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By C. W. Sherman, N. J. Grant

The correlation of the high temperature chemical properties of slag-metal systems with some easily measured property of either slag or metal at room temperature has been the goal of both process metallurgists and melting operators for many years. There are several rapid methods for estimating various constituents in steel in addition to the conventional chemical methods which are quite fast, but these do not reveal the nature of the slag as a refining agent, which is of primary interest to the steelmaker. Furthermore, there are several methods for examining slag, the three principal ones being slag pancake, petrographic examination, and the previously mentioned chemical analysis. The main objection to the last two is the lime required to make a satisfactory estimate of the mineralogical or chemical components. The objection to the first is the inadequacy of the information obtained. A new technique has been developed by Philbrook, Jolly and Henry1 whereby the properties of slags are evaluated from an aqueous solution leached from a finely divided sample of slag. It is known that the pH or hydrogen ion concentration (of saturated solutions that have dissolved certain basic oxides, notably calcium oxide) will indicate a pronounced basicity. Philbrook, Jolly and Henry devised the pH measurement technique in order to supply open hearth operators with a fast, reasonably accurate method of estimating slag basicity. They offered the method as an empirical observation and made no claims as to its theoretical justification. The results were presented as an experi-metally observed relationship which applied over an important range of basic open hearth slags. They found that, in plotting the measured pH against the basicity, the best relationship existed between the pH and the log of the simple V ratio, CaO/SiO2. Extensive investigation also showed that there were several variables in the experimental technique that influenced the results and necessitated following a standard procedure to obtain reproducible pH readings. These variables were: 1. Particle size of the slag powder used. 2. Weight of sample used per given volume of water. 3. Time of shaking and standing allowed before the pH was measured. 4. Exclusion of free access of atmospheric carbon dioxide to the suspension. 5. Temperature of the extract at the time the pH was measured. In subsequent investigations of the pH method by Tenenbaum and Brown2 and by Smith, Monaghan and Hay3 the general conclusions of Philbrook's work were reaffirmed. It was the object of the present investigation to extend the technique to a point where it could be used to evaluate slags of all types. Experimental Results PARTICLE SIZK OF SLAG POWDER A large sample of commercial blast furnace slag of intermediate basicity (V-ratio 1.15) was selected for the study. The slag had been put through a jaw crusher until all of it passed through a 20 mesh screen. Five fractions of this crushed material were separated, -20 to +40, -40 to +60, -60 to +100, -100 to +200, and -200 mesh. A representative sample of 0.5 g was removed from each fraction and the pH determined using the method of Philbrook. Check pH analyses on the sample fractions varied due to the different amounts of shaking. To eliminate this variable, a mechanical shaker was employed. In order to know the exact time of contact between the slag and water, it was found necessary to filter the extract at the end of the shaking period. Using the mechanical shaker and a filtering apparatus, similar runs were made on the five fractions for contact times of 5, 10, 20, and 40 min. Random checks gave reproducible results within 0.02 pH. The data are plotted in Fig 1. It can be seen from the plot that each slag fraction is hydrolyzed to an extent that is roughly proportional to the surface area exposed to the water. The (—100 to +200) mesh material changed very little in pH after 10 min. shaking time. The curves are symmetrical and lie in proper relation to one another. The —200 mesh curve appears to be somewhat flatter than the others, but this can be attributed to the portion of very fine material that is not present in the other fractions. The closeness of the (-100 to +200) mesh curve to the —200 mesh curve and the fact that a —100 mesh sample would contain amounts of slag down to 1 or 2 microns in diam were considered sufficient reasons for selecting a —100 mesh sample as representative of the whole sample of slag for the purposes of this investigation.

Jan 1, 1950

By W. H. Smith

IN connection with some recent work on the effect of impurities on the ductility of chromium, it appeared desirable to know the solid solubility of carbon in chromium. A literature survey indicated that this information was not available. Although considerable work has been done on the Cr-C phase diagram,&apos;.&apos; previous investigators have been more concerned with the structure and phase boundaries of the carbide phases than with the terminal solid solution. The phase diagram shown in Fig. 1 is taken from the work of Bloom and Grant&apos; and represents the most recent determination. As indicated by the dashed line, the a solid-solubility limit was not determined. Experimental Procedure Alloys of chromium were prepared from hydrogen-treated and vacuum-degassed electrolytic chromium plus spectrographic grade carbon. The oxygen and nitrogen content of the alloys was <0.002 pct. After melting, analysis of the alloys showed them to contain 0.02, 0.08, 0.15, and 0.55 pct C. Pieces of the alloys were heated in a protective atmosphere to various temperatures and then quenched after holding for a time sufficient to insure equilibrium. Microscopic examination of the as-quenched alloys for the presence of a second phase was used as a measure of the solubility limit. The heats were made in a multiple hearth arc-furnace using a zirconium-gettered static argon atmosphere. A zirconium melt was made before each Cr-C heat. Triple melting was used to insure ingot homogeneity as shown by microscopic examination. The alloys were prepared by adding portions of a 4.5 pct C-Cr master alloy to high purity chromium. The carbon contents listed previously were those obtained by analysis. The nitrogen and oxygen contents after arc melting were both <0.002 pct. Sections 1/8X1/4X1/2 in. were cut from the 100-g ingots and a hole drilled in one end in order to suspend the sample from a molybdenum wire. After the surface was carefully cleaned, a sample of each melt was hung in a mullite tube heated externally by a platinum resistance furnace connected to a vacuum system. The lower portion of the mullite tube was sealed to Pyrex and closed off several inches below the furnace. This was filled with sili-cone oil kept cold by circulating cold water around the outside of the Pyrex. Quenching into the oil bath was achieved by melting a fuse wire supporting the sample. It required about 4 sec for the sample to cool from 1400" to 600°C. This severity of quench was considered satisfactory to freeze-in the high temperature equilibrium. For tests made at temperatures of 900" to 1200°C, heating was done in vacuum; for tests above 1200°C, an argon atmosphere was used. The holding time employed ranged from 12 hr at 900°C to 6 hr at 1400°C. Experiments were performed at temperatures of 900°, 1000°, 1100°, 1200°, 1300°, and 1400°C. Microscopic examination for evidence of a second phase was done at X1500. Experimental Result The microstructures of a 0.08 pct C-Cr alloy as-cast and after quenching from 1300°C are shown in Figs. 2 and 3. A 0.15 pct C-Cr alloy quenched from 1300°C is shown in Fig. 4. The data obtained from the quenching experiments is shown graphically in Fig. 5. If the Van&apos;t Hoff equation is obeyed, a plot on a logarithmic scale of the mol fraction of solute vs the reciprocal of the absolute temperature should give a straight line. For dilute solutions the weight percentage can be substituted for the mol fraction without introducing any appreciable error. The Van&apos;t Hoff equation can then be written as where H is the heat of solution in calories per mol. The slope of the straight line on the log pct C vs 1/T plot gives the value of AH. Assuming that the Van&apos;t Hoff equation is obeyed, which is probably justified for the dilute solution of carbon in chromium, the heavy straight line shown on Fig. 5 represents the best fit of the data. This line was obtained as follows. On Fig. 5 the results of the microscopic examination of all alloys following quenching were plotted and designated as to whether one or two phases were seen. Below 1100°C all alloys showed a second phase on quenching. The heavy vertical lines shown in Fig. 5 therefore represent the possible range of the ter-

Jan 1, 1958

By B. C. Mariacher

EXTRACTION of uranium from ores is being ac-complished by processes which. for the most part, subject the entire ore to acid or carbonate leaching. Ore deposits with a U 3 O 8 content below 0.10 pct U 3 O 8 are seldom considered suitable for treatment by leaching. A preliminary concentration that would enrich the uranium content of an ore by a simple, low cost process based on physical properties of the ore might result in some low grade deposits becoming commercial ores. In addition, the process might be employed in existing operations to reduce transportation and leaching costs and to increase capacity of existing leaching plants. A study to attempt the development of a preliminary concentration process for primary uranium ores was undertaken by the Colorado School of Mines Research Foundation under sponsorship of the U.S. Atomic Energy Commission. The objective of this work was to produce concentrates containing 0.25 pct U3O8 from the low grade ores tested. Ores Tested: The main effort was devoted to the low grade primary uranium ores from northwestern Saskatchewan. Samples were obtained from the Beaverlodge operation of the Eldorado Mining & Refining Ltd. Additional primary ores, obtained from deposits in Gilpin County, Colo., contained from 0.07 to 0.10 pct U3O8. Summary of Concentration Tests: The Beaverlodge ore was tested to determine amenability of the ore to concentration by magnetic, electrostatic, gravity, and scrubbing processes. None of these produced satisfactory results. Both gravity and magnetic processes produced fairly good concentrates when closely sized fractions of the ore were treated, but on the basis of treating the total ore, recovery was poor. Preparation of sized fractions and the low capacity of equipment for suitable concentration made these methods impractical. As flotation offered the advantage of treating the total ore without intermediate sizing, the main effort was in this direction. A flotation process was developed that fulfilled the concentration objectives as set by the AEC. Pilot plant testing was used to verify results obtained from laboratory batch testing. Mineralogy: A petrographic examination of the Beaverlodge ore included a study of polished sur- faces and identification of the radioactive mineral by autoradiograph and X-ray diffraction. Approximate quantitative mineral identification was as follows: quartz, 60 pct; orthoclase feldspar, 20 pct; chlorite, 10 pct; carbonates, 5 pct; and miscellaneous minerals, 5 pct. Included in this last group were plagioclase feldspar, pyrite, mica, chalcopyrite, pyroxene, sericite, magnetite, galena, and uraninite. The most general occurrence of uraninite was in the form of crusts and thin coatings on limonite-stained grains of pyrite, quartz, and pyrite-quartz intergrowth. At least 90 pct of the uraninite was still attached to other minerals in a 100 by 200-mesh size fraction. The uraninite crusts were as small as 10 to 20 µ diam, and 5 to 10 µ thick. The Flotation Process Petrographic examinations of the Beaverlodge ore had indicated the impracticability of attempting to concentrate the uranium by floating individual grains of uraninite. Liberation of the uraninite required grinding to sizes below those suitable for flotation. However, there was preferential association of the uraninite with some minerals while others were free of uraninite attachment. The approach to the development of a flotation process was, therefore, based upon an attempt to concentrate the uraninite by floating carrier minerals. The following paragraphs discuss the various stages of the process with regard to the factors tested and the conditions under which best results were obtained. Grinding: The most effective size range for flotation was —150 mesh + 13 µ. The —13 µ material in the final concentrate had a higher U3O8 content than the total ore, but not as high as the average concentrate; however, rejection of slimes before flotation was prohibitive because of the loss in uranium carried in the —13 µ fraction. Grinding techniques which contributed to a minimum production of fines, such as stage grinding, were then employed. Quartz and Silicate Depression: These minerals represented approximately 80 pct of the ore and were free to a large degree of uraninite attachment. Significant improvement in the grade of the concentrate was obtained by depression of these minerals with hydrofluoric acid or sodium fluoride. Promoter: Selective stage flotation of uraninite carrier minerals was simplified by development of a single promoter mixture. The mixture consisted of an emulsion of a fatty acid, fuel oil, and a petroleum sulfonate and was selected after a comprehensive series of tests. It contained three parts by weight of an oleic and linoleic acid such as Emersol 300,

Jan 1, 1957

The pressure of the gas in equilibrium with sphalerite has been determined in the temperature range of 680&apos; to 825°C, using the Knudsen orifice method. A comparison of these experimental pressures with those calculated from thermal data and from other equilibrium measurements shows that the vapor above sphalerite is predominantly dissociated ZnS. Equations have been given for correctly calculating dissociation pressures using the Knudsen orifice method. It has been shown that the experimentally determined pressure is the same, whether the zinc sulphide is sphalerite or not, or a mixture of wurtzite and sphalerite. CONFLICTING points of view appear in the literature on the constitution of the vapor in equilibrium with solid zinc sulphide in the vicinity of 800°C. By comparing the dissociation pressure calculated from thermodynamic data and the vapor-pressure determination of ZnS by Veselovski,1 Lumsden2 has concluded that the vapor consists largely of dissociated ZnS. Sen Gupta,&apos; however, concludes from his spectroscopic determinations that the vapor is largely ZnS molecules. In view of the fact that the thermodynamically calculated&apos; dissociation pressure is higher than that experimentally measured by Veselovski, it seemed in order to repeat Veselovski&apos;s measurements. Experimental Procedure The method used for the determination of the pressures in this papel- is the Knudsen effusion cell. The apparatus and procedure were described in a previous paper- from this laboratory on the determination of the vapor pressure of silver. The only difference is that the Knudsen cell in this work is made from platinum and there is no external cover around the cell. The cell is an ordinary platinum crucible of 2.2 cm top diameter with a capsule cover. It was thought that platinum might stand up at these temperatures to the solid and gaseous ZnS, since it was found that the weight of the platinum cell itself did not change appreciably on heating ZnS in it at the working temperatures. To insure that reaction of the zinc sulphide with the cell was not giving&apos; a false value, a stabilized zirconia cell was employed for check runs. Fig. 1 shows the comparison, which is satisfactory. Veselovski previously had measured the vapor pressure of ZnS using a silica Knudsen effusion cell. On repeating his experiment in this laboratory, it was found that ZnS at-tacked the silica cell, giving it a marked frosty appearance. This led to the belief that Veselovski&apos;s result:; may be in error. Also, he was operating at pressures above the range ordinarily considered safe for the Knudsen method. The effusion rate was measured by weighing the cell before and after each run. The weight loss during heating to temperature and cooling down was measured and subtracted from the weight loss during the actual run. The zinc sulphide used in this investigation was from two sources: Fisher cp grade, and a sample of pure sphalerite supplied by Mr. E. A. Anderson of the New Jersey Zinc Co. Before and after the series of runs with Fisher ZnS, X-ray analysis showed that both wurtzite and sphalerite were present. However, the ratio of sphalerite to wurtzite increased. All measurements were made below the transition temperature which has been reported" to be 1020°C. The data obtained in this investigation are tabulated in Table I. The pressure was calculated by the usual Knudsen formula" on the assumption that ZnS molecules were effusing. From these data, using pure sphalerite in the platinum Knudsen cell, the vapor pressure of ZnS, in mm of Hg, as a function of temperature is given by the solid line in Fig. 1. The best straight line, as determined by the method of least squares, is given by 14405 logpzns =-14405/T +11.032. A comparison of these results with Veselovski&apos;s shows that his results are about 50 pct lower. Discussion The vapor in equilibrium with solid zinc sulphide in the temperature range of this study will consist of Zn, S2, and ZnS mol, since other species of zinc and sulphur&apos; are relatively unstable. The question to be settled is whether or not ZnS is largely dissociated. The derivation8 which follows gives the method of calculating the pressure of zinc and sulphur over solid ZnS, assuming complete dissociation, from Knudsen cell data. The free energy of the reaction 2 ZnS(solid) ? 2 Zn(gas) + S2(gas) is given by ?F?° = -RT In K = —RT In p12p2 where p1 is the zinc pressure and p is the sulphur pressure. If dissociation occurs in a closed system,

Jan 1, 1955

By M. G. Benz, J. F. Elliott

The austenite solidus of the iron-carbon system has been determined using a series of diffusion couples, each of which consisted of a specimen of austenite held in contact with a melt saturated with austenite. After the equilibrium distribution of carbon had been established by diffusion at a specified temperature, i.e. the austenite specimen had become austenite of the solidus conzposition, the diffusion couple was cooled, sectioned and anazlyzed for carbon. The solidus was found to be a straight line: A revised iron-carbon temperature-composition diagram is presented, COMPOSITION has a marked effect on the temperature at which austenite begins to melt and the austenite solidus of the iron-carbon system describing this effect has been the subject of many investigations.1-10 The significant results of these investigations are presented in Fig. 1. The experimental methods and purity of the materials used in them are summarized in Table I. In plotting the data in Fig. 1 no attempt has been made to convert these results to the International Temperature Scale of 1948," except for the data of Adcock,5 as this conversion would do little to reduce the uncertainty that exists as to the position and shape of the solidus. A point of major concern in evaluating these data is that the alloys studied, except those used by Adcock, were not binary alloys of iron and carbon, Table I. Also, it would appear that several of the methods did not permit equilibrium to be established through the system being studied. All that can be said for the results of these investigations is that they indicate only approximately the location of the solidus with the uncertainty as to its location at 1 pct C being approximately 100°C. The current investigation was undertaken to provide reliable data by which the austenite solidus could be established. It was hoped that information on the liquidus also could be developed at the same time, but experimental limitations prevented this as austenite segregated from the liquid on cooling. After a careful study of possible experimental methods and extensive laboratory tests, it was decided that the use of a series of austenite-liquid diffusion couples would provide the most reliable results. This paper describes the method and its results and also includes a complete iron-carbon temperature-composition diagram based on what are considered to be the best available data. EXPERTMENTAL METHOD The diffusion couple used for this investigation consisted of a small cylindrical pellet of austenite held in contact, at a specified temperature, with a melt saturated with austenite. The composition of the cylindrical austenite pellet was chosen to be approximately 0.1 wt pct C less than the estimated

Jan 1, 1962

By I. Nilsson, G. Sundkvist, A. Danielsson

A spectrochemical method of slag analysis is descibed which utilizes fusion of the sample with a flux, then cooling and crushing to put all samples into a common form. The powder, is then fed onto adhesive tape and passed through a spark by means of a special device to provide very reproducible discharge conditions. Combined with a direct-reading optical emission instrument, this system provides speed and accuracy of antilysis heretofore unobtainable for. slag samples by any other method. THERE are many suggested methods for spectro-chemical analysis of slags. The most important are fusion-pellet methods and solution methods. In our company the fusion-pellet method has been used earlier, and is described by Lounamaa. W. H. Tingle and C. K. Matocha have made refinements of the pellet method.&apos; A Committee of the British Iron and Steel Research Association has investigated different methods of spectrochemical analysis of slags. Its purpose was to formulate a method which would give the complete analysis in 30 min with an accuracy of ±3 pct. The committee recommends a solution technique, which was thought to correspond best to their requirements. The method to be described is a fusion-tape method. The sample is isoformed by fusion and grinding. The powder is analyzed with the tape technique. The tape machine and some of its applications are described earlier.4&apos;5 The powder to be analyzed is continuously fed onto a moving adhesive tape, which passes through the spark gap. The sparks break through the tape and vaporize and excite the material to be analyzed. The most outstanding feature of the tape machine is its very high reproducibility. The concept of isoformation has been introduced earlier.= It means a pretreatment of the samples to make them uniform from the spectralanalytical point of view, i.e., cancelling systematic differences between the samples. The purpose of the isoformation is to reduce the influence of particle size, as well as chemical and mineral composition. Before describing the isoformation by fusion plus grinding, which is the purpose of this paper, a few words will be said about two other types of isoformations, i.e., grinding with buffer and ion exchange plus grinding as they have been considered during the application of the tape technique for slag analysis. Grinding with buffer might be a sufficient isoformation in some special cases, where the mineral composition is defined. The time of grinding must, however, be rather long, at least 5 to 10 min, even when using such an efficient mill as the Swing Mill from Messrs. Siebtechnik, Mühlheim, Germany. This type of isoformation is not recommended due to its limitations and due to the fact that the gain in time compared with the fusion technique is almost negligible. The principle of ion exchange plus grinding and some of its applications have been described.5 The following elements of interest in slag analysis can be determined in this way: Na, K, Cu, Mg, Ca, Ba, Zn, Pb, Al, Cr, Mn, Fe, Co, Ni. The very important element Si, however, cannot be analyzed with this method. Although the ion exchange isoformation for slag analysis cannot be looked upon as a routine method, it can be used for

Jan 1, 1962

By M. S. Burton, J. E. Ritter

The sessile-drop technique was employed to study the effect of atmosphere and alloy additions of titanium and chromium on the surface tension and contact angle of nickel on sapphire substrates at 1500oC. Shear tests were conducted on the solidified sessile drops. The liquid-gas surface tension of pure nickel on sapphire was found to be 1747 ergs per sq cm, with a contact angle of 109.6 deg. The surface tension and contact angle were not affected significantly by the four atmospheres, vacuum, impure argon, pure argon, and pure hydrogen. Small additions of titanium and chromium decreased the contact angle and for the same alloy content, contact angles were lower in pure argon than in pure hydrogen. On the basis of shear-test results , the most probable cause for adhesion in the Ni-Al2O system is the formation of NiO:Al2O3 spinel at the interface; in the titanium alloy-Al2O3 system adhesion is thought to be due to a mechanical interlocking effect; in the chromium alloy-Al2O3 system adhesion is believed to be the result of solid-solution formation involving Cr2O3 and Al2O3 at the interface. In the last few years there has been considerable interest in reinforcing metals with ceramic whiskers. It has been postulated that, by reinforcing nickel with sapphire whiskers, high-temperature strengths su- perior to those of the best current nickel alloys can be achieved.&apos; To fabricate a whisker-metal composite having optimum density and strength, understanding of wettability and adherence in the system is of prime importance. Although there has been some previous research in this a a need for further studies has been cited4-8 to understand better the effects of impurities, alloys additions, and atmosphere on the wetting and bonding of metals to metal oxides. The purpose of this research was to investigate the factors involved in the wetting and adherence of nickel/nickel alloys to sapphire (single-crystal a Al2O3). Sessile-drop experiments were conducted in vacuum, impure argon, pure argon, and pure hydrogen, to determine the effect of atmosphere on the contact angle of the metals on sapphire, and the liquid-gas surface tension of pure nickel. The solidified sessile drops were sheared from the sapphire substrate to measure the bond strength between the metal and ceramic. The alloy additions chosen were titanium and chromium since both enhance the wetting of nickel on sapphire.2, 3c Also, titanium is commonly used when brazing metal-to-ceramic seals to improve adherence. Since chromium forms an oxide that is completely soluble in sapphire, it was thought that the oxide could serve as a transition phase to promote bonding between the Ni-Cr alloy and sapphire. I) EXPERIMENTAL APPARATUS AND PROCEDURE The sessile-drop apparatus was a horizontal furnace, with an induction-heated, cylindrical molybdenum susceptor in a water-cooled Pyrex chamber. This apparatus was patterned after that of Williams and Nielsen.7 A flat Pyrex window at each end of the furnace allowed temperature measurements to be made at one

Jan 1, 1968

By Morris Muskat, James M. McDowell

A report is given of electrical analog experiments on the effect of casing perforation completions on well productivity for ideal uniform reservoirs under steady state homogeneous fluid flow conditions. Graphical results are presented for the effect of perforations of different densities and various degrees of penetration into the formation surrounding the casing or cement sheath. The latter range from perforations which terminate flush with the casing to those which extend into the formation a distance equal to the casing diameter. For the special case where the perforations terminate immediately beyond the casing with semi-spherical protrusions the electrical analog results correct and supersede previously reported theoretical calculations. It is found that the penetration of the perforations into the surrounding productive section may so increase the resultant productivity as to approach or even exceed that for open hole completions. INTRODUCTION A theoretical analysis of the effect of casing perforation on well completion, without additional penetration of the formation, was reported several years ago.&apos; In this treatment the perforations were represented by mathematical sinks and no explicit account was taken of the imperviousness to flow of the casing in which the perforations were made. This procedure was justified by consideration of the mutual interference between the sinks, which seemed to indicate that the analytical method automatically eliminated flow across the casing radius between the perforations. However, both further theoretical investigation and the electrical analog measurements described below showed that this assumption in the previously developed theory was not valid and that the calculated well capacities would considerably exceed the correct values. § Even if this simplifying assumption were retained the generalization of the theory to situations where the perforations extend into the producing formation would be extremely difficult. On the other hand, the electrolytic model analog of this type of steady-state homogenous fluid system is, in principle, so simple that it has not been worthwhile to attempt to develop the exact analysis even for the more limited case of strict casing perforation. The whole problem has therefore been studied anew by electrical models to cover the range from holes in the casing which terminate flush with the casing surface to such as extend into the surrounding rock to a depth equal to the casing diameter. It is to be expected that the productivity of a well completed with casing radius* rw, perforated with holes of radius Tp, and extending to depths d into the surrounding rock, would depend primarily on the dimensionless geometrical parameters Te Tw TP d of the system, such as —, —, — , and —, where re is the Tw, a a rw external boundary radius and a is the mean vertical separation between the perforations. It will also depend, of course, on the number of perforation lines or total perforation density. While such parameters automatically control analytical treatments, it would require a very extensive series of model experiments to fully disclose their functional effect on the well productivity. For practical purposes, however, a rather limited range of the variables suffices to give the effects of interest. Accordingly, in the experimental study reported here the casing diameter has been kept fixed? at six in., the perforation diameter has been taken as either one-fourth in. or one-half in., their density has been varied from one to eight per ft, and their penetration into the formation has ranged from zero to six in., with a primary scaling factor of one to six. EXPERIMENTAL METHOD AND RESEARCH Although electrolytic model experiments have been made for years, there still seems to be some question as to what set of conditions will give the best results. For this reason a number of electrode materials and electrolytes were tried. Those chosen for the final experiments were copper electrodes and a weak copper sulphate solution as the electrolyte. This &apos;Assuming that the casing has been cemented with a uniform and impermeable cement sheath, the effective casing radius is to be interpreted as the external radius of the cement annulus. It is also assumed here that the casing is set through the complete producing section that it is perforated throughout with a uniform density and that tie formation has a a and isotropic permeability. As noted later, however, a uniform scale change permits reinterpreting the primary measurements to correspond to a casing diameter of 12 in.

Jan 1, 1950

By J. C. Cook

In solution-mining of underground salt and similar minerals, using drilled wells for access, it is desirable to monitor the lateral growth pattern of the resulting fluid-filled cavern. Therefore, a process of seismic surveying from the surface of the ground has been conceived in which the amplitudes of waves reflected from and transmitted through the soluble formation are measured. The large acoustic impedance contrast between solid and fluid should produce striking amplitude anomalies, especially if shear waves are employed, since thick fluid bodies are opaque to shear waves. Horizontally-polarized (SH) shear waves are best for preventing conversion to P waves at the numerous horizontal interfaces in the ground. Field tests to date have shown that a truck-mounted, half-ton hammer striking horizontally against the end of a trench produces usable SH-wave energy at lateral distances up to about 850 ft. Horizontally-directed explosive wave sources were effective to about 2000 ft. Conventional magnetic-tape recording and processing were used, but with the detecting geophones oriented to favor SH waves. An irregular solution cavity in bedded salt at 500-ft depth has apparently been located by SH-wave and SV-wave reflections. Further field work is planned to corroborate and extend this result. The Brine Cavity Research Group, an association of 11 chemical and salt producing companies, is supporting this work. Major deposits of salt in tabular beds lie beneath some 300,000 sq miles of land in the central and northeastern U.S. This salt is a basic source of soda ash and chlorine, and has been extracted as brine from drilled wells for about a century. During the past two decades, the U.S. solution-mining industry, following the lead of European operators, has greatly improved the extraction process through the application of engineering and science.&apos; In 1957, the Brine Cavity Research Group, an association of 11 chemical and salt producing companies, was formed. This group proceeded to attack certain common problems through the support of research. An outstanding problem has been that of determining the shape and location of the growing solution cavities in the underground salt, so that measures can be taken to maintain operating efficiency. The problem has been partially solved by the Dowel1 sonar mapping service, which employs a pulse-echo device lowered into the cavity through the well.2 However, the working range of this equipment is at present insufficient for large cavities, and echoes are not returned from highly sloping walls nor from behind such obstructions as rock debris. Therefore, an independent means of mapping the cavity, for example, from the surface without interfering with operation of the well, would be desirable. THEORY OF THE METHOD Seismic waves are the only physical agent known to be capable of sufficient resolution and penetration to define typical solution cavities from the surface of the ground. The geometry is unfavorable: cavity widths are generally less than half their depths below the surface; resolution and lateral location of boundaries and channels to within 50 ft at depths of 500 to 3000 ft is desirable. Conventional seismic surveying, as used for petroleum prospecting, is probably not the answer: isopach mapping, for example, is not thought accurate enough to define the cavity by the slight additional delay time it would introduce (of the order of 0.005 sec for a 50 ft-thick cavity in hard Paleozoic rocks). Refraction surveying has also been considered, but seismic specialists see little promise in it for this problem. In 1957, in correspondence with industry personnel, the writer suggested a seismic method based upon careful measurement of reflection amplitudes. As Table I illustrates, seismic reflection coefficients r for typical brine-rock interfaces are considerably higher than those for typical interfaces between different kinds of solid rock. This fact can be utilized in two ways, illustrated in Fig. 1: 1) If the cavity roof is reasonably flat (which it may sometimes be since the unsaturated top brine will be in contact with an insoluble rock stratum), extra-strong seismic reflections will be received from the salt stratum where the solid has been replaced by liquid.

Jan 1, 1964

By B. J. Kochanowsky

TO improve blasting methods it is necessary to know how the explosive force acts and how rock resists this force. Because of the tremendous power developed within milliseconds and the great number of other factors directly affecting the technical and economic results, an analysis of the fundamentals of blasting theory is difficult. But since the rules used for layout design and for calculations of size of explosive charges are based on theoretical assumptions, complete knowledge of blasting theory has great practical importance in mining. Analysis of Blasting Theory: It is interesting to note the opinion of blasting experts with respect to contemporary blasting theories. F. Stussi; Professor of the University of Zurich, stated: "We do not have enough experience yet to change our army engineering regulations in blasting and base it on new fundamentals. It is our duty to collect more practical data and to do more research in blasting to close this gap." K. H. Fraenkel,2 editor of the Manual on Rock Blasting published in 1953 in Sweden and written by well-known Swedish, German, Swiss, and French blasting and explosive experts, said: "To the best of our knowledge no suitable formulas for civil blasting work are to be found in the American, French or German literature." Present blasting theory is based upon two assumptions. 1) The blasting force of explosive acts in concentrical and spherical form. 2) Rock resistance against the explosive force is directly proportional to the strength characteristics of the rock. The first classical formula based on theoretical fundamental in blasting theory for explosive charge calculation was introduced by Vauban, a military engineer who lived 300 years ago. It was Vauban who proposed the famous formula L = w3 q, where L is the explosive charge, w = line of least resistance, and q = specific explosive consumption proportional to the weight of rock. Later engineers used q as proportional to the strength of the rock. Since Vauban&apos;s time different suggestions concerning blasting theory have been proposed. However, the principles stated at that time so affected the thinking of later generations that his formula is still in use and practically unchanged. The first controversy concerned the form of crater. It was found that geological features of rock affected its form. The factor q was analyzed thoroughly by Lares3 and later by Ohnesorge," Weichelt,5 Bendel,6 and others, but the assumption remained that resistance against explosive force is directly proportional to the strength of the rock blasted. The greatest controversy, which has not yet been settled, concerned w. It was noted that w3 is more appropriate for long lines of resistance and w2 for lines of resistance less than 15 ft. Based on the assumption that the explosive force acts concentrically and spherically, spacings between charges were limited to distances not greater than the length of line of least resistance. Sometimes larger spacing is recommended, but this is due to the advantageous geological and physical properties of rock and not to the action of an explosive force as such. In addition to the classical formula, empirical formulas are used widely. These state that the explosive charge is directly proportional to the volume of blasted rock in cubic yards, and the amounts of explosive required are usually expressed in pounds of explosive per cubic yard of rock. Empirical and classical formulas are contradictory. In the empirical formula, but not in the classical formula, explosive charge is taken proportional to all three space axes: line of least resistance, spacing, and bench height. In spite of this contradiction, both formulas give good results. This is possible because as now practiced the explosive charge calculation for heavy burdens need not be highly accurate. Each, open pit or quarry, usually works with a certain relation between bench height and line of least resistance and between charge spacing and line of least resistance. When these relations are changed, however, the specific explosive consumption q changes greatly. This is one of the reasons why the principles on which the formulas are based appear to be incorrect. In addition to the formulas discussed, others exist and are based more or less on the same theoretical

Jan 1, 1956

By H. A. Hoffman

Competition from an all-flotation plant, with demonstrated economies and efficiencies, plus a change in smelting contract and introduction of improved cyclones lead to conversion from gravity-flotation. Detailed descriptions are given of equipment installed and procedures used at St. Joseph Lead&apos;s Federal mill. Future plans include further quality control by instrumentation in all aspects of the mill operation. Also planned are improvements in materials handling systems. Competitive conditions will continue to dictate improvements and changes in the mill flowsheet. The advent of all-flotation mills in the Lead Belt was introduced by the Indian Creek mill in late 1953. This modern and efficient plant then became a pattern for the other mills in this area to re-evaluate their circuits in an effort to develop flowsheets that would improve operating conditions and metallurgy. The Indian Creek mill demonstrated that all-flotation would require considerably less operating and maintenance labor than the combination of tabling and flotation that was common in the Lead Belt at that time. Two significant changes occurred in recent years to allow all-flotation to be seriously considered in other Lead Belt mills. One was a change in the smelting contract which did not require gravity concentrate. Another was the development of cyclones which provided classification of the flotation feed in a very small space. Since the Federal mill was the largest concentrating plant in the Lead Belt it was felt that the greatest savings could be made by investigating the all-flotation possibilities at this mill. Interest was stimulated by the milling and ore dressing Depts. to determine if this mill would be converted without undue cost, provided the metallurgy could be improved. Accordingly, laboratory tests were initiated to learn what metallurgical benefit could be derived. Numerous tests were run which indicated that grinding to all-flotation would improve the tailing by as much as 0.02 pct Pb. This was quite significant when multiplied by the tonnage of ore treated. Projecting the added cost of power for extra grinding and flotation, and the additional flotation reagents required, plus additional new equipment that would have to be purchased, it would still add up to a considerable saving. The all-flotation mill would reduce man power by some 30 pct, and make a metallurgical improvement. Operating costs could be reduced bv 2$ per ton. The metallurgical improvement would amount to 4$ per ton, for a total of 6$ per ton of ore milled. An estimate of the cost of the conversion was set at $250,000. With the savings as estimated this could be paid off in about two years. On paper it therefore seemed attractive enough to justify a mill test. MILL TESTING One section of the Federal mill was made available for use as a separate test circuit. Cyclones and density controllers were borrowed from the Viburnum and Indian Creek mills. Denver flotation cells were obtained from the Desloge mill that was then shut down. Two 10-cell groups of Fagergren flotation machines, consisting of eight roughers and two cleaners in each bank, were segregated from the remainder of the plant. The 9x12-ft rod mill was continued as a primary grinding mill. The two 6%x12-ft mills on this section were converted from rods to balls, and the speed increased to 22.0 rpm. Cyclones were installed to close the circuit of these ball mills. The ground pulp from each of the ball mills was fed separately to its own bank of flotation cells so that two completely separated test circuits could be run in parallel. This test circuit operated on a three-shift basis from Dec. 22, 1959 to Mar. 21, 1960. The first few weeks were occupied in developing conditions for proper metallurgy and trouble-free operations. Results were rather erratic but as the ore dressing laboratory and the mill operators became more familiar with conditions they were able to obtain expected results, which could be duplicated day after day. The last five weeks of testing indicated the best results and are tabulated in Table I. During the first two weeks a Denver unit cell was used on No. 1 flotation circuit. Even though it recovered almost one half of

Jan 1, 1962

By W. E. Newell

The basic principles and assumptions involved in D. L. White&apos;s solution5 for ultrasonic wave amplification in piezoelectric semiconductors are summarized. If the gain per unit length is maximized at each frequency without regard to the drift-field power density, the gain increases linearly with frequency. Therefore it would seem that very high gain is possible for frequencies in the hundreds of megacycles. However, with present materials the resulting drift-field power density is so large that cooling would be a major problem. For this reason it is more realistic to judge the capabilities of an ultrasonic amplifier in terms of the gain that is possible with a specified power density. In this case the gain at high frequencies does not increase but decreases more rapidly than l/f. The calculation of the gain us frequency at a fixed power level involves the repeated solution of a cubic equation and is therefore tedious. For the purpose of comparing different materials, sufficient accuracy can be obtained from an approximate solution which may easily be plotted as three straight lines on logarithmic graph paper. This method is used to compare the Performances of CdS, CdSe, ZnO, and GaAs. At a power density of 10 watts per cu cm, the first three give maximum gains of 60 to 80 db per cm in the vicinity of 60 megacycles. At the same power density, GaAs has a maximum gain of about 7 db per cm near 150 megacycles. Although an increase in mobility usually increases the gain for a specified power density, it is shown that there is an optimum mobility above which the gain decreases. An approximate expression for the optimum mobility is established. It is well-known that the interaction between charged particles and an electromagnetic wave can be used to amplify the electromagnetic wave. In the conventional traveling-wave tube, electrons in a vacuum are caused to move at a velocity slightly greater than the wave velocity, thereby coupling energy into the wave.&apos; In principle, the same effect would be evident in a solid except that repeated collisions prevent the electrons from attaining a velocity greater than that of an electromagnetic wave. However, the drift velocity of electrons can be made to exceed the velocity of an acoustic wave in a solid. In 1956, weinreich2 noted that the deformation potential provided one means of coupling energy from drifting electrons into an acoustic wave, but the effect was too small to be of any practical importance. It was not until 1961 that White and Hutson demonstrated that the piezoelectric effect provided a strong enough coupling to give appreciable amplification of an ultrasonic wave and awakened wide interest in electron-phonon interactions. Qualitatively the effect may be described as follows. An acoustic wave propagating through a piezoelectric material is accompanied by an electric-field wave. If the vibrations are properly oriented with respect to the crystal axes of a piezoelectric semiconductor, the local electric fields are axially directed and cause bunching of the charged carriers. If the drift velocity of these carriers is less than the velocity of sound, they tend to be dragged along by the acoustic wave. This electroacoustic effect results in a net potential appearing across the material and in attenuation of the acoustic wave. On the other hand, if the drift velocity exceeds the velocity of sound, energy is coupled from the carriers to the acoustic wave and amplification results. Related effects which are being investigated include ultrasonic amplification in semimetals6-&apos; and semi-conductor, and current saturation in piezoelectric semiconductors.&apos;4-17 There are various problems which hinder the immediate application of ultrasonic amplification in a practical device. First, there are the traditional problems encountered in the design of acoustic delay lines: attenuation in the electromechanical transducers, reflected waves (which can lead to self-oscillation in an amplifying device), mechanical tolerances necessary to maintain phase coherence, and so forth. Second, there is the problem of selecting the best material from among the various piezoelectric semiconductors as they become available in single-crystal form with a wide choice of characteristics. This paper deals with the second problem and shows that the most realistic way of comparing materials is in terms of the gain which can be obtained without exceeding a

Jan 1, 1964

By Robin O. Williams

The increase in internal energy as the result of deformation has been measured for lead, aluminum, silver, nickel, iron, and zirconium by using rapid, adiabatic compression. The stored energy increase is roughly Proportional to the strain; the propor-tionality constant increases rapidly with increasing melting point. The fraction of the mechanical energy which is stored increases more slowly, since the strength of the metals also increases with melting point. The values of the stored energy are considered accurate to about 10 pet. The present values appear about 50 pet larger than the more reliable published results where comparisons are possible. It is possible that this difference is due to the high strain rate used in this investigation. Immediately after deformation all these metals release energy at a rate roughly proportional to (time)-&apos;. This release is considered to be associated with dislocation motion but in aluminum (and copper) some additional process seems to be present. This release can represent 20 pet or more of the stored energy. WHEN pure metals are plastically deformed, most of the mechanical energy is converted into heat. The energy remaining within the metal is significant in that it is the energy of the disorder produced and thus detailed knowledge of this energy is a powerful tool in understanding the nature of deformational disorder. While much effort has been expended on this problem, the amount of information available is limited. The situation as of 1958 has been carefully reviewed by Titchener and ever.&apos; The present results have been obtained by a new experimental approach to this problem. The method necessitates high-strain rates which make comparisons with published results less certain, but a high-strain rate is an advantage in that the energy release immediately after deformation can be followed. EXPERIMENTAL PROCEDURE In the experimental method used, the internal (stored) energy is given as the difference between the mechanical work used in deforming the sample and the heat which is released (the first law of thermodynamics). The work is supplied by two identical hammers swinging freely from a fixed height, the available energy being the product of the mass, the gravitational constant, and the distance through which the center of gravity moves. The initial temperature rise of the sample represents the heat produced by the deformation. The sample temperature is determined by a small thermocouple embedded in and supporting the sample. This process can be repeated over and over to produce increased strains. Most samples are run through about five cycles to a total strain of around 0.7. Further details are covered elsewhere. The determination of the heat is dependent upon the sample weight, its specific heat, the rise in temperature, and any gains or losses to the surroundings. One is dependent on published results for specific heals (the values were taken from a collection).3 The values must be accurate to about 0.1 pet in order that they not affect the results. The best values thus do not contribute to the uncertainty, but this is probably not always the case. The accuracy of the temperature rise is limited primarily by knowledge of the thermocouple characteristics over short temperature intervals, but careful calibration eliminates this as an important factor. One can calculate readily the heat flow between the sample and hammers if the time of contact and the sample temperature are known and if there were no oil at the interface. Assuming the maximum temperature difference, upper values for this interchange have been calculated (the time of contact is determined from the decrease in sample length) and it may or may not be significant. However, no correction is colnsidered necessary because of the presence of a thin oil film which has a thermal conductivity much less than the metals. Except for the possible uncertainty in specific heat, the heat is considered to be adequately known. The mechitnical losses which are recognized as important are: 1) friction between the sample and the hammer:;, 2) the kinetic energy in the hammer suspension system which may not be entirely usable, 3) the rebound energy of the hammers, and 4) the vibration of the hammer heads. All these have been covered in detail elsewhere2 and only the more significant points are made here. The friction turns out to be small except for soft materials (lead)

Jan 1, 1962

By F. V. Lenel, G. S. Ansell, J. A. Dromsky

The growth of aluminum oxide particles in a nickel matrix was studied eve?. the temperature vange of 2140° to 2470°F. The instability of the dispersed alumina was shown to be independent of the crystal structure of the alumina. The activation energy for the growth of the dispersed alumina was found to be 84.7 1 2.0 kcal. The particle radius increased as a function of time. These results indicate that the growth is not diffusion controlled. It is believed that the rate controlling mechanism is the dissolution of the aluminum and oxygen atoms into the nickel lattice. THE strength properties of alloys which consist of a finely dispersed second phase in a metallic matrix depend upon the spacing between the second phase particles. It is therefore desirable to achieve very fine dispersions in these alloys. Furthermore, to retain the properties these very fine dispersions must be stable during fabrication and service of the alloys. The best known of the dispersion strengthened materials, the SAP type alloys, which consist of a dispersion of aluminurn oxide in aluminum, have exceptionally good stability up to the melting point of aluminum. There is evidence, however, that other dispersion strengthened alloys, even those consisting of refractory oxides in a metal matrix, may be less stable. This investigation is concerned with the stability of Ni-Al2O3 alloys in the temperature range in which these alloys are usually fabricated. The mechanical properties of Ni-Al2O3 alloys at elevated temperatures have been previously investigated by Crelnens and rant,&apos; and Gregory and Goetzel.2 The behavior of these alloys in stress rupture tests appears to indicate that at temperatures below 1800°F they are highly stable. There is some doubt, however, as to their stability at the higher temperatures used during the conventional fabrication. Cremens and Grant, in preparing their test alloys, cousolidated, by powder metallurgical techniques, nickel powders as fine as 0.13 µ diam and alumina powders as fine as 0.018 µ. Metallo- graphic examination of the alloys following fabrication revealed that none had interparticle spacings of less than 2 µ. Considering the size of the original component powder particles, it is likely that the dispersions coarsened during fabrication. Gregory and Goetzel, in their studies of extruded alloys of 80 pct Ni—-20 pct Cr matrixes with nonmetallic dispersion, observed a definite coarsening of the alumina dispersions in alloys sintered at 2280°F as cantrasted to those sintered at 2000oF. Similar observations on the spheroidization and growth of thoria particles finely dispersed in a nickel matrix were made by D. K. Worn and S. F. Marton.3 As a result of such coarsening, much of the effort expended in the preparation of very fine powder mixtures would be lost. The mechanical properties of the alloys which had experienced coarsening would be expected to be poorer than if the original dispersions had been retained. EXPERIMENTAL PROCEDURE Ni-Al2O3 alloys were produced from powder prepared by a coprecipitation technique. Aluminum hydroxide and nickel hydroxide were coprecipitated from chloride solutions of the metals. The mixed hydroxides were calcined to form metal oxides and the nickel oxide in the mixture was selectively reduced to nickel by treating it in hydrogen. Specimens were compacted from the resultant powder which consisted of a fine, uniform mixture of aluminum oxide and nickel particles. The compacts were sintered by resistance hot pressing4, a densification technique which requires exposure times of the order of only a second or less at elevated temperatures. A conventional sintering process was not used, since the temperature required for densification would have to be in the region in which the stability of the dispersion was to be studied. A series of hot pressed specimens were treated in hydrogen at temperatures from 2140o to 2470°F (1171o to 1355oC, for times up to 120 hr. Changes in the microstructures were studied by electron microscopy using the two-stage preshadowed carbon replica method.5 In performing a lineal analysis on a series of micrographs from each specimen it was found more convenient to determine the mean free path between alumina particles rather than particle radii as the parameter of growth. Although these quantities are directly proportional for only spherical particles, the alumina particles in these alloys

Jan 1, 1962

By R. C. Davis, R. F. Berry, G. W. White, B. T. O’Connell, L. A. Stacha

The formation density logging tool provides a radioactivity measurement that yields formation densities in situ. The relationship between bulk density and porosity is well understood. With knowledge of grain and fluid densities, porosity may be computed from the indicated formation bulk densities in shale-free formations. The porosities thus determined may be used with a resistivity log for water-saturation determinations. One technique utilizes a density vs resistivity plut. A plot of density vs Sonic-log transit time is used for porosity determinations in shaly sands. This method is particularly suited to wells drilled with oil-base or salt muds. In shale-free formations, comparisons of density values nnd neutron-log readings are used to identify lithologr and, thus, to select appropriate values of grain density for porosity computations. Through the use of Formation Density, Sonic and neutron logs, the interpretation problems caused by complex matrix lithologies are simplified. Other applications of the Formation Density log are found in the identification of minerals in evaporite deposits and in yield determinations of "oil shales". INTRODUCTION Widespread field application has demonstrated that the measurement of formation density is a useful and revealing technique for well logging. Responding to the bulk density variations of the formation, the Formation Density log affords valuable data on the porosity, lithology and fluid content of the formations. Although not without its own limitations, the Formation Density tool may provide effective interpretation under conditions that hamper or preclude the use of other porosity devices. When used in conjunction with other devices, such as the Sonic or neutron, complex matrix conditions may be better understood, defined and evaluated. A previous paper&apos; described the valuable contribution of the Formation Density tool in the logging of empty, or gas-filled, holes. The purpose of the present paper is to describe applications of the device in liquid-filled holes. THE FORMATION DENSITY TOOL The Formation Density tool was devised to measure the bulk densities of formations in situ. Actually, the device responds to electron density, but in the overwhelming majority of cases of interest, the electron density is very closely proportional to the bulk density. In other cases appropriate corrections can be made if necessary. Comparisons of log-derived densities with true densities for the more common matrix minerals are shown in Table 1. The tool consists of a gamma-ray source and detector mounted in a skid which, during the logging operation, is in contact with the borehole wall (see Ref. 1 for schematic). Gamma rays are emitted by the source and diffused through the formation. The number of diffused gamma rays reaching the detector at a fixed spacing from the source are counted. An increase in counting rate by the detector indicates a decrease in bulk density in front of the skid. Conversely, a decreased counting rate signifies an increase in bulk density. A measurement of hole diameter, between the face of the skid and that of the eccentering arm, is recorded simultaneously with the measurement of diffused gamma rays. Since the tool is a wall-contact device, the size of the borehole has little influence, provided good contact is maintained with the wall of the hole. Only in extremely large or small boreholes does the actual diameter become significant. However, for most accurate measurements the borehole size should be taken into account. Fig. 1 presents the departure curves for the conversion of counting rate to bulk density for liquid-filled holes of various sizes. It is of utmost importance that the skid maintain good contact with the wall of the hole. If, due to roughness or caving, there is mud between the skid and the formation, the tool will include in its response the relatively low-density mud, and the apparent density reading will be too low. Normally, permeable beds do not cave appreciably, so that reliable readings are usually available for zones of interest. Nevertheless, the caliper reading over the zone of interest should be examined for any wall roughness. When mud cake exists between the skid and the formation, the Formation Density log sees it as part of the formation. When thick mud cakes exist, a correction is required. For best results in wells having thick mud cakes,

By A. Kenneth Schellinger

THE terms surface tension .and surface energy are well known when applied to liquids and are generally described by referring to the excess energy of the air: liquid interface as a result of unsaturated molecular forces surrounding the surface molecules of the liquid due to the presence of the air phase on one side. Such unbalanced forces produce the familiar water droplet of spherical form and are generally summed up as a surface tension measured in dynes per centimeter which can be shown mathematically to be equal numerically to a corresponding surface energy expressed in ergs per square centimeter. A specific surface energy, however, is best thought of as the energy necessary to produce one unit of new surface on a substance. Hence, in producing a bubble in a flotation cell the impeller must supply surface energy corresponding to the air: liquid interfacial area on the interior of the bubble. Inasmuch as it is relatively easy to extend or contract the surface of a liquid, there are a number of successful methods for liquid surface tension, or energy, measurement based upon surface deformation. This happy state of affairs does not, however, extend to solids, which are considered to possess surface energies for the same reasons as do liquids, i.e. because of unsaturated ionic bonds at the solid gas interface. As in the case of the flotation cell producing surface on liquids as new bubbles, it takes energy to produce new surface on solids as new particles. As every mill man knows, this surface is produced on mineral solids in a grinding mill by the action of a tumbling mass of iron balls. But here so much energy usually is wasted by the inefficient action of these balls that a large amount of heat is generated, and the surface energy production may be easily confused with the energy necessary to produce this ineffective heat. The tumbling balls and fracturing minerals ultimately take their energy from a rather large electric motor. It has been variously estimated that from 10 to 20 pct" only of this energy from the motor does not appear as heat and may be presumed to appear as surface energy on the minerals present.. Such a production of new surface on the mineral phases is accompanied, of course, by a size reduction that is inevitable as more and more mineral interior molecules become surface molecules by the fracture exposure. This size reduction of mineral particles, although the most obvious feature and perhaps the sole object of the milling operation, is from this energy viewpoint the outward manifestation of the production of surface energy only. Measurement of the characteristic surface energies of pure minerals and their various mixtures in ores would be a step towards understanding of the energetics of the commercial grinding operation. In addition, the characteristic surface energy of a mineral is probably a physical property specific for that mineral, and therefore, from a scientific standpoint, should be measured. It is interesting to note that, in contrast to the large body of work on the surface tensions of liquid systems and biological systems, the field of solid surface energies has been neglected. Prior to. 1920 it is difficult to find more than one or two references to work on solid surface energies in Chemical Abstracts. Since 1920 such references number somewhat less than 100, while those on liquid systems are numbered in the thousands. Much of this apparent neglect of the field of solid surface energies (the term is intended to be somewhat inclusive at this point and refers both to the solid: gas, and the solid: liquid interface) is because of the lack of a reliable method of measurement rather than any lack of scientific curiosity. It was, and still is, difficult to produce new surface on a solid without the simultaneous production of interior changes in the same solid which may consume part of the energy used. The extension in the surface area can be measured, but the interior crystal-

Jan 1, 1952

By R. J. Charles

SEARCH for a consistent theory to explain the relationship between energy input and size reduction in a comminution process has accumulated, over the years, an enormous amount of plant and laboratory data. Although some correlation of these data has been possible for purposes of engineering design and for the advancement of research in fracture, there is still great need of a means of predicting behaviour of a solid when it is reduced in size by mechanical forces. The best known hypotheses proposed to describe the energy-size reduction relationships in crushing and grinding stem from a common origin. The present article analyzes problems of comminution in the light of the precepts of this origin. Its object is to reconcile points of difference between these well known hypotheses and to present relationships more widely applicable to comminution studies. Theoretical Considerations: Most existing relationships between energy and size reduction of a brittle solid stem from a single, simple, empirical proposition.&apos; Although this proposition can be demonstrated by observation and experiment, no theoretical derivation is yet possible. Mathematically, the proposition may be stated as follows: dE = -Cdx/xn [1] where dE = infinitesimal energy change, C = a constant, dx = infinitesimal size change, x = object size, and n = a constant. Eq. 1 states that the energy required to make a small change in the size of an object is proportional to the size change and inversely proportional to the object size to some power n. No stipulations are placed on the exponent n in either magnitude or sign. In 1867 Rittinger2 postulated that the energy required for size reduction of a solid would be proportional to the new surface area created during the size reduction. As far as can be determined there is as yet no physical basis for Rittinger&apos;s hypothesis. Rittinger&apos;s hypothesis can be stated mathematically as follows: E, = K(oa-a-0 . [2] Er = energy input per unit volume, K = a constant, <ti = initial specific surface, and o2 = final specific surface. In the size reduction of particles of size x, to particles of another smaller size, x2, Eq. 2 becomes the well known relation: ET = K&apos; {l/x2-l/xx) [3] where K&apos; is a constant. Eq. 3 may be arrived at from the proposition given in Eq. 1 by integrating and by assigning a value of 2 to the exponent n. J dE = J - C dx/x2 E = Kt (1x - 1x) where K&apos; = C. In 1885 Kick3 proposed the theory that equivalent amounts of energy should result in equivalent geometrical changes in the sizes of the pieces of a solid. For example, if one unit of energy reduced a number of equal-sized particles to particles of one half the size, then the same amount of energy applied to the particles resulting from the first test should result again in a size reduction of one half or a final size one quarter the original size. The Kick concept may be expressed as follows: Ek = K" log x1/x2 [41 K" = a constant and E, = energy per unit volume. The expression for Kick&apos;s law may be arrived at by again integrating Eq. 1 and in this case assigning a value of 1 to the exponent n. dE= J - C dx/x Eh = - C In {x/x2) = K" log (x,/x,) where K" = 2.3 C. Application of Kick&apos;s and Rittinger&apos;s laws to comminution has met with varied success. Gross and Zimmerley4 and Piret5 have shown that Rittinger&apos;s equation applies under certain conditions of experimentation. Walker and Shaw6 express the belief that in metal turning and shaping and in grinding of both metals and minerals the production of very fine particles (less than lP) follows Kick&apos;s hypothesis, whereas Rittinger&apos;s concept is valid for the size reduction of coarse particles. For the practical case of crushing and grinding, however, neither of the above hypotheses has received general acceptance. Bond&apos; has lately proposed that since neither Kick&apos;s nor Rittinger&apos;s hypotheses seem correct for plant design work, an energy-size reduction relationship somewhere between the two would be more applicable. The fundamental statement of Bond&apos;s work

Jan 1, 1958

By R. A. Greenkorn

This project originated in a practical problem—we needed five tracers that could be used together to locate flow paths in a pilot flood. While tracers for subsurface liquids have been used since the turn of the century,1-15 none of those reported in the literature appeared to be either consistent or quantitative enough for our purposes. Most were used in field systems without controlled experiments to determine the accuracy and precision of analysis, and many were tracers that could not be used collectively. The ideal tracer, of course, would follow the fiuid of interest exactly, traveling at the same velocity as the fluid front. But the ideal is impractical to attain because adsorption-desorption effects cause the tracer to lag behind the front; these effects, plus diffusion-dispersion effects, cause the tracer front to spread more than the fluid front. Thus, our objective was not to locate a tracer that would be ideal for all circumstances but rather, to find one that would approximately follow the fluid, or one that under controlled conditions could be corrected to calculate the movement of the fluid front. We considered tracers satisfactory—(1) if they were easy to analyze; (2) if their breakthrough-elution curves were not too different from those for the chloride ion, a tracer believed to follow the fluid front closely; and (3) if we could calculate from the curves a material balance, at 1.25-PV (pore volume) injected, within 5 per cent of that calculated from chloride curves. Of a possible 35 materials, we selected 13 tracers that could be quickly and easily identified and whose analysis was claimed to be accurate within 5 per cent. Only one of these, tritiated water, was a radioactive tracer. Radioactive tracers are easy to detect even in small quantities, but they require special handling and special equipment. Also, those that can be used together are limited because special equipment is required to separate emissions from the various tracers. Two of the original 13 tracers were eliminated in static tests to determine how accurately and precisely they could be analyzed, and to check on gross adsorption. The remaining 11 were flowed through a 9-ft linear sandstone model, and breakthrough-elution curves were obtained. Finally, three tracers were field-tested as breakthrough tracers. These tests are described in the following sections. The 13 tracers considered in these experiments were EDTA (ethylene diamine tetra acetic acid), fluo-rescein, picric acid, salicylic acid and ammonium, boron (as borate), bromide, dichromate, iodide, nitrate and thiocyanate ions, plus chloride ion and tritiated water. All but the chloride ion and tritiated water were subjected to static sand tests to eliminate the tracers that could not be analyzed quickly and accurately and to eliminate those that showed excessive adsorption. All but two of the tracers, EDTA and salicylic acid, qualified for flow tests on this basis. The procedures used in the static tests (see Appendix A for analytical details) were as follows. Each tracer (in the amount shown in Table 1) was dissolved in 1,000 ml of water. Then, 800 ml of this solution was added to 500 gm of sand, and the remaining 200 ml was reserved as a control standard. The sand-tracer mixture was agitated once a day over a 10-week period, and during this period we analyzed five duplicate samples from this mixture, along with five duplicate samples from the control solution. From the control-sample analyses, we constructed a control chart on which the sand-tracer analysis results were plotted. The control chart, and its use to determine accuracy and precision of analytical results, as well as the amount of adsorption, is described in Appendix B. The results of the static tests are summarized in Table 1, which lists the concentration c (concentration at time t) divided by c, (initial concentration). If there was no adsorption, c/c, = 1. The acceptable deviation from this value varied from tracer to tracer, depending upon the limits of analytical precision established for the different tracers. The best results were obtained with boron, bromide and dichromate, with all values falling within limits of accuracy and precision. Ammonium, iodide, nitrate and picric acid also were satisfactory, although the ammonium results were erratic. Flourescein and thiocyanate were unsatisfactory ini-

By J. B. Wagstaff, R. A. Buchanan, J. F. Elliott

High speed photography through blast-furnace tuyeres showed coke particles moving rapidly. Model studies showed a raceway was formed and gave quantitative results which were correlated with actual blast furnaces. Another study showed the similarity between hanging and the flooding of a packed column. This was explored by models. THE combustion zone before the tuyere in an iron blast furnace is a vital region because here are generated: 1—most of the gases on which the furnace depends to carry out its basic operation of reducing iron ore to the metallic state, and 2—the major fraction of the heat required in the nearby regions of the furnace for the various reduction reactions, the fusion of the slag, and the melting of the iron. Since the greater part of the coke is consumed in this region, the descent of the burden must be greatly affected by the characteristics of the tuyere zone. This region then would seem to be a profitable field for study. Fortunately, a view into this important zone is available to the operator through the tuyere peep sight. Here he sees relatively dark pieces of coke "dancing" in the blast. What he sees is of considerable help in interpreting the behavior of the furnace at a given time but the very rapidly moving particles and the intense radiation obscures what is happening very deep in the zone. This investigation was initiated in the hope that a better understanding of the combustion region could be obtained by using a high speed camera with a maximum speed of 3000 frames per sec. It seemed the best practical method of "slowing down" this characteristically violent action within the highly luminous field. Model studies and tuyere probing also have been used to aid in explaining the observed phenomena. Above the combustion zone, but below the fusion zone, there is probably a region in which the coke is comparatively stationary. Here are zones in which the gases must flow up through the granular bed counter to descending liquid slag and metal. There is no easy way to observe this zone in a blast furnace, but model studies have been of some help in explaining the nature of the zone and the laws governing the flow of the fluids involved. The whole problem is difficult and involved and any approach to a complete solution may require long investigation. This preliminary report has been written, therefore, because it is believed that appreciable progress has already been made that would be of interest to others. Tuyere Studies, Chemistry and Kinetics It is well known from the early work of Kinney and coworkers1,2 that combustion of carbon before the tuyeres appears to occur in two zones: Zone A: C + O, = CO2; AH77°F. = — 14,108 Btu per lb of carbon [I] Zone B: CO2 + C = 2CO; H77°F = + 6,183 Btu per lb of carbon [2] Zone A (Fig. 1) is close to the tip of the tuyere and zone B is somewhat farther back; there being a transition region in which both reactions occur. It is interesting to estimate the rate at which coke is burned before a tuyere with a wind rate of 90,000 cfm in a modern furnace having 18 tuyeres. Approximately 0.55 lb of carbon is consumed by eq 1 per tuyere per sec. A like amount disappears by eq 2 for a total consumption of 1.11 Ib per sec per tuyere. Assuming the coke is 85 pct C and has a bulk density of 30 lb per cu ft, this figure can be converted to a total of 1.30 lb of coke with a bulk volume of 0.043 cu ft disappearing per sec per tuyere. At the temperatures prevailing in the combustion zone (according to Kozlovich,³ he maximum is about 3400°F), the rate at which carbon is con-

Jan 1, 1953

By B. H. Caudle, B. M. Hickman, I. H. Silberberg

Secondary recovery projects often are not started in oil reservoirs until dictated by rising GOR&apos;s or declining oil production. Such circumstances require a well dispersed injection pattern to prevent the oil bank from bypassing the production wells. Many times this purpose is served by using the five-spot or line-drive patterns, in which half of the wells are made injection wells. A regular injection pattern is proposed that is based on the same well spacing as the five-spot but in which only a third of the wells need be converted to injection wells. Fluid flow model studies on this proposed pattern show that production histories will be as good as those for a five-spot pattern at mobility ratios of three and above. The model data are presented in a form that may be used to predict recoveries from both homogeneous and stratified formations. Introduction The injection of fluid into a petroleum reservoir usually is prompted by an actual, or predicted, loss in the productivity of the reservoir. Often, an oil reservoir is produced by pressure depletion until high GOR&apos;s dictate a change in policy. Fluid injection also causes increased ultimate recovery, but this usually is of less importance to the operator than is the maintenance of the production rate. It is a fact that the ultimate recovery in any particular fluid injection project is relatively independent of the number and spacing of the injection wells as long as the reservoir voidage through the production wells is balanced by the total injection rate. However, the response of a production well is directly affected by the distance it lies from an injection well. In places where the well productivities are declining, the injection wells should be spaced as evenly as possible among the producing wells ("dispersed" injection pattern). More particularly, if the production response depends upon the formation (and subsequent production) of an oil bank, each production well should be surrounded by injection wells. Otherwise, the oil productivity will increase very little as the oil bank moves past the well.&apos;.&apos; An evenly spaced injection pattern has the best chance of generating an oil kick in the production wells. If reservoir voidage and injection rates are to be equal, the ratio of injection wells to production wells must be equal to the ratio of the average injectivity to the average productivity (in reservoir volumes). This ratio is in strumental in choosing the injection pattern. Table 1 shows the production well to injection well ratio for the dispersed injection patterns that have been described in the literature.&apos;-&apos; All of these patterns will have comparable recoveries and response times (for the same basic distance between wells). The choice of pattern there fore depends upon the relative injectivity and productivity of the wells and upon the type of drilling pattern employed. Another important factor may be the ability of the proposed production wells to make up the lost productivity from those wells converted to injectors. These factors become more pronounced at the higher oil viscosities (low gravity oils). All other things being equal, the probable ratio of single well injectivity to single well productivity will be equal to the water-oil mobility ratio of the proposed flood. Thus, high mobility ratios (due to low gravity oil) should call for fewer injection wells — as long as these injection wells are "dispersed" to obtain more even pro duction response for the remaining wells. Secondary re covery projects in oil reservoirs seldom, if ever, will have mobility ratios requiring more injection wells than production wells. Thus, only the last five of the patterns listed in Table 1 will be of significant interest in oil recovery. Almost every development drilling program calls for the wells to be drilled along equally spaced rows and

Jan 1, 1969