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By G. W. Tracy, R. D. Carter

Numerical calculations were made to determine the behavior of reservoirs with high-pressure drawdown and wide well spacing where the initial productivity is low and the wells are completed by hydraulic fracturing. The two-phase flow equations were solved for the flow into a single well. This well was assumed to be producing from a reservoir with hydraulically created horizontal fractures (four different systems with fractures were studied). For comparison purposes, additional two-phase flow calculations were made assuming a reservoir with uniform rock properties. The two-phase flow results were also compared with the conventional calculation methods, which do not include the effect of saturation gradients resulting from a simultaneous flow of oil and gas which are normal to this type reservoir. It was found that the conventional methods predict (1) a high and too optimistic value of ultimate recovery, (2) a high producing rate and a high reservoir pressure at a given oil recovery and (3) a low trend of gas-oil ratio with oil recovery. Included in the two-phase flow calculations were provisions to control the oil production rate by an allowable rate and, also, by a gas-oil ratio penalty rule. For the systems with hydraulic fractures, the producing rate was controlled by the gas-oil ratio penalty rule for most of the life. This is in contrast to the system with uniform rock properties which went "on decline" almost immediately. An unexpected characteristic of the systems which included fractures was the early rise in producing gas-oil ratio from 730 cu ft/bbl to approximately 1,200 cu ft/bbl, followed by a "leveling off" before the normally expected gas-oil ratio rise began. Additional features which are a result of hydraulic fracturing are (I) greater ultimate recovery, (2) higher average producing rates and (3) a lower average reservoir pressure at a given oil recovery. INTRODUCTION Some oil fields discovered during the past few years are producing from certain volumetric ally controlled reservoirs (often referred to as solution or internal gas- drive reservoirs) which are characterized by high-pressure drawdown at the wells. Since the available pressure drawdown at a well is limited by the static reservoir pressure and the producing rate is controlled by the available drawdown, wells completed in this type of reservoir usually produce at a rate less than the allowable from the time of completion. Because of this, this type of reservoir is referred to as a low productivity reservoir. Economic considerations require the use of wide well spacing and well stimulation by hydraulic fracturing to make commercial wells in this type of reservoir. Performance predictions for volumetrically controlled reservoirs have been made using a combination of two standard equations. 1. The "Schilthuis" or "Muskat" type material balance equation is used to relate the average reservoir pressure and the cumulative oil recovery. 2. The results from the material balance equation and the productivity factor as described by Pirson' are used to relate the cumulative recovery with producing rate and time. The material balance equation assumed uniform pressure and liquid saturation conditions throughout a reservoir. The steady-state radial flow formula allows for a pressure gradient toward a well but assumes uniform liquid saturation. These calculation methods are adequate for application to reservoirs wherein the drawdown at the well to realize satisfactory producing rates is small compared to the total pressure. In low productivity, volumetrically controlled reservoirs, the pressure drawdown at the well is large cornpared to the total pressure. Although a precise number cannot be given for the magnitude of a large pressure drawdown, values in excess of 1,000 psi would definitely be included. For practical considerations, this usually occurs when the formation flow capacity is less than about 100 md-ft. However, this limit of formation flow capacity will vary with the well producing rate. The low pressure in the neighborhood of the well which results from a high drawdown causes evolution of large volumes of gas. This causes the gas saturation to be higher near the well than at a greater distance—-hence, a non-uniform gas saturation. Also, the relationship between the relative permeability to oil (K/K) and gas saturation is nonlinear but decreases approximately in an exponential way with increases in gas saturation. Because of this, the following chain reaction is established.

The First Conference of the Powder Metallurgy Committee convened in the East Foyer of the Hotel Waldorf-Astoria, New York City, at 9:45 a.m., on Feb. 21, 1944, Mr. John Wulff, General Chairman, presiding. THE CHAIRMAN.-In behalf of the American Institute of Mining and Metallurgical Engineers I welcome all members and guests to this conference on Powder Metallurgy. We hope that this meeting will give expert and novice in the field a chance for discussion. Unfortunately, the subject has been overemphasized by some, and, of late, severely criticized by others. We have here today powder producers, fabricators, and engineers of different viewpoints, who can make the meeting a success. Such success depends not only on the caliber of the papers presented but more so on the discussion. To give you time for a free exchange of views, the papers have been shortened purposely. With the hope that you will all benefit by this conference, I shall turn the meeting over to the Chairmen of the morning session, Mr. Roland P. Koehring, of Moraine Products Division of General Motors, and Dr. R. K. Waring, of the New Jersey Zinc Company. SESSION ON DESIGN FACTORS IN POWDER METALLURGY R. P. Koehring and R. K. Waring presiding The opening paper of the session was presented by Mr. Fred P. Peters, as follows:

Jan 1, 1945

By P. Shahinian, J. Weertman

Minimum creep rates of nickel samples were measured in the stress region of 2.5x107 to 2.8xl0 dyne per sq cm and the temperature region of 400° to 1100°C. The creep rate seems to be proportional to (stress) at stresses below 7x10H dyne per sq cm. The activation energy of creep is approximately 65,000 cal per mol. IN a recent theory' of steady-state creep which is based on Mott's dislocation climb mechanism, the following creep equation was derived for creep in polycrystalline metals (if where K is creep rate, Q the activation energy of self-diffusion, S the entropy of activation of self-diffusion, L' the grain size, L the subgrain size, b the length of the Burgers' vector of a dislocation, u the shear modulus, u the stress, a the critical shear stress, M the density of active Frank-Read sources, v the vibrational frequency of a vacancy, and kT has its usual meaning. This equation predicts a creep rate which depends on the stress through a power law at low stresses. At high stresses the creep rate increases much more rapidly with stress. The theory breaks down for stresses great enough that the inequality holds true. It was the purpose of the present in-

Jan 1, 1957

By P. Somasundaran, K. P. Ananthapadmanabhan

A knowledge of the role of effects and interactions of chemical species is important in developing an understanding of the behavior of mixed minerals and natural ores in beneficiation processes such as flotation and flocculation. In this study the role of such species was examined for the calcite-apatite system by conducting flotation of each mineral in various supernatants prepared by mixing with water. Supernatants of apatite and even that of calcite depressed the flotation of calcite markedly in the pH range of 5 to 13. Addition of Ca(NO3)2, K2C03, and K3P04 also produced definite effects under various pH conditions. Apatite flotation was also affected by the mineral supernatants and by carbonate and phosphate solutions. The results are analyzed in terms of the surfactant's solubility properties and the mineral's electrochemical and dissolution properties. While depression of calcite flotation by the dissolved species is found to be governed by depletion of oleate by bulk precipitation, the depression of apatite flotation is caused by the carbonate and phosphate species in the system. Turbidity measurements and a thermodynamic analysis of possible interactions in the system support these considerations. The effect of the supernatant of minerals on their own flotation suggests the important role of kinetics of various surface interactions in comparison to that of mineral dissolution.

Jan 1, 1985

(Members are urged to send in for this column any notes of interest; concerning themselves or their fellow-members.) Members and guests who called at Institute headquarters during the period Nov. .10, 19 16 to Dec. 1.0, 1916: Chester Atkinson, La Fundicion, Peru. , Paul Llewellyn, East Chicago, Ind. F. J. Brule, Toronto, Ont., Canada. Harry March, London, England. Sterling H. Bunnell, New York, N. Y. E. P. Mathewson, Toronto, Ont., Canada. G. H. Cunningham, Hobart, Tasmania.' E. W. Moore, Budapest, Rumania. Courtenay DeKalb, Tucson, Ariz. W. J. Pentland, Guadalajara, Mex., E. H. Dickenson, New Y.. Heinrich Ries, Ithaca, N. Y. E. B. Durham, Mount Kisco, N. Y. W. E. Saunders, Philadelphia, Pa. L. B. Eames, Pueblo. Colo. J. G. Scrugham, Reno, Nev. N: H. Emmons, 2d, Copperhill, Tens. - W. H, Seagrave, Kennecott, .Alaska. R. E. Hoffman, Hannibal Mo.'s H. B. Small, Magangue, Colombia. B. B. Hood, Chronic, N. J. W. H. Staver, Washington, D. C. H. E. Jackman, Rochester, N. Y. R. K. Stockwell, Santiago, Chile. F. H. Jackson, Joplin, Mo. Warren D. Thompson, Boston, Mass. Knight S. Jordan, Provo. Utah. Thor Warner, Kingman, Ariz. William Kelly, Vulcan, Mich. S. T. Wellman, Cleveland, Ohio. W. H. Lanagan, San Francisco. Cal. F. H. Willcox, Pittsburgh, Pa. H. H. Lauer, Northampton, Pa. Arthur K. Adams has been appointed geologist to the Andes Copper Co.

Jan 1, 1917

The following is am incomplete list of members and guests who called at Institute headquarters during the period May 10, 1918 to June 10, 1918. Arthur K. Adams, Potrerillos, Chile. J. M. Mahoney, Wilkinsburg, Pa. John Carter Anderson, Tucson, Ariz. Benjamin L. Miller, South Bethlehem, Pa. George S. Blair, Camp Cordon, Ga. Wilbur A. Nelson, Nashville, Tenn. W. A. Deane, Summitville, N. Y. Miles G. Nixon, Chicago, Ill. Charles H. Fulton, Cleveland, Ohio. Walter G. Perkins, San Francisco, Cal. Rudolf Gahl, Inspiration, Ariz. G. M. Ponton, Ottawa, Canada. C. C. Griggs, Eureka, Utah. D. A. Powell, Columbus, Ohio. J. F. Hanst, Potrerillos, Chile. H. W. Reed, Salt Lake City, Utah. Stanley C. Herold, Pittsburgh, Pa. J. C. L. J. Seelig, Padong, East. Indies. Floyd D. James, Boston, Mass. Oberlin Smith, Bridgeton, N. J. Charles Janin, San Francisco, Cal. Harrison Souder, Cornwall, Pa. E. Horton Jones, Copper Cliff, Ont. Stanley A. Spellmeyer, Camp Meade, Md. William Kelly, Vulcan, Mich. Roger S. Sperry, Waterbury, Conn. Ichiro Kitsunezaki, Tokyo, Japan. D. R. Thomas, Toronto, Canada. P. K. Lucke, San Antonio, Tex. Thor Warner, Phoenix, Ariz. E. Francis McCrossin, Birmingham, Ala. L. Douglass Anderson, formerly superintendent of the United States Smelting Co., Midvale, Utah, is now manager of smelters, Intermountain District, United States Smelting, Refining & Mining Co., Salt Lake City, Utah.

Jan 7, 1918

By Horace Pops, L. L. Isaacs

SOLID-STATE transformations at low temperatures are frequently studied by optical metallography. Greninger and ooradian' and Hull and Gar-wood2 have examined the martensitic-type transformations in 0-phase Cu-Zn alloys during continuous cooling below room temperature. The lowest range of temperatures in the apparatus described by these investigators is limited to approximately 110°K. Present studies of reversible first-order phase transitions near liquid-helium temperatures have necessitated the design of a new cold-stage cryo-stat for optical metallography. The features of interest of this instrument are as follows: a) temperatures down to 4.Z°K are obtainable; b) the specimen is always under vacuum, thereby avoiding the condensation of moisture; c) specimens can be rapidly cooled or heated at varying rates, thus permitting studies of transformation hysteresis. Fig. 1 shows the details of the cryostat. All major parts are made of type 304 stainless steel. Both helium and nitrogen cans are Heliarc-welded to the helium filling tube, permitting the use of a common shielding can. Hence, the over-all weight and the area of the evacuated surface are mini- mized. The copper sample holder is screwed into the bottom of the helium can. To assure good thermal contact between the sample holder and the refrigerant, an indium ribbon is placed on the threads

Jan 1, 1964

By W. R. Hibbard Jr., R. W. Guard, N. G. Ainslie

Evidence is presented that copper-base solid solutions of different solutes having equal grain sizes, no preferred crystal-lographic orientation, equal electron-atom ratios, and, within experimental scatter, identical initial yield strengths, need not have identical stress-strain curves at strains larger than about 0.04. The stress-strain behavior is rationalized in terms of the proposed Suzuki chemical interaction between solute atoms and extended dislocations using what is thought to be a somewhat different means of representing stress-strain data. ALTHOUGH the effect: of alloying element upon the strength characteristics of sold solutions is a subject which has received considerable attention in the past, the exact relationships between the common deformation parameters and certain common variables are not really known in some cases. As a result some of the experiments reported in the literature in which these variables are inadequately controlled lose some of their persuasion regarding underlying principles. Nonetheless, facts are known which bear pointing up: When the true stress, a, and true plastic strain, E, of tensile deformatic~n are plotted on a double logarithmic coordinate system, one may observe a straight-line relationship at strains greater than 0.02. The form of the curve in the linear region is given by a = Ken! where a represents true stress, E, true strain, and K and tn, constants. If the relationship holds, K and m define the flow characteristics of the material being tested. m and K, however, may vary with other parameters. Hollomon found that in a-brass, m is influenced by grain size. French and HibbardZ found in alloys of copper that inverse relationships existed between m and 1) the solute concentration for a given solute, 2) the 0.01 yield strength, and 3) the constantK. Lacy and Gensamer3 observed (du/d~) (= U/Em) to increase with increasing values of K in systems of alloyed ferrites (although with considerable scatter of data which may be attributed to uncontrolled grain size). Brick, Martin, and Angier* deduced in copper-base alloys a straight-line relationship (with some scatter) between the change in the Dph number due to solid-solution strengthening and the change in the Dph number due to work hardening which suggested that copper-base alloys having equal yield strengths might have identical stress-strain curves in the plastic flow regions. French and HibbardZ concluded that the yield strength of copper-base solid solutions is the proper basis for comparing the effects of solute elements. Also, Allen, Schofield, and ate' showed that, within their experimental variation, copper-base alloys of zinc, gallium, germanium, and arsenic having the same electron-atom ratios have the same true-stress true-plastic strain curves. Dorn, Pietrokowsky, and ~ietz' also found that with aluminum-base alloys the stress-strain curves in the flow regions are approximately the same if "equivalent" concentrations of alloying elements are used. Solute valence and lattice parameter distortion were the parameters used to determine equivalency. The present report describes an investigation in which an attempt was made to obtain copper-base solid-solution alloys of four solute elements having within close tolerances equal grain sizes and yield strengths, and to see if the level of yield strength does indeed define the flow curve regardless of solute type. During analysis of the data certain unexpected features of the stress-strain curves became apparent which gave rise to some speculation and are discussed at length in the paragraphs that follow. EXPERIMENTAL PROCEDURES Alloy Preparation—Using the data of French and HibbardZ as a first approximation, four different binary copper-base alioys were designed so as to have the same yield strength. In addition, other alloys were prepared in which the solute aoncentrations varied slightly from those calculated above so as to span a range of yield strengths, see Table L The yield strengths of all alloys prepared except the copper-tin alloys were subsequently found to Lie fairly close to one another. The copper used in the alloys was produced by the American Smelting and Refining Co. and was of very high purity (99.999 pct). The alloy additions and their initial purities are as follows:

Jan 1, 1960

By R. W. Armstrong, P. C. Jindal

The hardness dependence on grain size for polycrys-talline cartridge brass and a leaded brass has been measured by Brine11 and Rockwell B testing. In each case, the hardness, H, depends on the average grain diameter, 1, according to: H =Ho + kHl-1/2 where Ho and kH are experimental constants. Diamond pyramid hardness values have also been measured as a function of the indentation size and grain size to give additional information on the nature of the hardness test and the dependence of hardness on micro-structure. The hardness of polycrystalline brass depends on its grain size. Bassett and Davis' demonstrated this as early as 1919 by making Brinell hardness measurements on cartridge brass. Since then, the hardness of this type of material has been measured as a function of grain size by making Rockwell,2'3 Vickers,4 and Brinell5 tests. he hardness dependence on grain size has also been measured for other materials. Angus and summers6 investigated the grain size dependence of the Brinell hardness of polycrystalline copper and a Cu-4.5 pct Sn bronze. In other studies, nickel,? Armco iron,Big an Fe-0.07 pct C alloy,I0 and an 0.39 pct C-12.45 pct Cr stainless steel" have been investigated. In some of the preceding cases, the hardness results have been analyzed to show that the hardness varies with the average grain diameter, 1, according to an l-l\4, l-1/4 or I-2 dependence,11-13 The studies of the influence of grain size on hardness have not been based on any theoretical model. This may be because the hardness of a material is itself a complicated property. However, attempts have been made to correlate, experimentally and theoretically, the hardness of a material with its unidirectional stress-strain behavior.14-l6 On this basis, Hall" proposed that the polycrystal hardness dependence on grain size might follow directly from the Hall-Petch18,19 relation for the grain size dependence of the yield stress. Thus, the hardness-grain size relation was given as: H = Ho + kHl-1/2 [1] where Ho and kH were taken as experimental constants. The relation was applied to the measurements on brass,' copper,6 bronze,= and Armco iron.' More recently, this relation was shown by Armstrong and jindal20 to adequately describe the measurements on cartridge brass made by Bassett and Davis' and Babyak and Rhines.5 In this case, the relationship was taken a step further by independently relating the values of Ho and kH to the values of oyand ky, previously reported by Armstrong, Codd, Douthwaite, and petch21 from measurements of the yield stress dependence on grain size for this type of material. In the present investigation, new Brinell and Rockwell B hardness measurements have been made as a function of grain size for a cartridge brass and a leaded brass. In addition, diamond pyramid hardness values were measured as a function of the indentation size. All these results are applied to a further analysis of the hardness dependence on grain size. MATERIALS AND EXPERIMENTAL METHODS Cartridge brass and a leaded brass were selected for this investigation for two main reasons: it was anticipated 1) that these materials could be cold-worked and recrystallized to a wide range in grain size and 2) that the results to be obtained on these typical industrial materials could be usefully compared with previous investigations. The chemical analyses of the actual materials which were employed are given in Table I. The as-received 1/2- and 3/4-in.-thick plates were given various reductions in thickness by cold rolling. The rolled material was heat-treated at various temperatures between 330" and 850°C for differing time periods from 5 min to 9 hr to achieve a variation in the average grain diameter between 0.0339 and 0.000543 cm.22 During heat treatment, the brass was protected from zinc loss by packing it in chips or foils of the same composition material. Reasonably equi-axed grain structures were obtained in each case. The metallurgical grain sizes of the specimens were determined from measurements of the average linear intercept on a random line. Annealing twin interfaces were not counted along with grain boundaries. The

Jan 1, 1970

By Shiro Ban-ya, John Chipman

The effects of many alloying eletnents on the acticity coefficient of sulfur in liquid iron have-been studied by the equilibriutn in the reaction Sfin Fe) + Hz = HzS at 1550°C'. Results are expressed in terms of a concentration variable for a nonmetallic or for a substitutional metallic solute. Activity coefficient of sulfur, defined as increased by B, Al, C, Si, Ge, Sn, P, As, Sb, Mo, W, Co, and PI. It is decreased by Cu,Au, Ti. Zr, V, h'b, Ta, Cr, ,23n, and Ni. Irulues oj. the interaction coejficient 0i = 6 In are labulated. The same interactions are expressed also in terms of atom fraction and of weight percent. The thermodynamic properties of sulfur in liquid iron have been fairly well established. Our recent paper1 reported new determinations of activity coefficient up an atom fraction of 0.12 and equations based on a careful review of all published data. The effects of alloying elements on the activity of sulfur have been studied by several investigators,2"11 especially by Morris and Williams for silicon,' by Morris and Buehl for carbon,~ and by Sherman and Chipman for manganese. phosphorus, and al~minum.~ However, the effects of some important alloying elements remain to be determined. The purpose of this investigation was to determine the effects of many alloying elements on the activity of sulfur in Fe-S-j ternary systems. EXPERIMENTAL METHOD This study was based on experimental determination of equilibrium in the reaction at 1550°C: The same apparatus and procedure as described in our previous paper have been retained, and the same corrections were applied for dissociation of H2S. The alumina crucibles used in the experiments consisted of four separate compartments. In a given experimental run. kach of three alumina crucibles held four different samples of about 3 g each which reached equilibrium in the same gas atmosphere and temperature. The charges were made up of electrolytic iron, pure iron sulfide, and desired alloying elements, which were pure metal or master alloys made in the laboratory. The weighed samples were held for 4 to 12 hr in the prepared atmosphere at 1550°C. They were then low- ered to be cooled as quickly as possible. The quenched metal beads were crushed to avoid the errors of segregation in the ingot. The sulfur content was determined gravimetrically and alloy content by appropriate chemical analysis. CALCULATIONS The apparent equilibrium constants of Eq. [I] are expressed as follows from the corrected gas ratios and sulfur concentrations: The term K" is the observed equilibrium constant in any given ternary solution, K' is the value for the Fe-S binary solution. and the limiting value of K' in the infinitely dilute solution is designated by K, which is the true equilibrium constant in Eq. [I]. In the thermodynamic treatment of nonmetallic elements in a metallic solution, it has been suggested1' that the lattice ratio has certain advantages over other variables to express the concentration of solute. In interstitial solid solutions the lattice ratio zj is proportional to the ratio of filled interstitial sites to those which remain unfilled. The equations derived for the activity of the solute using zj as the concentration variable are found also to be applicable to liquid solutions containing nonmetallic solutes when the nonmetal is treated as if it were interstitial. For this purpose we adopt the following definitions: The quantity vj which is negative for interstitial solutes is taken as -1 for nonmetallic and +1 for metallic solutes. For purposes of calculation however ; j may be assigned a value which results in a linear relation such as shown in Figs. 1 to 15. The activity coefficient of sulfur, Qs, and equilibrium constant. K(z). are defined as follows: According to a Taylor series expansion. the logarithm of the activity coefficient of sulfur in Fe-S-j ternary system is: However, the value of 6 In */6zi remains constant through a broad range of dilute solutions and the terms of higher order are negligibly small. As a consequence, Eq. [6] is simplified as follows:

Jan 1, 1970

By R. G. Wheeler, J. W. Goffard

The Larson-Miller parameter was used to correlate time, temperature, and indentation creep of magnesium, aluminum, and some of their alloys. In the temperature range 300" to 450°C, the short-time Meyer hardness of pure magnesium was less than that of the magnesium alloys tested, but for long times the pure magnesium has greater indentation creep resistance. Aluminum (1100 alloy) had 1.5 to 2.5 times more indentation creep resistance than magnesium at 300" and 450oC, respectively. Hardening of aluminum with a dispersion of Al2O3 was effective in the time and temperature ranges studied. New technologies have required the development of new materials and the utilization of the more familiar materials for new and unusual applications. The use of magnesium and aluminum and some of their alloys, because of their desirable nuclear characteristics, light weight, low cost, and ready availability, has been extended to the 300" to 450°C temperature range. In this temperature range the basic consideration of these materials must be their rate of plastic flow rather than offset yield strengths. The indentation testing reported here arose from a need for design data for the load-holding ability of supports made of these materials. Test Procedure—Hardness indents were made with a 0.275-in.-diam quartz indentor and a 10.65-lb load. The indentor was made by fire-polishing a spherical surface on the end of a fused quartz rod. The samples were held at temperature in a graphite crucible controlled to ±2°C. A thermocouple was attached to the sample and test temperatures were recorded. The diameter of the spherical indentation was measured at the end of a test period and the compression stress (Meyer Hardness) was determined by: H___________load__________ m = projected area of indent Samples were 1 in. in diam and at least 1/4 in. thick. It was observed that at the higher temperatures and longer times, the quartz indentor would stick to the magnesium sample. The quartz indentor was, therefore, frequently inspected and fire-polishing repeated when necessary. The area of sticking was always a small fraction of the area of indent and was therefore considered to have an insignificant effect on results. Correlation of Hot-Indentation Test Data with Time-Temperature Parameter—Sherby and Dorn' have correlated creep or tensile data of a' solid solutions of aluminum with a temperature and strain-rate parameter suggested by Zener and Holloman. underwood2 used this parameter to correlate creep properties of some steels with hot hardness, and upon the basis of this correlation a means of obtaining creep properties from short-time (and inexpensive) hot hardness tests has been demonstrated. Since the validity of the correlation of creep properties with a time-temperature parameter and the correlation of creep properties with hot hardness have been shown, it follows that hot hardness may correlate with the time-temperature parameter. The hot-indentation data obtained was expressed as Meyer hardness, and was shown to be time and temperature dependent. Correlation of Meyer hardness, time, and temperature with the parameter was made using the relationship: Hm = Meyer hardness t = time, hours T = absolute temperature, OK K = constant A value for the constant K was calculated by equating In l/t + K/T at different temperatures and times but at the same hardness. The correlation was tested by plotting Hm vs the parameter, In 1/t +K/T. Since materials are being sought which have high hardness at low indentation creep, i.e., a high Meyer hardness for long time at high temperatures, low values of the parameter are ofthe most interest. TEST RESULTS Magnesium—Pure magnesium (99.98 pct) cut from extruded rod was indentation tested perpendicular to the rod axis at temperatures of 300°, 350°, 400°, and 450°C for times ranging from 6 sec to 112 hr. Fig. 1 shows the time dependency of Meyer hardness at the four constant temperatures. Fig. 2 shows the correlation of the Meyer hardness of pure magnesium with the time-temperature parameter using a K of 22,720 in Eq. [I]. At the bottom of Fig. 2, the effect of doubling the time of indentation t2 = 2(t1), on the abscissa for any time is shown graphically. This effect is of constant magnitude. Also shown graphically are the magnitudes of the effects on the

Jan 1, 1960

By W. D. Ludemann, J. E. Dor, L. A. Shepard

Recovery of the creep resistance of 99.99 pct pure Al was studied at temperatures 540°, 573°, 600°, and 611°K. Poly-crystalline specimens crept under a stress of 950 psi to a strain of 5.5 pct were allowed to recover for periods of from 1 min to 16 days under a residual stress of 4.4 psi. Increased creep rates upon reapplication of the 950 psi stress evidenced softening of the material. The activation energy for the recovery process was found to be 64,000 cal-per mol. THREE major observations have clearly revealed that the creep of polycrystalline aluminum above about 510°K is controlled by the rate of climb of jogged edge components of dislocations past the barriers impeding their motion: 1) Extensive polygonization, characteristic of climb, takes place during creep.'9' 2) The activation energy for creep equals the estimated activation for self-diffusion. 3) The stress law for creep coincides with theoretical predictions based on the climb mechanism.4,5 The decreasing rate during the primary stage of creep must be ascribed to the introduction of additional barriers to the glide of dislocations. During secondary creep the density of barriers must remain constant, the rate at which new barriers are formed being equal to the rate at which they recover. For this reason the nature of the barriers, and their rates of formation and recovery, are significant to a complete understanding of creep. It is proposed here to study the kinetics of the recovery of barriers to creep of high-purity polycrystalline aluminum in the climb range. The technique will consist of creeping a series of tensile specimens under a prescribed stress to given state following which the specimens will be recovered for various times and temperatures under approximately zero stress. The amount of recovery will be determined by comparing creep curves following the recovery. EXPERIMENTAL PROCEDURE The material used for this investigation was a 99.99 pct pure Al supplied by the Aluminum Co. of America in sheets of 0.001-in. thickness having an H-18 temper. The spectroscopic analysis of impurities gave Cu-0.004 wt pct, Fe-0.002 pct, Si-0.001 pct, others-0.000 pct. Creep specimens were machined with their tensile axes in the rolling direction of the sheets. Annealing in a molten potassium nitrate-potassium nitrite bath for 1 hr at 686K, followed by air-cooling, resulted in a grain diameter of from 0.22 to 0.27 mm. Creep machines were equipped with constant stress lever arms of the type suggested by Fullman, Carreker, and Fishher,' which maintained the applied stress to within 0.04 pct of the reported value of 950 psi. Creep strains were calculated from extensions over a 6-in. gage section to the nearest 3 X 10"5. The temperatures of testing, 540°, 573", 600°, and 611°K, were obtained by immersing the specimen and extensometer assembly in a molten KNO2-KNO3 bath. Temperatures during the periods of creeping could be maintained constant to within better than ± 1°K. Correlation of creep data at different temperatures of testing demanded the use of an appropriate temperature-compensated time 8. Previous investigations have shown that the creep of pure metals at temperatures above about 0.55 of their melting temperatures can be correlated by the functional relationship3" e=f(0), s= const. [1] where e = total plastic strain during creep f = a function that depends on stress a = stress 6 = te-Q/RT = a temperature-compensated time t = time under test Q = 35,500 cal per mol = activation energy for creep R = gas constant, and T = absolute temperature In the present series of tests all of the creep was conducted under the same stress of 950 psi. To provide identical initial conditions for the recovery all specimens were first crept to a temperature-compensated time of = 47 X 10-14 min which resulted in a creep strain of 0.055 + 0.005 regardless of the creep temperature. During recovery, a small stress (4.4 psi) was permitted to remain upon the specimens to maintain tautness in the pulling assembly and to prevent mechanical damage to the soft specimen. After each recovery period, the full stress was reapplied and

Jan 1, 1961

By Steve H. Carpenter, Henry E. Otto

The explosive welding of metals is dependent upon the production of a jetting action caused by the collapsing of one metal plate against another. Successful welds are generally accomplished if the yield strength of the metals is in the range of 10,000 to 90,000 psi and the sonic velocity of the metal is greater than the detonation velocity of the explosive if direct contact explosive is being used.' Should the detonation velocity exceed the velocity of sound in the metal it may still be possible to obtain the jetting action and a good weld. However, in most cases where a high detonation velocity is used complications arise because of reflected shock waves which tear the bond apart as fast as it is put together.' Explosive welding of lead presents several problems since its yield strength and sound velocity are very low. Various values have been published3-5 for the velocity of sound in lead ranging from 2000~ to 23004 m per sec. Most of the high-order explosives have detonation velocities on the order of 6000 to 8000 m per sec, which precludes their use. The dynamites have a lower detonation velocity of around 2800 m per sec which is still somewhat too high. Lower-order explosives such as ammonium nitrate (1070 m per sec) must be used to weld lead in the as-received condition if the explosives are used in direct contact. Rather than use low-order explo'sives it was decided to alter the sonic velocity of the lead. The sonic velocity is directly related to the modulus of the material according to the following expression: Fig 1—Interface of explosive weld of lead to steel. Lead is on top As-polished Magnification 75 times as well as the yield strength. Bolling et al. 6 show that the shear modulus of lead single crystals increases from about 0.72 X1011 dynes per sq cm at 300°K to about 0.98 X1011 dynes per sq cm at 0°K, an increase of approximately 3 5 pct. This gives an increase in the sonic velocity of around 700 m per sec. Hence, the sonic velocity of lead at cryogenic temperatures is approximately equivalent to the detonation velocity of the low-order dynamites. We have obtained high-quality lead to steel explosive welds using a 40 pct dynamite in direct contact with the lead. Prior to detonation the lead was chilled with liquid nitrogen (78°K) to increase the strength and sonic velocity. Welds were made while the lead was cold. Specimen sizes were 3 by 6 in. A preset angle of 5 deg with a 0.10-in. standoff at the base was the geometrical setup used. The amount of explosive used for optimum welding of an 1/8 -in. -thick lead sheet to a steel plate was found to be 7 g per sq in. A PETN sheet explosive line wave generator was used to insure a linear detonation front through the dynamite. A photomicrograph of a lead-steel weld is shown in Fig. 1. The typical wave effect that constitutes a good explosive weld is present. When tested in shear, the weld failed in the lead, indicating that the bond is stronger than the lead base metal. Higher-order explosives were also tried without success. We believe this indicates the importance of matching the detonation velocity and the sonic velocity for successful explosive welding. Note Added in Proof. High quality explosive welds of lead to steel have recently been obtained at ambient temperature using a low velocity (1000 M per sec) free running dynamite. The weld interface obtained is comparable to Fig. 1. 'S. H. Carpenter, R. H. Wittman, and R. J. Carlson: Proceedings of the First International Conference of the Center for High Energy Forming, Syracuse University Press, syracu.se, N. Y., in press. 'A. HI Holtzman and G. R. Cowan: Welding Risearch. Council Bull., No. 104, April, 1965. 'Metals Handbook, 8 ed., p. 1062, Metals Park, Ohlo. 'J. M. Walsh, M. H. Rice, R. G. McQueen, and F. L. Yarger: Phys. Rev., 1957, vol. 108, pp. 196-216; 'L. V. Al'tshuler, K. K. Krupnikov, B. N. Ledener, V. I. Zuchikhin,

Jan 1, 1968

By D. S. Jacobus

It is proposed to give in this paper an estimate of the cost at which carburetted and uncarburetted water-gas will have to he sold, in order to compete successfully for steam-boiler use with anthracite coal. The following are analyses of the gas direct from the generator, and of the same after it has been carburetted for illuminating pnrposes. Per cent. by Volumes. I. 11. Uncarburetted. Carburetted. Nitrogen,.4.69 2.5 Carbonic acid,.3.47 .3 Ethylene,....... 0 12.5 Oxygen,....... 0 .2 Benzole vapor,...... 0 1.5 Carbonic oxide,.36.80 29.0 Marsh-gas,.2.16 24.0 Hydrogen,.52.88 30.0 100.00 100.0

Jan 1, 1889

By H. Brandhorst, C. G. Dunn

THE main purpose of the present note is to provide further information on the effect of orientation on strain-induced grain boundary migration in sheet material. A secondary purpose is to draw attention to the presence of a possible (hkl) dependent surface energy driving force, when the two grains of a bicrystal specimen have different (hk2) planes at the gas-metal interface, and to suggest means of eliminating this effect from the strain effect. If two grains A and B of a bicrystal have specific surface energies ? A and ? B respectively, there exists a driving force for grain boundary migration equal to 2(? B - ? A)/t, where t is the thickness of the specimen.' When t is quite small and the residual strain energy densities €A and €B of grains A and B, respectively, adjacent to the boundary are nearly equal, it is possible that the surface effect may be larger than the strain effect. he difference € B - € A gives a driving force per unit area of grain boundary due to an applied strain.)2 However, with increasing t the surface effect decreases while the strain effect presumably remains constant. Therefore, at some sufficiently large value of t, it is possible to ignore surface energy driving forces.* On the other hand, the surface effect is eliminated for all value of t when both grains have the same (hkl) orientation or have identical values of surface energy. Although the previous study provided information on the effect of orientation on strain-induced erain boundary migration,' no orientations with the (100) plane in the plane of the sheet were included. The present paper provides information of this kind. A seed crystal reorientation technique4 was used to prepare a large bicrystal of silicon iron (3 1/4 pct Si) consisting of two (100) grains in the (100) [001] and (100) [Oil] orientations. After a cold rolling strain (7 pct reduction to 3/4 mm final thickness), small specimens were prepared as before2 and then annealed in hydrogen. The boundary migration was such that the grain in the (100) [011] orientation always grew. After overnight anneals at 1100° or 1000°C, none of the initial (100) [001] grain remained. An anneal of 30 min at 950°c, however, provided information on the start of boundary migration. Fig. 1 shows both the initial position (lower line) and the final position (upper curved line) of part of the boundary, as revealed by thermal grooves. In a different area, part of the final boundary was not revealed by thermal grooves; the rate of boundary migration presumably was too high for the growth front to be defined by the time dependent thermal grooving process. In another area there was a vacated intermediate position connected to the initial position of the grain boundary. This indicates that only part of the boundary

Jan 1, 1962

By R. J. McNally

THERE are three primary plant nutrients—nitrogen, phosphorus, and potassium—expressed in any fertilizer compound as percent N, percent P 2 O 5, and percent K 2 O, in that order. This article will be concerned with the first two. The chief source of P 2 O 5 is phosphate rock. As found in the western states phosphate rock is essentially tricalcium phosphate-calcium fluoride (fluor-patite). As such, it is quite water insoluble.

Jan 1, 1957

By Robert J. White

Strong's equation for calculating bottom-hole pressure reduction due to gas cutting of drilling mud is corrected, resulting in a simpler equation which is easier to use. Use of the equation is illustrated by examples. It is shown that reduction of weight of a 10 lb/gal mud by 50 per cent at the surface due to gas cutting produces only n 3 per cent decrease in hydrostatic head at the bottom of a 5,000-ft well. It is also shown that at the surface 5 volumes of air per volume of mud are required to reduce the apparent mud weight from 8.5 to 6.5 lh/gal in a 3,000-ft well. Illustrative graphs are included to show the effect of various degrees of gas cutting on apparent mud weight at depths of 2,000, .5,000 and 10,000 ft and to show variation of apparent mud weight, with depth for a 100 lb/cu ft (13.37 lb/gal) mud gas cut to 90 lb/cu ft (12.03 lb/gal) at the surface. INTRODUCTION In 1938, Strong' published the following equation for calculating reduction in bottom-hole pressure due to gas cutting of drilling mud h = 1/D [p + pn/100 In p + p(1-n/100)/p(1- n-100)] where: h = depth in feet P = pressure in atmospheres at depth h due to mud column only D = hydrostatic pressure in atmospheres of a col-umn of uncut mud 1 ft high p = back pressure at well-head (in atmospheres) n/100 = fraction by volume of gas in mud at well-head at back pres-sure p This equation was recently found to contain an error due to an incor-rect expression for variation of vol-ume fraction of gas with pressure. Values calculated by the original equation are close to the correct values for small percentages of gas for which it was derived but become increasingly erroneous as the gas content increases and are completely unusable at the very high gas con-tents employed in aerated mud. DERIVATION The nomenclature used is the same as in Strong's paper. The pres-sure dP exerted by a lamina of thickness dh at a depth h ft is ex-pressed by Eq. 1 where x = volume fraction of gas at depth h dP = D (l - x)dh . . . (1) When we express x in terms of the wellhead per cent gas n, the well-head pressure p and the pressure P at depth h, the result is Eq. 2. x = (np/p+p)/(100-n) + (np/P + p) When this is substituted in Eq. 1 and rearranged to separate the var-iables the result is dh = 1/D [dp + np/100-n dp/(P + p]. Integration between appropriate lim-its results in or if the wellhead is open so that p = 1 atm and we rearrange Eq. 4, the result is loss in head = hD — P = n/100-n In (P + 1) ...(5) Eq. 5 can be solved easily by successive approximation using hD as a first approximation for P on the right-hand side and calculating a first value for loss in head. This can then be used to get a new value of P using the left-hand side of the equation. Values converge very rap-idly even for quite large values of per cent by volume gas n. EXAMPLES The effect on bottom-hole pressure of 50 per cent gas cutting of the mud in a 5,000-ft well using 10 Ib/ gal mud will be calculated, we have: h = 5,000 ft 10 X 7.48 144 X 14.7 = 0.0353 atm/ft hD = 176.5 atm n = 50 Substituting these values in Eq. 5 and using hD as a first approxima-tion of P on the right, we have, approximate loss in head = 50/50 In (176.5 + 1) = 2.30 log 177.5 = 5.17 atm. We calculate a new value of P as follows:

Jan 1, 1958

By E. P. Jennings

The abundance and value of the tellurium minerals of Colorado is well known, but, as yet, few analyses have been made of them, and I offer these as a small contribution to the chemistry of these valuable ores. 1. Native Tellurium.—The specimens from which the analyses of this mineral were made are from the " John Jay" Mine, Boulder County, Colorado, where it occurs in quite large masses, though mixed with more or less silica and iron pyrites. It is usually a finegrained, tin-white mineral, but sometimes occurs in distorted, hexagonal prisms in cavities in the quartz. Before the blowpipe it gives the reactions for tellurium, sulphur and iron; by cupellation, it yields a small amount of gold. An analysis of a coarsely crystallized specilnen gave the following results : Specific gravity, 5.10.5. Tellurium,.........68.40 Gold, :.........1.36 Iron pyrites,........24 92 Ferric oxide,.....4.37 Silica and silicates,........11.54 Silver, lead, and mercury,... traces. 100.59 Deducting the pyrites, iron oxide and silica, we have for the con]position of the mineral: Tellurium,..........97.78 Gold,.......... 2.27 100.00 Or, considering the gold to be in combination with tellurium to form sylvanite, we have : Nativc tellurium,........96.50 Sylvanite (An, Te3,),........4.50 100.00

Jan 1, 1879

By H. Eklund, R. T. Hukki

This article presents a simple arithmetic derivation for the relationship between sharpness of classification and circulating load, as well as world-wide industrial data which are compatible with the derived equation. It is shown that the sharpness of classification decreases with increasing circulating load. Based on the evidence available a comparison is presented between the performance of the present-day hydraulic classifiers. In a continuously operated closed circuit grinding system the tonnage and the fineness of the components may be indicated as follows: Eq. 8 expresses the relationship between sharpness of classification and circulating load in closed grinding circuits. If CL = 0, E = 100% according to the definition used. This, however, is a purely theoretical case because any apparatus to be called a classifier must produce the conventional two products. Furthermore, if CL = m, E =0%. In order to visualize the meaning of Eq. 8, the effect of factors d (fineness or percentage of under-size of classifier overflow at size x) and b (fineness or percentage of undersize of classifier sands at size x) should be studied. By the most rigid standard, factor d should be given the value of 100%. By so doing the size of classification is defined as that screen size x through which 100% of the classifier

Jan 1, 1965

By J. F. Lewis

Believing that one of the essential points in mining, as in all other business, is to know the expense incurred in each particular department, I have carefully kept an account with each department for the past three years; and, as it may be of interest to some of our members, I herewith present it to the Institute, reduced to per centages of the total yearly expense, showing the cost for materials, repairs, expenses, tools, team accounts, powder, oil, and fuel, also for labor under its several heads: 1875—Materials. 1875—Labor, Repairs,...040 Expenses,....016 Team,. .. .. .017 Machinery,. .. .055 Tools,..006 Repairs,. .. .027 Improvements,.....030 Washer,. .. .076 Oil ..008 Pit,.. 178 Powder,..,043 Dirt,.. 130 Fuel,. .325 Superintendence,. ..050 .485 .516 100.1 1876—-Materials. 1876-Labor. Repairs,. . • .. .043 Expenses,......012 Team,.011 Machinery,. .. .090 Tools,..005 Repairs,... 027 Improvements,.....007 Washer,. .. .085 I,. ...,015 Pit,.. 139 Powder,. .. .. .030 Dirt,.. 160 Fuel,...321 Superintendence,. ..078 .444 .559 100.3 1877—Materials. 1877—Labor. Repairs,......102 Expenses,......019 Team,..031 Machinery,. .. .050 Tools,..030 Rrpairs,. .. .046 Improvements,....,031 Washer,. .. .057 I,...009 Pit,.....179 Powder,...035 Dirt,.. 162 Fuel,...200 Superintendence,. ..054 .457 .548 100.5 Average for the three years 1875, '76, and '77. Materials. Labor. Repairs,...062 Expenses,...016 Team,..016 Machinery,. .. .065

Jan 1, 1879