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By A. F. van Everdingen

The pressure drop in a well per unit rate of flow is conrolled by the resistance of the formation, the viscosity of the fluid. and the additional resistance concentrated around the well bore resulting from the drilling and completion technique employed and, perhaps, from the production practices used. The pressure drop caused by this additional resistance is defined in this paper as the skin effect. denoted by the symbol S. This skin effect considerably detracts from a well's capacity to produce. Methods are given to determine quantitatively (a) the value of S, (b) the final build-up pressure, and (c) the product of average permeability times the thickness of the producing formation. INTRODUCTION Equations which relate the pressure in a well producing from a homogeneous formation with pressures existing at various distances around the well are generally used within the industry. The relation ii quite simple when the fluid flowing is assumed to be incompressible. It becomes somewhat more complicated when the flowing fluid is considered compressible so that the duration of the flow can he considered. In each case the major portion of the pressure drop occurs close to the well bore. However analyses of pressure build-up curves indicate that the pressure drop in the vicinity of the well bore is greater than that computed from these equations using the known, physical characteristics of the formation and the fluids. In order to explain there excessive drops it is necessary to assume that permeability of the formation at and near the well bore is substantially reduced as a result of drilling. completion and, perhaps. production practice. This possibility has been recognized in the literature. A method to compute the pressure drop due to a reduction of the permeability of the formation near the well bore. which is designated as the skin effect. S, is given in the following paragraphs. To start, equations normally used to describe flow in the vicinity of a well are given without considering this effect. These equations then are modified to include the effect of a skin on the pressure behavior. Finally a method is given to estimate the effect of the skin on the pressure and production behavior of a well. PRESSURE EQUATIONS Incompressible Fluid Flow If p is defined as the flowing pressure in a well of radius the pressure at distance r from the well has been shown to be:" The total pressure drop between the drainage boundary, and the well bore is given by These equations are valid only if the flow towards the well occurs in a horizontal homogeneous medium and the fluids are incompressible. The assumptions imply that all fluid taken from the well enters the system at r a condition rarely encountered in practice. Compressible Fluid Flow, Steady State A more realistic equation is obtained if it is assumed that the compressibility, c, of the flowing fluids is small and has a constant value over the pressure range encountered. After the well has been producing for some time so that its rate has become constant and steady state is reached, the pressures throughout the drainage area are falling by the same amount per unit of time, and the pressure differences between a point in the drainage area and the well are constant. When these conditions are met. the rate of production, q, from a well is equal to where dp/dt is the pressure drop per unit time. The fluid flowing at a distance from the center of the well is equal to From the last equation and from Darcy's law it can be shown that The equation holds for a depletion-type reservoir of radius drained by a well located in its center, provided the compressibility of the fluid per unit pressure drop is small and constant, and no fluid moves across the boundary Compressible Fluid Flow — Nonsteady State Table 111 of reference (5) shows the relationship between the pressure at the well bore and the reduced time, The pressure-drop function, p represents the drop below the original reservoir pressure, p caused by unit rate of production for several values of R, the ratio of drainage boundary radius to well radius, r In most reservoirs the values of approach infinity. and under these conditions the values of p shown in Table I of reference (5) can be used where p then signifies the difference between the pressure in the well and the prevailing reservoir pressure per unit rate of flow. The total pressure drop below prevailing reservoir pressure amounts to where the factor converts the cumulative pressure drop per unit rate of production to cumulative pressure drop for actual rate. q. For values of T > 100 the P function may be written (equation VI-15 of reference 5) as Using the time conversion the difference in pressure between reservoir and well becomes If values for the physical constants of the formation and the fluids are inserted, it is found that T exceeds 100 after a few seconds of production (or closed-in time), so that the approximation becomes valid almost at once. A simple relation between the pressure in the well and in the reservoir can also be derived by considering the well as a point source"" '" instead of a unit circle source, that is, by using Lord Kelvin's solution instead of the unit circle source

Jan 1, 1953

By HENRY M. HOWEL

1. Introduction.-The first part of this papers treats of the causes and the restraining of piping in steel ingots; the second& considers the causes and the restraining of -segregation; and the third proposes certain precautions in engineering specifications concerning these two defects. Into their causes I have looked carefully, with the purpose of arriving at rational methods of restraining them, and at efficient ways of detecting. and measuring the harm which they cause, so as to benefit the public by reducing this harm at once effectively and with the least expense to the manufacturer, and therefore in the end with the least expense to the consumer. In Part I., I infer that the pipe is chiefly due to what I, call the virtual expansion of the outer walls of the ingot in the early part of the freezing. I find that the upper and smooth-faced part of the pipe probably forms while the interior is still molten, but that the lower, steep, and crystal-faced part probably forms in metal which is already firm. Of the five causes which may co-operate to limit the depth of the pipe, I find that three-blow-holes, sagging, and the progress of freezing from below upwards-are usually effective. I find that the pipe may be lessened by casting (1) in wide ingots,; (2) in sand molds, especially if these are pre-heated (this is rarely expedient); (3) at the tops instead of at the bottom; (4) slowly; (5) and with the large end up; (6) by the use of a sinking-head or other means of retarding the cooling of the top; (7) by permitting blow-holes to form; and (8) by liquid compression.) Most of these I consider in some detail, and in particular I dwell on the advantages of casting with the large end up, and I propose certain administrative arrangements to permit this.

Mar 1, 1907

By Edward Judd

CANADA'S mining industry is rapidly recovering from the depression through which it passed in 1921. Its total output of $183,029,600 in 1922 was 6.4 per cent. greater than that of 1921, and was exceeded by only three previous years, 1917, 1918, and 1920. Table 1 compares the output of a few of 'the more important items selected from preliminary data published' by the Dominion Bureau of Statistics. TABLE 1.-OUTPUT OF CERTAIN MINERAL PRODUCTS IN CANADA PER CENT. 1921 1922 CHANGE Cobalt, metal and in compounds, lb 252,000 443,800 +76.1; Copper contents of blister, matte, and exported ores, lb 47,620,820 43,321,400 - 9.0 Refined copper, lb 4,286,000 730,000 -83.0 Gold, fine oz 926,329 1,230,985 +32.8 Pig iron, sh. tons 665,676 429,024 -35.5 Lead, sh. tons 33,340 47,085 +41.2 Nickel contents of matte, etc., lb. 19,293,060 17,496,490 - 9.3 Silver, including that in base bullion, gold bullion, etc., fine, oz. 13,543,198 17,611,646 +30.0 Zinc (nearly all refined), sh. tons. 26,545 28,199 + 6.2 Asbestos shipments, sh. tons 92,761 136,657 +47.3 Coal, all grades, sh. tons 15,057,500 15,045,300 Gypsum shipments, sh. tons 386,550 441,160 +14.1 Natural gas, M. cu. ft 14,077,600 14,954,100 + 6.2 Petroleum, bbl : 187,540 178,570 - 4.8 Cement, bbl 5,752,885 6,943,968 +21.0 Brick, structural, all kinds, M. , , 109,009 127,137 +17.0 On the basis of estimated market values, the whole output of 1922 was contributed as follows: Metals, 33.4 per cent.; non-metallic minerals, 45.1 per cent.; structural materials and clay products, 21.5 percent.; this distribution indicates a return of the metal mining. industry nearly to the position of relative importance that it occupied. before 1921, in which year metals contributed only 28.7 per cent. to the total value. of output while non-metallics gave 51.1 per cent. Canadian cobalt originates entirely in the ores of the Cobalt district, which are mainly treated at smelters in southern Ontario, although some quantities of residues have been exported to England and Europe. Exports during 1922 increased even more than production, consisting of about four-fifths . cobalt oxides and salts, and one-fifth of cobalt alloys and other metal combinations.

Jan 8, 1923

NEW MEMBERS. The following list comprises the names of those persons who became members during the month of April, 1913: BARNES, BLAKESLEE, Min. Engr Burrwood, La. BOYLSTON, HERBERT M., Cons. Met. Engr 26 Abbot Bldg., Cambridge, Mass. BUEHLER, HENRY A., State Geol Rolla, Mo. CASTO, WILLIAM H., JR., Mining Bonanza, Idaho. COHEN, MAXWELL B., Mill Operator Miami, Ariz. EVANS, MILTON R., Shop Draftsman 92 Division St., Kingston, Pa. HARPER, WALTER S., Asst. Treas 42 Broadway, New York, N. Y. JAMES. JAMES S.. Min. Engr Telluride. Colo.

Jan 5, 1913

By ALBERT F. J. BOARDEAUX

(Canal Zone Meeting, November. 191(j.) I. GENERAL INTRODUCTION. 1. Historical. ALLUVIAL gold was first discovered in Guiana in 1852, in the sands of the Arataye river; by Paulino, a Brazilian convict. During the following years, gold was found also in the rivers Orapu, Cirubé, etc. In 1873 the famous placers of the Sinnamary system were opened: Saint-Elie, Dieu-Merci, Adieu-Tat, and Couriége. This group of mines has produced nearly $10,000,000, according to official records, not including the gold that escaped the taxes. The discoverer was a mulatto named Vitalo. Except in a few rich spots, the gold was rather evenly distributed along the creeks. In one instance, gold was found in the red dirt from the slope of a hill, which, after transport to the creek, gave an amount of 150 kilograms. The placers of the Mana system, Enfin, Elysée, Pas-Trop-Tot, date from 1878, and their production has been about $5,000,000. In 1888, the Awa placers, along the boundary between the French and Dutch Guianas, on the Maroni and its tributaries, were discovered. They have yielded $12,000,000. The only industrial company,, the Dutch Guiana French Mining Co., produced in 15 years about 2,500 kg. of gold, worth $1,500,000. From 1893 dates the famous Carsewene discovery, in territory then in dispute between France and Brazil. A settlement was made recently in favor of Brazil, by arbitration of the Switzerland State Council. Carsewene is said to have pro-duced about $18,000,000 in six years (1894-1900), but not even one-fourth of the production went through French Guiana and

Nov 1, 1910

By R. E. Hudrlik, G. W. Preckshot

The diffusion coefficients of silver from solid silver in molten lead were measured to within ± 0.8 pet in a columnar type diffusion cell ower, the temperature range of 326° to 530°C. Fick's law describes the process up to 530°C where the laminar mechanism appareltly breaks down. These is negligible resistance at the interface as shown by mathematical analyses. The diffusion coefficients are found concentration independent. IT would seem that diffusion in liquid metals would be free of such effects as molecular structure, dissociation. polarization. and compound formation. This view was taken by Gorman and preckshot in their study of diffusion of copper from solid copper into molten lead. They reported diffusion coefficients which were independent of the concentration over the range of 478° to 750°C. They found that the Stokes-Einstein equation with constant radius of the diffusing specie represented the diffusion data better than Eyring's rate theory equation and Sheibel's correlation. The radius of diffusion was found to be that of the doubly charged copper. There appeared to be no resistance across the solid-liquid boundary. In the present work the diffusion coefficients for silver in liquid lead were measured over a range of temperatures of 350° to 505°C. The solubility of silver in lead over the range of 303° to 630°C was also obtained. These results are compared with calculated or correlated values or with data in the literature. EXPERIMENTAL Procedure—The experimental equipment techniques and procedures were those reported in detail by Gorman and preckshot9 and will not be repeated here. Measured values of WT, Co, A. L were obtained for various diffusion times and the diffusion coefficient was computed for the case of no resistance at the interface9, 11 by: WT/CoAL = 1- 8/p2 n=1 1/(2n - 1)2 exp[-(2n - 1)2p2 Dt/4L2] [1] or where there was resistance at the interface by: WT = 1- ?n=1 2h2/ap2L [sxp [-Dan2t]/[(h2 + an2) L + h] The roots an are those of the transcendental equation3 tan (an L) = Iz/cun. The diffusion coefficient is that defined by Hartley and Crank.7 The total silver in the lead cylinder and equilibrium slug was determined by a cupellation technique' with proper correction for losses. Analysis of known samples showed that this method is surprisingly accurate. The amount of silver in the lead adhering to the silver cylinder was obtained in the same fashion as shown by Gorman and preckshot.9 The small errors involved in this determination are not critical since the silver in this adhering lead layer is only 3 to 15 pet of the total diffused. Materials—Electrolytic silver containing 99.9+ pet Ag obtained from General Refineries of Minneapolis, Minn. was used for all but runs 7 and 8. For the balance of the runs this silver was reduced with hydrogen at 1100°C and its oxygen content was found to be about 0.017 pet. For the runs. 7 and 8, phosphorous-reduced silver of the same purity was obtained from Handy and Harman Co. of Chicago, Ill. The densities of the phosphorus-reduced silver and the hydrogen-reduced electrolytic silver were 10.484 and 10.487 g per cm3, respectively. These values agree with those reported for pure silver. Silver which was reduced at 900 C had an average density of 9.998 g per cm3, indicating porosity. This silver was used for a number of runs which were not tabulated in Table I. These are indicated by crosses on Fig. 2. The 99.999 pet Pb was obtained from the National Lead Co. Research Laboratory of Brooklyn, New York. DISCUSSION OF RESULTS The diffusion and solubility results are reported in Table I for eleven runs using either phosphorus-reduced electrolytic silver or hydrogen-reduced silver at 1100° C. The solubility data shown in Fig. 1 show the excellent agreement with that reported by Heycock and Neville.8 The data of Friedrichs5 apparently are in error. The experimental solubility data of this work are reported to 0.3 pet. The experimental diffusion coefficients computed from Eq. [1] are reported within 1.2 pet of the mean and are plotted in Fig. 2. These are expressed within +0.8 pet of the experimental values over the entire temperature range by: D= 8.26 x 10 -5 e-1925/RT . [3] There appears to be little difference due to the

Jan 1, 1961

By Mario L. Villa

Another increase in production and the discovery of new pools arc the outstanding developments of the year 1937. Production in 1937 totaled 16,354,706 bbl., compared to 15,457,953 bbl. in the previous year, an increase of 5.8 per cent, of which 5 per cent was due to the Yacimientos Petroliferos Fiscales (Argentine Governnlent Oil Fields) and 0.8 per cent t,o private companies. Table I shows that the most important gain in output was obtained in zone B of Comodoro Rivadavia, partly offset by a 5.7 per cent decrease in the Neuqu6n district. The fields of Salta and Mendoza show an increase of 4.4 and 39.1 per cent, respectively. The determination of bottom-hole pressures was started by Yaci-mientos Petroliferos Fiscales (Y.Y.F.) in Comodoro Rivadavia and

Jan 1, 1938

By J. T. Lapsley, I. I. Cornet, A. E. Flanigan, R. Hultgren, J. E. Dorn

With the greatly expanding use of magnesium during the war, it appeared necessary to the War Metallurgy Committee that procedures of heat treating common magnesium casting alloys be investigated systematically. Accordingly, the National Defense Research Committee of the Office of Scientific Research and Development placed a research contract with the University of California, supervised by the War Metallurgy Committee. Research on the solution heat treatment and aging of magnesium alloy AZg2, (formerly ASTM No. 17; also known as Dowmetal C or AM26o) which was done under "Restricted" Project NRC-2I, in 1942-1943, and reported in detail in a final report to the OSRD on September 3, 1943, is the basis of this paper, which has been released for publication by the OSRD. American experience with magnesium alloys prior to World War II was limited, although some of these alloys had been in commercial use since 1909. Requirements of the aircraft industry for light alloys made it imperative to understand and utilize the advantageous strength-weight properties of magnesium castings. Magnesium casting alloys are commonly solution heat- treated to increase their ultimate tensile strength and ductility; this treatment may be followed by an age hardening at elevated temperatures, which raises the tensile yield strength but diminishes the ductility. In the present investigation, AZp was studied to determine the effects on properties of various solution heat treatment and aging schedules. The principles of heat treatment of magnesium alloys are the same as for other non-ferrous alloys. The alloy studied, AZp, has a nominal composition of 9 pct aluminum, 2 pct zinc, and minor constituents. Fig I shows, by the projection of isothermal sections on the concentration plane, the solubility surface1 of the ternary magnesium-rich solid solutions as determined by X ray 'analysis. From this figure it may be seen that above approximately 375°C (707OF), AZp alloy is a single phase alloy at equilibrium; below this temperature the equilibrium condition is a two phase alloy. The beta constituent which precipitates from the solid solution exerts a hardening effect. Because the zinc concentration is only 2 pct, ancl because of its solubility relations, AZqz resembles a binary alloy of magnesium with aluminum. The solubility curve1 of Fig 2 shows how rapidly the solubility of the beta phase decreases with decreasing temperatures. Unlike many aluminum alloys, magnesium alloys do not age harden at room temperatures; precipitation hardening of AZ² alloy is performed at about 177°C (350°F). At this temperature about 3 pct aluminum

Jan 1, 1949

By D. I. Bardos, Paul A. Beck

A MARK, Boren, and westgrenl in their X-ray diffraction study of manganese alloys with 10 to 25 at. pct Si reported the occurrence of a phase with complex crystal structure in a Mn + 14.5 at. pct Si alloy after annealing at 800° or at 600°C. Recently Kuzma and Gladyshevskii2 identified Mn6Si as an R phase,3,4 the second binary R phase known. (A binary R phase was previously found in the Mn-Ti system by Waterstrat.5) A ternary R phase was reported earlier0 near the Mn-Si binary border of the Ti-Mn-Si system at 1000°C. In the light of the Russian work it now appears that this "ternary" R phase may be in fact an extension of the binary (Mn6Si)R phase. As already found by Amark, Boren, and Westgren, the corresponding binary phase is absent at 1000°C; the effect of titanium is evidently to stabilize it up to higher temperatures. In a recent paper Wieser and Forgeng7 gave the boundaries of this binary phase, which they referred to as 6. In order to re-examine the identity of this phase, an alloy of Mn + 14.5 at. pct Si was prepared by induction melting in helium atmosphere and annealed for 3 days at 800°C. The powder pattern, taken with an asymmetrical focusing camera of large dispersion and shown in Table I, was found to be that of the R phase, in agreement with the results of Kuzma and Gladyshevskii. For comparison, Table I also lists

Jan 1, 1965

By E. A. Nesbitt

A new permanent-magnet material has been developed with unusual mechanical as well as magnetic properties. Specimens that have been cast or subjected to a small amount of hot reduction by rolling or swaging may be machined, punched, tapped or drilled. The composition range of the alloys is 30 to 52 per cent iron, 36 to 62 per cent cobalt and 4 to 16 per cent vanadium. After being either quenched, annealed or given the usual cold finishing passes and then heated for 2 hr. at 600°C., such materials have a magnetic energy product of 1.0 X 106 gauss-oersteds. This product is equivalent to that of the well-known Honda steel (36 per cent Co, 4W, 2 Cr, 0.8 C. 0.3 Mn, balance Fe). Material handled in the manner just described does not depend on cold-working for its magnetic properties, and is known as Vicalloy I. The preferred composition for Vicalloy I is 38.5 per cent iron, 52 per cent cobalt and 9.5 per cent vanadium. When the alloys are first hot-worked, then considerably reduced in area by cold-swaging, drawing or groove rolling and then heat-treated, the magnetic energy product measured in the direction of previous extension is increased to 2.0 to 3.5 X 106 gauss-oersteds. These higher values have been obtained only after cold reductions in area of 75 to 95 per cent. Material handled in this manner is known as Vicalloy II and the preferred composi-

Jan 1, 1947

By E. A. Nesbitt

A new permanent-magnet material has been developed with unusual mechanical as well as magnetic properties. Specimens that have been cast or subjected to a small amount of hot reduction by rolling or swaging may be machined, punched, tapped or drilled. The composition range of the alloys is 30 to 52 per cent iron, 36 to 62 per cent cobalt and 4 to 16 per cent vanadium. After being either quenched, annealed or given the usual cold finishing passes and then heated for 2 hr. at 600°C., such materials have a magnetic energy product of 1.0 X 106 gauss-oersteds. This product is equivalent to that of the well-known Honda steel (36 per cent Co, 4W, 2 Cr, 0.8 C. 0.3 Mn, balance Fe). Material handled in the manner just described does not depend on cold-working for its magnetic properties, and is known as Vicalloy I. The preferred composition for Vicalloy I is 38.5 per cent iron, 52 per cent cobalt and 9.5 per cent vanadium. When the alloys are first hot-worked, then considerably reduced in area by cold-swaging, drawing or groove rolling and then heat-treated, the magnetic energy product measured in the direction of previous extension is increased to 2.0 to 3.5 X 106 gauss-oersteds. These higher values have been obtained only after cold reductions in area of 75 to 95 per cent. Material handled in this manner is known as Vicalloy II and the preferred composi-

Jan 1, 1947

By David L. Sikarskie

The measurement of residual stress fields using X-ray diffraction techniques requires the removal of successive layers of material from the specimen. In the process of removing these layers, the underlying residual stress field is altered; hence, if the original stress field is desired, corrections must be made to the measured stresses. Although these corrections already exist for a number of cases, an alternate procedure is outlined herein whereby the corrections are presented in series form. This form is numerically more convenient within certain ranges of correction depths and in its simplicity gives additional insight into the factors affecting the corrections. It, further, readily permits determining the proper slice depth to remove and the effect on the correction of both specimen thickness and magnitude and form of the measured residual stress itself. ONE of the techniques currently being used to determine residual stress fields is X-ray diffraction. Since X-rays are diffracted essentially from the layers of atoms near the surface of the specimen, of the order of 0.0001 to 0.001 in. depending on conditions, the method can only determine stresses* in this very thin surface region. Therefore, if the residual stress field at some depth into the specimen is required it is necessary to remove successive layers of material taking measurements after each cut. In the process of removing a thin surface layer of stressed material, however, the over-all equilibrium of a cross section of the specimen is disturbed with the result that the internal residual stress which existed before the slice of material was removed is altered. This alteration of stress occurs after each slice and its effect is cumulative. Thus, if the original stress distribution is desired, corrections must be applied to the measured stresses. These corrections can be found by satisfying equilibrium on each new cross section. These corrections have been derived in detail for a number of cases, e.g., cylinders, bars, plates,' and also are given in Appendix VI of Ref. 2. In each of the above cases the correction terms require the evaluation of definite integrals of the measured residual stress distribution. In general, this is indeed the way one would proceed with the corrections. There are a number of instances, however, where the integrals can be replaced by a series form of correction which is considerably more convenient numerically and, also, gives added insight into the factors which influence the corrections. Such a form of the correction is particularly useful, for example, if one is interested in designing a test such that stress corrections will be small. Also, the question of what depth of slice to use in relation to both specimen thickness and residual stress distribution itself must invariably be answered. Questions of this type can be readily answered using a series form of correction. In addition, if the correct residual stress distribution is needed only for limited depths into the specimen the series correction provides numerical results which are equivalent to the integral correction. I) DERIVATION OF THE SERIES CORRECTION The problem to be considered here is that of a bar or plate,* i.e., either one or two dimensions of the specimen is large compared with the third. Also, the residual stress distributions considered depend only on z, see Fig. 1. In view of this it can be shown' that a stress correction, based on simple beam theory, satisfies all conditions of "elasticity theory" and hence is the correct (and only) solution. The integral form of the correction (this assumes that the measured residual stress is a piecewise continuous function) as given in Ref. 1 is:

Jan 1, 1968

By ERNEST A. HERSAY

ACCURATE ore-sizing with screens is drawing attention to certain details that now, more than ever before, require attention. There are many tests that must be preceded by careful sizing. The assayer often could profit by a more careful selection of screens. In milling, more attention is given the slimes produced. Cement-manufacturers are pulverizing and screening finer than they formerly did, and others are reducing materials to fine sizes at high cost, with screens used to govern the fine¬ness of the pulverized product. Fine screens are expensive, easily injured by mis-use, are carried in stock sparingly by most dealers, and are handled often by those who know little about them except their designated number. More attention, on the whole, needs be given the actual size of the mesh-openings, and less emphasis placed upon any custom or conventionality in numbering. An effort to classify wire screens, in this respect, leads at once into computations, where one is confronted with details of sizes and standards, of different wires, different gauges, and different customs. There is always uncertainty about the exact working-size of a screen until one gives the matter special attention, and devotes more time to it than its simplicity seems to demand. To know only the number is not sufficient for all uses. Often, in sets, superfluous sizes are used; and sizes are omitted that are of critical importance. In wire screens, the use of different standard sizes of wire makes important differences in dimensions that must be taken into account. The dealer usually grades screens by the number of openings per linear dimensions, regardless of the size of the openings or of the wire. Certain 100-mesh screens in use are found, by measurement, to he actually coarser than others of 90-mesh, a result which is due, of course, to the use of larger

May 1, 1906

By D. J. Mack, R. E. Reiswig

Six examples of the peritectoid transformation were selected from the literature and studied by the method of isothermal transformation. The kinetics and mechanisms of five of the examples are presented as TTT diagrams and photomicrographs. The exist-enc- of a peritectoid in the sixth case is doubtful. ALTHOUGH the peritectoid transformation per se has been known for many years, no precise published data exist concerning the kinetics or mechanisms involved in transformations of this type, except for the brief treatment by Rhines, et al. 1,10 Bearing in mind the fact that investigations of recent years are uncovering more and more peritectoids and suspected peritectoids, a thorough study of the well-established peritectoids appeared to be in order. It was for this reason that a study of the kinetics and morphological mechanisms of six binary peritectoids was undertaken. The six peritectoids selected from the literature for study were those reported at 7.02 wt pct Al-Ag, 26.0 wt pct Sb-Cu, 30.5 wt pct Sb-Cu, 32.3 wt pct Sn-Cu, 8.35 wt pct Si-Cu, and 21.2 wt pct Al-Cu. These selections were based on availability and purity of components, ease of preparation and heat-treatment, and estimated reliability of the available equilibrium diagrams in the regions of interest. EXPERIMENTAL PROCEDURE The alloys used in this investigation were induction melted in electrode-grade graphite and chill-cast in cast-iron split molds. In all cases, the alloys were so brittle that they could easily be broken into samples weighing 1 or 2 g. Chemical analyses showed that the alloys used were close to the respective peritectoid compositions reported in the literature and that the impurity levels were low in all cases. Metallographic examination showed uniform distributions of phases in all samples, indicating uniformity of composition in the samples studied. Isothermal transformation studies were carried out in fused-salt media, using the familiar inter-rupted-quench method. Uniformity of temperature in the salt baths was maintained by continuous stirring with a stainless-steel agitator. On the basis of actual observations of the temperature fluctuations, the estimated temperature control was + 10C for the Ag-Al and Cu-Sb alloys and ±30C for the Cu-Sn, Cu-Si, and Cu-Al alloys. The accuracy of all temperature measurements was estimated to be ±1°C. It was found necessary to mount metallographic specimens of the Ag-Al alloy in cold-curing methyl methacrylate, since the temperatures encountered in mounting in bakelite or lucite caused an appreciable degree of transformation to the ß phase. For the other alloys, wood-flour-filled bakelite mounts were used to avoid extraneous X-ray diffraction lines during the later examination of the metallographic specimens on a Norelco Geiger-counter d if f r ac tomete r. In the X-ray diffraction procedure, agreement between the published diffraction patterns and those obtained in this study was good. This was particularly important for phase identification, since the literature contained little in the way of micrograph description in some cases. Etching of the silver-aluminum alloy for metallographic examination was done by swabbing with either of the following reagents: 1) 10 g CrO3, 1 g (NH4), SO2, 0.5 g NH4NO3, 100 ml H2O, or 2) 10 ml NH4OH, 1 ml 20 pct KOH, 4 ml 3 pct H2O2, 5 ml H2O. The other alloys were etched with the usual bichromate etchant: 2 g K2Cr2O7, 1.5 g NaC1, 8 ml conc. H2SO4, 100 ml H20 (swabbed vigorously). EXPERIMENTAL RESULTS A) The Ag-Al peritectoid at 7.02 wt pct Al— The phase equilibrium involved in this peritectoid is shown in Fig. I.2 The phase boundaries in the vicinity of the peritectoid were most comprehensively established by Hume-Rothery, et al,3 who placed the equilibrium temperature at 448 °C and the equilibrium compositions of the a ß' and y phases at 6.11, 7.02, and 7.24 wt pct Al, respective The alloy used in this study analyzed4 6.95 wt pct A making it slightly hypoperitectoid according to the accepted equilibrium diagram. The rate of the transformation a+ y — ß' varies rapidly with degree of undercooling below the equilibrium temperature, passing through a maximum in the vicinity of 350°C. Thus the TTT dia-

Jan 1, 1960

By G. B. Misra

While investigating on the aerodynamic resistance of airways supported with peripheral timber sets, at regular intervals, the following theoretical equations were developed by the author to estimate the resistance coefficient of such airways: [ ] for S < 1, where f is Darcy-Weisbach resistance coefficient of the airway, C is modified drag coefficient of the supporting member, D is equivalent diameter of the bare airway, 8 is ratio of the approach velocity over the sets to the average velocity of the bare airway, A is cross-sectional area of the bare airway, a is projected frontal area of the sets, A., is cross-sectional area of the air stream at the vena contracta inside the set, S is spacing of the sets, f, is resistance coefficient of the bare airway, l is length of aerodynamic influence of sets, p is perimeter of the bare airway, p, is setted portion of the perimeter of the bare airway, pe is unsetted portion of the perimeter of the bare airway, and P shielding factor. The equations were verified experimentally in a model rectangular airway supported with one- (bars), three-, and four-piece sets of square-section timber of three different sizes and were found to hold true. The work has been further extended to one-, three-, and four-piece sets of round timber of 2.6, 3.2, and 3.8 cm diam with the same experimental set up. Tests have been carried out for spacings of 25, 50, 75, 100, 150, and 200 cm over a regime of flow defined by the Reynolds number (with respect to the equivalent diameter of the bare duct) ranging from about 1.5 X 106 to 5 X 106 using the same experimental techniques. The values of f are calculated in the manner indicated in [Ref. 1]. Unlike with square-section timber, the resistance coefficient f of the airway setted with round timber shows a distinct variation with the Reynolds number of flow. This conforms to observations made by Sales and Hinsley.2 In order to have a comparable value of f for all types of sets with all sizes of timber, it was necessary to select the value of f at a fixed Reynolds number of flow. Since f is chiefly a function of the drag coefficient of the sets, the appropriate Reynolds number RE is that with respect to the diameter of timber in the set. Considering the diameters of timber used and the regime of flow over which measurements were made, f was chosen at a value of RE = 20,000 in all cases. The f vs. S curves are maximal in nature and in conformity with theory, the f vs. 1/S curves are straight lines up to a value of S = 1 beyond which they show a distinct flexure. The observed values of 1, the length of aerodynamic influence of sets, agree with the relation 1 = 42 e, developed for square-section timber sets, thus suggesting that the shape of timber has little influence on the length of aerodynamic influence. The value of the modified drag coefficient CD for round timber was calculated in the same way as for square timber in Ref. 1, taking the contraction factor Z = 1.5 for round-edged constrictions. CD has an average value of 0.96 with a standard deviation of 6.08% as compared to the free stream drag coefficient of 1.2 at RE = 20,000 for long cylindrical obstructions The shielding factor [ ] is plotted against S/1 in [Fig. 1]. The curves are more or less independent of the size of timber, but are different for the different types of sets, possibly due to their different degree of symmetry. Values of f calculated by the author&apos;s [Eqs. 1 and 2], using experimental values of CD&apos; and [ ] and taking I = 42 e, are plotted in [Fig. 2] against experimentally measured values of f for different types of sets with different sizes of round timber. The values agree closely with a standard deviation of only 5%, thus establishing the veracity of the theoretical equations developed by the author for round timber as well. A comparison was made between the Xenofontowa4 equations (the only other reasonable relations available for the estimation of the resistance coefficient of supported airways) and the author&apos;s [Eqs. 1 and 2] by comparing in [Fig. 3] the values of the resistance coefficient f computed by the Xenofontowa relations with those experimentally measured by the author. In order to make

Jan 1, 1975

Jan 1, 1935

By Helmut Thielsch

IN recent years an ever increasing amount of interest has been directed toward research studying the principles and various applications of sonic and supersonic waves. Though still in their early stages of practical development, sonic vibrations are already used in the emulsification and degasification of liquids. Metals exposed to sonic or ultrasonic vibrations while solidifying show a considerable amount of grain refinement. Often sound waves are applied instead of radiography to test engineering materials for internal cracks and flaws.1 In the field of pure research these waves are used in dispersion and also in coagulation of particles or liquids in gaseous or, under certain conditions, in other liquid systems. In the settling and thickening of slurries considerable time is necessary to compress the solid particles and to squeeze out the liquid to obtain as low a dilution (liquid to solid ratio) as possible. Various methods have been developed to increase the amount of coagulation of the very fine solids (colloidal or semicolloidal) and to shorten the over-all time. The addition of small amounts of electrolytes and the warming of the suspension represent merely the more important techniques. Some of the effects of supersonic vibrations have been reported previously.2,6 From preliminary studies, therefore, it was hoped that by application of sonic vibrations it would be possible to reduce the time required to thicken such materials to a specific dilution, as well as to thicken to lower ultimate dilutions than could be obtained by quiescent settling alone. By increasing the volume thickened per unit time-i.e., improving the plant efficiency-great savings in equipment and time would be obtained for industrial processes. Also, faster settling rates should result if coagulation of particles could be increased. Experiments have been conducted for a period of several months in the Allis-Chalmers laboratory to study the effect of sonic vibrations on settling of particles of different sizes and concentrations. APPARATUS The sedimentation apparatus used in these experiments is illustrated in Figs. I and 2. The essential features are the stationary field coil and the movable voice coil. Both windings are placed around a solid iron core. A leather diaphragm connected to the steel frame holds the voice coil in place. A brass rod is fastened to the voice coil with a metal disk connected to the other end. This disk is sealed to the lucite cylinder with a flexible rubber diaphragm. The lucite tube is 17 in. long; its inner diameter is 2 ½in. and the wall thickness is ¼ in. The tube is calibrated on the outside in 10 c.c. divisions for a total of 1000 cubic centimeters.

Jan 1, 1946

By S. J. Hruska

Rate expressions for the formation of two-and three-dimensional nuclei on foreign substrates are developed, taking into account previously neglected contributions to the standard Gibbs free energy of formation of critical nuclei. The temperature dependence of critical super saturation data predicted using these expressions is in accord with data for cadmium on copper and sodium on CsCl. EXPERIMENTAL data on the heterogeneous nuclea-tion of metal crystals from the vapor phase1&apos;2 exhibit the temperature dependence predicted by a nucleation rate equation derived by Pound et al.3 In their treatment, the critical nuclei are visualized according to the Volmer4 model as cap-shaped (three-dimensional). Accordingly, it seems desirable to compare these data with a nucleation rate equation which is derived on the assumption of disk-shaped (two dimensional) nuclei. Further, Lothe and Pound5 have recently shown that the standard Gibbs free energy of formation of these critical nuclei contains a contribution which has heretofore been neglected. Thus it is necessary to re-examine these nucleation data using a rate equation which contains this contribution. The van&apos;t Hoff isotherm relates n(i), the concentration of nuclei of critical size i (i = number of atoms), to nil), the concentration of adsorbed single atoms: where standard Gibbs free energy of formation of critical nuclei given by is temperature insensitive and is the bulk free energy change/volume of transformed material], T = substrate temperature and k = Boltzmann&apos;s constant. Previously,3 was determined by considering only the contributions of bulk and surface free energies in transforming i atoms from the population nil) to a cluster of i atoms. It has been shown5 that this procedure does not take into account the free energy contribution arising from the multiplicity of sites, q, where the clusters can be situated. If this contribution, -kT In q/n(l),is added to iG3 [Note that this increases n(i) by a factor q/n(l).] Since the above does not affect the remaining terms in the rate expression of Pound et al., the details are referred to their paper. The resulting nucleation rate is If the experimental AGV and T values at some common value of are employed, a plot of vs T(ln C3/l + In p&apos;) should yield a straight line of slope k/B<p and intercept . The corresponding plots for / = 1 nucleus per sq cm sec and C3 = 1018 are shown in Figs. 1 and 2 for cadmium on copper1 and sodium on CsCl2 and the values of obtained therefrom are entered in Table I. It is apparent that the data yield reasonable straight lines with about the same scatter as found using the equation of Pound et al. When the configuration of minimum free energy for a nucleus is a circular monatomic layer, the standard free energy of formation is

Jan 1, 1963

By William Fink

MANY investigators have attempted to determine the true nature of the internal changes taking place during aging. Merica, Waltenberg and Scott1 were the first to propose a theory of age-hardening. They attributed the age-hardening of duralumin to the precipitation of minute particles of the compound CuA12. Later Zay Jeffries and R. S. Archer2 augmented the above theory by suggesting that the small CuA12 particles acted as "keys" causing "slip interference." Many other investi-gators3 have devoted much time to the mechanism of age-hardening, some corroborating the "precipitation" and "slip interference" theory, others coming to different conclusions because of effects that to them seemed unexplainable by the early theories; e.g., the increase of electrical resistance upon aging, the fact that no change in lattice parameter could be detected during the early stages of aging even at elevated tempera-tures, and the fact that the density did not change as would be predicted. In 1932, Merica revised4 his earlier precipitation theory to take care of these presumably anomalous effects. This revised theory, the "knot" theory, assumes that substantial age-hardening occurs before actual precipitation of solute as discrete particles. The assumed mechanism is one of diffusion of solute atones into groups forming distorted regions which act as "hard" spots and cause slip interference. These "knots" are assumed to have approximately the same lattice arrangement as the solvent.

Jan 1, 1936

By T. D. Tiemann

The chemical and mineralogical composition of Caribbean bauxite ores are described. Extraction of alumina by several processes from both Haiti and Jamaica bauxites is discussed and data presented. IMMENSE deposits of bauxite occur in the Caribbean islands of Hispaniola and Jamaica in the high plateau lands and have been excellently described by 0. C. Schmedeman.&apos; The bauxite occurs as deposits in catchments or etched depressions in Tertiary limestone believed to have been deposited in the Eocene and Oligocene periods.&apos; In appearance both the Haiti and Jamaica bauxites resemble a relatively high iron clay and have indeed been mistaken for such.&apos; They are very soft and friable and disperse readily on vigorous agitation in water. The color range in general is light brown to red. Chemically, the outstanding characteristic of the bauxites is the low silica and high ferric oxide content. The extremely low silica makes them particularly valuable for the production of alumina in the Bayer plant since silica is responsible for the loss of both alumina and soda chemically combined as XNa,OYSiO2,ZAl2O2. The ferric oxide, only traces of ferrous iron are present, offers no interference in the production of high grade alumina. Typical oxide analyses of three types of ore are given in Table I2 and a list of the elements occurring in spectrographic quantities in Table 11." The size of the individual particles in the ore makes successful petrographic examination extremely difficult. The ores contain some relatively coarse grains of heavy minerals such as ilmenite, magnetite, and rutile, but other than occasional crystals of a few microns, the greater portion of the minerals are submicroscopic in size and approach colloidal dimensions. The mineralogic composition of the ores has been investigated by X-ray and differential thermal analysis.&apos; These investigations indicate that the predominant mineral phases present are gibbsite (A1203.3H2O), boehmite (Al2O3.H2O), hematite (Fe2O3), and goethite (Fe2O3-H2O). There is no evidence of the occurrence of diaspore (Al2O3.H2O) in either the Haiti or Jamaica ores, but some type of "amorphous" alumina may be present in some of the bauxites of Jamaica." The temperature stability regions in the alumina-water system have been investigated and are given in recent literature. In the temperature range where the hydrated forms are stable, as determined by hydrothermal bomb methods," ibbsite is the stable phase to 155°C (311°F), boehmite from 155°C (311°F) to 280°C (536oF), and diaspore from 280°C (536°F) to 450°C (842°F). Although quite similar in many characteristics, the Haiti and Jamaica ore show a divergence in mineralogic composition that is reflected in the extractability of the alumina described in later paragraphs. Two principal differences occur in mineralogic composition. The iron-bearing mineral in the Haiti ores is predominantly hematite, while in the Jamaica ores goethite is predominant.4 Directly related to the extraction of alumina are the two minerals, gibbsite and boehmite. Boehmite is relatively high in the Haiti ores and in some of the less soluble Jamaica ores, while gibbsite predominates in the ores in Jamaica amenable to the American Bayer process of extraction. Pedersen and Related Processes In general, all processes for the extraction of alumina involving sintering or fusion of bauxite ores with limestone, soda ash, or a combination of limestone and soda ash followed by leaching, are based on the formation of alumina compounds that. yield alumina soluble in the subsequent leach. The principal idealized reactions in respect to alumina and silica for the three types of processes are as follows: Soda Ash Sinter: A12O3 + Na2CO3 = Na2O-Al2O, + CO2 SiO2 + Na2CO3 = Na2O . SiO2 + CO2 A12O2 + SiO2 + Na2CO3 = Na2O.Al2O8. SiO2 + CO2 Leach (with excess water): H2O + Na2O-A12O3 = 2 NaOH + A12O3 (insolution) H2O + Na2O-SiO2 = 2 NaOH + SiO2 (in solution) Soda Ash— Limestone Sinter: Na2CO2 + A12O3 = Na2O.A1203 + CO2 2CaCO3 + SiO2 = 2CaO . SiO2 + 2CO2 Leach (with excess water): Na2O&apos; A1208 + H2O = 2NaOH + A13O3 (in solution) These latter reactions are the basis of the sinter process currently used for the recovery of soda and

Jan 1, 1952