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By D. Dever, E. S. Fisher

Measurements of the temperature dependence of the elastic moduli in single crystals of hep ruthenium, rhenium, cobalt, dysprosium, and erbium were carried out for various temperature ranges so as to investigate the correlation, suggested by prior work, between the shear anisotropy ratio, A = C44/C66, and the occurrence of the hcp — bee phase transformation. These measurements confirm the suggestion that A has a positive temperature dependence in that group of hcp metals that undergo thermally induced transfornzations to the bee structure and a negative or zero temperature dependence in the other hcp metals. It appears, from indirect evidence, that the hcp -fee transformation in cobalt is preceded by a highly negative temperature dependence of A. These results indicate that elastic anisotropy is an important factor in determining the temperatures at which martensitic phase transformations occur. Two possible roles for elastic anisotropy are proposed: 1) the shear-modulus ratio within the habit planes must be nearly similar for the two phases and 2) a large anisotropy decreases the stress necessary for the movement of the transfornzation dislocations. FUCHS' calculations of the elastic moduli in the alkali metals have shown that the high shear-anisotropy ratios, c/c', in certain bee metals and alloys are the result of large negative contributions to c' = (c11 - c12)/2 arising from the nearest-neighbor repulsive forces.' On this basis, and following Zener,2 the association between high c/c' ratios and the martensitic phase transformations that occur upon cooling certain bee metals is explained as a unique characteristic of the bee structure. Recent measurements of the elastic moduli in hcp titanium and zirconium show, however, that a high elastic anisotropy also exists in these hcp structures at the temperatures at which they transform to bee upon heating3. If there exists a direct and consistent correlation between the elastic anisotropy in close-packed structures and the occurrence of transformations to the bee phases then there is evidently a need to re-examine the conclusions of Zener theory. Elastic anisotropy may also be the result of the effects of temperature on the stability of the low-temperature close-packed structures or it may play an important role in the mech- anism of the martensitic transformations. The present measurements were aimed at establishing the phenomenological correlation between elastic shear anisotropy in hcp structures and the thermally induced hcp —bee transformations that occur in the majority of the twenty-three hcp metals, as shown in Table I. Prior to the present work the temperature dependence of the anisotropy ratio, A = c44/c66, was known at various temperatures for nine of the metals listed. The data showed a negative temperature dependence of A for cadmium, zinc, magnesium, and cobalt, which do not transform to bee, and a positive temperature dependence of A for thallium, zirconium, titanium, hafnium, and yttrium. The correlation was, however, ambiguous in that these two groups of metals are also separated with respect to the c/a ratios as noted in Table I. There remained the possibility that the temperature dependence of A is a function of c/a and not consistently associated with the transformation. The measurements of the elastic moduli in rhenium and ruthenium, in which hcp —bee transformations do not occur, were needed to help decide this question. The studies of dysprosium and erbium were undertaken to determine whether the correlation holds for the heavy rare earth metals.

Jan 1, 1968

By J. J. Arps

n approach to the study of the electrical properlies of drilling muds, their cakes and their filtrates was made by treating the drilling fluid as a porous medium. Lluring this study it was found that the weight pararneter was omitted from previous investigations on electrical properties. Patnode in 1949 made a similar approach to ,his investigation. His work showed that there was a variation of resistivity relationships with per cent Puid present in a given suspension. This present study ex-tends Patnode's investigation to one in terms of the solids fraction of the drilling fluids. Previous investigations were made on low weight muds where the effect of the rolids fraction was obscured. The following equationr were fitted to data taken from 94 field muds and 47 laboratory muds (see Tables I and 2). The parameter, C, is a complex function of the solidr content, or mud weight, of a drilling fluid. It was also found that for all drilling muds examined. A nomograph is presented combining Eqs. I and 2. INTRODUCTION It is generally recognized that the materials present in drilling muds affect the relationship between mud filtrate and mud resistivities. However, most electric log interpretations proceed with the assumption that the mud resistivity and temperature are the only important parameters needed to obtain a filtrate resistivity or a mud cake resistivity. Lamont1 suggests that only average relationships exist between mud cake, mud filtrate and mud resistivities. He indicates that there is limited accuracy when these intercorrelated factors are used since no other measure-able variable is apparent. A previous paper by Patnode indicates that drilling fluids may be considered to be a system of fluids in solid particles which may be correlated electrically in a manner similar to rock solids. 1 he equation for the resistivity factor. F = (per cent fluid) is satisfied for a given clay type in water, but the value of m varies as different materials are used in the water. The resistivity factor is not constant for a given amount of clay. As is suspected it varies as the solids fraction conducts electrical current. Since both weighting material and clay solids are present in commonly used drilling fluids, it is expected that both materials contribute to the variation of the m factor in Eq. 3. An extension of Patnode's work is presented in this paper to show some of the interrelations which exist between the resistivities of mud cake, mud filtrate and mud. Use of these data enable a more accurate calculation of mud filtrate and mud cake resistivities if only the mud resistivity and weight are measured. EXPERIMENTAL The measurements of mud weight, fluid and solids resistivity, alkalinity, and chloride content of mud samples were made in this research. Mud samples representing drilling fluids from 94 Louisiana and Texas wells (Table 1) and 47 laboratory-constructed systems (Table 2) were used in the experimentation. The measurements of the mud properties were made both in the field and in the laboratory. The tests on the properties of weight, alkalinity and chloride ion were standard tests as described by API specifications. The resistivity measuring devices were constructed in the laboratory for this study. For details on the resistivity equipment see Fig. 1. The fluid cell

By J. E. 214-000-000-010 Warren, M. R. J. Wyllie, T. Meidav, L. Scharon, R. Uhley, A. J. deWitte

By considering the stoichiometry of the underground combustion process, an equrztion was derived relating the point velocity of the combustion front as a function of the air flux, fuel content, efficiency' of oxygen uitilization, hydrogen:carbon ratio, and ratio of carbon dioxide In carbon monoxide produced. In addition, an equation for cnlcrllating the amount of injected air necessary 10 produce the oil from I Cu. ft of reservoir space was derived. This equation has a direct bearing on evaluating compression costs for the process. Values calculated from these equations are in good agreement with experimentnlly obscrvcd values obtained from laborator) tube runs reported in the literature. The equations are also u\eful for atlcrlyzinf: experinlental data for inconsistencie.r.. I NTRODUCTION The injection of energy in the form of heat into an oil-bearing formation as a means of increasing the recovery of oil has been the subject of much discussion and experimentation as far back as 1920. The ideas have ranged from the injection of steam to the direct use of electricity as a means of getting thermal energy into a formation. However, most laboratory and field studies have been confined to the process whereby a portion of the crude in the reservoir is burned to generate the necessary heat to increase the mobility of the oil by reducing its viscosity. A recent paper by W. L. Martin, et al.', described the results of a number of laboratory experiments in which the combustion process was studied in a sandpack. Studies such as this indicate that with the temperatures involved, the oil is partially coked in this process and it is this coke which provides the fuel for combustion. The combustion of this residual coke can be analyzed theoretically by applying simple stoich-iometric principles to the combustion process. It is the purpose of this paper to compare the results reported in these experiments with those obtained from theoretical considerations. The variables studied by Martin, et al, among others, include combustion front velocity, air flux, oxygen utilization, fuel concentration, ratio of carbon dioxide and carbon monoxide in combustion gases, and the hydrogen:carbon ratio of the residual fuel. All these variables come into consideration when the stoichiometry of the combustion process is studied. The experimental conditions and results are tabulated in Tables 3 and 4 of Ref. 1. For purposes of comparison with calculated results, it was necessary to change the units of a number of the variables. UNDERGROUND COMBUSTION STOICHIOMETRY The combustion or oxidation of the carbonaceous residue or "coke" on the sand can be described in terms of the equation: where n is atomic ratio of hydrogen to carbon, m is ratio of moles of CO2 to CO produced, and CH. is taken as the unit molecular weight, realizing that actually the coke has a large range of high molecular weights. Assuming that all the fuel laid down in the sand is burned, the ratio of moles of oxygen consumed to moles of coke can be written as follows. Moles 0MolesMolescoke In terms of moles O2 per pound of coke, where 12 + n is the molecular weight in pounds per mole. If the 0, consumed is measured in standard cubic feet (60°F and 1 atm) and the coke in pounds per cubic foot of formation, 2, then:

By W. A. Rachinger, C. Graeme-Barber, R. L. Bell, R. C. Gifkins, T. G. Langdon

R. L. Bell. C. Graeme-Barber, and T. G. Langdon (Imperial College. London)— The internal-marker technique developed by Ishida, Mullendore, and Grant has enabled them to make some interesting observations on the role of grain boundary sliding in creep. Certain of their conclusions are supported by our own similar experiments on Magnox AL80 (Mg-0.8 pct Al) specimens containing several markers, full details of which will be published shortly. In particular, we would agree that: 1) Using the internal-marker method, there is little difference between Egb, the contribution made by grain boundary sliding to the total strain, measured at the surface and in the interior of a specimen. 2) The measurement of the change in grain shape during creep leads to an underestimation of the grain strain, and hence an overestimate of Egb.. However, the discrepancies between the values obtained by this method and those obtained using markers are not as great as Tables IV and V of Ishida, Mullendore, and Grant would suggest; see below. The authors' Eq. [I] which is used to compute Egb from the transverse displacement ITt of longitudinal marker lines is not given in the reference quoted,'' where in fact only relations for Egb in terms of the longitudinal displacements of markers were developed. As first pointed out by Gifkins and Gittins,12 a problem arises in the use of longitudinal markers. and we will show that Eq. [1] underestimates Egb in the interior by a factor of 2. In Fig. 12, two grains X and Y have become displaced by the vector AC which lies in the plane of the grain boundary ABCD separating them. A longitudinal marker has been split by this displacement into the two parts LA and CAW. If these were surface grains the transverse displacement, Ut. could be obtained by viewing normal to the "top" surface. If interior, a section through CD parallel to the top surface would show the same result, provided the longitudinal internal markers delineated planes normal to the top surface. (This is an essential feature of the markers not pointed out in the paper.) The important point is that the quantity Ut tan B (=BE=DF) only gives the elongation due to the one component AB of the sliding. The elongation V/tan 8 (=GD) due to the component AD must be added to produce the total elongation resulting from the boundary displacement AC. If the grain boundaries in a poly crystalline specimen are randomly oriented with respect to the stress axis it follows that In the interior of a specimen the two sums depend for any difference simply on the definitions "top'' and "side". On the surface it is possible that the two sums could differ somewhat. In either event it is clear that the authors' Eq. [I] underestimates Egb, and in the interior, and perhaps at the surface also, the appropriate formula is given by The suggested modification probably makes little difference to the comparison between surface and interior values of Egb where both were obtained from marker measurements. For the estimation of the correction becomes extremely important where the boundary contribution is large. In our own work on magnox, for example, we have obtained values of as large as 70 to 80 pct, under conditions of high temperature and low strain rate. The use of planar markers transverse to the stress axis would simplify the comparison between surface and interior behavior, because measurement of the longitudinal offsets Us of these markers could be summed to give the total elongation di-

Jan 1, 1965

By E. Miller, J. M. Eldridge, K. L. Komarek

The thermodynamic properties of- liquid Mg-Pb allojs have been determined by an isopiestic method from 18 to 42 at. pct Pb and by a thevmodynumic analysis of the phase diagram frofiz 0 to 100 at. pct Pb. In the overlapping composition range the magneszupn activity values derived by the two methods are in excellent agreement, thus mutually supporting the correctness of the Mg-Pb phase diagram previously determined by the authors and of the acticitzes deriz~ed isopiestically. SEVERAL studies have been made of the thermody-namic properties of liquid Mg-Pb alloys. Wagner and Engelhardt,1 Lantratov,2 Knappwost,3 Sryvalin et al.* and Wilson5 used the electromotive-force method, Scheil and Wolf8 and Schmahl and Sieben" applied the transpiration technique, and the present authors8 utilized the phase diagram to determine the activity of magnesium in the Mg-Pb system. The results of these studies are not in very good agreement and could not be incorporated into a general systematic analysis of the thermodynamic properties of the homologous series of the Mg-Group IV B systems Mg-Pb,8 Mg-Sn,° Mg-Ge,10and Mg-Si.11 The thermodynamic properties of the Mg-Pb system were therefore re investigated by an isopiestic technique which has been developed for similar studies in the Mg-SnB and Mg-Ge10 systems- Lead specimens, contained in iron or graphite crucibles, were heated in a temperature gradient in an evacuated and sealed titanium reaction tube and equilibrated with magnesium vapor of known vapor pressure to form alloys of compositions which depended on their temperatures, the temperature of the magnesium vapor source, and the thermodynamic properties of the system. EXPERIMENTAL PROCEDURE Magnesium (Dominion Magnesium Ltd., Toronto, Canada) of 99.99+ pct purity and lead (American Smelting and Refining Co.) of 99.999 pct purity were used. In the early experiments, Runs 2 and 3, the alloys were contained in uncovered high-purity iron crucibles. Alloys formed in the uncovered iron crucibles had to be chemically analyzed owing to the slight volatility of lead under the imposed experimental equilibration conditions. The compositions of these alloys were determined by a gravimetric analysis of lead as lead chromate. To avoid this problem, the remaining runs were made in covered graphite crucibles machined from high-density (1.92 g per cu cm) graphite rods (Basic Carbon Corp., Sanborn, N.Y.) which had a maximum ash content of less than 0.04 pct. The non- i reactivity of graphite with lead and magnesium has been previously established,' and the experimental procedure has been described in full detail.' In the runs using covered graphite crucibles it was found that the weight increases of the crucibles and their contents after equilibration equaled the magnesium contents of the alloys within the accuracy of the chemical analysis (i0.3 at. pct Pb). Clearly, the small lid openings of the graphite crucibles prevented significant lead losses during a run, and the weight increase was therefore taken as the magnesium content of the alloys. EXPERIMENTAL RESULTS At thermodynamic equilibrium the magnesium partial pressure of the specimens equaled that of the reservoir. Since the magnesium reservoir was always maintained at the temperature minimum of the system, the activity of magnesium of any specimen was given by the ratio of the magnesium reservoir pressure to the vapor pressure of pure magnesium at the specimen temperature. The standard state was chosen as liquid magnesium and the vapor pressure of liquid magnesium

Jan 1, 1968

By D. C. Ganow, N. J. Grant, I. R. Silver, A. R. Chaudhuri

The structural changes that result when a metal is "cold worked" lead to higher values of yield and tensile strength on subsequent deformation at room temperature. Further it has been shown that the beneficial effects of cold work are, to some extent, maintained even at elevated temperatures. The strength improvements from prior cold work decrease as the temperature is raised and are a function of grain size, amount of cold work, and strain rate (or time of test). If recrystallization occurs during test, the cold-worked material may even show weaker stress-rupture properties than the annealed material. A question that arises is whether there is a significant effect on the subsequent creep behavior if the prior deformation is performed under creep conditions at high temperatures not too different than the test temperature, but at significantly different strain rates and for various amounts of strain. An answer to this question was sought in the work described in the present paper. PROCEDURE Two materials were used in this work, high-purity aluminum and a solid-solution A1 2 pct Mg alloy. The compositions are shown in Table I. The grain size in the two materials was 0.2 to 0.3 mm. The deformation for both the prestraining and for the creep tests was at constant stress. The procedure adopted was to prestrain a specimen to the desired elongation, remove the load, and cool to room temperature rapidly by spraying. the test bar with cold water. The specimen was then placed in a creep machine, held at the test temperature for less than 5 min, and loaded. Less than 15 min was required to bring the specimen to temperature. The creep stress was based on the diameter resulting from the prior strain, and values of elongation at fracture listed in the tables do not include the respective elongations resulting from the prestrain. The choice of the stresses for the prestrain and for the creep tests was made so that the tests could be completed in relatively short times to maximize any effect of prestrain. The specimens had a gage length of 1 in., the pure aluminum specimens having a diameter of 0.150 in. and the alloy specimens a diameter of 0.125 in. For pure aluminum, prestrain was at 400' and 600°F with testing at 500°F; for the alloy, prestraining was at 700°F and testing at 600°F. RESULTS The prestrain conditions for the aluminum and the alloy specimens are shown in Tables I1 and IV. In addition to showing the time required to achieve the desired prestrain, the expected rupture Lives are given which would have resulted had the creep prestrain been continued to fracture. The prestrained and the annealed specimens were then tested in creep to fracture; the temperature and stress for the pure aliminum specimens being 500o F and 1800 psi and for the alloy, 600' F and 3400 psi. The creep curves for the prestrained and the annealed specimens of pure aluminum showed all three stages of creep; hence in addition to the effect of prestraining on the rupture life, it was also possible to determine the effect of prestraining on the minimum creep rate, and on the time and elongation at the end of each of the three creep stages. The results are shown in Fig. 1 and Table 111.

Jan 1, 1960

By A. D. Marlin, A. J. Gentile, E. F. Jordan

Metallurgical changes in SAE 52100 ball-bearing components resulting from overload testing are described. Changes in microstructure, hardness, and resiclctal stresses crre discussed zuitlz re.ference to material cleanliness obtained by various steel-melting practices and are compared with work by otlzer investigators. Evidence is presented to show that the initialion and development of microstruc-tural alterations are characterized by two separate reactions: the appeavance of a "dark etchingJ' constituent, and "gray lines" or a light etclzing constituent. The dependency of these tzvo reactions on material cleunliness, running tirne, and contact stresses is discussed and a failure mode related to material cleanliness and microstructural transformation is proposed. THE study of ball- and roller-bearing contact fatigue has been paced by a strong emphasis on bears ing application performance. Particular attention has been paid to conditions that effect the spalling-type failure that is characteristic of rolling contact fatigue in through-hardened components. Some of the conditions investigated are lubrication and atmosphere,1-3 material characteristics and finish,475 and speed and design fa~tors."~ A typical spalling-type failure is shown in Fig. 1. The arrow shows the motion of the ball relative to the inner-ring race surface. The leading edge of the spall is usually sharper than the trailing edge. The race surface near the trailing edge also shows small dents caused by debris from the spall. In this type of testing very little metallurgical investigation is done on failed bearings. Emphasis is placed on test conditions and statistical analyses of endurance data. More basic work has been done relating micro-structural changes to fatigue performance. Dyer" and Wood, Cousland, and sargant9 have used mostly simple materials, such as single crystals and single-phase polycrystalline specimens, under simple alternating strain to identify a systematic process of fatigue damage. drutowski" was concerned primarily with the relationship between steel structure, contact stress, and energy losses in rolling contact. dones11 and Bush, Grube, and Robinson12 utilized changes in microstructure and residual stress in overload-tested rolling contact elements as a means of investigating the fatigue process. Work is being done on an ASME-sponsored contract,13 using both simple and complex materials, but there is still a long way to go before such theories as pore and void growth in simple structures can be applied to the relatively complex bearing steel microstructure. The purpose of this paper is to report on an investigation into the effect of steel cleanliness on the structural alteration and residual stress changes found in overload-tested ball bearings. Using these results and those of previous investigators, we will propose probable failure mechanisms in both overload- and normal load-tested ball bearings.14,15 PROCEDURE Ball bearings? 3208 size, were fabricated from SAE 52100 steel obtained by five different melting practices. The melting practices, chemistry, and inclusion ratings for the five lots of steel are summarized in Tables I and 11. The nonmetallic inclusion ratings were determined by the Jernkontoret method described in ASTM E45-51 Method A. This technique consists of microscopically examining a series of polished samples taken from specified locations in the ingots, billets, or bars. Each sample is surveyed at XlOO magnification and the inclusion types and sizes are compared to standard fields. Because of the nature of these ratings all values in Table I1 are rounded to the nearest half. The elec-

Jan 1, 1965

By J. B. Clark, A. S. Yue

The zone-melting technique can be adapted for the de-termination of the eutectic composition in complex metal systerrzs. The application of this method is demonstrated in a simple eutectic system, Mg-AE, in which the eutectic composition is known and in a complex ternary system, Mg-Al-Zn, in which the literature is uncertain as to the composition of the ternary eutectic. The advantages and limitations of this unique approach for the determirution of the eutectic composition are discussed. ThE eutectic composition in phase diagrams is usually determined by thermal analysis of a series of arbitarily selected alloy compositions. The temperatures of the liquidus and eutectic arrests for each alloy are plotted and the eutectic composition is estimated by extrapolation to the entectic temperature of the curve formed by the liquidus arrest temperatures for the series of alloys. Although this approach readily yields the eutectic temperatures, several dekrminations are needed to estimate the eutectic composition, even in a simple system. In a complex ternary system, a great many determinations are often necessary to estimate, even approximately, the ternary eutectic composition. Thus, the conventional method is inherently tedious and time consuming. The application of zone melting provides a relatively efficient method of determining the eutectic composition.' As an illustration, consider the zone melting of an alloy composition C, in the simple eutectic system A-B, shown in Fig. 1, under the ideal conditions of infinitely rapid diffusion in the liquid, no diffusion in the solid, and ease of nucleation of both phases. As the zone moves along the bar, the composition of the zone is enriched by solute rejected during the freezing of the a phase and the zone composition approaches the eutectic composition CE.Once the zone composition attains the lowest melting composition, i.e., the eutectic composition, it remains at this composition as the zone moves along the bar and finally freezes as such at the end of the bar. Chemical analysis of the end of such a zone-melted bar then should yield the eutectic composition CE of the system A-B. A corresponding analysis can be made for a ternary eutectic system. Under the ideal conditions noted above, only one pass of the molten zone is required to yield the eutectic composition. Experimentally, however, a solute-rich layer forms at the solid-liquid interface2 and the composition of the zone does not attain the eutectic composition as rapidly or as uniformly as in the ideal case outlined above. But with agitation of the melt, the ideal conditions can be approximated experimentally. Also, as shown below, zone melting permits a cumulative build-up of the solute at the end of the bar to the eutectic composition. The purpose of this paper is to demonstrate this unique method for determining the eutectic composition. The method is here applied to two systems: first, to the binary Mg-A1 system, in which the composition is well established, and second, to the complex Mg-Al-Zn system in which there is doubt concerning the composition of the ternary eutectic. EXPERIMENTAL PROCEDURE The zone-melting apparatus used in this study is described in detail elsewhere.3 Briefly, the binary alloy rods (5/8 in. in diam and 9 in. long) and the ternary alloy rods (5/8 in. in diam and 6 in. long), with the compositions given in Table I, were zone

Jan 1, 1962

By Roscoe E. Bell

BETWEEN 1945 and 1948 the author made studies of the western phosphate industry and its potentialities. These included an appraisal of the opportunities for western development of the industry, studies of production costs, of market potentials, of transportation economics, and of industry location. This paper will be directed toward pointing up the factors which have an important bearing on the establishment of fertilizer plants in the western area. Industry Location Factors: There are, of course, an infinite number of possible organizational setups which might require consideration. However, the phosphate industry is simple enough so that studies of the most probable alternatives can be made conveniently. The salient factors which require special consideration in such a study are: (I) the location of the raw materials, (2) the location, size, and character of the present and potential markets, (3) the location of energy sources and materials required for fertilizer processing, (4) the location and capacity of present manufacturing facilities, (5) the cost of assembling the materials and energy needed in manufacturing, and (6) the cost of distributing the manufactured product. Raw Material Supplies: Rock phosphate is the raw material for the manufacturing of phosphate fertilizer. In the United States the important known deposits of this material are located in three general areas (fig. 1). The western deposits, comprising about 60 pct of the nation's supply, are in the four-state area—Idaho, Wyoming, Utah, and Montana. The Florida deposits comprise roughly 38 pct of the national supply. The Tennessee deposits, comprising about 2 pct of the national supply, have been the most important source until recent years. The western deposits, which are virtually undeveloped, have not been used to any extent to meet the nation's need for phosphate rock and phosphate fertilizer. Fertilizer Markets: The large national markets for fertilizer are in the midwestern and eastern United States (fig. 2). The principal far-western markets are along the Pacific Coast, especially in California. Until recent years the western markets have been extremely limited, whereas the markets in the eastern United States have long been established and manufacturing facilities have been provided to meet these needs (fig. 3). In recent years the western markets have expanded very rapidly, continuing to grow throughout the war years and postwar period at a similar rate. The question always arises as to whether this is a temporary war-swollen market which will shrink back to its original size as soon as the present agricultural price levels drop. In order to answer this question consideration must be given to the character of the market (fig. 4). I have considered seventeen western and midwestern states in the western market area where transportation costs from the western deposits are equal to or lower than those from Florida. They include all states west of a line drawn through Chicago, Kansas City and the western boundary of New Mexico. In the mewar period this was a small market totaling only 37,000 tons of P,O, annually. The 1946 total for this same area was approximately 200,000 tons. Considerably more fertilizer would have been used in 1946 had adequate supplies been available. Estimates of future markets are difficult to make, but we do have some indices that are useful. The

Jan 1, 1951

By Roscoe E. Bell

BETWEEN 1945 and 1948 the author made studies of the western phosphate industry and its potentialities. These included an appraisal of the opportunities for western development of the industry, studies of production costs, of market potentials, of transportation economics, and of industry location. This paper will be directed toward pointing up the factors which have an important bearing on the establishment of fertilizer plants in the western area. Industry Location Factors: There are, of course, an infinite number of possible organizational setups which might require consideration. However, the phosphate industry is simple enough so that studies of the most probable alternatives can be made conveniently. The salient factors which require special consideration in such a study are: (I) the location of the raw materials, (2) the location, size, and character of the present and potential markets, (3) the location of energy sources and materials required for fertilizer processing, (4) the location and capacity of present manufacturing facilities, (5) the cost of assembling the materials and energy needed in manufacturing, and (6) the cost of distributing the manufactured product. Raw Material Supplies: Rock phosphate is the raw material for the manufacturing of phosphate fertilizer. In the United States the important known deposits of this material are located in three general areas (fig. 1). The western deposits, comprising about 60 pct of the nation's supply, are in the four-state area—Idaho, Wyoming, Utah, and Montana. The Florida deposits comprise roughly 38 pct of the national supply. The Tennessee deposits, comprising about 2 pct of the national supply, have been the most important source until recent years. The western deposits, which are virtually undeveloped, have not been used to any extent to meet the nation's need for phosphate rock and phosphate fertilizer. Fertilizer Markets: The large national markets for fertilizer are in the midwestern and eastern United States (fig. 2). The principal far-western markets are along the Pacific Coast, especially in California. Until recent years the western markets have been extremely limited, whereas the markets in the eastern United States have long been established and manufacturing facilities have been provided to meet these needs (fig. 3). In recent years the western markets have expanded very rapidly, continuing to grow throughout the war years and postwar period at a similar rate. The question always arises as to whether this is a temporary war-swollen market which will shrink back to its original size as soon as the present agricultural price levels drop. In order to answer this question consideration must be given to the character of the market (fig. 4). I have considered seventeen western and midwestern states in the western market area where transportation costs from the western deposits are equal to or lower than those from Florida. They include all states west of a line drawn through Chicago, Kansas City and the western boundary of New Mexico. In the mewar period this was a small market totaling only 37,000 tons of P,O, annually. The 1946 total for this same area was approximately 200,000 tons. Considerably more fertilizer would have been used in 1946 had adequate supplies been available. Estimates of future markets are difficult to make, but we do have some indices that are useful. The

Jan 1, 1951

By J. B. Clark, A. S. Yue

PfANN1 has shown that when a cylinder of molten binary alloy freezes directionally, the solute distribution can be described analytically by cg=k(l-g)k-1 [1] in which Cg is the solute concentration in the solid at the point where a fraction g of the original liquid has frozen and Co is the initial solute concentration. The term k is the effective distribution coefficient of the solute and is defined as the ratio Cx/CL where Cl is the solute concentration in the main body of the liquid. Both the slope and the intercept at -log (1 - g) = 0 of a logarithmic plot of Eq. [I.] provide a measure of k. Under conditions of freezing where diffusion in the solid is negligible and the solute concentration in the liquid is uniform, the effective distribution coefficient k, derived as above, is equal to the equilibrium distribution coefficient taken from the phase diagram. However, under ordinary freezing conditions, even though solid-state diffusion is negligible, the solute rejected from the freezing solid does not have sufficient time to diffuse uniformly throughout the main body of the liquid. A concentration gradient is formed in a boundary layer in front of the advancing solid-liquid interface as pointed out by Rutter and Chalmers.' Thus, under these conditions, the concentration of the freezing liquid in the boundary layer is higher than that predicted from the equilibrium phase diagram and consequently the effective distribution coefficient k, obtained from directional freezing experiments, is larger than the equilibrium distribution coefficient. The symbol k will designate the effective distribution coefficient in the discussion which follows. In this paper, the determination of the effective distribution coefficient is demonstrated for several dilute binary alloys and a polynary magnesium alloy. The effect of freezing rate on the value of the derived k is presented in detail. An example for the calculation of the solidus in a dilute binary solution using the experimentally determined effective distribution coefficient is given. MATERIALS STUDIED Binary magnesium alloys of copper, nickel, and zinc containing approximately 0.10 wt pct solute and a polynary alloy containing approximately 0.10 wt pct each of several elements were selected for study. The spectrographic analyses of these alloys are given in Table I. The analyses are believed accurate to within +5 pct of the stated value. EXPERIMENTAL PROCEDURE Extruded rods of the alloys, 3/8 in. in diam and 11 in. long were used for directional freezing studies. The alloy rods were melted horizontally in a high-purity graphite boat by a Nichrome-wound tube furnace which moved parallel to the length of the rod. The boat was supported inside a Vycor tube suitably connected to provide a protective atmosphere of dry SO2. For an experimental run, the following procedure was used. The alloy rod was cleaned in dilute HNO, and dried. The graphite boat containing the alloy rod was placed within the Vycor tube and the tube connected to the gas train' The 'ystem was purged for 20 min with dry argon and then a flow of dried SO, was maintained for the duration of the run. The movable furnace was positioned and either all or a desired portion of the alloy rod was melted. After attainment of steady-state temperature gradients the molten bar was solidified from one end to the other at a controlled rate by pulling the furnace along the length of the bar at the desired speed. At the conclusion of the run, the directionally frozen alloy rod was analyzed spectrographically at 1 1/4-in. intervals.

Jan 1, 1961

By Pol Duwez, Spencer R. Baen

A LTHOUGH the practical importance of Fe-Cr--iV Mo alloys has long been recognized, constitution studies have been limited to a few alloys within rather narrow ranges of composition. The purpose of the present study was to establish the phase boundaries in the ternary diagram at a temperature of 1200°F (650°C).* The identification of phases and the determination of phase boundaries were based primarily on X-ray diffraction measurements and occasionally on microscopic observation. The methods used for locating the phase boundaries were essentially those described in detail by Andersen and Jette,' and by others.', The compositions of 180 alloys, prepared by powder metallurgy techniques, are shown in Fig. 1. The chemical analysis and mesh size of the powders which were used for the preparation of the alloys are given in Table I. The powders were mixed for 48 hr or longer, then compacted under 80,000 psi in a %-in. diam steel die. Each specimen weighed approximately 5 g. The compacts were sintered for 4 hr at 2500°F (1371°C) in an atmosphere of pure dry hydrogen (dew point near the temperature of liquid nitrogen). An open tray of chromium powder was placed upstream of the compacts to act as a "getter" for the last traces of oxygen or water vapor. In many cases this chromium powder was bright after sintering. Occasionally the upstream side of the powder was slightly greenish, but in all cases the downstream side was metallic. Some of the alloys contracted during sintering and some expanded as much as 20 pct. The latter alloys, which in all cases were brittle, were crushed in a tool steel mortar, repressed, and resintered for 4 hr at 2500°F. After sintering, the alloys were aged for ten days at 1200°F (650°C) in evacuated (105 mm Hg or better) fused silica tubes and were cooled rapidly to room temperature following the aging treatment. The use of the powder metallurgy technique in preparing alloys for structural investigation offers a simple method 'of avoiding contamination or non-homogeniety which could result from a melting operation. It is very often possible to dispense with chemical analysis of the alloys which have been prepared by the powder metallurgy method. In lieu of chemical analysis, it is necessary to determine the weight of the compact before and after sintering. The chemical composition of the alloy may be considered as that of the green compact, within the limits of accuracy determined by the loss of weight during sintering. In phase-diagram studies it is important to achieve homogeniety in structure, whether the alloys are prepared by powder metallurgy or by melting. Homogeniety means complete diffusion during the sintering of the alloys which are prepared by powder metallurgy. It has been found from experience that the best criterion for establishing the completeness of diffusion is the sharpness of the X-ray diffraction patterns. This criterion has been used throughout the present study. The X-ray diffraction data were obtained using powder cameras of either 214.86 or 71.62 mm diam. Copper, cobalt, or chromium Ka. radiation was used, the choice being based on the alloy composition. The powder samples were obtained by filing or crushing, depending on whether the alloy was ductile or brittle. In some cases, the powder was annealed for 4 to 6 hr at 1200°F in vacuum. The measurements were corrected for film shrinkage and absorption. The large camera, in which the film is mounted

Jan 1, 1952

By E. N. Cameron

GRAPHITE has been included in U. S. lists of strategic minerals since the problem of mineral deficiencies was revealed during World War I. Since 1918 the domestic graphite industry has led a precarious existence, and there has been much uncertainty as to the amounts of usable graphite of various grades that would be available from domestic sources in time of emergency. In 1950-1951 therefore, the writer, assisted by Paul L. Weis, undertook a review of domestic graphite sources for the U. S. Geological Survey.' The conclusions of this study are presented here, with a discussion of some technologic and politico-economic factors bearing upon the problem. Uses of Graphite: Natural graphite as marketed exhibits a wide range of properties, which determine the uses to which it is put. The most essential uses are in the manufacture of crucibles and related refractory articles, in lubricants and packing materials, and in the manufacture of batteries, foundry facings, pencils, and carbon brushes. Numerous specifications covering the mineral in its various applications must be met by producers and processors of graphite. The problem of supply is therefore not simply one of procuring a sufficient total tonnage, but the more difficult problem of procuring enough of each different grade to meet foreseeable needs. The amount of graphite required by American industry is not large. Ordinarily only a few thousand tons of strategic grades are consumed annually, yet the elimination of this small tonnage would have serious effects in several industries. Strategic Graphite: Since World War I, 60 to 100 pct of the country's annual supply of graphite has been furnished from imports. At present, natural amorphous graphite for use in pencils and batteries is produced largely from American-owned mines in Mexico. Graphite for foundry facings is obtained from a number of sources. Neither grade is a serious problem. High purity graphite for carbon brushes and for pencil leads, however, is imported, largely from Ceylon, in the form of amorphous lump graphite. Most of the flake graphite used for crucibles and related refractory articles is likewise imported, largely from Madagascar, and much of the lubricant and packing grade graphite used by industry is obtained from the same source. The strateg'ic grades of graphite are therefore amorphous lump of the Ceylon type, crucible flake, and flake suitable for lubricants and packing. Ceylon lump and Madagascar flake have for many years been accepted as standard by domestic consumers of graphite, and various essential manufacturing processes are geared to the use of graphite from these sources. Ceylon graphite as marketed is classified into several grades based on particle size and purity. Processing methods are said to be simple, but the products marketed are carefully graded and are consistent in their characteristics, an important matter to the consumer. Nearly all the graphite produced in Ceylon is from veins. Resources are reported to be large, labor is cheap, production costs are low, and world competition is slight—factors accounting for the commercial success of the graphite mining industry in Ceylon. Madagascar is reported to have deposits of the Ceylon type, but its output consists almost entirely of flake. Madagascar graphite as received in the U. S. is further processed by importing organizations, and a large number of grades are produced to meet industry requirements, especially those for crucible flake and for lubricant and packing grade flake. Madagascar crucible flake as marketed is noted for coarseness, uniformity, toughness, clean-

Jan 1, 1957

By W. O. Philbrook, K. Natesan

A mathematical model was derived for the temperature change in a particle undergoing heterogeneous chemical reaction and heal exchange with a stream of fluid. The model has been applied specifically to the exothermic oxidation of spherical particles of zinc sulfide. Very good agreement was obtained between the theoretical prediclion and experimental observation. It was found that at no stage of the reaction was the particle subjected to a state of thermal instability. In studies of gas-solid reactions, it is generally assumed that the gaseous and the solid phases are at the same temperature throughout the reaction period. This is not strictly true since most of the reactions are either exothermic or endothermic in nature. This paper deals only with heterogeneous gas-solid reactions of noncatalytic type. In the case of exothermic reactions (e.g., roasting of sulfides), there may result an increase in temperature of the particle due to the release of the heat of reaction, and this increase in temperature may enhance the reaction rate and thus cause further release of heat. Such a "spiralling" effect may lead to a thermally unstable situation within the particle. On the other hand, in the case of endothermic reactions (e.g., calcination of limestone), there may occur a decrease in temperature of the particle as the reaction proceeds, leading to a virtual "quenching" of the reaction front. A general discussion of autothermic processes with emphasis on properties and reactor design is given by Van Heerden. 1 Levesque and cubicciotti 2 observed self heating of the sample in the oxidation of thorium. Anous et al. 3 observed self cooling of the sample in their dehydration studies on chrome alum. Cannon and Denbigh, 4 and Ong et al.5 reported self heating of the sample in their studies of the kinetics of oxidation of zinc sulfide. A typical plot of heat generation and heat loss rates with reaction temperature is shown in Fig. 1.'14 The Sigmoid curve represents the heat generation rate while the straight lines represent the heat loss rate. The main objectives of this analysis are to estimate the temperature increase of a single particle undergoing an exothermic reaction and to study the possibility of a thermally unstable situation within the particle. Also, a study of the dependence of the tempera- ture increase on different process variables has been attempted. A "she ll-by-shell" method has been proposed to analyze the problem. The shells may be made as small as necessary, and equations may be set up for heat transfer by various mechanisms. Such equations will have to be solved for each shell, with the boundary conditions for ith shell being obtained from the (i - 1)th shell, using a high speed digital computer. The oxidation of spherical particles of zinc sulfide is considered for this analysis, but the treatment is general enough to be applicable to other reactions and particle shapes. The oxidation reaction can be written as AH =« -115 kcal/mole ZnS [1] Such a reaction has been found to proceed in a topo-chemical manner; i.e., as the reaction proceeds, a progressively thicker outer shell of zinc oxide is formed, while the inner core of unreacted sulfide decreases. It has been found experimentally, both in the present work and in the previous investigations,4-6 that the particle retains its original dimensions. Therefore, at any given time, the particle may be

Jan 1, 1970

By C. R. Claus, G. A. Standish

Since March. 1945, the Magnolia Petroleum CO. has drilled 39 wells in Southwest Coastal Louisiana. All wells were drilled within a comparatively small radius, but the area provides a large variety of problems. The deepest well drilled was 13,518 ft, and the total depth averaged 10,977 ft. Throughout this period drilling mud control and types of mud handled were: (I) phosphate, (2) red lime (late conversion), (3) red lime starch (early conversion), (4) red lime starch oil emulsion, (5) precision controlled low alkalinity-low lime content. and (6) gel muds for completion purposes. Improvement has been obtained in effecting some or all of the following: (I) more rapid penetration, (2) reduction in drilling hazards, (3) better evaluation of cores and logs, and (4) better completions. The geological sequence of zones penetrated range from recent sediments at the grass roots through the Frio section. Anticipation of high-pressure zones and incompetent formations entails precision control of drilling mud weights, and the unconsolidated nature of the various zones requires constant attention to the filtrate, viscosity, and gel strength values. In the Chalkley field, particularly, this combination of problems exists, where the formation pressures and overburden weight density values are in very close proximity. Design of casing and drilling mud programs must be modified to fit each well. INTRODUCTION Field and research work on drilling fluids has made constant progress, enabling operators to prospect progressively deeper horizons. Numerous papers have been written on the theoretical aspects of drilling fluid devel- opment, but in the field engineers have found it difficult to evaluate the role of specific mud constitutents when dealing in terms of thousand barrel mud systems. For that reason field data is somewhat lagging in technical report writing. However, applications of new techniques in the field have usually paralleled, and in numerous instances preceded, research work. The information obtained by Magnolia Petroleum Co. in the course of drilling 39 wells within a comparatively small area in Southwest Coastal Louisiana provides an excellent opportunity of reviewing a specific example of drilling mud evolution. A large variety of problems has been coped with, the most important result being that every well was successfully drilled to its projected total depth. The discussion begins with the advent of deep drilling in this area in March, 1945, and is concluded with a resume of recent drilling operations in the Chalkley field. The primary purpose of this paper is to describe the evolution in types of drilling fluids as it occurred and its application in the solution of various drilling problems. All of this information and experience resulted in the successful drilling of the three wells in the Chalkley field, where a combination of the most sound techniques was necessary in carrying drilling operations to the projected total depths. Other operators along with service company engineers have contributed considerably through the interchange of ideas and information to this paper, but the data and conclusions which are contained are based on first-hand observation of Magnolia Petroleum Company's drilling operations. The 39 wells drilled by Magnolia Petroleum Co. average in depth 10,977 ft per well, while the maximum depth penetrated was 13,518 ft. The cost of drilling fluids have varied from $8,700 to $165,000, with the over-all drilling costs ranging from $74,000 to $543,000 per well. This wide variance illustrates the unpredictable nature of each well and the effects on over-all cost when high density muds are required to control

Jan 1, 1955

By J. D. Forrester, Erich Sarapuu, T. C. Cheasley

Electrocarbonization of coal will produce cheap fuel for electric power plants. The complete electrification of industry and domestic power consumption of gas generated as fuel in situ is a worthwhile goal for the coal industry. Production of synthetic oils, gasoline, and coal chemicals from coal gas will create additional new markets for the coal industry. RANKING high in the nation's wealth of natural resources, readily available liquid and gaseous hydrocarbons are nevertheless falling steadily in supply, while industrial requirements for hydrocarbon compounds are greater today than during the peak period of World War 11. Theoretically, several processes will increase the future supply of liquid and gaseous fuels, but the practical application of these methods depends on two controlling factors: 1—that enough carbon-bearing material be available to warrant industrial exploitation, and 2—that the given process be physically, chemically, and economically applicable. With regard to the first factor, the Western Hemisphere is fortunately well supplied, see Table I. Table I not only shows the extensive occurrence of many fuel sources, but also the wide discrepancy among quantities of fuel substances in various materials. Great quantities of potentially available fuel have not been recovered. Many coal seams and other hydrocarbon-bearing deposits are so situated that production is uneconomical by present-day mining or oilwell pumping methods, and even in many exploitable deposits where the most efficient production methods are used a large proportion of material is never recovered. Industrial production of hydrocarbon liquids and gases must be better balanced, and processes must be developed which will convert coals, oil sand, and oil shales into fabricated commodities. Among the techniques employed by scientists and engineers to secure fuel masses not economically available at present are several processes of underground gasification. These are all concerned with converting raw materials into gaseous products by thermal treatment of source substances while they are still in the ground and therefore require that a subsurface heat (fire) zone be induced to affect pervasively the buried raw fuel deposit. This is possible only where sufficiently high temperature exists and where the fuel material is satisfactorily opened or channelized. Also, to compete successfully with common mining or oilfield practices, a given method must be controllable and must not involve greater operational expense than regular methods. Preferably, it should be less expensive. Since the close of World War 11, England has continued field studies of underground gasification methods. Experiments have also been conducted in Sweden, Estonia, France, Belgium, Italy, and Germany. The U. S. Government has sponsored field studies at Gorgas, Ala., and because gasification in situ is vitally important to establishment of the nation's fuel resources, the mining engineering department at the Missouri School of Mines has been actively interested in developing the process of underground electrocarbonization. Research was conceived by Erich Sarapuu, and preliminary experiments in treating bituminous coal were begun at the school in September 1947. The work consisted of laboratory experimentation until June 1948, at which time, through a cooperative agreement with the Sinclair Coal Co. of Missouri, pilot plant studies were instituted at the Tiger mine of the Hume-Sinclair Coal Co. near Hume, Mo., to test the encouraging laboratory findings. This comprehensive field program was pursued continuously until the beginning of 1952."'" The broad term underground electrocarbonization describes a unique gasification process that releases by electricity the desired economic constituents from a raw carbon-bearing material, converting the substance of such deposits into deliverable form and greatly reducing the cost-of-mining factor. Underground electrocarbonization is not subject to the major limitations of many other underground gasifi-

Jan 1, 1955

By R. Frenkel, O. D. Sherby, J. E. Dorn, J. Nadeau

A method is shown for the study of the creep rate dependence of metals on the applied stress under the condition of constant structure. The method was applied to pure aluminum and to dilute solid solution alloys of magnesium, copper, germanium, zinc, and silver in aluminum. A linear relationship was found to exist between the true stress and the logarithm of the creep rate. ALTHOUGH extensive creep data are now avail-Aable, the fundamentals of the creep phenomena are as yet only vaguely understood. Many attempts have been made to formulate theories for creep. Eut their agreement with fact has been disappointing. It appears that merely pyramiding more of the same type of data that is now available will not provide the essential aid toward formulating a better understanding of the complicated process of creep. Perhaps attempts to construct better models for the mechanism of creep might have to be tentatively abandoned until new types of definitive creep data are uncovered. The question therefore arises regarding what type of data might be needed to provide the essential knowledge for formulating better and more realistic theories of creep. Perhaps one source of the failure to uncover an adequate theory arises from the fact that practically all theories for creep and nearly all analyses of experimental data on creep disregard the well-known fact that the structure of metals changes during creep. For example, it is customary in evaluating the effect of stress on the creep rate to correlate the secondary creep rate with the applied stress. But, as has been demonstrated recently,' the structures obtained during secondary creep tend to exhibit deformation banding at high stresses and polygoniza- tion at the lower stresses. Consequently the stress-secondary creep rate relationships found in this way are not fundamental, inasmuch as they reveal not only the effect of stress but also the effect of differences in structure on the secondary creep rates. It is the purpose of the study reported here to isolate the effect of stress alone on the creep rate in an attempt to provide new data for possible formulation of a better theory of creep. In addition an attempt will also be made to ascertain how structure, temperature, and alloying might affect the stress-creep rate relationship. The procedure that was adopted was simple: A specimen was precrept at a given engineering stress U, (initial engineering stress during creep under constant load, namely the load divided by the initial area of the specimen) and temperature T to a selected engineering strain, e (engineering strain, namely, the instantaneous gage length minus the initial gage length divided by the initial gage length), at which time the true stress was reduced to some lower value of the true stress, ^ (the true instantaneous stress, namely, the load divided by the instantaneous area). The instantaneous true creep rate, i, (the true strain rate; with E, the true strain, namely, the natural logarithm of the instantaneous over the initial gage length) following reduction of the true stress to U, was then determined. Second, third, etc., tests were conducted under identical conditions except the stress was reduced to yet lower values, us, u,, yielding yet lower instantaneous creep rates, ;, and i,. Inasmuch as the precreep conditions were identical in each series of tests, the instantaneous structures obtained immediately after reducing the stress were presumed to be identical.

Jan 1, 1955

By F. A. Crossley

The key to disagreements between Blackburn's findings and mine is the word equilibrium". My work attempted to define the equilibrium diagram of the titanium-rich end of the Ti-A1 system. It can readily be shown that Blackburn's conclusions are based primarily on the examination of structures substantially removed from equilibrium. The diagram presented in Fig. 16 is properly labeled a "phase diagram". However, it appears that Blackburn either does not understand or does not accept the difference between "phase diagram" and "equilibrium diagram" as defined in the Metals Handbook.17 The conflict lies not in Blackburn's data but in his interpretation of it, and his use of "transformation", "phase diagram", and "equilibrium diagram" as synonymous terms. I share his view that the light microscope is much inferior to the transmission electron microscope for the study of transformations; but this fact does not render the light microscope useless or untrustworthy. The difficulties experienced with the Ti-A1 system have not been due to the limitations of the light microscope, but rather to the extreme sluggishness in achieving equilibrium at temperatures below 1000° C. Were it not for the light microscope employed with polarized light, the twin phase syndrome' might still be unrecognized and, as a consequence, still adding to the confusion of Ti-A1 investigations. (Ref. 1 should read ... Contract No. N161-25952 ... vol. 236.) Other, more sophisticated techniques, including electron transmission, simply confirm the erroneous tentative conclusions drawn from observations of structures due to the twin-phase syndrome. By the standards of most of the investigations of the Ti-A1 systems, seven of the fifteen compositions investigated by Blackburn were seriously contaminated with oxygen. The writer has found that 0.1 wt pct 0 shifts the a + Ti3A1 boundary to 1 at. pct lower A1 content at 700°C. At constant aluminum content, this corresponds to a temperature shift of the boundary of +25°c.18 Blackburn advises that the first group of alloys contained 0.1 to 0.15 wt pct 0, bur he does say whether the analyses were performed on as-received material or on specimens in their final state of heat treatment. This is especially important considering the 20-mil-thick starting materials. If specimens had been annealed in the two-phase a + 6 region it would have provided an indication of the final degree of oxygen contamination since up to about 12 at. pct A1 the boundaries of this region are well-defined for low-oxygen alloys. Blackburn questions the capability of light microscopy in determining phase boundaries in the Ti-A1 system. I submit that the a/a + Ti3A1 boundary in Fig. 1 of Ref. 1 over the composition range from 10 to 18 at. pct A1 was determined by dilatometry and supported by electron diffraction. Specimens of alloys containing 8, 10, 12, and 14 at. pct A1 were aged at 550°C for 1000 hr (under stress of 5000 psi to accelerate the tendency to equilibrium) and then fractured in tension at room temperature. Collodion was applied to the as-fractured (unetched) surface and, when stripped, carried away particles identified by electron diffraction as Ti3A1. Perhaps Blackburn will explain why these electron diffraction data were ignored. At this time, a technique for revealing or indicating

Jan 1, 1969

By T. K. Perkins, L. E. Bartlett

Values of rock surface energy (i. e. energy required to form a unit area of new surface) are useful for interpretation of drilling and fracturing phenonema This paper describes the adaptation of a cleavage technique (splitting of large rocks under controlled conditions) for measuring surface energies. Values of surface energy obtained at room temperature and at low crack extension rates are reported for a variety of sandstones and limestones. Elastic moduli, tensile strengths and compressive strengths of the samples are also reported. The values of Young's moduli (measured in bending) are relatively low, probably because of the low stress levels imposed. Measured values of surface energy me generally higher than anticipated and probably reflect inelastic yielding near the extending tip of the crack. INTRODUCTION The technology of petroleum production includes many operations such as drilling and fracturing, which involve rock breakage. One of the fundamental properties of a rock needed to fully explain breaking and fracturing phenomena is the surface energy (i. e. the energy required to form a unit area of new surface). In this paper we describe an adaptation of the cleavage method (splitting of the rock under controlled conditions) to utilize large rock samples. Application of the theory of elastic cantilever beams and the Griffith concept of mechanical stability permits the calculation of surface energies from simple measurements. Values of surface energies obtained at room temperature on dry samples and at low crack extension rates are reported for a variety of sandstones and limestones. Measured values of Young's Moduli, compressive strengths and tensile strengths are also reported for the rocks. THE EXPERIMENTAL METHOD Equipment designed to cleave large rock samples is shown on Fig. 1. This equipment consists essentially of two steel blocks cemented to a rock sample and forced apart with a steel rod. A ball joint and a pivot prevent bending stresses in the rod. A differential thread arrangement permits the rod to advance only 0.012 in./revolution of the driving nut. The axial force in the rod is measured with type FA-50-12 Baldwin Lima Hamilton strain gauges and a BLH type 20 strain gauge reader. Separation of the blocks is measured with a Starrett 656617 dial gauge. The massive nature and design of the equipment minimize the amount of elastic energy stored in the steel parts as the stress in the rod is increased. This will permit the rock to split under controlled conditions as will become clear later. Fig. 2 shows a sketch of the rock sample during cleavage. Guide slots are cut longitudinally along the rock sample as suggested by Berry.1 An initiating slot is also cut across the top of the block to a depth of 1 to 2 in. During cleavage, elastic energy is stored in the flexed beams of rock of length C. If the length of steel rod L is held constant and the crack extends in length, then the elastic potential energy stored in the rock decreases. However, surface energy must be supplied as the crack extends in length. Griffith6 has proposed the following criteria for mechanical stability. The crack will extend as long as the potential energy available is greater than the surface energy required. However, the crack will stop extending when the change in potential energy with change in crack length is just equal to the change in surface energy with change in crack length. See Eq. 1.

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

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