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By F. W. Bloecher

DETERMINATION of the surface area of finely divided minerals is of interest to mineral engineers engaged in flotation, comminution, and de-watering studies. In the industrial minerals field, many materials are classified as to fineness according to their specific surface (surface area per unit weight). A method of surface area determination has been tested and used in the Richards Mineral Engineering Laboratories at M.I.T. It involves low temperature krypton adsorption measurements using the technique described by Beebe.' During the past fifteen years a number of new surface measurement techniques have been developed. Those that are broadly applicable to materials dealt with by mineral engineers include the permeability method in which a gas or liquid is passed through the sample, and the low temperature gas adsorption methods first described by Brunauer, Emmett, and Teller."" Efforts to make surface determinations from size distribution curves have long been attempted"."." but because of the uncertainty of sub-sieve size distribution and inaccuracies in screen analyses, the method is at best only a rough approximation. The most widely used gas adsorption method utilizes nitrogen gas." Nitrogen adsorption, however, is not particularly suited as a tool for most mineral engineers because the method is not applicable for surface determinations on coarse materials, that is, materials coarser than approximately 150 to 200-mesh. Other gases have been used in mineral engineering studies, particularly ethane."' lo The use of ethane gas, however, involves .a technique that is too sensitive for most mineral engineering work. The permeability method of surface area determination has the disadvantage of not being sensitive enough to detect the surface represented by minute cracks, the so-called internal surface of a particle. The low temperature krypton adsorption method described by Beebe1 utilizes apparatus and techniques that are essentially the same as those used in the ethane adsorption method."1° The surface area is calculated by the B.E.T. method."-' The krypton adsorption technique is particularly suited to the needs of the mineral engineer because: (1) The method can be used for making surface area measurements of rather coarse materials (35 to 48-mesh), as well as extremely fine materials, such as clays or colloidal slimes with specific surface that might be as high as 20 to 30 mb er g. (2) The use of krypton gas offers the advantage of low saturation pressures (2-3 mm) at the conveniently obtained liquid nitrogen temperature. Therefore the krypton vacuum system need not be designed to measure or withstand internal gas, pressures above one atmosphere as is the case with the nitrogen gas method. (3) The krypton technique offers the safety feature of employing liquid nitrogen, as contrasted to the ethane technique in which liquid oxygen is required. Furthermore, ethane vapor pressure at liquid oxygen temperatures is low (about 10 microns), and a high sensitivity McLeod gage is required for pressure readings. (4) The measurement technique with krypton gas is much simpler and faster, and the apparatus is less elaborate than that required with either nitrogen or ethane gases. Apparatus A krypton surface measurement apparatus like that used at M.I.T. is shown in Fig. 1. It is constructed of pyrex glass. A vacuum is maintained by two mercury diffusion pumps in series backed by a mechanical vacuum pump."' The vacuum thermocouple gage is used for checking the vacuum within the system. This type of gage is quite sensitive down to a pressure of 1 micron of mercury," but may be used to indicate pressures much lower than that

Jan 1, 1952

By A. D. Rich

The term "bleaching clay" or "bleaching earth," as used in the oil industries, refers to clays that in their natural state, or after chemical or physical activation, have the capacity for adsorbing coloring matter from oil. There are three common types of bleaching clays: fuller's earth, activated clays, and activated bauxite. Fuller's earth, or naturally active clay, is prepared from bentonites (see Chap. 5) that possess natural activity. It is not activated commercially; in fact, earths of this type ordinarily do not respond satisfactorily to acid activation. Fuller's earth is prepared in pulverized as well as granular form for use in the contacting and percolation processes, respectively. Acid-activated clays also are of bentonitic origin. The basic raw clay, however, is of a type that has a very low natural activity but is highly activable by treatment with mineral acid. Commercial acid-activated clays generally possess several times the decolorizing power (bleaching efficiency) of the best quality of fuller's earth. The former are prepared commercially only in the pulverized grade because of the difficulties in obtaining a satisfactory granular product, and hence are used only in the contact process. Activated bauxite is made by heat-treating bauxite ore, which in its natural state has very little natural activity. The commercial product is prepared in granular form for use in the percolation process on petroleum oils. For the most part, bleaching clay is used commercially in the decolorization of animal, vegetable and petroleum oils, fats and waxes. It is applied in two ways: (1) by the percolation method and (2) by the contacting method. Percolation refers to the passage of oil through a bed of granular clay whereas contacting refers to direct agitation of oil and pulverized clay followed by removal of the clay from the oil by filtration. In either case, the decolorizing effect is obtained by intimate contact between the liquid oil and the solid adsorbent. Petroleum oils are treated commercially by either the percolation or the contact process. Animal and vegetable oils are treated by the contact process only. Composition The raw clays from which both fuller's earth and acid-activated clays are prepared are composed of hydrous aluminum silicates containing varying quantities of magnesium, iron, calcium and other elements. These raw materials are usually nonswelling bentonites derived from volcanic ash or lava by weathering and hydrothermal chemical reactions. The bentonites have as their chief mineral constituent montmorillonite, which has the formula [(OH)4Si6A14O20•nH2O], according to Grim. (See Chap. 5, ref. 6, p. 91.) The underlying reasons are not fully known for the natural activity of the fuller's earth type of clay and its usual failure to further activate with mineral acid in contrast to the natural inactivity of the activatable type of clay. However, it may be said that the bentonites that are responsive to the acid-activation treatment generally have not undergone any drastic metamorphism. The chemical composition is not a reliable means of discrimination between a nonactive, a naturally active, and a nonactive but activable clay, therefore it is not possible to forecast the ultimate quality of a clay on the basis of the raw-clay analysis alone. Table 1 gives typical analyses of representative clays of the foregoing classifications.

Jan 1, 1960

By B. F. Buie

For over 200 years meerschaum has been a significant item of trade between the Near East and countries to the west. Best-known for its use in making smoking pipes and cigar and cigarette holders, it is also used in making a variety of decorative and ornamental items. It is easily carved, and is given an attractive, lustrous finish by rubbing. No published specifications are known, but compact form, purity, uniform whiteness or light color, and uniform, porous texture appear to be requisites. Fig. I a shows the appearance of a piece of crude meerschaum from Turkey; Fig. lb a carved item; and Fig. lc, d, and e show the fibrous and porous texture as revealed by the scanning electron microscope. Neither a major industrial mineral nor a precious stone, meerschaum nevertheless holds a record of long-and continuing-association with art and personal affairs of man. It is also a mineral to which modem methods of exploration and production probably could be profitably applied. An interesting account of the preparation and use of meerschaum in the early part of this century is given by Sterrett (1907). Geology and Mining Mineralogy Meerschaum is recognized now to be the compact variety of sepiolite, the claylike variety of which is one of the minerals included in the chapter on clays. The word meerschaum, from the German meaning "sea foam," was in earlier times used synonymously with sepiolite, a word of Greek origin suggestive of the resemblance of the compact variety-then the only variety known-to cuttlefish bone. At one time meerschaum was used as the commercial name, and sepiolite for the scientific name. However, to think of meerschaum as the name by which sepiolite is known commercially is no longer valid, in view of the recent emergence of the earthy variety as a competitor of bentonite and other clay materials. Present tendency is to restrict the term meerschaum to the compact variety, and to use the term sepiolite as a more general name to include both the compact and earthy varieties. This is the terminology followed in this publication. Meerschaum typically is white to light gray, has a hardness of 2 to 2 ½ , conchoidal to irregular fracture, and specific gravity varying with porosity from about 2 to less than 1. The composition is somewhat variable,- but is near that determined by Schaller (1936) for sepiolite as 2MgO.3SiO2.4H2O. A more modern for mula based on X-ray determination of the crystal structure is given by Caillére and Henin (1961) as (Site) (Mg9)030(OH)6(0H2)46H20. The reason for the firm, compact nature of meerschaum, in contrast with the earthy variety of sepiolite, is not fully understood. It may be due to the presence of a very minor amount of some bonding material such as silica. Scanning electron microscope (SEM) photographs of a specimen from Turkey (Figs. lc-le) indicate that the meerschaum is composed predominantly, if not entirely, of crystalline fibers which merge into sheetlike forms in a complex, intertwined mass. Detailed X-ray and crystal structure data, as well as some data on thermal stability range, are given by Caillère and Hénin (1961) for the sepiolite family of minerals. Mode of Occurrence and Origin Most authors have attributed the origin of meerschaum to alteration of serpentine or other magnesian minerals. The occurrence in alluvium and other surficial deposits does not necessarily indicate that the alteration was supergene. In fact, hydrothermal origin appears more likely for some deposits, though not for all.

Jan 1, 1983

By B. H. Kear, H. G. F. Wilsdorf

After a few percent strain, dislocations in disordered Cu3Au are arranged in groups in ulell-defined slip planes, which contrasts with the more or less random distribution of dislocations in the corresponding ordered alloy. Unusually long and straigkt dislocation segments observed in the ordered alloy are interpreted in terms of cross slip of screw dislocations from their slip planes into cube planes. It is proposed that cross slip, and also dislocation reactions of the Lomer type, play an important role in work hardening of the ordered alloy. ACCORDING to to dislocations in the disordered lattice are only partial dislocations in the corresponding super lattice, so that in the super-lattice dislocations must occur as pairs, with each pair connected by a ribbon of antiphase boundary. Recently, striking confirmation of the theory was obtained by Marcinkowski, Brown, and Fisher3j4 in a study of dislocation configurations in thin foils of the Cu3Au alloy by transmission electron microscopy. In the present investigation, the observations made by these workers have largely been confirmed. Moreover, it has been found that dislocations in the plastically deformed ordered alloys are often unusually long and straight. This paper is mainly concerned with these new observations. A tentative explanation is offered in terms of cross slip of dislocations in the ordered alloys. PREPARATION OF SPECIMENS An alloy close to the stoichiometric composition Cu3Au was prepared by melting together high-purity copper and gold (99.995 pct) under vacuum in a graphite mold. The resulting ingot was rolled down and cut into strips 1 1/2 by 1/8 by 0.005 in. in thickness. All strips were annealed at 900°C for 3 hr and cooled to 500'~. A few of the strips were quenched from ~OO'C, while the remainder were slowly cooled in the temperature range 400" to 150°C at intervals of a few degrees every 24 hr to produce a high degree of order. After this annealing treatment the average grain size of the material was about 0.1 mm. Material in different states of order was obtained by reannealing fully ordered material at temperatures below the critical temperature: followed by quenching. The equilibrium degree of order attained at a particular reannealing temperature was obtained from the paper by Keating and warren.' A simple hand-operated tensile jig was used to give the strips the required amounts of plastic strain. Following straining, a number of specimens were cut from each strip by means of an electrolytic cutting device.= Finally, each specimen was thinned electrolytically using the polishing procedure described by Bakish and Robertson,7 and these thin sections were examined in the Philips EM-100B electron microscope operating at 100 kv. EXPERIMENTAL OBSERVATIONS Antiphase boundaries. The average domain size in the ordered alloys was found by direct observation to be about 0.25 p. Also, it was observed that the grown-in configuration of antiphase boundaries was changed little by plastic deformation, at least up to 6 pct strain. Fig. 1 shows an electron micrograph of a thin foil of partially ordered alloy (S - 0.8) after 3 pct strain. The micrograph shows a few dislocation pairs and a somewhat crystallo-graphic network of antiphase boundaries. The normal to this foil was found by diffraction analysis to be approximately 11121, with principal directions in

Jan 1, 1962

By J. F. Evers, S. Sadiq, F. W. Preston, G. W. Swift

Proper scaling of unsteady-state flow in laboratory gas reservoir models can be achieved if the permeability/fractional porosity ratio is less than 0.5 md. Porous media meeting this specification can be obtained from mixtures of sand and Portland cement provided (1) the water/cement ratio is in the range of 0.35 to 0.40, (2) the sand/cement ratio is in the range of 1/1 to 2/1, (3) the sand grain size is in the range of 48-100 to 18-28 mesh, (4) the mortar curing time is 7 days or more and (5) the cured mortar is dried under vacuum to reduce the temperature level employed during the drying process. The areal homogeneity of the mortars tested is reasonably good, although significant trends in vertical permeability were noted. The Klinkenberg and non-Darcy coefficients of mortar are such that proper scaling of these effects in the laboratory model could be expected. INTRODUCTION A long term deliverability prediction for a gas well is generally based on data determined from flow tests that are of short duration relative to the producing life of the well. These data, together with an estimate of gas reserves in place, form the basis for establishing the parameters of the mathematical model used to predict performance at future times. Results obtained from a mathematical model represent only an interpretation of the physical process being modeled. Experimental verification of the production process from discovery to abandonment is needed where production occurs under carefully controlled conditions. Ideally, one might consider such an experiment to be conducted in the field. Even if the cost of such an experiment could be justified, the time required would make it impractical to consider. However, if the time scaling problem could be handled properly, an experimental model of the gas reservoir production process could provide the necessary data to study the mechanisms of the production process in a reasonable time period. An experimental model has been designed and constructed using the data of this study as a basis. The model reservoir system consists of one producing well located at the center of a right-circular cylinder of porous material. Ten to 15 observation wells are located at strategic offset positions from the producing well. These wells, and the producing well, are fitted with pressure transducers so that the pressure-time history can be recorded at various radial and azimuthal positions in the drainage area during the entire production life of the system. Time is scaled in the model so that the time required to produce gas from discovery pressure to abandonment pressure is about 2 hours. This compares with a 20-year producing life in the model's field counterpart and gives a time scale factor of approximately 1:100,000. DESIGN CRITERIA To establish design criteria for the experimental model, the reservoir is considered to be a finite right-circular cylinder of radius rr, and height h with a producing well of radius rw located at the center and completed through the producing formation. This reservoir consists of a porous medium which has a uniform permeability k and gas porosity and the gas contained in the reservoir has density p, viscosity µ and molecular weight M. Initially, the pressure at all points within the reservoir is uniform at po. and the reservoir temperature is T. Since the reservoir production process has been demonstrated to occur in two distinct transient modes for either Darcy or non-Darcy flow,l it is

By P. E. Schauer

During the initial nine-year deple-tion of the McKamie-Patton pool gas-condensate reservoir, the pressure behavior and fluid analyses indicated pressure maintenance by gas injection would be attractive relative to continued pressure depletion. As a result, a gas cycling program was inaugurated in Aug., 1949, which has since maintained reservoir pressure. In order to evaluate the benefits of this program, the recoveries for natural depletion and for cycling followed by blowdown were determined by calculating the fractional balance of the molar quantities of vapor and liquid remaining in the reservoir and produced at the surface for various stages of depletion. The results of the investigation show theoretical ultimate recovery due to the cycling program will be 42 per cent greater than would be realized under pressure depletion type operation. INTRODUCTION The benefits of gas injection pressure maintenance programs in condensate reservoirs have been recognized and qualitatively described in several papers1-8 during the past 15 years. Some of these papers also describe methods for calculating the increased recovery realized from cycling; however, as a rule, hypothetical reservoirs were used as examples".'.. This paper presents an evaluation of the pressure maintenance program for the McKamie-Patton condensate reservoir and includes a description of the fractional balance method employed to determine the benefits. Reservoir Development and Characteristics The McKamie-Patton pool, Lafayette County, Ark., was opened in June, 1940, with production obtained from the oolitic Smackover lime at a depth of approximately 9,300 ft. The structure is an anticline 8 miles long by 1 to 2 miles wide, and is one of many productive Smackover structures in Southern Arkansas. Of predominant importance is the condensate-bearing gas cap portion of the reservoir, which covers approximately 4,000 acres, attains a maximum thickness of some 200 ft, and has an average thickness of 90 ft. Development of the cap was accomplished with 21 wells drilled on 160 acre spacing. An isopach map of the cap is shown in Fig. 1. In addition, an oil rim is present along most of the periphery of the pool. Production practice includes field separation of black oil, and a high pressure gathering system which carries total well stream from gas cap wells to a plant where condensate is separated and the gas is processed for recovery of natural gasoline, butane, and propane. Since the gas contains appreciable hydrogen sulfide, it is removed by amine contact, after which free sulfur is produced by the Claus process. Core analyses from 1,767 gas cap formation samples averaged 14.2 per cent porosity and 379 md dry air permeability. Connate water was restored on seven samples of gas cap rock by air-brine capillary techniques, from which the interpreted water saturation averaged 28.17 per cent. During the early life of the field, it was believed the recovery mechanism, based on several of the other regional Smackover reservoirs, might be a natural water drive. However, subsequent production and pressure history revealed that the gas cap would not be produced by water drive, but would behave as a closed reservoir. In this respect, during the nine-year period of natural depletion from initial production to Aug., 1949, the cap production of 84.3 billion

Jan 1, 1958

By E. A. Elevatorski

Wollastonite, named after William H. Wollaston, an English chemist, is a calcium metasilicate, CaSiO3. It has a short history as an industrial mineral. The earliest production of wollastonite is reported to be from a deposit near Code Siding, located north of Randsburg, Calif. At this locality small tonnages of wollastonite were quarried during 1933-34 and 1938-41, and processed into mineral wool. This operation was largely experimental and virtually no United States production was again reported until the 1950s when a large deposit near Willsboro, N.Y., was developed by the Cabot Corp. A processing plant was placed on-stream in 1953, with nearly continuous production to date, and it is currently operated by Interpace Corp. Since 1958, wollastonite deposits in the Little and Big Maria Mountains of Riverside County, and in the Panamint Range of Inyo County, both in California, have operated intermittently for production of both ornamental and commercial wollastonite. During 1973, the United States was the major producing country, furnishing about 75% of the world's output. Recent production also has come from Finland, Mexico, and Kenya. Small amounts have been shipped intermittently from India, USSR, New Zealand, Republic of the Sudan, Republic of South Africa, and South-West Africa. The principal use of wollastonite is in the manufacture of ceramics, especially wall and floor tiles. Other uses are for paints, fillers, adhesives, reinforcing agents, plastics, fluxes, and glazes. Mineralogy Pure wollastonite, CaSiO3, has the composi¬tion of 48.3 % CaO and 51.7 % SiO,. However, it is seldom found in the pure state due to the ease with which it takes into solution the metasilicates of manganese, magnesium, iron, and strontium. Predominantly, wollastonite occurs as a contact metamorphic deposit forming between limestones and igneous rocks. Commonly associated minerals are garnet, diopside, epidote, calcite, and quartz. It has a specific gravity of 2.8 to 3.0, and hardness of 4.5 to 5 on Mobs' scale. When pure, it has a brilliant white color, but with impurities it may be grayish or brownish. Luster is vitreous to pearly. Melting point of wollastonite is about 1540° C. Wollastonite occurs in coarse-bladed masses, rarely showing good crystal form. It is usually acicular or fibrous, even in the smallest of particles. The most unique property of crushed and ground wollastonite is its cleavage. Fragments of crushed wollastonite tend to be needle-shaped, imparting a high strength, and this property is the basis for many of its uses. The fiber lengths are commonly in the ratio of 7 or 8 to 1, length to diameter. Some crystals of wollastonite fluoresce under short-wave or longwave ultraviolet light, or both; colors ranging from yellow-orange to pink-orange. Specimens may also show phosphorescence. The brightness of wollastonite is a property of considerable importance to the paint industry. Material, 99% pure, with a size of -325 mesh, has a General Electric reflectance rating of 92 to 96%. Chemically, wollastonite is inert and this property makes it useful as a filler and reinforcing agent. There are two polymorphs of calcium silicates: wollastonite, a low temperature form, and pseudowollastonite, a high temperature form. Inversion of wollastonite to pseudowollastonite occurs at about 1120° C, resulting in an increase in the coefficient of expansion and a color change. Pure white wollastonite, on inversion, may change to a cream tint, or various shades of red or brown. The color change is thought to be due to the presence of iron and strontium.

Jan 1, 1975

By E. T. Turkdogan, L. S. Darken

Using the quadratic formalism, thermodynamic equations are derived for the composition dependence of the heat and entropy of mixing. The applicability of these equations is confirmed by available experimental data on the activities and heats of mixing for binary metallic systems of Group ZZB elements. In a recent paper arkeen' introduced a quadratic formalism describing the composition dependence of the activity coefficient in the terminal regions of binary metallic solutions. That is, in the terminal region, which may extend to as much as 60 at. pct, the logarithm of the activity coefficient, log y,, of component 2 is a linear function of (1 - N,)' where N2 is the atom fraction of component 2. Similarly, for the other component, log yl is a linear function of (1 - N,)'. A number of iron-base binary liquid alloys were shown to obey this quadratic formalism. arkeen' extended this formalism also to any corner of a ternary system and showed that the activity coefficients of the components 1, 2 and 3 (1 is taken as the solvent) can be represented by quadratic terms involving five parameters, four of the binaries and one for the ternary system. Numerous examples given by arkeen' demonstrated the general applicability of the quadratic formalism to iron-base systems over a wide composition range. In this paper further examples are given of binary liquid systems (Group IIB elements, Zn, Cd, and Hg) and of several solid solutions, again demonstrating the appropriateness of this concept. A further purpose of this paper is to extend the quadratic formalism to the enthalpy and excess entropy of binary metallic solutions and to test the equations so found using available experimental data. QUADRATIC FORMALISM FOR HEATS AND ENTROPIES OF MIXING OF BINARY METALLIC SOLUTIONS The following equations, reproduced from Darken's paper, are for the two terminal regions of binary systems. at infinite dilution and a's are temperature dependent parameters to be determined from the experimental data. Although the quadratic formalism is an assumed representation of the data, Eqs. [I] to [4] are thermo-dynamically consistent with the Gibbs-Duhem relation and satisfy Raoult's and Henry's laws as limiting cases. As pointed out previously,' the following form of the Gibbs-Duhem equation facilitates the integration in general but particularly in regions I and 11, where each of the derivatives is constant. The partial molar enthalpy of solution i, (and i; the value of i, at infinite dilution) are related to the activity coefficients y, and y," by the thermodynamic relation Differentiating Eq. [l ] with respect to 1/T and substituting the above thermodynamic relation gives for region (I) It is reasonable to assume that over a temperature range of experimental interest, the enthalpy of mixing is essentially independent of temperature, implying from Eq. [7] that the derivative da,,/d(l/) is also independent of temperature. On the basis of this argument, the temperature dependence of a has the form where £ and S have the units of enthalpy and entropy respectively; they are characteristic parameters for a terminal region of a binary system, e.g. for region (I), C12, S12 and for region (II), d:,,, S2,. Using this equation gives for dff ,/ d(l/), From Eqs. [7] and [9] an expre_ssion is obtained for the composition dependence of L,. Similar calculations are made for El and the results are summarized below for the two terminal regions. For region (I), The corresponding expressions for the molar heat of solution, AHM, are readily obtained from the above equations for the two terminal regions: For region (I),

Jan 1, 1969

By D. J. Pye

Certain high molecular weight synthetic polymers in very dilute solutions decrease water mobility in porous media 5 to 20 times more than would be expected from the solution viscosity. This indicates that increasing water viscosity to reduce adverse mobility ratios in water floods is economically feasible in many situations. Laboratory results are consistent with accepted theory with respect to improved areal sweep, permeability distribution and displacement efficiencies as would be predicted from the solution mobility measured in the core. The laboratory results have been confirmed by field pilot floods which recovered 80 per cent and 100 per cent more oil than comparative water-flood pilots in fields containing 16 cp and 130 cp oil respectively. Economic analyses based on pilot data indicate the method to be profitable. INTRODUCTION The desirability of improving the water-oil mobility ratio in waterflood-ing operations has long been appreciated, especially for high viscosity crudes. Methods of reducing the oil viscosity by application of heat, gas resaturation and miscible drives have met with some success. Conversely, it has been generally conceded that increasing the water viscosity would also be effective, but the amount of thickening agent required to effect an appreciable increase in viscosity is discouragingly high. The use of such materials as glycerin, sugar, or glycols is completely out of the question economically, so that considerable attention has been given to the use of the much more efficient synthetic water-soluble polymers as viscosity improvers; but even these materials are not economically attractive. If increased water viscosity could be economically realized, marked improvements in areal sweep efficiency, as discussed by Caudle and Wittel and others, would be realized in field operations. Similarly, the improved mobility ratio would bring about increased recoveries by correcting permeability distribution problems as discussed by Stiles2 and Dykstra and Parsons,' and improvements in displacement efficiency would be obtained as recognized by Buckley and Leverett4 and Welge.5 LABORATORY STUDIES THE RESISTANCE EFFECT In the course of research to develop a more efficient water-soluble polymer viscosity builder, we discovered that a very few types of water-soluble polymers exhibited a most unusual and very interesting property not previously observed. Among the earliest materials showing such activity were polymers containing acry-lamide. Fig. 1 shows a typical plot of the solution viscosity vs concentration for one of these polymer solutions as determined in an Ostwald viscometer. As usual, such a plot is an approximate straight line on semi-logarithmic paper. Now, an inspection of Darcy's law, shows that a viscosity value can also be determined in a formation sample if the pressure, flow rate and permeability are known. If the core permeability is previously determined with wa- ter or brine, then the viscosity of another aqueous fluid may be determined from the equation. The viscosities so determined for glycerin (glycol or polyvinyl alcohol solutions, for example) agree with the viscometer determinations. However, in the case of the water-soluble polymer solutions in which we are interested, the viscosities measured in the formation sample depart very markedly from the viscometer values. A typical relationship for a polymer solution is also shown in Fig. 1. This unusual departure from the expected response is referred to as a resistance property of the polymer and is quantified as "resistance factor". Since the resistance factor R can best be determined in a core under study, the term has been defined on the basis of the ratio of the brine mobility to the polymer solution mobility at residual oil saturation so that:

Jan 1, 1965

By R. D. Reiswig, J. M. Dickinson

The 0s-Ir equilibrium diagram was determined. The diagram is of the simple peritectic type, with a peritectic temperature of about 2660°C. The solid miscibility gap is narrower than previously reported, the nearly vertical solvus lines occurring at about 42 and 63 wt pct 0s. Widmanstaetten figures resembling martensite in some of the two-phase alloys account for a previously suspected transformation. In view of the long history of use of such alloys, it is surprising that the 0s-Ir equilibrium diagram has not yet been completely determined. The boundaries of the miscibility gap in this system have been estimated to be between 24 and 39 wt pct 0s and 79 and 100 wt pct OS. It has been predicted3 that alloys of ruthenium, osmium, and rhenium with the fcc platinum metals should solidify peritectically in their two-phase regions. The metallographic examination of natural osmiridium alloys has been said4 to indicate, by the presence of a martensitic structure, the existence of a transformation or a phase separation. On the basis of superconducting transition temperature measurements, a 70 at. pct 0s alloy was found5 to be two-phase prior to annealing. EXPERIMENTAL The elemental components used in this work were obtained from several suppliers as sponge. The purities, stated by each supplier to be in excess of 99.8 pct, were confirmed in each case by a semiquantitative spectrographic analysis. The pure components were premelted in an inert-gas tungsten arc furnace with the evolution of some fume, crushed, and pickled for use as alloy melting stock. Upon arc melting to the final compositions, no fume evolution was observed. Because weight losses of the order of 15 mg or less were observed in preparing alloy buttons weighing 15 g, "synthetic analyses" were used in determining the compositions of the alloys. Alloys used in this investigation contained 15, 20, 33, 40, 42, 43, 45, 50, 55, 60, 63, 64, 66, 70, 79, and 80 wt pct 0s. Heat treatments of the alloy buttons and pieces thereof were performed in a previously described6 tungsten tube furnace under pressures of 105 torr or less. It was found that homogenization treatments on the specimens were essential to remove the severe coring which was present, a 3-hr treatment above 2300°C removing all the metallographi-cally visible evidence of coring. Following the various heat treatments, the specimens were "vacuum-quenched" by melting a tungsten fuse wire and allowing them to drop onto a water-cooled copper plate. In a few instances, specimens were quenched into molten tin for comparison, but no difference was apparent. Vacuum-quenched specimens cooled from 2400°C to below a red heat in less than 60 sec. Typical equilibration times varied from 3 hr above 2300°C to 88 hr near 1100°C. The utilization of successively longer equilibration times and the approach to equilibrium from both directions indicated that the times used were sufficient to give a close approach to true equilibrium. Heat-treatment temperatures were measured with a calibrated Leeds and Northrup optical pyrometer through a 0.120-in. lateral sight hole in the tungsten heater tube. It was known that the assumption of black-body conditions inside the 1-in.-diam by 10-in.-long tube was unwarranted. The empirical results of work with thermocouples and melting

Jan 1, 1964

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By Robert B. Hall, Charles W. Bauer

Alunite, KA13(SO4)2(OH)6, was used from the 15th century until early in the present century as a source of potash alum and aluminum sulfate. Since early in this century its use for this purpose has declined to virtually nil with acid treatment of bauxite or clay replacing alunite as a source of alum. During the First World War alunite served as an emergency source of potassium sulfate fertilizer in the United States and Australia. More recently, alunite has been investigated as a nonbauxite ore of aluminum, with potassium sulfate and sulfuric acid as recoverable byproducts. The Soviet Union established a commercial-scale plant in the mid-1960s producing cell-grade alumina from alunitic ore and recovering byproduct potassium sulfate and sulfuric acid. Interest in nonbauxite ores, including alunite, is expected to continue in countries that presently are dependent on imports of bauxite or alumina to support their aluminum industries. The US has the largest aluminum producing and fabricating industry in the world but imports more than 90% of its aluminum-bearing raw materials. This chapter reviews the status of alunite as a potential source of aluminum with byproduct fertilizer, and the resources available to support this industry, whenever this becomes economically feasible. Historical Background Alunite has received little attention until recently, yet for centuries it held a higher place than many of the industrial minerals considered essential today. The deposits of alunite at Tolfa, northwest of Rome, were mined almost continuously from 1462 until about the middle of the present century (DeLaunay, 1907; Lombardi, 1977). The potash alum made from the alunite, called Roman alum, was a valued commodity in international trade, being used in the making of paper, in tanning leather, and as a mordant in textile dyeing. The industry at Tolfa is said to have been controlled by the Vatican and was a source of revenue for the Papal State until fairly recent times (Lombardi et al., 1977). Since early in the present century, the preferred method for making alum has been by acid treatment of bauxite, clay, or other aluminous material, so that alunite has fallen into near-total disuse as a source of alum chemicals. Appreciable quantities of mixed alunite-kaolin rock still are quarried in the Tolfa district for use by the Italian cement industry (Lombardi and Mattias, 1979), but the role of this material in the making of Italian cement is not clear. A large deposit of alunite-bearing rock in Chekiang province, mainland China, is said to have yielded a "great quantity" of alum over a period of several centuries (Yih, 1931). During the 19th century, alunite deposits in France, Spain, Australia, and other countries were exploited as raw material for making potash alum and aluminum sulfate. Interest in alunite was revived during the First World War, not for alum, but as an emergency source of potassium sulfate fertilizer. Large veins of nearly pure alunite had just been discovered on Alunite Ridge, 11 km southwest of Marysvale in Piute County, Utah (Butler and Gale, 1912), and these were quickly brought into production for making potash fertilizer to replace supplies cut off from the famous deposits at Stassfurt, Germany. An estimated 225 kt of Marysvale alunite was mined and processed at that time (Callaghan, 1973). Similarly, Australian alunite deposits were mined as a source of potash fertilizer during both world wars (Hall, 1978).

Jan 1, 1983

John Duer Irving, who left his post as Professor of Economic Geology at the Sheffield Scientific School, New Haven, Conn., to join the Eleventh Regiment of Engineers shortly after the declaration of war, died in France, July 26, 1918, from an attack of pneumonia. Through the initiative of Mr. Benjamin B. Lawrence, a memorial service to Captain Irving was held at St. Paul's Chapel, Columbia University, on Sunday afternoon, August 4, which was' attended by members of Captain Irving's family, and about four hundred of his friends from Columbia, Yale, the American Institute of Mining Engineers and the Association of the 11th Regiment of Engineers. Professor James F. Kemp delivered the memorial address, and has prepared for the Institute the following account of Captain Irving's life, Professor Kemp and Captain Irving having been associated on the most intimate terms for a number of years. , The war has brought home to friends and kin in the western shores of thc Atlantic many losses whose suddenness has the shock of a blow. Many more will follow, but none can leave a sharper sense of regret than the news that the keen and productive mind; the inspiring teacher; the successful and considerate editor, the fine, true man and friend had all passed away when John Duer Irving made the final great gift to the service of his country, in the cause of decency and right. In the closing days of July, the cable brought the tidings that toward midnight on the twentieth of the month pneumonia had proved too great a tax upon one already worn by excessive labors. John Duer Irving was born in Madison, Wis., August 18, 1874. His father, Roland Duer Irving, was at the time professor of geology, mineralogy and metallurgy in the State University of Wisconsin.' Roland . Irving, the father, had entered Columbia College in 1863, but trouble with his eyes compelled him to suspend his studies in the classical course in his sophomore year, and to replace study with some months of life and travel in England. Ultimately his eyes became stronger, and he entered the School of Mincs, completing the course for the degree of Engineer of Mines in 1869, with the third class graduated. The class of eleven contained other future geologists. It numbered on its roll Henry Newton and Walter P. Jenney of the early survey of the Black Hills, where John, future son of Roland, was in the course of years to make his doctor's dissertation, and with its publication his really serious entrance into the profession. Roland Irving was a favorite student of Professor J. S. Newberry, affectionately known to all of his students as "Uncle John," and after some experience in mining and smelting in Pennsylvania and New Jersey, joined the Ohio Survey under Dr. Newberry. The work in Ohio was largely performed during the vacations of the University of Wisconsin, to whose chair Roland Irving was called in 1870. Later, his residence in Wisconsin led to two events of prime importance in the history of American geology. He began the study of the Gogebic iron range and caught the clue to the origin and stratigraphy of the iron ores of all the Lake Superior ranges; and he later undertook the mapping and description of the copper-bearing rocks of the Lake Superior basin. The formative years of the son, John, were passed in a home where the father.

Jan 1, 1920

By Charles R. Cavanaugh, John F. Elliott

The activity of nickel in liquid Pb-iVi alloys which are rich in lead was measured in the temperature region of 700° to 1100°C by means of the galvanic cell: The electrolyte used was stabilized zirconia. Tlze data were correlated using the a function, and a plot of the temperature coefficient aE/aT All subsequent calculations of the thermodynamic properties are based on these two functions. The activity, activity coefficient, and molar properties of mixing of nickel are reported. Nicke1 shows extreme positive deviations frorn ideality while lead shows a very slight positive deviation in the composition range studied The study of the activity of nickel in liquid Pb-Ni alloys reported herein was undertaken to explore the use of stabilized zirconia, an oxygen-ion electrolyte, with liquid-metal electrodes, and to obtain further information on the thermodynamic properties of the liquid binary Pb-Ni system. The cell The reversible electromotive force of the cell results from the difference in the chemical potential of the oxygen at the two electrodes: po, (left) - p~ (right) = -4E5 [I] The chemical potential of oxygen on the right is fixed by the activity of nickel in the solution and pure solid nickel oxide. That on the left is set by pure solid nickel in equilibrium with pure solid NiO. By definition: Since the chemical potential of nickel is related to the chemical potential of oxygen through the equilibrium constant for the formation of NiO from nickel and oxygen gas, the electromotive force of the cell is also expressed In this case, n is 2, E is the reversible potential of the cell, and 5 is Faraday's constant. The work of Kuikkola and wagnerl and Schmalz-reid2 has shown that the stabilized zirconia electrolyte is essentially an ionic conductor at the oxygen levels encountered in the experimental arrangement of the work, i .e., PG > 10-l7 atm. THE EXPERIMENTS The advantage of this type of reversible cell over those using a liquid electrolyte is the simplicity arising because the electrolyte also functions as one of the containing crucibles. A further simplification was the choice of the Ni (sat.)-NiO electrode as the standard. This permitted a ready check on the behavior of the electrolyte, as the potential of the cell must become zero when the right electrode becomes saturated with nickel, either because of a change of temperature or because of the addition of nickel to the electrode. It also permitted the potentials being measured to lie in the most satisfactory experimental range of 0 to 100 mv. Although it was not theoretically necessary, lead was included in the standard electrode as it assured good contact between the electrode and electrolyte. Cell Design. The general arrangement of the experimental cell assembly is shown in Fig. l(a) and the details of the cell itself are contained in Fig. l(b). The anode lead wire on the interior of the cell was connected to a coil of perforated sheet nickel. Within this coil were nickel oxide pellets which were held beneath the surface of the liquid Pb-Ni alloy. A disc of nickel oxide was held at the bottom of the external crucible (alumina) by means of the thermocouple protection tube. The nickel oxide disc and pellets were compressed dry at 10,000 psi and sintered at approximately 1000°C for an hour in air. A major experimental difficulty of reversible electromotive force cells with liquid electrodes is the selection of suitable materials for connecting

Jan 1, 1964

By H. R. Brannon, F. M. Perkins, Weldon O. Winsauer

Both the abnormal resistivity exhibited by shaly reservoir materials and their potential are due to adsorption of ions. Interrelationships between the two have been derived and verified by laboratory results. These relations which have resulted from this work may be used in a qualitative manner to estimate whether or not a particular shaly reservoir contains hydrocarbons, and also to estimate the porosity of shaly sands. INTRODUCTION In spite of the progress which has been made in the last decade toward a better understanding and utilization of the electric log, there remain a number of problems in the interpretation of the log. One of these which is often troublesome is that of divining the nature of the fluids in sandstones or carbonate rocks which contain appreciable amounts of shale. It was shown by Patnode and Wylliel in 1949 that shaly rocks exhibit an abnormally low resistivity when saturated with solutions of low ionic concentrations. This phenomenon has been demonstrated to be due to the adsorptive properties of shale or clay in the rock.' In estimating the fluid content of shaly sands or carbonates from the electric log, it is desirable and sometimes necessary to correct for the abnormally low resistivity. A similar correction is likewise often necessary if attempts are made to estimate the porosity of a stratum from resistivity measurements. The correction may be made from data obtained on core samples and from information on salinity of interstitial water. Cores, however, are not always available. Moreover, even if cores are at hand, their examination is time-consuming. It would be most desirable, therefore, to make corrections of this nature from the log itself. Since both the abnormal resistivity and the potential' are consequences of the adsorption of ions on shale, it should be possible to utilize the potential curve to give better interpretation of resistivity data obtained in logging shaly materials. The work described in following sections was directed toward this end. THEORY Relation of Resistivity of Shaly Reservoir Rock to Adsorpttve Properties In discussing the effect which the presence of shale or clay exerts on the resistivity of a reservoir rock, it is convenient to make use of the resistivity factor.4,5 This quantity has been defined as the ratio of the resistivity of the rock when it is completely saturated with an electrolyte to the resistivity of the electrolyte itself. When the rock, such as a clean sand or carbonate, is free of shale the resistivity factor is virtually independent of the ionic concentration of the electrolyte used to saturate the sample, so that F = R0/Rw = constant for a clean rock . . (1) where F is the resistivity factor, R0 is the resistivity of the rock saturated with electrolyte, and Rw is the resistivity of the electrolyte. When the rock contains argillaceous material, the resistivity factor as defined above is no longer independent of the concentration of the electrolyte used to saturate the rock, but decreases as the ionic concentration of the electrolyte decreases. In explanation of this behavior, it is instructive to consider a sample of shaly porous rock placed in contact with a large volume of a dilute electrolyte. The sample is considered to become saturated with the electrolyte, and to attain equilibrium with it. As a result of adsorption by the shale surfaces within the rock, there is a greater concentration of ions in the solution adjacent to the shale particles in the interstices of the sample than there is in the external solution with which the

Jan 1, 1955

By W. B. Gogarty, H. R. Bailey

Methods are presented for determining molecular diffusion coefficients by using data from, capillary flow experiments. These methods are based on a numerical solution (presented in a previous paper) of the partial differential equation describing the combined mechanisms of flow and diffusion. Results from this numerical solution are given and compared with the approximate analytical solution of G. I. Taylor. The numerical solution is valid over a much larger time range. These methods are applied to experimental results for the fluid pairs water-potassium permanganate solution and amyl acetate-orthoxylene. Both of these fluid pairs have approximately equal densities and viscosities. Graphical and numerical techniques are presented for deter mining diffusion coefficients from the flow data. Values obtained by these techniques are compared with values obtained by other methods. INTRODUCTION The molecular diffusion coefficient is known to be a variable in determining the amount of mixing in a miscible displacement process. The effect of molecular diffusion on dispersion in longitudinal flow through porous media -has been examined by different investigators. These investigators concluded that at low velocities of flow, the amount of dispersion is approximate1y proportional to the molecular diffusion coefficient. The influence of diffusion on fingering, channeling, and overriding has been mentioned by other investigators.4 Recent studies5,6 have been made on the effects of molecular diffusion in connection with the problem of gravity segregation. Many different methods have been developed for the experimental determination of molecular diffusion coefficients? These methods differ mainly according to boundary conditions selected and analytical procedures used. Nevertheless, all of these methods have the condition in common that the bulk fluids in which diffusion is occurring are stationary with respect to each other. In connection with a series of papers on mixing in capillary flow,8-10 Taylor suggested the use of a flow method for determining molecular diffusion coefficients. Additional studies 11-13 have been conducted on miscible displacements in capillary tubes, but the data from these studies were not used for the specific purpose of determining diffusion coefficients. The flow method proposed by Taylor results in a single value of the diffusion coefficient for the fluid pair used in the displacement experiments. This single value represents the true value for the fluid pair when the diffusion coefficient is independent of concentration. If the diffusion coefficient is a function of concentration, the single value obtained by the flow method gives an average value for the coefficient of the fluid pair. These average values are based on diffusion taking place over the entire range of concentration, i.e., from 0 per cent of one fluid to 100 per cent of that same fluid. In field applications of the miscible displacement process, gradients occur over the same range of concentration as are found in the displacements in capillary tubes. Molecular diffusion coefficients obtained from the capillary flow method should, therefore, be especially relevant to field operations. This investigation was undertaken to evaluate the feasibility of obtaining molecular diffusion coefficients from capillary -flow experiments. In making this evaluation, diffusion coefficients were first determined for two systems from data obtained in capillary flow experiments. These values of the diffusion coefficient were then compared to values obtained by other methods. MIXING IN CAPILLARY FLOW—THEORETICAL The theoretical basis for determining molecular diffusion coefficients from capillary flow experiments is the partial differential equation relating the mechanisms of flow and diffusion. For the case of laminar flow and with a fluid pair having equal densities and viscosities, the equation is given by

By J. D. Rice, P. L. Wearden, W. L. Hensou

Solutions to the unsteady-state partial water-drive reservoir performance problem can be obtained through the use of analogue computers or high-speed electronic digital computers. The solutions that have previously been resolved for use on digital computers, however, demand a knowledge of the aquifer parameters. Generally, the analogue computers now in use do not require this knowledge. A solution is presented herein where the aquifer performance, expressed in terms of difference equations, is related to the reservoir performance as expressed by the modified Scbiltbuis material-balance equation. A numerical procedure for a medium-sized digital computer also is presented in which a solution to the set of equations defining the aquifer and reservoir performance is obtained and the aquifer parameters (permeability and sand thickness) are automatically optimized while simultaneously matching the known pressure behavior. Predicted pressure behavior can be calculated using rates from any assumed future production practice. The procedure provides an output format which presents the cumulative, incremental and average rate of natural water influx, the per cent gas-cap expansion, the calculated reservoir pressure, the measured reservoir pressure, and the difference between the measured and calculated pressures. Results of a test problem are presented in comparison with results obtained by the Bruce Analyzer, Ohio Oil Co. 's Pace General Purpose Analogue Computer, and Sun Oil Co.'s Single-Pool Electronic Reservoir Analyzer. These results indicate that unsteady-state reservoir perlormance for a single-pool system can be adequately simulated by a numerical method employing a digital computer and that the special-purpose analogue computer can be supplanted by this method. INTRODUCTION The numerical approach to the unsteady-state partial water-drive reservoir performance problem heretofore has been limited in that solutions have been resolved only for certain fixed parameters. Also, prior to the advent of high-speed electronic digital computers in the last few years, calculations were so tedious and time-consuming that they ordinarily were neglected, or some other means of obtaining the solutions were used. The analogue approach had been used for obtaining solutions to the transmission-of-heat problem and, consequently, means were developed for applying the electrical analogue to the unsteady-state reservoir performance problem. Bruce submitted a paper for AIME publication in Sept. 1942, in which he described an electronic device (now called the Bruce Analyzer) for analyzing the water-drive performance of any reservoir, based on either steady or unsteady-state flow characteristics. 1 Sun Oil Co. adopted the analogue approach in 1949 and now has two special-purpose high-speed electronic reservoir analyzers in use.2,3 Two main features of Sun's analyzers are (1) the high repetitive rate of reproducing the entire history of reservoir performance cyclically a number of times per second, and (2) the elimination of the necessity of knowing the properties of the associated aquifer. Since the advent of larger and faster digital computers, the possibility of incorporating this second feature into a numerical approach appeared feasible. Previous work has been done and material published covering the application of numerical methods to the behavior of the pressure with respect to time at any point in an associated aquifer? However, the aquifer parameters must be known from some source. The material presented in Ref. 4 has been used to a great degree in developing the numerical method described herein. DIFFERENTIAL EQUATION AND BOUNDARY CONDITIONS The problem of simulating the performance of a reservoir and the associated aquifer is to determine the characteristics of the aquifer such that the

By H. R. Brannon, R. J. Robinson, G. W. Kattawar

Accurate prediction of storm wave characteristics are needed for design of offshore structures. Statistical methods of random noise analysis provide techniques for predicting required wave properties. These techniques have been used to analyze and characterize storm wave profiles from Gulf of Mexico recording installations in 34, 65 and .98 ft of water. Correlations based on the results can be used to predict wave crest probabilities and wave shapes for a range of Gulf water depths and storm conditions. Example predictions of wave crest probability as a function of water depth for a particular set of storm conditions are given. INTRODUCTION Accurate predictions of wave crests and wave shapes are needed for design of offshore structures. With predictions of wave crests, platform deck elevations giving adequate protection from exposure to storm waves can be selected. Use of hydro-dynamic wave theories with the wave crest and wave shape predictions permits an estimate of the wave forces an offshore structure must withstand. Observation of ocean waves suggests use of statistical analysis for studying wave characteristics for water depths beyond the breaking wave zone; recent wave generation theories lend support to this approach. l-3 One of the most powerful methods of statistically analyzing wave profiles was introduced by Cartwright and Longuet-Higgins; most of the basic relations used were developed by Rice5.6 in studies of random noise theory. This method predicts wave crest elevation probabilities from two parameters characterizing a wave profile. The statistical approach also provides a means for predicting wave shapes. In the random noise model of a wave profile, surface elevation is represented as an infinite sum of sine waves with closely spaced frequencies and random phase angles. Power density is proportional to the sum of the squares of the amplitudes of sine waves having frequencies within a narrow band, and the distribution of power density as a function of frequency is called the power density spectrum, or power spectrum. The power spectrum characterizes an irregular sea, and hence finds use in motion studies of ships, barges and semisubmersible drilling platforms. From the power spectrum, a wave profile of any duration of time can, in principle, be calculated; this long wave profile depicts the many wave shapes to which a structure may be exposed. Thus, the statistical methods of wave analysis provide an approach to selecting wave shapes as well as wave crest elevations needed for design of offshore structures. For practical application of these techniques, power spectra and related quantities must be predicted from storm properties. Barber and Tucker 7 have reviewed correlations of wave properties and storm conditions. Their review summarizes work of Darbyshire,8 among others, in which a correlation of power spectra with wind intensity of the North Atlantic was developed. These results, plus more recent work by Pierson and Moskowitz and Kitaigorodskii,10 establish feasibility of correlation, but there is no theoretical basis for modifications extending the relations to other areas as remote as the Gulf of Mexico. Hence, to predict characteristics of Gulf of Mexico waves, a study of local observations is needed. This paper presents (1) a practical approach to computing wave profiles hat depict shapes of waves for use in force calculations, (2) a summary of relations for predicting probabilities of wave crest elevations, (3) correlations of parameters needed to apply these methods in the Gulf of Mexico and (4) examples of application of the techniques. THEORETICAL BACKGROUND The following sections summarize relations needed to calculate wave profiles and to estimate wave crest probabilities. These relations also identify quantities that must be related to storm

By John W. Wagner, Robert K. Willardson

Single crystals of Pbl-xSnXTe have been grown from The melt under liquid B2O3 using the Czochralski technique. The PbTe-SnTe crystals were grown from near-stoichiometric melts and from melts with slight deviations from sloichiometry. Crystal growth rates ranging from 1 mm per hr to 1 cm per hr were employed, the latter being generally used. Several investigations were performed to characterize the single crystals grown In this study. The phase diagram of the PbTe-SnTe system was examined. X-ray analyses verified the single-crystal character of the crystals, and powder pattern lattice parameter determinations showed that Vegard's law was followed within the limits of the experimental error. The as-grown crystals were p-type with apparent carrier concentrations of -8 x 1018 to -8 x 1020 carriers per cu cm. Hall coefficients, resistivities, and carrier mobilities were determined as a function of composition. Dislocations were revealed by an electrolytic etch, and the crystals were found typically to contain 2 to 4 x 105 dislocations per sq cm. Microhardness measurements were performed; no maximum in the Vickers hardness us composition curve was seen. Mass spectrometry was used for impurity analyses, and the crystals were found to contain 1 to 2 x 1017 total p-type impurities per cubic centimeter. Distribution coefficients were calculated for the major impurities which were Na, Mg, Al, Si, Cl, and Zn. RECENTLY interest has been stimulated in the preparation and characterization of many alloys of the binary compound semiconductors. This interest is due primarily to the almost unlimited possibilities of adjusting the semiconducting characteristics of these materials by varying the alloy compositions. One alloy system which has been receiving extensive investigation is the PbTe-SnTe system, since these alloys show promise of being useful as emitters and detectors of electromagnetic radiation in the spectral range of 8 to 14 µ. This paper reports on the growth of PbTe-SnTe single crystals by the Czochralski technique and investigations of the general properties of these crystals. The phase diagram of the PbTe-SnTe system was investigated so that specific alloy compositions could be attained. I) CRYSTAL GROWTH The PbTe-SnTe single crystals were pulled from the melt using the Czochralski technique. Generally, the crystals were grown from near-stoichiometric melts, although special growth runs were made from both lead-rich and tellurium-rich melts. Growth of single crystals from up to 5 pct lead-rich melts presented no problems; however, melts with tellurium in excess of -1 pct caused volatilization problems which generally made crystal growth impossible. All melts were prepared from high-purity materials as follows: 1) lead— 6 N— Cominco (Cominco Products, Inc., Spokane, Wash.); 2) tin—5N—Cominco; and 3) tellurium— 5N+— American Smelting & Refining Co., Plainfield, N.J. No further purification of materials was undertaken in this study. The elements were reacted at -1000°C in a vacuum-sealed silica tube for a few hours, a gentle rocking action being used to ensure thorough reaction. The cast ingots were then transferred to a silica crucible for crystal growth. A schematic diagram of the growth apparatus is shown in Fig. 1. The Vycor tube is sealed at both ends by O-ring flanges so that a vacuum or a positive pressure may be maintained in the growth chamber. The pull rod and crucible may be rotated; all crystals produced in this study were grown with the crucible sta-

Jan 1, 1969

By D. J. Carney, E. Van Meter, J. J. Oravec

A study was made of combustion-air temperatures and factors affecting air temperatures in the open-hearth regenerative systems. Air-temperature surveys in the regenerative system revealed marked thermal gradients in the air above the checkers. The design of the fantail-uptake region plays a prominent part in increasing the heat recovery of the regenerative system. THE efficiency of the open-hearth regenerative system is one of the most important factors affecting open-hearth performance. Until recently, this factor has not received the attention in the literature given to many other items affecting performance, such as the type of charge, speed of charging, and the mechanical equipment of the open hearth. J. S. Marsh' emphasized the importance of the flame temperature and its dependence upon the combustion-air temperature. By means of measured air temperatures in open-hearth furnaces, data were presented which showed a remarkable degree of correlation between production rate and combustion-air temperature. This correlation was extremely good in view of the numerous factors, other than air temperature, which affect open-hearth production rates. In Marsh's work, a 100°F increase in air temperature reduced the heat time by approximately 45 min. Realizing the importance of combustion-air temperature, it is desirable to know which factors control the regenerative efficiency of the open-hearth furnace. B. M. Larsen recently discussed this subject.' The present paper illustrates a few of the more important items that affect regenerative efficiency and combustion-air temperature. In the latter part of 1951, a study of open-hearth combustion-air temperatures was begun at the South Works of the United States Steel Corp. In the initial work at open-hearth shop X, which produces low carbon steel products, temperatures were measured in the uptake in a manner similar to that used by Marsh' and the results obtained were very similar to the Bethlehem data. When it was decided to expand the study of combustion-air temperatures, open-hearth shop Y was selected because of the greater variety of furnace-design features, types of steel produced, and firing rates used. With the use of aspirating thermocouples, continuous gas analyzers, thermocouple and optical pyrometers, a study was made of: 1—effect of combustion-air temperature on open-hearth production rate, 2—thermal gradients present in various zones of the regenerative system, 3—effect of furnace-design variations on air temperature and heat recovery, 4-—effect of furnace-operating variables on heat recovery, and 5—variation in heat recovery with furnace age during the normal furnace campaign. Data collected on individual heats at 15 min intervals included air-flow rate, firing rate, checker temperature, combustion-air temperature, and furnace pressure. These data were collected on approximately 230 heats of steel. In addition, information was obtained at random on air infiltration and combustion-gas compositions. The data gathered have shown the desirability of closer control of open-hearth firing practices, a need for reducing air infiltration in the uptake zones, and a need for further study of design of checkers and of uptake-fantail areas. Equipment Air is practically a nonradiating medium. Consequently, in the measurement of air temperatures, the principle of heat conduction must be used rather than heat radiation. For this reason, aspirating-type thermocouple pyrometers normally are used to measure air temperatures. With these devices, air

Jan 1, 1956