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By J. D. Milburn, H. J. Hill

In quantitative interpretation of electrical logs the presence of clay minerals introduces an additional variable which further complicates an already complex problern. Although recognizing the difficulties introduced as a result of the heterogeneity of natural sediments and despite the present incomplete state of knowledge regarding electrochemical behavior of shales, dissemirzated clay minerals and concentrated electrolytes, it was felt that useful empirical correlations might be obtained from experimental investigation. Six typical sandstone formations, having a wide variety of petrophysical properties, were selected for the study. Approximately 45 samples from each formation were selected to satisfactorily represent the range of pore size distribution within the particular formation, As a matter of general interest, four limestone formations were also included in the investigation. Previously proposed equations relating to resistivity, SP and interrelationship of the two phenomena have, where possible, been tested with data obtained in this investigation. These equations do not satisfactorily describe experimental behavior of samples through all degrees of shaliness or throughout the range of brine solution resistivities normally encountered in logging practice. An empirical equation has been developed which quantitatively relates formation resistivity factor to satirrnting solution resistivity, porosity, and "effective clay content." This relation is indicated to be uniformly applicable to clean or shaly reservoir rocks. It is shown that both the SP and resistivity phenomena of shaly samples are related to the sample cation exchange capacity per unit pore volume. The independent chemical determination of this parameter is thus a means of determining the "effective clay content" of samples. Some implications regarding theory and electric log interpretation of shaly sands are discussed. INTRODUCTION The use of electrical resistivity logs as a means for estimating formation porosity is based upon the original work of Archie1. It was shown by empirical methods that the resistivity of a rock, when 100 per cent saturated with brine solution, could be related to rock porosity through the equation, F = Ro/ RW = f-m.......(1) where F, the formation resistivity factor, is defined as the ratio of the resistivity of the 100 per cent water saturated rock, Ro, to the saturating solution resistivity, Rw; f is the ratio of pore volume to bulk volume; and m is the slope of the average line when the data are plotted on log-log paper. This relation was established for relatively shale-free formations containing water having high salt concentrations, and under these conditions F may be considered constant for a given rock sample. Applications of Eq. 1 to interpretation of logs of shale-free formations has been quite successful when satisfactory formation water resistivity data could be obtained. The most readily available means of estimating formation water resistivity is the self-potential log. Conventional methods of SP log interpretation involve correct.

Jan 1, 1957

President-Mrs John R C Mann, 90 Edgemont Road, Scarsdale, N Y First Vice-President-Mrs C P Pollock, 27 Dante Street, Larchmont, N Y. Second Vice-President-Mrs Mendum B Littlefield, 40 Lincoln Street, Larchmont, N Y Third Vice-President-Mrs J B Cunningham, 236 East 2nd St , Tucson, Ariz Fourth Vice-President-Mrs Theodore Loftus, 410 Cowles St, Fairbanks, Alaska Fifth Vice-President-Mrs George L Craig, 109 Calumet Avenue, Calu¬met, Mich Recording Secretary-Mrs Arnold H Miller, 601 West 115th St, New York 25, N Y Assistant Recording Secretary-Mrs R J Mechin, 66 East 79th St, New York 21, N Y Corresponding Secretary-Mrs John A Poulin, 4 East 70th St , New York 21, N Y Treasurer-Mrs Robert W Rowen, 29 West 39th Street, Room 914, New York 18, N Y Assistant Treasurer-Mrs Samuel H Dolbear, 1000 Park Avenue, New York 28, N Y Assistant Treasurer-Mrs Roger H Sherman, 8 Roman Avenue, Forest Hills Gardens 75, N Y.

Jan 1, 1957

By H. W. Mead, C. E. Birchenall

SELF-DIFFUSION of iron in austenite is a process which may play a significant role in some of the practically important reactions which occur in solid irons and steels. It also provides a system in which the interaction of vacancies on substitutional sites and atoms in interstitial positions may be investigated. For both purposes, accurate values of the diffusivities are required. Two sets of previous measurements exist, each containing features which require checking. In the course of an investigation to determine the rate of diffusion of iron in certain steels, Garwick and Rosenqvist' measured the self-diffusion coefficient of iron in a 0.10 pct* C steel and obtained a dicated that while at lower temperatures D increased with increasing carbon content, at the higher temperatures it first increased and then decreased. At the same time the activation energy decreased linearly from a value of 69,000 cal per g-atom for pure iron to 33,000 cal per g-atom at 1.06 pct C. This rapid decrease in activation energy implies that iron at higher temperatures within the austenite range would diffuse more slowly in high carbon steels than in steels of lower carbon content. Experimental Procedure The radioactive iron used in this work was obtained from Oak Ridge National Laboratory. The unit consisted of about 1 microcurie each of Fe7 and Fe It was allowed to decay for two years. At the end of this time most of the Fe with a half-life of 46.3 days, had decayed, while most of the original Fe(half-life 2.91 years) still remained. The iron as chloride was extracted into an ether layer, using the method of Ashley and M~rray. After evaporation of the ether the iron chloride was dissolved in 250 ml of aqueous solution containing 2.4 gpl Fe. The compositions of the steels used are listed in Table I. Disks of ¾ in. diam and about ¼ in. thick were machined from these steels for use in diffusion couples. The disks were surface ground on both sides to ensure parallel opposite faces. One face of each disk was polished through 000 emery paper. Half of the prepared disks were plated with radioactive iron. For this, 1 ml of the radioactive iron

Jan 1, 1957

Jan 1, 1957

By Murray F. Hawkins

Horner1 and van Everdingen8 ave shown that the pressure drop within the wellbore, as a result of having produced the well at a constant rate q for time t, where t is sufficiently large, is: van Everdingen observed that better agreement between theory and well performance can be obtained if, instead of assuming the permeability is kc everywhere about the well, it is assumed the permeability near the well-bore is substantially reduced as a result of drilling, completion and/or production practices. In order to account for the additional pressure drop he introduced the dimensionless quantity S, the skin effect factor, so that Eq. 1 becomes: Eq. 2 might have also been obtained as follows. Assume a zone of altered permeability k, exists about the well out to a radius r and beyond that the unaltered, external permeability k. The additional pressure drop required to overcome this skin of reduced permeability may be calculated with sufficient accuracy using the incompressible flow equation; for Browns-combe and Collins1 have shown almost no difference between compressible and incompressible steady-state flow, in the vicinity of the wellbore, and the small volume of fluid in the vicinity of the wellbore makes unsteady-state mechanics unnecessary. Then. The sign of this skin pressure drop will be positive or negative depending upon whether the altered permeability k, is smaller or larger, respectively, than the external permeability k... Adding the pressure drop of Eq. 3 to Eq. 1 to find the total pressure drop: Comparing Eq. 4 with Eq. 3 it is seen that the skin effect may be defined by: be determined from pressure build-up tests1,3,4,5,6,7,8 The average permeability kavg including the altered and external permeabilities, can be determined from PI tests, and may be defined approximately on the basis of steady-state flow, as was done by Thomas' in defining the damage factor, by: The productivity ratio is the ratio of the average to the external permeability, kavg/ke or This equation shows that the productivity ratio and the skin effect are not uniquely related, because of the uncertainty in the drainage radius, and also, in many instances, the wellbore radius. Fortunately, they enter in the logarithm. The curves of Fig. I are plots of Eq. 8 for values from 100 to 50,000. The points represent the skin effects and corresponding productivity ratios from a large number of well tests, taken from Fig. 15 of Ref. 5 or Fig. 13 of Ref. 9. While some of the data

Jan 1, 1957

By Nicholas J. Grant, H. C. Chang

Microscopic observations during creep tests were made on AI-20 pet Zn, 80 pet Ni-20 pet Cr, and 25 and 3S aluminum specimens. All these materials failed in an inter-crystalline manner under certain stress and temperature conditions. Particular atten-tion was given to the initiation and propagation of intercrystalline cracks in coarsegrained AI-20 pct Zn specimens. The geometry of the grains and grain boundaries in these specimens was known before the tests. On the basis of the observations and a knowledge of the interaction between grains and grain boundaries, a mechanism of intercrystalline fracture and propagation of the fracture has been proposed. METAL, and alloy fracture occurs essentially in two ways: transcrystalline and intemrystalline. In the past most of the work done in this field was centered on the determination of stress criteria for fracture. The specimens used for these studies were tested under varying conditions of stress state, temperature, and strain rate. Unfortunately, very little attention was given to the initiation and propagation of the fracture, whereas the nature of fracture was examined closely only after failure. Several extensive reviews of these studies have been published by Orowan, Smith, Barrett, and Petch.1, 4 It is well known that a material which exhibits a ductile and transcrystalline fracture can be made to exhibit a brittle and intercrystalline fracture by modifying its composition and by heat treatment. This modification may or may not result in microscopically observable precipitation in the grain boundaries." In the creep of any one alloy the transition of transcrystalline to intercrystalline fracture is a function of stress, strain rate, and temperature." The tendency for intercrystalline fracture to occur increases as the strain rate decreases and the testing temperature increases. Extensive work on high purity aluminum (99.995 pet) under creep conditions showed the importance of the interaction between grains and grain boundaries, and the different responses of grain and grain boundaries to the variables: stress, strain rate, and temperature.7, 8 It was also shown that grain boundary deformation necessarily has to be accommodated in the grains by various deformation means as. for example, fold formation. The type of fracture resulting from the creep of high purity aluminum was invariably found to be transcrystalline. On the other hand, 2S and 3s aluminum were, under certain conditions, found to fracture in an intercrystalline manner." One reason given for this was that the grains could accommodate to a lesser extent the deformation of the grain boundaries.19 It was decided to examine this line of reasoning in greater detail and to investigate the particular interactions between grains and grain boundaries that result in the incidence and progression of inter-ct,ystalline fracture. It is also the purpose of this paper to show where and how intercrystalline cracks start and how they propagate to result in fracture. Several alloys—Al-20 pct Zn, 80 pet Ni-20 pet Cr, 2S and 3s aluminum-— were used for this study, but attention was paid mainly to the behavior of an A1-20 pet Zn alloy, since its general creep behavior has been established." From the results of this study a mechanism of intercrystalline fracture is proposed. Experimental Procedure The experimental procedure was similar to that used in previous work and has been detailed elsewhere.' Two parallel flat surfaces were milled from an originally round specimen, giving a gage portion which was 1x0.09X0.17 in. Some round specimens, 1/4 in. round by 1 in., were also tested. The A1-20 pet Zn specimens. which were annealed at 1030°F for 24 hr, showed two to four grains across the width of the test bar, and most of the grains occupied the whole thickness of the specimenu. Before some of the specimens were subjected to creep, the grain arrangement was mapped out in a development drawing, Fig. 1. The initiation and

Jan 1, 1957

By J. A. Morgan

IN the art of roasting sulfides it is well known that the lower the temperature and the higher the pressure of SO, the larger will be the amount of sulfate present in the product. However, the mechanism of sulfate formation is not generally understood. The following experiment" demonstrates in a direct way that, in the roasting of Cu2S, the sulfate forms from the reaction of Cu2O, formed by the oxidation of Cu2s, with gaseous SO, (or SO3) and 0,. Thus, the sulfate does not form at the sulfide surface. The reaction at the sulfide surface is the same whether or not sulfate is formed. Using an indirect method, Ong, Fassell, and Wadsworth' infer that sulfate forms after oxidation, during the roasting of sphalerite, agreeing with the observations of this paper. The method presented here of demonstrating that sulfate forms after formation of Cu2O is to roast a sample of Cu2S and then to locate and identify the phases formed.' A solid cube of cuprous sulfide, made by melting Fisher reagent grade Cu2S powder and measuring about 1.5 cm on edge, was placed on a Nichrome wire grid suspended over the top of an Alundum combustion boat. The assembly was placed in a tube furnace at 600°C and oxygen gas, flowing at 0.60 liters per min, was passed around the specimen for 24 hr. The furnace tube diameter was 1.5 in. The partially roasted sample was removed from the furnace and impregnated with resin No. BR 0014, obtained from the Palmer Products Co., and the impregnated sample was then mounted in Lucite. A cross section was obtained by grinding and the surface was prepared by the following steps: 1) grinding—60 grit, 3M disk, dry; 2) preliminary polishing —60 through 600 grit, 3M disk, dry; 3) polishing— 8 µ diamond putty, silk cloth; and 4) final polishing —1evigated magnesia in isopropyl alcohol, Selvyt cloth. The color micrograph of the polished surface is shown in Fig. 1. The layers present in the micrograph are given along the side. The comwositions of the various layers were established by Debye-Scherrer patterns. From this evidence the following sequence of reactions which occur in the roasting of Cu2S is inferred: 1) The oxidation of Cu2S occurs with oxygen which has been transported through the oxide-sulfate layer by either gaseous or solid state diffu- sion. The products of this reaction at the Cu2S surface are Cu2O and SO,. 2) The SO, diffuses out through the pores in the Cu2O and finally reaches a position in the Cu2O where the oxygen pressure and the SO, pressure have values such that the thermodynamic conditions for the formation of CuSO4 are fulfilled. Then, the mixture of SO2, SO3, and oxygen reacts with the Cu2O to form CuSO1. 3) The CuSO, decomposes by the evolution of SO,, or SO, and O2, to form the basic sulfate. This is reasonable, since the SO, gradient will decrease toward the oxygen gas phase from the CuSO4 layer. 4) For this same reason the basic sulfate will decompose to form CuO. The above sequence of events is based on the assumption that diffusion through the oxide and sulfate layers, rather than the reaction at the sulfide-oxide interface, is rate-determining. This assumption is supported by the observation that these oxide and sulfate layers combined are almost nonperme-able to the flow of gases through them. Acknowledgments This research was supported by the U. S. Air Force, through the Office of Scientific Research of the Air Research and Development Command. The authors wish to acknowledge the helpful suggestions of Ralph Wells of the Applied Research and Developmeit Laboratory, U. S. Steel Corp. References E. A. Peretti: A New Method for Studying the Mechanism of Roasting Reactions. Discussions Faraday Soc. (1948) 4, p. 174. - J. N. Ong, Jr., M. E. Wadsworth, and W. M. Fassell. Jr.: Kinetic Study of the Oxidation of Sphalerite. Trans. AIME (1956) '206, pp. 257-263; Journal OF Metals (February 1956).

Jan 1, 1957

By L. L. Seigle

Free energies, heats, and entropies of mixing of solid Fe-Au alloys have been measured by the galvanic cell method between 800° and 900°C. A positive deviation from Raoult's law and a large excess entropy of mixing were observed, both attributable to lattice distortion caused by the disparity in component atom sizes. Since the terminal solid solutortiontions are not regular, thermodynamic properties computed from the location of the mis-cibility gap do not agree well with measured quantities. The electromotive force data suggest some changes in the existing Fe-Au phase diagram. ALTHOUGH a considerable amount of information has been accumulated about the thermodynamic properties of metal solid solutions which exhibit negative deviation from Raoult's law, particularly those in which ordering occurs, relatively few experimental measurements have been made on solutions with positive deviation. This is due to the infrequency of broad homogeneous regions suitable for experimental measurement in solutions of this type, since any marked positive deviations from ideality lead to restricted solubility and the formation of miscibility gaps. Thermodynamic data reported in the literature for such systems have usually been calculated from the location of the miscibility gap boundaries under the assumption that the entropies of mixing are ideal, i.e., the terminal solutions are regular.' One of the few binary systems with both positive deviation and a wide homogeneous range in the solid is the Ni-Au system. A recent investigation of solid Ni-Au alloys' revealed that the entropies of mixing were much larger than ideal and consequently thermal data computed from the phase boundaries assuming regular solutions were seriously in error. Theoretical considerations put forward by Zener indicated that high entropy values should generally be associated with systems possessing a miscibility gap in the solid, when this is due to differences in the size of component atoms. These facts suggest that the regular solution assumption is a poor approximation for many solid solutions with positive deviation and that reliable thermodynamic data generally cannot be obtained by conventional methods from the location of miscibility gap boundaries. The Fe-Au system, Fig. 1, resembles the Ni-Au system in certain respects. The presence of a miscibility gap in the solid indicates a large positive deviation from ideality, but there is nevertheless an extensive single phase region suitable for experimental measurement. The following investigation of solid Fe-Au alloys was carried out in order to obtain additional data on the thermodynamic properties of metal solid solutions with positive deviation from Raoult's law and to further compare thermodynamic data computed from miscibility gap boundaries with those measured experimentally. Experimental Method The thermodynamic properties were derived from measurements of the potential developed between pure solid iron and Fe-Au alloys in a high temperature galvanic cell. The experimental apparatus and technique were the same as those used for the Ni-Au alloys and described in a previous report.' Cell electrodes were 1/16 in. diam rods swaged from chill-cast ingots and annealed for one week at 850°C. The alloys were prepared by melting fine gold granules under argon with pure iron obtained from the National Research Co. The cell electrolyte was

Jan 1, 1957

By J. P. Zannaras

If we assume that testing of the model started at time t1, that time t2 was the instant at which the elastic limit of the material was passed at the points of the maximum stress, and that at time t3 the failure of the model was completed as shown in the typical photograph (Fig. I), then actually the photograph shows the final results of what took place between time t2 and t3. By the principle of similitude all conclusions drawn from the behavior of the model were applicable and valid for actual mine roofs up to the time t2 after time t2 motions and friction came into play during the destruction of the model. The events between t2 and t3 and the photograph itself are not representative of the events expected in an actual mine roof unless corrections imposed by the principle of similitude are made. It can therefore be stated that all conclusions and observations of the author from the photographs are applicable only to his small-scale experiments and not to actual mine roofs. Without investigation of the true stresses or the combined maximum stress induced in the beds it has been assumed by the author that failure occurred solely due to bending stress caused by loading of the beds. (The author states that D was taken to be the theoretical strain given by elementary beam theory.) Fig. 1 shows that the beds were clamped together. This clamping was necessary to prevent slipping of the beds due to the horizontal shear. However, this clamping caused an uncontrolled and undertermined com-pressive stress S at the end of the beds, and this com-pressive stress caused a true tensile stress ?S (? PoiS-son ratio). This true tensile stress combined with the tensile stress produced at the end of the beds due to loading (fixed beam uniformly loaded), and the horizontal shear which is maximum at the end appears to be the most probable maximum stress produced in the beds. It is therefore evident that the author in performing this experiment has introduced stresses in the model not existing or dissimilar to actual mine roofs, and therefore his conclusions may be applicable to his small-scale experiments but inapplicable to actual mine roofs. Louis A. Panek (author's reply)—The discusser's difficulty is related to mechanics of materials rather than similitude. The effect of time did not enter into the tests in any way, being simply excluded from consideration in this study, because all quantitative results entering into the design equations are based on measured (between time t1 and time t2) bending strains that are well below the breaking strain (i.e., in the elastic range) for the model material. Time does not become a significant factor until the rock stress reaches 80 to 90 pct of the breaking stress." The objective of this investigation was not to predict that bolted roof will fail after time t, but was instead to develop a safe roof, that is, roof in which the bending strain is much less than (say less than 50 pct of) the breaking strain. The models tested to failure had no direct bearing on the design equations. Although for some rocks time may influence the magnitude of stress or strain at which fracture occurs, breaking stress or breaking strain values were not employed for any purpose in this investigation. Tests to failure were made only to obtain additional evidence regarding the behavior of the bolted laminae' as evinced by the locations of the cracks. As stated in the last paragraph of the paper, if one wishes to predict the time or stress conditions for which the roof will fail, additional information is required. The reason for clamping the laminae is to make them behave liked clamped beams, which closely approximate the clamped-plate condition of the actual mine roof beds (Ref. 5, p. 1; Ref. 6). The writer has previously demonstrated that the bending stresses induced by centrifugal loading in a clamped model beam are in agreement with those predicted by theory;' hence clamping has no significant effect on the bending ,trains measured during a test. Moreover, actual ,in, roof beds are likewise subject to a clamping effect due to weight of superincumbent strata carried by the pillars or ribs on each side of the opening. It is emphasized that this study was restricted to evaluating only the reinforcing effect produced by the bolts. Procedures employed in the experiments and in the data analysis were such as to deliberately exclude the effects of other factors. The objections offered are therefore invalid,

Jan 1, 1957

By W. E. Bron, E. S. Machlin

GRAIN boundary migration in V-shaped thin specimens of high purity silver was studied. Each specimen contained two crystals having the relative orientation: (111)A/(111)B; (ll0)A/(101)B. The boundary between these two crystals varied between a continuous curved and an alternating two plane interface. The plane interfaces were oriented parallel to (101)A/(011B) and (121)A/(211)B. Traces of these planes are shown in Fig. 1. Evidently the two plane interface, although of higher area, comprises lower total interface energy than the average curved boundary it replaced. The plane boundaries were found to move at 650 °C to consume the broad segment of the V opposite to the direction of interface area and energy decrease. On investigation, using the thermal etching technique of Hendrickson and Machlin,1 it was found that the outer grain contained 8.3x108 more dislocations per cm" than the grain at the apex of the V. Consequently, the boundary moved to decrease the strain energy associated with the difference in dislocation density across the boundary. The rates of motion of specific {110} and {112} boundaries were measured during interrupted anneals at 650°C by referring the position of the boundaries to each other and a fiducial line on the specimen surface. The measured rates of motion are 0.075 and 0.025 mm per hr for the {110} and {112} boundaries, respectively. Plots of grain boundary motion vs time of annealing show straight lines with little deviation of data points from these lines.

Jan 1, 1957

By Jack L. Taylor

As expected from similar crystal structures and favorable atomic size factors, titanium, vanadium, and molybdenum are completely soluble in one another above the transformation temperature of titanium. The fl phase parameters of the continuous solid solution are shown graphically. Limiting compositions for retained fl phase have been determined. VANADIUM and molybdenum both have body-centered-cubic structures at all temperatures and, from the atomic diameter comparison factor, 3.9 pct, would be expected to form a complete series of solid solutions. The existence of complete solubility has been confirmed by work' at the Jet Propulsion Laboratory. Furthermore, vanadium and molybdenum have favorable atomic size factors to form complete binary solid solutions with the B phase, high temperature form of titanium, which also has body-centered-cubic structure. Pietro-kowsky and Duwez' and Hansen et al." have established the existence of the complete series of solutions in these binary systems. It would be logical, therefore, to expect that p-titanium, vanadium, and molybdenum would be completely soluble in one

Jan 1, 1957

By D. Moskowitz

IN the course of a general investigation of boride systems, sponsored by the Office of Naval Research, various vanadium boride powders of relatively good purity were prepared which could be used for a determination of the phases present. The X-ray pattern of one of these lots showed, in addition to the known VB1 and VB22 phases, an additional phase, almost certainly of composition V3B4, isomorphous with Cr3B4, Cb3B4, Ta3B4, and Mn3B,. Its pattern fitted in well with the indices worked out by Kiessling for Mr3B4.3 The unit cell for this new compound is orthorhombic, with the dimensions a = 3.030A, b = 13.18A, c = 2.986A7 V=119.2A.' Table I lists the X-ray diffraction data for V.3,.

Jan 1, 1957

ON THIS page is a photograph of a machine that has played a key role in the recent history of Kennecott's Ray mine, situated in the Mineral Creek District, Pinal County, Arizona. It is a huge, rugged, Diesel-powered, rubber-tired truck, having a capacity for carrying fifty tons of ore. It has, to a substantial degree, revolutionized the business of moving broken rock by cutting down both maintenance and operating costs. From 1911 until the end of 1954 Ray had produced 79,000,- 000 tons of ore by underground block-caving. However, in 1947 [ ]

Jan 1, 1957

Executive Committee, Board of Directors Grover J Holt, Chairman, C E Reistle, Jr , Vice-Chairman, A W Thornton, A B Kinzel, J L Gillson Finance Committee, Board of Directors Andrew Fletcher, Chairman, R B Caples, Gail F Moulton Investments Erle Daveler, '60, Chairman, Henry Krumb, '59, John Warren, '60, C R Dod¬son, ex off as Treasurer, Andrew Fletcher, ex off as Chairman, Finance Committee Endowment Andrew Fletcher, Chairman, N G Alford, E V Daveler, W J Coulter, J V N Dorr, R B Gilmore, J B Haffner, 0 H Johnson, D H McLaughlin, J R McMillan, L F Reinartz, C E Weed, Wilfred Sykes, J R Suman Honorary Memberships L F Reinartz, Chairman, C E Reistle, Jr , H DeWitt Smith, ex off as Past Presidents of AIMS, Grover J Holt, ex off as President AIMS, P D Merica, '59, Henry Krumb, '58, M L Haider, '60, D H McLaughlin, '61

Jan 1, 1957

By W. C. Winegard, W. J. Bratina

Internal friction characteristics and temperature dependence of the torsion modulus for iodide zirconium containing 2.4 pct Hf were investigated, using a low frequency pendulum technique. The internal friction curve consists of a background which increases as the temperature increases, a maximum at 860°C apparently a background due to the al-lotropic transformation, a maximum due to grain boundary relaxation with an associated heat of activation of 58,000 cal per mol, and an anomaly below 350°C which may be associated with a precipitation perphenomenon, Oxygen in below small amounts reduces the grain boundary maximum substantially. The variation of the torsion modulus at 20°C was found to be 3450 Kg per mm2 for the zirconium used in the present work. IT is well known that small amounts of certain solutes materially affect the ductility of zirconium. Lely and Hamburger,&apos; as early as 1914, found that high purity zirconium exhibited a remarkable ductility, while Fast&apos; has shown that oxygen and nitrogen can cause substantia1 embrittlement. Treco" has recently demonstrated that the ductility decreases sharply with the oxygen content, and that 2 atomic pct O2 embrittles zirconium to such an extent that cold working is impossible. The marked decrease in ductility is difficult to understand in view of the fact that Domagala and McPherson4 report the solid solubility of oxygen in zirconium to be 29 atomic pct at 500 °C. Another metal which behaves much the same as zirconium in this respect is titanium. Pratt et al." investigated the internal friction characteristics of titanium and the effect of oxygen on the internal friction values. It is evident that internal friction measurements are of value for studying grain boundary segregation, as shown by Pratt et al. for oxygen in titanium, by Pearson for oxygen in copper, and by Maringer and Schwope for oxygen in molybdenum. With this in view, the internal friction characteristics of zirconium and the qualitative effect of oxygen on the grain boundary relaxation phenomenon were investigated. Materials and Experimental Procedure The zirconium used in the present work was supplied by the Foote Mineral Co. in the form of wire 0.05 in. diam. The analysis supplied by the manufacturer indicates the amount of hafnium as 2.4 pct, less than 0.01 pct O less than 0.01 pct N,, less than 0.02 pct H,, and less than 0.001 pct C. Additional spectro-graphic analysis indicates the other main impurities as follows: 0.01 pct Fe, 0.05 pct Si, 0.008 pct Cu, <0.005 pct W, <0.001 pct Al, <0.05 pct Mg, <0.001 pct Ni, <0.02 pct Ca, and <0.01 pct Ti. Microscopic examination of the material in the as received condition revealed very fine grains with numerous twins. Specimens were annealed either in situ in the internal friction apparatus or in evacuated silica tubes in an auxiliary furnace. When the specimens were annealed in the auxiliary furnace, they were wrapped in identical zirconium wire to prevent contamination by the container. Metallographic sections were taken in all cases. Some were taken from the specimens used for internal friction measurements after completion of the experiments, while others were taken from control specimens at intermediate stages of the experiments. lnternal friction values were obtained by measuring the free decay of a low frequency torsion pendulum (1 cycle per sec), the suspension of which was

Jan 1, 1957

By R. A. Bloom, John Birtalan

CONSIDERABLE interest has been shown in recent years toward determining the crystal structure, mode of formation, and chemical composition of the x phase, designated as such by Andrews,&apos; who was the first to establish its presence in Fe-Cr- Ni-Mo alloys . Later work2 by the same author has shown that the occurrence of x depends on the presence of some molybdenum in the alloy. The phase, which appears to be identical or very similar to a manganese, has a body-centered-cubic structure and is closely related to s phase. Koh observed a similarity in composition between x and s and speculated as to whether x might be an ordered structure of u which is known to have a tetragonal crystal

Jan 1, 1957

By P. F. Allen

WITH capacity of 51,000 tpd, the Morenci concentrator produces approximately 49,000 tons of tailing for final deposition. Disposal involves distribution of thickened tailing to dams in such a manner that solids can be used for dam construction and water can be impounded for reclamation. During early operation, although tonnage treated was lower, it was necessary to use orthodox disposal practices in the areas available for tailing. Trestles mounted on a series of dams, constructed of borrow material, carried the pipelines from which tailing were spigoted behind the dams. When adequate disposal areas were finally established, it became desirable to look for more efficient methods. The idea of placing the distribution pipe or manifold directly on the crest of the dam was advanced in 1945. After a period of testing, that procedure in modified form replaced the older trestle arrangement. Marked economies resulted, and time required to prepare dams for succeeding storage cycles was greatly reduced. The tailing disposal area for the Morenci concentrator lies south and southwest of the concentrator building. Ample storage space is available. A wide valley contains three sharply defined ravines lying on an average slope of 4 pct. The more central of these ravines, and the largest of the three, is known as Morenci canyon, which provides substantially more tailing storage area than the other two. Stargo canyon lies to the west; the other is appropriately named East canyon. Total area of the tailing disposal site is nearly 31/4 sq miles, or about 2000 acres. The storage area in use was somewhat more than 850 acres at the end of 1954, or 16 acres per 1000 tons of tailing to be stored daily. At the present time none of the east side dams are in regular use but they are available in emergency. There are five dams on the west side (in Morenci and Stargo canyons) as well as two auxiliary dams adjacent to No. 4 West and No. 5 West. This has made it possible to concentrate men and equipment in a smaller area with consequent savings in both manpower and machinery. Tailing Thickening: Tailing from the flotation process reaches the thickeners with a solid content of about 18 pct. The launder carrying this pulp is subdivided at a central point into seven launders carrying a proportional share to each of seven tailing thickeners, which are located in Morenci canyon close to the concentrator. Five of these thickeners are 300 ft diam and two are 325 ft diam. Thickeners are of the peripheral traction type and rakes travel at the rate of one revolution in 37 to 39 min. The entire installation provides 500,000 sq ft of settling area, or approximately 101/2 sq ft per ton of tailing to be thickened daily.

Jan 1, 1957

By L. D. Wooddy, Robert Moscrip

The simultaneous solution of the volumerric balance and the unsteady-state equation has been used for several years to make performance calculations for combination drive reservoirs. This method makes possible the calculation of volumetric changes of fluids in the gas cap, oil zone, and aquifer which occur as a result of withdrawals and reservoir pressure changes. It does not provide a means for the determination of reservoir fluid distribution changes corresponding to these vollrmetric changes. A knowledge of the fluid saturation distribution in the reservoir at various stages of depletion is important for the determination of the efficiency of gas and water as oil-displacement media and, therefore, for the reliable predicrion of ultimate oil recovery. To provide this knowledge, the displacement equations are solved simultaneously with the volumetric balance and unsteady-state equations. The described calculation procedure has been used satisfactorily to analyze the past performance and to predict the future behavior of combination drive reservoirs under both primary and pressure-maintenance operations. INTRODUCTION The three basic mechanisms by which oil is displaced from a reservoir are: (1) dissolved gas drive—the displacement of oil by the expansion of liberated solution gas, (2) water drive—the displacement of oil by water which enters the oil zone from the aquifer, and (3) gas cap drive—the displacement of oil by gas which ex- pands into the oil zone from the gas cap. The action of gravitational forces may be effective in increasing the efficiency of the basic drive mechanisms. Gravitational forces favor the segregation both of gas and oil and of oil and water, thus tending to shorten the transition zone between oil and displacing fluids. Most reservoirs produce under the influence of a combination of these drives and are designated "combination drive reservoirs". Fig. 1 is a cross section of a typical combination drive reservoir. A calculation procedure for analyzing the performance of combination drive reservoirs has been developed by combining the displacement equations&apos; with the volumetric balance equation&apos; and the unsteady-state equations. The pressure-production performance and the positions of the gas-oil and oil-water contacts are calculated for several stages of reservoir depletion by solving these equations simultaneously, thus affording a basis for: 1. Determining instantaneous and ultimate oil, gas, and water production under various operating conditions. 2. &apos;Establishing a maximum efficient rate of production, 3. Determining the advantages of pressure maintenance and unitization, and 4. Designing surface installations necessary for primarv and pressure-maintenance operations. DEFINITIONS The calculation procedure for combination drive res-

Jan 1, 1957

By J. T. Dewan

An experimental setup is described whereby the responses of Neutron logging instruments have been determined opposite formations of different porosities and under various borehole conditions. The results of these tests are presented in several charts which show how the Neutron log is affected by the following factors: hole diameter, casing, cement, salinity and weight of drilling mud, and position of logging tool with respect to the wall of the hole. The responses in the case of empty holes are also shown. A chart is furthermore presented which shows the shapes of the Neutron log, as a function of logging speed and time constant, at the boundaries between two formations with different porosities. These were derived mathematically using as a basis laboratory determination of the shape of the curve under static conditions, i.e. at very low logging speed. Corrections for the readings made opposite thin beds are given by these computations. The correction is found negligible under usual logging conditions for beds thicker than about 4 ft. INTRODUCTION The Neutron log is used in borehole surveys both for the delineation of porous formations and for the quantitative estimation of their porosities.1,2,3,4,5 It is common practice to calibrate the response of the Neutron log in terms of porosity values for each given geological unit by means of empirical comparisons between the deflections of the neutron curve and the porosity values given by the core analysis in a sufficient number of wells. Usually, the plots of the porosity values vs Neutron log deflections show a definite trend. It is therefore possible to trace an average line across the plotted points. This average line constitutes a calibration curve which can be used to evaluate the porosities from the Neutron logs in the other wells drilled in the same region. Futhermore, when the porosity values are plotted on a logarithmic scale and the Neutron log deflections on a linear scale, the calibration curve is practically a straight line. Accordingly the calibration curves are often determined by simply tracing a straight line between two points corresponding to two widely different porosities. Different choices are made for these two points, depending on local conditions. For example, one point will be defined by plotting the deflection of the Neutron curve opposite a formation known to be very tight, for which an average porosity value of 1 or 2 per cent is assumed. The other point may correspond to shale sections, to which a porosity of around 40 per cent is ascribed. The information provided by the eletrical logs — in particular the Laterolog, Limestone log or Micro-Latero-log — is also very often a help in the calibration of the Neutron logs. Empirical approaches such as these make possible the derivation of fairly reliable porosity values from the Neutron logs in many cases, at least in open holes and in essentially clean formations. There are, however, several causes of uncertainty which may sometimes entail appreciable errors. On the one hand, the Neutron log readings are influenced by the borehole conditions: hole diameter, presence or absence of casing and cement, presence or absence of drilling mud, characteristics of the mud, and position of the logging instrument with respect to the wall of the hole. The amplitudes of the curves opposite thin beds are furthermore atfected by the bed thickness,

Jan 1, 1957

By Homer N. Mead

This report develops equations for decline curve analysis based upon the premise that the rate of change of the reciprocal of decline for succeeding time intervals is constant when the reservoir is produced under a fixed set of conditions. A method is shown for predicting maximum production rate against cumulative production for any reservoir. A method is also presented for predicting future production rate by an analysis of past production performance after decline has been esrahlished. INTRODUCTION No significant contribution to the analysis of decline curves by the loss-ratio method has been made since J. J. Arps paper1. The concept of loss-ratio that was developed by Arps and his contemporaries has been redefined in another way and the concept of instantaneous loss-ratio at time zero has been added. In the mathematical developmerit by Arps, production rate was related as a continuous function with time and his equatlons were developed on that basis. In this paper, production is considered to be a series of segments for equal time intervals and equations have been developed based upon these finite differences. It is realized that decline curve analysis is not the answer to all predictions of reservoir behavior. However, as production must decline from an initial maximum rate to zero in any reservoir, if such decline can be expressed as an infinite series, this series should accurately predict production. Decline curve analysis should be considered a valuable tool that may be used in conjunction with predictions of future recoveries by other methods. Various uses of the decline curve method will be discussed in this paper. Equations predicting production rate at any time and cumulative production by exponential and hyperbolic decline will be developed. Characteristic values of b related to various types of drive will be discussed. After that a hypothetical reservoir will be studied and ultimate recovery by natural depletion and pressure maintenance compared, then actual field examples will be shown and discussed. The rate-cumulative curve introduced by H. N. Marshs in 1928 is an important one for use in estimating future production rate and ultimate recovery. This graphical method is the one that is used in conjunction with the equations to be developed for predicting production behavior. EXPONENTIAL DECLINE In exponential decline each succeeding production rate per unit of time is a constant percentage of the production rate just before it. Since (1 — r) is the common ratio, where r is the constant decline rate, this condition may be expressed as a geometrical progression; thus Pn = P (1 - r)n-1 . ......(1) Where r is less than unity, r Since P1 (1 - r)n = Pn+1 P1 - Pn+1 C =P1-Pn+1/r........(2) LOSS-RATIO In this paper the calculation for loss-ratio has been changed from the method presented by Johnson and Bollens2. The first loss-ratio to be calculated is a,; it is the initial production per unit of time after decline has set in divided by the difference between the initial and the second production rate. This loss-ratio is for the first time interval. After b (which is the constant change

Jan 1, 1957