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By John Tyssowski

IN 1925, Harry Howard Stout, then metallurgist for Phelps Dodge Corporation, while investigating the cleaning of cathode copper by various gases at elevated temper-atures below the melting point of the metal, observed in the laboratory that particles of pure copper heated in a closed tube filled with hydrogen seemingly "stuck together." By further investigation he found that there was actual crystal growth across the boundaries of the particles of pure metal; in other words, there was a complete new crystal realignment and growth throughout the newly formed copper mass. It was coalescence, not adhesion; the several parti-cles had become one unit. From this dis-covery has been developed the coalescence process, whereby copper of cathode purity is squirted out in semifabricated form from an extrusion press, by the appli-cation of about 3000 tons pressure on a 10-in. piston. Stout decided that cathode copper pro-duced by electrolytic deposition was the logical source of the pure copper required for the coalescence process, but as there was no way of reducing the ordinary tough commercial cathodes to the small particles required he was confronted by a serious problem at the outset. Under his direction, this problem was solved by William H. Osborn and Harry Howard Stout, Jr. They developed the process and technique for producing cathode copper in brittle, friable

Jan 1, 1940

By G. Barbery

Since the original paper, two methods have been introduced to compute the parameters of the three parameter size distribution equation: [ ] Both of them are based on graphical means, which are time-consuming and of little statistical significance. A program has been developed, using the Gauss-Newton method to compute by nonlinear regression analysis the parameters of the equation. Although the method is quite general in curve-fitting applications, it does not appear to be used in the field of size analysis, and a brief description is given. As applied here, the Gauss-Newton method involves the minimization of the least squares: [ ] where n is the number of sieves used. The second member of Eq. 2 can be approximated by a multiple Taylor's series expansion of first order about a starting value [ ] The minimization of Q (r,s,Xo) means: [ ] Putting Eq. 3 into Eq. 2 and differentiating, we obtain a system of equations which can be represented in matrix symbolism (box) The system can be solved for: [ ] and the operations repeated with new values: [ ] The starting values for r and s are taken as 1, for Xo, a value higher than the maximum sieve opening value. Applied to the data given by Herbst 5,6 for batch grinding of 7 X 9 mesh dolomite, the parameters given in Table 1 were obtained. The discussion of the significance of the residual sum of squares is a difficult subject in multiple nonlinear

Jan 1, 1972

By Mohamed Mortada

A practical analytical method is developed in this paper which provides the practicing reservoir engineer with a handy method for analyzing oilfield interference problems. The procedure employed entails the principle of superposition of individual eflects. A set of charts has been developed and can be used to evaluate the individual effects. The charts represent non-steady state pressure distribution in an extensive aquifer due to a constant rate of production from an oilfield which can be approximated by circular geometry; they are constructed from solutions to the diffusivity equation considering a circular sink as distinguished from a point sink. The solutions are obtained partially from mathenlatical considerations and partially from analog and digital computations. By virtue of the method of images, the charts can be used also to treat the case of production near a fault. In addition, provisions are made for treating oil fields, which are produced by partial water-drive. Treating an actual field case is deferred to a subyequent writing; however, illustrative example is presented to demonstrate the method of application. The pressure distribution in linear and limited radial aquifers is currently under study. INTRODUCTION With the increasing difficulty of discovering new oil reserves, attention is necessarily focused on the efficient development and production of existing reservoirs. Efficient production depends on the availability of reliable means for predicting the pressure-production behavior of oil fields. The prediction is usually performed by analytical methods or computers. Analytical methods are often limited to systems which can be approximated by simple geometry. However, analytical methods have the distinct advantage of being readily performed without special equipment. Analog and digital computers lend themselves to a variety of problems, but are not always locally available and consequently their use is limited. One particular situation in which analytical techniques are needed involves studies of multiple, water-drive oil fields sharing a common aquifer. Such oil fields are in hydrodynamic communication. Therefore, production from any of the oil fields is accompanied by a pressure decline which is transmitted through the aquifer to the other oil fields and manifested as pressure interference. The rate of propagation of the pressure decline is such that the pressure may be significantly reduced many miles away from a producing pool. An example of pressure interference is found in the Woodbine formation in East Texas. There. a dozen or more pools, including several of major size, draw on the Woodbine formation for water drive. The pressure in the water-bearing portion of the formation has been significantly reduced over an area of several thousand square miles. This reduction of pressure has been such that when the Hawkins pool was discovered in 1940, the pressure in it had already been reduced 280 psi below the initial value in the aquifer. This resulted from prior production from other Woodbine sand pools, including, in particular, the East Texas field some 20 miles to the east of Hawkins.' The above example indicates that the interference effect can be significant and should be taken into con-

Jan 1, 1956

By E. C. Barfield, D. G. McCarty

Two-dimensional analyses offer considerable promise in providing the basic information required to effect more precise control of petroleum reservoir performance. This paper describes a method for conducting some engineering analyses of this type using a high-qreed digital computer. The general approach is to (I) develop a representative numerical model of the reservoir and (2) employ a suitable numerical technique to solve the basic equation of flow and to develop the required engineering information for the particular case represented by the model. This technique has been used to calculate pattern performance in connection with several field projects involving water injection into oil reservoirs. This type of analysis involves sequentially (I) calculating the pres-' sure distribution in the reservoir and (2) tracking the progress of the interface between the displaced and displacing fluids in a step-wise manner to provide a depletion history of the operation. The particular analysis presented in this discussion is subject to the restriction that the mobility of the displaced and displacing fluids be equal and assumes that the fluids are incompressible and that gravity and capillary pressure do not affect the shape of the flood pattern. Complete two-dimensional .flexibility is maintained with regard to definition of reservoir rock and fluid characteristics, placement of physical restrains and boundary conditions, investigation of flow characteristics in the reservoir, and movement of the displaced and displacing fluid interface. The results of these studies indicate that the highspeed digital computer is well suited for conducting reservoir performance studies in two-space dimensions and that dependable numerical techniques are available for making such analyses. INTRODUCTION One of the problems facing petroleum engineers is that of providing more precise engineering control over reservoir operations at all stages during the depletion cycle. The most direct approach to this problem is to simulate the reservoir with some type of physical or mathematical model and use the information developed from the behavior of the prototype to predict the performance of the actual reservoir. This principle is, of course, not new, and a variety of simulation techniques have been developed to provide information on the behavior of oil and gas reservoirs. One straightforward refinement of present reservoir analysis techniques is the progress from one-dimensional reservoir models to those where the reservoir can be represented in two- and three-space dimensions. Multidimensional reservoir analyses are desired in order to show not only what is happening in the reservoir but in addition to show where in the reservoir the various phenomena of interest are occurring. Thus far, two-dimensional analyses have been confined predominantly to potentiometric and electrolytic model studies. However, when large numbers of wells are involved and where large-scale models are required, such problems become very tedious and instrumentation problems become acute." It is possible through use of numerical methods and general purpose digital computers to avoid many of the instrumentation difficulties and to relax some of the restrictions of previous techniques. The purpose of this paper is to discuss some recent experiences with the use of high-speed digital computers for predicting pattern performance in fluid injection operations and to describe the numerical procedures which have been used for making such analyses. THE NUMERICAL MODEL The problem of representing the reservoir with an appropriate numerical model is composed of at least two important considerations. The first requires that an adequate description of the reservoir mechanism be formulated in the form of the basic differential equation describing the process. The second consideration is definition of the physical characteristics of the reservoir. The latter requires that representative basic data be obtained, examined, and interpreted to provide sufficient detailed definition of the pertinent physical properties throughout the system. The Differential Equation One of the basic assumptions made for the purpose of performing the two-dimensional studies being dis-

By W. M. Peirce

FOR many years it was considered quite the proper introduction to any discussion of zinc metallurgy to remark that the methods of extracting zinc from its ores were archaic. Often there was an added implication that the industry in every phase savored of the days of alchemy. On rare occasions comments of this sort may still he heard. Fortunately, not only for the zinc industry but for the world at large, there is today no longer a basis for considering zinc metallurgy unprogressive. Progress in any industry is possible along three distinct lines. The methods of production may be improved, thereby reducing costs. In the case of basic materials, this may also have the important effect of increasing potential supply. Second, quality may be improved. Finally, the product may be made more valuable to consumers through increased knowledge of its utilization, thus holding old markets or opening new.

Jan 1, 1931

By William P. Blake

THE use of diamonds upon a large scale in drilling rocks, and the substitution to a certain degree of rotary diamond drills for the ordinary steel percussion drills, marks a new era in the art of mining. Since the invention by Leschot of the diamond drill, it has steadily advanced in its utility and range of application, and in the appreciation of miners and engineers. I t must be claimed as one of the many gifts of science to the arts ; and it is, in particular, one of the fruits of the scientific education given at the Ecole Centrale, at Paris. Members are all, doubtless, more or less familiar with the construction of the drill and of the machinery by which it is applied in boring. I t is, therefore, my present purpose only to direct your attention to some recent marked improvements, made by the American Diamond Drill Company, by which the economy and efficiency of the machines have been increased. Form of Bit.-The annular or ring form of the drill-head or bit was, I believe, the earliest; and it is still in use, without essential modification, wherever it is desired to obtain a sample " core" or specimen of the rock traversed. But for mere drilling, regardless ~f the preservation of a test-core, a solid-head bit is preferred, except for very large holes. Until recently, these solid-head bits were made with a pointed cutting face shaped like an obtuse cone. This form was assumed to be the best, being most in accordance with the experience obtained with percussion drills. I t is found, however, that the exact reverse

By W. B. Braden

This paper presents a suitable method for predicting gas-free oil viscosities at temperatures up to 500F knowing only the API gravity of the oil at 60F and the viscosity of the oil measured at any relatively low temperature. The API pravity and the one viscosity value are used as parameters to determine the slope of a straight line on the ASTM slanaord viscosity-temperature chart. Then, knowing the slope of the line and one point on the line, the vrscosities at higher temperatures can be determined. The line slope correlations were developed at I00 and 210F since viscosity data are frequently measured at these temperatures. A procedure is given for predicting line slopes from measurements at other tetnperatures. A nomogram is furnished for solving the relationship. The correlation has been evaluated at temperatures up to 5OOF for oils varyzng in gravity from 10 to 33 " API. The correiution is applicable only to Newtonian fluids. Comparison at 500F of true viscosities and those predicted from values at 100F shows an average deviation of 3.0 per cent (maximum deviation of 6.0 per cent). Predictions from the values at 21 0F for the same oils how an average deviation of 1.5 per cent (maximum deviation of 3.4 per cent). INTRODUCTION Correlations have been developed by Beal' and by Chew and Connally' for predicting viscosities of gas-saturated oils at reservoir conditions. Each of these correlations requires a knowledge of the solution gas-oil ratio and the viscosity of the gas-free oil at the reservoir temperature. For temperatures below 350F, measurements of the gas-free oil viscosities can be made easily using commercially available equipment. In thermal recovery processes, however, reservoir temperatures well in excess of 350F are encountered. Viscosity measurements at such conditions are more difficult and time consuming and require modification of existing equipment or the construction of new equipment. Measurements are further complicated by the difficulty of handling highly viscous oils associated with thermal recovery processes. Therefore, it is desirable to have a correlation which allows accurate prediction of viscosities at high temperatures. A commonly used technique for predicting viscosities at high temperatures is to measure the viscosities at two lower temperatures, plot the values on ASTM standard viscosity-temperature charts and extrapolate to the temperatures desired. If either of the values is slightly in error, the extrapolated value can be significantly in error. To justify an extrapolation, three points are actually necessary. This procedure can consume much time, particularly with heavy oils. Considering the cost of viscosity measurements, it would be desirable to eliminate the need for direct measurements by having correlations which would allow viscosity predictions from other physical or chemical properties. Beal1 investigated the possibility of correlating viscosity with oil gravity at temperatures from 100 to 220F. While showing that a general relationship exists, he also found significant deviations. It is possible that correlations will be developed based on oil composition as more information becomes available. While not eliminating the need for viscosity rneasurements, the method presented herein requires that only one viscosity measurement be made. The API gravity must also be known. The theory is based on the fact that the viscosity of paraffins (high gravity) changes less with temperature than does the viscosity of naph-thenes or aromatics (low gravity). The gravity. therefore, is used as a parameter to determine the slope of a straight line on the ASTM standard viscosity-temperature charts. The correlation is applicable only to Newtonian oils, and deviations due to thermal decomposition and nonhomo-geneity cannot be predicted. Oils containing additives have not been evaluated. PROCEDURE Fifteen oils were used in developing the correlation; eight were crudes and seven were processed oils. Oil gravities varied from 9.9" API (naphthene base) to 32.7' API (paraffin base). The temperature range studied was 81 to 516F. Each oil used had a minimum of three viscosity measurements and each plotted essentially as a straight line on the ASTM charts. In all, 91 viscosity measurements were used in the correlation. Saybolt, rolling ball and capillary tube viscometers were used for the measurements. Viscosity data for Samples 1, 2, 4, 7, 10, 11 and 14 were obtained in Texaco, Inc. laboratories. The data for Samples 3, 5, 6, 8, 9, 12 and 15 were from Fortsch and Wilson,3 and data for Sample 13 were from Dean and Lane.' All data points used in the correlation are plotted in Fig. 1. It is seen that some of the viscosity values deviated slightly from the straight-line plots at the higher temperatures. Properties of the oils after exposure to the

Jan 1, 1967

By R. Van A. Norris

The following tests were made, during 1889, for the Susquehanna Coal Company, to determine the relative efficiency of several styles of mine-car wheels in use at their collieries at Nanticoke, Pa. The wheels experimented upon may be divided into two classes: The "old style" (Figs. 1 and 2), which are oiled at every trip; and the "new style" (Figs. 3, 4, and 5), which require oiling about once in two to four months. Fig. 1 shows a section of a plain cast wheel, with patent annular oil-chamber. This is held in position on the axle by a square, split cotter-pin. Fig. 2 is a similar wheel, with a patent cast bushing, which is readily replaced when worn. The lubrication is effected by a simple oil-hole, but the oil is delivered a little inside of the gaugeline of the wheel, where it is most needed. Figs. 3, 4, and 5 are sections of a " new style " patented, self-oiling wheel. In this, the outer end is cast closed, and the wheel is fastened to the axle by a spring cotter-pin passed through one of the plugged holes. Dirt is prevented from entering the open end by a cap, with faced end and packing-ring, fitting over the end of the hub. The lubricant is introduced into the oil-chamber through one of the plugged holes in the hub. When the wheel is in motion, the lubricant is thrown by centrifugal force away from the axle, enters the two ports shown, and is

Jan 1, 1890

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members) The following is a partial list of members and guests who called at Institute headquarters during the period May 10,1917, to June 10, 1917. F. J. Anderson, Cali, Colombia. W. F. Jahn, Kirkland Lake, Ont., Canada. George J. Bancroft, Denver, Colo. W. McA. Johnson, Hartford, Conn. W. F. B. Berger, Denver, Colo. J. E. Jopling, Marquette, Mich. F. J. Brulé, Toronto, Ont., Canada. William Kelley, Vulcan, Mich. J. Murray Clark, Toronto, Ont., Canada. H. M. LaFollette, La Follette, Tenn. Will L. Clark, Jerome, Ariz.. Dorsey A. Lyon, Washington, D. C. G. H. Clevenger, Palo Alto, Cal. James F. Magee, Lancaster, Pa. Paul S. Couldrey, Sound Beach, Conn. M. Ortin, Nijni-Novgorod, Russia. C. W. Crispell, Kingston, N. Y. - C. H. Palmer, Jr., Los Angeles, Cal. George A. Easley, La Paz, Bolivia. Edison S. Pettis, ?Mill Valley, Cal. Bancroft Gore, Butte, Mont. Mortimer A. Sears, Paintsville, Ky. John B. Guernsey, Roanoke, Va. W. J. Uren, Houghton, Mich. Rush M. Hess, St. Louis, Mo. C. E. Visel, New Haven, Conn. E. Hibbert, Nickelton, Ont., Canada. Percy E. Barbour, has resigned his position as managing editor of the Engineering & Mining Journal, to accept the appointment of Deputy Superintendent of the New York State Troopers, with headquarters at Albany, N. Y., with the rank of captain.. He has also been commissioned as captain in the 22nd Regiment, N: Y. N. G., having been formerly 1st Lieutenant.

Jan 7, 1917

By A. J. Erickson, W. J. Garmoe

In mid-1970, Park City Ventures, a Utah partnership of Asarco and the Anaconda Company, initiated a six-phase exploration and development program in the Park City District, Utah. Geologic studies had delineated a number of exploration targets in several areas of the district. Discovery of ore in any of the target areas and continued favorable downdip development below then productive ore bodies would allow for reserve expansion and mill construction. The targets were: replacement mineralization in the Mississippian Humbug formation below productive ore bodies on the east flank of the Park City anticline; replacement mineralization in the Humbug formation in an unexplored fault block in the footwall of the Hawkeye structure on the east flank of the anticline; vein and replacement mineralization along the Silver Fissure; potentially higher grade replacement mineralization in the Humbug formation in a theorized structural block on the west flank of the anticline beneath the Ontario vein; replacement mineralization in the Permian Park City formation in the West End shaft area of the Silver King mine; vein mineralization along the Back vein in the Judge mine. In 1971 the Judge and Silver King Projects were suspended, due to a 30% cutback in the exploration budget. In spite of the cutback additional reserves were developed below the Humbug East Flank ore bodies; a major zone of ore grade mineralization was discovered along the Silver Fissure, five new ore bodies were found in the Humbug and Doughnut formations on the west flank of the anticline beneath the Ontario vein. First concentrates were shipped from a new mill in May 1975.

Jan 1, 1979

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst' shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.' The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy's equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By J. N. Ong

The oxidation of tantalum is assumed to occur by four simultaneous first-order chain reactions; solution of oxygen in the metal, nucleation and growth of a suboxide phase at the metal surface and two phase boundary processes which give rise to two different modifications of Ta2O5. A rate equation is then formulated which accounts for all principal details of oxidation behavior, unifies and correlatss the results of the principal investigations, and expresses the rate as a function of pressure, temperature, and time. For purposes of practical application, the expressions: may be used below and above 700T respectively to determine the regression rate of tantalum in cm per hr, where T is to be expressed in "K and P in atmospheres pressure of oxygm. The equations will reproduce within a factor of two all reported experimental rates in the temperature range 475" to 1400°C and pressure range 0.000026 to 40.8 atm 0. 1 HE oxidation kinetics of tantalum have been investigated thoroughly in the temperature range 50" to 1400 and pressure range 1.32 x l0-' to 40.8 atm pressure of 0,and as a result, the principal features of the oxidation of tantalum are known and have been described in considerable detail. The exposition of the characteristics of the behavior of tantalum in oxygen has been largely descriptive, with considerable attention being devoted to elucidating the structure, composition, and morphology of the resulting oxide products. The weight change vs time results have usually been reported graphically. With the exception of the linear rate below 700 C and the process of diffusion of interstitial oxygen into the metal,6'9 no effort has been made to characterize the reaction rates in functional form. It is the purpose of this paper to demonstrate that when the fundamental principles of chemical kinetics are rigorously followed, the results of the principal investigations will be correlated and unified and the oxidation rale may be expressed as an analytic function of pressure, temperature, and time. In addition to accounting for the temperature and pressure dependency of the oxidation rate, the following minor features will be accounted for as a result of the basic analysis: the initial period of nonline-arity in rate at low temperatures, which decreases with increasing temperature;3'5'7 the rate vs temperature cusps obtained at constant pressure"5 the concentration gradient of oxygen interstitially dissolved in the metal.5'7 The analysis will also be consistent with the overall chemistry of reaction and with all visual, microscopic, and X-ray observations. DEVELOPMENT OF RATE EQUATION As a fundamental basis for the treatment of metal-oxygen reaction kinetics, it will be regarded that the rate of reaction is determined by the concentration and not the activity or chemical potential. It is further assumed that all metal-oxygen reactions are first order complex chain reactions" whose rate is dependent on the concentration of an intermediate species which is a complex function of the oxygen concentration, or oxygen pressure, only. The basic rate equation is therefore: is the weight of oxygen consumed by the reaction, A is that portion of the area of the metal over which the reaction is occurring (cm2), t the time (sec), kf the rate constant for forward reaction, C the intermediate species concentration and f '([Oz]) and f (Po,) are complex functions of oxygen concentration and Oxygen pressure respectively. Reverse reactions may usually be neglected in metal-oxygen systems since a large negative free energy generally accompanies these reactions. Eq. [I] takes different forms when the rate of reaction is controlled by diffusion into or through a phase or at a phase boundary. For diffusion into the metal phase, the rate is given by1' Di is the diffusion coefficient of species diffusing into the metal phase (cm2/sec), and Q is the corre-

Jan 1, 1962

By M. T. Hepworth, T. P. Papazoglou

Hydrogen diffusion in hcp and bcc titanium in the temperature range 610° to 900°C was measured by reacting cylindrical specimens of high-purity titanium at constant temperature with small constant pressures of hydrogen of the order of a few Torr. In the range 0 to 6.7 at. pct H in hcp titanium, the diffusion coefficient D in sq cm per sec is given by: where T is in °K and R in cal per g-atom OK. Only three measurements of diffusivity in bcc titanium were made: at 900' : the diffusivity in ß titanium was found to be 1.8 x 10-4 sq crn per sec. McQUILLAN1 has studied the constitution of the Ti-H system and reported the concentration of hydrogen as a function of pressure of hydrogen and temperature. He found hydrogen absorption was reversible and rapid at temperatures above 500°C in both crystallographic modifications, the a (hcp) phase and the ß (bcc) phase, with the latter phase stabilized by hydrogen additions. Wasilewski and Kehl 2 measured the diffusivity of hydrogen in hcp and bcc Ti-H alloys. For bcc alloys, they reacted cylindrical specimens of titanium with hydrogen gas at 1 atm pressure. They measured the rate of absorption of hydrogen isothermally on specimens ranging from zero hydrogen content when above the transformation temperature to hydrogen contents sufficient to stabilize the bcc phase when below the transformation temperature. By integrating Fick's second law for a cylindrical geometry, assuming a diffusion coefficient independent of composition, they calculated diffusivities as a function of temperature. In the range 650" to 1000°C their results in bcc titanium yielded the expression: where D is in sq cm per sec, T in OK, and R the gas constant in cal per g-atom-OK. Their studies on the hcp a phase were conducted by exposing long cylindrical titanium specimens to hydrogen at a sufficiently high pressure to establish a surface layer of fl phase 80 to 120 u thick for the duration of an isothermal experiment. Concentration profiles were then determined by hydrogen analysis from chips obtained upon machining quenched specimens. The diffusivity of hydrogen was then calculated yielding the expression: The present investigation was undertaken principally to redetermine the diffusivity data on a titanium by a direct absorption from the gas phase at sufficiently low hydrogen pressures to avoid the presence of a surface bcc phase and also to check the diffusivity data at low hydrogen concentrations in the bcc stmcture. EXPERIMENTAL PROCEDURE High-purity electrolytic sponge titanium (99.9 pct) of BHN 91 was arc-melted, forged, rolled, and machined into cylinders of final hardness, upon annealing, of BHN 92. Cylindrical specimens of two sets of dimensions were used: 1.524 by 2.931 cm and 1.905 by 3.663 cm diam and length, respectively. The experimental apparatus used for annealing specimens and for admitting known amounts of hydrogen at constant pressure is shown in Fig. 1. In a typical experiment, a specimen was lightly abraded with fine-grain silicon carbide, washed with water and detergent, and then thoroughly degreased with reagent-grade tri-chlorethylene and acetone. The specimen was suspended by a Chrome1 wire in the center of a quartz furnace tube, without contact with the tube, and heated to 925°C (as measured by a thermocouple adjacent to the specimen, outside the tube) for a period of at least 4 hr under a vacuum of from 10-6 to -7 Torr as measured by an ionization gage. The furnace temperature was then adjusted to the temperature chosen for the particular diffusion study and the specimen allowed to equilibrate thermally. Hydrogen was then ad-

Jan 1, 1969

By H. Kenworthy, R. B. Fisher, R. G. Knicherbocker, M. M. Fine

The progress made to date in the mineral dressing of complex Arkansas titanium ores is reported in this paper. Concentrates of rutile, a dioxide of titanium, were produced by treating a submarginal ore from the Magnet Cove Rutile Co., Inc., Magnet, Ark. The rutile recovery at present is 45 to 50 pct of the total TiO2, with the possibility of increased recovery with additional research. The work reported herein is part of a general study which will later include results of investigation of other titanium ore bodies in the Magnet, Ark., area. The fragile character of the rutile minerals, the softness of the gangue, the occurrence of pyrite and leucoxene, and the considerable proportion of extremely small size rutile in the presence of montmorillonite- and illite-type clays in the Magnet Cove open-pit mine are the important factors in the mineral dressing of this submarginal rutile ore. History The occurrence of titanium minerals in the Magnet Cove area of Arkansas was recognized as early as 1890, but it was not until about 1912 that any appreciable prospecting for the minerals was undertaken. At that time drilling was begun, a shaft was sunk, and several drifts were driven, but beneficiation to recover the titanium minerals was not attempted. The only successful mining and milling operation of the Magnet Cove rutile deposit was begun in 1932 by the Titanium Corp. of America and continued until 1942. The ore was washed by means of a rotary scrubber and then deslimed in a drag classifier. The discharge was ground in a rod mill, classified, and tabled to recover a rougher rutile concentrate, which was screen-sized and retabled on cleaner tables. The cleaner concentrates were given a reducing roast, screen-sized, and magnetically separated to produce a finished rutile concentrate. Most of the rutile produced during this period was sold abroad. In 1942, the Titanium Alloy Corp. of Arkansas (a subsidiary of the Titanium Alloy Manufacturing Co. of New York) purchased the property and rebuilt the mill. Subsequently, the plant and property were acquired by the Magnet Cove Rutile Co., Inc., of Little Rock, Ark., the present owners. Very little titanium has been produced since 1942. Although the Titanium Corp. activities yielded enough returns to allow continued operation for approximately 10 years, certain factors must be recognized. These are: (1) production of rutile in that period was during a low in the economic cycle which permitted low-cost operation on a small scale, and (2) a considerable portion of the production was above the water level and no drainage problems existed. Prior to this paper there has been no published report of any mineral-dressing investigation of the lower levels of the ore body. Reference is made in another paper1 to an earlier investigation of Magnet Cove rutile by the Rolla laboratory, in which it is stated that recoveries of 12 to 17 pct of the rutile were obtained. The present investigation was undertaken to improve the known milling processes and to provide adequate metallurgical information about the ore treatment. Titanium Technology The titanium mineral of primary interest in the present investigation was the titanium dioxide, rutile. Rutile is one of the industrial minerals whose annual consumption is relatively small but strategically important. The domestic production of rutile was 7100 tons in 1948. The imports of rutile in the same year were approximately 8000 tons.2 A major use of rutile is in the production of welding-rod coatings, for which a product containing a minimum of 92 pct titanic oxide is desired. Other constituents, such as lime, silica, and sulphur, must be held to a minimum, but hard-and-fast specifications for these elements cannot be drawn. It is necessary to incorporate the rutile in a welding-rod coating, make a sufficient number of test welds, and then determine the tensile strength of the weld metal in the as-welded and stress-relieved conditions. Such a test gives

Jan 1, 1950

By H. Dykstra

Calculated wellbore pressures were obtained for parameters of radilcs ratio and permeability. In all cases bur two, after-production was allowed to occur for one day. The calculated pressure build-up data were compared with actual pressure build-up data from a condensate well. The paper discusses the comparison, gives reasons for, inability to match calculated (2nd actual data, and presents conc1usions derived from the comparison. INTRODUCTION Considerable information has been published on the decline in wellbore pressure for oil and gas fields resulting from production of fluids. Considerable information also has been published on pressure build-up for oil fields, but relatively little has been published for gas and condensate fields. Perrine' summarized the equations derived for pressure build-up in oil wells and showed how the different methods could be applied. On the other hand, very little theoretical information has been published on pressure build-up in gas or gas-condensate wells.2-4 Tracy,' by pointing out the similarity between the equation describing oil wellbore pressure decline and the equation describing gas wellbore pressure decline, showed how methods of pressure build-up analysis could be applied to a gas well. In analyzing pressure build-up data for gas or gas-condensate wells, it would be very desirable to compare actual pressure build-up data with calculated pressure build-up data. Such a comparison would lead to a better feeling for the quantitative picture of gas-well build-up curves and would help to establish a degree of confidence in a given build-up curve. This paper discusses the comparison and presents conclusions made from it. Calculated wellbore pressures are given for parameters of radius ratio and permeability. In all cases but two, after-production was allowed to occur for one day. The work was done in an attempt to evaluate the reserves of a gas-condensate field. As will be discussed later, it was not possible to make an evaluation. METHOD OF CALCULATION The method used for solving the depletion and pressure build-up behavior for a gas-condensate well was that developed by West, Garvin and Sheldon.5 or the IBM 704 computer program used, it was assumed that liquid condensing out of solution would have only a minor effect on the flow behavior. Therefore, the field was treated as having single-phase flow, with the gas saturation S, remaining constant at unity minus the connate-water saturation Sw. As will be discussed later, this may not have been a good assumption. It also was assumed that oil production could be considered as equivalent gas production by using a conversion factor based on an analysis of the liquid produced. An outer boundary condition of no-flow was assumed. BASIC DATA The data required for the study were reservoir properties, fluid properties and production data. Reservoir properties included the following: thickness h, 179 ft; porosity, 0.194; connate-water saturation, 0.43; gas saturation, 0.57; permeabilities k, 1.0, 0.5, 0.25 and 0.15 md; radius ratios re/rw, 800, 1,000 and 2,000; wellbore radius rw, 5 in.; initial reservoir pressure P, 6,529 psia; and reservoir temperature, 272°F. The selection of permeabilities was based on core-analysis data showing an average air permeability of about 2 md. With a relatively high connate-water saturation, the average effective gas permeability would be about one-half, or less, of the air permeability. The selection of radius ratios was based partly on the observed rapid decline in wellbore pressure during production and partly on the fact that the well was believed to be located in a relatively small fault block. Reservoir fluid properties were obtained from a reservoir fluid study on a recombined sample of gas and condensate. Gas formation-volume factors were calculated from pressure-volume measurements made at reservoir temperature. Gas viscosities were calculated by the method of Carr, et al,G from an analysis of the re-combined sample. These data are shown as a function of pressure in Table 1. The production schedule from the gas-condensate

By Henry Rogatz

Oil.—During the year 1938, there were 434 oil wells drilled in the Texas Panhandle, increasing the daily initial production by 192,706 bbl. —that is, 229 fewer oil wells drilled than in the previous year, with a decrease in total daily initial production of 129,626 bbl. The total daily potential of the field on Dec. 1, 1938, as determined by the Texas Railroad Commission, was 1,250,645 bbl., an increase of 210,663 bbl. over the previous year. On Dec. 1, 1938, the daily allowable of 82,466 bbl. was assigned to the field to be produced from 3931 wells. The total amount of oil produced for the year was 23,227,170 bbl. The total proven productive area includes 148,298 acres. This is 30,248 acres more than for last year, and represents a more accurate calculation of the areas and not new discoveries. Gas.—There were 103 gas wells drilled during 1938, having a combined open flow of 3,166,300,000 cu. ft.; that is, 65 less than the number of wells drilled in 1937, with a decrease in the open flow of 3,144,488 cu. ft. per day. Pipe-line Gas.—The pipe-line companies withdrew 230,307,854,000 cu. ft. of gas (a daily average of 630,980,000 cu. ft.). The total withdrawals by pipe line decreased 5,624,481,000 ft. from that of 1937. Natural Gaso1ine.—Throughout the greater part of the year, 46 gasoline-extraction plants processed 1,376,186,000 cu. ft. per day, a total of 502,308,010,000 cu. ft. for the year. This gas yielded about 275,875,000 gal. of natural gasoline. The total daily capacity of all the plants is 2,519,500,000 cu. ft. During the latter part of 1938, one of these plants was shut down, leaving 45 plants operating at the close of the year. Carbon Black.—Thirty carbon-black plants operated during 1938, burning 266,881,000,000 cu. ft., or a daily amount of 731,180,000 cu. ft. This produced approximately 400,000,000 lb. of carbon black. During the year one plant was dismantled and two plants were shut down.

Jan 1, 1939

By Henry Rogatz

Oil.—During the year 1938, there were 434 oil wells drilled in the Texas Panhandle, increasing the daily initial production by 192,706 bbl. —that is, 229 fewer oil wells drilled than in the previous year, with a decrease in total daily initial production of 129,626 bbl. The total daily potential of the field on Dec. 1, 1938, as determined by the Texas Railroad Commission, was 1,250,645 bbl., an increase of 210,663 bbl. over the previous year. On Dec. 1, 1938, the daily allowable of 82,466 bbl. was assigned to the field to be produced from 3931 wells. The total amount of oil produced for the year was 23,227,170 bbl. The total proven productive area includes 148,298 acres. This is 30,248 acres more than for last year, and represents a more accurate calculation of the areas and not new discoveries. Gas.—There were 103 gas wells drilled during 1938, having a combined open flow of 3,166,300,000 cu. ft.; that is, 65 less than the number of wells drilled in 1937, with a decrease in the open flow of 3,144,488 cu. ft. per day. Pipe-line Gas.—The pipe-line companies withdrew 230,307,854,000 cu. ft. of gas (a daily average of 630,980,000 cu. ft.). The total withdrawals by pipe line decreased 5,624,481,000 ft. from that of 1937. Natural Gaso1ine.—Throughout the greater part of the year, 46 gasoline-extraction plants processed 1,376,186,000 cu. ft. per day, a total of 502,308,010,000 cu. ft. for the year. This gas yielded about 275,875,000 gal. of natural gasoline. The total daily capacity of all the plants is 2,519,500,000 cu. ft. During the latter part of 1938, one of these plants was shut down, leaving 45 plants operating at the close of the year. Carbon Black.—Thirty carbon-black plants operated during 1938, burning 266,881,000,000 cu. ft., or a daily amount of 731,180,000 cu. ft. This produced approximately 400,000,000 lb. of carbon black. During the year one plant was dismantled and two plants were shut down.

Jan 1, 1939

Abbott, Argyle Campbell 1209 Sherwin Ave., Chicago, Ill. Almstrom, Adne A., Student, Met. Engrg., Washington State College Pullman, Wash. Ankudinoff, N., School of Mines, Univ. of Utah Salt Lake Cite, Utah. Apter, Robert F., Student, McGill Univ Montreal, Que., Canada. Bailey, Donald G 798 Kensington Rd., Los Angeles, Cal. Baker, Kenneth B., Met., Aluminum Co. of America Pittsburgh, Pa. Barger, Thomas, Student, Univ. of North Dakota Grand Forks, N. D. Bartholomees, Geo. C Box 304, Bonne Terre, Mo. Bates, Walter, Student, Univ. of Utah, School of Mines Salt Lake Cite, Utah. Bobb, Russell V 16 College Ave., Houghton, Mich. Boswell, John C., Stripping Asst., Fairbanks Exploration Co Fairbanks, Alaska. Brandenburg, E. C., Student, Univ. of Kentucky 112 Church St., Lexington, Ky. Brannen, John, Chemist, Assay Office, Consolidated Min. & Smelt. Co. of Canada, Ltd., Tadanac, B. C., Canada. Brooker, Edgar, Jr., Student, Ferrous Met., Stanford Univ., Stanford University, Cal. Brooking, Leslie E 738 Lakoma, Norman, Okla. Clark, Martin Lester, Student, Missouri School of Mines Rolla, Mo. Collins, Edward D., Jr Box 1597, Ribbing, Minn. Comeau, Faye Bernard, Student, New Mexico State School of Mines Socorro, N. M. Conder, Henry S., Student, Pet. Engrg., College of Min., Univ. of California, Berkeley, Cal. Cotton, John Francis, Metallographist, Stealton Plant, Bethlehem Steel Corp., Steelton. Pa. Dahlgren, Elmer George, Student, Univ. of Wisconsin, Tripp Hall, Madison, Wis. Dale, James L., Student, Colorado School of Mines Golden, Colo. Dashti, Mirza Abdullah Khan, Graduate Student, Columbia School of Mines, Engrg. Chemistry, New York, N. Y. DeHuff, Gilbert L., Jr., Student, Lehigh Univ Bethlehem, Pa. de Romana, Enrique P., Jr. Engr Casilla 22, Arequipa, Peru. Oresbach, Charles Howard, Geol., Gulf Production Co Box 1428, Amarillo, Tex. Evens, Howard G., Student, Michigan College of Min. & Tech Houghton. Mich. Fassler, Glen Emerson Rodman, Inspiration, Ariz. Feight, Charles Donald, Foreman, Clairton By-Product Coke Wks., Carnegie Steel Co., 319 5th St., Wilson, Pa. Floe, Carl F., Student, State College of Washington Pullman, Wash. Fuentes, Vicente, Student, Pet. Engrg., Univ. of Oklahoma, School of Mines, Norman, Okla. Fuhrman, Carl F., Student, New Mexico School of Mines Socorro, N. M. Goergen, Gerald G., Cerro de Pasco Copper Corp Casapalca, Peru. Grove, Hubert A., Training Course, U. S. Aluminum Co New Kensington, Pa. Gastetter, Robert E 1010 N. Cherry Ave., Tucson, Ariz. Halbouty, M. T., Student, Texas Agriculturcl & Mech. College, Box 254, Faculty Exchange, College Station, Tex. Halfast, Edgar 710 E. Okmulgee Ave., Muskogee, Okla. Hall, Robert Lee 121 58th St., Niagara Falls, N. Y. Hanson, Rolf H., Student, Colorado School of Mines Golden, Colo. Hillyer. Shaler G., Student, New Mexico School of Mines Socorro, N. M. Hoertel, Frederick W., Met., R. W. Hunt Co., Engrs St. Louis, Mo. Holtz, Henry G., Student, Ohio State Univ Columbus, Ohio. Hon, Richard J Box 721, Miami, Ariz. Huffman, James O'Neil, Student, College of Min., Univ. of California Berkeley, Cal.

Jan 1, 1929

By L. R. Shoenberger

Boron has been used to produce nonaging low-carbon sheet steel. Retention of the necessary minimum amount of about 0.006 pet partially killed the steel. Amounts exceeding about 0.012 pet increased the degree of deoxidotion, piping tendencies, and possibility of hot tearing in primary rolling. Semikilled practice resulted in good ingot yields and satisfactory surface quality. Aluminum added with the boron provided a protective de-oxidizer. Good drawobility was indicated by performances of the steel in a limited number of deep-drawing trials. Some problems with hot-tearing and boron-analysis procedures were overcome. Metal lographically, the boron semikilled steels revealed some structures not usually found in plain low-carbon steels. IN 1943 Low and Gensamer1 reported that strain aging, which hardens and embrittles ordinary low-carbon rimmed steel, was due to nitrogen and carbon, and that oxygen played a relatively unimportant role. Since then, many investigators have substantiated their findings and indicated that nitrogen is particularly potent. Commercially, today's most widely produced non-aging sheet steels for deep drawing are either aluminum killed or vanadium rimmed types. The difference in deoxidation practice, alone, is evidence that oxygen is apparently not an important consideration in control of strain aging. The fact that nitrogen is important is apparent in the consideration that has been given, knowingly or unknowingly, to the amount combined with aluminum and vanadium. Patents were granted to Hayes and Griffis2 for the processing of aluminum-killed steel, and to Epstein" for the manufacture of vanadium rimmed material. Certain prescribed steps in producing these steels can be correlated with the formation of the respective nitrides within certain temperature ranges below the usual hot-finishing temperatures. The potential nonaging properties of either type can be reduced or suppressed by cooling too rapidly to permit the aluminum or vanadium to combine with nitrogen. Subsequent suberitical annealing of the cold-rolled strip, however, normally forms the nitrides and produces the resistance to strain aging. Titanium-killed nonaging steel, described by Comstock,1 forms a nitride in the molten state and is essentially nonaging throughout its processing. Zirconium-killed steel, which was investigated briefly by the author,* appeared to have similar nitride- forming characteristics. It is known" that chromium can produce nonaging rimmed steel, but relatively little is known of the potentialities of some of the other nitride-forming elements such as boron, silicon, columbium, and cerium. In attempting to develop a new nonaging cold-rolled sheet steel with good drawability, the following factors were considered pertinent. Such a steel would necessarily have a low carbon content and therefore have a relatively high degree of oxidation when made in a basic open-hearth furnace. If the denitriding element were also a deoxidizer, a part of the addition would be lost as oxide. The degree of deoxidation would determine whether the steel is rimmed, semikilled or killed, and also could be expected to have an important bearing on ingot yields and ultimate surface quality. Assuming that the pattern for the production of cold-rolled sheets would not be changed to any great extent, the nitride must form in the molten steel, in hot rolling, in subsequent cooling, or in annealing. The nitride, once formed, should resist dissociation and be stable in the final product. Usually an excess of the nitride-forming element is required to combine with sufficient nitrogen. If the element used is a strong ferrite strengthener, a small excess may markedly decrease drawability. With aluminum and vanadium, about 0.03 to 0.05 pct in the steel is preferred. Epstein has said" that about 0.30 pct chromium is required. Titanium nonaging steels are hard unless a sufficient amount (about 0.30 pct) is added also to combine with the carbon. The cost of the necessary amounts of these latter two elements discourages commercial acceptance. Silicon was considered as a possible nitride former, but since amounts up to 0.10 pct in rimmed and semikilled steels do not induce marked resistance to strain aging, larger amounts are apparently required, which would tend to harden and strengthen the ferrite. Of the other elements mentioned, all but boron are expensive heavy-metal elements. Stoichi-ometrically, almost an equal weight of boron would be required to combine with the nitrogen—-ordinarily about 0.003 to 0.006 pct in scrap-practice open-hearth steels. Boron is a slightly stronger deoxidizer than carbon but is less powerful than zirconium, aluminum, or titanium. Thus a rimmed-steel practice might be possible. There is much in the technical literature concerning the hardenability effects of minute amounts of boron in killed steels but very little about its behavior in low-carbon material—particularly as a ferrite strengthener. The available data indicated a need for better information concerning the effects of boron in low-carbon strip steels. Experimental Work Development of a Boron-Treated Nonaging Strip Steel—Initial attempts to produce a boron-rimmed strip steel employed 3-ton basic open-hearth heats which could be teemed into molds large enough to sustain a normal rimming action. Boron as ferro-boron was added to the ladle in small amounts because of the reported hot-short character of aluminum-killed heat-treating grades containing more than about 0.005 pct boron. Actually, the amounts used, i.e., 1/8 and 1/4 lb per ton, would be large for

Jan 1, 1959