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By H. J. Ramey

As fluids move through a wellbore, there is transfer of heat between fluids and the earth due to the diflerence between fluid and geothermal temperatures. This type of heat transmission is involved in drilling and in all producing operations. In certain cases, quantitative knowledge of wellbore heat transmission is very important. This paper presents an approximate solution to the wellbore heat-transmission problem involved in injection of hot or cold fluids. The solution permits estimation of the temperature of fluids, tubing and casing as a function of depth and time. The result is expressed in simple algebraic form suitable for slide-rule calculation. The solution assumes that heat transfer in the wellbore is steady-state, while heat transfer to the earth will be unsteady radial conduction. Allowance is made for heat resistances in the wellbore. The method used may be applied to derivation of other heat problems such as flow through multiple strings in a wellbore. Comparisons of computed and field results are presented to establish the usefulness of the solution. INTRODUCTION During the past few years, considerable interest has been generated in hot-fluid-injection oil-recovery methods. These methods depend upon application of heat to a reservoir by means of a heat-transfer medium heated at the surface. Clearly, heat losses between the surface and the injection interval could be extremely important to this process. Not quite so obvious is the fact that every injection and production operation is accompanied by transmission of heal between wellbore fluids and the earth. Previously, the interpretation of temperature logs',' has been the main purpose of wellbore heat studies. The only papers dealing specifically with long-time injection operations are those of Moss and White3 and Lesem, et al.' The purpose of the present study is to investigate wellbore heat transmission to provide engineering methods useful in both production and injection operations, and basic techniques useful in all wellbore heat-transmission problems. The approach is similar to that of Moss and White:' DEVELOPMENT The transient heat-transmission problem under consideration is as follows. Let us consider the injection of a fluid down the tubing in a well which is cased to the top of the injection interval. Assuming fluid is injected at known rates and surface temperatures, determine the temperature of the injected fluid as a function of depth anti time. Consideration of the heat transferred from the injected fluid to the formation leads to the following equations. For liquid, Eqs. 1, 1A and 2 are developed in the Appendix. These equations were developed under the assumption that physical and thermal properties of the earth and wellbore fluids do not vary with temperature, that heat will transfer radially in the earth and that heat transmission in the wellbore is rapid compared to heat flow in the formation and. thus, can be represented by steady-state solutions. Special cases of this development have been presented by Nowakl and Moss and White.3 Both references are recommended for excellent background material. Nowak' presents very useful information concerning the effect of a shut-in period on subsequent temperatures. Since one purpose of this paper is to present methods which may be used to derive approximate solutions for heat-transmission problems associated to those specifically considered here, a brief discussion of associated heat problems is also presented in the Appendix. Analysis of the derivation presented in the Appendix will indicate that many terms can be re-defined to modify the solution for application to other problems. Before Eqs. 1, 1A and 2 can be used, it is necessary to consider the significance of the over-all heat-transfer coefficient U and the time function f(t). Thorough discussions of the concept of the over-all heat-transfer coefficient may be found in many references on heat transmission. See McAdams5 or Jakob," for example. Briefly, the over-all coefficient U considers the net- resistance to heat flow offered by fluid inside the tubing, the tubing wall, fluids or solids in the annulus, and the casing wall. The effect of radiant heat transfer from the tubing to the casing and resistance to heat flow caused by scale or wax on the tubing or casing may also be included in the over-all coefficient. According to McAdams, on page 136 of Ref. 5>

By J. Orkiszewski

A method i.s presented which can accurately predict, with a precision of about 10 percent, two-phase pressure drops in flowing and gas-lift production wells over a wide range of well conditions. The method is an extension of the work done by Grifith and Wallis and was found to be superior to five other published methods. The precision of the method was verified when its predicted values were compared against 148 measured pressure drops. The unique features of this method over most others are that liquid holdup is derived from observed physical phenomena, the pressure gradient is related to the geometrical distribution of the liquid and gas phase (flow regimes), and the method provides a good analogy of what happens inside the pipe. It takes less than a second to obtain a prediction on the IBM 7044 computer. INTRODUCTION The problem of accurately predicting pressure drops in flowing or gas-lift wells has given rise to many specialized solutions for limited conditions, but not to any generally accepted one for broad conditions. The reason for these many solutions is that the two-phase flow is complex and difficult to analyze even for the limited conditions studied. Under some conditions, the gas moves at a much higher velocity than the liquid. As a result, the down-hole flowing density of the gas-liquid mixture is greater than the corresponding density, corrected for down-hole temperature and pressure, that would be calculated from the produced gas-liquid ratio. Also, the liquid's velocity along the pipe wall can vary appreciably over a short distance and result in a variable friction loss. Under other conditions, the liquid is almost completely entrained in the gas and has very little effect on the wall friction loss. The difference in velocity and the geometry of the two phases strongly influence pressure drop. These factors provide the basis for categorizing two-phase flow. The generally accepted categories (flow regimes) of two-phase flow are bubble, slug, (slug-annular) transition and annular-mist They are ideally depicted in Fig. 1 and briefly described as follows. RUBBLE FLOW (FIG. 1A) The pipe is almost completely filled with the liquid and the free-gas phase is small. The gas is present as small bubbles, randomly distributed, whose diameters also vary randomly. The bubbles move at different velocities depending upon their respective diameters. The liquid moves up the pipe at a fairly uniform velocity and, except for its density, the gas phase has little effect on the pressure gradient. SLUG FLOW (FIG. 1R) In this regime, the gas phase is more pronounced. Although the liquid phase is still continuous, the gas bubbler coalesce and form stable bubbles of approximately the rame size and shape which are nearly the diameter of the pipe. They are separated by slugs of liquid. The bubble velocity is greater than that of the liquid and can be predicted in relation to the velocity of the liquid slug." There is a film of liquid around the gas bubble. The liquid velocity is not constant—whereas the liquid slug always moves upward (in the direction of bulk flow); the liquid in the film may move upward but possibly at a lower velocity, or it may move downward. These varying liquid velocities will result not only in varying wall friction losses, but also in a "liquid holdup" which will influence flowing density. At higher flow velocities, liquid can even be entrained in the gas bubbles. Both the gas and liquid phases have significant effects on the pressure gradient. TRANSITION FLOW (FIG. 1C) The change from a continuous liquid phase to a continuous gas phase occurs in this region. The liquid slug between the bubbles virtually disappears, and a significant amount of liquid becomes entrained in the gas phase. Although the effects of the liquid are significant, the gas phase is more predominant.

By F. D. Rosi, C. A. Dube, B. H. Alexander

WHEN a deformed polpcrystalline metal is heated to a sufficiently high temperature, a recrystallized structure develops which consists of small, essentially stress-free grains. This transformation is referred to as primary recrystallization. Under certain conditions, on prolonged annealing of the specimens, a type of grain coarsening occurs in which a small number of grains commence to grow at various points by devouring the neighboring finegrained primary structure, which, in itself, exhibits a marked stability toward normal grain growth. This grain coarsening process has been referred to by Burgers' as "secondary recrystallization" or "exaggerated grain growth." Although much work has been done on recrystallization and growth processes, present knowledge of the factors which determine the occurrence and growth of secondary grains is inadequate for the advancement of a theory which accounts for the observed characteristics of this recrystallization phenomenon. In this respect, it would be important to make measurements of the velocity of growth of these large secondary grains. The early work of Feitnecht2 on aluminum showed that the size of secondary grains increased with temperature and time, suggesting that such measurements would be possible. More recently, Burgers1 found that the growth velocity of these grains in aluminum was constant over a large time interval, as is generally found for the growth velocity of primary grains in a uniformly deformed test piece.3-5 It is reasonable to expect that the determination of the activation energy of the secondary growth process might lead to a better understanding of the underlying atomic mechanism. This investigation, therefore, is one of a series primarily designed to measure the growth velocity of secondary grains at various temperatures for silver, copper, and aluminum. It is hoped that these studies along with those of orientation relationships, will establish a sound basis for theorizing as to the origin and nature of the secondary transformation. Experimental Procedure The metal used in the present investigation was high-purity silver (999.9 fine), which was supplied in the form of cold-rolled plates 0.250 in. thick. These plates were annealed at 500°C for 1 hr and then straight-rolled to a thickness of 0.04 in. in three reductions of approximately 45 pct, followed in each case by an anneal at 450°C for 1/2 hr. The 0.04 in. sheets were given a final reduction of approximately 50 pct, which resulted in a thickness of 0.02 in., thereby insuring two-dimensional crystal growth. Individual specimens of this material about 1x3 cm were used for all heat treatments, unless otherwise noted. The annealing was carried out under an atmosphere of argon in an Inconel tube furnace whose temperature was controlled to within -+2°C. Metallographic examination of the secondary transformation was accomplished by mechanically polishing the specimens on one side to approximately one half their thickness through 2/0 metallographic emery paper, and then electrolytically polishing in a solution of potassium ferrocyanide and sodium cyanide. With a current density of approximately 20 amp per sq dm, the time required to obtain a satisfactory surface varied from 3 to 5 min. Standard potassium bichromate was used to etch the electrolytically polished surfaces. A heavy etch with this solution produced a sharp contrast between the secondary grains and the fine-grained primary structure, darkening the latter while leaving the large secondary grains bright. All area measurements of the secondary crystals were made with a planimeter on enlarged tracings of the grains.

Jan 1, 1953

By W. Rostoker, A. S. Yamamoto, K. Anderko

ALTHOUGH the corrosion resistance of magnesium and its alloys is closely related to iron content, there has been no direct measurement of the solid solubility of iron in magnesium. Bulian and Fahrenhors;1 and Mitchel]2 agree that pure iron or a limited terminal solid solution crystallizes from the Mg-rich liquid. For this reason a magnetic-moment method was selected to estimate that portion of the total iron content which is not in solid solution. Since iron in solid solution in magnesium cannot contribute to ferromagnetism, the difference between chemical and magnetic-iron analyses should yield the solid solubility. By experimentation it was found that the melting of pure sublimed magnesium (99.995 wt pet purity) in Armco-iron crucibles at about 800°C is a convenient way to introduce small amounts of iron. Melts retained 5, 10 and 20 min at 800°C analyzed 0.003,, 0.005,, and 0.018 & 0.001 weight pet Fe, respectively, after being stirred, heated to 850°C, and cast into graphite molds. The as-cast alloys were pickled in acid (dilute HC1 + HNO3), annealed at 600°C for 3 days, scalped on a lathe to remove the pitted surface, pickled again, extruded at about 100°C to 3-mm wire, reannealed 41/2 days at 500°C, and water-quenched. The specimens were again scalped, pickled, and used both for chemical and for magnetic analysis. Most of the precautions described were intended to prevent iron pickup by contact with tools or superficial iron enrichment by volatilization of magnesium during heat-treatment. It is believed that the specimens ultimately used for test were homogeneous and characteristic of phase equilibria at 500°C. Magnetic Analyses A susceptibility apparatus of the Curie type was used for magnetic analyses. Field strengths of up to 10,400 oersteds could be generated. By this method, an analytical balance measures the force of attraction which a calibrated magnetic field exerts on a suspended specimen. The force equation is as follows f/m = M dh/dy where f/m = force per unit mass of sample M = magnetic moment per unit mass dH/dy = magnetic field gradient The dH/dy characteristic of the instrument is determined by the use of a standard palladium sample, and the calibration is made independently for all values of H. Since a large finite field is required to saturate an assembly of ferromagnets, it is necessary to measure the apparent magnetic moment for increasing steps of H until a saturation value is obtained. The percentage of iron in the sample as free ferromagnetic iron may then be computed simply C= 100 (M1/M1) where C = percent content of undissolved iron in sample M1 = saturation magnetic moment of sample per unit mass M1 = saturation magnetic moment of iron per unit mass taken as 217 emu-cm per gm There is no serious difficulty in applying this method except for the unusual magnetic behavior of very fine particles of ferromagnetic substances. It has been found and is the basis for a widely accepted theory that with sufficient subdivision, the magnetic fields required to saturate and the coercive force after saturation rise to exceedingly high values. Recent work on precipitates of Fe and Co from copper solid solutions8 showed that about 5000 oersteds were necessary to approach saturation. The magnetic moments as a function of field strength measured in the present investigation are listed in Table I. Only the 0.018 wt pet Fe alloy yielded a magnetization curve with a fairly well-defined saturation plateau at 3.76x10 -2 emu-cm/ gm. This corresponds to 0.017 & 0.001 wt pet Fe in the alloy. This indicates that the solid solubility must be of the order of 0.001 wt pet Fe. The magnetic-moment data of the other two alloys are badly scattered, indicating that the amount of ferromagnetic iron in these samples is so low that the magnetic forces acting on them cannot be measured accurately by the analytical balance used. Nevertheless, the fact that even the 0.003, wt pet Fe alloy shows ferromagnetism indicates that the solid solubility must be below that value. Acknowledgment This work was sponsored by the Pitman-Dunn Laboratory of Frankford Arsenal, Philadelphia, Pa. The support and permission to publish are gratefully acknowledged. References W. Bulian and E. Fahrenhorst: Zeic. Metallkunde, 1942, vol. 34, pp. 116-170. 2 D. W. Mitchell: AIME Transactions, 1948, vol. 175, pp. 570-578. 3 G. Bate, D. Schofield, and W. Sucksmith: Philosophical Magnsine, 1955, vol. 46, pp. 621-631.

Jan 1, 1959

By H. Wilton Clark

VARYING in thickness and in number from place to place, coal seams in the Canadian Rockies also range in pitch from nearly horizontal to vertical, sometimes with overturns. Over the entire coal-bearing area there are considerable differences of rank in coals of the same geological age, and there are marked differences in ash content and wash-ability characteristics. Correlation of seams at mining operations within a few miles of each other has often proved impossible. These factors influence mining methods, and, of course, production results. The oldest coal formations of western Canada are of Lower Cretaceous age, as the carboniferous sediments are marine and contain no coal. Coal is also present in formations of Upper Cretaceous and Tertiary ages. The rank of coal varies from semi-anthracite in some operations in the Kootenay and Luscar formations of the Lower Cretaceous in the Rockies to lignite in the Tertiary fields of the Saskatchewan prairies. Fig. 1 shows the general extent of the formations. The pitching seams, chiefly Lower Cretaceous, occur in the western belt of the Rocky Mountain foothills and the eastern slopes of the Rockies themselves. (The road to Tent Mt. strip pit, elevation 7000 ft, is shown on p. 832.) Formations extend from the U. S.-Canadian boundary for several bundred miles in Alberta and continue for a similar distance in British Columbia. Present geological estimates show a probable reserve of the order of 25,000 million tons of coal ranging from high volatile bituminous to semi-anthracite, with a large percentage of coking coal, constituting one of the major world reserves of that type. It should be noted that although the quoted estimate probably errs on the conservative side, the question of access to the seams in a mountainous terrain will always be a problem; a wide divergence may exist between actual reserves and the quantities of coal economically recoverable. An excerpt from the Canadian government Report of the Royal Commission on Coal 1946 states that conditions favorable to coal formation were intermittent and these intervals relatively brief in comparison with periods in which no coal was formed. Conditions were favorable to the growth or accumulation of vegetation in one area, while fresh water sediments and marine shales were being deposited in other areas. During periods of emergence the coal deposits were subjected to erosion or were covered by coarse sands and gravels from the mountains, whereas during submergence they were covered by fine clays deposited in embayments of the sea. During some of the periods of coal formation, volcanic activity deposited beds of fine volcanic ash and dust with the coal-forming vegetation. Coal deposits reach their greatest development in the mountains and thin rapidly to the east into the plains area, where they are deeply buried beneath younger sediments. For example, in the Fernie area of southeastern British Columbia there are in places 22 seams having an aggregate thickness of 150 ft in a stratigraphic interval of 3500 ft, whereas at Cole-man in the Alberta Crowsnest area the measures are only 800 ft in thickness and contain a maximum of five seams aggregating about 47 ft of coal. At Belle-vue, 10 miles further east, the measures are reduced to 430 ft with only three seams aggregating about 37 ft of coal. Subsequently the tremendous forces involved in the upthrust of the Rocky Mountains produced great displacement of the coal-bearing formations and at the same time a change in geologically young coals from low to high rank. The floor or footwall of most seams consists of carbonaceous shales, which are almost as adaptable to bending as the coal seams themselves. The seams show very few cleats or cleavage planes and have been so weakened structurally that as mined 50 pct or more will pass through a ¼-in. screen, seldom

Jan 1, 1955

By E. S. Anolick, Joseph Singer

The magnetic after-effect, in the form of time decay of permeability (l/µ), has been used to obtain independent data on the solubility of' carbon in pure iron. The results differ slightly from the solubilities obtained through internal -friction experiments. The mechanism of the time decay being the magnetic analogue of internal friction, it appears necessary to explain the observed discrepancies, and some suggestions are made. THE purpose of this work was to establish the reliability of the time decay of permeability as a measure of dissolved interstitial in the body-centered-cubic lattice, and further, to establish techniques suitable for such measurements with samples of a form convenient for various other measurements. This particular sample form was the "epstein" strip, i.e., 25 cm by 3 cm by 0.035 cms. While the general conclusions are not limited by this geometry, there are two aspects of the samples that may be relevant: a) texture, and b) grain size, which ranged generally from 1 to 10 mm. Effects due to these two possible parameters were thought to be small and were not investigated. Calibrating the time decay technique and the other experimental procedures by measuring the solubility of carbon in pure iron suggested itself because of the accumulation of data on this subject through the related technique of the internal friction'; The essentials of this report have been published in a somewhat condensed form.5 Since then some additional data have been taken. It is the purpose of this paper to add these data and to provide more complete description of the experimental techniques than was possible then. The time decay of permeability is a form of the magnetic after-effect.6,7 Permeability is measured immediately after demagnetization (µº) and also long after (µ8). The time decay, ?(l/µ), is the difference 1/µ8 - 1/µ0 and has been considered to be proportional to the concentration of a dissolved interstitial6,8,9,12 The relaxation time! 7, is characteristic of a particular diffusion, and affects the permeability as follows: where he being the activation energy for diffusion of the interstitial. Reference is made to the works of snoek6 and Neel7 for a complete discussion. A brief exposition of the principal ideas may be in order here, as follows. On the basis of the simplest model, resistance against domain wall motion increases with time after demagnetization due to the diffusion of interstitials to preferred sites created by the magnetostrictive tetragonolization under the strong magnetic field. Thus permeability, measured with a small field after the abrupt removal of the large field, will continuously fall with the process of diffusion of the interstitials, and the total "time decay" (or "time decrease") should be proportional to the amount of interstitial in solid solution. In the present report, use is made only of the total time decay rather than of the nature of the progress of the decay; the only problem involved in this approach is the need for assurance that only one interstitial is contributing to the effect as used. It is felt that the special use made here of the total time decay warrants the conclusions. Other work has been going on elsewhere on the detailed study of the nature of the time decay.8'9 EXPERIMENTAL A) Materials—12-lb ingots were made in a vacuum furnace from high-purity iron and by a series of hot and warm reductions were brought down to 14-mil strip. This was cut into 25-cm epsteins. The pure iron was decarburized at 750 °C by hydrogen. The time decay measurement for the decarburized iron (see below) indicated a satisfactorily low starting level of interstitials. Grain growth to grain sizes of 1 to 10 mm was produced in the pure iron by a 700" anneal in hydrogen after a critical reduction of about 7 pct as suggested by previous trials. No measurement of texture in the pure iron was made. The grain size was taken to be large enough to be beyond any sharply critical size regarding solubility. B) Infusion of Carbon—Since the permeability measurement required about two dozen epsteins, a special method of carbon infusion had to be developed to ensure homogeneity of infused carbon. This was accomplished by setting the samples edgewise in a

Jan 1, 1961

By O. Jay Myers

The war effort has furnished the necessary impetus for better magnesium foundry practice. Four or five years ago, there were but a few formulas in general use for core-sand mixtures for magnesium castings. Certain sands, binders, and inhibitors were specified and the proportions of these materials in each mixture were maintained between very narrow limits. As more and more war industries entered the field, much research was carried out and methods and practices were improved. Magnesium founding is still in a state of flux; therefore it is not uncommon to find one foundry spraying inhibitors on its cores, and another foundry using sand mixtures with incorporated protective agents. The basic core or dry-sand mold mixture for magnesium in use today is compounded with sand, core oil or resin binder, cereal, and moisture. Core oil or resin binder are added for baked strength while the cereal binder and moisture are for green strength. The normal mixtures (based on the weight of the sand) contain from o.5 to 1.5 per cent of both cereal binder and core oil, and the moisture content variesbetween 1.5 and 5 per cent. The ratio of core oil to cereal binder varies from 60:40 to 40:60, while the correct amount of moisture depends upon the method of coremaking. Protective Agents In all magnesium practice, protective agents are used in conjunction with the core and molding sands to prevent oxidation of the metal. The use of these inhibitors is not novel, but publications covering this field are not entirely adequate. Beck1 says: Magnesium alloys decompose water to form magnesium oxide, hydrogen being liberated in the process (Mg + H2O ? H2 ?+ MgO). This reaction results in the blackening of the skin and the appearance of areas of porosity on the casting surface, the cavities of which are filled with a grey oxide powder (these are termed 'burns'). Although sand cores for magnesium castings are thoroughly dried during the baking cycle, burning will take place on the casting5 unless the metal is protected properly. This type of burning is more difficult to define than the "water-magnesium" reaction cited by Beckl A possible explanation may lie in the following equation: 2Mg + O2—> 2MgO Here, the source of the oxygen is not water, but the air in the mold cavity, together with the chemically combined oxygen in the core-binding media. Generally, two methods are used to prevent this reaction from taking place.

Jan 1, 1945

By F. S. Jr. Norcross

MANGANESE has long been considered one of the United States' most important strategic raw materials. Its indispensabil-ity in steel manufacture makes it vital to the nation's industrial life. Coupled with this indispensability is the fact that domes-tic producers have not been able as yet to supply more than a small part of the nation's manganese needs; consequently the United States has had to depend upon such distant foreign sources as the U.S.S.R., British India, the African Gold Coast and Brazil for the major portion of its ore. The great bulk of the mineral is con-sumed in the form of ferromanganese, an alloy that averages 8o per cent manganese and 20 per cent mainly iron and carbon. Manganese is used as a deoxidizer and desulphurizer in steel manufacture. By combination with the residual oxygen and sulphur of the bath, it helps to produce a clean, sound metal. Approximately 14 lb. of manganese, it is estimated, is used in making one ton of steel. For standard-grade ferromanganese, the ore should have a minimum of about 48 per cent Mn and preferably more. Beneficiation methods have not yet been developed for making the immense low-grade deposits in the United States salable at prevail-ing prices.

Jan 1, 1940

By J. E. McDonald, J. G. Eberhart

A model is discussed from which the work of adhcslon .tor liquid transition metals on aluminum oxide surfaces can he calculated, A close-packed (00011 oxygen surface on A12O3 is assumed with two different types of surface sites: one type involving metal-oxygen bonds and the other man der Waals into actions. The work of adhesion is thus expressed as the sum of these two bonsding free energies. Calculated works of adhesion for nickel, titanium, chromium, and zirconium on sapphire agree well with the experimentally determined quantities. The model is extentled to the calculation of the work of adhesion and shear stress required to remove a thin metal film from a sapphire substrate and is in good agreement with experimental values. The obsewed dependence of the work of adhesion on the free energy of oxide formation of the metal is shown to also provide an interpretation of the tittle dependence of thin-film adhesion. THIS paper presents a model for the type of bonding which occurs across a metal-A12O3 interface. The model is used to explain the results of two types of experiments in which such an interface exists: 1) the adhesion of thin metal films on Al2O3 substrates and 2) the wetting of A12O3 by liquid metal drops. The adhesion of thin films to various substrates has been the subject of a variety of investigations.'-' Benjamin and weaver3 and Bowie,6 using the scratch test developed by Heavens,10 studied the adhesion of metallic films to glass substrates. Their observations for noble-metal film adhesion agree well with an adhesion model involving a van der Waals type of bonding between the film and the substrate. For films of metals whose free energy of oxide formation. ?F°f, has a negative value. Benjamin and weaver3 and Bowie6 found a time-dependent adhesion with an initial value that can be interpreted in terms of van der Waals interactions but a larger terminal value which was related to ?F°f, Karnow-sky and Estill7 deposited films on sapphire at elevated temperatures and noticed no time dependence of film adhesion but a similar correlation with ?F°f. Because of the kinetic problems associated with thin-film adhesion it is desirable to examine adhesion in an equilibrium system. The wetting behavior of liquid-metal drops on Al2O3 provides such a system. Systems of this metal-ceramic type have been studied extensively.11 Humenik and Kingeryl2 have measured the wetting of A12O3 (and other substrates) by several metals and have pointed out that the wetting ability of these metals increases with increasing values of -?F°f. It is thus seen that thin-film adhesion and metal wetting on A12O3 are both related to the tendency of the metal to react with the surface oxide ions of the Al2O3 substrate and, because of this, both phenomena should be explainable by an appropriate model for the metal-Al2O3 interfacial bonding. In the sections that follow, wetting and adhesion data on A2O3 are reviewed and a model is presented by which these phenomena can be interpreted. ANALYSIS OF WETTING EXPERIMENTS In an equilibrium system involving a liquid-metal drop on a solid Al2O3 substrate, the work of adhesion, WAD, is defined by the Dupre, equation as WAD = ?s + ?L -?sL [1] where ?s and ?L are the surface free energies of the solid substrate and the liquid drop, respectively, and ?sL is the interfacial free energy. The work of adhesion is the work required to separate a unit area of the solid-liquid interface into two surfaces. The work of adhesion is usually determined from a sessile-drop experiment in which yL and the contact angle, ?, are measured. The Young-Dupr6 equation is then used to calculate WAD Wad = ?L (1+ cos ?) [2] The literature of this subject has been examined and Table I shows work of adhesion data for various liquid metals as measured on A12O3 substrates. The standard free energy of oxide formation of the metal at the temperature of the wetting experiment, ?F°f . is also tabulated in kcal per g-atom of oxygen. The data is grouped according to the gaseous atmos-

Jan 1, 1965

By H. J. Ramey

Conventional calculation of total system isothermal compressibility for a system containing a free gas phase involves, among other things, evaluation of the change of oil and gas formation volume factors and the gas in solution with pressure. Preferably, this information should be obtained from laboratory measurements made with particular oils and gases. Often, experimental measurements are not available. In this case, it is necessary to obtain pressure-volume-temperature relationships from general correlations such as those of Standing' for California oils. In order to speed estimates of compressibility, generalized plots have been prepared of the change of both oil formation volume factors and gas in solution, with pressure from Standing's correlations. A generalized plot for estimating the change in the two-phase (oil and gas) formation volume factor with pressure is also presented. Usually, the effect of gas dissolved in reservoir water upon the total system compressibility is neglected for gas saturated systems, due to the low solubility of gas in water. Results of this study indicate that the increase in total system compressibility caused by solution of gas in water is often as large as the compressibility of wafer, and can be magnitudes larger for low pressure systems. Generalized results for estimating the change of gas in solution in water with pressure are presented in tabular and graphical form. INTRODUCTION During the past decade, pressure build-up and drawdown techniques have gained an important place in reservoir engineering. Build-up and drawdown analyses are only two special applications of the broad field of transient fluid-flow theory. All solutions of transient fluid-flow problems contain a parameter called the total system isothermal compressibility. This property of fluids and porous rock is a measure of the change in volume of the fluid content of porous rock with a change in pressure, and it may vary considerably with pressure. Evaluation of total system isothermal compressibility is not difficult, but it is tedious and time-consuming. Often compressibilities are estimated roughly, or transient flow methods are neglected completely. The benefits of using accurate system compressibility in properly-executed build-up or drawdown analyses are: 1. Better planning of pressure build-ups may be achieved to avoid unnecessary loss of revenue due to excessively long shut-in periods, or to shut-in periods too short to yield useable data. 2. Better and more reliable estimates of static formation pressures for reserves estimates and rate performance estimates. 3. Reliable information for evaluation of well completion effectiveness, and planning and interpretation of well stimulation efforts. The purpose of this paper is to clarify the nature of the total system isothermal compressibility, and to present useful methods for estimation of compressibility, particularly for systems containing a gas phase. DEVELOPMENT Numerous publications have presented solutions to transient single-phase flow of slightly compressible fluids, stressing pressure build-up applications. In transient flow, a compressibility* term arises to permit volume content of fluids in porous rock to change as pressure changes. The basic nature of the compressibility term is usually taken for granted. Problems arise in practical applications of transient fluid theory because most published works consider only one flowing fluid—in an ideal porous system containing only one fluid. In 1956, Perrine2 presented an intuitive extension of single-phase flow pressure build-up methods to multiphase flow conditions. Later, Martin- established conditions under which Perrine's multiphase build-up method had a theoretical foundation. Perrine has shown that improper use of single-phase build-up analysis in certain multiphase flow situations can lead to gross errors in estimated static formation pressure, permeability and well condition. It is likely that, much pressure build-up data for oil wells should be analyzed on the basis of multiphase flow. For both single-phase and multiphase build-up analysis, the isothermal compressibility term in dimensionless time groups often should be interpreted as the total system compressibility. All real reservoirs contain one or more compressible fluid phases. In addition, rock compressibility can contribute in an important way to the total system compressibility. The proper total system compressibility expression may contain terms for compressibility of oil, gas, water, reservoir rock and terms for the change of solubility of gas in liquid phases.

Jan 1, 1965

By R. H. Frazier, C. H. Lorig, F. W. Boulger

This investigation establishes the effect of ferrite grain size resulting from various heat treatments on the transition temperature of a semikilled steel plate. Different austenitizing temperatures and various cooling rates were used. The ductile-brittle transition temperatures were determined by the Navy tear test and the keyhole Charpy test. THE data presented in this paper deal with quality characteristics of ship-plate material which were investigated in a research project sponsored at Battelle by the Bureau of Ships, Dept. of the Navy. Specifically, the object of this investigation was to establish the effect of ferritic grain size (resulting from various heat treatments) on the so-called transition temperature of ship-plate steel. Transition temperature is not a fixed property of steel. It is derived from a series of static or dynamic tests made at various temperatures and is qualified by specifying the type of test employed as well as the testing criteria. Because in earlier investigations of ship-plate quality1,2 the so-called Navy tear test and standard notched-bar tests (keyhole Charpy) proved to be useful in interpreting instances of brittle behavior of ship plate in service, these tests were used in the investigation reported in this paper. By definition,' in the Navy tear tests the highest temperature at which one or more of four specimens breaks with a brittle fracture (that is, when less than 50 pct of the fracture area has a dull fibrous texture) is termed "transition" temperature. In the Charpy tests, the 12 ft-lb level of energy absorption was used as a criterion indicating the "transition" temperature, although other levels of energy absorption were also used for comparison. Earlier work" on ship-plate steels indicated that the temperature at which ship plate is finished has a very significant effect on its notched-bar properties. Plates rolled in the laboratory, where the finishing temperature can be carefully controlled, showed a 16°F decrease in tear test transition temperature when the finishing temperature was lowered 200°F (from X" to Y°F). The same plates showed a drop of 10°F in the keyhole Charpy transition temperature from the same decrease in finishing temperature. Commercially finished plates' exhibit a similar trend. When the ferrite grain size of the hot-rolled laboratory plates was determined, a close relationship was found between the ferrite grain size and the notched-bar transition temperature." " he indicated relationship between grain size and transition temperature was in agreement with the findings on low carbon steels of Hodge, Manning, and Reichhold' despite the differences in composition of the steels. The cooling rate after rolling varies from one steel plant to another. This variation changes the micro-structure" and appears very likely to affect the notched-bar properties of the steel plates. In the investigation summarized in the present paper, heat treatments simulating finishing practices in the hot rolling of ship plate were used in order to vary the ferritic grain size. It is believed that the indicated relationship between grain size and transition temperatures of the ship-plate material will prove useful in estimating the effect of rolling temperature and of cooling rates from rolling temperatures on the notched-bar properties of semikilled steel plate. Material The semikilled steel plate used in this investigation was a ¾ in. hot-rolled plate from an open hearth heat. Other plates from this heat have been used on many other studies performed for the Ship Structure Committee," "," and the heat has been identified as project steel "A". The chemical composition of the plate1 was 0.25 pct C, 0.49 pct Mn, 0.011 pct P, 0.045 pct S, 0.04 pct Si, and 0.004 pct N.

Jan 1, 1956

By M. R. Tek, R. L. Nielsen

The scaling laws as formulated by Rapoport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions. Two hypothetical systems — a gas reservoir subject to water drive and the laboratory scaled model of that reservoir — were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these par ticular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system. This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. INTRODUCTION Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models. To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoportl and others.2-5 Rapoport's scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems. It will be recalled that these scaling laws presuppose three conditions: (1) the relative permeability curves must be identical for the model and prototype; (2) the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; and (3) boundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because: (1) The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media. (2) The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent. (3) Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible. The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible. The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. The numerical treatment employed was similar to that of Douglas, Peaceman and Rachford6 and it included both capillary and gravitational forces as

By W. A. Tiller

The unidirectional freezing of a semiinfinite liquid from one end has been treated by calculating the solute and temperature distributions in the liquid and solid phases with time, when the solid-liquid interface advances at a rate proportional to (time)lt2. The nucleation probability for new grain formation is calculated as a function of the constitutional and thermal properties of the alloy, the pouring conditions and the catalytic efficiency of the nucleating agents. The transition from columnar crystal formation to equiaxed crystal formation is assumed to occur at a critical nucleation frequency for a particular alloy and the quantitative dependence of the ratio (columnar zone length/equiaxed zone length) upon the freezing conditions has been predicted. The effects of (i) fluid flow in the liquid, (ii) heat transfer through a mold wall, and (iii) a finite ingot length, have been explicitly tveated as departures from ideality. These departures from ideality are found to have very important consequences on the ingot stmcture. In Part I&apos; of this series, a qualitative description of the general ingot structure was developed. The factors that determine i) the ratio of the equiaxed zone length to columnar zone length and ii) the grain sizes in these zones, were discussed. In the present paper, topic (i) will be treated quantitatively, and it is intended that topic (ii) will be treated quantitatively in Part 111. The complete treatment has been split in this manner for ease of development and coherency of presentation. The treatments are quite mathematical in nature and, although some of the conclusions to Part 11 depend upon the treatment presented in Part 111, it was felt that the intended audience would find the material more readable and more useful in its present form. To this same end, it seems worthwhile to reiterate some of the qualitative aspects of grain nucleation during ingot solidification before embarking on the mathematical description. QUALITATIVE ANALYSIS In the conventional method of casting, a liquid alloy with a certain degree of superheat is poured into a mold. The outer rim of liquid metal cools rapidly to the liquidus temperature of the alloy and begins to undercool. As the degree of undercooling increases, nuclei of solid begin to form in this chill layer, this nucleation being catalyzed by certain heterogeneous particles in the liquid. The grains in the chill layer which are generally of random orientation, begin to grow inwards because of heat conduction through the mold. The grains usually develop a columnar shape since the frequency of nucleation of new grains in the liquid ahead of the advancing interface is generally insufficient to seriously impede the growth of the original grains. Due to the slow diffusion rate of solute in the liquid, a solute distribution is formed in the liquid adjacent to the interface which is either an excess or a depletion if the partition coefficient, ko, of the solute is < 1 or > 1, respectively. Thus, the liquidus temperature of the liquid adjacent to the interface is a function of position. The actual temperature in the liquid is also a function of position and the temperature gradient at the interface decreases as the interface moves away from the mold wall. Since the rate of advance of the interface decreases with time, the equilibrium temperature distributions and the actual temperature distributions as a function of interface position, X, can be illustrated as in Fig. 1. Thus, a region of liquid may exist in which the actual temperature is below the liquidus temperature. This liquid is contitutionally supercooled and therefore unstable with respect to the nucleation of new grains. Now, since the supercooling in Fig. 1 increases as the interface moves further away from the mold wall, the nucleation rate of new grains will increase. When the nuclea-

Jan 1, 1962

By D. D. Dunlop, J. R. Welker

The growing interest in the use of CO, in crude oil recovery increases the need for data on the effect of CO, on hydrocarbon physical properties. Data are presented on the solubility of CO, in various dead oils, the swelling changes in CO2-oil solutions and the effect of CO, on dead oil viscosity. This latter property shows the most pronounced effect, with viscosity reductions up to 98 per cent of the uncarbonated viscosities. An empirical method of estimating the viscosity of carbonated oils is presented. The apparatus and procedures used are described in sufficient detail to allow others to make similar studies. INTRODUCTION The effect of dissolved carbon dioxide on the swelling and viscosity reduction of specific hydrocarbon oils has been observed and recorded by a number of investigators.&apos;- me object of this paper is to offer a means of predicting these effects for crude oils free from natural gas, using the dead state viscosity and gravity of the crude oils. The CO, solubility and swelling of numerous crude oils were determined in a visual cell at various pressure levels. The viscosity of the oils carbonated to various pressure levels was then determined by measuring the pressure drop across a capillary tube. From these data, the physical properties were correlated empirically. The resulting correlations allow the prediction of CO, solubility, swelling and viscosity reduction if the dead state gravity and viscosity of the oils are known. SOLUBILITY AND SWELLING MEASUREMENT EQUIPMENT AND PROCEDURE A high pressure visual cell was installed in a constant temperature cabinet. A test gauge was attached at the top of the cell for pressure measurement, and a line was run through the cabinet wall to a wet test meter which was used for volumetric measurement of the gas. The first step in making a test run was to put the oil in the cell up to a level about half to two-thirds of the total volume. This required about 50 to 65 ml of oil. carbon dioxide was then bubbled up through the oil for a time during which the pressure of CO2 in the cell was kept above 800 psia. Saturation of the oil with CO2 at this pressure and ambient temperature was confirmed by slowly bleeding CO2 through a valve to the atmosphere. If the oil was completely saturated with CO2, bubbles of gas would form in the oil at the first small decrease in pressure. If the oil was under-saturated, no bubbles formed until the pressure was decreased to the saturation pressure existing in the oil. If this saturation pressure was lower than that desired, more CO2 was bubbled through the oil until the desired level was reached. After saturation at ambient temperature was completed, the cabinet temperature was adjusted to the desired level and the cell was allowed to reach temperature equilibrium. After temperature equilibrium was reached, the pressure was again decreased slightly, and the oil again checked for full CO2 saturation at the cell pressure. The pressure now had changed because of the difference in solubility of the CO, in the oil at higher temperatures and the expansion of CO2 as the temperature increased. The outlet tube from the cell was then connected to the wet test meter and the CO2 was allowed to flow slowly out of the cell and through the wet test meter at ambient temperature and pressure. The water in the wet test meter had previously been saturated with CO2 at ambient temperature and pressure by allowing CO2 to flow continuously through it lor a period of several hours. The gas flow was stopped at several pressures during the run and the cell was allowed to come to equilibrium; this made possible the measurement of solubility and swelling data at the intermediate pressures. The volume of the oil in the cell was recorded at each of the equilibrium pressures in order to obtain swelling data. DATA AND RESULTS The solubility of CO2 in the oil was calculated by the relationship V — V, where R. = solubility of CO, in crude oil, cubic feet of CO, measured at 60F and 1.0 atm/ bbl of dead state oil at the temperature under which solubility was measured, V, = volume of gas released from the cell between the saturation pressure and zero pressure, corrected to 60F and 1.0 atm, cu ft, V, = volume of CO: contained in the gas space above the oil, corrected to 60F and 1.0 atm, cu ft, and V, = volume of the dead oil in the cell in bbl at the temperature of the run. The volumetric data of Sage and Lacey&apos; were used to calculate V., from the volume of CO2 at high pressures. The swelling factor was calculated as where V, is the volume of the C0,-

By Robert L. Slobod

In much of the work reported in the literature on long cores. true connate water value, probably have not been obtained because of insufficient flow of 011 to attain equilibrium. A -.satisfactory method for establishing connate water in long cores has been developed in which oil flow is maintained until no additiona1 water is displaced. INTRODUCTION Long cores have been used by sev-erals investigators in an effort to evaluate the efficiency of oil recovery for various producing schemes. The effects of many variables such as rate of displacement. pressure drop, volume of displacing medium, gas-oil ratio, inter-facial tension, and others have been investigated, and the merits of gas drive have been compared with water drive. In the older experiments no connate water was used. but in the more recent stndies the philosophy of the experiment calls for a core containing oil and connate water (irreducible water) as the starting point of the experiment. The method generally used to establish this condition in long cores involves dynamic&apos; displacement wherein one or more phases are forced through the core. flow being maintained at a constant rate or at a constant pressure until a steady state is reached wherein there is no change of saturation with time. It is one purpose of this paper to point out that in much of the work reported in the literature true connate water values probably have not been obtained. The reason for this failure is pointed out. and a method for obtaining more reliable connate water values on long cores is presented. It is impossible at this time to completely evaluate the effect on the conclusions in the earlier papers resulting from the failure to obtain true connate water in the long cores, but some data are presented which indicate that serious errors may he present in many cases. MATERIALS AND APPARATUS Cores cut front outcrop sandstones (Strawn. Torpedo, and Elgin sandstones) with permeabilities of the order of 300 md were used. The major experiments were made with a core 18-in. long and 2-in. in diameter. Cores of the same diameter but only 12-in. long were used in a few tests? and in some work a core I-in. in diameter and 11-in. long was used. These materials were all somewhat bentonitic. &apos;To reduce the effect of such constituents, one of the cores (Torpedo No. 10) on which the most work was performed was acid extracted at the start of the experiment. Brine containing 50,000 ppm chloride and naphtha (Stoddard&apos;s Solvent) were used as the water and oil phases, respectively. The core was mounted in a rubber sleeve which forms the inner lining of a brass cylinder. In this arrangement2 the rubber sleeve is forced against the core by applying pressure to water in the annular space between the rubber sleeve and the brass cylinder wall. The core is therefore sealed in rubber so that all fluids introduced at the input end of the core flow through the core. With this equipment the core may be easily removed for inspection and analysis. Also, other cores may be introduced for study with no extra time for preparation such as is required when plastic mounting is used. When pressure or conductivity measurements are desired at intermediate points along tile length of the core, the brass cylinder comprising the outer jacket of the core holder is cut into section, of the desired length. Each section is then made up as an individual unit with its own rubber sleeve (see Fig. 1). The individual units are then butted up against a ring of plastic or other insulating material which carries an electrical contact for resistivity measurements and an opening which can be used for the measurements of fluid pressures. The individual units are forced tightly against the plastic ring separators and held in place with several tie rods. Inlet and outlet end butts of the same diameter as the core and several inches in length are provided to control the introduction and withdrawal of fluids and to complete the arrangement for sealing the core within the rubber sleeve. Fluid flow is maintained either by applying pressure to the liquid confined in a reservoir or by the use of a gear pump. The latter is preferable where continuous flow at a moderate rate over a long time interval is desired since a small volume of liquid can be readily recirculated using filters to prevent plugging of the core. EXPERIMENTAL The oven-dried core is weighed and is then completely saturated with brine

Jan 1, 1950

By Robert E. Green, Wolfgang Sachse

Simullaneous ultrasonic attenuation measurements of both quasishear waves propagating in single cryslals of aluminum indicate that, in the undeformed annealed state, the dislocation density is generally not uniform on all slip systems. Change oof attenuation measurements made during plastic defortnation of crystals , which possessed specific orientations ideal for studying the orientation dependence of dislocation damping, indicate that, for low strain levels, dislocation motion occurs on additional slip systems besides the primary one, even for crystals oriented for plastic deformation by single slip. THE sensitivity of internal friction measurements permits such measurements to be used successfully in studying the deformation characteristics of metal crystals. On the basis of experimental observations, T. A. Read1 was the first to associate internal friction losses with various dislocation mechanisms. Since that time further work2-&apos; has been performed and a dislocation damping theory has been formulated by Granato and Lucke.6 In the amplitude independent region, this theory predicts the attenuation a to be dependent on an orientation factor O, a dislocation density A, and an average loop length L. if is a constant, independent of crystallographic orientation. For a given crystallographic orientation, changes in dislocation density and loop length give rise to the observed attenuation changes accompanying plastic deformation. The Granato-Liicke theory suggests the investigation of the orientation dependence of attenuation measurements in hopes of obtaining information to separate dislocation motion losses from other losses.7 An experimental study of the orientation dependence of attenuation in undeformed annealed single crystals should yield an insight into the uniformity of dislocation distribution throughout the entire specimen. A similar study on crystals plastically deformed in a prescribed fashion should give information about the alterations in the dislocation distribution on the slip systems activated during plastic deformation. The possible modes of elastic waves which can be propagated in aluminum,8 copper,9 zinc,10 and other hexagonal metals" have been calculated. Associated with each mode of wave propagation are dislocation damping orientation factors, which are based on the resolution of the stress field of that particular elastic wave onto the various operative slip systems in the material. These orientation factors have also been calculated as a function of crystallographic orientation in the papers cited above. Einspruch12 obtained agreement between predicted and observed attenuation values of longitudinal and shear waves in (100) and (110) directions of two undeformed aluminum crystal cubes. He ascribed the slight deviations between predicted and observed values to a nonuniform dislocation distribution, or to other loss mechanisms. In shear deformation of zinc crystals, Alers2 found that the attenuation of shear waves having their particle displacements in the slip plane was very sensitive to the deformation, while the longitudinal wave attenuation was affected only when the wave propagation direction was not normal to the slip plane. Using aluminum single crystals oriented for single slip, Hikata3 et al. found that during tensile deformation the change of attenuation of the shear wave (actually quasishear) having particle displacements nearly perpendicular to the primary slip direction exhibited the easy-glide phenomena, while longitudinal waves did not. Similar results were reported by Swanson and Green5 during compressive deformation of aluminum crystals. These results are in qualitative agreement with the calculated orientation factors for specimens of this orientation. In well-annealed, undeformed aluminum crystals, the damping is expected to be due to dislocations vibrating on all twelve slip systems. The orientation factors associated with this initial damping will be designated by O2 and O3, where a, represents the average orientation factor for the slow shear (or quasishear) wave and O3 represents the average orientation factor for the fast shear (or quasishear) wave. The calculation of these values for aluminum crystals by Hinton and Green8 shows that they vary very little as a function of crystallographic orientation—at most, by a factor of 2.47. If the dislocation density and loop length are uniform, then in the initial undeformed state, Here the subscript zero refers to the initial value of the attenuation. Also for aluminum, the calculations8 show that the orientation factors for primary slip only, associated with each shear wave, exhibit a sharp minimum for particular crystallographic orientations. A composite plot of the two shear wave orientation factors for primary slip only is shown in Fig. 1. Since these orientation factors are associated with dislocation motion occurring on the primary slip system only, the proper condition to check these factors might be attained by slightly deforming a single crystal oriented for primary slip. For dislocation motion on the primary slip system only,

Jan 1, 1969

By F. W. Jessen, H. Kazemi

A washing technique has been developed to form a spherical cavity in massive salt. The technique is, basically, a process of controlling the fluid motion in the cavity, the concentration distribution of brine, the rate of dissolution at the walls of the cavity, and the particular settings of the wash pipe, or pipes (inlet and outlet pipe) employed. For a particular arrangement of tubing and casing, fresh water enters from the casing annulus at a position above the bottom of the tubing, and the dissolved material leaves the cavity through the tubing near the bottom of the projected hole. The initial configuration of the cavity is cylindrical, representing the drilled hole situated at the axis of the projected cavity. As washing progresses the original hole is enlarged radially (any direction perpendicular to the axis of the hole). An inert fluid (generally a hydrocarbon, natural gas, or air) which serves as a blanket is injected through the annular space between the original hole and the casing. The controlled downward motion of this blanket maintains the upper edge of the brine region that is expanding on the surface of the projected sphere. A large spherical glass container and a radial model were used to investigate the flow patterns and the concentration distribution of brine occurring during the progress of solution of the salt. Aluminum flakes and dye were injected and flow patterns were observed and recorded on motion picture film. Based on the results of these model studies and other work carried out in this laboratory, the controlled washing technique was formulated. INTRODUCTION Underground cavities leached in salt beds and salt domes have been used extensively for storing hydrocarbons. Little attention has been focused on the shape of the cavities as long as large volumes were obtained and the cavities were structurally stable. The general process involves circulating fresh water and removing brine. Two distinctly different circulating systems can be employed, each of which yields characteristically different shapes. By far the most generally accepted method of washing storage caverns in salt domes is the direct circulation system. Water is introduced through the innermost pipe of a concentric pipe system, and brine is withdrawn through the annulus. In the reverse-circulation method, water enters through the annulus and is discharged through the smallesc tubing string. The size of the operation, and hence the size of tubing and casing used, depends on such factors as cavity volume, length of hole, availability of water, disposal of brine and power requirements. Underground caverns are from 100 to 1,000 ft or more in length, and when completed vary from 40 to 100 ft in diameter, providing storage of 100,000 bbl or more. The volumes of water required per volume of salt removed vary from 6 to 7 for the reverse circulation method to 10 to 11 for the direct circulation method. Up to 80,000 BWPD are often circulated. In the direct circulation method, because water enters near the bottom of the projected cavity, solution of salt is greatest at this point, particularly in view of the fact that when the washing is begun turbulent flow undoubtedly exists in the immediate vicinity of the discharge of the inlet water. As the diameter of the hole increases, flow rates also are increased, so perhaps the condition of fluid turbulence is maintained for some time. During the later stages of leaching, when capacity of equipment may be the limiting factor in maintaining flow rates, there may still exist some turbulence adjacent to the point of influx; however, for the most part laminar flow conditions prevail. There appears, therefore, rather good evidence to indicate that the state of fluid motion is responsible for the typically shaped cavity which results from such washing — namely a cylindrical form, generally somewhat larger at the bottom than at the top. Depending on the number of so-called stages which might be employed, the walls or surfaces of the salt diminish rather uniformly from bottom to

Jan 1, 1965

By Nathaniel Arbiter

THE separation of minerals by flotation can be regarded as a rate process, with the extraction of any one mineral determined by its flotation rate, and the grade of concentrate by the relative rates for all the minerals. So regarded, the significant variables for the process are those that control the rates. These variables are of two types, the first describing the ore and its physical and chemical treatment prior to flotation and the second characterizing the separation process in the cells. This paper will examine the variation in rates for a group of separations, will show that a simple rate law appears to govern, and will consider the relation of the control variables to the rates. The use of rate constants for evaluation of performance and efficiency will be discussed. Flotation involves the selective levitation of mineral and its transfer from cell to launder. The flotation rate is the rate of this transfer. It may be defined by the slope of a recovery-time curve for any cell in a bank, or at any time in batch operation. The objective in flotation rate study is an equation expressing the rate in terms of some measurable property of the pulp. This can be either the concentration of floatable mineral in weight per unit volume1,2 or a relative concentration, which will be a function of the recovery." A rate equation for an actual flotation pulp will contain at least two constants, both to be determined from the data. One of these, the initial concentration or proportion of floatable mineral, is not necessarily equal to the feed assay because of nonfloatable oversize or locked particles." The other, a rate constant, is a measure of proportionality between the rate and the pulp property on which the rate depends. The value of the rate constant will be determined by the values of all variables which control the process and will be changed by significant changes in any of them. It is, therefore, a direct measure of performance. Where recovery or grade change continuously with flotation time, the rate constant will be independent of time and will characterize the entire course of the separation. Development of Rate Equations Rate equations can be developed either by analysis of the mechanism of the process or by direct fitting of equations to recovery-time data. Sutherland&apos;s attempt by the first method&apos; suggests that the effect of particle size variation on the rate complicates the derivation of a simple equation applicable to an ore pulp. A further problem with an ore is the concentrate grade requirement, which usually involves a variable rate of froth removal. Thus the final rate for any cell may depend on the froth character and froth height, as well as on the pulp composition. This does not imply that each cell cannot reach a steady state2 in which the rate will depend ultimately on pulp composition. The second method is the fitting of rate equations consistent with the necessary boundary conditions* to experimental recovery-time curves. On the assumption that under constant operating conditions the flotation rate is proportional to the actual or relative concentration of floatable mineral in the pulp, a generalized rate equation may be expressed as follows: Rate = Kcn [I] where K is the rate constant, c is some measure of the quantity of floatable mineral in the pulp at time t, and n is a positive number. In previous rate studies, the value of n has been taken as 1, either by direct assumption," or as a result of the hypothesis that bubble-particle collision is rate determining.&apos; A first order equation results, which after integration in terms of cumulative recovery R, leads to Loge A/A-R = Kt [2] The quantity A is the maximum possible recovery with prolonged time under the conditions used. No conclusive proof for the validity of this equation in flotation has been advanced. The evidence cited in its support consists entirely in the demonstration that it appears to apply to a limited number of recovery-time curves."&apos; It will be shown subsequently that this procedure is not sufficient to establish the order of a flotation rate equation. The possibility that the equation may be of higher order therefore requires examination. If, in particular, the exponent in eq 1 is assumed to be 2, then after integration there results R = A2Kt/1 + AKt [3] with K again a rate constant and A the maximum proportion of recoverable mineral. Eq 3 may be

Jan 1, 1952

By Hsun Hu, R. S. Cline

The formation of annealing textures during the course of recrystallization in 2 pct Al-Fe crystals rolled in the (111) [112], (112) [111], and (112) [Till orientations has hem studied in detail. When the rolling texture is composed of both (111) [121] and (001)[110] components, the annealing texture consists of mainly (110) [001] and (113) [332] components. As the (001) [110] component diminishes from the surface to the interior of the rolled crystal, the relative concentration of the (113) [332] component in the annealing texture decreases accordingly, whereas that of the (110)[001] component increases with the (111)[112] component in the rolling texture. Such dependence of the annealing texture on the composition of the rolling texture is in accmdance with the oriented growth mechanism. Grain-growth characteristics during recrystallization, hence the annealing texture, can he considerablv different in (112) [111]-type crystals depending sensitively on the initial orientation of the crystal. In a previous publication,&apos; the formation of rolling textures in 2 pct A1-Fe single crystals with initial orientations of approximately (1ll)[112], (112)[111], and (112)[111] was studied in detail. The deformation texture of these crystals consisted of either a single (111)[112] or a combination of (111)[112] and (001)[110] components in various concentrations. For the (lll)[112] crystal, the deformation texture was a single (lll)[112] up to 70 pct rolling reduction, but it became (lll)[112] plus (001)[110] after -90 pct reduction. For the (112)[113.]-type crystals, the relative concentration of the (111)[ 112] and (001)[110] components varied with the depth below the surface of the crystal, as well as with the amount of deformation. These series of specimens, having deformation textures with a range of concentration of the (111)[112] and (001)[110] components, could therefore be used for a thorough investigation of the effect of deformation-texture components on the formation of annealing textures. In a study of rolling and annealing textures in Si-Fe crystals, Dunn and Koh3 noted that the addition of a (001)[110] component to the (111)[112]-type deformation texture had practically no effect on the recrystallization texture.* According to the ori- ented growth mechanism for the formation of annealing textures, nuclei related to the deformation texture by approximately 30-deg rotation around a common [110] axis have the highest rate of growth and the resulting annealing textures generally have such an orientation relationship with respect to the deformation textures.314 It was reasoned by Dunn and Koh3 that if the oriented growth mechanism operated the recrystallization texture developed from a deformation texture containing both (111)[112] and (001)[110] components should be strongly centered around (113)[332], because (113)[332] is approximately midway between the (111)[112] and (001)[110], and is related to both of these two orientations by [110] rotations of 25 to 30 deg. Hence, nuclei of (113)[332] orientation should have a high rate of growth in the deformed matrix. However, their results were not in accord with this prediction. It was felt by the writers that a detailed study was needed to clarify the effect of deformation-texture components on annealing-texture formation. For this reason, the present investigation was conducted. EXPERIMENTAL PROCEDURE Specimens used for the present investigation were taken from the crystals rolled previously for deformation-texture studies.&apos; In order to follow the progress of annealing-texture formation during the course of recrystallization, a single specimen was taken from each rolled crystal and its textural changes examined after successive anneals until recrystallization was complete. The specimen was carefully cut from the rolled strip with a jeweler&apos;s saw. Prior to annealing, the sawed edges were etched to remove distorted metal, while both faces of the specimen were protected from the etching solution by acid-proof plastic tape. After annealing, the specimen was etched from the "bottom" face only (the reference or "top" face of the specimen was protected by plastic tape) to one half of its original thickness, so that the texture at the surface and at the central section of the strip could be determined by the reflection technique. The

Jan 1, 1965

By M. F. Williams, L. G. Hendrickson

IN classification of pulps bearing magnetized ferromagnetic particles, depolarizing is of great importance. If size separation is to be effective, particles must be individual rather than in floes. Depolarizing is also practiced in heavy medium separations in which ferrosilicon or magnetite is the medium. When particles of ferromagnetic material have been removed from a magnetic field, residual magnetism causes agglomeration. The term depolarizing refers to the operation of reducing or eliminating this residual magnetism and may thus be considered magnetic deflocculation. The terms demagnetizing and randomizing are also used. At the Research Laboratory of Oliver Iron Mining Div. in Duluth a method was developed for measuring depolarization of the pulp of ferromagnetic material. Experiments were made with Mesabi taconite,&apos; a natural magnetite of low coercive force. Ferromagnetic materials of higher coercive force, such as lodestone or the artificial magnetite produced by reduction roasting of hematite, present a more difficult problem, which was not within the scope of this investigation. It is possible, however, that some of the techniques evolved for measuring and calculating electrical characteristics of alternating current coils would be of use in depolarizing high coercive force material, particularly in conjunction with high-frequency alternating current, as proposed by Hartig and others.&apos;," Properties of Ferromagnetic Materials:&apos;7 Experimental work, described below, has shown that if a sample in the magnetized state is heated above the Curie point and cooled, much of the preferred orientation is destroyed and the sample is substantially depolarized. It has been thought that when the sample cools below the Curie point the domains cancel each other, leaving a zero net moment. However, such particles still exhibit a tendency to cohere, and undoubtedly this is caused by the forces of residual magnetism. -AS measured by the percent depolarization, this tendency is reproducible for any sample upon repeated heating above the Curie point and subsequent cooling and is independent of the initial state of magnetization. It is postulated, therefore, that as the material is cooled below the Curie point the domains in any particle do not completely cancel each other, but rather are preferentially oriented to some extent. Mechanism of Depolarizing with Alternating Current Magnetic Fields: It is believed that when ferromagnetic material is passed through an alternating magnetic field, depolarizing occurs in the decaying portion of the field. As the particles pass through the portion of highest intensity they become magne- tized. If the particles are not free to move, the polarities of the particles will be reversed (by a mechanism similar to that described above for magnetism) at a frequency equal to that of the applied field. As the material moves through the decaying field, intensity levels become such that a domain does not completely reverse, but stops on an axis of easy magnetization. By the time the material reaches the point of zero field intensity, a state of fairly random orientation of domains is achieved. If conditions are such as to give a completely random orientation, the particle will have little or no external magnetic field, and a pulp of such particles will be depolarized. Previous Work In 1918 E. W. Davis was granted a patent for demagnetization of magnetite pulps.&apos; His method consisted of passing the pulp through a tapered coil, activated by alternating current of normal frequency (60 cycle). This method, with minor modifications, has been used almost universally in all pilot plants and commercial installations in which depolarization of low coercive force materials has been required. Hartig, Onstad and Foot2,3 avd made a detailed study of the factors involved in depolarizing both low (below 100 oersteds) and high (above 100 oersteds) coercive force material. They developed a method for evaluating the relative degree of depolarization of any pulp based on the settling characteristics of the pulp. Their standard of comparison was a sample heated to above the Curie point and cooled in a zero field, all in a neutral atmosphere.* For low coercive force material they found treatment.Thisprocedure is subsequently called, in this report,theCurie that results equivalent to Curie treatment could be

Jan 1, 1957