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By W. M. Rust, W. D. Mounce

THE almost universal acceptance of electrical logging by the petroleum industry calls for a critical examination of the physical bases of the common methods. This is particularly needed for the natural potential log. The conventional explanations are based on the phenomena of electrofiltration and electro-osmosis. However, experimental data show that they fail to give a basis that is quantitatively sound. Moreover, they lead to interpretations of details of electrical logs that are erroneous. It was found experimentally that when a plug of shale is placed in a chain of dissimilar electrolytes, a current flow results. Experiments on oil-well cores and fluids similar to those existing in wells show that potentials are set up which are in reasonable agreement with those encountered in electrical logging. Doubt- less other sources of potential are important but this explanation not only accounts for much of the potential but also clarifies some fairly familiar examples of misinterpretations.

Jan 1, 1944

By R. C. Dorward

DIFFUSION considerations are necessary to describe many technologically important metallurgical and physical processes. Since most commercially important alloys are comprised of more than two components, diffusion calculations applicable to binary systems are often unjustified. However, in many instances the more general equations valid for three-component systems may be employed. The phenom-enological description of ternary diffusion is now well-established,1-4 and the theory has been applied with some success to a few practical situations.5"7 The flux equations for the solutes (components 1 and 2) of a ternary solution may be expressed by:

Jan 1, 1969

By P. L. Lavery

A numerical method to derive approximate solutions for stress intensity factors for rectilinearly anisotropic bodies without resolving to complex variable approach is presented. The method is based on the assumption that the crack opening profile can be simulated by a simple curve such as an elliptic function and a relationship is found for the stress intensity factor in terms of near tip displacements. An example solution is derived for a transversely isotropic body and the results are verified with Westergaard's stress function approach. The proposed model has a great potential for the applications to fracture mechanics of anisotropic rock materials.

Jan 1, 1984

By P. L. De Bruyn

The behavior of collectors at the mineral-solution interfaces is usually explained in terms of an ionic adsorption process. Through the distribution of collector ions between the solid surface and the co-existing solution phase the mineral is believed to acquire a water-repellent surface coating. Quantitative adsorption studies have been made on simple flotation systems only within the last few years. Such investigations were made possible by the adoption of the radiotracer method of analysis. As a consequence of these studies a new parameter has been added to aid the understanding of the flotation process.

Jan 3, 1955

By P. Somasundaran

Adsorption of a nonionic polyacrylamide (PAM), an anionic polyacrylamide with sulfonate functional groups (PAMS), and a cationic polyacrylamide with amine functional groups (PAMD), on hematite was investigated as a function of different solution conditions. Adsorption results indicate that the major mechanisms of adsorption of polyacrylamides on hematite is through hydrogen bonding, with electrostatic forces playing a secondary role. All the polymers exhibited irreversibility of adsorption upon dilution. Also, entropic effects were determined to be important in adsorption. Surface chemical properties of hematite and solution chemistry of the polyacrylamides are considered to explain the polymer adsorption behavior on hematite.

Jan 1, 1985

By F. M. F. Cazin

Some twenty years ago the author of a book,* by which, for the first time, molecular action was made to account for nearly all phenomena in hydrodynamics, began his preface as follows: " It is contrary to all experience, that any branch of science should suddenly cut short its own line of reasoning, and drop all connection with its past, and yet as quickly re-establish itself on an entirely new basis. It is, therefore, not without justification that this book should be met with caution and even distrust." When the newly-discovered natural facts and laws presented in this paper were, in 1891, first laid before the officers of the American Institute of Mining Engineers, they might have been preceded by a preface to the same effect; and the expression would have found its justification by the actual experience these facts and laws met with. Since then, as the result of their publication in one of the most prominent

Jan 1, 1895

By A. S. Richardson

THE recent installation of a high-pressure propeller type fan at the Moose shaft of the Anaconda Copper Mining Co. at Butte, Mont., is of interest on account of novelty of design and also because an appreciable saving was made over the cost of a reversible centrifugal fan such as is ordinarily used where a high pressure is required. The lower cost is due solely to the fact that by means of controls 'on the power supplied to the three-phase, alternating-current, induction. motor, directly connected to the propeller it is possible to reverse the direction of rotation of the propeller and thus reverse the direction of air flow. The extra air ducts and reversing doors required for this purpose with centrifugal fans are not necessary, and their elimination greatly reduces these construction charges, which form a great part of the total expense. The Badger State mine for which the Moose shaft is used as the main outlet air course is now being-developed to the 4100-ft. level. The old centrifugal fan, formerly used at the collar of the shaft, was installed 15 years ago at a time when most of the stoping was being done above the 2400-ft. level, and when the temperature of the rock was much lower than it is now on the bottom levels recently opened. The old fan, therefore, became inadequate to maintain desirable ventilation conditions, on account of the increase in resistance to air flow incident to the greater depth of the mine workings and because a much larger volume of air is required to offset the higher rock temperatures. Propeller, or disk, fans commonly used in the ventilation of mines are not suited to high-pressure work, but economies in the cost of their installation have long been recognized. In South Africa use has been made of a number of propellers placed in series along a common shaft, the number of propellers used being varied with requirements for meeting different conditions of mine resistance, but the mechanical efficiency is described as being low. In Butte, experimental work was done by the writer along similar lines under somewhat different conditions, but with poor results as to both pressure capacity and mechanical efficiency. Tests were also made of two different types of propeller fans of moderate size, which were said by the manufacturers to be suited to high-pressure mine ventilation.

Jan 1, 1932

By A. S. Richardson

The recent installation of a high-pressure propeller type fan at the Moose shaft of the Anaconda Copper Mining Co. at Butte, Mont,., is of interest on account of novelty of design and also because an appreciable saving was made over the cost of a reversible centrifugal fan such as is ordinarily used where a high pressure is required. The lower cost is due solely to the fact that by means of controls on the power supplied to the three-phase, alternating-current, induction motor, directly connected to the propeller it is possible to reverse the direction of rotation of the propeller and thus reverse the direction of air flow. The extra air ducts and reversing doors required for this purpose with centrifugal fans are not necessary, and their elimination greatly reduces these construction charges, which form a great part of the total expense. The Badger State mine for which the Moose shaft is used as the main outlet air course is now being developed to the 4100-ft. level. The old centrifugal fan, formerly used at the collar of the shaft, was installed 15 years ago at a time when most of the stoping was being done above the 2400-ft. level, and when the temperature of the rock was much lower than it is now on the bottom levels recently opened. The old fan, therefore, became inadequate to maintain desirable ventilation conditions, on account of the increase in resistance to air flow incident to the greater depth of the mine workings and because a much larger volume of air is required to offset the higher rock temperatures. Propeller, or disk, fans commonly used in the ventilation of mines are not suited to high-pressure work, but economies in the cost of their installation have long been recognized. In South Africa use has been made of a number of propellers placed in series along a common shaft, the number of propellers used being varied with requirements for meeting different conditions of mine resistance, but the mechanical efficiency is described as being low. In Butte, experimental work was done by the writer along similar lines under somewhat different conditions, but with poor results as to both pressure capacity and mechanical efficiency. Tests were also made of two different types of propeller fans of moderate size, which were said by the manufacturers to be suited to high-pressure mine ventilation.

Jan 1, 1932

By A. S. Richardson

THE recent installation of a high-pressure propeller type fan at the Moose shaft of the Anaconda Copper Mining Co. at Butte, Mont., is of interest on account of novelty of design and also because an appreciable saving was made over the cost of a reversible centrifugal fan such as is ordinarily used where a high pressure is required. The lower cost is due solely to the fact that by means of controls on the power supplied to the three-phase, alternating-current, induction motor, directly connected to the propeller it is possible to reverse the direction of rotation of the propeller and thus reverse the direction of air flow. The extra air ducts and reversing doors required for this purpose with centrifugal fans are not necessary, and their elimination greatly reduces these construction charges, which form a great part of the total expense. The Badger State mine for which the Moose shaft is used as the main outlet air course is now being developed to the 4100-ft. level. The old centrifugal fan, formerly used at the collar of the shaft, was installed 15 years ago at a time when most of the stoping was being done above the 2400-ft. level, and when the temperature of the rock was much lower than it is now on the bottom levels recently opened. The old fan, therefore, became inadequate to maintain desirable ventilation conditions, on account of the increase in resistance to air flow incident to the greater depth of the mine workings and because a much larger volume of air is required to offset the higher rock temperatures. Propeller, or disk, fans commonly used in the ventilation of mines are not suited to high-pressure work, but economies in the cost of their installation have long been recognized. In South Africa use has been made of a number of propellers placed in series along a common shaft, the number of propellers used being varied with requirements for meeting different conditions of mine resistance, but the mechanical efficiency is described as being low. In Butte, experimental work was done by the writer along similar lines under somewhat different conditions, but with poor results as to both pressure capacity and mechanical efficiency. Tests were also made of two different types of propeller fans of moderate size, which were said by the manufacturers to be suited to high-pressure mine ventilation.

Jan 1, 1932

By R. W. Fountain, J. Chipman

THE solubility of nitrogen in iron and steel has been of considerable interest due to the role of nitrogen in strain-aging and in quench-aging. It is generally considered that quench-aging is the result of precipitation of carbide and nitride particles from supersaturated solid solution, while strain-aging results from the segregation of carbon and nitrogen atoms to dislocations.1-9 The rate of strain-aging is controlled primarily by the amount of carbon and nitrogen in solution and the temperature. In experiments on strain-aging of pure iron with only carbon or nitrogen as impurities, Fast" has shown that even after 40 hr at 50°C carbon did not give any strain-aging while

Jan 1, 1959

By R. F. Frantz, T. P. McNulty

The upper-level mineralization of the din Buttes, Arizona copper orebody consists primarily of dilute copper silicate impregnation in fault clay and throughout the altered limestone hostrock. Cuprite and native copper are minor with true chrysocolla rare. Owing to the high calcium carbonate and to the hydrogen ion exchange capacity of the clays, acid leaching would be economical only with cheap acid available. Leaching of the silicate copper with reagents other than sulfuric acid is slow and incomplete unless the ore is first heated to disorder the mineralized grains and to reduce partially the contained copper. Following heat treatment, 70 to 90 percent of the nonsulfide copper can be dissolved in aqueous anrmonium carbonate. Recovery of a pregnant solution by counter-current decantation is effective provided ammonium carbonate solution is added to the washing stages in order to oppose adsorption of dissolved copper by clays in the residue. Thermal stripping of the pregnant solution permits recovery of ammonia and carbon dioxide while precipitating copper either as oxide or carbonate. The research program was carried from batch tests through continuous miniplant operation to a five-month campaign in a 20 TPD continuous pilot plant. Pilot plant results, the relationships among key varibles, and a detailed flowsheet are given.

Jan 1, 1973

By J. R. Campbell

During the past few years, the writer has had occasion to take several excursions into the realms of the washability of beds 3 and 4 of the Pocahontas coal and the proper handling of these coals in prepared sizes Fig. 1.—Washability curve for 4 by 2½-in. egg, PocahoKtas coal. Note that definite break occurs at about 1.60 sp. gr., and washing at this gravity removes all heavy rock and slate, amounting to about 5 per cent. Curve 2 indicates a bony coal, and washed egg coal might not have a good appcarance, and would be condemned by visual inspection, although it would be well prepared mechanically. to attain the greatest realization for the operator and yet produce a market product acceptable to the consumer. Preparation is not new in the southern field, but some new angles have presented themselves in recent years on account of the progress of mechanical preparation. Mechanical methods are entirely devoid of the five senses given to

Jan 1, 1931

By G. Derge, R. E. Grace

Diffusivity of bismuth in liquid Pb-Bi alloys has been measured by the capillary reservoir method as a function of temperature and composition. Fair agreement between theory and experiment is found for the measured diffusion coefficients and activation energies of diffusivity and viscosity in dilute lead alloys. The measured diffusion coefficients in the high bismuth alloys describe mass transport in special concentration gradients. THE study of diffusion in liquid metals has been restricted largely to the amalgams over small ranges of temperature and composition. In contrast to this, diffusion and transport of ions and molecules in aqueous and organic solvents have been studied extensively for the past 50 years. The general difficulty of measuring diffusion coefficients in both gases and liquids at high temperatures has been that of eliminating convection currents. Measuring techniques based on freezing and sectioning after the diffusion period1 are not particularly satisfactory because of the volume changes and segregation which occur during freezing. The most promising technique which is currently being developed for liquid metals is the capillary reservoir method. This eliminates convection currents from the diffusion zone and requires measurements only of the length and initial and final compositions of the alloy within the capillary. Anderson and Saddington' have measured the diffusion coefficient of tungstate anions in aqueous Na,W04; Wane4' and Hoffman- ave studied structure and self-diffusion in water and self-diffusion in mercury, respectively, by similar techniques. Selection of the Pb-Bi system for initial study was made for several reasons: I—It afforded a low temperature system for development of techniques which would be suitable for high temperature measurements in liquid iron. This research on diffusion in liquid iron is now in progress as a part of a general program on the rates and mechanisms of slag-metal reactions. 2—Activity data on liquid Pb-Bi alloys of all compositions are available from the emf meas- urements of Strickler and Seltz.9 3—Some data are available on the diffusion of bismuth into solid lead. The measurements on solid alloys were made by von Hevesy and Seith7 for the concentration range of 0 to 2 pct Bi. An appropriate solution to Fick's law (unsteady state) for the capillary reservoir has been found by considering the mass flow which passes through a unit area of surface on a slab of infinite thickness as a function of time. This is the first application of this solution to diffusion measurements, although a similar solution is available for identical boundary conditions.' By analogy with heat conduction, the problem reduces to a perfectly insulated infinite slab at temperature C,, one surface of which is quenched to C, for all times, t. Heat is permitted to flow from quenched surface of the slab to an infinite supply of coolant at C.' (see Appendix). For the corresponding solution for diffusion in liquids, these terms become Where Cu is the initial concentration of component A" in entire capillary at t - 0, C, is the final con- In this case. component A is bismuth, and C, = 0. centration of component A in entire capillary at t = t, C, is the concentration of component A in bath for all t, 1 is the length of the capillary in centimeters, t is the time of diffusion period in seconds, and D is the diffusion coefficient in square centimeters per second. By comparison with solutions to Fick's law used in the solid state, this solution for liquids is similar to the Grube solution for solids, where the change in D with chemical composition is not taken into consideration. Difficulty is to be expected if large concentration gradients are employed and if the concentration gradients extend over an appreciable length of the capillary.

Jan 1, 1956

By H. Foster Bain

Steel for any large structure must be imported, the Hanyang works being entirely unable to supply local demand. The United States Steel Products Co. has warehouses and small stocks at Shanghai and at normal times there are heavy importations from Europe. It is difficult to obtain any accurate index of prices, but comparison of customs valuations with Pittsburgh quotations shows angles, bars and plates to have averaged $10 gold per ton higher in China in 1914, while on galvanized and tinned plates the excess was- $38 per ton. The margin since has been greater. Previous to the war little machinery was manufactured in China. There were shipyards at Shanghai and at Hong Kong which built a small number of engines, and small foundry and repair works are found at a number of ports. Their capacity was limited and the difficulties and delays incident to transport in China so numerous that in practice every important mine has a small foundry, boiler works, and machine shop. This must be taken into account in plans for work in the country. While skilled workmen can be found it is to be noted that most of them have been trained

Jan 1, 1921

By W. C. Leslie

The textures of cold-rolled and of annealed iron are compared with those of an iron-0.8 pct copper alloy in which the amount of precipitation after cold rolling was controlled. Previously published pole figures -for cold-rolled and for annealed iron are confirmed. The effects of precipztatiotz after cold rolling are to retain the cold-rolled texture after annealing, to inhibit the formation of the usual allnealing texture, and to produce elongated recrys-tallized ferrite grains. It is suggested that the inhibition of new textures by precipitation after cold rolling is a general phenomenon. A great deal of attention has been paid to the development of texture during the secondary or tertiary recrystallization of ferritic alloys, but very little work seems to have been done on the control of texture during primary recrystallization. If such control were attained, it might be possible to simplify the processing of oriented materials or to change the characteristics of current cold-rolled and an-nealed products. From previous experience, it seemed likely that texture could be controlled by recrystallizing a supersaturated solid solution. Green, Liebmann, and Yoshidal found that the formation of preferred orientation in aluminum (40 deg rotation about <111> relative to the deformed matrix) was inhibited when iron was retained in supersaturated solid solution in the strained aluminum. The authors attributed this inhibition to iron atoms in solid solution. There is, however, an alternative explanation. Green et al, took a highly supersaturated solution of iron in strained aluminum and heated it to an unspecified temperature for recrystallization. It is probable that precipitation occurred prior to and during recrystallization, and it is proposed that the inhibiting agent is this precipitate, rather than the iron atoms in solid solution. It is important to note that precipitation before cold work is ineffective; the effective precipitate is that formed after cold working and either before or during recrystallization. The location and distribution of the precipitate are critical. Precipitation in such a manner has been found to have profound effects upon kinetics of recrystallization and the microstruc-ture of the recrystallized alloys.2-4 It would be surprising, indeed, if this were accomplished with no change in texture. Because of the relative simplicity of the system, and because of previous experience,4-7 it was decided to determine the effect of precipitation on texture in an alloy of iron and copper. Bush and Lindsay5 found an unspecified change in texture in cold-rolled and annealed low-carbon rimmed steel sheets when the copper content exceeded 0.1 pct. MATERIALS In earlier work, the rate of recrystallization of a low-carbon steel was greatly decreased by 0.80 pct copper, and, after the proper treatment, the recrystallized ferrite grains were greatly elongated.4 Accordingly, it was decided to investigate the effect of precipitation on texture at this level of copper content. The iron and the iron-copper alloy were made from high-quality electrolytic iron and OFHC copper, vacuum-melted in MgO crucibles, cast, hot-rolled to 0.2 in., then machined to 0.150 in. The compositions are given in Table I. The plates were heated to 925°C and brine quenched, twice. This produced a ferrite grain size of ASTM 0 in the iron and ASTM 1 in the Fe-Cu alloy. Disk specimens were cut from the heat-treated plates, repeatedly polished and etched, then used to determine (110) and (200) pole figures by reflection. Despite the complication of large grain size, these pole figures strongly indicated a random texture. PROCEDURES The copper content in solid solution in ferrite before cold rolling and recrystallization, and hence, the amount that could precipitate during the recrys-tallization anneal, was controlled at three levels by heat treatment. The specimens as quenched from 925° C were presumed to have all the copper, 0.80 pct, in solid solution. Other samples of the quenched alloy were aged 5 hr at 700°C to retain about 0.5 pct Cu in solid solution.6 A third set of quenched specimens was reheated to 700°C, then slowly cooled in steps, to reduce the amount of copper in solid solution to a very low level. All specimens were cold-rolled 90 pct, from 0.150 to 0.015 in. thick. The rolling was done in one direction only, i.e., the strip was not reversed between passes, with a jig on the table of the mill to keep the short specimens at 90 deg to the rolls. The rolls were 5 in. in diameter and speed was 35 ft. per min. Machine oil was used as a lubricant. In a supersaturated alloy, the maximum effect of the copper precipitate on microstructure and on recrystallization can be developed by a treatment at 500°C, after cold rolling and before recrystallization.&apos;

Jan 1, 1962

The apparent small effect of skimming on desulphurization is somewhat misleading because the data was collected during the first months of use on the skimmer. During this period of time, the operators were, of course, just learning to use the equipment and, consequently, in many cases a so-called skimmed heat may have only been partially skimmed. In addition, during this period, the percentage of sulphur in the blast furnace slag was gradually increasing because of the increasing oil injection rates being employed at the blast furnace. An additional factor that cannot be disregarded is the apparent slower slag formation rate obtained in the BOF when the blast furnace slag is removed. This is evidenced at our shop by a much stronger tendency toward sparking and related lance skulling problems with deslagging, in spite of satisfactory manganese levels in the hot metal. Naturally, slower slag formation could account for poor desulphurization which would partially offset the beneficial effect of a lower sulphur input.

Jan 1, 1972

By Walter Renton, Ingalls

SEVERAL years ago I became interested in computing the historic lead production of the United States, and the mines, or mining districts whence derived. This led me subsequently to an examination of the recent records- of some of the American zinc-mining districts and of the great lead and zinc-mining districts in foreign countries. My present article thus will be to a large extent an addendum to my book, "World Survey of the Zinc Industry," which was published by the Mining and Metallurgical Society of America in 1931, and to which I shall refer hereinafter as Ingalls, op. cit. Throughout this article all expressions of tons mean the ton of 2000 lb. Where original data have been given in metric tons I have converted in many instances simply by multiplying by 1.1, and long tons by 1.12. I have not been fussy about digits and have rounded off many figures. These may explain differences between data herein and other data.

Jan 1, 1946

By Edwin F. Brush, John Chipman

Published data on the activity of carbon in binary and ternary austenite at 1000°C are reviewed. The composition variables are . The coefficient, Vj, has the value for substitutional elements but may be assigned a ualue -1 for silicon to effect a simplification on the mathematical treatment. The activity coefficient PC = is obtained from gas equilibrium data. For the ternary systems studied the Henrian activity coefficient is given by the expression: The principle advantage in cornparison with the analogous expression in terms of atom fractions is found in the fact that for most systems the final term and in many the last two terms are zero. Values of the interaction parameters are tabulated and the graphical comparison of the equation with experirt~ental data is sho,wn in several figures. The thermodynamic properties of the solid solution, austenite, are of considerable importance in the heat-treatment of alloy steels and in other aspects of ferrous metallurgy. Early studies embodied in the Fe-C diagram have been extended to include other binary and some ternary diagrams. Our best hope of obtaining a useful thermodynamic treatment of reactions in complex alloy steels will not be found in quaternary and quinternary phase diagrams but in determinations of activities and interaction relations among the several solute elements. The foundation for such a development was laid by smith&apos; in his early studies of the activity of carbon in Fe-C alloys and his subsequent work on Fe-C-Si, Fe-C-Mn, Fe-C-Ni, and Fe-C-Co solid solutions.2"4 Other observers have also made noteworthy contributions and these will be discussed and correlated here in the light of a somewhat simplified mathematical treatment of solute interactions. Fe-C AT 1000°C In a recent review of the thermodynamic properties of binary Fe-C austenite it was shown that the simple mathematical treatment employed by smith&apos; was capable of describing all the published results on this solution. The treatment utilizes the atom ratio, yc = nC/nF,, rather than the atom fraction. The activity of carbon is proportional to the equilibrium gas ratio, either measured on a scalk in which the activity of graphite is taken as unity or, alternatively, aC may be set equal to yc at infinite dilution. In either case the ratio aC/y = (PC, the activity coefficient. It was found that the experimental data of smith1 and those of Diin-wald and wagner; Bungardt, Preisendanz, and Lehn-ert,&apos; and Scheil, Schmidt, and Wiinnings at temperatures of 800" to 1200° C as well as reliable data on the solubilities of graphite and cementite could be represented by the equation for which graphite is the standard state: The data on alloyed austenite have been obtained at 1000°C. For this temperature, the "Henrian" activity coefficient (which is unity at infinite dilution) is: FOr an interstitial solute such as carbon in austenite it has been shown by statistical mechanicsg that the activity in the infinitely dilute solution is proportional to the ratio of the number of lattice sites occupied by carbon to the number of yet unfilled lattice sites. A variable zz proportional to this ratio serves as a useful measure of concentration:" in which b is the number of lattice sites provided by each atom of solvent; in austenite b = 1. The Henrian activity approaches zz at infinite dilution and the ratio a is the activity coefficient. The effect of a change in concentration is then given by: It has been shown further that in some systems the derivative in Eq. [4] remains constant over a wide range of concentrations. In such a case second-order terms become negligible and the Henrian activity coefficients is:

Jan 1, 1969

By Robert G. Nisle

The classic theory of pressure build-up in shut-in oil wells as developed by Horner and van Everdingen is based on two-dimensional radial symmetry in the well-reservoir system. Such symmetry does not exist in the case of a well which parfiially penetrates the producing formation. As a result of this lack of symmetry the use of the classic theory in such cases become questionable. In this paper the mathematical theory has been extended to include the case of partially penetrating wells. Numerical solutions illustrating the up-dication of the equations are presented. The effect of partial penetration on pressure build-up is shown by a comparison of synthetic pressure build-up curves derived from the numerical solution of the equation for partially penetrating wells for various degrees of penetration. It is shown that partial penetration is detectable from the characteristic shape of the pressure build-up curve and that formation productivity may be calculated from the pressure buildup data in a manner identical to that described by the classic theory. INTRO DUCTION The use of pressure build-up data on shut-in oil wells is a well-established technique for the measurement of reservoir productivity. The work of Homer&apos; and van Everdingen&apos; is well known. Since the publication of their pioneering work, others"&apos; have elaborated and extended the technique. These authors have dealt exclusively with the case of wells that completely penetrate he producing formation. Two-dimensional radial symmetry is achieved, thereby, and the problem is greatly simplified. This ideal situation is seldom encountered in practice. But, in spite of this, the technique is often employed anyway. The question, therefore, arises: how much confidence can be placed in the results of such calculations when the data are taken on wells that only partially penetrate the producing formation? It is the purpose of this work to answer this question. Only the single-phase fluid case will be considered. van Everdigen&apos; has presented a rigorous solution of the two-dimensional case, but because of mathematical complexity, this solution has not proved to be particularly useful. Horner&apos; utilized Kelvin&apos;s point source solution in two dimensions and showed that it is a sufficiently good approximation for oil reservoir studies. The geometry of the well and the producing formation is illustrated in Fig. l. Geometrically the formation may be described as an infinite slab. The infinite slab is defined as the solid (the porous medium in this case) bounded by two parallel planes. Thus, the slab extends to very great distances in both the positive and negative directions of two of the coordinate axes, but is finite in

By PERCY E. BARBOUR

SECONDARY copper1 has &come more or less of a bugbear generally. What is its influence is often the subject of heated argument. The inedapable fact usually quoted is that since in 1929 primary production of copper in the United States was 1,026,348 tons and secondary production was 626,550 tons, there- fore, 0.6 lb. of secondary is produced for every pound of primary, and "How can you get around that?" The matter seems very plain, now that I have reached my conclusions, but they are the result of much laborious study and research. I shall show that&apos; the production of secondary copper is not 0.6 per lb. of primary, in spite of statistical appearances; that the production of secondary is a function of primary production rather than of price; that secondary production has &apos;only a sub-. ordinate influence on the price of copper and then only in abnormal times; that there is not an accumulating reservoir of secondary from which the country is some- time to be drowned in copper, as is believed by some, or a reservoir from which we are going to draw much needed and more or less inexhaustible stores in the future, as is believed by others; and finally, that the United States always produces more copper than it uses and exports the surplus. These are all controversial points, and for that reason and to anticipate argument I have set forth my reasoning in considerable detail.

Jan 1, 1931