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By C. Graeme-Barber, R. L. Bell, T. G. Langdon

An analysis is made of the formulas and ,methods used to estimate the contribution of grain boundary sliding to the overall strain of a polycrystal. The errors involved in the approximations and/or ,mistakes in earlier work are assessed quantitatively so as to make possible the critical use of previously published data. SINCE it has been found that, under conditions of very slow creep, the strain due to grain boundary sliding (?gb) may contribute as much as 80 pct of the total creep strain,1,2 it is obviously important to have reliable methods for estimating this grain boundary strain. In two recent papers Stevens3,4 has drawn attention to the pitfalls encountered in assessing ?gb. He criticizes 1) the assumptions made in the derivation of some of the formulas for ?gb, and 2) the indiscriminate averaging procedures used for obtaining the quantities substituted in these formulas. These and further criticisms of earlier work are mostly valid. Unfortunately the only formulas and procedures recommended are either impossible or very difficult to apply in practice. Furthermore no attempt is made to assess the errors involved by the earlier approximations or mistakes, and so it is not possible to make critical use of any of these early dab. The present article attempts to improve on these shortcomings by reference to empirical verification of easily applied formulas whose theoretical derivations involve some otherwise unjustifiable assumptions, and by a quantitative assessment of the errors in previous work. DEFINITIONS First it is necessary to define the terms and symbols to be used. The choice of symbols preferred here is a logical combination and extension of the v introduced by McLean5 and the u by Brunner and rant.' In Fig. 1 the two grains X and Y are displaced by the sliding vector AC. u is the component of sliding resolved along the stress axis, v is that measured perpendicular both to the stress axis and to the specimen surface, and w is that measured perpendicular to the stress axis but in the plane of the surface. Two angles define the orientation of the grain boundary: 8, between the stress axis and the surface trace of the boundary, and +, the internal angle on a longitudinal section cut perpendicular to the surface. In computing the strain resulting from the boundary displacement at all the in- dividual boundaries in a polycrystal the components u, v, or w are sometimes averaged along a longitudinal line (i.e., parallel to the stress axis), sometimes along a transverse line, and sometimes at randomly chosen boundaries. Averages obtained in these three ways are given subscripts 1, t, and r, respectively. Stevens rightly calls attention to the possibility of non-equiaxed grain shapes either at the start or at the end of deformation. In this article all values of numbers of grains per unit length will refer to measurements made before deformation. The subscripts 1 and t will be used for the number of grains per unit length obtained along longitudinal and transverse lines, r for that obtained by averaging along a number of randomly directed lines. FORMULAS FOR ?gb ?gt, as a Function of u. An obvious truth is that cgb can, in principle, be obtained by summation of all the v components at the boundaries intersected by a longitudinal line of known length I, viz.: where nl is the number of grains per unit length, parallel to the stress axis, in the unstrained specimen. There are assumptions in the analytic derivation of Eq. [I] due to Brunner and rant' but ~achinger' arrived at Eq. [la] by a rigorous method. Unfortunately the experimental procedure required by Eq. [ la] proves very difficult as boundary migration tends to obscure the points at which the longitudinal line meets the grain boundary and the errors on such measurements tend to be large, see Fig. 2. For example, on a specimen of Magnox AL 80 at a creep strain of 9.7 pct, 300 measurements of u obtained from the points of intersection of a longitudinal line with the grain boundaries gave ul = 8.95 ± 3.58 pm, or an error of ±40 pct, at the 95 pct confidence limit. These large errors due to migration may be avoided by measuring u from the separation of the segments

Jan 1, 1968

By James A. Clem

Approximately 2000 years ago, the Lord admonished the scribes (lawyers) and pharisees (religious leaders of that time) that they had paid the tithe but had omitted the weightier matters of law, judgment, mercy, and faith. (Matt. 23:23) I want to talk about "The Weightier Matters of Law." In a situation where big government is trying to have an effect on even small details of a work activity, otherwise simple situations become complex. Regulations are written to such detail that constant compliance with strict interpretations can be a nightmare-not to mention off the target of the intended purpose for the regulation. One soon recognizes the onerous characteristics of federal statutes. Another admonition the Lord gave those lawyers and pharisees back then was that they tended to strain at a gnat and swallow a camel! He meant that the pharisees were given to devoting themselves to the strict interpretation of law by writing hundreds of subrules or interpretation to law. In doing so they eventually lost sight of the original purpose of the law. I think they were being told, keep the law-but don't neglect to humanize it Keep it simple Recognize the purpose of why the law. "Mix in" a common sense approach. Someone once said, "Common sense is instinct -enough of it is genius." Today, as 2000 years ago, we need more "genius" displayed by legislators in considering the weightier matters of law. First of all true legislature genius calls for a declarative statement about the purpose of the statute and a fair, objective analysis of the ground rules by which it will be implemented. In the Health & Safety Act of 1969, the "findings and purpose" as set forth in Section 2 do define its purpose. I believe most of us affected can be in accord with the reasons advanced for the legislation. However, beyond those well-intentioned few paragraphs, we very quickly run into trouble. Congress complicated the simplicity of the statement of purpose by mandating government intervention into areas that cannot be effectively legislated, nor even should be legislated. The Act provided for broad gaged regulation which is unnecessary, inappropriate, and tremendously costly. Frankly, it detracts from a constructive, cooperative effort by the parties involved. These are strong negatives which characterize inappropriate legislation. Appropriate legislation and subsequent regulation, which is realistically conceived and practically enforced must be born of an honest desire for improvement, based on a working knowledge of common problems which are thoughtfully analyzed. Then the legislation must be written in clear concise language so that there can be little or no doubt as to its literal meaning and intent. To be practically enforced, it must be understood by all who will enforce it and by all who are subject to it. That is to say, an effective law or standard cannot be fixed or inflexible so that it cannot be tempered in human judgment. There must be an elasticity in the statute to provide for consideration of all of the relevant facts of a given situation. Such elasticity makes the compliance effort as meaningful as it can be for the time and dollars invested. Meaningful compliance requires room for common sense. Today, we in business along with our associates in government and labor, urgently need to pause, and assess our current situation. The problems arising from the 1969 Act have been intensified through the Mine Safety & Health Act of 1977. After reading the "findings and purpose" of this legislation, and by process of elimination, we should all clearly see what is and is not the purpose of the Act. 1) It is not to turn the management of private industry over to government. 2) It is not to impair the efficient operation of business. 3) It is not to reduce productivity and profits. 4) It is not to reduce national unemployment. 5) It is not to perpetuate the bureaucracy. 6) It is not to increase the tax burden on an already overburdened people. 7) It is not to increase our balance of payments deficit. 9) It is not to replace management/labor relations in working together to solve problems.

Jan 1, 1981

By P. Somasundaran, D. W. Fuerstenau

The length of the collector is found to influence the flotation of the mineral even at incipient conditions, which are below the concentration at which interaction at the solid-liquid interface begins to take place to form hemi-micelles. To study this dependence, concentration for incipient flotation of quartz was determined as a function of pH with collectors of various chain lengths. The observed effect of chain length on flotation is ascribed to that of collector adsorbed on the bubble surface. In previous studies, it was shown that at low concentrations the alkyl collector ions adsorb at the solid-liquid interface as individuals.''2 At higher concentrations, the collector ions adsorbed at the solid-liquid interface associate with each other to form two-dimensional aggregates called hemi-micelles. Above the hemi-micelle concentration, the length of the hydrocarbon chain is extremely important since the hydrocarbons are in effect removed from water during the association, making the energetic conditions more favorable for adsorption at the interface. Because of this enhanced adsorption, one observes a very rapid increase in flotation associated with the hemi-micelle formation at the solid-liquid interface. However, a dependence of flotation on the chain length at concentrations below that required for hemi-micelle association was also observed,' and this cannot be explained by the above mechanism which postulated hydrocarbon chain interactions only at the solid-liquid interface. This prompted an investigation into other possible reactions of the hydrocarbon chains and an examination of the conditions at the bubble surface involved in the flotation system and how these observations might explain the reactions at the solid-gas interface which cause the particle-bubble attachment required for flotation. To obtain more information on chain length effects, flotation, under incipient conditions, was tested by vacuum flotation techniques. The collector-concen-tration-pH relationships for flotation of quartz with alkyl ammonium acetate collectors was delineated by observing the pH at which quartz particles begin to float to the liquid surface. By investigating flotation as a function of pH, it was also possible to study the effect of neutral molecules on incipient flotation conditions, since the aminium ions hydrolyze to amine molecules at higher pH values. EXPERIMENTAL WORK Brazilian quartz specimens were crushed and sized, and the 270 x 400 mesh fraction was used for flotation studies. The samples were leached with concentrated hydrochloric acid until no coloration of the acid occurred. The leached material was washed free of chloride ions and stored in distilled water. The vacuum flotation technique developed by Schuhmann and prakash3 was used to determine the critical pH-concentration curves. This method, which can be used to delineate conditions for incipient flotation, is fairly simple and rapid. About 0.5 gm of 270 x 400 mesh quartz was placed in a 100 ml graduated cylinder which was then filled to the 100 ml mark with the collector solution made from high-purity alkyl ammonium acetate salts. The water used for the test was conductivity water saturated with air that had been passed through a cleansing train consisting of Drierite, Ascarite, a water wash bottle, and a trap. After the pH was adjusted, the cylinder was then conditioned for thirty minutes. In the tests where an acid pH was desired, sufficient acid was added before the collector solution to avoid any effect due to slow desorption of collector from the quartz surface. After conditioning, vacuum was applied to the system and the flotation or nonflotation of the quartz was noted. The pH at which the quartz particles began to float to the liquid-gas interface was taken as the critical PH. Critical pH curves were thus determined for different concentrations of the various collectors. Hallimond tube flotation data were taken from the authors' previous publication1 for correlation with that from the vacuum flotation. RESULTS AND DISCUSSION The results of vacuum flotation studies for determining critical pH-concentration curves, i.e., curves which delineate conditions for incipient flotation, are shown in Fig. I. In generaI, all the curves exhibit an upper and lower pH limit between which flotation will

Jan 1, 1969

By J. Lohrenz, C. R. Clark, B. G. Bray

Procedures to calculate the viscosities of in situ reservoir gases and liquids from their composition have been developed and evaluated. Given a composition expressed in methane through heptanes-plus, hydrogen sulfide, nitrogen and carbon dioxide together with the molecular weight and specific gravity of the heptanes-plus fraction, the procedures are capable of calculating the viscosity of the gas or liquid at the desired temperature and pressure. The procedure for reservoir liquids was developed using the residual viscosity concept and the theory of corresponding states, and was evaluated by comparing experimental and calculated results for 260 different reservoir oils ranging from black to highly volatile. The average absolute deviation was 16 per cent. This is the first known procedure for calculating the viscosity of reservoir liquids from their compositions as normally available, i.e., including the heptanes-plus fraction. The procedure for reservoir gases uses a sequence of previously published correlations. Evaluation of the procedure was accomplished by comparison of 300 calculated and experimental viscosities for high-pressure gar mixtures in the literature. The average absolute deviation was 4 per cent. The calculations are useful for (I) determining viscosities in compositional material balance computations and (2) predicting the viscosity decrease which occurs when gases, LPG, or carbon dioxide dissolve in reservoir oils. INTRODUCTION Methods to predict viscosities of reservoir fluids from the normally available field-measured variables have been presented. Beal,1 Standing,2 and Chew and Connally3 orrelated oil viscosities with temperature, pressure, oil gravity and gas-oil ratio. Carr, Kobayashi, and Burrows4 and Katz et al.5 have presented correlations for reservoir gas viscosities as a function of temperature, pressure and gas gravity. Lie all intensive physical properties, viscosity is completely described by the following function: Eq. 1 simply states that viscosity is a function of pressure, temperature and composition. These previous correlations1- hay be viewed as modifications of Eq. 1, wherein one assumes more simple functions may be used. The assumptions are practical, because the composition is frequently not known. Further, the assumptions are sufficiently valid so that these correlations are frequently used for reservoir engineering computations. In compositional material balance"' computations, the compositions of the reservoir gases and oils are known. The calculation of the viscosities of these fluids using this composition information is required for a true and complete compositional material balance. For reservoir gases, Carr, Kobayashi and Burrows4 have presented a suitable compositional correlation. For reservoir oils, no correlation is available, and data from reservoir fluid analyses have been used7-9 for compositional material balance calculations.* From a theoretical point of view, this is entirely invalid. The reservoir fluid analysis, whether flash, differential, or other process, does not duplicate the compositions which occur during the actual reservoir depletion process, therefore the viscosities measured during reservoir fluid analysis are not those which occur in the reservoir. From a practical point of view, the "error" of using viscosities from reservoir fluid analysis is of varying and unknown significance. One can say qualitatively that the error is greatest where compositional effects are greatest, i.e., for volatile oil and gas condensate reservoirs and pressure maintenance operations. The first requirement to obtain a quantitative estimate of the significance of the error is to develop a reliable compositional correlation for the viscmities of reservoir oils. No such correlation has been available. Consistent with this requirement, the objective of this study was to develop a procedure to predict the viscosity of reservoir fluids from their compositions. Normally, the compositions of reservoir fluids are available expressed as mole fractions of hydrogen sulfide, nitrogen, carbon dioxide and the hydrocarbons methane through the heptane-plus fraction, with the average molecular weight and specific gravity of the latter. The final correlation was to use the composition in this form. While the more challenging objective of the study was the development of a correlation for the viscosities of reservoir oils, the viscosities of reservoir gases were also studied. The end result of the study was a procedure to calculate the viscosities of reservoir gases and liquids suitable

Jan 1, 1965

By W. F. Hosford, E. W. Kelley

Deformation studies have been conducted at room temperature on single crystals of magnesium and magnesium alloys with thorium and with lithium. Single crystals oriented to suppress shear on the easily activated basal slip systems were deformed by plane-strain compression. Compression along the C axis was accommodated by {1011} banding. Compression perpendicular to the unconstrained c axis activated {1012} twinning, and, after virtually complete twinning, deformation continued by {1011) banding in the twinned material. Compression perpendicular to the constrained c axis was accommodated by the simultaneous operation of (1012) twinning against the constraint and (1011 ) banding. Although this orientation was favorable for {1010)(1210) prism and {1011}(1~10) pyramidal slip, these modes were not observed in pure magnesium or in Mg-0.5 pct Th. However, {10i0)(1~10) prism slip was observed in crystals of Mg-4 pct Li during compression perpendicular to the constrained c axis. Fracture in all materials occurred parallel to (1124) or {l~il) depending on the orientation and composition of the specimen. THE mechanical behavior of the hcp metals is strongly anisotropic. Although several slip systems have been reported the slip is cpmmonly in the directions of closest packing, the (1210),' and this does not produce strains parallel to the c axis. Hence the inherent anisotropy. The deformation mode most easily activated in magnesium at room temperature is (0001)(1210)- basal slip. Also {1010}(1~10) prism slip and {1011)(1210) pyramidal slip have been reported, primarily at elevated temperatures.2"4 However, at room temperature the shear stresses to activate the prism and pyramidal modes are roughly a hundredfold greater than that required for basal slip.'j4 Thus prism and pyramidal slip may be expected only under special conditions of loading. Strains normal to the basal plane can be produced by twinning, however. Many twinning modes have been reported for magnesium,' with (1012) twinning the most common and relatively easy to activate. Magnesium can deform by (1012) twinning when stressed along the c axis jn tension, but not in compression. In contrast, (1011) twinning is activated by compression along the c axis and not by tension. In addition to primary twinning, secondary twinning or slip can occur within the reoriented material of primary twins.' In general at least five independent shear systems must be active to bring about an arbitrary shape change such as that in the individual grains of a deforming polycrystalline material.' Because basal slip can_ provide only two independent shear systems and (1012) twinning can only accommodate an extension of the c axis, other deformation modes must be active in magnesium for an arbitrary shape change to occur. The purpose of this investigation has therefore been to study the various deformation modes in magnesium at room temperature, with special emphasis on those modes that are less easily activated. The effect of the alloying elements, thorium and lithium, has also been investigated. In polycrystalline aggregates, unambiguous identification of deformation modes is extremely difficult and the direct evaluation of the resolved shear stresses to activate them is not feasible. On the other hand, uni-axial tension and compression experiments on single crystals may not activate some of the- deformation modes because basal slip and/or {1012) twinning cannot be suppressed in most orientations. However, it should be possible to activate all possible deformation modes using oriented single crystals and plane-strain compression. Identification of active deformation systems and evaluation of the resolved shear stresses required to activate them should be facilitated. Wonsiewicz and Backofen have recently completed an investigation of the plasticity of pure magnesium crystals at various temperatures utilizing plane-strain compression and selected crystal orientations. This technique has also been used in the present work. The seven orientations selected for study are indicated in Table I. Plane-strain compression along the c axis (orientations A and B) should activate some deformation mode _other than basal, prism, or pyramidal slip, or (1012) twinning. In orientations C and D, prism or pyramidal slip would be expected to take place. When the compressive load is applied perpendicular to an unconstrained c axis (orientations E and F) the three slip modes should be suppressed but not (10i2) twinning. In orientation G, basal slip should occur.

Jan 1, 1969

By Nicholas J. Grant, A. W. Mullendore

Measurements of grain boundary sliding were made on polycrystal and bicrystal tensile creep specimens of Al-2 pct Mg at 500oand 700oF. Grain and pain boundary orientation factors were studied with respect to their effect on the magnitude and direction of grain boundary sliding. It was concluded that a large part of the observed sliding may be caused by the operation of slip crossing the grain boundaries. Supporting evidence for this model from other investigations is also given. GRAIN boundary sliding in metals during elevated temperature deformation has frequently been thought of as an independent mechanism with its own characteristic stress, temperature, and structure dependence. Further, it is common to regard the grain boundary as the weak link during creep deformation since: 1) the strength of apolycrystallinemetal, as meas-sured by creep rate or rupture life, decreases at\a more rapid rate when sliding comes into action, and 2) grain boundary sliding, as revealed by "boundary darkening" and fold formation is often the first visible deformation. On the other hand, more quantitative observations, in both polycrystals and bicrystals, have shown boundary deformation to be closely related to the over-all deformation of the specimen. The curve of grain boundary contribution to elongation vs time takes a shape similar to that of the total creep curve,',' and the apparent activation energy for sliding appears in most cases to have the same value as that for total creep.3 In order to reconcile these observations, one is left with these possibilities: 1) The grain boundary and grain deformation rates are both controlled by the same rate limiting processes. 2) The rate of sliding is limited by accommodation deformation in the grains. 3) Sliding is the consequence of grain deformation. 4) Grain deformation is dependent on prior grain boundary deformation. Alternatives 2) and 3) would view grain boundary sliding as occurring in series with another deformation process which could be rate controlling. McLean prefers item 3) as the sliding basis,4 where subgrain rotation results from dislocation accumulation in the substructure at the grain boundary. Crussard and Friedel's5 treatment of grain boundary migration considers that dislocations are forced into the grain boundary and are dissociated into dislocations with Burgers' vectors nearly parallel to the grain boundary. The movement of these partial grain boundary dislocations then produces the sliding. The results of this investigation have indicated alternative 3) to be the most appropriate and it is this aspect of grain boundary sliding which will be analyzed. EXPERIMENTAL PROCEDURE Three types of tensile creep tests were employed in this study: (I) A constant load test of one very coarsegrained polycrystalline specimen at 500° F, 3600 psi, 1 pct per/hr strain rate to examine the grain and grain boundary orientation factors in grain boundary sliding. (II) Constant strain rate tests of polycrystalline specimens at 510o and 715o F, 2 pct per/hr strain rate to determine the grain boundary contribution to elongation at very low total strains. (m) Constant strain rate tests of bicrystals of various grain and grain boundary orientations at 500°F, 2 pct per/hr strain rate to obtain further information on the orientation effects in grain boundary sliding. The material used in the tests was a high-purity Al-1'.92 mg alloy, kindly furnished by Alcoa. Its composition is given in Table I. The alloy is a solid solution at the test temperatures. The coarse grained polycrystalline specimen for test (I) was prepared by recrystallizingthe machined specimen, straining it about 1pct intension at room temperature and annealing at 900°F for 8hr. The constant strain rate specimens (11), with an 178 in. sq. by 1/2 in. long gage section, were cut from 1/8 in. thick sheet of cold rolled and annealed (8 hr at 1000oF) material. The latter specimens were supported in a special jig during the milling operations to avoid any bending, and the gage section was subsequently heavily electropolished to remove the cold-worked surface layer. The bicrystals (ID) were machined in the same

Jan 1, 1963

By A. L. Jr. Pozzi, A. O. Garder, D. W. Peaceman

A new numerical method is proposed for the solution of multidimensional miscible displacement problems. Besides the usual stationary grid associated with numerical procedures, the method uses moving points for which positions and concentrations are computed each time step. Based on the method of characteristics for treating combined transport and dispersion, the method applies equally well to any number of dimensions and, in contrast with other numerical procedures, properly takes into account the physical dispersion, no matter how small. Extensive tests show that accurate solutions of one-dimensional problems can be obtained over a wide range of values of the dispersion coefficient, including zero. They also show that the moving points do not need to be uniformly spaced, and that increasing the number of moving points beyond 2/grid interval does not significantly improve the accuracy of the solution. Two-dimmsional calculations using the new method were carried out to simulate laboratory model displacements in which gravity caused overriding of solvent. Good agreement between observed and computed profiles and measured and computed concentrations of produced fluid was obtained for a viscosity ratio of 1.89; at higher viscosity ratios, fair agreement was obtained Computed results were found to be significantly affected by vertical dispersion, and negligibly affected by dispersion in the direction of flow, in agreement with conclusions based on experimental observations. INTRODUCTION Although miscible displacement processes are potentially of great economic significance, limited progress has been made in developing mathematical methods for predicting the outcome of a solvent flood. Because of the complexity of the partial differential equations which describe multidimensional miscible displacement, numerical methods are a natural approach to their solution. The task of finding suitable numerical approximations to one of the partial differential equations, which involves both dispersion and convective transport, has been particularly difficult. Dispersion in the absence of transport is described by the heat flow equation, a second-order equation of parabolic type. This equation has been very successfully treated by numerical methods. Transport in the absence of dispersion is described by a first-order equation of hyperbolic type. This equation has been treated numerically with some success in one dimension, both by Lagrangian and Eulerian techniques, 1.2 but extension to two or more dimensions has not been satisfactorily accomplished. Usually one of two things happens: either the numerical solution develops oscillations or it becomes smeared by artificial dispersion resulting from the numerical process. When transport and dispersion are considered simultaneously, this numerical dispersion may dominate the low physical dispersivicy that generally characterizes miscible displacement. Stone and Brian2 have developed a new difference equation for treating combined transport and dispersion in one dimension. By suitable choice of certain parameters, they succeeded in markedly reducing both oscillation and numerical dispersion. However, a satisfactory extension to higher dimensions has not yet been found. Peaceman and Rachford3 presented a centered-in-time and centered-in-distance difference equation combined with a 1,transfer of overshoot" procedure which was demonstrated to work well in one dimension. The technique was applied to the two-dimensional miscible displacement problem, but subsequent calculations with zero dispersivity showed little change in results compared with the calculations they presented. This indicates that their method involved a numerical dispersion of the same order as the physical dispersion. The present paper describes an alternate method for solving the combined transport-dispersion

Jan 1, 1965

By Earl R. Hoskins, James E. Russell

The electrical resistivity of rocks has been studied quite extensively, in particular, the effects of temperature and confining pressure on resistivity. References 1 through 6 at the end of this chapter pertain to electrical resistivity of rock and contain further references on the same topic. The present study is motivated by an interest in determining the in-situ properties of rock as well as the stress state of the rock and how these quantities are changing with time. Most of the previous work on the electrical resistivity of rocks has been directed toward saturated rocks at relatively high confining pressures and temperatures. The present study was oriented towards air-dry surface rock that might occur in mine pillars. The mean stress and temperature under such conditions are comparatively low. It has been demonstrated that the resistivity of rock is highly dependent upon the porosity. In fact, for saturated rocks, a relationship referred to as Archie's law has been established between porosity and electrical resistivity. In the case of saturated rock, the property that is actually being measured is the resistivity of the solid/fluid system. Since the resistivity of the fluid alone is usually much lower than that of the dry rock, it is understandable that the resistivity of a saturated rock is in general several orders of magnitude lower than the resistivity of a relatively dry rocli. For dry rock, it seems reasonable that the electrical resistivity should increase as microcracks open within the material. Since microcracks open as material is stressed closer and closer to its failure point, it appears that there should be a correlation between electrical resistivity

Jan 1, 1970

By William L. Boyd, Eugene L. McCarthy, Laurance S. Reid

Proper control of the moisture content of natural gas is essential to reliable operation of gas transmission and distribution facilities serving northern markets. The moisture content of natural gas is usually determined by dew point measurement at the existing pressure. For any gas of constant moistrire content. the dew Point varies with the pressure. A correlation of the data of several investigators is prezented in graphical form by the authors. These data were correlated by the authors and F. M. Townsend, C. C. Tsao. M. I). Rogers. Jr.. and J. A. Porter. graduate students in chemi(.a1 engineering at the University of Oklahoma. Of articular interest are the hitherto unpublished low temperature data observed by Wickliffe Skinner. Jr., which are included in this correlation. PRESENTATION OF DATA The problem of interpreting water dew points, or saturation temperatures. of natural gas in terms of specific moisture con-tent has increased in importance during the past decade bec.arl.;e of extensive development.; in the transmission and petro-chemical phases of the natural gas industry. Virtually all gas transported to northern and eastern markets must be dehydrated to a low water vapor content to prevent hydrate formation in transmission and distribution lines and resultant interruption.; in gas deliveries. Complete dehydration is required in certain phases of tile petro-chemical industry involving low-temperature operations. It is a well-known fact that the water vapor content of pure hydrocarbon vapors and their mixtures at superatmospheric pressures cannot be predicted with accuracy by assuming validity of the ideal gas laws." Earlier interest in the general problem was concentrated on the water vapor content of pure hydrocarhons and hydrocarbon mixtures in the pressure and temperature ranges common to gas and oil producing reservoirs in order to obtain fundamental data for the improvement of production techniques and the furtherance of reservoir studies. Excellent data are published for pressures ranging from atmospheric to 10,000 psig and for temperatures ranging from 100° to 460° F4,9,10,11 and are found to be in close agreement. However, experimental data at high pressures and temperatures below 100°F are comparatively limited in scope. Experimental data in the lower temperature range have been reported by Laulhere and Briscoe.8 Deaton, et al,2,3 Hammerscllmidt,5,6 and wade," In general, the pressures employed in these investigations ranged from atmospheric to 1.000 psig while temperatures ranged from 32° to 120°F; i.e., the usual conditions encountered in gas transmission line operations, Additional data were reported by Russell, et al,12 at pressures as high as 2.000 psig and covering a rather narrow atmospheric temperature range. In 1947, Hammerschmidt published a correlation of all available data,' in which the water vapor content of gases at saturation. under high pressure and low temperature. was predicted by extrapolation. In 1948, Wickliffe Skinner. Jr.. presented data on the moisture content of a low nitrogen content gas at low temperature and at pressures ranging upward to 1.500 psia.1-3 Comparison of Skinner's experimental data with the extrapolated data of Hammerscllmidt revealed an appreciable variation in the lower temperature range. emphasizing the need for a new correlation which would rely on Skinner's data at lower temperatures. Careful scrutiny of available data suggested that presence of an appreciable quantity of nitrogen in a gas mixture may affect its saturated moisture content so that data obtained from gases with more than three per cent nitrogen were not used in this correlation. CORRELATION OF DATA Data employed in this correlation are presented in Table I. The data of Dodson and Standing.4 McKetta and Katz,9 and Olds, Sage and Lacey10 were compared and found to be in close agreement so that the data of Olds. et al, re-plotted in a more convenient form by the Humble Oil and Refining Co.,' were used for temperatures of 100°F and above. Skinner's data were used for temperatures below 40°F. Between these intermediate temperature limits, the data of Hammerschmidt.7 Wade" and extrapolated data of Olds. et al.1 were tabulated

Jan 1, 1950

By G. H. Shefelbine

DISCOVERED during the time of the Spaniards, the Namiquipa silver-lead-zinc mines in Chihuahua, Mexico, remained idle until 1916, when mining claims were first denounced. About 1922 a Japanese company, the Santo Domingo Mining Co., was formed to mine the oxide silver ore. The company built a 75-tpd cyanide plant and mined in the area for a number of years. Because of an error in surveying in one of the company's mines situated in another district, mining was carried over into a claim owned by General Marcel Caraveo, at that time governor of Chihuahua. Santo Domingo Mining Co. lost the resulting lawsuit and consequently had no capital to continue operating at Namiquipa. Later, Ray Brown and Eugenio Caballero formed a company to operate the mine, shipping crude ore to the American Smelting and Refining Co. smelter at Avalos, Chihuahua. The cyanide plant was changed to flotation with a capacity of 75 tons per 24 hr. In 1936 the property was again closed owing to labor trouble, a drop in the price of silver, and increased water in the mine.

Jan 10, 1957

Jan 1, 1947

By L. D. Godshall

A great deal has been written of late regarding the loss of silver in assaying; very discordant results have been published by different writers, and much uncertainty exists concerning even approximate losses in a careful determination of silver, as represented by a fire-assay. In the present paper it has been the aim of the writer to determine as accurately as possible the losses sustained by silver, under certain specified conditions, during the process of cupellation. Such losses are well known to be due to absorption by the cupel and volatilization. The conditions, however, which govern these losses are not believed by the writer to be so well understood. The most important of these are : 1. The effect of variable quantities of silver used. 2. The temperature of cupellation. 3. The character and quantity of impurities in the lead button. 4. The weight of the lead button. 5. The nature of the cupel. The following experiments were made for the purpose of demonstrating, as nearly as possible, the total loss of silver in cupellation under the most favorable conditions to be obtained in commercial assaying. Chemically pure silver and pure lead were taken. The latter was obtained from test-lead, first melted into a bar, from which pieces of the desired weight were cut and accurately weighed. The experiments recorded in this paper were planned by the writer, but executed throughout by Mr. J. N. Walker, whose ability as an accurate, careful and painstaking assayer is too well known and recognized throughout the West to require any further endorsement from me.

Jan 1, 1897

By C. Scala, F. Bernstein

General expressions are derived relating the streaming potential to the electrochemical potential of a permeable junction separating two electrolytic solutions. By the methods of irreversible thermodynamics, these potentials are related to the flux of mobile species arising from differences in pressure and chemical composition. The flux is conveniently expressed as a transference number, the equivalents of a mobile species transferred through the junction per faraday of electricity. At constant pressure, the flux equation gives the electrochemical potential across the permeable junction. The streaming potential across the junction is obtained by imposing the condition of constant chemical composition. The familiar expression for the borehole SP is shown to be a particular solution of the general flux equation. The derived exprersions were verified in experiments with seven shale samples. Both the theory and experimental data provide additional proof of the presence and magniturle of the streaming potential in shales. INTRODUCTION In the interpretation of electric logs, there has been much concern over the correction to be made to the recorded SP for an electrokinetic or streaming potential originating from the difference in pressure between the mud column and the formation. It was long recognized by M. R. J. Wyllie that such an electrokinetic potential source mas in the mud cake opposite permeable sands.' More recently, M. Gondouin and C. Scala2 showed an additional but opposing electrokinetic source of potential to be in shale beds. Their work was supported by the very extensive and excellent work of Hill and Anderson.3 n the present contribution, the general relationships between the electrochemical potential and the corresponding streaming or electrokinetic potential are examined and clarified. A notable advance towards understanding the relation between the various sources of electrical potential in a borehole has been the application of the now common methods of irreversible thermodynamics to describe the passage of ions and water through charged electrolyte junctions such as in shales.' The advantages of these methods are twofold. Unlike classical thermodynamics, they can be applied to non-equilibrium sys- tems, i.e., systems in which flow takes place, provided the flow processes have reached a steady state. They also permit conventional thermodynamic properties to be related to the steady-state dynamic properties. These methods arc used here specifically to derive expressions relating the potential behavior of shales in terms of ion and water transport. Experimental verification of the expression for the shale streaming potential is given which in turn offers theoretical support to the existence of a streaming potential in shales.' Importantly, the relative contribution of transport parameters to the SP is clarified. The theoretical treatment is essentially that of Lori-mer, Boterenbrood and Hermans3 ut has been extended to derive the general expression for the SP.

Jan 1, 1947

By J. W. Spretnak, V. Kandarpa

Stress -induced ordering of carbon atoms is studied in a series of Fe-Mn-C alloys. A prominent peak is found in the vicinity of 280°C at frequencies of the order of 1.0 cps, with an associated activation energy of 37 kcal per mole. The height of the peak is linearly rekzted to the concentration of carbon in solution. The distortion of octahedral holes by manganese atoms appears to be predominant over carbon-carbon pair interactions. RELAXATION by stress-induced ordering of point defects is expected whenever the introduction of these point defects produces distortions which have a lower symmetry than that of the lattice. Under zero stress, the isolated point defects occupy the crystallographic-ally equivalent positions in the lattice, as these represent states of equal energy. However, if the defect sites are asymmetric, application of an uniaxial stress will split the energy states, and a redistribution of the defects among various states will take place. This is the case of the internal friction peak called the Snoek peak,1 resulting from isolated interstitials in bcc metals. The interstitial sites in this case have tetragonal symmetry. In the case of fcc and hcp lattices, such an effect is not expected from isolated point defects because of the symmetrical nature of the interstitial sites. However, internal friction peaks arising from interstitial diffusion have been reported both in hcp2,3 and fcc4-8 lattices. These peaks are often explained on the basis of stress-induced ordering of interstitial solutes, caused by the deviation of interstitial sites from their cubic symmetry through the presence of nearby defects. In the case of fcc lattices, evidence for interactions of both the substitutional-interstitial4,6,13 and interstitial-interstitial types5'798'14 have been presented by various investigators. The purpose of the present investigation was to study the internal friction peak attributed to the diffusion of interstitial carbon atoms in high purity austenitic manganese steels and to account for the peak in the light of the existing models. MATERIALS The Fe-Mn-C alloys used in the present investigation were made in two different ways, designated as Type I and Type 11. Type I alloys were made from high purity Fe-Mn alloys obtained in the form of 0.04- in.-diam wires from Materials Research Corporation, Orangeburg, N.Y. These alloys were carburized to different levels using gas mixtures of H2 and CH4 at 1000°C. Type I1 alloys were made in this laboratory starting with zone refined iron, spectrographically pure manganese, and spectrographically pure carbon. They were melted in an argon arc melting furnace and drawn into 0.04-in.-diam wires. All the wires were annealed at about 900°C for 3 hr prior to the internal friction experiments. After the measurements of internal friction, the phases in the samples were identified by X-ray diffraction and the carbon determined by the combustion method. EXPERIMENTAL PROCEDURE In the present work, a classical Ke-type pendulum was used. The details of the equipment were described previously by D. T. Peters.9 Dry helium at 40 torr was used in all the experiments. The internal friction, measured as the logarithmic decrement of the torsion amplitude of vibration was determined as a function of temperature, from ambient to about 500°C. The background internal friction was assumed to have the form of the exponential of the inverse temperature and was subtracted from the raw data. The height of the peak was measured at the position of the maximum in the plot of the internal friction versus temperature. The activation energies of the peaks were measured by the peak shift method. The internal friction values for an alloy were obtained as a function of temperature at different frequencies of vibration. The position of the peak changes with frequency, the higher the frequency the higher the peak temperature. The activation energy of the process associated with the peak is obtained using the formula

Jan 1, 1970

By B. H. Caudle, W. J. Bernard

Factors which influence the success or failure of a waterflood can seldom be determined in the laboratory. For this reason pilot waterfloods are initiated in a repreventative portion of the oil reservoir in question. For a pilot flood to predict quantitatively the recovery to be expected in a field-wide waterflood operation, the pilot area must behave as though it were confined (surrounded by similar areas). In this study, laboratory fluid-flow models were used to determine the simplest pilot pattern, for particular conditions of mobility ratio and initial gas saturation, that would behave as though it were confined. Pilot patterns studied ranged in complexity from a single inverted five-spot to a grouping of nine regular five-spots. Only the innermost producing well in each pattern was studied. Model results showed that the optimum number of wells in the pattern depends upon the oil-water mobility ratio and the expected oil-bank size. Unfavorable mobility ratios will, in general, require more wells in the pilot pattern than will favorable mobility ratios. Pilot patterns in reservoirs which contain a dispersed, flowable, free gas saturation will require fewer wells than for the under-saturated case. The single inverted five-spot pattern was found to be unsatisfactory for predicting behavior of fully developed waterfloods. In particular, it is possible that, in reservoirs which contain a flowable, dispersed gas phase, the oil bank will never be observed at the producers due to the large amounts of free gas which continue to be produced with the oil. INTRODUCTION One method which has been used to predict the performance of a waterflood is the pilot flood. The pilot waterflood is a flood which involves only a small cluster of the reservoir wells and is located in a small, representative portion of the reservoir. The object is that oil produced from the pilot can, in some way, be related to the oil recovery to be expected from a field-wide expansion of the waterflood. However, these field pilot waterfloods have often been unreliable in the prediction of oil recovery in a fully developed waterflood. This unreliability has also been demonstrated in several laboratory studies of pilot floods. Some of the investigators have shown that there are situations in which the pilot flood oil production is far too optimistic with respect to the oil recovery in the fully de- veloped flood. Others4-G have shown that the pilot results can also be pessimistic, especially if the pilot waterflood is initiated in an oil reservoir which has been depleted by primary recovery and is at very low pressure. The major reason for this unreliability of pilot water-floods is the migration of fluids into or out of the pilot area. By the well-known method of images, if straight lines can be drawn to represent vertical planes of symmetry in a porous medium which contains pressure sources and sinks (injectors and producers), then these lines are invariant streamlines, or lines across which there is no potential gradient, and therefore no flow. In an actual reservoir, these lines of symmetry can never be established exactly because of reservoir inhomogeneities and irregular reservoir boundaries. However, if the reservoir is relatively large and contains wells in repetitive patterns, these lines of symmetry are commonly assumed to exist for the pattern units sufficiently far removed from the reservoir boundary. Lines of symmetry for the five-spot injection pattern are shown in Fig. 1. Each five-spot unit in this figure can be considered confined with respect to flow across its boundary. In pilot floods this is not the case. The lines of symmetry for the pilot patterns investigated in this study are shown in Fig. 2. It is obvious that the fluid within these pilots is not confined and is therefore able to migrate into or out of the pilot area. Intuitively, one can see that, if more wells are added to the pilot, the innermost unit tends to behave more and more like the confined pattern. However, there is a practical limit to the number of wells which should be placed in the pilot. This limit is usually determined by economic factors. It was the purpose of this study to use laboratory fluid-flow models to determine which of the previously mentioned pilot patterns will force the innermost producing well to behave as it would in a fully developed waterflood. Since fluid migration is influenced by initial saturation conditions and the mobility ratio, these factors were included in the study. The ultimate objective of this study was to develop data which would allow the operator to choose a pilot pattern and operating conditions that will yield a production history which can be applied directly as an estimate of the performance of each production well of the fully developed waterflood. BASIS FOR THE STUDY The basic problem of field pilot floods is the migration of the reservoir fluids into or out of the pilot area. This problem has been the subject of previously reported model studies on pilot floods. These studies have been concerned mainly with the development of arbitrary "correction factors" to be applied to the simple, unconfined pilot systems such as the single five-spot. The correction factors were intended to adjust the production history of the un-

By Richard D. Hagni

Although the ore microscopist routinely examines polished sections to determine the mineralogy and texture of ores, his importance to the solution of problems peripheral to geology is not always fully realized. The techniques which he uses can be applied with little modification to the solution of a wide variety of beneficiation problem. By extending his studies beyond those normally considered to be of interest to the geologist, he can include examinations of polished sections of selected mill products. This is a logical extension, because the minerals and textures in the polished sections of ores are the same as those in millproducts. The mill dressing engineer should be more aware of the types of beneficiation problem that can be solved by the ore microscopist and what the ore microscopist can do for him. A greater degree of cooperation between the ore microscopist and the mill dressing engineer can be of significant mutual benefit. Ore microscopy holds an advantage over chemical analysis, because the interrelations and combinations ofthe mineral constituents of an ore or mill product can be visually determined. This advantage provides solutions to many beneficiation problem. Locking is a type of beneficiation problem that is particularly amenable to ore microscopy. The percentage, type, and distribution of locked particles can be readily determined with the aid of an ore microscope and an estimate made of the extent of additional grinding required for liberation. The extent of intimately locked types, which no reasonable amount of grinding will liberate, can also be evaluated. Mineral coating conditions, free particles of a deleterious mineral, and free particles of a valuable mineral held in flocculated clusters of gangue are other features that can readily be observed. In some instances, visual examination may show that the problem is not one of locking. Photomicrographs illustrate the variety of beneficiation problems for which the ore microscope is applicable. These problems and their resolution demonstrate the importance of the instrument and show the value of close coordination between the mill dressing engineer and the ore microscopist.

Jan 1, 1979

EXECUTIVE COMMITTEE OF THE BOARD OF DIRECTORS CHESTER A. FULTON, Chairman CARROLL A. GARNER H. Y. WALKER WALLACE E. PRATT FELIX E: WORMSER PAUL D. MERICA, Consultant FINANCE COMMITTEE OF THE BOARD OF DIRECTORS ERIE V. DAVELER, Chairman WILBER JUDSON RUSSELL B. PAUL HENRY KRUMB, Consultant

Jan 1, 1944

By W. K. Godfrey

The highest compressive strength cement has the highest bond strength in tests in which the cement is subjected to a confining pressure. After perforating, the bond strength is reduced to nearly zero when the pipe is supported by weak cement. Perforating does not affect the bond strength, however, when the pipe is supported by strong cement. Pipe supported by weak cement is damaged by perforating with expendable capsule jets, but is not damaged by perforating with the hollow carrier gun. High strength cements are recommended for oil wells that are to be perforated. Introduction The purpose of this work is to determine the effect of jet perforating on the bonding strength of oilwell cement at simulated down-hole conditions. Bond strength is a good criterion for determining the effectiveness of cement in performing its main function, i.e., that of isolating zones. According to the literature on the subject, the optimum cement strength for perforating is low and should not exceed 2,000 psi compressive strength. This conclusion was based on the appearance of bullet and jet perforations in neat and gel cements largely done in the absence of a confining pressure more than 15 years ago. Discussion Literature A relatively weak cement has been recommended in the literature as having optimum properties for perforating. In 1947, Oliphant and Farris tested bullet perforating of neat cements at various curing times.' Some of the tests were made at down-hole conditions. They reported that the optimum cement strength for perforating was about 2,000 psi compressive strength. Enlarged holes occurred when strength was too low, and the cement shattered and cracked when the strength was too high. In 1951, Morgan and Dumbauld tested bullet and jet perforating of neat and gel cements at surface conditions.' They reported that optimum cement has a compressive strength less than 2,000 psi. In their tests at atmospheric pressure, high strength cement shattered and cracked when perforated. Thus, the optimum cement strength was based on the appearance of neat and gel cement after perforating. In 1953, Clark showed a relation between cement strength and fluid shutoff.' He concluded that a 500 psi compressive strength is required for good fluid shutoff and that maximum bonding ability is developed at approximately 1,000 psi compressive strength. In 1964, Bell and Shore invalidated most of the conclu sions by the previous authors when they demonstrated that atmospheric pressure tests cannot be used to determine casing deformation and damage that will result from perforating under down-hole conditions.' They showed that the higher the hydrostatic pressure, the more restricted will be the expansion of gases generated by the charge. Less casing deformation and damage occurs under down-hole conditions than at atmospheric pressure. In recent work, Bearden et al. reported that jet perforating at surface pressure with the hollow carrier gun caused the cement sheath to shatter and crack.' The perforating, however, did not seriously affect the pressure required to leak past the casing cement bond. Only three cementing mixtures were tested, and presumably they had strengths in excess of 2.000 psi. Bearden et al. also reported that the hydraulic bonding strength increased as the compressive strength increased. Their hydraulic test showed that approximately 1,000 psi pressure is sufficient to break the casing cement bond for a well aged neat Portland cement sheath. Unfortunately, the tests were not run with a confining pressure, so Bearden et al. were merely measuring the strength of their outer 8%-in. casing. In our investigation, we measured the hydraulic bond strength of cement to pipe under a confining pressure and found that the bond strength was not limited to 1,000 psi. Cement Bond The bond strength is a good criterion for measuring the effectiveness of cement in performing its main function, that of preventing interzonal communication of fluids behind the casing. Measuring bond strength after perforating should be a good quantitative method of determining optimum cement properties, and should be a better method than that used by previous investigators,11 ' who simply observed the appearance of the cement after perforating.

Jan 1, 1969

By Hobart M. Kraner, E. B. Snyder

THIS paper shows that volume stability, low porosity and decreased pyroplasticity are desirable for blast-furnace linings, particularly for the hearth. It shows further that a hot load test is a valuable means of testing the fusion or softening behavior of a refractory at operating temperatures. The effect of carbon monoxide on commercial blast-furnace refractories in their as-received condition and after refiring is reported, showing that many commercial blast-furnace refractories disintegrate badly but that refiring decreases the effect and certain special refractories are now available which are almost free of the tendency. FACTORS AFFECTING CHOICE OF REFRACTORIES If one were to depend entirely upon experience or trial in the selection of clay refractories, the solution of a problem would be a slow process. Furnace campaigns are so long and attended by so many variables that it is difficult to draw fine distinctions within a reasonable period of time in regard to the quality of refractories used. It could be said, of course, that if service results do not yield the proper information for intelligent choice, there is no difference in the quality of brick being considered, but this is not necessarily true. Conventional ceramic tests are designed to give the ceramic engineer information as to the refractoriness and firing temperature, which he in turn interprets in terms of volume stability, ability to withstand load at high temperature (pyroplasticity), permeability, chemical stability and resistance to the action of slag. In most refractory applications several of these factors are involved. In a particular instance, one requirement may be predominant, while in others some other factors may be of primary importance. In this country, clay refractories are generally made from mixtures of plastic and flint fire clays. The process of firing a clay refractory is one of slowly melting the constituents, and during this operation its porosity is gradually reduced. The process is arrested, of course, in its incipient stages and the progress is determined by measuring slight changes in. porosity, volume, bulk gravity, etc., that have taken place. Often the temperatures to which clay refractories are exposed in service are higher than those employed in their firing. However, if the manufacturer were to fire them at such high temperatures the brick would distort. Therefore it would be difficult for the manufacturer to fire all of his clay refractories to temperatures . at which they are to be used, although in many cases it would be desirable from the user's point of view if he would do so. The porosity of clay refractories decreases by firing, to a minimum limit, after which a further increase in the temperature causes expansion in certain clay constituents and bloating in others. -Both may occur in the same refractory containing two such clays.

Jan 1, 1944