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By Henry Emmett Gross

Two types of decline curves are considered and their applications are discussed. The first is the well-known semilogarithmic decline curve having the rate of production plotted on the logarithmic scale and the time on the horizontal scale. The other curve is the percentage of oil in the fluid versus cumulative production, and it is plotted on Cartesian coordinate paper. These curves are illustrated by carefully and adequately labeled graphs. Where conditions permit application of both types of curves for rationally determining the reserves of a well, both should be applied and the most conservative reserve should be chosen. Formulas are given for determining the economic limits. For a semi-l~~arithmic~decline curve the formula is: A = B X C X D X E X F or B = A/C ? D X E X F A = total monthly operating cost (average of past year), B = economic limit in barrels of oil per day, C = days in an average month = 30.4, D = market price of crude per barrel, E = 1-royalty, F = 1-gross production tax, G = water production in barrels per day at the economic limit, H =per cent oil in fluid at economic limit. The economic limit for a per cent oil in the fluid curve is: H = B/B+G X 100 The semilogarithmic decline curve is treated first. Straight-line extrapolations on semilogarithmic paper follow the compound interest compound discount law, hence the ensuing formulas derived from this law may be used in computing reserves for such extrapolations: [1___1/(1+Y)]

Jan 1, 1939

By R. M. Brick, F. L. Vogel

THE elementary mechanism of deformation in the body-centered cubic metals has been a subject of dispute for many years. If the problem were merely that of designating the crystallographic plane or planes of slip, the solution would have appeared long ago. However, there must be greater differences in the deformation behaviors of the body-centered and face-centered types than the differences in their lattices would suggest. The lines of slip formed on the polished surface of a strained face-centered cubic metal conform to glide over a single plane of the crystal. Slip in body-centered cubic iron, however, is frequently observed as curved and forked lines which could not possibly define a single plane of atoms. This alone is sufficient reason to expect different modes of deformation to operate in the two lattice types. The literature in this field now has generally accepted the proposition that {110), {112), or (1231 planes will act as slip planes in iron. It is essential that the experimental evidence supposedly supporting this proposition be critically examined. Taylor and Elam1 in 1926, using relatively small single crystals, determined the operative slip systems by measurements of the distortion of a grid engraved on the specimens prior to deformation. Their results indicated that shearing had taken place in the close-packed direction on a plane adjacent to or coinciding with the plane of maximum shear which contained the slip direction. This led the authors to propose a theory of noncrystallographic or banal slip. The authors considered an alternate rationalization of banal glide. Slip on two (1101 planes or possibly two {112} planes containing the same <1ll> direction could produce the wavy slip lines. By employing plane segments of varying widths, the integrated plane could take any position in the <111> zone. They rejected this explanation, however, feeling that the preponderance of evidence was against it. Taylor&apos; continued the investigation of the plasticity of the body-centered cubic lattice on ß brass. He reasoned that the resistance to shearing of a given plane in the zone of the slip direction was a function of the angle between the glide plane and the closest (110),: P F=—cose sine cos(X —?) [1] where F is the resistance to shear; P, the axial load at yielding; A, the cross sectional area; e, the angle between slip direction and load axis; x, the angle between plane of maximum shear containing the slip direction and the (101) pole; and ?, the angle between observed glide plane and the (101) pole. Differentiating Eq. 1 and rearranging, dF — = tan(x-?) d? [2] F which expresses the variation of the shear resistance with the angle $. Integrating this equation between the limits 0 and ? yields In F/F0 = ?0?tan(x— ?) d? [3] Here, F, is the resistance to shear of the (110) plane and F is the resistance to shear of a plane $ degrees from the (110). Thus, the variation of shear resistance with $ can be calculated from an experimentally measured x vs $ relationship. Fahrenhorst and Schmid8 sed several methods, none of them involving direct observation, to determine the glide system in ferrite. They determined the variation of critical resolved shear stress with

Jan 1, 1954

By L. D. Jaffe, D. C. Buffum

EARLY papers1-&apos; reported that temper brittleness is influenced by microstructure. This conclusion was based on room temperature impact tests, the inadequacy of which has been pointed out. Pellini and Queneau7 measured impact energy absorption at —80O to +25oC for several microstructures. On the basis of the shift, associated with temper brittleness, in the energy vs testing temperature curve they concluded that tempered martensite is somewhat more susceptible to temper brittleness than is tempered pearlite. The range of temperatures was insufficient to give complete curves covering the transition from tough to brittle behavior, so it is difficult to evaluate quantitatively the shift for the different microstructures. Also, the smaller shift of pearlite might be attributed to its already being temper embrittled at its temperature of formation. Accordingly, blanks 2 3/16 in. long were cut from a heat of SAE 3140 hot rolled steel barstock, 5/8 in. diameter, on which other work has been reported? A set of blanks was austenitized 1 hr at 900°c, water-quenched, tempered 16 hr at 675oC, and water-quenched, giving a microstructure of 100 pct

Jan 1, 1954

By Lucius W. Mayer

The iron-mines of the Ilsede Hütte Co. are at a town called Peine, about 20 miles east of the city of Hanover, on the railroad to Brunswick (Braunschweig). Hanover, the capital of the province, is a military city, of approximately 250,000 inhabitants, and Brunswick, 33 miles to the westward, has half this number. The mines here described are located in a hamlet called Bülten. The Ilsede Hütte Co. operates two mines, 1.5 miles apart, in this district, Gruber Bülten Adenstadt and Gruber Lengede Bodenstadt. It also operates an iron-mine north of Hanover, known as Eiserhaven, and one in the Harz mountains, the Georg Friedrich, at Grauhof. At Bülten a coarse conglomerate, a, Figs. 1 and 2, contains nodules of limonite, cemented together by calcium phosphate. The ore contains Fe, 25 to 45; Mn, 3 to 4; P, 0.6 to 1.4; S, 0.02 to 0.09; and CaCO3, 40 per cent. Directly above the conglomerate is limestone, b, followed by a mixture of clay and sand, c. Below the conglomerate is a hard clay floor, d. The ore-body, from 10 to, 12 km. long, and from 3 to 4 km. wide, has a maximum thickness of 20 m. It clips approximately 10° S.E., and strikes N. 45° E. Diamond-drill prospecting shows that the thickness diminishes to 1 m. as the end of the deposit is approached to the northward. At this point the deposit is 250 m. below the surface. In Fig. 2, the arrow, A, indicates the general direction of the work along the face, a, which is carried forward in a straight line for its entire length. At B, a train is approaching, which has come from the bench-track, shown at G, by a circuitous route, and is dumping the overburden behind the face, in the space left by the excavated rock. Formerly the work at this mine was essentially open-cut, the deposit having a very strong outcrop. Figs. 1 and 2 show also

Sep 1, 1908

By I. H. Warren, E. A. Devuyst

The selective dissolution of pyrolusite (MnO2) in presence of goethite (FeO•OH) in aqueous ammoniacal ammonium carbamate solution has been investigated: various reducing agents were studied, in particular sodium sulfite (Na2SO3,) and hydrazine hydrate (N2H4•H2O). Sodium sulfite was found to be an unsatisfactory reducing agent for both goethite and pyrolusite, for the leaching rate decreased steadily with time to an impractical level because of the limited solubility of the reactions products. Hydrazine hydrate was an effective reducing agent for pyrolusite even at low temperature, whereas goethite required much higher temperatures for any appreciable dissolution. A 1-hr leach at 35°C dissolved 90% of the pyrolusite but only 0.1% of the goethite. An activation energy of 17.0 Kcal per mole was found for the dissolution of pyrolusite with hydrazine. A reaction mechanism for the leaching of pyrolusite with hydrazine is proposed in which a reduction reaction on the surface of the mineral is the rate-determining step. The application of ammonium carbamate to the beneficiation of ilmenite is briefly described.

Jan 1, 1973

By H. A. Baumann, A. J. Rostosky

EVER since the first installation of wet-washing methods of coal preparation, the removal of the water added by the washing process has created serious technical and operating problems. The rapid development and widespread adoption of wet washing has necessitated a corresponding development of dewatering methods and equipment. The amount of water retained by coal varies with the size of the coal. The moisture that is largely on the surface of the particles is easily shaken off coarse coal; thus coarse coal can be dried comparatively easily and quickly. Fine coal presents a larger surface area than does coarse coal, so its capacity for retaining moisture is greater. In fine coal, moisture below about 5 per cent is held between the coal particles and its removal is difficult. Draining and drying of the finer sizes is a major problem at many washeries. Two common problems of coal-washing practice that are intimately connected with dewatering and drying are the clarification of washery water and the prevention of stream pollution. The first field has been studied from many angles, including the use of coagulating and settling agents followed by vacuum filters to remove the solids, and the use of sludge tanks with dewatering screens incorporated therein. In many districts, the disposal of sludges into streams has been stopped by law. The lack of space for impounding sludges has created problems of disposal in other districts. Reduction in moisture means a saving in freight costs as well as the elimination of difficulties in unloading and storing. Excess moisture in coal causes it to freeze in localities where severe climatic conditions pre¬vail. Excess water in coals to be used in the production of coke and manufactured gas has a chilling effect on the walls of the oven or retort. Dryness of coal is important in producing good briquettes.

Jan 1, 1943

By C. Y. Wang

China now leads the world in antimony production, having contributed during recent years something over 60 per cent. of the world&apos;s production. The history of the antimony industry of China dates back to 1897 when the Tai Shing Co. was formed, under contract with the Hunan Bureau of Mines, for the smelting of the ore to crude; and in 1908 the Wah Chang Mining & Smelting Co. was formed for the smelting and refining of the ore and crude to regulus. The writer was then asked to take charge of the erection and control of this first plant for regulus production in China and has, since then, been more or less connected with the antimony industry in this country. This paper contains the results of many years&apos; experience in connection with the Wah Chang Mining & Smelting Co., Changsha; the Pao Tai Mining & Smelting Co., Wuchow; the Loong Kee Smelting Works and the To-Cheng Smelting Works, Hankow; as well as information gathered from various other small smelters, scattered in different parts of the Provinces of Hunan, Hupeh, Kwangsi, and Kwangtung. An idea of the growing importance of regulus production in this country can be gleaned from the fact that, within a period of about 8 years, the export of regulus from Hunan alone jumped from 3 tons in 1908 to about 6000 tons in 1915; that a production of about 23,000 tons of regulus per year could easily be effected from all the smelters, as tabulated below, most of which were erected a year or two ago under the stimulus of the war booms, if the price at Hankow were to stay somewhere about $900 (Mexican) per ton, half of what it was at its height, thus enabling the utilization of ores from the hinterlands of the provinces; and even under the present ruling of prices and the closing of the less favored smelters, the production of regulus should not be less than 12,000 tons per year.

Jan 1, 1919

By H.A. Schwartz

From time to time, one of the authors has had occasion to investigate the graphitizing reaction and has published the results mainly as discussion&apos; of the work of other investigators. In view, therefore, of the diversity of both observations and interpretation, it seemed well to attempt, a revision of the entire subject in the Research Laboratory of the National Malleable Castings Co. The work consisted of a careful study of a single, impure, iron-carbon alloy. The material, which may be considered typical low-carbon white cast iron of the malleable industry, was an air-furnace iron of the following composit,ion: carbon 2.30 per cent., silicon 1.20 per cent., manganese 0.29 per cent., phosphorus 0.156 per cent., sulfur 0.048 per cent. The freezing range extended from 1213&apos; to 1132&apos; C., the latter figure agreeing with Gontermann&apos;s data.2 We have attempted to define the equilibrium diagram of this alloy, in the stable condition as related to the mctastable diagr,aui,- from a temperature somewhat below the euteetic freezing point to a temperature l>clow Arl and for a graphitic-carbon content from practically notliing to the original total rarbon of the specimen (see Fig. 6). More csp~c~ially we desired to locate the line in the stable diagra~n corrcspo~idi~lg to thc Ac, line of the metastable syst,ern, which is designated by analogy, thc At, line (t, from tcrnpcr carbon); also to dctermirle the locat&apos;ion of A tm witah respect, to Acm t,o~vard their lowcr extremities at Arl in ordei to determine whether or not graphitization is completed by th~ separation of an iron-carbon entectoid analogous to pearlite in the iron-cementite system. This would involvc furthcr a colnparison of thc locations of Ihc stablc and met.astable 41 points. As the carbon concelltrations of thc solid solutions of the two syste~~ls are probably not, identical, an explanation of t>lieir differences and of thc,

Jan 1, 1923

By H. A. Schwartz

From time to time, one of the authors has had occasion to investigate the graphitizing reaction and has published the results mainly as discussion&apos; of the work of other investigators. In view, therefore, of the diversity of both observations and interpretation, it seemed well to attempt, a revision of the entire subject in the Research Laboratory of the National Malleable Castings Co. The work consisted of a careful study of a single, impure, iron-carbon alloy. The material, which may be considered typical low-carbon white cast iron of the malleable industry, was an air-furnace iron of the following composit,ion: carbon 2.30 per cent., silicon 1.20 per cent., manganese 0.29 per cent., phosphorus 0.156 per cent., sulfur 0.048 per cent. The freezing range extended from 1213&apos; to 1132&apos; C., the latter figure agreeing with Gontermann&apos;s data.2 We have attempted to define the equilibrium diagram of this alloy, in the stable condition as related to the mctastable diagr,aui,- from a temperature somewhat below the euteetic freezing point to a temperature l>clow Arl and for a graphitic-carbon content from practically notliing to the original total rarbon of the specimen (see Fig. 6). More csp~c~ially we desired to locate the line in the stable diagra~n corrcspo~idi~lg to thc Ac, line of the metastable syst,ern, which is designated by analogy, thc At, line (t, from tcrnpcr carbon); also to dctermirle the locat&apos;ion of A tm witah respect, to Acm t,o~vard their lowcr extremities at Arl in ordei to determine whether or not graphitization is completed by th~ separation of an iron-carbon entectoid analogous to pearlite in the iron-cementite system. This would involvc furthcr a colnparison of thc locations of Ihc stablc and met.astable 41 points. As the carbon concelltrations of thc solid solutions of the two syste~~ls are probably not, identical, an explanation of t>lieir differences and of thc,

Jan 1, 1923

THE following employment items are made available to AIME members on a nonprofit basis by the Engineering Societies Personnel Service, Inc , operating in cooperation with the Four Founder Societies Local offices of the Personnel Service are at 8 W 40th St , New York 18, 100 Farnsworth Ave, Detroit, 57 Post St , San Francisco, 84 E Randolph St , Chicago 1 Applicants should address all mail to the proper key numbers in care of the New York office and include 6c in stomps for forwarding and returning application The applicant agrees, if placed in a position by means of the Service, to pay the placement fee listed by the Service AIME members may secure a weekly bulletin of positions available for $3 50 a quarter, $12 a year MEN AVAILABLE Executive Engineer, 37, married, 3 children Now Resident Manager nonmetallic underground mine and processing plant Management and operational experience in gold, copper, zinc, limestone and lime products manufacture Mine plant design and construction, underground mines and quarries Excellent references Currently employed but available reasonable notice Prefer U S M-687-426-E-5-San Francisco Metallurgical Engineer, 29, married, one child, B S Metallurgical Engineering Five years&apos; practical experience in milling and laboratory research Available thirty days Prefer West or Southwest U S A M-689¬522-E-1-San Francisco Experienced Mining Engineer, university graduate, 40, married Twenty years&apos; experience all phases metal mining, past 13 years as manager, excellent cost and safety record Available short notice Best references and complete professional record available upon request M-690

Jan 1, 1952

By G. D. Cremer, J. J. Cordiano

Aluminum powder is a well-known article of commerce and in various forms has been marketed widely for use in paint, for pyrotechnic purposes and for exothermic mixtures. For a number of reasons, however, aluminum powder has not been employed extensively in powder metallurgy, although a great many proposals along this line have been offered. Aluminum and alumiuum-alloy powders oxidize readily upon exposure to air and the thin film of oxide (or hydroxide) thus formed is highly refractory, in that ordinary gaseous reducing agents such as hydrogen or carbon monoxide do not reduce the oxide to metal at temperatures below the melting point of aluminum. It has been thought that the presence of these films of oxide on aluminum particles would interfere markedly in powder metallurgical work and a number of suggestions have been made, either for preventing the formation of the film through the production of the powders in inert or reducing atmospheres, or for the removal of the oxide by means of powerful reducing agents, including "nascent" or atomic hydrogen released from metal hydrides. A second and more serious difficulty in the use of aluminum and aluminum-alloy powders in powder metallurgy resides in the fact that during compression such powders tend to adhere or cold-weld to the die walls, thus interfering with the formation and ejection of a compact. A third difficulty, which has been encountered only with aluminum-alloy powders, is their hardness when compared with elemental aluminum. Certain of these powders are susceptible to age-hardening, which further hinders the formation of strong green compacts. These conditions are particularly true of atomized aluminum-alloy powders. Even in the annealed condition, plastic deformation of alloy powders under pressure is low when compared with unalloyed powders. This fact, coupled with the lower corrosion resistance of the alloy powders. is probably the significant factor in our failure to obtain strong sintered pieces. Methods of Puoducing the Powder Many methods have been proposed for manufacture of aluminum powder, only a few of which are used commercially. Several of the more important processes include: (I) atomization of the molten metal; (2) mechanical pulverization and other types of comminution; and (3) graining, in which molten aluminum is stirred during freezing. For pigment and certain pyrotechnic uses aluminum flake powder is desirable, because of its greater proportion of surface to volume; and large quantities of such material are made by a procedure that involves stamping or ball milling. In making flake intended for use as pigment,

Jan 1, 1943

By G. D. Cremer, J. J. Cordiano

Aluminum powder is a well-known article of commerce and in various forms has been marketed widely for use in paint, for pyrotechnic purposes and for exothermic mixtures. For a number of reasons, however, aluminum powder has not been employed extensively in powder metallurgy, although a great many proposals along this line have been offered. Aluminum and alumiuum-alloy powders oxidize readily upon exposure to air and the thin film of oxide (or hydroxide) thus formed is highly refractory, in that ordinary gaseous reducing agents such as hydrogen or carbon monoxide do not reduce the oxide to metal at temperatures below the melting point of aluminum. It has been thought that the presence of these films of oxide on aluminum particles would interfere markedly in powder metallurgical work and a number of suggestions have been made, either for preventing the formation of the film through the production of the powders in inert or reducing atmospheres, or for the removal of the oxide by means of powerful reducing agents, including "nascent" or atomic hydrogen released from metal hydrides. A second and more serious difficulty in the use of aluminum and aluminum-alloy powders in powder metallurgy resides in the fact that during compression such powders tend to adhere or cold-weld to the die walls, thus interfering with the formation and ejection of a compact. A third difficulty, which has been encountered only with aluminum-alloy powders, is their hardness when compared with elemental aluminum. Certain of these powders are susceptible to age-hardening, which further hinders the formation of strong green compacts. These conditions are particularly true of atomized aluminum-alloy powders. Even in the annealed condition, plastic deformation of alloy powders under pressure is low when compared with unalloyed powders. This fact, coupled with the lower corrosion resistance of the alloy powders. is probably the significant factor in our failure to obtain strong sintered pieces. Methods of Puoducing the Powder Many methods have been proposed for manufacture of aluminum powder, only a few of which are used commercially. Several of the more important processes include: (I) atomization of the molten metal; (2) mechanical pulverization and other types of comminution; and (3) graining, in which molten aluminum is stirred during freezing. For pigment and certain pyrotechnic uses aluminum flake powder is desirable, because of its greater proportion of surface to volume; and large quantities of such material are made by a procedure that involves stamping or ball milling. In making flake intended for use as pigment,

Jan 1, 1943

By B. V. P. Rao, H. L. Lovell, G. Simkovich

In the study described here, flotation tests were conducted on pure CaF2, on CaF2 doped at several concentration levels with either NaF or YF3, and on natural fluorite samples containing various amounts of impurities in an effort to extend previous knowledge of the influence of crystalline point imperfections on the flotation properties of solids. The results of these tests showed that although recoveries generally decreased as impurities increased, the differences in recovery were not nearly as striking as those detected in earlier experiments. A number of experimentalists have shown an interest in the way in which crystalline point imperfections affect the flotation properties of solids. As long ago as 1953, Welch hypothesized that it might be possible to control surface imperfections and thereby also control the flotation of solids.&apos; A few years later, in some rather extensive work, Plaksin and his coworkers varied the surface imperfections of a number of compounds by oxidation or reduction processes and found that significant variations in flotation properties resulted.2-4 More recently, Simkovich showed that the recovery of both AgCl and PbS could be markedly varied by adding solid-solution impurities, which acted as doping agents, to these compounds.5 Then Mular studied the flotation of ZnO as a function of the doping agents Al2O3 and Li2O.6 Once again, it was found that these impurities, even in very low concentrations, had profound effects upon flotation recoveries. From an imperfection point of view, the defect structures of the compounds tested previously are as follows:7 PbS — amphoteric semiconductor with a Frenkel-type defect structure in the cation sub-lattice.8 AgCl - ionic conductor-Frenkel type defect structure? ZnO — n-type semiconductor, zinc ion interstitials and quasi-free electrons.10 All of these works undoubtedly bear some relation to the findings that the flotation properties of seemingly identical minerals from different ore deposits often exhibit extreme variation in flotation behavior, i.e., that small amounts of analytically undetectable impurities often have a great influence upon flotation

Jan 1, 1969

By T. N. Dixon, J. E. Briggs

A study was made of numerical techniques for solving the large sets of simultaneous equations that arise in the mathematical mode ling of oil reservoir behavior. It was found that noniterative techniques, such as the Alternating Direction Implicit (ADI) method, as well as some other finite difference approximations, produce oscillatory or unsmooth results for large time steps. Estimates of time step sizes sufficient to avoid such behavior are given. A comparison was made of the Point Successive Over-Relaxation (PSOR), Two-Line Cyclic Chebyshev Semi-Iterative SOR (2LCC), and iterative ADI methods, with respect to speed of solution of a test problem. It was found that, when applicable, iterative ADI is fastest for problems involving many points, while 2LCC is preferable for smaller problems. INTRODUCTION With the advent of high speed, large memory, digital computers, there has been an increasing emphasis on the development of improved methods for simulating and predicting reservoir performance. Two-dimensional, three-phase reservoir models with various combinations of PVT effects, as well as gravity and capillary forces, are common throughout the industry. Such models are also available through consulting firms, to anyone desiring to use them. Three-dimensional models will probably be practical in only a few years. We conducted a study of some of the numerical methods used for solving the large sets of simultaneous equations that arise in such models. A typical set of equations for a reservoir model is shown below:

Jan 1, 1969

By E. I. Alessandrini, A. U. Seybolt

Selective oxidation (preferential oxidation of a single alloy component) can be an important oxidation mode in the case of alloys such as Si-Fe, Al-Fe, and so on, when heat-treating in atmospheres of low oxygen potential. It was the purpose of this work to identify the oxide films formed on iron containing 31/4 pct Si at low oxygen potentials, and to make some observations on the H2O/H2 ratios required to form them. EXPERIMENTAL METHOD HYDROGEN of varying water content offers a very convenient method of establishing a wide range of oxidizing power, or oxygen potential. The method chosen to provide a desired H2O/H2 ratio was to nearly saturate hydrogen at room temperature by bubbling the gas through water at room temperature, and then to wring out the excess water by passing the wet gas through a long glass spiral immersed in a refrigerated liquid at a desired dew point. After oxidation, the samples were examined by electron diffraction in order to identify any film which might be present. PREPARATION AND TREATMENT OF SAMPLES The samples were prepared from a Si-Fe alloy made in the laboratory using electrolytic iron and 96 pct ferro-silico11, vacuum-induction melted, hot-rolled then cold-rolled to 0.015-in. thickness. After the cold-rolling the samples were annealed at 1000°C. Transmission Laue X-ray patterns showed very little evidence of preferred orientation, but it is likely that a weak texture could have escaped notice. The chemical analysis was as follows: 3.34 Si, 0.01 Al, 0.001 0, 0.006 C, 0.002 N. Before each sample was oxidized, it was polished through 4/0 emery paper, cleaned and dried using benzene, carbon tetrachloride, acetone, absolute alcohol, and ether. The method of oxidizing the samples was as follows: Samples about 1/2 by 1 by 0.015 in. were held in the upper, cool part of a vertical vacuum furnace until the desired temperature was established in the furnace, Fig. 1. The sample was then lowered into the uniform hot zone where it was heated quickly to the desired temperature, and subjected to hydrogen of controlled moisture content (dew point) as mentioned previously. Temperatures from 400" to 1000°C were used, and dew points from room temperature to —78°C were explored. In general, the runs lasted about 6 hr, but a few runs were of different duration, as will be indicated later. After the predetermined period of time had elapsed, the specimens were withdrawn by the hollow stainless steel-quartz holder to a cool zone at the top of the furnace. EXPERIMENTAL RESULTS The results are summarized in Table I. Most of the electron-diffraction patterns were obtained by glancing-angle reflection, but in a few cases it was possible to strip the oxide films from the surface by a total immersion in a 3 pct bromine-methanol solution. Some of the thinner stripped films yielded quite satisfactory transmission patterns. However, both diffraction techniques yielded the same results; the patterns while most frequently showing a (low) tridymite, also showed a (low) cristobalite in some cases. A few patterns showed evidence of both phases. Because of the known nonequilibrium behavior of silica, it is not surprising that both forms of silica could coexist on one sample. It was noted that at fairly low dew points such as —40°C, there was a tendency for diffuse diffraction rings, suggesting a very small crystallite size. Also some subsequent experiments to be reported later show that thin silica films can be amorphous.

Jan 1, 1959

By M. R. J. Wyllie, Walter D. Rose

The use of electrical well logs for the quantitative determination of such reservoir parameters as connate water saturation, formation permeability and connate water salinity has recently been attracting the attention of a number of workers1,2,3,4,5. While the theory of the determination of connate water salinity from the self potential S.P. log has received rather detailed treatment, relatively little attention has been paid to the theoretical aspects involved in the quantitative interpretation of resistivity data. It is clear that if electrical well logs can be used for the quantitative evaluation of physical characteristics of reservoir rock, they will provide a valuable tool to supplement cheaply information obtained by more laborious core analysis. In certain cases it is conceivable that the coring program could be considerably curtailed if the electric log could be relied upon to give reasonably accurate quantitative information. It is our object in this paper to examine the theoretical basis of quantitative log interpretation as expressed in such well-established logging concepts as formation factor and cementation factor. It is also our object to investigate the physical aspects of the rela- tionship which is presumed to exist between resistivity index and brine saturation in reservoir rock. In particular, we will endeavor to draw attention to the fact that it is possible to express these logging concepts in terms of capillary pressure-saturation relationships, permeability and tortuosity, parameters which we will consider in this paper to be fundamentally indicative of rock texture. The probability of being able to obtain from log recordings alone the data theoretically essential to permit quantitative log interpretatiou will be examined, and consideration will also be given to the problem of formulating simple semi-empirical relationships for use in the field. THEORETICAL CONSIDERATIONS The concept of formation resistivity factor, or as it is now commonly called, formation factor, appears to have been introduced by G. E. Archie",". Formation resistivity factor as defined by Archie is the resistivity of a rock 100 per cent brine-saturated divided by the resistivity of the brine. This relationship had previously been used by physical chemists and the concept is, for example, implicit in an early treatment by Fricke7 of the conductivity of aqueous slurries. Archie was able to establish the fact that although the relationship between formation factor and porosity did not change too greatly for different rock textures, the relationship between formation factor and permeability was markedly dependent on rock texture. The relationship found by Archie between formation factor and porosity was expanded by H. Guyod8. Archie had suggested that the formation factor, F, could be expressed in terms of the porosity, F, as follows: F =F-m .... (11 where, F = effective porosity fraction of the sand, and, m = an exponent greater than about 1.3. Guyod introduced the term cementation factor for the exponent, m, since it may be qualitatively shown that formation factor for any given porosity tends to increase as the sand becomes more cemented. It would appear that the concept of m as an exponent representing the cementation in a sand is strictly only of qualitative value, since the quantitative estimation of m by means other than the determination of F and F has not been possible. Guyod suggests that m can be estimated from a visual examination of a sample of rock, but this method appears to be both arbitrary and unreliable. It can be said, however, that in intergranular reservoirs of practical interest, the range of m is from about 1.4 to 3.0. A possible explanation for the fact that m is found to lie between these limits will be offered below. The determination of formation factor is an essential preliminary to the

Jan 1, 1950

AIME 1953 DIRECTORY SUPPLEMENT OFFICERS AND COMMITTEES OF LOCAL SECTION; COUNCIL OF SECTION DELEGATES Linwood Thiessen, Chairman H. D. Vaughan, Vice-Chairman John H. Melvin, Secretary EXECUTIVE COMMITTEE L. E. Thelin, Connecticut J. B. Cunningham, Arizona W. L. Penick, San Francisco G. L. Yates, Kansas DELEGATES Adirondack - C. DeWitt Smith &apos;54 Alaska - Robert 11. Chapman, ?54 Arizona J. B. Cunningham, &apos;53 Black Hills - Sidney M. Runke, &apos;54 Boston -R&apos;. Schuhmann, Jr. ?54 Carlsbad Potash - W. P. Wilson, &apos;54 Central Appalachian - Charles T. Holland, &apos;54 Chicago - H. A. White, &apos;54 Cleveland - Milton Tilley, &apos;54 Colorado - J. Paul Harrison &apos;54 Columbia - Harold Kirkemo, &apos;54 Connecticut - Lewis E. Thelin, ?53 Dallas - Kenneth F. Anderson, &apos;54 Delta - Roy S. Sullins &apos;54 Detroit - F. P. Bens, &apos;53 East Texas - Joseph A. Morris, &apos;54 El Paso Metals - E. M. Thomas, &apos;54 Florida - W. O. McClintock &apos;54 Fort Worth - Ray Elner, &apos;51 Gulf Coast - H. E. Treichler, &apos;53 Kansas - G. L. Yates, &apos;53 Lehigh Valley - H. R. Gault &apos;54 Lima, Peru - R. P. Koenig, ?54 Lou-Ark - A. H. Crawford. &apos;53 Mexico - W. G. Kane, &apos;54 Mid-Continent - J. H. Beesley, &apos;53 Minnesota - J. R. Stuart, &apos;54 Montana - F. W. Strandberg, &apos;53 Nevada - Albert Silver,&apos;53 New York - P. Malozemoff, &apos;54 North Pacific - A. H. Mellish, &apos;54 North Texas - K. F. Anderson, &apos;54 Chio Valley - J. H. Melvin, ?53 Oklahoma City - Charles Miller, &apos;53 Oregon - T. C. Matthews, &apos;54 Penn. Anthracite - D. C. Helms, &apos;54

Jan 1, 1953

By G. H. F. Gardner

The boundary conditions F = 1.0 and 4 = 1.0 (100 per cent) are dictated by the definition of F in the equation 1/F = aFp. These conditions have physical significance as the "limiting conditions" for the observed behavior in systems of dispersed particles. The other boundary conditions, cited by Gardner in his Eq. 3 as applying to this system, have no significance in the systems we studied. Maxwell&apos;s equation (Eq. 2) cited in Gardner&apos;s comments was developed for and limited to a regular, rather than random, dispersion of spheres which are sufficiently removed from each other so that they do not interfere with current flow about their neighbors. These restrictions also apply to Rayleigh&apos;s analysis. The title of Rayleigh&apos;s paper cited by Gardner is "On the Influence of Obstacles Arrayed in Rectangular Order upon the Properties of a Medium". He is not discussing randomly dispersed spheres. It might be inferred from Gardner&apos;s comments that Rayleigh specifically considered the differential equation (Gardner&apos;s Eq. 3). This is not the case. Mathematically, Gardner&apos;s Eq. 3 is exactly true for the system to which it applies, however, as both Rayleigh and Maxwell note that their equation for F in terms of F is not for randomly dispersed spheres. At the time we wrote our paper, we were aware of the work of Wyllie and Gregory as cited by Gardner. We cited their work in Ref. 5 of our paper. Our comment on page 287 of the paper about the validity of an m value of 1.3 for spheres with a porosity of 38 per cent remains as our answer to Gardner&apos;s question on this point. Our data, at 38 per cent porosity, show that the condition a = 1 and m = 1.3 holds for spheres near 40 per cent porosity.

New York Meets first Wednesday after first Tuesday of each month. J. E. JOHNSON, JR., Chairman. EDGAR RICHARD, Vice-Chairman. D. M. LIDDELL, Secretary, 7 Wall St., New York, N. Y. C. A. BOHN, Treasurer. JOHN V. N. DORR, LEWIS W. FRANCIS. Boston Meets first Monday of each winter month. R. L. AGASSIZ, Chairman. JAMES G. CARLETON, Vice-Chairman. E. E. BUGBEE, Secretary-Treasurer, Mass. Inst. of Technology, Cambridge, Mass., W. E. C. EUSTIS. G. A. PACKARD. Columbia Holds four sessions during year. Annual meeting n September or October. W. H. LINNEY, Chairman. OSCAR LACHMUND, Vice-Chairman. LYNDON K. ARMSTRONG, Secretary-Treasurer, P. O. Drawer 2154, Spokane, Wash. STANLY A. EASTON, S. SHEDD. Puget Sound Meets second Saturday of each month SIMON H. ASH, Chairman. I. F. LAUCKS, Vice-Chairman. CHARLES SIMENSTAD, Secretary-Treasurer, 425 Lyon Bldg., Seattle, Wash. GLENVILLE A. COLLINS, JOHN N. POTT

Jan 7, 1917

New York Meets first Wednesday after first Tuesday of each month. J. E. JOHNSON, JR., Chairman EDGAR RICHARD, Vice-Chairman D. M. LIDDELL, Secretary, 7 Wall St., New York, N. Y. C. A. BOHN, Treasurer JOHN V. N. DORR LEWIS W. FRANCIS Boston Meets first Monday of each winter month. R. L. AGASSIZ, Chairman JAMES G. CARLETON, Vice-Chairman E. E. BUGBEE Secretary-Treasurer, Mass. Inst. of. Technology, Cambridge, Mass. W. E. C. EUSTIS G. A. PACKARD Columbia Holds four sessions during year. Annual meeting in September or October. W. H. LINNEY, Chairman OSCAR LACHMUND, Vice-Chairman LYNDON K. ARMSTRONG, Secretary-Treasurer, P. O. Drawer 2154, Spokane, Wash. STANLY A. EASTON S. SHEDD Puget Sound Meets second Saturday of each month SIMON H. ASH, Chairman I. F. LAUCKS, Vice-Chairman PERCY E. WRIGHT, Secretary-Treasurer, 2012 L. C. Smith Bldg., Seattle. Wash. GLENVILLE A. COLLINS JOHN N. POTT

Jan 11, 1917