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By M. L. Fuller

DURING the last several years many papers have appeared dealing with the structure of highly polished metal surfaces. The awakening of interest in this subject is due to the applicability of the electron diffrac-tion technique to the study of surfaces. The original theory of Beilby1 considered the surface of polished metals as of the nature of a super-cooled liquid or a vitreous, amorphous solid. The electron diffraction effects from polished metals have been interpreted by many to be a direct experimental proof of the correctness of the Beilby theory. This inter-pretation has been strongly opposed by others, so that at the present time the subject is in an uncertain and controversial state. In the present paper new, and hitherto unpublished, electron diffrac-tion effects from polished zinc are described. These observations indicate that the polished surface of zinc is crystalline.

Jan 1, 1938

By Richard Addison, Ronald O. Cranor

Tailings dam construction and operation of Rosario Dominicana's gold/silver mine in the Dominican Republic is described. Impoundment of 8.5 kt/d of cyanide-process tailings is required in an intensive agricultural area which is also an earthquake and high rainfall zone. The earthfill embankment dam, incorporating internal gravel drains, is described together with methods of construction used. Methods of tailings transport, solution reclaim, and runoff water diversion that have evolved are discussed.

Jan 1, 1982

By Edward H. Robie

OF the current Adirondack iron mine development, the Benson Mines operation of the Tones and Laughlin Ore Co. (Jones & Laughlin Steel Corp. wholly owned subsidiary) is the last to go into operation. Following an active construction program in 1943, the mine. concentrator and sintering plant were scheduled to enter production in the fall. This description therefore cannot include any operating data, and details of equipment and flowsheet have not as yet been released.

Jan 1, 1943

By AIME AIME

AT bottom of this page is a photograph recently taken by a student-John E. Stewart-of the most northerly situated college in the world, the Alaska Agricultural College and School of Mines. It is situated at College, near Fairbanks, Alaska, approximately on the 65th parallel of latitude, and therefore just south of the Arctic Circle. It is farther north than Hudson Bay, and in about the same latitude as southern Greenland.

Jan 1, 1932

By C. D. Thompson, D. C. Violetta, C. A. Czako

The mechanics of the continuous sintering process are briefly reviewed and the application of this process for the beneficiation of principal minerals used in making cement is shown. Pilot plant tests using pyrobeneficiation techniques were conducted with mixtures of limestone and shale in various ratios. Results are illustrated and show the percentage removal of carbon, carbonates, sulfur, alkalies, and volatiles as a function of the limestone-shale ratio. Tests with varying quantities of solid fwls, added to mixtures containing limestone and shale in a 4 to 1 ratio, were made to attain optimum elimination of the volatile constituents. Experimental results show that 90 pct of these constituents were removed during the calcination sintem'ng process. The advantages of using the beneficiated material for making cement are discussed with regard to prepam'ng, handling, and clinkering operations. A sintering process for treating raw materials or kiln waste products which contain high amounts of alkaline materials is described. Tests were performed with a high alkaline waste dust mixed in a 1 to 1 ratio with raw cement meal. The data from these tests and others using different halides for aiding alkali removal are evaluated by the alkali content of the cement clinker. Test results showed that the Dwight-Lloyd process could be applied with facility in beneficiating raw materials for cement making. Substantial quantities of deleterious volutile constituents were removed by calcining and sintering techniques. The continuous sintering process has been applied for a number of years as a means of beneficiating minerals for subsequent conversion to merchantable products. The process was developed and first used for nonferrous metallurgical applicatfons. However, it has risen to prominence for ferrous metallurgical applications where last year in the U.S. and Canada nearly 40 million tons of iron ore were treated by grate firing processes. Through the years of process development many investigators have realized the versatility of the sintering process and have directed experiments toward the use of it for applications with nonmetallic minerals. These have included calcining limestone, carbonizing coal, expanding shale, and burning cement raw meal. Today commercial sintering plants produce cement clinker from mixtures of limestone and shale, lightweight aggregate from shale or clay, and calcined products from phosphate shale. The mechanics of the downdraft sintering process have been presented by many authors. In general practice the materials to be agglomated are mixed as moistened fines with a solid fuel and this mixture is spread uniformly on the grates of the sintering machine. The charge is then momentarily directed under an ignition furnace. After ignition a continuous downdraft of air promotes combustion of the fuel and through heat transfer particles become partially fused into a coherent mass. This is cooled from continued draft induced after combustion. Many investigators have shown that distinct zones are formed during the process of sintering iron ores. At the midway point of the sintering process these are prominent and are, respectively, from the top of the bed to the bottom, comprised of a cooling zone of sintered material, a combustion zone of sinter formation, a calcination zone, a drying zone, and a zone of unreacted materials. Completion of sintering occurs near the discharge end of the machine where the firing zone approaches either the grates or grate dressing material called hearth layer. Here the peak draft temperature usually can be noted in the windboxes. The zonal pattern has been illustrated with the use of graphs which show thermal gradients as they progress through the bed of materials during sintering. Fig. 1 shows, in simplified form, thermal gradients existing when clinkering cement on a sintering machine. The thermal gradients illustrated are for periods of initiation, midway and completion of the clinkering process. The occurrence of these zones has importance for the beneficiation of cement raw materials. A research program was performed at the Dwight-

Jan 1, 1961

By E. S. Bumps, H. D. Kessler, M. Hansen

The titanium-rich end of the Ti-AI phase diagram has been determined to the compound TiAI3 (62.7 pct Al), thus joining the aluminum-rich portion previously investigated by others and completing the diagram. Micrographic analysis and X-ray diffraction were the chief methods used to determine the phase relationships. THE Ti-Al phase diagram has been investigated as part of a program on titanium phase diagrams for the Wright Air Development Center. Included in the available information concerning the phase relationships in titanium-rich Ti-A1 alloys is a brief statement by Brown' that: "aluminum raises the transformation temperature to 1000°C (183Z°F)." This observation is interesting in that it is the first example of a metallic alloying component raising the transformation temperature of titanium, and consequently widening the field of the a solid solution. Busch and Freyer' presented resistivity data which indicated the formation of titanium-rich solid solutions of 1 and 3 pct A1 alloys prepared by powder metallurgy methods. Duweza found that there is only one other intermediate phase other than the known compound TiA1, (62.7 pct Al). This phase, designated as y, is of variable composition; its crystal structure is of the AuCu type and is therefore based on the composition TiAl (36.02 pct Al). Earlier work on the constitution of the aluminum-rich alloys has been reviewed by Hansen, and need not be discussed here. The tetragonal crystal lattice of TiAl,, as found by Fink, Van Horn, and Budge," was confirmed by Brauer." Recently, Schubert7 has reported that TiA1, is homogeneous within a limited composition range; however, the solubility limits were not given. The Ti-A1 phase diagram as presented in. this paper was determined by micrographic analysis of alloys containing from 1 to 62 pct Al, annealed at and quenched from temperatures between 700" and 1400°C. The phases and phase ranges investigated extend to the compound TiA1, (62.7 pct Al) to join the aluminum-rich end of the system determined by other investigators, thus completing the diagram. Methods of Investigation Preparation of Alloys: Iodide titanium, 99.9+ pct pure, obtained from the New Jersey Zinc Co., and high-purity (99.99+ pct) aluminum sheet from the Aluminum Co. of America were used to make up alloy ingots weighing 10 to 20 g. Detailed descriptions of melting techniques have been presented previously for work on the Ti-Mo and Ti-Cb> nd Ti-Si" phase diagrams. Briefly, the melting practice consisted of arc melting an accurately weighed charge in a copper block crucible insert in a non-consumable tungsten electrode furnace, under helium at atmospheric pressure. All ingots were carefully weighed after melting to detect possible losses. Comparison of weight before and after melting showed no appreciable weight changes. Also, chemical analyses were in close agreement with nominal compositions, Table I. The diagram as presented is, therefore, based on nominal compositions. Alloys were prepared having the following nominal aluminum contents: 1 ... 36 (1 pct increments), 38, 40, 41, 42.5, 44, 45, 46, 47.5, 49 . . . 64 (1 pct increments), 67, 70, 80, and 90. Ingots with up to 14 pct A1 were cold-pressed various amounts in order to increase the rate of attaining equilibrium structures on heat treatment. The amount of cold deformation that could be applied decreased with increasing aluminum content, until alloys containing 12 pct A1 or more cracked after only a few percent deformation. Annealing Treatments: Samples annealed at temperatures of 700" to 1000°C were sealed in

Jan 1, 1953

By K. C. Hong, R. B. Jensen

The problem of determining the optimum set of steam volumes and cycle lengths for a single well undergoing multicycle steam stimulation in order to maximize the cumulative discounted net income has been formulated mathematically and programmed for a digital computer. The mathematical fonnulation of the problem and the method for its solution are discussed in this paper. The oil production performance during each stimulation cycle was simulated by either a constant percentage or a harmonic decline. Using simple analytical expressions for production performance, the cumulative discounted net income and cumulative time of operation were related to the pertinent process and cost parameters and two principal process control variables (cycle length and steam injection volume). The discrete maximum principles was used to transform the equations for cumulative time of operation and cumulative discounted net income into a set of simultaneous equations. The simultaneous equations then were solved by trial and error on a digital computer to determine the set of cycle lengths and stem injection volumes that gives maximum cumulative discounted net income over the project life. INTRODUCTION Steam stimulation is a process for improving the oil recovery rate from wells producing high-viscosity crudes. The process is applied on an individual well basis and is executed in a series of cycles, each consisting of three phases: steam injection, soaking (steam condensation), and production. Significant increases in production rate following the stimulation operation result from heating the reservoir around the wellbore. As heat is removed with produced fluids and dissipated into nonproductive formations, the production rate declines, usually to near the prestimulation value. Typical production responses are given in case histories reported by Owens and Suter,l and are depicted in Fig. 1. Duration of the production phase is equal to the time for the oil production rate to decline to some specified value and is called the cycle length. (Cycle length is defined as the producing portion of the cycle and does not include the downtime required for steam injection and soaking operations.) Termination of the production phase coincides with the start of steaming for the next cycle. The process is continued, cycle by cycle, until it becomes unprofitable. Models 2-4 have been developed to simulate behavior of a single well during one cycle of steam stimulation and have been used to investigate the effects of system and operating conditions on the production responses. However, these investigations have not shown how the models can be used to determine a most profitable set of operating conditions for a multicycle stimulation project. Perhaps these models are too complicated mathematically to be adapted readily to an optimization study. This paper presents a method for optimizing a multicycle steam stimulation project based on simple production performance models. First, the performance of a steam-stimulated well during each cycle was simulated by either a constant percentage or a harmonic decline model. Using these simple analytical expressions for production performance, the cumulative discounted net income (before tax) and cumulative time of operation for each cycle were related to the pertinent process and cost parameters and two process control variables—the cycle length and the steam injection volume. Finally, the profit function to be maximized was formed. The analogy between the above problem and problems of optimizing multistage decision processes that have been reported extensively in the chemical engineering literatures5-10 in recent years has led this investigation to the use of the discrete maximum principle.5-7 This principle was used to transform the equations for cumulative discounted net income and cumulative time of operation into a set of simultaneous equations characterizing the optimum operating conditions in terms of the two control variables. These equations

Jan 1, 1970

By T. D. Mueller, H. Dykstra

This paper describes a method for obtaining compositions of gas and oil phases in equilibrium with each other at a given reservoir temperature and pressure as lean or enriched gas is injected into a reservoir oil not in equilibrium with the gas. The method is based on calculation of equilibrium constants, K, from the equation log Kp = A + B F, where p is pressure and F is component characterization factor. A and B are constants that vary with a composition parameter. The paper explains how A and B could be determined with a minimum amount of data. The method consists of calculating equilibrium constants as a function of liquid composition and using the K's to calculate changes in compositiort of injection gas as it successively contacts original resetvoir oil at the gas-oil front and the change in composition of reservoir oil as it is successively contacted by the injection gas in the vicinity of an injection well. An iterative process is required. Two examples of the method are given which show how oil and gas compositions and properties are calculated with the aid of a computer. INTRODUCTION The calculation of recovery from lean-gas or enriched-gas injection into a saturated or under-saturated reservoir oil requires a knowledge of how phase properties change in a reservoir between injection well and producing well. To determine the phase compositions or properties experimentally would be difficult and time consuming, especially if one wanted to look at the effect of various injection gas compositions. For some fields an engineer would want to make preliminary calculations on the economics of gas injection before he makes the decision to spend a corrsiderable sum of money for laboratory work to obtain the necessary fluid properties. A method for calculatine compositions and properties based on a minimum of laboratory data is described. The minimum amount of data required is injection gas and reservoir oil composition and injection gas solubility as a function of pressure for an undersaturated oil, or the compositions of mixtures of reservoir fluid with two or more enriched gases, which mixtures have a bubble-point pressure that is the same as the expected average displacement pressure. On the other hand, if the economics appear to be attractive, more laboratory data can be obtained in the form of equilibrium constants for three or more mixtures of the reservoir fluid and injection gases. The method is based on the calculation of K's from the equation, log Kp = A + B F, where K is equilibrium constant, p is pressure and F is component characterization factor. This method of plotting K data by means of the above equation is described by Hoffman, Crump and Hocott.1 A and B are constants that vary with a composition parameter. It is shown how experimental data are used to determine how A and B vary with composition. BASIS OF METHOD EQUILIBRIUM CONSTANTS Equilibrium constant (K) data are required for this method. The K of each component is obtained from an equation that gives the product of K and pressure as a function of component characterization factor. The characterization factor F = b(l/Tb — l/T), where b is a constant characteristic of a given component, Tb is the boiling point in OR at atmospheric pressure of the given component, and T is the temperature of the system in OR. This method of plotting K data is described by Hoffman, Crump and Hocott.l The straight-line equation of the log Kp - F plot is log hp = log Kop +BFi, where Kop is at F =0, i designates the component, and B is the slope of the line. The factor F can be

Jan 1, 1966

By W. A. Young

Polynomial functions of temperature were obtained for the specific heats, thermal diffusivities, and thermal conductivities of zirconium hydrides containing 4 at. pct U. Three hydrides (H/Zr atom ratios of 1.58, 1.65, and 1.70) were studied over the range a" to 900°C and a fourth (H/Zr = 1.81) was studied over the range 0° to 760°C. The specific heats were determined from enthalpy measurements which were obtained using a unique drop calorimeter specifically designed for use with materials in which high temperature phase transitions and/or high dissociation pressures occur. Thermal diffusivities were measured by the flash method using a pulsed laser. The thermal conductiuities were obtained as the product of specific heat, thermal diffusivity, and density. The specific heats agree, within 10 pct, with values derived using a theoretical model in which the hydrogen and zirconium atoms are treated as Einstein and Debye oscillators, respectively. RELIABLE values of the thermophysical properties of the fuel are required to predict the operating temperatures and temperature response of SNAP nuclear reactors. Among the most important of these properties are the thermal conductivity, specific heat, and thermal diffusivity. A considerable number of investigations1-4 have been made of these properties for the Zr-H and Zr-H-U systems.* However, little of the drides, however, this direct method cannot yield meaningful results, since the hydrogen will redistribute under the influence of the thermal gradient, thus forming a concentration gradient; hence, one has a spectrum of compositions, rather than a homogenous alloy. Although the "average" composition of the material may be identical to the initial uniform concentration, the directly measured value of conductivity will be dependent on the thickness of the specimen, due to the highly sensitive dependence of transport properties on hydrogen content. This dependence is strikingly illustrated by the work of Bickel,5 who found that the electrical conduction of zirconium hydrides ranges from primarily hole conduction to primarily electronic conduction, depending upon the hydrogen content. Fortunately, the direct measurement of thermal conductivity is unnecessary, since it can be expressed as the product of the specific heat, thermal diffusivity, and density, all of which can be directly measured with considerable accuracy. EXPERIMENTAL Specimen Preparation. The combined fuel-moderator material used in SNAP reactors is a hydrided zirconium-uranium alloy containing -10 wt pct U. The alloy used in this work was representative of that used in nuclear reactors except that normal uranium was substituted for the enriched uranium required for reactor usage. It was produced by a triple-arc-melt and double-extrusion process. All specimens were prepared from a single cylindrical extrusion which contained 10.30 pet U, 89,35 pct Zr, and 0.35 pct impurities, The specimens for each composition were hydrided simultaneously with ultrapure hydrogen (10 ppm total impurities) using standard fuel production techniques which routinely yield homogeneous, crack-free fuel with negligible increases in the impurity levels. The hydrogen content of each specimen was determined from its weight gain and the density was measured by liquid displacement, Chemical analyses yielded hydrogen concentrations which agreed with the weight gain data within ±0.02 in H/Zr atom ratio) the concentrations of all other elements agreed almost exactly with the initial values after adjustment for the added hydrogen. The specimens used for the determination of specific heat were centerless ground to 2.00 cm diam after hydriding. A thin slice was carefully removed From each end for metallographic examination. In every case, this examination revealed a uniform structure as evidenced by the appearance and distribution of the two phases present in the fuel at the hydrogen concentrations used. TWO specimens (H/Zr = 1.600 and 1.632) appeared to be entirely 6 phase with equi-axed grains; the specimen with H/Zr = 1.756 showed

Jan 1, 1970

By R. F. Yap, N. Arbiter, C. C. Harris

A fully-instrumented driving mechanism has been constructed to study the power, aerating and solid suspension characteristics of several laboratory flotation machines. Machines operating over normal flotation speed ranges give substantially constant power numbers in liquid systems indicating that they operate close to fully baffled turbulent flow conditions. Owing to lack of geometrical scaling, power numbers for different sizes of cells of the same make are different. Even larger differences occur between cells of different manufacturers. For a given impeller, varying the tank size did not significantly affect the power consumption. Tank geometry and baffling has a slight effect on power consumption with shrouded impellers. For a given impeller speed, suspension height decreases while power increases with increasing mass of solids in suspension. While power consumption is hardly affected by particle size and clearance between the impeller and tank bottom, the suspension height significantly increases as clearance increases and as particle size decreases. Aeration was found to affect not only power but also the suspension characteristics of the machine. For closely sized particles, drastic sedimentation occurred when a critical value of the air flow number was exceeded. The critical air flow number decreased with increasing particle size. This effect was less marked with a wide particle size range. The self-aerating capacity of flotation machines increases with cell size at a given speed for the same impeller-shroud system, but decreases in the presence of frother and solids. Equations have been established for correlating all of the studied variables. Data taken from the literature were also correlated with these equations. The modern mechanical flotation machine has, over a period of 60 years, displaced other designs to become the dominant type. Once the correct chemical environmental conditions have been established, the major requirement, selective mineral-air adherence, is essentially a function of two operating variables — impeller speed and air rate. The special nature of this dependence is such that in the same apparatus, but under different operating conditions, adherence can be either prevented or destroyed. Another aspect of this observation is that flotation machines though differing in detail to a considerable extent can produce similar metallurgical results. It must be concluded that having determined the correct reagent levels, establishing the correct operating conditions are at least as important as machine design. Since about 1960, after 30 years of fairly stable circumstances, manufacturers have been developing new types of machines whose major feature is emphasis on pulp flow characteristics by virtue of new im-peller-stator designs. As far as can be ascertained, these new designs necessitate radical departures from accepted impeller speed-air rate values. Performance data are still awaited. Flotation machine development has been empirical, as is selection of operating conditions. The purpose of the work at Columbia University has been to elucidate the fundamentals of the subject so that the purely mechanical aspects of the flotation process can be understood in hydrodynamic terms.1-6 Hopefully, this might lead to intelligent selection of a particular machine and its operating conditions for a specific ore based on a minimum of testing, or even to new types of flotation machines. The present investigation is the most comprehensive to date.7,8 Earlier work, which was largely exploratory, has been repeated and extended and employes the most accurate measuring techniques available. Additionally, sufficient hydrodynamic data were obtained under flotation conditions to delineate the relevant operating ranges. Attention has been given to scaling in that several geometrically scaled tanks and impellers have been constructed and tested; it has been pointed out elsewhere that undistorted geometrical scaling rarely pertains in flotation machine design.5 This paper is divided into sections dealing with relevant combinations of the three phases: liquid, air and solid. Summaries of the literature have been given in previous publications2-4 and will not be repeated here. Recently, several reviews of mixing have appeared, which can be usefully referenced.9-11 It is of interest to note that flotation is not included

Jan 1, 1970

By F. W. Glaser, Benjamin Post

A LTHOUGH most transition metals form a wide variety of boride compounds, the existence of only one zirconium boride, ZrB2, had been established prior to this investigation.' The crystal structure and some properties of a hitherto unreported zirconium boride, ZrB12, are described in this paper. Only one other dodecaboride of a transition metal, UB12, has been reported up to the present.' Chemical analysis of the new compound showed 44 pct Zr and 56 pct B, compared with 41 pct Zr and 59 pct B computed for ZrB12. The difference is within the range of error of the analytical method employed. ZrB12 shows marked metallic properties. It is obtained as a fine black powder. Measurements of electrical resistivity were made at —79°C, + 22°C and +64°C. At 22°C the electrical resistivity is approximately 60 microhm-cm. Over this range the temperature coefficient of resistivity is +0.00162. The thermal conductivity at room temperature is 0.122 watts per cm per "C. The product of the electrical resistivity and thermal conductivity is therefore 8.05, which is not far from the normal Wiedemann-Franz ratio (approximately 7.5 at room temperature). These measurements were made on hot pressed samples which were not always high density specimens. The hardness of ZrB12 on the Rockwell A scale varies between 92 and 92.5. Crystal Structure Determination Single crystals of ZrB12 of a size suitable for X-ray diffraction analysis could not be obtained and powder samples had to be used. Filtered Cu radiation was used throughout. Powder diagrams were indexed on the basis of a face-centered cubic unit cell. After correction for film shrinkage, a Bradley and Jay extrapolation³ to ? = 90" indicated that a, = 7.408 ±0.002A. The volume of the unit cell is 406.5A.V he assumption that there are four "molecules" of ZrB12 per unit cell leads to an X-ray density of 3.63 g per cc. The measured density is 3.7 g per cc (as measured by the immersion method). Relative intensities of reflections were determined by integrating the intensities of diffraction peaks using the count register of a North American Philips wide range spectrometer. Intensities measured in this way showed good agreement with photographic intensities estimated visually using multiple film techniques. The usual Lorentz, polarization, and multiplicity corrections were applied to the observed intensity measurements. There are striking similarities between ZrB12, and UB12. The unit cell of the latter is also face-centered cubic and contains four molecules. a, = 7.473, compared with 7.408 for ZrB12. The radius ratio rB/rU is 0.57; rB/rZr is 0.54. In both ZrB12, and UB12 the four metal atoms in each unit cell are in special positions; only the boron positions need be determined. The latter may be inferred from the extent to which diffraction of X-rays by the 48 boron atoms reinforces or weakens the diffraction by the metal atoms. This effect is relatively much greater in the case of the zirconium compound. In their determination of the crystal structure of UB12, Berthaut and Blum' assumed holohedral symmetry (space group Oh5 , Fm3m) and reported that the U atoms are in positions 4(a): 000; 01/2 1/2; ½ 0 ½ ; ½ ½; the boron atoms were reported to be in positions 48(i) with x = 1/6: ½xx; ½xx; x½x; x½x; xx½; xx½; ½xx; ½xx; x½x; x½x; xx½; xx½

Jan 1, 1953

By Jack White

MUFULIRA Copper Mines, Limited, conducted tests on the concentrator in 1942 to determine which type of ball mill, that is, Conical Trunnion overflow or Cylindrical Grate discharge, produced the greater quantity of finished product at the lowest cost. All the data which follows applies to Mufulira ore and to the particular degree of grinding produced with the classifiers installed at Mufulira concentrator. JACK WHITE, Member AIME, is Concentrator Superzntendent, Mufulira Copper Mines, Ltd., Mufulira, Nortltern Rhodesia. Sun Francisco Meeting, February 1949. TP 2729 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received Feb. 28, 1949. Test Procedure: The test was carried out using ball mills No. 1 to 9 (conical trunnion overflow) as the standard with which to compare No. 10 (cylindrical grate discharge mill). The conical trunnion overflow ball mills are 10 ft diam by 72 in., and the cylindrical grate discharge mill is a No. 99. Each mill runs in closed circuit with a Dorr type DSFX classifier 8 ft wide by 30 ft long. The feed is considered as being identical to all ten units. The figures for the test were derived as follows. Dry Tons Milled: For No. 10 unit (cylindrical grate discharge mill) this figure was taken from the ball mill weightometer, which was corrected for error, and then for moisture content. The weightorneter was checked twice a week during the test, and the error did not exceed 3 pct at any time. The moisture was obtained from a 24 hr moisture sample taken by the ball mill operator hourly, and placed in a closed bucket. The sample was cut where the conveyor drops the feed into the ball mill chute. The Mill Sampling Department made a daily moisture determination on this sample. To obtain the dry tons on units No. 1 to 9 the No. 10 figure was deducted from the month's dry tons milled figure, which, in turn, was taken from the crusher weightometer tons corrected for weightometer error and moisture. All tons reported in this test are short tons of 2000 lb. Ball Mill Hours: This was taken daily from the Shift Boss reports giving actual running hours for each unit. Screen Analyses: Coarse Heads (Ball Mill Feed): The monthly composite coarse heads screen analysis, done by the Mill Sampling Department, was used for the minus 200 mesh in the feed to the mills. F. X. Classifier Overflow: The ball mill operators took an hourly 24 hr sample of the overflows of units No. 1 to 9. This was a hand sample, but cut with a special cutter, and is believed to be very reliable. On No. 10 unit, an hourly 24 hr sample, and an hourly shift sample were cut in the same way. These five samples were split, filtered, and dried by the Research Department and were then wet screened on a 200 mesh screen. The average of the three shifts samples on No. 10 unit had to check the 24 hr sample within 1.5 pct to be acceptable. A weighted composite was cut each day from both 24 hr samples, and at the end of each month it was screened as follows: Wet screened through 325 mesh, the plus 325 then screened on a rotap for 15 min through 65, 100, 150, 200, and 325. This was done in duplicate. All splitting, drying, and screening of samples was done by one of the Mill Research staff, to insure accuracy. F. X. Classifier Overflow Densities: These were taken from the Shift Boss reports. Densities were taken by the ball mill operator every hour. Circulating Loads: These were taken a number of times during the test both by direct method (weighing a measured portion of classifier rake sand, and deducting moisture) and by calculation using the formula:

Jan 1, 1951

By M. S. Hunter, D. L. Robinson

An extremely fine subgrain structure found in aluminum and aluminum alloys is shown and a method for revealing this structure is described. The appearance and some of the characteristics of this structure are described and the possible significance of subgrain structure in terms of chemical, electrochemical, and metallurgical processes is considered. GRAINS and grain boundaries, which constitute the principal manifestations of the crystalline aggregates known as metals, play such an important part in determining the characteristics and properties of metals and alloys that their nature and behavior have long been of much concern to the met-allographer. Many investigators have speculated on the possible existence of a finer structure within the usual grain structure and, through X-ray diffraction and metallographic techniques, have revealed evidence that such finer structures exist. Among these structures are the mosaic blocks and domains described by Burgers1 and others in their contributions on crystalline structure and the dislocation theory, the small units associated with polygoniza-tion described by Cahn,2 and the intragranular blocks revealed more recently by Lacombe and Beaujard.3 his paper describes some novel methods for clearly revealing a very fine granular substructure within the usual grains of pure aluminum and aluminum alloys. It also compares the characteristics and behavior of this subgrain structure with those of the ordinary grain structure and gives some examples of the manner in which this substructure may influence the characteristics of aluminum alloys. Metallographic investigations of aluminum and its alloys have dealt extensively with the functions and behavior of grains and grain boundaries and have evolved a definite concept of the relation between grain structure, orientation and physical, mechanical, chemical, and electrochemical behavior. During the examination of etched samples, a roughening or mottling of the body of certain grains has occasionally been observed. Such roughening obviously represented differential attack by the etching solution, but its true significance was not at first realized. It is now known that this roughening probably rep- resented a subgrain structure, although the particular etching treatments used were not capable of revealing this subgrain structure clearly. Also, in practically all cases, the subgrains were apparently far too small to be resolved by the light microscope. Recently, a method has been developed for revealing clearly the subgrain structure of most aluminum alloys. This method is somewhat unique in that it eliminates much of the usual tedious mechanical polishing and the attendant danger of a surface layer of flowed metal and at the same time is simple, rapid, and effective. It involves the use of the Alcoa R5 Bright Dip, a patented chemical polishing treatment licensed by Aluminum Co. of America. This treatment produces a bright, highly polished surface at least the equal of any mechanical polish and also etches the subgrain boundaries as well as the ordinary grain boundaries to reveal both the grain and subgrain structure simultaneously. Metallographic specimens to be examined are taken through the customary grinding and polishing operations used for aluminum alloys.' The usual care required in the final polishing operation to prevent a flowed surface layer and to obtain a high polish is not necessary, however, because any flowed layer is eliminated and a high polish is produced by the final immersion in the Alcoa R5 Bright Dip. Depending on alloy type, this dip takes from a few seconds to about 3 min, after which the sample is rinsed well, blown dry, and is ready for examination. The substructure can be revealed by some of the usual metallographic methods such as electropolish-ing or mechanical polishing and etching but no method has been found which is the equal of the new chemical polishing treatment. Mechanical polishing followed by the usual metallographic etching is not entirely satisfactory for revealing this substructure, probably because of the flowed surface layer resulting from the mechanical polish. If the usual etching methods are prolonged sufficiently to remove this layer, the specimen surface becomes quite rough and the substructure is not defined clearly.

Jan 1, 1954

By Jack White

MUFULIRA Copper Mines, Limited, conducted tests on the concentrator in 1942 to determine which type of ball mill, that is, Conical Trunnion overflow or Cylindrical Grate discharge, produced the greater quantity of finished product at the lowest cost. All the data which follows applies to Mufulira ore and to the particular degree of grinding produced with the classifiers installed at Mufulira concentrator. JACK WHITE, Member AIME, is Concentrator Superzntendent, Mufulira Copper Mines, Ltd., Mufulira, Nortltern Rhodesia. Sun Francisco Meeting, February 1949. TP 2729 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received Feb. 28, 1949. Test Procedure: The test was carried out using ball mills No. 1 to 9 (conical trunnion overflow) as the standard with which to compare No. 10 (cylindrical grate discharge mill). The conical trunnion overflow ball mills are 10 ft diam by 72 in., and the cylindrical grate discharge mill is a No. 99. Each mill runs in closed circuit with a Dorr type DSFX classifier 8 ft wide by 30 ft long. The feed is considered as being identical to all ten units. The figures for the test were derived as follows. Dry Tons Milled: For No. 10 unit (cylindrical grate discharge mill) this figure was taken from the ball mill weightometer, which was corrected for error, and then for moisture content. The weightorneter was checked twice a week during the test, and the error did not exceed 3 pct at any time. The moisture was obtained from a 24 hr moisture sample taken by the ball mill operator hourly, and placed in a closed bucket. The sample was cut where the conveyor drops the feed into the ball mill chute. The Mill Sampling Department made a daily moisture determination on this sample. To obtain the dry tons on units No. 1 to 9 the No. 10 figure was deducted from the month's dry tons milled figure, which, in turn, was taken from the crusher weightometer tons corrected for weightometer error and moisture. All tons reported in this test are short tons of 2000 lb. Ball Mill Hours: This was taken daily from the Shift Boss reports giving actual running hours for each unit. Screen Analyses: Coarse Heads (Ball Mill Feed): The monthly composite coarse heads screen analysis, done by the Mill Sampling Department, was used for the minus 200 mesh in the feed to the mills. F. X. Classifier Overflow: The ball mill operators took an hourly 24 hr sample of the overflows of units No. 1 to 9. This was a hand sample, but cut with a special cutter, and is believed to be very reliable. On No. 10 unit, an hourly 24 hr sample, and an hourly shift sample were cut in the same way. These five samples were split, filtered, and dried by the Research Department and were then wet screened on a 200 mesh screen. The average of the three shifts samples on No. 10 unit had to check the 24 hr sample within 1.5 pct to be acceptable. A weighted composite was cut each day from both 24 hr samples, and at the end of each month it was screened as follows: Wet screened through 325 mesh, the plus 325 then screened on a rotap for 15 min through 65, 100, 150, 200, and 325. This was done in duplicate. All splitting, drying, and screening of samples was done by one of the Mill Research staff, to insure accuracy. F. X. Classifier Overflow Densities: These were taken from the Shift Boss reports. Densities were taken by the ball mill operator every hour. Circulating Loads: These were taken a number of times during the test both by direct method (weighing a measured portion of classifier rake sand, and deducting moisture) and by calculation using the formula:

Jan 1, 1951

By J. R. Kyte, V. O. Naumann, C. C. Mattax

Imbibition and waterflooding tests at reservoir conditions show that conventional tests at room conditions sometimes lead to recovery estimates that are too low. Core samples which are of intermediate wettability at normal test conditions may be strongly water-wet at reservoir conditions. This was found to be true for samples from two of three reservoirs investigated. For the other reservoir, less difference was observed between the wettability of samples at normal test conditions and at reservoir conditions. Samples which became more water-wet at reservoir temperature and pressure also water flooded more efficiently at reservoir conditions. These results show that core analysis tests on intermediate wettability samples should be performed at reservoir conditions to obtain representative data. INTRODUCTION Throughout the oil industry, core analysis tests normally are performed using refined oils and at room temperature and pressure. This procedure has always been subject to question because the possibility is generally recognized that the reservoir environment may influence displacement behavior. Burkhardt, et al,' have performed waterflood tests at reservoir conditions on East Texas cores. They found little difference between results obtained at reservoir conditions and results of conventional flooding tests at room conditions. As they pointed out, however, this situation might not be general since they obtained data on only one rock and crude-oil system. This paper presents data which demonstrate that it is sometimes necessary to perform core analysis tests in a simulated reservoir environment to properly represent the reservoir wettability and displacement characteristics. The work is specifically concerned with reservoirs which were thought to be of intermediate wettability on the basis of conventional test results at room conditions, i.e., core samples imbibed only small amounts of either oil or water and exhibited no decided preferential wettability characteristics. Tests were performed on cores from three such reservoirs to determine their behavior in the reservoir environment. lmbibition and waterflood tests were used to demonstrate the effect of reservoir environment on reservoir rock wettability and displacement characteristics. Results of tests performed at reservoir conditions were compared with results from conventional tests. Imbibition tests were performed on samples from all three reservoirs. Waterflood tests were performed on samples from only one reservoir. Fluid properties for the three reservoirs studied are shown in Table 1. Tests at reservoir conditions were performed using bottom-hole crude oil at reservoir temperature and pressure. The aqueous phase used in these tests was a synthetic brine approximating the reservoir brine composition. Conventional tests were performed at room conditions with refined oils and synthetic reservoir brine. The oil-to-water viscosity ratios were adjusted to the reservoir values. The cores used in all the tests were taken from the reservoirs using either brine alone or a bentonite-car-boxymethylcellulose mud without additives as coring fluids. Previous tests show that these fluids have no significant effect on the wettability of reservoir rock samples.1 The cores were preserved in brine at the wellsite to prevent wettability changes during shipment and storage. Wellsite imbibition tests have been performed on fresh samples from several reservoirs (including Reservoir A) and compared with later laboratory imbibition tests on samples preserved in brine. The comparison showed that the wettability of the preserved cores was the same as that of fresh, surfaced cores at the wellsite.2 IMBIBITION TESTS Conventional imbibition tests were performed on preserved cores using the apparatus and procedures described by Bobek, et al.2 A sketch of the apparatus for imbibition tests at reservoir conditions is shown in Fig. 1. The preserved samples were first centrifuged to expel excess water and then placed in a stainless-steel container which served

By Peter M. Fozzard

The San Bartolomt silver deposit was discovered by a United Nations team of geologists working with a counter- part team of staff of the Ecuadorian Government's General Directorate of Geology and Mines (DGGM). The Phase I project over five areas of operation during which this discovery was made was financed through a United Nations Development Program contribution of $860,000 and an Ecuadorian Government participation of about $680,000 equivalent. Existence of mineralization at San Bartolomé was first recognized in 1966 when a reconnaissance geochemical stream-sediment program was carried out over a 10 500 km2 (4,054 sq mile) area centered around the city of Cuenca in southern Ecuador. Over the course of this project more than 10,000 samples of stream-sediment, soil, and rock materials were collected. Average costs per sample were $10.00, as follows: collection, $5; sample preparation, $1.60; assay work, $3.40. Initially in the program (1965-1966) sediments were collected along all motorable roads and tracks. Routine analyses, originally by colorimetry and later by AAS, were for Cu, Pb, Zn and occasionally As, Ni, and Co. Discovery geochemical samples from the San Bartolomé drainage area were among the first to be taken in 1965. As luck would have it, the road along which this traverse was taken passes only some 100 m (328 ft) downstream from the mineralized suboutcrop. The relevant two streams sampled are of inconsequential size, some 1 m (3.3 ft) in width, with a limited flow volume throughout the year. Original anomalies were recognized through cold-extractable Cu/Zn analyses. The pH of all river waters was also recorded at sample sites. Resampling the discovery sediments when AAS became available showed total extractable values of between 150 ppm-300 ppm Zn, 550 ppm Pb, and 10 ppm Ag. In 1967 the first followup was by rough-and-ready means. Dithizone field-kits (THM) were used to rapidly test soils from the surrounding area. The area has no outcrop. This work allowed the definition of an area of interest of some 2 km (1.2 miles) x 500 m (1640 ft). Six approximately 1 km (0.6 mile) to 1.5 km (0.9 miles) lines spaced at approximate 250 m (820 ft) intervals were established and used for IP surveys and soil sampling at 50 m (164 ft) intervals. Where one of the lines crossed the westernmost geochemical discovery creek a first-priority geophysical anomaly coincided with a major Zn/Pb (and later Ag) soil anomaly. A pit was sunk and encountered mineralized vein material at a depth of 1.5 m (5 ft). This lucky glory hole confirmed the geochemical discovery and prompted systematic followup. Immediately, costeaning of the west bank of the discovery creek, the Quebrada Ocashuaico, was carried out and exposed weathered and leached mineralization. Nearly 100 mineralized veinlets ranging in thickness from 0.5 cm (0.2 in.) to 8 cm (3 in.) were exposed across the 180 m (59 1 ft) costean. Sixty mineralized veinlets were determined over a 90 m (295 ft) wide zone. Sampling delineated minable widths averaging between 0.16 and 0.31 kg/t (5 and 10 oz per st) Ag with associated copper (very sporadic) lead and zinc. Over the period 1968- 1972 a considerable amount of detailed work was completed: detailed IP, EM Turam, magnetic and mise-a-la-masse geophysics, very detailed soil- sampling, trenching, drilling and glory-hole drifting, and cross-cutting. Numerous problems were encountered: the area was found to be a most difficult geoelectrical target; zero outcrop; pyrite (nonargentiferous zones) associated with faulting; mineralized groundwater; extensive clay development; loss of diamond drill-core, and no two-dimensional surface information. As the program developed the complexity of the structure was slowly unravelled, using a degree of good guesswork. Apart from photogeological and ground geological mapping at various scales, the following

Jan 1, 1985

By Donald L. Katz

The compressing of gas into a partially depleted gas drive oil reservoir to bring the contents to a single phase miscible with gas is proposed as a process worthy of serious study. The compressed gas and vaporized oil would be recovered by cycling. This paper explores the Possibility of recovering oil from reservoirs of 6,000 ft or more by this method. INTRODUCTION Many new methods for increasing the recovery of oil from reservoirs are under consideration in the various research laboratories. One method which should be considered for recovering oil From partially depleted gas drive fields is to compress gas into the reservoir until the contents become a single phase miscible with more gas. Natural gas then may be cycled through the reservoir to recover the oil. This procedure ideally will eliminate the capillary effects of the liquid ill the porous media and should permit recoveries similar to those obtained in cycling operations, probably of the order of 80 per cent. This paper explores the information now available for the prediction of the performance of such a project and discusses the problems likely to be encountered in recovering oil by cycling. For many years dry natural gas has been passed through oil reservoirs to recover natural gasoline which would vaporize from the oil. Recently a process of recovering more of the high boiling hydrocarbons has been described by employing high pressures at which the heavier hydrocarbons have a higher volatility. Nevertheless. this reported method does not eliminate the differential nature of the vaporization process and capillary forces are still present in the reservoir. The process under discussion in this paper would minimize differential vaporization and would remove capillary forces which are responsible for low oil recoveries. Higher gas pressures are required to accomplish this removal of the miniscus, but it does not follow that more gas is required for oil recovery. The process is limited to reservoirs deep enough to permit the use of the required pressure — Probabably 6,000 it and deeper. DESCRIPTION OF THE PROCESS Briefly, the process is to compress natural gas into an oil reservoir which is partially depleted so that it has an oil saturation in the range of 40 to 60 per cent of the hydrocarbon pore space. The injected gas will pass through the channels formerly carrying gas to the wells to build up the pressure and dissolve in the oil phase. This injection will continue without production from the field until the reservoir reaches a single phase. If one were to select unique conditions such that the gas composition, the reservoir oil composition and the Per cent saturation would bring the mixture in the reservoir to the critical temperature and pressure simultaneously the phase behavior accompanying injection is shown by Fig. 1. The oil-gas mixture in the depleted reservoir has a critical temperature at C,. Addition of natural gas to the mixture will give a new critical temperature for each addition. Mixture No. 3 is shown to have its critical temperature at the reservoir temperature and reservoir pressure at P: the critical pressure. Under ideal behavior, the entire reservoir would be at iti critical temperature and pressure and the entire hydrocarbon content would be at a single phase. If the reservoir content were a binary system of methane and a heavy constituent. it would be miscible with more methane. However, for complex mixtures the critical locus does not confine the two phase region, and the dew point curves of Fig. 1 occur above the critical locus. If fluid which was injected into the rezervoir at the critical point were of the

Jan 1, 1952

By W. F. Hosford

A series of aluminum single crystals was subjected to axially symmetric flow by drawing through dies. The orientation dependence of the drawing stress, which indicates the resistance to this type of flow, compares reasonably with predictions of Taylor and of Bishop and Hill. Measured lattice rotations likewise are generally consistent with theory. The most successful analyses of the plastic behavior of polycrystalline metal and its relationship to single crystal behavior are those of Taylor1-3 and of Bishop and Hill.4-6 The purpose of this paper is to provide a critical test of some of the basic assumptions involved in these theories. Both treatments apply to fcc metals and assume the shape change of each grain in a polycrystal to be the same as that of the polycrystal as a whole. Thus for a randomly oriented polycrystal extended under uni-axial tension each grain is assumed to undergo axially symmetric flow. dey = dez = -1/2dex, deyZ = dezx = dexy = 0 [l] where x, y, and z are a set of orthogonal axes, x being the tensile axis. Although [011.] oriented grains in bcc and fcc metals may depart markedly from this ideal behavior,7,8 the assumption is probably quite reasonable for most grains. Under a uniaxial tensile stress, ox, the work dW per unit volume expended in producing an increment of axial strain dex is, dW=oxdex [21 Since this work is expended in slip, dw =STi dyi 131 where Ti and yi are the shear stress and shear strain on the active slip systems. In both analyses Ti is taken to be the same on all slip systems, and dependent only on the total prior shear strain on all systems, so dw = Tdy [41 where t is the shear stress required for slip and y is the sum of the shear strain yi on all slip systems. Combining 121 and [4] and defining M = oX/T The ratio M is a generalized Schmid factor. It relates the tensile stress required for axially symmetric flow, ox, to the basic shear stress, 7, and it also expresses the ratio of crystallographic strain, y, to the tensile strain, Ex It depends only on the orientation of the crystal. Taylor evaluated M for various orientations by finding the least value of dy/dEx which could satisfy the shape change. Bishop and Hill, on the other hand, found M by considering the relative work (1/T)dW/dEx expended by stress states which could activate enough slip systems to produce the shape changes. The results of both methods appear to be equivalent, although certain omissions were made in Taylor's original work. The orientation dependence of M, calculated by the second method,9 is shown in Fig. 1. Taylor used the average 2= 3.06 for all possible orientations to predict the tensile stress-strain curve (oxvs Ex) for a random polycrystal from the shear stress-strain curve (t vs y) of a single crystal. Changes in M from lattice rotation were neglected so points on the ox vs ex curve were simply taken at ox = 3.06t and e = y/3.06 from corresponding points on the t vs y curve. Recent extension of the analyses of Taylor and of Bishop and Hill to crystallographically textured metals has been used to relate plastic anisotropy to textures, and to predict the potential texture hardening that could result from texture control.9 Unfortunately there have been relatively few experimental tests of the underlying theory. Taylor found that the tensile stress-strain curve of polycrystalline aluminum did agree reasonably well with that predicted from a single-crystal T-y curve. Had the single crystal undergone easy glide, how-

Jan 1, 1965

By T. M Morris

THE rate of flotation of solid particles determines the percentage recovery of these particles which can be obtained during a given time interval. It is an established fact that the recovery is greatest in the fine sand size range and falls off on either side of this size range. It is also a fact that the history of the development of concentrating devices has been marked by a desire to recover the small particles: tables were developed to treat material too fine to recover in jigs; flotation recovers material too fine to be recovered on tables. As our ores become more complex and require finer grinding, a greater proportion is in the slow-floating size range. It is therefore of economic importance that the effect of size of particle upon rate of flotation be studied. Many studies have been made along this line. The present investigation attempts to quantify the rate of flotation by means of a rate equation, and then compares the effect of size upon the rate of flotation. It was found that the flotation rate constant increases with increase in diameter of particle in the size range smaller than the optimum size particle. The flotation rate constant decreases with an increase in diameter of particle in the size range coarser than the optimum size particle. This suggested two different actions taking place, and these are discussed. Suggestions for further work in order to improve the flotation rate of both fine and coarse particles are made. The usual method of expressing rate is to plot cumulative percent recovery vs time. If we knew the equation of this kind of curve we could replot it as a straight line, and the slope of the line would be an index of the magnitude of the flotation rate. It is easier to compare straight lines than curves. The basis used for obtaining the equation of the recovery vs time curve is the law of mass action. This law states that the "rate of a chemical reaction is proportional to the 'active masses' of the reacting substances present at any given time." This, of course, implies a constant temperature. We can modify this for our use by using the term flotation reaction instead of chemical reaction and the term floatable particle instead of active masses. dC Thus----— kc [1] where C denotes concentration of particles, t denotes time, k denotes a proportionality constant. If the exponent of C is 1, then we have a first order rate reaction. If the exponent of C is 2, then we have a second order rate reaction. For a first order rate reaction, we obtain, after integration, where k is again a proportionality constant and has the dimension of the reciprocal of time. C, is the original concentration or weight or percentage of floatable particles. C, is the concentration or weight or percentage of floatable particles remaining in the flotation cell after time t. If all particles of the mineral to be floated were capable of floating we could take C, as 100 and C, would be 100 - R, where R is the cumulative percentage recovery of mineral at time t. But it is not usual for all of the particles to be capable of floating, because of surface oxidation, etc. Therefore, we must introduce a factor x which is the percentage of un-floatable mineral. Hence the first order equation is It has been proposed by various workers1-' that this equation describes the flotation rate. More recently N. Arbiter4 states that a second order rate equation fits the recovery vs time curve more closely than does a first order rate equation. Morris- as discussed the evidence presented for this statement. It has been concluded that the first

Jan 1, 1953

By R. G. Grieves, G. Thodos

A method is presented for the accurate calculation of the cricondentherm and cricondenbar pressures of multicomponent hydrocarbon mixtures of known composition. The mixtures may contain six and quite possibly any number of components including paraffins, isoparaffins, olefins, acetylenes, naphthenes and aromatics. The approach is similur to that used for calculating critical pressures and cricondentherm and cricondenbar temperatures. The critical pressure, the normal boiling point and the approximate vapor pressure behavior of each component are all that art required. A stepwise culculation procedure is necessary for mixtures containing more than two components. From an analysis of 22 binary systems and 118 mixtures, the average deviation of calculated cricondentherm pressures from reported values is 2.4 per cent. For nine multicomponent mixtures the average deviation is 1 per cent. Considering 19 binary systems and 108 mixtures, the average deviation of calculated cricondenbar pressures from reported values is 1.7 per cent. For 15 multi-component mixtures, the average deviation is 2.2 per cent. INTRODUCTION A knowledge of the phase behavior in the critical region of multicomponent hydrocarbon mixtures is of value both in industrial processing operations and for the optimum operation of gas condensate reservoirs. Accurate methods of calculating the critical temperatures and critical pressures4,6,7,8,9,23 and cricondentherm and cricondenbar temperatures6p10 of multicomponent hydrocarbon mixtures are available in the literature. If the cricondentherm and cricondenbar pressures could be calculated with equal accuracy, the entire phase diagram of a multicomponent hydrocarbon mixture could be well approximated. The work of Etter and Kay6 is limited to systems containing the normal paraffins and has not been tested on systems containing a heavier component than heptane. In addition, the development of their multicomponent equations is based upon a limited number of mixtures containing from three to six components. Silverman and Thodos have considered systems containing both paraffinic and non-paraffinic hydrocarbons, but their correlation is limited to binary systems and is highly inaccurate for methane systems. Eilerts has done extensive work on the cricondenbar pressure; he has produced an excellent correlation for binary systems. However, his procedure for multicomponent mixtures is chiefly useful for highly complex mixtures requiring a knowledge of the vapor-liquid equilibrium behavior of the mixtures; he has not considered the cricondentherm pressure. The objective of this study was the development of an accurate and rapid method for the calculation of the cricondentherm and cricondenbar pressures of multicomponent mixtures containing all types of hydrocarbons and having a wide volatility range. The approach that was adopted is similar to that used by Grieves and Thodos for cricondentherm and cricondenbar temperaturesl0 and for critical pressures.9 However, methane systems had to be considered separately and a modified stepwise calculation procedure was utilized for the cricondertherm pressure. The correlations were developed in a manner similar to those for critical pressures and cricondentherm and cricondenbar temperatures. Based upon binary data reported in the literature it was observed that the ratios of cricondentherm and cricondenbar pressure to the pseudocritical pressure (molar average), pt/ppc and pp/ppc, respectively, in two-component systems depended upon the mole fraction of the low-boiling component and upon the diversity in properties of the two components. A dimensionless boiling-point parameter Tb,/Tb was chosen to represent the diversity in properties of the components. For a binary system, Ti,'is the molar average of the normal boiling points of the two components involved. For a multicomponent system it is either the molar average of the normal boiling points of all of the components involved or the molar average of the normal boiling point of the pure low-boiling component and of the atmospheric boiling point of the low-boiling-free mixture of

Jan 1, 1965