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By R. D. Carnahan, J. E. White

ThE use of strain gages in the measurement of microplastic behavior of materials is well-known.'-3 Recently it has been suggested that similar techniques might be useful for determining stress relaation. It is the purpose of this report to comment on the use of strain gages in the measurement of strains in the vicinity of 10"6. We will also discuss observations of an anomalous anelastic behavior apparently associated with small temperature changes, which accompanies the unload portion of a load-unload microstrain test. The key to successful strain determinations at levels below 1 pin. per in. is a good gage-mounting technique and either precise ambient temperature control or a set of matched temperature-compensated gages. The importance of good mounting cannot be overemphasized, for example, as in the use of Eastman 910 contact cement. If the cement layer is not sufficiently thin and properly hardened, it is possible to observe anomalous negative stresses when small loads are removed, which relax back to zero in an orderly way with time. Such anomalous behavior, thought to be due to gage bonding, has been reported in microstrain experiments by Thomas and verbach' who observed a negative strain of -3 X lo-' upon unloading. This kind of behavior severely limits the over-all strain sensitivity which can be achieved in such tests. The relaxation of a small positive strain subsequent to unloading in a load-unload experiment is quite normal, however, and is to be expected. The occurrence of an apparent negative strain is also encountered in those instances where the elasticity of the bonding cement is exceeded—for example 0.5 pct or 5000 pin. for cured Eastman 910. An elastic strain of this magnitude can be encountered during load-unload type testing particularly in higher-strength materials (-150,000 yield strength). During the course of microplasticity studies on pure nickel and nickel alloys,' the authors have made the following observation. In a four-point bending test, two active gages are mounted one on each side of the beam as arms R1 and R z of a conventional strain-gage bridge circuit shown in Fig. l(a). This technique provides two advantages: the sensitivity is doubled because R1 and Rz experience opposite strains and temperature compensation is provided automatically because any ambient temperature change would cause both gages to see a strain of like sign whose signals would cancel in the circuit.

Jan 1, 1964

By S. M. Parmley

Experience has shown that there are some factors connected with the drying of fine washed coal that are not present in drying of slack coal as normally practiced at cement kilns or pulverized coal plants. It is the purpose of this paper to show some of these variations as they have been encountered under actual operation. The Champion No. 1 cleaning plant of the Pittsburgh Coal Co. uses the wet system of cleaning coal. The plant is equipped to produce commercial sizes or mixtures, the primary sizes being plus 6 in. and 4 by 6 in., which are hand-picked. Minus 4-in. sizes are all cleaned by the wet process. To produce a commercial product as free of moisture as possible, the washed coal is first passed over sizing and dewatering screens, then each size except the — ?-in. coal is conveyed to loading booms by slow-moving draining conveyors. As the +?-in. sizes are not heat-dried, no data will be given, as it is the purpose of this paper to describe the heat drying of — ?-in. coal as practiced at the Champion No. 1 plant of the Pittsburgh Coal Company. To fully appreciate the conditions, it must be remembered that the — ?-in. product is now shipped at a lower moisture content than when received from the mine. The incoming coal in the — ?-in. size will average 5 per cent. moisture and the shipped product 3 per cent. moisture. This is a case where a wet process gives a reduction of both ash and moisture in the fine sizes. The shipped product, therefore, is more uniform in all characteristics, and uniformity of product is the most important single factor in coal preparation. The 0 by ?-in. coal is first dewatered on slow-moving continuous bucket dewatering elevators, running at the rate of 40 ft. per minute, with 48-in. perforated buckets with ¼ by 1½-in. slots, spaced ? by 2?-in. centers staggered. The moisture in the coal discharged from the elevators runs 20 to 28 per cent., depending on the fineness of the product. The discharge from the dewatering elevator is further drained on a drag-type conveyor equipped with ½-mm. wedge wire screen. The conveyor discharges coal with an 18 to 25 per cent. moisture to three centrifugal dryers of the Carpenter type. The Carpenter dryers

Jan 1, 1931

By Leon Hart

THE nickel-chromium alloys of importance are those containing iron and those free from iron. The most important alloys containing iron, with regard to high tonnage, are the nickel-chromium steels. Straight nickel steel was introduced about the year 1889, but it was not until 1895, when it was found that the addition of chromium greatly increased the FIG. 1.-RESISTIVITY OF NICKEL-CHROMIUM-IRON ALLOYS. strength and resistance to shock, that nickel-chromium steels came into use. The three types of nickel-chromium steels developed at this time were: Type 1, containing 3.50 per -cent. nickel and 1.50 per cent. chromium; type 2, containing 2.00 per cent. nickel and 1.00 per cent. chromium; and type 3, containing 1.50 per cent. nickel and 0.50 per cent. chromium.

Jan 1, 1921

By John Burns

THE object of this chapter is to present data concerning the effect of the introduction of relatively slight amounts of carbon and nitrogen into supersaturated solution in iron. The study is confined to the alpha temperature range of both the Fe-C and Fe-N systems. The age-harden-ing characteristics of these two systems are considered. These data are compared to those of other age-hardening alloy systems and a "classifica-tion" is essayed. A.-RELATION OF LATTICE PARAMETER AND ELECTRICAL CONDUCTIVITY TO CHANGES IN PHYSICAL PROPERTIES DUE TO AGING OF FE-C ALLOYS Since Whiteley1 in 1927 showed that some of the iron carbide that is normally present in slowly cooled low carbon-iron alloys disappears on rapid cooling from just below the A1 point, interest has been manifested in the possibilities of age-hardening in these alloys. Masing and Koch,2 and at the same time and independently, W. Koster,3 proved these alloys to be age-hardenable. A. A. Bates4 a little later also published an interesting paper on changes in physical properties due to the aging of low-carbon steels. Many other papers have appeared showing changes in physical properties in specific instances due to this same phenomenon.

Jan 1, 1934

By W. W. Harvey, F. O. Dudas

Toward hot hydrochloric acid, the usual order of reactivities of the common copper sulfide and associated minerals is reversed, and the rates of H2S formation vary as [ ]. The iron component of chalcopyrite and bornite reports to the solution as ferrous chloride, while pyrite remains essentially unreacted. If a pressure of H2S is maintained in the reactor, copper solubilization is suppressed, and the primary copper sulfides are converted to finely divided secondary sulfides (principally covellite). The HCl leach reside then consists mainly of covellite, pyrite and acid-insoluble gangue. Copper can be selectively leached from this upgraded concentrate to yield a clean, strong copper sulfate solution for direct electrowinning. Preliminary analysis indicates competitive economics with respect to established hydrometallurgical processes. Other concentrate treatments based on an initial HC1 leach are proposed and relative advantages compared. The common denominator of the major process routes considered is the requirement to regenerate HC1 from an FeC12 solution. Five distinct concentrate compositions were employed in the experimental study, which included some attention to the fates of selected minor constituents of the copper concentrate, especially gold, silver, molybdenum, arsenic and selenium. Significant mineralogical features of reactants and products are described.

Jan 1, 1978

By G. P. Pilling

The use of magnetic ore in the blast furnace is a subject of increasing importance. The end of the deposits of lake ore is in sight, although not imminent, and unless some new field is discovered, the use of magnetites will be an increasing factor in the iron production of the country. Enormous deposits of magnetic ore in the country that have been practically untouched contain ore of sufficient richness and purity to prolong materially our ore supply without extensive importation of foreign ores. Magnetic ores can be divided into three general classes: Fine un-sintered, or raw ore; raw lumpy ore; fine ore that has been sintered. Fine Unsintered Ore Typical analysis and screen test of this class of ore from the Adirondack region is as follows: Per Cent. SCREEN TeST pER Cent. Fe.................... 58.00 Remaining on 4 mesh........... 7.50 SiOz.................. 7.50 Through 4 on 8 mesh........ 13.75 Al,O,................. 1.60 8 on 10 meah........ 3.75 Baseg................. 2.77 10 on 20 mesh........ 22.50 P.................... 1.00 20 on 40 mesh........ 27.50 Mn................... 0.13 40 on 60 mesh........ 2.50 S..................... Trace 60 on 80 mesh........ 10.00 80 on 100 mesh........ 2.50 100 mesh........ 10.00 100.00

Jan 1, 1923

By G. P. Pilling

The use of magnetic ore in the blast furnace is a subject of increasing importance. The end of the deposits of lake ore is in sight, although not imminent, and unless some new field is discovered, the use of magnetites will be an increasing factor in the iron production of the country. Enormous deposits of magnetic ore in the country that have been practically untouched contain ore of sufficient richness and purity to prolong materially our ore supply without extensive importation of foreign ores. Magnetic ores can be divided into three general classes: Fine un-sintered, or raw ore; raw lumpy ore; fine ore that has been sintered. Fine Unsintered Ore Typical analysis and screen test of this class of ore from the Adirondack region is as follows: Per Cent. SCREEN TeST pER Cent. Fe.................... 58.00 Remaining on 4 mesh........... 7.50 SiOz.................. 7.50 Through 4 on 8 mesh........ 13.75 Al,O,................. 1.60 8 on 10 meah........ 3.75 Baseg................. 2.77 10 on 20 mesh........ 22.50 P.................... 1.00 20 on 40 mesh........ 27.50 Mn................... 0.13 40 on 60 mesh........ 2.50 S..................... Trace 60 on 80 mesh........ 10.00 80 on 100 mesh........ 2.50 100 mesh........ 10.00 100.00

Jan 1, 1923

By Hans Lundberg

IN ORDER to comprehend the help and information that may be expected from electrical prospecting, it is necessary to have at least a general knowledge of the methods and principles involved in preparing and interpreting results obtained in the field. Electrical prospecting is rather complicated, both in theory and practice, and in order to make a brief description clear to the practical mining man it has been necessary to idealize and generalize the problems, at the risk of having such simplification criticized by the theoretical man. This simplification must not be misinterpreted as showing a lack of theoretical knowledge. FIG. 1.-FLOW OF CURRENT IN AND AROUND A CONDUCTING BODY. For its operation, electrical prospecting mainly depends on the fact that most metallic ores conduct an electric current much more readily than barren rocks. If an electric current flows through a block of ground within which a body of chalcopyrite is enclosed in country rock of schist, the current will find less resistance to its passage through the chalcopyrite than through the schist, even though the passage through the latter be much shorter. This is because the longer path through the chalcopyrite offers less resistance, owing to the superior electrical conductivity of the chalcopyrite (Fig. 1).

Jan 1, 1928

By R. F. Bell, L. W. Eastwood, R. W. James

Among those concerned with the annealing and heat-treating of aluminum and aluminum alloys, it is well known that after co1d-working a coarser grain is usually produced by slow heating than hy more rapid heating. Consequently, for the control of the grain size produced by annealing or heat-treating cold-worked aluminum and aluminum alloys, the heating rate is of considerable practical importance. References in the current literature on the effect of heating rate are numerous, but it appears neither necessary nor desirable to give here a review of the former nark done on this subject. It became evident during some preliminary work on the recrystallizn-tion of aluminium and aluminum alloys that the effect of heating rate depended upon the type of microstructure of the metal. This observation led to the following study of the relationship of the type of microstructure of the alloy to the effect of the heating rate. Materials Investigated Analyses of the aluminum and aluminium alloys investigatted are given in Table 1. Three classes of material are listed, as follows: Class I.— Belonging to the first class are pure aluminium and aluminium containing a second constituent that is soluble in the aluminium matrix at

Jan 1, 1939

By R. F. Bell, R. W. James, L. W. Eastwood

Among those concerned with the annealing and heat-treating of aluminum and aluminum alloys, it is well known that after co1d-working a coarser grain is usually produced by slow heating than hy more rapid heating. Consequently, for the control of the grain size produced by annealing or heat-treating cold-worked aluminum and aluminum alloys, the heating rate is of considerable practical importance. References in the current literature on the effect of heating rate are numerous, but it appears neither necessary nor desirable to give here a review of the former nark done on this subject. It became evident during some preliminary work on the recrystallizn-tion of aluminium and aluminum alloys that the effect of heating rate depended upon the type of microstructure of the metal. This observation led to the following study of the relationship of the type of microstructure of the alloy to the effect of the heating rate. Materials Investigated Analyses of the aluminum and aluminium alloys investigatted are given in Table 1. Three classes of material are listed, as follows: Class I.— Belonging to the first class are pure aluminium and aluminium containing a second constituent that is soluble in the aluminium matrix at

Jan 1, 1939

By H. H. Einstein

Swelling ground is one of the most feared problems in tunneling. Although usually not causing sudden failures during construction, the very large and longlasting deformations give contractors and designers the impression of facing an inevitable phenomenon against which there is no technical defense. Examples are concrete liners up to 1 m (3 ft) thickness that have been cracked or crushed, tunnel inverts that are heaving at 0.1 m (0.3 ft) per week during construction and continue to heave during decades. This paper summarizes essential components of design construction procedures where tunnels in swelling rock can be built to perform satisfactorily. It is important to point out that design and construction cannot and should not be separated. The way the tunnel will be built has to be an integral part of the design. Swelling can be defined as time dependent volume increase and is distinguished from squeezing, another time dependent phenomenon occurring in tunneling. Squeezing involves exceeding the shearing resistance while swelling usually does not. Swelling of rock masses can occur as swelling of the intact rock, swelling of wall rock, of gouge and of filler in the discontinuities of a rock mass, and as a combination of the above. Swelling mechanisms have been discussed elsewhere (ISRM 1983).

Jan 1, 1984

By Edward Sayre

IN shaft sinking for coal mines, the cost item greatly influences the method adopted. This holds true especially when soft material must be traversed. The average life of a coal mine is short. This is clue either to the limited area of the coal basin or to the great expense of maintenance and haulage underground when the entries are extended a considerable distance from the hoisting shaft. Therefore, the engineer in opening a coal mine is confronted with the fact that the cost must be kept within certain bounds else the venture will prove unprofitable. For this reason he may be prohibited from adopting certain safe, but expensive, methods that are used in sinking caissons for foundations, driving transportation tunnels, or other work of permanent construction. A common method of sinking through difficult ground employs the aid of a steel shoe pushed ahead of the shaft timbers. Another is the drop-shaft method. These two methods were used in sinking the main shaft and the air shaft of the Eagle No. 3 mine, at Des Moines, Ia., and the following data show the relative success and cost of the two methods of sinking under the same conditions. A drill log of the material to be penetrated was as follows (see Plate 1, Fig. .1)

Jan 9, 1916

By J. Kent Smith

Vanadium is generally spoken of as a rare element; but, even in the light of our resources as known a couple of years ago, this description could be accepted in a qualified sense only. In fact, vanadium is very widely distributed, being a constituent of most clays, while even caustic soda has been shown to contain almost regularly a minute proportion of it, although the quantity in each case is so small as to render impracticable the extraction of the metal therefrom with profit. The opening-up of a large deposit of vanadium sulphide ore in South America has put a new phase on the commercial outlook of vanadium, the technical value of which for the improrement of steel has been proved by rigorous scientific investigation. This sulphide ore has the following analysis: Per Cent. Vanadium sulphide,.39.84 Molybdenum sulphide,.1.57 Nickel sulphide,.........1.49 Iron sulphide,.........4.07 Arsenic sulphide,.. nil. Copper sulphide,.. nil. Manganese sulphide,..nil. Free sulphur,..30.57 Phosphorus,...nil. Silica,....13.60 Alumina,..........2.46 Combined water, 5.00 Carbonic acid, Lime, magnesia, potash, soda and unaccounted for, 100.00 Being a free-burning ore it is calcined with ease, losing 45 per cent. of its weight in the process. The calcined ore has the following analysis:

Jan 1, 1908

By D. L. Albright, R. W. Kraft

A technique is described whereby the study of crystal perfection through the use of conventional X-ray rockite curves is extended to three dimerzsions. Specinzens of unidirectionally solidified eutec-tic alloy which consist of a nearly perfect parallel arrangement of alternating Platelets of Al and CuAl2, but which contain lamellar faults have been analyzed by this technique in conjunction with X-ray microscopy. Analysis of the data has shown that some rotational symmetry about the growth direction occurs, that small groups of lamellae between faults diffract as a unit, and that the misorientation caused by a fault is on the order of a degree of arc. A eutectic-grain can be defined as that portion of a eutectic specimen in which the crystallographic orientation of each phase AND the microscopic or met-allographic orientation of the phase particles have fixed angular relationships one to another. Eutectic-grains of the A1-CuA12 eutectic, which is a normal lamellar eutectic, have been grown by unidirectional solidification and identified as such.1-3 To a first approximation, a eutectic-grain in this system consists of two interpenetrating single crystals which are related to each other and to the lamellae themselves as follows:

Jan 1, 1962

F. C. LANGENBERGW.*at 8ertoivn,M ass. (written cliscussiont).-I am inclined to the view that the change in physical properties encountered in the material with which the authors are working is due to the relief of internal strains. The statement, on page 1.098 of their paper, calling attention to the fact that this phenomenon disappeared when the material was rolled into 1 7/8 -in. square billets is of particular interest. It is certain that the internal strains set lip by cooling in a small billet of this size would be much less than those produced in a billet having a larger cross-section cooling under the same conditions. The statement that the physical properties of a given test bar were materially changed by standing has been brought to my attention in connection with the testing of gun forgings. I have made a number of observations on forgings produced at Watertown Arsenal to ascertain whether any change in ductility was produced by the aging of the test specimens. The results were always negative, but this can be explained by the fact that ii gun forging is generally a forging that has been quenched and subsequently drawn at a relatively high temperature.

Jan 10, 1919

By R. C. Hall

DEVELOPED to grow single crystals of alloys of high hardness and high melting points is a simple but effective apparatus described in this note. Growth from the melt, that is, by the Bridgman technique, hay be applied to metals or alloys which are physically hard as long as no phase transformation occurs on cooling to room temperature. The present apparatus was employed to grow single crystals of the ferromagnetic AI-Fe alloys above 1 wt pct Al and the Si-Fe alloys above 3 wt pct Si. Single Crystal Growth In a simple form, the method for growth of single crystals from the melt requires a molten metal charge in a pointed crucible which is slowly low-ered through a heated zone into a colder zone. Solidification starts at the bottom point and continues up the charge as the crucible is lowered through the heated zone. If a single crystal nucleates at the bottom, one crystal may grow throughout the charge under ideal conditions of slow growth.4,5 The presently developed method of growth was designed so that the chances that more than one crystal would grow were small. The single crystals were growth by the apparatus illustrated in Fig. 1. The charge was in the form

Jan 1, 1958

By J. A. Herrick Nashua

IN this country steel made in a Siemens furnace or Bessemer converter, is generally tapped into a ladle or shoe, and then drawn through an aperture in its base into the various moulds. In order to regulate the flow of the molten mass a refractory valve is arranged at the aperture. A plumbago nozzle is fixed firmly in this aperture, and a stopper of like material is fitted to it, making a socket valve. In order to raise and depress this stopper at will, a rod is fastened-to it, extending through, the metal and over the brim of the ladle, where it is bent back in a half circle and secured in a slide. This slide plays vertically in a frame, permanently fastened to the outside of the ladle, and is moved by a lever having as a fulcrum a pin fixed in this frame, one end, of the lever being temporarily fixed to the slide, and the other end being moved by hand. Reference being had to the drawing (see Plate 1, Fig. 1), E is the nozzle, D is the stopper, A is the rod, protected as hereinafter described, C is the cast-iron framework, B is the wrought-iron slide, B' is the offset into which the rod, A, enters, and is secured in the usual manner by a key, a. Section J, K, shows the manner of hanging the lever. J is a pin attached to the slide by which the end of the lever raises the slide, B. J is the fulcrum fastened to the frame, C. K (Fig. 1) is a hand-nut fastening the slide, B, to the frame, C, at will. Fig. 2 is a side elevation of ladle, showing the outside working of the parts above described. It is the common practice to protect the rod, A, by a coating of clay and fire-sand, kneaded to the right consistency and applied to the rod, and then thoroughly dried. Just before casting, the plumbago stopper, D, is heated at its extremity to redness separate from the ladle and, at the moment of pouring, is placed in the ladle and slide, and adjusted as well as practicable. Some very serious defects ensue, causing much trouble and vexation as well as actual loss. The fire-clay coating in drying becomes cracked and seamy, and at its best is more or less loose on the rod. The hot metal sometimes cuts

Jan 1, 1879

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 W. M. Robertson

The rate of crack Propagation thvough a solid meta1 in the presence of a liquid metal has been calculated. The crack is assumed to propagate by solution of the solid in the liquid under the influence of an applied stress, with volume diffusion of the dissolved solute through the liquid controlling the propagation. The calculated velocities can be tens of centimeters per second or higher. THE embrittlement of normally ductile solid metals by liquid metals has been the subject of extensive study, as summarized in the book by Rostoker, McCaughey, and arkuus.' In experimental studies of liquid-metal embrittlement it is usually concluded that the observed crack-propagation rates are too high to be accounted for by diffusion processes. Diffusion is considered to be an unimportant factor and various other mechanisms are invoked to account for the experimental observations. The similarities of liquid-metal embrittlement to stress-corrosion cracking, to hydrogen embrittlement of steel, and to low-temperature embrittlement of bcc metals are frequently used as analogies for these mechanisms.1"3 The present paper assesses how rapidly a crack could propagate by a mechanism of volume diffusion through the liquid metal. We assume that the crack propagates by solution of the solid in the liquid at the crack tip under the influence of the applied stress and diffusion of the dissolved solute away from the crack tip. The model uses only macroscopic thermodynamic, kinetic, and elastic concepts. The calculations indicate that this dissolution-diffusion mechanism can give high crack velocities. In some previous treatments4'' of crack propagation in a liquid-metal environment the fundamental step has been the breaking of atomic bonds at the crack tip. The liquid greatly decreases the energy necessary to break these bonds. The present model assumes the crack is filled with liquid metal; the presence of the liquid is essential because diffusion through the liquid is assumed to control the rate of propagation. With proper modification this model could also apply to stress corrosion in a liquid environment. THEORY Consider a crack in a homogeneous elastic continuum, ignoring all the structural details of the solid. This neglects a host of metallurgical details which can be significant in the problem of liquid-metal embrittlement;' but this simple assumption is a useful approach in evaluating the role of diffusion through the liquid. The stress distribution around the crack tip establishes a gradient in the chemical potential at the tip, which causes a diffusion flux through the liquid away from the tip. The solid-liquid interfacial tension works against crack propagation, since propagation requires creation of interfacial area. From these two considerations we derive the diffusion flux, which then yields an expression for the velocity of the crack tip. The concentration of the solute in the liquid, C, is equal to the equilibrium concentration in the presence of an unstressed, flat surface, Co, plus the excess concentration due to the stress, AC(a), plus the excess concentration due to capillarity, AC(y): We calculate AC(o) and AC(y) and then obtain the diffusion flux. Consider (Fig. 1) a long flat crack of length 2L, thickness 2r, and tip radius r, where r remains constant as the crack propagates in the positive x direction. There is no stress ay in the y direction across the flat surfaces of the crack. The magnitude of the stress at the crack tip due to the applied stress, a,, is given by the relation6 ^=^[l-2^] 12] which, for long narrow cracks, becomes The stress increases the chemical potential in proportion to the strain energy.? The excess chemical potential due to the stress, Ap(a), is given by where 52 is the atomic volume of the solid and E the Young's modulus. Inserting Eq. [3] gives Now consider the crack to be filled with a liquid metal. The excess solubility due to stress, hC(a), is given by the excess chemical potential due to capillarity, Ap(y), is given by8 where y is the solid-liquid interfacial energy, and v1 and YZ are the two principal radii of curvature of any surface point. At the crack tip, r1 = -r and vz = m, so TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME

Jan 1, 1967