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By T. A. Pollard, C. R. Sandberg, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler', and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl' have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949

By C. R. Sandberg, T. A. Pollard, E. B. Elfrink

This paper presents an evaluation of compressibility factor data and a discussion of their application to the estimation of gas reserves. A correlation is presented which provides compressibility factors for use in both two-phase and single-phase hydrocarbon systems. Accuracies comparable to those obtained previously for single-phase systems only can be expected. A simple means of predicting the presence or absence of a liquid phase in a condensate system of known composition is illustrated. The correlation is based on 1,030 compressibility determinations from 21 hydrocarbon samples taken from eight oil fields. Of the data used, 75 per cent were from California, 15 per cent were from the Mid-Continent area, and 10 per cent were from South America. The average numerical deviation of the experimental data from this compressibility chart is 1.22 per cent. Charts and tables are included and discussed which illustrate the errors involved through the misuse or nonuse of compressibility factors in estimates of gas-in-place. INTRODUCTION The compressibility factor is a coefficient which expresses the deviation of a gas of given composition from the Perfect Gas Laws. A factor such as this is necessary in any calculation involving volumes of gaseous mixtures, and finds extensive application in the estimation of natural gas and condensate reserves. It is used in the decline curve, the volumetric, and the material balance methods of gas reserves estimation. The behavior of gases at high pressures has been investigated extensively in recent years and considerable data have been assembled on the compressibility characteristics of a number of gases. Notable among the investigators of high pressure gas relationships are Kvalnes and Caddya, Kay" Sage and Laceys, and Brown, Standing" and Katz4. Other contributors are Smith and Watson, Roland and Kaveler', and Stevens and Vance". The data on compressibility factors assembled by these investigators have been presented and correlated in numerous ways; particularly noteworthy is the method first presented by Kay5 which relates compressibility factor "Z" to pseudo-reduced temperature and Pseudo-reduced pressure. Other investigators have used this empirical relationship successfully and numerous charts covering a large number of gases have been constructed on this basis. It is the purpose of this paper to evaluate compressibility factor data and to illustrate the importance of their proper use in the estimation of gas-in-place for both gas and condensate reservoirs. EVALUATION OF COMPRESSIBILITY FACTOR DATA The compressibility chart presented by Standing, Katz, Brown and Holcomb in 1941 is probably the most recent and reliable chart for natural gases. The reliability of the Katz chart has been investigated by the writers for a fairly large number of gases (single-phase) in the pressure range from 500 to 10,000 psia and temperature range from 80 to 400°F. A summary of this comparison is presented in Table I. The numerical average deviation of the chart compressibility factors from the experimental compressibility factors is 1.05 per cent, and the algebraic deviation is -0.28 per cent. The Katz correlation appears to be quite accurate for single-phase hydrocarbon systems. It was based on single-phase systems and does not necessarily provide a means of accurately predicting the behavior of two-phase systems which might be encountered in condensate work. Data published recently by Sage and Oldsl' have enlarged the knowledge of phase behavior in condensate systems by covering extensively the Compressibilities of systems in the two-phase as well as single-phase regions for a wide range of temperatures, pressures and gas-oil ratios. An evaluation of these data indicates that conditions can arise, especially in condensate systems having fairly low gas-oil ratios, in which two phases occur and the usual gaseous compressibility factors do not accurately apply. The measured PVT data of Sage and Olds covering two-phase systems have been correlated with additional such data from the Mid-Continent area and South America; these are presented in Fig. 1. This chart is the result of 1,030 compressibility* determinations from 21 hydrocarbon samples taken from eight oil and condensate fields. Of the data used, 74.75 per cent were from California, 15.45 per cent were from the Mid-Continent area, and 9.80 per cent were from South America. The chart construction is based on the original

Jan 1, 1949

By Arnulf Muan, Klaus Schwerdtfeger

Activity-composition relations in Pt-Cr and Pd-Cr alloys of low chromium concentrations UCr < 0.3) have been determined in order to ascertain quantitatively the extent of reactions to be expected between Cr2O3-containing oxide phases and platinum or palladium crucibles used as containers in studies of oxide equilibria at low oxygen pressures. This work is a continuation of similar work previously

Jan 1, 1965

Eckley B. Coxe, Drifton, Pa.: Anthracite coal differs from other fuels in its greater solidity. It does not burn like coke or wood, or like bituminous and coking coals, which become more or less spongy when heated, so that combustion can take place to some

Jan 1, 1892

By Read Winterburn

This discussion covers only one method of pressure drilling—that developed in the Kettleman Hills field. Thus it is probable that many departures from the procedure herein described would be advisable, and perhaps necessary, in using this method of drilling wells in other localities. Purpose of Pressure Drilling By the early part of 1936, formation pressures in the heavily produced north end of the Kettleman North Dome field had declined to range from 1000 to 1500 lb. per sq. in. This low pressure, combined with the depth of the wells (8000 to 9000 ft.) permitted water to be filtered out of the mud into the producing sands during drilling operations. The loss of water was indicated by loss of fluid from the suction tank while drilling, accompanied by an increase in mud weight. It was found that when water was added to the mud stream at such a rate as to keep the fluid level in the suction tank constant, the mud weight would not vary. This indicates that water only was forced into the sands. The rate of this loss at various wells ranged from 2 to 5 bbl. per hour. At some places complete loss of circulation occurred, and drilling mud to the extent of 200 to 1000 bbl. had to be pumped into the sands before returns were regained. It was believed that these conditions had already begun to harmfully affect production, and that such effect would become more pronounced as formation pressures continued to decline. Pressure drilling with oil was introduced because it eliminated the danger of loading the formations with mud and water. The method also afforded a convenient means of testing as drilling progressed, lessening the amount of formation testing, which had become necessary because of encroaching edge water.

Jan 1, 1938

By C. E. Reistle, G. L. Nye

The East Texas field is in Smith, Rusk, Gregg, Upshur and Cherokee counties, Texas. The discovery well was completed Sept. 8, 1930, near the eastern limit of the field. Within less than one year the new field became the dominant factor in the world production of crude oil. On Aug. 16, 1931, eleven months after completion of the discovery well, there were 1644 wells in the field, and the average daily production was 584,475 bbl. Since that time the number of wells has increased to 8195 on Oct. 1, 1933, and the field has produced 385,979,691 bbl. of oil. The geology of the East Texas field has been discussed by Lahee,1 Levorsen,2 Minor and Hanna3 and others, and it will not be discussed in detail here. The field is a structure of the monocline type on the westward dipping homocline between the Sabine uplift and the East Texas geosyncline. Production is obtained from the Woodbine group, which has been truncated and then sealed by the Austin chalk, which rests unconformably upon it. The oil-saturated part of the sand lies bettween a sub-sea depth of 3050 ft. on the east side of the field, where the Woodbine sand stops and the Austin chalk rests directly upon older formations, and a sub-sea depth of 3320 ft., which was the average depth of the water table in the sand at the time the field was discovered. The field is about 40 miles long and has an average width of approximately 4 1/2 miles. The area within the proven limits of the field is close to 116,580 acres and the normal Woodbine water underlies nearly 62,000 acres on the western side of the field at the present time. The field is unusual in several respects: (1) the tremendous size of the reservoir system and the quantity of oil in place; (2) the large area of the oil and water contact, which makes water movement possible into the oil-bearing part of the structure; (3) the absence of free gas within the main producing sand of the field. Changes in the reservoir pressure during the production history of the field have been greatly affected by

Jan 1, 1934

By S. Zador, C. B. Alcock, K. Sudo

Measurements have been made of the standard free enevgies of formation of the sulfates of cobalt, Cupric copper, nickel, and ferric iron in the temperature range of 750° to 950°C. Dynamic gas-solid techniques have been employed in which oxide-sulfate and basic sulfate mixtures were placed in a stream of gas of controlled SO3 potentials. Thermal analysis and thermogvavimetry were used as detection methods, and it was found THE formation of sulfates during the roasting of sulfide ores is now considered to arise in many cases from the interaction of sulfur trioxide in the gas and the metal oxide which is formed on the sulfide as a first step.&apos; As a preliminary to the investigation of the kinetics of sulfate formation during roasting, measurements have been made of equilibria from which the free energies of formation of cobalt, copper, nickel, and iron sulfates can be that the range of temperatures which could be investigated and the choice of method was largely controlled by the kinetics of these gas-solid reactions. The results are compared with previous results obtained from static measurements with which they agree quite well, and calculations have been made employing themal data to interrelate the present results with those for other sulfates. calculated. The method used has been to expose the solid sulfate (or basic sulfate) to a controlled flowing gas mixture of SO,, 02, and SOs and to observe the temperature of decomposition. The onset of decomposition was detected by thermal analysis or thermogravimetry. EXPERIMENTAL METHODS The thermal-analysis method was similar to that employed by Dewing and Richardson.&apos; The sulfate was dehydrated at 250°C in air, and placed in a small alumina crucible which was held by a quartz ring in the hot zone of a horizontal furnace. The reaction tube of this furnace was made of mullite.

Jan 1, 1965

By F. C. Schora, H. P. Meissner

COUNTERCURRENT staged processes involving chemical reactions between solid and gas streams are becoming more common. Such operations are generally carried out in a series of fluidized beds with each bed acting as a stage. Fig. 1 is a schematic illustration of a series of stages located in a single column, with a solid stream moving down through this column from stage to stage counter to a rising gas stream. The reduction of iron oxides with hydrogen and carbon monoxide is one of the reactions which can be advantageously carried out in such a countercurrent system. Calculation of the performance of a countercur-

Jan 1, 1961

By Klaus Schwerdtfeger, Leo Zwell

The equilibrium between Ir-Fe or Rh-Fe alloys, iron oxide (wüstite or magnetite), and CO2-CO atmospheres has been determined at 1200°C. The data are used to derive the activities in these binary solid solutions. Both systems show negative deviations from Raoult&apos;s law. The lattice parameters are given for the investigated Ir-Fe and Rh-Fe alloys. IRIDIUM and iron form a continuous series of fcc solid solutions at elevated temperatures.&apos; Rhodium-rich Rh- Fe alloys have fcc structure.&apos; In the medium concentration range an ordered bcc phase is stable at temperatures up to about 1300°C. Phase relations in iron-rich alloys are not well-known. No thermody-namic data are available for these alloys. EXPERIMENTAL METHOD The experimental method used was to measure the equilibria between a gas phase of known CO2/C0 ratio, the alloy, and iron oxide (wüstite or magnetite). In one series of experiments the alloys of known composition were heated in CO 2-CO gas mixtures. After treatment (usually 1 day) the sample was quenched to room temperature and its surface examined visually to determine whether an oxide tarnish had formed. The procedure was repeated at slightly higher CO 2/CO ratios until the CO 2/CO ratio of incipient oxidation was found. Subsequently, the CO 2/C0 ratio was lowered again in small increments until the tarnish was reduced. In other experiments mixtures of alloy and iron oxide powders were pressed into pellets and equilibrated with the CO2-CO gas phase. In order to ensure that equilibrium was attained, two specimens with different starting iron content were heated side by side; in most cases, equilibrium was approached in one pellet by reduction of iron oxide and in the other pellet by oxidation of metallic iron. The sample was quenched to room temperature, and the composition of the equilibrated alloy was determined by X-ray measurements of lattice parameters and comparison of these values with calibration curves obtained from alloys of known composition. The oxides present in the specimens were identified by comparison of their diffraction patterns with those in the ASTM Card File. It may be expected from the noble character of iridium and rhodium that no appreciable amount of iridium or rhodium is dissolved in wiistite and magnetite under the present experimental conditions. The activity of iron in the alloy is then equal to that established in the iron oxide by the COrCO atmosphere. The activities of iron in wüstite and magnetite, as a function of oxygen pressure, were taken from the work of Darken and Gurry,

Jan 1, 1969

By H. E. Howe, A. A. Smith

The creep properties of lead alloys have been studied by a number of investigators but most of the work has been done on extruded material and the amount of data available on rolled alloys is surprisingly limited. Greenwood1 and his collaborators investigated various rolled commercial leads containing relatively small amounts of impurities, Phillips2 likewise studied rolled commercial leads, although he did include a few alloys— such as tellurium lead and one per cent antimonial lead. But as far as the authors are aware no data on the creep properties of so-called "hard leads"-—i.e., containing from 4 to 8 per cent antimony—have been published. In this paper some data are presented on a few antimonial lead alloys and compared with a copper-bearing lead. Preparation OF Specimens All the alloys used in this investigation were cast at a temperature of 400°C. into an open cast-iron mold preheated to Ioo°C., the resultant casting being % by I by 10 in. The copper-bearing alloy was cold-rolled by 10 per cent passes to a thickness of 0.100 in. Creep specimens 16 in. long were prepared by clamping the strips between wooden blocks and machining the edges of the strips parallel by means of a plane. Careful manipulation gave parallel specimens with no reduced section and with a minimum of distortion. The antimonial lead castings were hot-rolled in 10 per cent passes at a temperature of I50°C. to a thickness of 0.400 in., the heating being carried out in an electric oven after each pass through the rolls. After the castings had been broken down to 0.400 in., they were allowed to cool to room temperature and then cold-rolled to 0.100 in. with the usual Io per cent passes. Sufficient time was allowed after each pass for the strips to cool to room temperature. The apparatus and method of measuring strain have been adequately described in a previous paper3 and essentially the same practice was used in obtaining the present data. Time-extension curves for only two alloys are given, since these are typical of all. Figs. I and 2 show the time-extension Curves for the copper-bearing alloy A at 30°C. and loo°C., and Figs. 3 and 4 show

Jan 1, 1945

By W. A. Wood, W. H. Reimann

A study is made of the creep that can be induced in armco iron at room temperature by superposing small amplitudes of alternating torsion on a tensile creep load. It is shown that the creep differs from that in comparable tests on copper in being trmsient only. At the same time, though transient, the creep can produce extensions of some 10 pct under creep loads less than the tensile yield stress of the material. The creep can be largely suppressed b$ applying cyclic strain of suitable amplitude before applying the creep load and the metal thereby stabilized. At room temperature, plastic flow in a metal under steady load is normally limited by strain-hardening processes. However, if a small cyclic stress is superposed on the steady load these processes may be more or less neutralized and, as shown in recent investigations,&apos;-4 plastic flow may continue. In this way annealed copper, for example, can be induced to creep continuously to fracture under loads as small as 1 tsi. Dislocation mechanisms possibly responsible for this room-temperature creep have been usefully reviewed by Feltner.But discussion so far has been based mainly on creep as it is found in close-packed metals initially in the annealed state, and their behavior may not be general. In fact, recent work shows that the form of creep in annealed copper is different from that even in cold-worked copper;7 the creep thus depends on the dislocation pattern already in a metal as well as on the metal itself. This paper describes the creep in annealed armco iron, tested in the same way as the above-mentioned copper. One object was to see how creep in a typical bcc metal compared with that in the annealed close-packed metals. Another object was to utilize the fact that a bcc metal like iron has a more pronounced elastic range than close-packed metals like copper and to find to what extent the creep load or superposed cyclic stress had to exceed their re-

Jan 1, 1964

By J. W. Littleford

The Roan Antelope Copper Mines Ltd. are situated in the north central part of Northern Rhodesia, at an altitude of 4000 ft. and 13" south of the Equator. The town site (Luanshya) is well situated and enjoys among other things a really temperate climate for 10 months of the year. The two spring and summer months, October and November, while hot and humid, do not bring any great discomforts as compared with many other mining camps. Strictly modern brick homes, with electric lights, purified water, telephone and water-borne sewage, add to the comfort of the employees. A rainfall of approximately 60 in. per year furnishes ample water for both industrial and domestic purposes. The rainy season generally begins in October and lasts through until March. As much as 3 to 4 in. is recorded in 24 hr., but this offers no difficulties because the runoff is very rapid. The property is connected by a 24-mile branch line from Ndola with the main line of the Beira-Mashonaland and Rhodesia Railways Ltd. Practically all supplies from overseas are transported over this line from Beira, 1743 miles distant on the east coast in Portuguese East Africa. The mine output also leaves Africa from this port. Passenger service is principally via Cape Town or Durban, a distance of about 2100 miles to either port. The Imperial Airways maintain a service from Cape Town to Croydon, taking 9 days for the trip. Connections can be made with this service at Broken Hill, 150 miles south of Luanshya, by either rail or automobile. Thus, after several days of travel through virgin bush, a visitor arrives at a typically modern town site in the heart of Africa. Every development in mining, milling and smelting practice is used to advantage. Plan of Mill The practice in the three principal phases of the production of copper from the ores of this company have been published from time to time. Milling practice, however, is continually changing and what may be

Jan 1, 1935

By S. Gilbert, G. R. Bailey

A further evaluation of the bomb-sampling method for determining the oxygen content of liquid steel is presented. The results of this study and their close agreement with the results of an earlier evaluation confirm the conclusion that the bomb-sampling method is valid for obtaining representative samples for the determination of the oxygen content of a liquid steel bath. WHAT constitutes the most desirable procedure for obtaining a sample suitable for determining the oxygen content of a liquid steel bath has been a controversial subject for several years. In 1952 Huff, Bailey, and Richards&apos; described a modification of the bomb-sampling technique originated by McCutcheon and Rautio.&apos; In both the modified and original techniques, a small cast-iron or steel mold containing aluminum wire and appropriately covered is inserted into the furnace, coated with slag, and then plunged into the metal bath. Upon entering the metal, the cover melts and a sample of the steel bath enters the mold. The data presented by Huff, Bailey, and Richards&apos; indicated that reproducible samples could be obtained by their method. Furthermore, the oxygen analyses from samples obtained by their method agreed better with those from controlled laboratory experiments than did analyses from samples obtained by methods previously suggested for sampling large liquid-metal baths. Most techniques, other than bomb-sampling, require that a sample of liquid steel be removed from the furnace in a well slagged spoon and poured into an iron mold containing aluminum or into a massive copper mold for rapid chilling. Pouring in this manner requires that the sample pass through the air. The controversy, then, is somewhat as follows: Proponents of the spoon-sampling method and similar dip-and-pour methods feel that the introduction of a cold steel mold into a molten steel bath may result in a localized boiling condition that may deplete the steel of oxygen to a significant degree in the area where the bomb is introduced. Conceivably this boil could cause results that are, on the average, too low and nonrepresentative of the bath composition. On the other hand, samples that are spooned and then poured through the air may also be nonrepresentative because of oxidation by the atmosphere. The restrictions imposed in sampling with a spoon are much more stringent than those imposed when sampling with the bomb-type mold within the furnace. The spoon sample must be taken in a well slagged spoon, a requirement that depends on the condition of the slag in the furnace. Also, the samples must be poured as quickly as possible, without shaking the spoon and without allowing slag to enter the mold. The necessity of fulfill-

Jan 1, 1955

By Alfred F. Brainerd

The subject of the supply and the quality of the iron-ore and coke of this State has suffered exaggeration and misrepresentation in both directions. Unsophisticated persons have made extraordinary reports of quality and richness, which could not be supported by facts; while, on the other hand, experts have selected inferior samples, and upon the average of these, which was not by any means the average known to our practice, have based comparisons favorable to other States. Our furnace-records give much better testimony as to the run of our ores, the calorific duty of our coke, and the burden and blast which it will bear. Some of them show poorer ore-mixtures than others; but it is safe to say that the Birmingham furnaces produce from 40 to 60 per cent.. of iron from a mixture of equal parts of the leanest and the richest ores, as classified in large quantities. And certain performances on record here, while they do not represent the regular or average practice, ma: be fairly urged as proof of excellence of raw material, since they would otherwise have been impossible, even as exceptional achievements. Thus oue of our furnaces has made iron with 2500 pounds of coke to the ton of 2300 pounds (Mr. Stratton, 1888); another, with a ton of coke to the ton of iron (Mr. Gordon, 1888); another, with 1.27 ton of coke to the ton (2300 pounds) of iron, the product in the last case being from

Jan 1, 1889

By N. Van Wingen

EFFECTIVE sand permeabilities can be ascertained from core analysis if the laboratory data are compensated to allow for the presence of connate or residual water. Such adjustments can be made by applying empirically derived correction factors. Effective sand permeabilities can be estimated also from analytical studies of field depth-pressure measurements. In one method the time rate of pressure build-up after a well is shut in from steady-state flow is required, and in the other the direct measurement of a steady-state rate of flow and the corresponding equilibrium pressure. The results of the investigation discussed in this paper demonstrate that these methods for determining mean effective sand permeabilities can be correlated.

Jan 1, 1942

By L. Himmel, R. F. Mehl, C. E. Birchenall

The rates of self-diffusion of iron in artifically prepared wustites of various compositions have been determined using the decrease in surface activity technique. Similar measurements are reported for artificial magnetites of nearly stoichiometric composition and for natural hematite single crystals. These data, together with appropriate thermodynamic data derived from the present study or from the literature, are used to calculate the rates of oxidation of iron and its oxides, taking as a basis the theoretical rate equations developed by Wagner. The calculations are compared with experimental rate constant data for these same reactions and are shown to provide essential confirmation for the Wagner theory. For the most part, the results are also consistent with the previously proposed transport mechanisms in the oxides of iron. WHEN a metal is exposed to an oxidizing atmosphere at elevated temperatures, a superficial oxide layer is formed which then thickens according to some characteristic rate law. Provided that the oxide layer is dense and continuous and does not present any paths for gaseous diffusion, continued growth must inevitably involve the migration of the reactants—either the metal or oxygen or both—through the lattice of the solid oxide. This is true whether the reaction rate is controlled by the diffusion process itself or by a slow step in a reaction at one of the interfaces. If the overall rate is limited by diffusion, and if the concentrations or thermodynamic activities of the reactants at the boundaries of the oxide layer are independent of time, the familiar parabolic rate law is observed. Under these conditions, Wagner1 has shown that the rate constant may be expressed in terms of the mobilities of the reacting components and the appropriate concentration or activity gradients which are established across the growing oxide layer. In presenting the phenomenological basis for the theory, Wagner has emphasized the role played by lattice defects in diffusion processes in oxides. The essential validity of this theory has been confirmed by experiment for a number of simple systems including the growth of Cu2O on copper.&apos;-&apos; One of the objectives of the present study has been to extend the Wagner approach to the more complex process of the oxidation of iron and its oxides, and particularly to wustite, which is normally the major constituent of the oxide scales formed on iron at temperatures above approximately 570°C. For this purpose the rates of self-diffusion of iron in w?stite, magnetite, and hematite have been measured by tracer techniques and the necessary thermodynamic data have been obtained from equilibrium studies involving the oxides and their atmospheres. These data have subsequently been used to test the underlying assumptions of the Wagner theory as well as the detailed mechanism of the scaling of iron previously proposed by Davies, Simnad, and Birchenall.5 Lengthy treatments of diffusion and conduction phenomena in ionic crystals have been published." * The latest, by Jost,8 also summarizes much of the existing experimental data. In general, however, the oxides of iron have not been considered specifically and hence a brief review of the available

Jan 1, 1954

By B. Ramaswami

INTERNAL oxidation occurs readily in silver due to the rapid diffusion of oxygen in silver.&apos; It has a marked effect on creep in polycrystalline silver2 and raises the critical resolved shear stress in single crystals of silver.3 However, the effect of oxygen on the work-hardening parameters of silver is not known. It is the aim of this paper to describe the effect of internal oxidation on the work-hardening characteristics of single crystals of silver and an Ag-0.1 at. pct A1 alloy. The materials used were: 99.99 pct Ag from Handy and Harman and 99.993+ pct A1 from Alcoa. Single crystals, 6 mm by 6 mm in cross section of silver and Ag-0.1 at. pct A1 of mo.5 orientation, i.e., the orientation with the Schmidt factor m = 0.5. were grown by the Chalmers technique.4 One set of specimens, referred to herein as oxidized specimens, was annealed at 940°C for 24 hr in a muffle furnace, in air, and furnace-cooled to room temperature. Another set of specimens, referred to as nonoxidized specimens, was annealed in oxygen-free helium at 940°C for 24 hr and furnace-cooled over a period of 7 hr to room temperature. The annealed single crystals were tested at room temperature in a floor-model Instron testing machine. The results are presented in Figs. 1 and 2. A

Jan 1, 1965

By J. L. Huitt, S. R. Darin

The use of a partial monolayer of propping agent to obtain a high flow capacity for a hydraulically induced fracture is discussed. From the results of laboratory work it was shown that a modified form of the Kozeny-Carman relation could be used to describe the flow in the partial monolayer propped fracture. With equations presented in the paper, the density pattern of the propping agent (number of particles per unit of fracture surface) that results in the maximum flow capacity for the fracture can be determined. The maxitnum flow capacity obtained with a partial monolayer is often an order of magnitude greater than the flow capacity obtained in greater width fractures containing multilayers of the propping agent. INTRODUCTION One of the predominant factors controlling the success of a hydraulic fracturing operation is the propping of the fracture. The trend in hydraulic fracturing recently has been an increase in the ratio of propping agent-to-fluid. The primary purpose of this increased ratio is to sustain a propped fracture of greater width. It was shown in a recent study&apos; that for some formations low concentrations of propping agent would result in "closing" or "healing" of the fracture. In some cases, in an effort to insure sufficient propping agent concentration, the fracturing operation is designed to obtain a pack of the propping agent in the fracture. The placing of a pack of propping agent in the fracture provides a fracture of maximum width; however, the width alone does not control the flow capacity of the fracture. The flow capacity is dependent on the permeability of the fracture, as well as the fracture width. Thus, increasing the permeability to obtain larger flow capacities is as important as obtaining a greater width fracture. By increasing the concentration and particle diameter of the propping agent, fractures of sufficient flow capacities are obtainable for effective well stimulation in a number of formations. However, in some of the recovery techniques, the fracture capacity obtained by commonly used practices in fracturing is inadequate. One such recovery technique is gravity drainage via a horizontal fracture placed near the base of the productive zone. For this recovery technique, the fracture capacity desired is usually one to two orders of magnitude greater than the fracture capacity normally obtained in fractures propped with the size of sand commonly used (20-40 mesh). By the use of particles of larger diameter, the permeability of a pack2 is increased; however, even a multilayer pack results in a fracture flow capacity lower than that desired for some formations. For example, a fracture of 1/4-in. width, packed with 8-12 mesh sand of about 2,000 darcies permeability, would result in a fracture flow capacity (permeability X fracture width) of only 40,000 md-ft. If the fracture flow capacity needed is an order of magnitude greater than that cited in the example, an approach different from the formation of a pack in the fracture is needed. One approach is a partial monolayer of large-diameter propping agent. In working with this type of fracture system, it was found that the flow problems were unique to the system; therefore, the study discussed in this paper was made. THEORY AND RELATED STUDIES Previous studies, although related to that described in this paper, have not pertained directly to the flow in a fracture propped with a partial monolayer of propping agent. However, studies such as flow between parallel plates,&apos; flow in packed columns,&apos; fracture flow capacity&apos; and flow in simulated fractures reduce the scope of this flow problem considerably. A fracture propped with a partial monolayer of dropping agent may be considered to be between two extremes — between an open fracture and a bed of particles packed In a conduit of fracture geometry. Thus, it seems appropriate to review the extreme cases.

By P. M. Robinson, M. B. Bever

THE heats of formation at 273°K of the compounds InBi, In2Bi, and TIBi2 have been determined by metal solution calorimetry with bismuth as solvent. The published information on the thermody-namic properties of these compounds is limited. The structure of the compound InBi (mp, 383°K) is tetragonal of the PbO (B10) type.1 The compounds In2Bi (mp, 362°K) and TIBi2 (mp of highest-melting composition, 486°K) are now believed to have structures of the NizIn (B8) type273 and not the A1B2 (C32) structures reported earlier.4, 5 The compounds In2Bi and TIBi2 have limited homogeneity ranges at room temperature, while the compound InBi has no detectable homogeneity range.&apos; Samples of the compounds were prepared from 99.99 pet Bi (Mallinckrodt Chemical Works), 99.999 pet in (American Smelting and Refining Co.), and 99.99 pet Tl (Amend Drug and Chemical Co.) by melting the components in sealed, evacuated Vycor tubes. The compounds InBi and in2Bi were of the stoichiometric compositions. The compound TIBi2 contained 40 pet T1; this composition was chosen because at room temperature the alloy of stoichiometric composition does not lie within the homogeneity range.&apos; The melts were held approximately 50°C above the liquidus for 8 hr and then quenched into iced brine. The samples were homogenized for 48 hr at temperatures 20°C below the temperature of complete solidification. Metallographic examination of sections taken from the center and the ends of the ingots did not reveal second phases or segregation . The heats of formation were determined as the difference in the heat effects on solution of a compound and of a mechanical mixture of its components added from the reference temperature of 273°K to liquid bismuth at 623°K. The details of the calori-metric procedure and method of calculation have been described elsewhere? The calorimeter was calibrated by adding bismuth at 273°K to the bismuth bath at 623°K. The calculated values of the heats of formation of the compounds, listed in Table I, are based on a value of 4.96 keal per g-atom for the difference between the heat contents of bismuth at 273" and 623oK7 No published values are available for the heats of formation of the compounds InBi and In2Bi. Hultgren et a1.7 have calculated a value of -0.50 i 0.10 keal per g-atom for the heat of formation at 423°K of the compound TIBi2 containing 40 at. pet T1 from heat-content measurements in the range from 398" to 700°K and the heats of formation of the liquid alloy. The difference between this value and the value of -0.66 * 0.01 keal per g-atom at 273°K is too large to be attributed to a difference between the heat capacities of the compound and the components over the temperature range 273o to 423oK7 However, the direct determination of the heat of formation by a calorimetric method should give a more accurate value. The heats of formation at 273°K of the compounds InBi and In2Bi lie on a straight line when plotted as a function of composition, Fig. 1. The compound In2Bi, therefore, appears to be barely stable with respect to its neighboring phases. In order for the free energy vs composition curve to be concave towards the composition axis, the entropy change on formation of In2Bi must be more positive than that on formation of InBi. As the compounds are ordered,2, 3, 8 there is no configurational entropy change on formation. The difference between the entropy changes on formation of the two compounds, therefore, is probably associated with the vibrational entropies. In view of the low heats of formation, the changes in vibrational entropy, due to changes in bond strength on formation of the two compounds, are likely to be small. Owing to the volume contractions on formation of the two compounds,5 the vibrational entropies probably decrease slightly but the decrease of the vibrational entropy of InBi is expected to be larger than that of In2Bi.

Jan 1, 1965

By M. T. Martinson, I. W. Nicholson, C. J. Chindgren, F. P. Williams, L. C. Bauerle, S. F. Ravitz

The vanadiferous shales of southeastern Idaho and southwestern Wyoming constitute the largest known reserve of vanadium in the United States.&apos; These deposits have never been exploited except for the relatively small amounts of vanadium recovered by the Anaconda Copper Mining Co. in the treatment of phosphate rock from southeastern Idaho. The maior domestic source of vanadium has been the sandstone ores of southeastern Utah and southwestern Colorado. Early in World War 11, it appeared that these ores could not meet the greatly increased demand for vanadium, so the investigation described in this report was undertaken to develop processes for the recovery of vanadium from the Idaho-Wyoming deposits. The utilization of these deposits became unnecessary, however, because of greatly expanded production from the Utah-Colorado sandstone ores and the continued availability of vanadium from other sources, chiefly Peru. The major use of vanadium is as an alloying agent in the manufacture of high-quality steels. Vanadium constructional steels usually contain 0.05 to 0.20 pct vanadium, which refines the grain and increases the strength, elastic limit, and resistance to shock and fatigue. Vanadium tool steels not used in high-speed work contain 0.10 to 0.60 pct whereas high-speed tool steels contain 1.0 to 4.0 pct. Vanadium compounds are used as catalysts (principally for the oxidation of SO2 to sulphuric acid and of naphthalene to phthalic acid) and in the paint, chemical, ceramic, dye, and printing industries. The selection of the particular ore deposit to be exploited would involve consideration of many factors besides the metallurgical results that might be obtained. Chief among these would be the reserves of ore available, the grade of the ore, and the mining costs. As very little was known about any of these factors, it was necessary to investigate methods of treatment of all the ores under consideration, working with samples obtained in the course of the exploration work, even though they were not positively representative of the whole deposit from which they were taken. Because of wartime conditions prevailing when this investigation was started, first consideration was given to processes that could be put into operation most quickly and would involve minimum use of strategic materials, even though these processes might not be the most economical.

Jan 1, 1949