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By Larry Kaufman

A useful method for estimating the entropy of NaCl type compounds has been developed by combining the Debye theory of specific heat with the Lindemann formula. This method pemnits calculation of the entropy from a knowledge of the atomic weight, atomic volume, and melting point of the compound. Comparison of the calculated and observed entropies of 35 NaCl type compounds over a wide temperature range yields good agreement thus establishing the usefulness of the method. Application of the method to other crystal types is also discussed. KUBASCHEWSKI~ has suggested a useful method of estimating the enthalpy of formation of inter-metallic compounds from a knowledge of the crystal structure, lattice parameter, and heats of sublimation of the component elements. This method is quite valuable in predicting the tendency for compound formation in a given system and is of particular value in considering systems for which no experimental data are available. In order to supplement the enthalpy calculation afforded by Kubschewski's method, it would be of value to be able to estimate the entropy of compounds so that the entropy and free energy of formation could be evaluated. Although a considerable body of such data determined by calorimetric and equilibration techniques exists at present, the difficulty of making such measurements (particularly at high temperatures) and the ever increasing number of new compounds which are of interest make the desirability of such a computational method clear. This paper deals with a method for calculating the entropy of a compound from a knowledge of the atomic weight, atomic volume, and melting point. Since these data are generally easier to determine and therefore more readily available than thermo-dynamic data, they should provide an additional tool in estimating the stability and reactivity of compounds at high temperatures. I) THE ENTROPY OF PURE METALS As a first approximation, the specific heat of a pure metal can be represented by a sum of terms where C,($/tI is the vibrational specific heat calculated on the basis of the Debye theory, lo4 TC, (0/T) is an approximation to the Cp - C, correction. T is the electronic specific heat, and Cp (p) is the magnetic specific heat. Although the Debye theory does not provide a complete description of the vibrational specific heat, i.e., the Debye temperature 0 is not a constant, it does provide a good approximation when used properly. Blackman6'7 has written several reviews on this subject discussing the different values of 0 determined by various methods (specific heat, X-rays, elastic constants, electrical resistivity, and so forth), as well as the observed temperature dependence of 0 with T. In the present case the 0 in Eq. [I] naturally refers to the specific heat 0. The variation of Debye 0 (as determined from specific heat measurements) with temperature is observed to exhibit its most radical behavior at very low temperatures. At higher temperatures the 8 values are observed to become more nearly constant. Blackman6'7 has presented the variation of 0 with temperature for several metals. His tabulation is reproduced in Table I. Reference to Table I shows that above a certain temperature level, 0 remains fairly constant. The value of 0 which is most useful in computing the specific heat, and hence the entropy, is the value of 0 in the range 0/6 « T « 0. In 1910, Lindemann' suggested a relation for estimating Debye 0 values. According to this formula, where V is the atomic volume, T is the melting point in 'K, M is the atomic weight, and CL is a constant. Mott and Jones9 present this formula and state that there is at present no satisfactory theoretical explanation, but that it does have an empirical basis. By using the valuesof 0 in Table I along with known1' values of M, T, and the molar volume VM, where the Lindemann constant can be evaluated. This

Jan 1, 1962

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs.' Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster" and was first reduced to practice by the experimentation of Welge. In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid Phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always ereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By W. C. Lilliendahl, G. Meister

Uranium metal with a purity of about 99.9 pct was produced on a large scale by fused salt electrolysis with a material efficiency of about 90 pct. The material efficiency depends mainly on bath composition, electrolysis temperature, electrode smothering, and elutriation during washing of the powder. RESEARCH and development work on fused salt electrolysis carried on by the Westinghouse Lamp Div. Bloomfield, N. J., was done under the Manhattan District Corps of Engineers and later under the Atomic Energy Commission for the commercialization of uranium production for the first atomic pile at the University of Chicago in 1942. From the conception of the atomic bomb project it was recognized that metals with impurity levels having little metallurgical significance would be required. Permissible impurity levels were based on neutron absorption. Of particular significance was boron, which could not be present in amounts exceeding 1 ppm. The electrolytic method as developed in 1930 by Driggs and Lilliendahl,1,2 and later improved, yielded uranium of very low boron and other deleterious impurity content. No other method was capable at that time of producing uranium metal of the required purity.' The low boron content of uranium produced by the electrolytic process resulted from the availability of the reactants which were low in boron content, and from the inherent elimination of boron in the fused salt bath. Since the heart of any electrolytic process is the electrolysis cell, this paper will deal with the development of the original bath composition for the efficient production of uranium from a batch process to one of continuous operation. Emphasis also will be placed on other factors which will affect the material efficiency of the process. With the laboratory cell the material efficiency of uranium powder recovery in the early electrolysis was relatively low, about 35 pct based on the ratio of uranium recovered to uranium added. This early process also had other defects. The electro- lytic bath could not be used continuously. After three runs from a freshly charged crucible, the deposit showed a tendency to slip off the electrode as it was raised from the bath. This condition necessitated pouring the charge every fourth run and preparing a new bath. It was assumed at that time that this condition was caused by the increasing fluoride concentration with each addition of uranium salt, which adected the mobility of the uranium ions. Experimental The electrolysis cells differed in size only. They were of the floating cathode type. The laboratory cells were 21/2 in. ID and 6 in. deep and operated at 30 amp and 5 volts. Production was about 150 g metal powder per 8 hr. The plant cells (5 units) were 9 in. ID x 21 in. deep and operated at 1800 amp at 12 volts. The total production unit was designed to produce 250 lb of uranium powder per 8 hr day. Because of the tendency of uranium fines toward spontaneous combustion, material efficiencies were based only on the recovery of useful coarser metal which could be safely handled. The reported efficiencies are of particular significance only as related to the same group of experimental procedures. At the start of the project no changes were contemplated until previous data could be definitely confirmed. Therefore, the first experiments were with the 50 pct CaCl2-50 pct NaCl mixture. The material efficiency of uranium deposition as a function of the number of electrolyses is shown in Table I. In Table I, the decrease in efficiency at 800°C with number of runs is apparent and confirmed the earlier data. Operating at 900°C enabled the number of runs to be doubled, but before pouring the charge the efficiency of recovery became poor. This test indicated that the improved efficiency might have been caused by an increase in the fluidity of the bath.

Jan 1, 1958

By C. H. Li, J. A. Sarteli, W. Bonfield

The stress to cause a permanent micros train of 2 x 10-6 in. per in. (defined as the microscopic yield stress) in beryllium is found to be very sensitive to surface condition. The initiation of plastic flow in as-machined specimens, which contain a high density of twins and large residual compressive stresses to a depth of about 0.010 in. from the surface, occurs by the nucleation of slip from high stress fields around twin tips in the surface layers. Removal of the damaged surface layers by chemical polishing results in an appreciable increase in the microscopic yield stress, which is attributed to the remoual of stress raising twins rather than to the release of residual stresses. IT is well known that the macroscopic mechanical properties of beryllium are very sensitive to the nature of its surface finish. Matthews and coworkers1 have shown that the tensile strength of rolled beryllium sheet can be considerably enhanced by chemical polishing, presumably due to the removal of the high concentration of notches, twins, and large residual compressive stresses normally found in the surface layers of ground specimens. There was no similar effect of surface condition on the macroscopic yield stress (the stress to produce 0.2 pct strain), a point to which we shall return. To date there have been no extensive studies on the effect of surface condition on the microstrain region of beryllium. Recent measurements2 of the stress to cause a permanent microstrain of the order of 10-6 in. per in. on machined hot pressed QMV beryllium, gave values ranging from about 600 to 3500 psi. Reasons for the considerable scatter in the results were not discussed. In this paper, we wish to show that the microstrain region of polycrystalline beryllium is, in fact, very sensitive to surface condition. The stress to cause a permanent strain of 2 x 10-6 in. per in. which for convenience we will refer to as the microscopic yield stress, can be increased by almost a factor of 2 by minimizing the amount of surface damage. The variation of microscopic yield stress is attributed to the presence of twins in the surface layers, rather than to residual compressive stresses. EXPERIMENTAL PROCEDURE The starting material for this investigation was commercial purity hot pressed QMV beryllium, with an average grain size of about 20 . The effects of surface treatment were assessed by comparing the microstructure with residual stress measurements and microstrain properties. Specimens were prepared for metallographic examination by wet grinding with 240, 400, and 600 papers, followed by polishing with a suspension of fine alumina in warm 20 pct oxalic acid. After this treatment, the surface could be examined, either in the unetched condition with polarized light, or after etching in 2 pct hydrofluoric or boiling 20 pct oxalic acid with normal light. Thin films of beryllium suitable for electron transmission study were prepared from bulk specimens by chemical polishing with hydrofluoric and phosphoric acids, and were examined in an RCA-EMU-3 electron microscope. Residual stress measurements were made by a procedure similar to that of Treuting and Read.3 Specimens 4.0 in. by 0.625 in. by 0.080 in. were prepared by three different machining procedures, namely: turning, grinding, and sawing, in order to introduce different levels of residual stresses. An electrical resistance strain gage was attached to one side of the specimen, and that surface was then protected by an acid-resistant enamel, while the opposite surface was removed by etching approximately one thousandth of an inch at a time. The change in specimen curvature in the longitudinal direction was noted and the residual stress was calculated by the following formula:

Jan 1, 1963

By H. E. Cline

A criterion for stability of a lamellar structure in two-phase alloys ulas derived froflr perturbation analysis of the steady-state solutions for eutectic growth. Both the mass and thermal diffusion were considered with boundary conditions for coupled lamellar growth. The concept of an effective liquidus slope was introduced. Excellent agreement was found with the experiments of Mollard and Flemings and the theory predicted a range of compositions on one side of the eulectic composition in which stable growth may occur with zero temperature gradient. The lamellar structure was found to be more stable than predicted by simple constitutional supercooling. The effect of impurity additions was also considered. DIRECTIONALLY solidified eutectic alloys may have a structure consisting of parallel plates or rods. It is important to know the range of composition and growth conditions that produce this ideal composite structure. Breakdown of the planar solid-liquid interface during growth may lead to a dendritic or cellular structure as in single-phase alloys. In the case of single-phase alloys, the concept of constitutional supercooling1 may explain breakdown, but in two-phase alloys the concept is no longer valid because the melting point is not given by the liquidus of one phase. Both phases must be considered in the mass and thermal diffusion problem. In the following theory a boundary condition at the solid-liquid interface was determined by using the steady-state equations of Jackson and ~unt' to relate the average temperature and composition of the liquid at the interface. Then a sinusoidal perturbation in the shape of the interface was introduced to test for stability as in the analysis of Mullins and ~ekerka.~ The wavelength of the important perturbation was assumed to be much larger than the lamellar spacing, h, and the perturbation was assumed not to change the lamellar spacing, A. Both the mass and thermal diffusion equation were used with averaged quantities at the boundary to determine whether the perturbation grows or shrinks in time. A stability criterion was determined by considering the case in which the perturbation remains stationary. An example of Pb-Sn alloys was used to illustrate the validity of this theory. I) THEORY A) Temperature at the Interface. The temperature of the interface in coupled two-phase growth is close to the eutectic temperature TE even for alloys off eutectic composition. It is assumed that the interface is in local equilibrium and one expects the temperature at the intersection of the liquid phase and the solid phases a and 0 to be near the eutectic temperature. The interface is undercooled because of curvature and the deviation of the composition in the liquid from the eutectic composition. The average interface temperature Ti for steady-state growth of a lamellar eutectic with a plane interface was determined by Jackson and Hunt' as given in their Eq. [17c]. Instead of using the ratio of the lamellar widths hp/h, as a parameter, the volume fraction of the 0 phase, +, will be used as it simplifies the algebra. The average interface temperature using this notation becomes: The average temperature of the interface depends on the volume fraction of the 0 phase, +, which may be related to the composition of the solid or the bulk composition of the liquid Co by: where C, and Cp are the average compositions of the solid phases. In steady-state growth, the composition of the solid is equal to the composition in the liquid far from the interface. The variation of the average interface temperature with composition is illustrated in Fig. 1 for the case of Pb-Sn alloys with a 10"4 cm lamellar spacing as calculated from Eqs. [I] and [2]. The interface temperature goes through a maximum at a composition near but not exactly at the eutectic composition. There is no reason why the composition corresponding to the maximum temperature should be equal to the eutectic

Jan 1, 1969

By M. C. Flemings, A. A. Tzavaras

Analytical and experimental procedures are descrihed for quantitative determination of volume-fraction microporosity in metals by mimorarlio-graphg. The analysis assumes spherical pores but allows for the observed fact that pores or portions of pores smaller than a given thickness do not project an image on the film. Volume-fraction microporosity was measuured in cast low-alloy steel and shown to vary from 0.6 x 10-4 to 10 x 10 depending on mode of solidification and on whether the material was air- or vacuum-cast. The aim of work described herein was to develop a method of quantitative measurement of the volume fraction of microporosity in cast metals. Microporosity, present in nearly all castings and ingots, is always interdendritic in nature and may be large enough to be seen on a polished surface with the naked eye. More generally, it is smaller in size, and its detection more difficult. Three techniques might be considered for measurement of microporosity: 1) lineal analysis of a polished metallographic surface, 2) density measurement, or 3) quantitative microradiography. As will be shown later, volume fractions of porosity in directionally solidified castings may be the order of 10-4 to 10-3; such small amounts of porosity are difficult to identify and measure on a polished surface. Density measurement is also not a suitable technique (for alloys) when the volume fraction of porosity is low. This is because the density of the base metal is often not known within the necessary accuracy, due to microsegregation or partial phase transformations. In general, it is not possible to completely eliminate microsegregation without also altering the porosity. Because of the limitations of the foregoing techniques, quantitative microradiography was employed to determine amount of porosity. In recent work, microradiography has been found to be useful for qualitative measurement of porosity, including determination of size and shape of individual pores;&apos;)&apos; however, quantitative determination of amount of porosity has not been attempted. I) CALCULATION OF VOLUME-FRACTION POROSITY The following analysis employs procedures similar to those of Cahn and Nutting3 and Hilliard.4 Major simplifications are that pores are assumed to be spherical and to be present in sufficiently small quantities that no overlapping occurs. A basic difference from the previous treatments is that the limited "sensitivity" of microradiography is considered. Assume first 1) cavities are spherical and of uniform diameter, 2) cavities are randomly distributed, 3) volume-fraction porosity and specimen thickness to pore radius ratio are sufficiently small that overlapping of the projected images of cavities is negligible, 4) sensitivity is limited (i.e., holes or portions of holes of less than a given thickness do not project an image on the film). The sensitivity, is defined as: where 5 = minimum thickness of void from which an image will be projected on the film and t = specimen thickness. Now, from Fig. 1, it is possible to distinguish between two different types of holes. These are 1) holes whose centers lie within the region t/2 > X > 6/2, where X is distance from one surface of the specimen (positive into the specimen), and 2) holes whose centers lie within the region (6 — r) < X < 6/2, Holes whose centers lie outside X = (6 -r) project no image on the film. These two types of pores are considered separately below. Type 1 Pores. When 6 is greater than 0, the image of a spherical cavity of radius r appears on the film as a circle of radius a which is smaller than r. From geometry, Fig. 1: a2=r2-52/4 [2] where a = radius of image of pore on film and r = radius of pore. Since the pores are randomly distributed and spherical V =4/3pr2Nv [3] where V = volume fraction of voids and Nv = number of pores per unit volume and the number of images of Type 1 pores per unit area of film, N&apos;A, is

Jan 1, 1965

By W. A. White

UNDERCLAY squeeze is the plastic flowing of underclay below coal pillars into mined-out entries and rooms. Squeezes may be caused either by wet mine conditions where the moisture is taken up by the clay—making it more plastic—or by the presence of certain clay minerals, such as mont-morillonite, which are plastic when there is enough natural moisture. Under either condition, sufficient stress will cause the underclay to flow. Squeezes may fill an entry or room within several hours, or it may be several months before movement stops. Squeeze areas commonly cover hundreds or thousands of square yards. The Coal Div. of the Illinois State Geological Survey has collected samples of underclays from various mines and from cores drilled by coal companies in the state. From these samples natural moisture content, particle size and particle size distribution, and clay mineralogy are determined. Data from samples collected from the underclay below Herrin (No. 6) coal in the Lumaghi Coal Co. mine near Collinsville, Ill., are used in this report to clarify points in the discussion. Data from samples taken from other mines lead to the same conclusions. A generalized geological section for the area is given in Table I. The underclay below coal No. 6 ranges from a few inches to 3 or 4 ft thick. The upper 6 to 18 in. are noncalcareous; the lower part becomes more calcareous with depth. Limestone nodules become larger with depth, almost grading into the limestone below. In areas where the clay is nearly absent the limestone may thicken to take its place; thus they may complement each other in thickness. There are two types of squeeze areas in a mine. In one type up to 3 or 4 ft of underclay lie in what appears to be a depression in the limestone underneath. This is suggested by a rim surrounding the squeeze area where the underclay is thin and the limestone lies within a few inches of the coal. In the second type the underclay of the squeeze area is surrounded by underclay of similar thicknesses which does not squeeze. Test Methods: Natural moisture content, particle size and particle size distribution, and clay mineralogy were determined by the following methods: Natural moisture is the moisture content a clay contains in its natural environment, expressed in percentage of the weight of ovendried clay (110°C or 230°F). To obtain the natural moisture content, given in Table 11, the clay samples were sealed in containers as soon as the samples were taken in the mines. Particle size and particle size distribution were determined by the pipette method,&apos; and the data were plotted as cumulative curves, Fig. 1, on semi-logarithmic paper. Particle size was plotted on the logarithmic scale and percentage on the arithmetic scale. The quartiles (diameters that correspond to frequencies of 25 and 75 pct) and medians (diameters that correspond to the frequency of 50 pct) of the samples were determined from these curves. The clay minerals were identified from the data obtained by differential thermal&apos; and X-ray powder" techniques. The differential thermal analyses were made on the whole samples, whereas the X-ray analyses were made on fractions of less than 2p. Data and Discussion Moisture Content: After the sealed jars had stood for 24 hr, those that contained squeeze samples had perspired, so that droplets of water had accumulated on the insides of the jars. Table II shows the moisture in the clay after it had perspired for 24 hr. (This perspiring was not noted in samples from nonsqueeze areas.) After perspiration one of the squeeze samples still had a higher moisture content than the samples that did not squeeze. Clay Mineralogy: The thermal analysis, Figs. 2 and 3, indicates that the clay minerals are chiefly micaceous in type; the low-temperature endothermal

Jan 1, 1957

By A. Gittens

In two recent papers stevens13,14 has compared the methods used by various investigators to calculate the contribution of grain boundary sliding to the total creep strain. In previous work Gittins15 has shown that the strain due to grain boundary sliding Egb may be estimated from the lateral, d, and vertical, v, displacements of a longitudinal marker line as it crosses a grain boundary. He obtained the formula, where nL is the number of grains per unit length measured on the specimens before creep, and \p and ?2 are, respectively, the angle between the grain boundary and the stress axis in the plane of the surface and normal to the surface (see Ref. 13, Fig. 1). The subscript L indicates that observations are made in a longitudinal direction parallel to the stress axis. It was generally found more convenient to measure the grain size of a specimen before creep; this was necessary to characterize the specimen. Stevens13,14 however prefers to define Egb in terms of NL, the number of grains per unit length after creep. Since nL - NL(l + €1) where cr is the total strain, Eq. 1 11 becomes The quantities d and ?, can be determined directly from the marker lines, while v and ?2 are found by sectioning normal to the surface. In the interior when symmetry considerations suggest that v = d and ?1 - ?2 the strain due to grain boundary sliding may be estimated from a suitable internal longitudinal marker line by the equation To determine cgb at the surface using either Eqs. |1| or [2] requires a large number of observations, particularly if many estimates of cgb are required, and also it is impossible to determine the variation of cgh with creep strain on the same specimen because the specimen must be sectioned to determine ?2. Gittins15 found that for a number of materials the sliding vectors d and v were related to each other so that provided one was measured the other could be estimated. Also during creep, grain boundaries tend to migrate to meet the surface at angles close to 90 deg,16 so that the term nL(v/tan?2)L was comparatively small when 4,- 90 deg. By determining the frequency distributions of ?2 on control specimens this term can be estimated without sectioning the creep specimen. In this way an empirical equation based on Eqs. |1| and |2| enables cgb to be determined with reasonable accuracy with fewer observations of the angles and sliding components. For B brass, the relationship between the sliding vectors indicated that ceb = 0.85nLVL . In Table I of Stevens paper this equation is stated to be incorrectly derived. However it should be pointed out that this is an empirical equation derived from Eq. |1|, based on a knowledge of the relationship between d and v and on the frequency distributions of ?1 and ?2 for a particular material under given experimental conditions. It was used only when these relationships were known, to reduce the number of observations required to estimate cb. Therefore the comment "derivation incorrect does not apply. Gittins did in fact make use of Eqs. |1| and 131. Author&apos;s Reply I must apologize to Dr. Gittins for the inadvertent misrepresentation of his work. Other slight errors in Table I have been pointed out to me. Langdon (No. 12 Table I), Gifkins (No. 7, Table I), and possibly other workers did not measure the number of boundaries per unit length after creep (A&apos;) but the corresponding quantity bejove creep (n). As Dr. Gittins points out, a completely analogous set of equations to those given in the paper can be derived by the same method: using the number of boundaries per unit length before instead of after creep. The basic equations corresponding to Eqs. [2] and 171 of the paper, from which all the others can be derived, are

Jan 1, 1968

By Michael A. Gustafson, Fernando B. Sotelino

INTRODUCTION The degree of success of any new project will ultimately depend on two factors: (i) the underlying economic strength of the project; and (ii) how successfully the parties involved can coordinate their interests to establish a financing structure which indeed capitalizes on the project&apos;s inherent economic attractiveness. A project&apos;s underlying economic attractiveness is determined by its inherent comparative advantage in accessing the factors of production, combining these factors of production to create a product and marketing this product. Initially, the decision regarding whether to go ahead with the project - the go/no go decision - has to be based on its total ability to generate cash flow returns to project participants to compensate them for resources committed and risks undertaken. The extent to which project sponsors will actually benefit from the project&apos;s inherent economic attractiveness is fundamentally dependent on their ability to establish the long-term financing arrangement which best meets the objectives and constraints of each project participant and sources the most advantageous funding. The decision regarding the financing of the project, the "how-to-go" decision, is then an attempt to find the capital structure, consistent with market terms and conditions and sound financial management policies which will best: (i) match planned outflows with cash inflows; and (ii) maximize the return for project sponsors. This article makes use of a case study to illustrate the analytical process involved in dealing with the go/no go and the how-to-go decisions on a project. Though most commonly applied to project finance situations, the guideline described herein is equally applicable to other financing situations, such as leveraged buyouts and debt restructurings, where timely repayment of debt depends largely on the future cash flows to be generated by the entity being financed. Our case study is of a hypothetical expansion of an existing copper mining operation in Latin America. The company, Latin American Copper (LAC) currently has 147 million metric tons of proven sulphide ore reserves. The existing mine complex consists of an open pit mining operation and a conventional flotation plant with a processing capacity of 20,000 metric tons of ore per day. LAC sells copper concentrates primarily to Japanese custom smelters. The mine has been in operation for 5 years, fine copper production last year was 108,240 metric tons, and LAC currently has assets of $175 million and net worth of $135 million. Due to a recent increase in proven reserves, LAC is considering doubling the treatment capacity of its flotation plant to 40,000 tons per day, and expanding its mining capacity to meet the additional concentrator capacity (the "Project"). Project capital expenditures and incremental working capital have been estimated at approximately $210 million. The construction period is expected to cover one year, including a three-month start-up phase. The Project is to be funded by a combination of equity, senior debt, including both supplier credits and/or commercial bank term loans, and subordinated debt. LAC&apos;s shareholders are willing to commit a maximum of $50 million to the Project. A government development agency, which is also a minority shareholder, might be willing to lend approximately $40 million to LAC in the form of subordinated notes, depending on the ability of the Project to generate foreign exchange reserves. Commercial banks cannot be expected to offer loans with maturities longer than ten years. The Project is expected to increase the value of the firm because: (i) It will solidify the Company&apos;s position as a low-cost copper producer by taking advantage of economies of scale. As a result of the expansion, cash production costs are expected to decrease 7.0[c]/lb. and all-in costs 11.0[c]/lb; (ii) The potential earnings stream from the sulphide ore reserves will be realized

Jan 1, 1985

By Michel Elle, John Chipman

The equilibrium of gaseous H20-H2 mixtures with liquid iron-columbium alloys in the range 0.2 to 2.4 pct Cb shows that the activity coefficient of oxygen is strongly diminished by Cb. The oxide in equilibvium with the melt is identified as CbO2. The equi-librium constant at 1600 deg C is [%Cb][fo. % 0]2 = 2.9 x 10-4 where log fo= —0.14 [%Cb]. The deoxidizing power is comparable to that of vanadium, COLUMBIUM (niobium) is finding increasing use as an alloying element in steel. It forms several stable oxides and is removed from the steel bath by oxidizing slags. The specific oxide formed in steel-making is not known although Sazanov snd Shvarts-man,&apos; in their study of its partition between slag and metal, have assumed this to be Cb2O5 It is the purpose of this study to determine its deoxidation equilibrium at 1600°c, the nature of the oxide formed and the interaction between columbium and oxygen in the melt. The investigation was based on the reaction H2 + O=H2O; Kl=ph2o/(pH2[%O]) [1] in which 0 signifies oxygen dissolved in the liquid Fe-Cb alloy. The method and equipment of recent studies2,3 were utilized. In brief, the molten alloy, contained in a small crucible, is held in a controlled mixture of steam, hydrogen, and argon until equilibrium is reached. It is then cooled quickly in a stream of helium and analyzed for columbium and oxygen, the latter by vacuum fusion.4 The solubility of the oxide in liquid iron is determined by visual observation of scum formation on the surface of the melt. Crucibles of MgO proved unsatisfactory because of partial reduction at the metal interface. Pure A12O3 crucibles were heavily blackened by the melt and could not be used at high concentrations of columbium. Silica crucibles were more satisfactory but these introduced some silicon into the melt thus necessitating an uncertain but small correction for its effect on the activities of the other solutes. In silica it was possible to observe the scum formation when the melt became saturated and there was no apparent reaction between scum and crucible. The procedure for saturated melts was as follows. The alloy charge composed of electrolytic iron and columbium grain was melted and held at constant temperature. The gas ratio H2O:H2 was progressively increased by raising the saturator temperature until a point was reached at which a bright film appeared on the surface and covered it completely. This film could be dissolved by raising the temperature of the melt and it reappeared when the temperature was lowered. Under a partial film covering, utilizing bare areas for temperature measurement, the melt was brought to equilibrium with the atmosphere by holding at temperature for about 1 hr as suggested by Dastur.5 INTERACTION IN THE MELT Several experiments were made without columbium to establish a base in silica crucibles. The results are shown in Table I. Except for one run, they agreed well with Floridis1 comparable results in other crucibles. The value of log K1 is taken from Table I as 0.58. This is slightly larger than Floridis&apos; result, probably because of less elaborate safeguards against thermal diffusion. Results obtained in the Fe-Cb-0 series in which no scum formed are shown in Table 11. The equilibrium ratio Kl is defined as ph2o/(ph2[%O]). It is related to the equilibrium constant K1 as follows:

Jan 1, 1962

By G. C. Wallick, W. R. Foster, J. G. Savins

A comprehensive review of the salient features of the differentiation method of rheological analysis in Poiseuille flow from its inception circa 1928 is presented. Here no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical parameters are required in the data-analysis process. In contrast, the integration method involves interpreting flow properties in terms of a particular ideal model. It is shown that, although both methods represent modes of solution of the same integral equation, being relatively bias-free, the differentiation method offers a more discriminating procedure for rheological analysis. The application to problems involving plane Poiseuille flow is also described. INTRODUCTION In most instances, the approach to the problem of interpreting the rheological properties of various compositions as they are affected by changes in chemical or physical environment, assaying the characteristics of a particular constituent of a suspension, analyzing flow behavior in terms of interactions between components in a system, to cite but a few examples, has been in terms of what Hersey1 terms the integration method. Briefly, it consists of interpreting flow properties in terms of a particular ideal model. The usual practice of the integration method is to choose a model with a minimum number of parameters because, other things being equal, it is desirable to use the simplest model which will describe the behavior of a real material and yet be mathematically tractable for the requirements of data analysis. This expression is then substituted into an equation which relates observed kinematical and dynamical quantities, such as volume flux Q and pressure gradient ], and angular velocity and torque T, in a capillary and concentric cylinder apparatus, respectively. The rheological parameters appear on integrating, in an expression relating the pairs of observable quantities such as those just given. In many instances a particular model provides a good representation of rheological behavior over a reasonable range of compositional and environmental changes. Just as often, however, it is obvious that the interpretation of rheological changes by the integration method is not providing realistic information about changes in flow behavior. A more general method of interpreting rheological data for a given material is to make no initial assumptions regarding the nature of the function relating rheological parameters to observed kinematical and dynamical quantities, e.g., flow rate and pressure drop in capillary flow or angular velocity and torque in a rotational viscometer. This general method Hersey1 terms the differentia-ation method. Instead of integrating, one differentiates the integral equation with respect to one of the limits, i.e., one of the boundary conditions; the resulting expression contains the same observable quantities just given, their derivatives, and the rheological function evaluated at that boundary. By obtaining these derivatives from experimental data, graphically or by a computer routine, they can be substituted into the differential equation and a graphical form of the function derived. THEORY OF THE DIFFERENTIATION METHOD FOR POISEUILLE-TYPE FLOWS In this introductory paper, two flow cases which are important in viscometry are considered (one for the first time) from the differentiation method of analysis, flow in a cylindrical tube and flow between fixed parallel surfaces of infinite extent, the basic integral equations being formulated in a manner analogous to the way they originally appeared in the literature. In addition, the following ideal conditions will be assumed: (1) an absence of anomalous wall effects, (2) isotropic behavior everywhere, and (3) steady laminar flow conditions. Before proceeding it would seem appropriate to preface the analysis of these flow geometries with the comment that the basic philosophy of the differentiation method could be said to stem directly from the efforts of Herzog and weissenberg2 to indicate systematically the various ways of using

By G. K. Dumbauld, B. E. Morgan

Kesults of laboratory investigations of the effects of drilling muds on oil well cements are presented which show that relatively large quantities of untreated muds do not seriously interfere with the setting of cement slurries, but that relalively small quantities of treated muds seriously retard the setting of cement slurries. Laboratory results also indicate that the harmful effects of contamination with treated muds can he counteracted by the addition of activated charcoal to cements. Also described is the successful use of cement containing activated charcoal for the placement of plugs in oPel hole after previous attempts with ordinary cement had been unsuccessful. INTRODUCTION The contamination of cement slurry by dilution with drilling mud has long been considered a cause of failure in oil well cementing. The cement slurry must displace the drilling mud from the annulus between the casing and the walls of the borehole. and it is probable that some mixing of the slurry and the mud occurs even under the most nearly ideal displacement conditions. Hole enlargement, failure to center the casing in the hole, and formation of gel structure in the drilling mud increase the probability of contamination. In some cementing operations, such as the placement of a cement plug in open hole, considerable mixing of the mud and slurry is likely. Many cement failures which can be attributed logically to no cause other than contamination of the cement slurry by the mud attest the need of a better understanding of this problem. Considerable attention was given to the problem of mud contamination of cements about 20 years ago.The effects of field mud upon cement slurries prepared with different amounts of mix water were investigated thoroughly, and the data obtained were invaluable in determining the causes of the high percentage of failure in oil-well cementing at that time and in bringing about improved cementing results. Since then, many aspects of the problem have changed, due primarily to advancements in cement and drilling mud technology. Today, several types of portland cement are used in well cementing and numerous chemical additives are used in drilling muds. An excellent report on the effects of drilling mud additives on oil-well cements was issued during 1951 by the American Petroleum Institute. Data in the report revealed that many mud additives, notably organic materials in relatively small amounts, produce a marked effect on the properties of cements. Prior to this time, little information has been available on the effects of chemicals commonly used in the treatment of drilling muds upon the properties of cements. Another aspect of the problem of mud contamination of cements, which has received no attention heretofore, is the possibility of producing a cement having properties unaffected by a reasonable amount of mud contamination. In view of the need for additional information on the contamination of present-day cements by currently-used drilling Muds, the investigation described herein was initiated Several years ago with a two-fold purpose: first, to determine the capacity of cement slurries to tolerate contamination by both untreated and treated muds without loss of ability to set and develop strength within a reasonable time; and, second, to investigate the possibility of enhancing the ability of cement slurries to withstand mud contamination by incorporating additives in the cement. The data for this study were obtained by mixing drilling mud with cement slurry and testing the resulting slurry-mud mixture for rate of set and development of strength. Also, several materials were tested for their possible improvement of the property of cement slurry to withstand mud contamination; these materials were tested in both contaminated and uncontaminated cement slurries.

Jan 1, 1952

By A. Kenneth Schellinger

DURING the comminution of a brittle material in the presence of dry air, no known phase change or chemical reaction takes place. The energy changes associated with the comminution are those of the transformation of kinetic energy into heat energy and the energy absorption represented by the actual rupture of molecular and/or ionic bonds. The random nature of the actual grinding process in a tumbling-mill often precludes the effective application of a rupture force on each individual particle of brittle mineral present. The result must be a great deal of useless vibration on an atomic scale in both the brittle mineral and the grinding medium below the elastic limit, which vibration is eventually manifested as heat energy in the mill. The actual rupture of molecular, or ionic, bonds creates new surface on the brittle minerals; each square centimeter of this new surface then must possess a number of potential bonds, each of which could reform theoretically with the release of energy. The sum total of this potential energy of bonding per unit of new surface, minus bond satiation effects of the enclosing gas or liquid, must be the surface energy of the mineral. If the comminution of the brittle mineral were carried out within the chamber of a calorimeter, the energy released as heat could be determined rather accurately. Moreover, the total kinetic energy input to the comminuting mass (mineral and medium) conceivably could be derived by a suitable torquemeter and revolution counter if the whole calorimeter were revolved. The difference between these two energy figures should then represent the net energy (gross energy input—heat enerb output) used in creating new surface, gliding or slip on atomic planes, twinning, and possibly other lattice rearrangements within the mineral. If it be postulated further that with a hard, brittle crystalline material, such as quartz, the energy used to produce gliding, twinning, and other permanent lattice movements is a very small fraction of the total net energy absorbed, then this energy absorption within the grinding calorimeter can be ascribed to the creation of new surface energy alone. Such energy is, from the thermody-namic standpoint, the true effective work of the grinding device, in this case a tumbling-medium mill. The ratio of this effective work (in calories) to the total energy input (in calories) should express the thermodynamic efficiency of the comminution taking place under the conditions used in the grinding calorimeter. This approach to the measurement of the energetics of tumbling-mill grinding was suggested by some previous work by Fahrenwald and coworkers&apos; with a laboratory ball mill and a thermometer. They measured the efficiency of grinding based on the formula: Pct Grinding Efficiency = Energy (calories) — Thermal Energy x 100 1npZ Output (calories) Energy input (calories) Efficiencies thus measured, while grinding quartz sand, ranged from 19.7 pct to 7.4 pct. Cook in 1915,&apos; used this approach to the problem of grinding efficiencies in stamp batteries and obtained the energy input by stamp weights times drop distances and the energy output by means of thermometers and pulp flow rates. He calculated that 80 pct of the input energy to the stamp shoes was wasted as sensible heat in the ore pulp. No other studies of comminution by this method of energy differences came to the author&apos;s attention. Reasonable agreement as to the order-of-mag-nitude of comminution efficiencies in tumbling-media mills is lacking in the literature. There is a widespread impression among technical workers that the grinding efficiency of the industrial ball mill may be on the order of 1 pct, or even a fraction

Jan 1, 1952

By Walter Rose

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs. Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster and was first reduced to practice by the experimentation of Welge . In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz&apos; comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat&apos;s argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz&apos; postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize Welge&apos;s theoretical treatment of his problem. It can be shown that Welge&apos;s method of measuring values for &apos;&apos;capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always gereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By J. Chipman, N. J. Grant, E. C. Roberts

An equilibrium study was made of the distribution of chromium and oxygen between liquid iron, containing less than 1 pct Cr, and simple slags of the CaO(MgO)-Si02-FeO-Cr& type in the temperature range 1526&apos; to 1734OC. The effects of slag oxidation, temperature, and basicity were observed. IN spite of the fact that chromium is one of the most important alloying elements in steel, and exists in almost all steels as a significant residual element, little research has been done to determine its behavior in basic steelmaking processes. Considerably more work has been done under silica-saturated acid slag conditions. Korber and Oelsen,&apos; Herasymenko,&apos; and others have generally agreed that in acid steelmaking practice the chromium in the slag behaved as if it were present as the chrom-ous ion (CrO). Work by Hilty- ir, high chromium slags also indicated that chromium may exist as CrO. In basic slag systems no equilibrium data exist. Based on individual studies of basic open hearth and electric furnace practice, Bardenheuer," Rock-rohr,% nd HauckQ oncluded that: 1—chromium recovery increased with decreasing basicity, and 2— chromium recovery increased with increasing temperature, although the effect was small. In similar studies Yavioskii and Dzemyen&apos; concluded that: 1— slag FeO is the most important variable, 2—the basicity of the slag has no effect on chromium recovery, and 3—slag viscosity is not high even when 20 pct Cr,O, is present. Lapitskii\ oncluded that chromium recovery improved as the basicity of the slag decreased and increased with increasing manganese in the metal. Regarding the effectiveness of CrZ08 as a base or acid in basic slags, both Kristofferseno and Trojer" reported that Cr,08 was an acidic component requiring neutralization as 2CaO-Cr,O,. Experimental Procedure The experimental apparatus and procedure used for the present research were similar in most details to those used by Winkler and Chipman" and were described in detail by them. A magnesia crucible was used, holding 60 to 80 lb of Armco iron which was decarburized with hydrogen to about 0.010 pct C. Since all the metal samples solidified without gas evolution, this carbon level was assumed not to be significant. Synthetic slags made by mixing pure oxides were used throughout the study. Temperatures were measured by means of calibrated W-Mo thermocouples and were checked by Pt-Pt-Rh thermocouples. The range of temperatures covered in this study was from 1526" to 1734°C. The chromium content of the iron was in the range 0.032 to 0.82 pct, although the bulk of the tests showed 0.04 to 0.2 pct. The slags were of the CaO(MgO)-SiO,-FeO-Cr,O, type in which the Cr,O, content was from about 2 to 20 pct, although most of the slags showed from about 2 to 10 pct. The FeO range was from about 10 to 65 pct. CaO and SiO, were in the range of about 5 to 45 pct each, yielding a rather wide range of basicity values. The first 12 heats were made without a sulphur addition, and with only 30 min allowed for slag-metal equilibrium to be reached. In previous research it had been shown that less than 30 min was adequate to achieve equilibrium in slags free of Cr2O8.11,14.15 A study of the present data indicated that some of the tests may not have reached equilibrium in this time; accordingly four additional heats were made in which at least 1 hr was permitted for equilibrium to be reached. For reaching

Jan 1, 1955

By Larry J. Tucker

INTRODUCTION The orebody at Pea Ridge strikes NE-SW and dips at about 800 to the SE. The ore and surrounding rocks are Pre-Cambrian in age. These rocks are usually very competent. Locally strong jointing has caused problems and toward the hangingwall dikes have caused particular problems during or after the open stoping phase of production. About 396 m of sediments lie over the ore. The shape and mineral content of the orebody has been fairly consistent so far with production areas lying from the 1375 to the 2475 levels. The deeper limits of the ore- body haven&apos;t been found yet. The ore is high grade magnetite with a strike length of over 600 m and a maximum width of over 180 m on some levels at the center of the orebody. Production at Pea Ridge for the first three years of operation came from two types of open stopes. The original stopes were recovered with horizontal production rings being drilled and blasted from vertical raises. Later a more typical sublevel stoping method using vertical production rings from one or more drilling sub- levels was used. There were a number of reasons for the selection of open stoping as the initial production method at Pea Ridge. First, it was judged that the ore was not of a block cave quality. After fifteen years of production, this assumption can be verified. There was some concern during the planning days for the potential for high flow rates of water into the mine from aquifers in the sediments lying over the orebody. Dewatering wells from surface and underground were put in as a precaution and nothing came of this potential problem. Open stoping and its resulting pillar structure put off this problem by supporting the sediments a few years longer. For a moderate investment in level development some production from open stoping was quickly realized. The first open stopes were brought in on what was then the bottom mine production level (2275), near the shaft pillar and situated on the footwall. This production practice of stoping on the heels of development from shaft pillar westward and from footwall to hangingwall continued through the open stope phases of production at Pea Ridge for many years. From the standpoint of mine efficiency and pillar stability, this would not seem to be a recommended mining practice. 74 570 w electric slushers, using 1.37 m dippers, pulled the open stope ore out into 18 ton bottom dump cars. Ordinarily five of these cars made up a train, which was pulled to the dump area by a trolley powered electric locomotive. Open stoping had the disadvantage that 100% of the recoverable portions of the orebody had to be developed in order to recover 33% of the ore. 67% of the ore was left behind in a large pillar system. For many years we had no planned method for recovery of these pillars. Mining methods are of course, limited by the existing technology. Advancing technology, coupled with the limited production capabilities of open stoping, low efficiencies and high relative cost early in the history of the operation recommended that other mining methods be looked at. In Sweden, considerable practical experience, coupled with a large amount of theoretical work had become available on sublevel caving. To Pea Ridge it offered the apparent benefits of: 1) The flexibility of diesel powered trackless haulage. 2) The efficiency of two machines to one operator on longhole drilling. 3) A multilevel production picture with a large number of drawpoints for ore recovery. 4) 100% recovery of the mineable portion of the orebody in one production pass, with no pillar recovery problems left behind. This paper outlines the experiments and experiences which Pea Ridge has gone through with sublevel caving from 1967 to this date.

Jan 1, 1981

By Herbert H. Kellogg

Graphs representing the standard free-energy of formation as a function of temperature for 21 fluorides are presented, along with estimated values for the standard free-energy of formation of 20 atedadditional fluorides. A few of the many possible uses of these data in metallurgical calculations are discussed, including the fluorination of oxides, sulphides, metallurgicaland chlorides, and the reduction of metal fluorides. RECENT papers which have presented free-energy data for oxides, sulphides, chlorides, carbonates, sulphates, and silicates in the form of free energy vs. temperature plots,1-5 have found important uses in teaching and metallurgical development work. This method of presentation of thermo-dynamic data serves to make available in readily usable form thermodynamic constants which are scattered throughout the literature, and to show by graphical means the stability relations which exist between the compounds of a given type. It is certainly desirable to have these free-energy-temperature diagrams for as many types of compounds as are of present or potential use in metallurgical processes. Thus, even though there are but few uses of metallic fluorides in extractive metallurgy today, the potential uses of fluorine processes are of great importance and serve as the principal justification of this paper. Recent developments in the production of fluoro-carbons have resulted in vastly improved methods for the production and handling of fluorine and corrosive fluorides, with consequent reduction in costs.".&apos; The extractive metallurgist should no longer overlook possible fluorine processes when development of a new process for a relatively high unit-price metal is being considered. In a previous paperv he author outlined in some detail the importance and use of free-energy data in metallurgical calculations and also discussed the properties of a standard free-energy vs. temperature diagram. The same method of presentation is adopted in this paper, and the reader is referred to the earlier work for explanations of the use of free-energy data. Thermodynamic Data This paper presents standard free-energy vs. temperature diagrams, Figs. 1 and 2, for those fluorides for which the major thermodynamic constants are known. In the calculations of the standard free-energy of formation (AGO), values of the enthalpy of formation at 298°K (?Ho,) were taken from "Selected Values of Thermodynamic Constants"8 most of the values of standard entropy at 298°K (S°298) were taken from "Selected Values"," but in a few cases the values given by Kelley9 ere preferred; data for the Phase changes came from "selected Values" and several of Kellley&apos;s publics- tions;0-12 and most of the specific-heat data were taken from Kelley.l0 The appendix gives a detailed list of the sources of the data. As explained in an earlier paper,6 he accuracy of some of the standard free-energy relationships is not high. An error of +1 kcal at 1000°C is expected in most of the curves of Figs. 1 and 2. The error may be as high as +3 kcal in some of the curves. Rather than attempt to estimate the reliability of each curve, the source of the data used is reported in the appendix, and the reader may compare these data with newer values as they become available. Figs. 1 and 2 fail to show values for the fluorides of many important metals. In most cases this is because the entropy of the metallic fluoride is unknown. For preliminary calculations it is often useful to have available the best estimate of an unknown datum, rather than no information at all. With this in mind, Table I lists estimated standard free-energy values for a number of important metallic fluorides not included in Figs. 1 and 2. The values reported in Table I were, calculated by Brewer et al.13 and are based on estimated entropy values. The estimated uncertainty of the values for each fluoride were calculated from the uncertainty values given by Brewer1&apos; for ?H°, and the entropy function.

Jan 1, 1952

By W. R. Strickler, P. Hazebroek, M. Prats

The pressure and production behavior of a homogeneous cylindrical reservoir producing a single fluid through a centrally located vertical fracture of limited lateral extent was determined by using mathematical methods to solve the appropriate differential equation. It is assumed that there is no pressure drop within the fracture — that is, that the fracture capacity is infinite. It was found that the production-rate decline of such a reservoir is constant (except for very early times) when the flowing bottom-hole pressure remains constant. The production-rate decline increases as the fracture length increases. Thus, the lateral extent of fractures can be determined from the production-rate declines before and after fracturing or from the decline rate after fracturing when the properties of the formation and fluids are known. The production behavior over most of the productive life of such a fractured reservoir can be represented by an equivalent radial-flow reservoir of equal volume. The effective well radius of this equivalent reservoir is equal to one-fourth the total fracture length (within 7 per cent); the outer radius of this equivalent reservoir is very nearly equal (within 3.5 per cent) to that of the drainage radius of the fractured well. The effective well radius of a reservoir producing at semisteady state is also very nearly equal to one-fourth the total fracture length. It thus appears that the behavior of vertically fractured reservoirs can be interpreted in terms of simple radial-flow reservoirs of large wellbore. INTRODUCTION An earlier report1 has considered the effect of a vertical fracture on a reservoir producing an incompressible fluid. That investigation of the fractured reservoir producing an incompressible fluid was started because of its simplicity. Thus, pertinent behavior of fractured reservoirs was obtained at an early date, while experience was being gained of value in the solution of more complicated fracture problems. One of these more complicated problems, and the one discussed in this report, considers the effect of a compressible fluid (instead of incompressible fluids) on the production behavior of a fractured reservoir. In the incompressible-fluid work mentioned, it was shown that the production rate after fracturing could be described exactly by an effective well radius equal to one-fourth the fracture length whenever the pressure drop in the fracture was negligible. Because of the simplification in interpretation, it is a matter of much interest to determine whether the production behavior of reservoirs producing a compressible liquid could be described in terms of an effective well radius which remains essentially constant over the producing life of the field. The details of the mathematical investigation are given in the Appendixes. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable circular cylindrical outer boundary of radius re. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir just described. When gravity effects are neglected, the flow behavior in the reservoir is independent of the vertical position in the oil sand. Thus, the flow behavior in the fractured reservoir is described by the two-dimensional flow behavior in a horizontal cross-section of the reservoir, such as the one shown in Fig. 2. Production is due to the expan-

By J. O. Brittain, E. Lautenschlager

Yield point measurements were made on polycrys-talline specimens of a iron deformed various amounts at 770, 1950, or 273°K, aged, and redeformed at 77: 195°, or 273°K. When the prestrain temperature is lower than that subsequent to aging, the yield point return is suppressed relative to specimens deformed at the same temperature both before and after aging. The degree of suppression is a function of both the magnitude of prestrain at the lower temperature and the difference between the deformation temperatures before and after aging. It is proposed that the suppression is caused by the formation of dislocation barriers during the initial low-temperature deformation. The aging kinetics of polycrystalline a-iron wires deformed at 77o or 303oK were studied at 44 " and 64 "C using internal friction measurements. No change was noted as a result of the difference in prestrain temperature. IN an earlier investigation1 it was observed that the return of the yield point was suppressed when a poly-crystalline specimen of a iron was plastically deformed at 77oK, aged at room temperature, and subsequently tested at room temperature. In order to investigate this observation, a research program was undertaken to measure the effect of prestrain temperature on the strain aging of a iron.&apos; According to Thomas and Leak,3 return of the yield point and internal friction are similar measures of strain aging since both are dependent on solute atoms leaving the solid solution. The decrease in internal friction as a function of aging time is indicative of the removal of solute atoms from the solution, while the return of the yield point as a function of aging time gives the rate of arrival of solute atoms at the dislocations. According to Cottrell and Bilby,4 the solute atoms create an "atmosphere" which locks the dislocations and causes a return of the yield point upon restraining. In this experiment, both methods of measuring strain aging were employed in order to have two independent measurements of the strain aging phenomenon. In a previous study,5 the strain aging kinetics of a similar lot of a iron were measured for specimens which were prestrained and tested at the same temperature over the range of 77" to 273°K. Although some differences were found in the correlation of the two methods employed for measuring strain aging, the kinetics of strain aging were unaffected by the change of prestrain and test temperature. In another study,6 dislocation line tension and the density of the solute atmosphere were found to contribute to the return of the yield point when ingot iron specimens were prestrained at 303°K and tested at a lower temperature, namely 77°K. This paper is concerned with changes in strain aging kinetics produced by pre-straining at 77" to 303°K and testing at either the prestrain temperature or at higher temperatures up to 273°K. EXPERIMENTAL PROCEDURE The polycrystalline a iron specimens used in both the tensile and internal friction tests were 0.033-in. diam ingot iron wires, wet hydrogen treated and re-carburized. A more detailed procedure for processing a 3/16 in. ingot iron rod (nominal wt. pet composition: Fe - 0.013; C - 0.0125; Mn - 0.023; Si -0.005; P - 0.0023; S - 0.11; Cu - 0.004 N) to 0.033 in. diam specimens containing approximately 0.020 wt pet C and no detectable nitrogen with a grain diameter of 0.033 to 0.040 mm is given elsewhere.5 Immediately prior to testing, specimens were solution treated for 15 min at 700o ± 2°C in a static vacuum of less than 50 ?. of Hg and rapidly quenched into an ice-water bath while still enclosed in a 3 mm quartz vial. The internal friction specimens had 8-in. gage lengths and the tensile specimens had 2-in. gage lengths. The wires used as tensile specimens were first run as internal

Jan 1, 1962

By Robert L. Davidoff

INTRODUCTION The impact of taxation differs substantially from state to state in a complex fashion that depends on both the physical characteristics of a mineral deposit and on the price of the mineral commodity relative to its costs of production. A comparative analysis of the tax structures of eight states (Arizona, Colorado, Idaho, Montana, Nevada, New Mexico, Utah and Wisconsin) showed wide variations in rates of return for any given type of mineral property, with no state having either the most burdensome or least burdensome tax structure under all circumstances. Three hypothetical mineral operations were analyzed: a producing open-pit copper property, a non-producing underground platinum operation, and a non-producing underground gold operation. None of them corresponds exactly to an existing property. Each of these property types is further defined to have ore feed grades at three different levels, leading to three potential profitability levels, referred to in this paper as "economic", "marginal" and "subeconomic". Thus the differential impact of state tax structures is measured for mineral properties of different types, as well as for different profitability levels. Montana is used as the base case. This study does not address the topic of corporate structures or tax consolidation. There are no costs assumed external to the operation of the deposit (e.g. exploration to locate additional deposits). Two types of analyses were performed for this study. The first calculates the total cumulative tax payments in each state using all applicable taxes (including U.S. federal income taxes and examines the resultant differences in discounted cash-flows rate of returns DCFROR&apos;s amoung the eight states. The second is a sensitivity analysis that examines each type of state tax separately (i.e. state income, property, and severance taxes) in order to isolate and examine the differences in tax payments that are due to the difference in rates and methods of computing specific types of taxes in each state. The results of this study serve to illustrate the complex nature of interactions among various taxes. For example, property tax is a deduction in calculating severance tax in some state. Changes in property-tax and severance-tax payments both enter into the calculation of state and federal income-tax liability. This, in turn, could change the timing and usage of tax-loss carry forward amounts and investment tax credits. Additionally, the physical characteristics of a property, the method and costs at which the mineral will be extracted, and the profitability level at which each property operates will affect tax treatment. Each mineral operation was evaluated at three different predetermined profitability levels, referred to using the terms economic, marginal and sub-economic. These three profitability levels are defined by the ore feed grades of the primary commodity that yield in constant terms, approximately an "economic" 18% DCFROR, "a marginal." 10% DCFROR, and a "sub-economic" 5% DCFROR, respectively, under the Montana tax structure. In the analyses, the mining and processing parameters for each of the three types of properties were assumed to be identical for each of the eight states. It was assumed that each operation produces at full operating capacity throughout its life. This implies the level of mineral commodity demand will support the inferred commodity price, such that each operation will be able to sell all its output. The analyses performed for this study were done using a comprehensive economic evaluation simulator that is used in the Bureau of Mines, Division of Minerals Availability MAS program to perform DCFROR analyses. All economic evaluations performed upon these data (see appendix 2) were in constant January 1981 dollars. By-product prices used for the analyses were: [Gold $425.00/troy ounce Palladium$200.00/troy ounce Silver $ 10.00/troy ounce] Typical cash-flow calculation layout is given in Appendix 3. The initial step for each evaluation is to define an "economic" profitability level scenario. An 18% DCFROR rate in Montana was considered the

Jan 1, 1985