonstrated that this assumption is valid for normal waterflood applications with small mobility ratios. To extend Prats' technique to other types of well patterns has required either an experimental model study or a numerical solution of a multiple-fluid system to describe the performance of an individual homogeneous layer. Sheldon and Dougherty2 presented an exact numerical solution employing any arbitrary well pattern. This technique is complex to apply, requiring (1) numerical solution of the single-fluid system, (2) conformal mapping of the streamlines and iso-potential lines to form a new grid network, and (3) a numerical solution of the multi-fluid system on the new grid network. A method was developed in this paper to approximate areal sweep efficiency and injectivity as functions of time for an individual homogeneous layer for arbitrary well patterns and mobility ratios. Analytic expressions were derived to directly apply this method to five-spot and direct line drive well patterns. For other types of well patterns, this method is similar to the approach of Higgids and Leighton,6 in that it utilizes the stream tubes and iso-potential lines obtained by the solution of differential equations when the mobility ratio is unity. However, this method is easier to apply than the Higgins-Leighton method since it does not require knowledge of the variation between oil and water relative permeabilities and saturation. Using the relationship between areal sweep efficiency, injectivity and the volume of water injected into an individual homogeneous layer as obtained by the method presented in this paper, and Prats' technique for the superposition of individual layers, one can predict the production performance of any water flood. ASSUMPTIONS GENERAL Basic assumptions made in this report are that fluids are incompressible and the layers are horizontal, homogeneous and uniformly thick. It is assumed that as water is injected into the layer, three distinct regions are formed —a water bank, an oil bank, and an unflooded region. Each region is assumed to displace other regions in a pis-tonlike manner, with only one fluid flowing in each region, so that there is no change in unit displacement efficiency with time after the flood front has passed in the reservoir. Therefore, the residual oil saturation in the water bank and the oil saturations in the unflooded region are constant throughout the layer. The ratio (F) of the bulk volume of a layer occupied by the oil and water banks at any time before oil breakthrough, to the corresponding bulk volume of a layer occupied by the water bank, is given' by the equation BREAKTHROUGH AREAL SWEEP EFFICIENCY To predict the behavior of any type of waterflood pattern, one must know the breakthrough areal sweep efficiency Eb(Mc,o, F) for the pattern for any water:oil mo-

Jan 1, 1965

By E. A. Swedenborg

The unit agreement for the Wertz Dome field, Wyoming, was approved by the Acting Secretary of the United States Department of the Interior on November 4, 1937, effective on December 1, 1937. The stated objectives of the agreement are to conserve and put to beneficial use all oil and gas produced; to make possible a uniform withdrawal of oil and gas in order to maintain equalized reservoir pressures; to provide for an orderly determination of the structural features of the productive horizons; and to permit the injection of gas for pressure maintenance. The purpose of this paper is to show by a discussion of the problems involved and the engineering practices employed by the unit operator, how well the objectives of the unit agreement have been accomplished in the development and production of oil and gas from the field. HISTORY AND DEVELOPMENT The Wertz Dome oil and gas field is located 88 miles southwest of Casper and 38 miles north and westerly from Rawlins, Wyoming. It is served by a state secondary oiled road connecting with U. S. Highway No. 220 at Lamont, a distance of 3 miles from the field. It has been a producing field for 27 years, first as an important producer of gas and more recently of oil. The Producers and Refiners Corp. completed Well No. 1, NE1/4SW1/4 sec. 7, T. 26 N., R. 89 W., the first productive well in the field, in September. 1921, in the Muddy sandstone of Upper Cretaceous age, at a depth of 3435 feet for an initial production of 42,000,000 cu. ft. of gas per day. In 1922 pipe lines were laid to Casper, Wyoming, for supplying fuel to the Standard of Indiana refinery, 'the adjoining town of Mills. and the Producers and Refiners Corp. pump station No. 6 in Mills; and to Parco (now Sinclair), Wyoming, for supplying that refinery with fuel. The gasoline content of the gas was extracted in an absorption plant located near the town of Mills. No compressors were used as the line pressure was sufficiently high to flow the gas through the absorbers. As high as 30,000,000 cu. ft. of gas per day were treated in the plant extracting 6000 gallons of gasoline. In September 1937, the pipe line was discontinued and the plant was dismantled at which time 61,000,000,000 cu. ft. of gas had been produced from the seven Muddy, Cloverly, and Sundance gas wells drilled in the field. Of this volume of gas 800,000,000 cu. ft. were produced from the Frontier formation, 34,200,000,000 cu. ft. from the Muddy sandstone, 24,000,000,000 cu. ft. from the Cloverly, locally called Dakota, and 2,000,000,000 cu. ft. from the Sundance formation. The pipe line was discontinued because of the near depletion of the gas reserves in Wertz and nearby fields, and hecause of the local field requirements demanding the retention of the remaining gas reserves. In December 1936, the Sinclair Wyoming Oil Co. completed Well No. 10, SE1/4NW1/4 sec. 7. T. 26 N., R. 89 W., at a depth of 5886 feet. as the first Tensleep sand producer with an intial of 1700 barrels of oil per day. The well was originally drilled only 14 feet into the sand and in August 1939 was deepened to a depth of 6161 feet, 289 feet in the sand, and the daily produe tion increased to 8350 barrels of oil. In February 1948 Well No. 22, SE1/4 SE1/4 sec. 1. T. 26 N., R. 90 W., was deepened from the Tensleep to the Basal Amsden sand and completed at a depth of 6635 feet for an intial of 600 barrels of oil per day in the Basal Amsden. In April 1948, Well No. 2. SW1/4 NE1/4 sec. 1, T. 26 N., R. 90 W.. was deepened from the Tensleep to the Madison limestone and was completed at a depth of 7193 feet for an intial of 1145 barrels of oil per day in the Madison. Well No. 26, SE1/4SE1/4 sec. 1, T. 26 N.. R. 90 W., was deepened from the Ten-sleep to the Cambrian and in October 1948 it was completed in the Cambrian for an intial of 277 barrels of oil per day. GEOLOGY AND PRODUCTIVE ACREAGE The surface is Steele shale of Upper Cretaceous age, covered in part by gravel beds. The topography of the field is that of a rolling hill with a steep draw or gulch along the northern edge of the field. The Steele shale lies conformably on the lower formations as

Jan 1, 1949