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By G. Thomas, O. Johari

MEIERAN and Richman' have proposed a method for the determination of electron-diffraction patterns from twinned bcc crystals. It is the purpose of this note to present a general method capable of predicting the positions of all reflections from both matrix and twin regions for all possible orientations of cubic crystals. The method has been verified for twinning in explosively deformed copper, and is found to be a very useful tool when used in conjunction with stereographic projection, and dark-field electron microscopy. Let an isometric crystal be twinned in any (hkl) plane. The twinning can be considered either as a reflection in the twin plane or as a 180-deg rotation about the twin axis. In reciprocal space, the 180-deg rotation about the twin axis would place a given point p, q, Y to a new position P, Q,R, such that both will be equally inclined to the twin axis. This is represented in Fig. 1. If the coordinates of three such pairs of points are determined, the matrix of the transformation can be obtained.' It is also seen that such pairs would satisfy another condition, i.e., the vector [p,q,r] plus the vector [P,Q,R] will yield a multiple of hkl, i.e., the indices of the twin plane, because in isometric systems the axis [hkl] is perpendicular to the plane (hkl). This can be simplified by taking the points along the three axes. If a point h2 + k2 + 12, 0, 0 is taken along the x axis, it is seen that its new indices should be so as to yield a sum 2h2, 2hk, 2hl,i.e., 2h(h,k,1). (Also the points h2 - k2 - 12, 2hk, 2h1, and h2 + k2 + 12, 0, 0 are equidistant from the origin and both points make equal angles with the twin axis, i.e., cos-' h/dh2 + k2 + l2.) Similar operations for the points yield respectively, after the 180-deg rotation about the twin axis. Following the method due to Buerger,' the matrix of the transformation is obtained as follows: Using this matrix the indices of any other point in reciprocal space can be determined. This matrix is much simplified for (111) twinning commonly encountered in fcc metals, since are each equal to —1; hence

Jan 1, 1964

By A. F. Taggart, Nathaniel Arbiter

The chemical reaction occurring in collection of nonmetallic minerals with amine-type collectors was early postulated by students of flotation phenomena to be metathesis between the mineral and the collector, involving exchange between the amine-bearing (aminium) ion and the cation of the mineral, and formation at the mineral surface of an oriented film of the amine salt of the mineral anion. Qualitative evidence of exchange has been obtained on several occasions at Columbia. Thus 1000 C.C. of a solution containing 495 mg of laurylamine hydrochloride was shaken 17 min. with 100 grams of barite and ground in a porcelain mill to pass a 200-mesh screen; the mixture was then set aside for 48 hr. Filtrate therefrom analyzed 476 mg. per liter of laurylamine hydrochloride. There was no substantial loss of chloride ion (78.4 mg. per liter in the original; 74 in the filtrate). No successful analyses were concluded for barium ion. Earlier, confessedly rough work with scheelite indicated a solution gain in Ca++ equivalent to about one-half the aminium ion lost. Real quantitative roof of the exchange, in the form of an established stoichiometric balance, is unknown to the authors. The data of the present paper, however, obtained from experiments designed on the basis of the exchange hypothesis, constitute strong evidence of its truth, and at the same time point the way to economic utilization of the expensive nitrogen-bearing collectors in concentration of the low-priced nonmetallic minerals. The basic postulate underlying the experiments performed was that, if the collecting reaction is of the type R+ + Y- + MX = RX + M+ + Y- where R = aminium ion, Y = the anion of the amine salt, and M and X are, respectively, the cation and anion of the mineral, the reaction should obey qualitatively the implications of the mass-action and solubility-product laws. This is to say that coating and collection should be aided by the addition to the solution of either ion (R+ or X-) of the collector-coating compound, and hindered by the addition of either of the ions M+ or y-. Experimental work comprised determination of (,) the relative solubilities of the laurylammonium salts of a variety of nonmetallic-mineral anions; and (21 the contact angles' of various minerals in solutions containing different concentrations of the postulated controlling ions. Semiquantitative flotation tests were run With barite as checks on the diagnostic character of the contact angles. The amine

Jan 1, 1947

By Maynard H. Jameson

EARLIER investigations of the potential-drop-ratio method of electrical prospecting have indicated that under suitable conditions this method is well adapted to the location of formation boundaries in stratified ground. A description of this development was given several years ago by H. Lundberg and Th. Zuschlag.1 The curves published by these authors for the potential-drop-ratio variation above a horizontal contact indicated a definite relation of the position of the curve peak to the depth of the interface. The theory underlying this relation was subsequently studied by Z. Mitera in greater detail,2 and the theoretical deductions were compared with the results of tank experiments. The investigations available at this writing were confined to studies of horizontal formation boundaries. It is the purpose of this paper to extend the scope of the previous work to the problem of dipping layers. THEORY Consider the case of three media of different resistivities, whose interfaces are not parallel. If a point-source is located in one of these interfaces, its images do not lie in a straight line, but on the circumference of a circle whose center is at the hypothetical junction of the interfaces. R. F. Aldredge3 determined the relation that exists between the degrees of dip of the two interfaces and the distances between the various images and the point for which the potential is to be found. As seen in Fig. I, three media of resistivities po, pi, and p2 are involved, and the source I is located at the interface of the media (po) and (pi). The perpendicular depth of the lower interface is h,? is the dip, R is the distance between source I and potential point P, and r is the distance between the images and that point. To distinguish between images lying above the ground interface and those below, the notation "odd" and "even" images will be employed; images below the ground interface will be termed "odd" and those above "even." The following relations govern the distances between either kind of images and the potential point: [ ] As previously pointed out, the images of the source are on the circumference of a circle. If the angle of dip is ?, the angle measured from the horizontal to the first image is 2? to the second image it is 4?,, and so on. Since the limit of the reflecting interface is at its outcrop, the last possible

Jan 1, 1941

By Nathaniel Arbiter, A. F. Taggart

The chemical reaction occurring in collection of nonmetallic minerals with amine-type collectors was early postulated by students of flotation phenomena to be metathesis between the mineral and the collector, involving exchange between the amine-bearing (aminium) ion and the cation of the mineral, and formation at the mineral surface of an oriented film of the amine salt of the mineral anion. Qualitative evidence of exchange has been obtained on several occasions at Columbia. Thus 1000 C.C. of a solution containing 495 mg of laurylamine hydrochloride was shaken 17 min. with 100 grams of barite and ground in a porcelain mill to pass a 200-mesh screen; the mixture was then set aside for 48 hr. Filtrate therefrom analyzed 476 mg. per liter of laurylamine hydrochloride. There was no substantial loss of chloride ion (78.4 mg. per liter in the original; 74 in the filtrate). No successful analyses were concluded for barium ion. Earlier, confessedly rough work with scheelite indicated a solution gain in Ca++ equivalent to about one-half the aminium ion lost. Real quantitative roof of the exchange, in the form of an established stoichiometric balance, is unknown to the authors. The data of the present paper, however, obtained from experiments designed on the basis of the exchange hypothesis, constitute strong evidence of its truth, and at the same time point the way to economic utilization of the expensive nitrogen-bearing collectors in concentration of the low-priced nonmetallic minerals. The basic postulate underlying the experiments performed was that, if the collecting reaction is of the type R+ + Y- + MX = RX + M+ + Y- where R = aminium ion, Y = the anion of the amine salt, and M and X are, respectively, the cation and anion of the mineral, the reaction should obey qualitatively the implications of the mass-action and solubility-product laws. This is to say that coating and collection should be aided by the addition to the solution of either ion (R+ or X-) of the collector-coating compound, and hindered by the addition of either of the ions M+ or y-. Experimental work comprised determination of (,) the relative solubilities of the laurylammonium salts of a variety of nonmetallic-mineral anions; and (21 the contact angles' of various minerals in solutions containing different concentrations of the postulated controlling ions. Semiquantitative flotation tests were run With barite as checks on the diagnostic character of the contact angles. The amine

Jan 1, 1947

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By William Marsh Baldwin

TWO of the most useful and important equations available to the metallurgist for the study of plastic deformation of metals are the Huber-von Mises-Henckyl-~ and the St. Venant7-10 equations. Huber-von Mises-Hengky Equation The Huber-von Mises-Hencky equation answers the question: When does plastic flow occur in metal that is subjected to a multi-axial stress? It occurs, according to this equation, when the three principal stresses,t UI, u2, and u3 satisfy the equation: (<ri - <r2)2 + (<r2 - <rsY + (ff! - <r3)* = 2Ki [i] Here K is the yield strength of the material as determined in an ordinary tensile test. If the quantities ul, 52, andas are assigned to the coordinates of a Cartesian three-dimensional system, this expression describes a cylinder whose axis of symmetry is inclined at equal angles to the three coordinate axes4s6 (Fig. I). The radius of this cylinder is .\/%K. For the purpose of simplicity, it is sometimes advantageous to ascribe the values al/K = sl, az/K = s2, UD/K = SJ to the three coordinate axes instead of the principal stress alone. In this case, Eq. I becomes (*i - s*)1 + (s2 - S3)2 + (si - SiY = 2 [2] and the radius of the cylinder becomes \/%. In the latter method of representation, a point lying inside the cylinder indicates that the metal will react elasti-cally, whereas a point lying on the cylindrical surface indicates that the metal will behave plastically. Some of the geometric features of this cylinder are worthy of study. Let us inquire first as to what interpretation may be placed upon what we will choose to call the "circles of latitude" of the cylinder (L in Fig. I) and the "meridians" of the cylinder (M in Fig. I). Circles of Latitude Circles of latitude are formed by allowing a plane, passing perpendicular to the cylinder axis, to intersect with the cylinder. Any point, P, on this circle is presumed to have the coordinates sl, SZ, and s3. The coordinates of the point resulting from the intersection of the plane and the cylinder axis will be a, a, and a (since the cylinder axis is equally inclined to the three coordinate axes). L?t US now pass a line through the point on the circle and the point on the axis.

Jan 1, 1946

By Nathaniel Arbiter, Arthur F. Taggart

THE chemical reaction occurring in collection of nonmetallic minerals with amine-type collectors was early postulated by students of flotation phenomena to be metathesis between the mineral and the collector, involving exchange between the amine-bearing (aminium) ion and the cation of the mineral, and formation at the mineral surface of an oriented film of the amine salt of the mineral anion. Qualitative evidence of exchange has been obtained on several occasions at Columbia. Thus 1000 c.c. of a solution containing 495 mg. of laurylamine hydrochloride was shaken 17 min. with 100 grams of barite and ground in a porcelain mill to pass a 200-mesh screen; the mixture was then set aside for 48 hr. Filtrate therefrom analyzed 476 mg. per liter of laurylamine hydrochloride. There was no substantial loss of chloride ion (78.4 mg. per liter in the original; 74 in the filtrate). No successful analyses were concluded for barium ion. Earlier, confessedly rough work with scheelite indicated a solution gain in Ca++ equivalent to about one-half the aminium ion lost. Real quantitative proof of the exchange, in the form of an established stoichiometric balance, is unknown to the authors. The data of the present paper, however, obtained from experiments designed on the basis of the exchange hypothesis, constitute strong evidence of its truth, and at the same time point the way to economic utilization of the expensive nitrogen-bearing collectors in concentration of the low-priced nonmetallic minerals. The basic postulate underlying the experiments performed was that, if the collecting reaction is of the type [R+ + Y- + MX =± RX + M+ + Y¬] where R = aminium ion, Y = the anion of the amine salt, and M and X are, respectively, the cation and anion of the mineral, the reaction should obey qualitatively the implications of the massaction and solubility-product laws. This is to say that coating and collection should be aided by the addition to the solution of either ion (R+ or X-) of the collector-coating compound, and hindered by the addition of either of the ions M+ or Y-. Experimental work comprised determination of (1) the relative solubilities of the laurylammonium salts of a variety of nonmetallic-mineral anions; and (2) the contact angles1 of various minerals in solutions containing different concentrations of the postulated controlling ions. Semiquantitative flotation tests were run with barite as checks on the diagnostic character of the contact angles. The amine

Jan 1, 1944

PRESIDENTS DAVID THOMAS 1871 R W RAYMOND 1872-1874 A L HOLLEY1875 ABRAM S HEWITT 1876 T STERRY HUNT 1877 ECKLEY B COXE 1878 - 1879 WILLIAM P SHINN 1880 WILLIAM METCALF 1881 RICHARD P ROTHWELL 1882 ROBERY W HUNT 1883 JAMES C, BAYLES 1884-1885 ROBERT H RICHARDS 1886 THOMAS EGLESTON 1887 WILLIAM B POTTER 1888 RICHARD PEARCE 1889 ADAM S HEWITT 1890 JOHN BIRKINBINE 1891-1892 H M HOWE 1893 JOHN FRITZ 1894 J D WEEKD 1895

Jan 1, 1923

By L. Dr. Edeleanu

CRUDE petroleum is a mixture of various groups of hydrocarbons and some bodies containing oxygen or sulphur. These constituents possess properties differing considerably one from another and the proportion in which they are contained in the crude oils is also very different. Owing to this complicated composition the practical use of crude petroleum is much restricted. For example it is sometimes used as a liquid fuel. But its employment in this way is uneconomical because various valuable qualities of the individual constituents are not made use of. The rational utilization of petroleum can only be accomplished if the various groups of hydrocarbons are separated. The mixture of hydro-carbons present in the crude oil must be split up in such a way that the hydrocarbons are divided into various groups having certain predominant characteristics and uses. To accomplish such a separation is the aim of the technical refining of petroleum. ORDINARY REFINING BY DISTILLATION AND CHEMICAL TREATMENT Hitherto this has been accomplished by two processes, namely, fractional distillation and chemical treatment of the distillates obtained. Distillation Process The process of distillation consists in the separation of the constituents of petroleum into various fractions, the boiling points of which lie within certain defined limits. The fractions so separated possess certain special qualities in common, which enable them to be applied for specific purposes in practice. For example, we have the fractions known as benzene, illuminating oils, heavy oils, lubricating oils, etc.

Jan 9, 1914

By R. S. Busk, R. F. Marande

The magnesium-aluminum-zinc &apos;system contains most of the magnesium-base alloys used commercially, although in practice the ternary alloys are usually modified by the addition of a small amount of manganese. Table I contains the magnesium-base commercial sand-casting alloys most widely used throughout the world, together with their typical tensile properties. These alloys may be regarded as a single family of varying aluminum and zinc content, disregarding manganese. A concise means of presenting data for them is by means of iso-property lines plotted on triangular coordinate paper. Constitutional, casting, and mechanical properties are presented in this manner. The data are given with the obiect of providing reference material, and to aid in the choice of a commercial alloy to serve a particular purpose. Detailed, critical analysis of the commercial alloys has been covered in a previous paper.&apos; All alloys reported were made in rj-lb. melts, superheated to r700°F. for 15 min., cooled to r400°F. and poured in sand molds. The test bars produced had a 1/2-in. reduced section and were about 6 in. long. Except for the data represented in Figs. I and 3 the alloys used were of commercial purity and contained 0.1 to 0.2 per cent Mn in addition to the aluminum and zinc. Constitutional Data Under the heading of Constitutional Data are included all known data on con-

Jan 1, 1946

By R. F. Marande, R. S. Busk

The magnesium-aluminum-zinc &apos;system contains most of the magnesium-base alloys used commercially, although in practice the ternary alloys are usually modified by the addition of a small amount of manganese. Table I contains the magnesium-base commercial sand-casting alloys most widely used throughout the world, together with their typical tensile properties. These alloys may be regarded as a single family of varying aluminum and zinc content, disregarding manganese. A concise means of presenting data for them is by means of iso-property lines plotted on triangular coordinate paper. Constitutional, casting, and mechanical properties are presented in this manner. The data are given with the obiect of providing reference material, and to aid in the choice of a commercial alloy to serve a particular purpose. Detailed, critical analysis of the commercial alloys has been covered in a previous paper.&apos; All alloys reported were made in rj-lb. melts, superheated to r700°F. for 15 min., cooled to r400°F. and poured in sand molds. The test bars produced had a 1/2-in. reduced section and were about 6 in. long. Except for the data represented in Figs. I and 3 the alloys used were of commercial purity and contained 0.1 to 0.2 per cent Mn in addition to the aluminum and zinc. Constitutional Data Under the heading of Constitutional Data are included all known data on con-

Jan 1, 1946

By Bruce W. Gonser

TIN is not yet classed as a rare metal, but it has taken a long stride in that direction in the last ten months. It is now in Group 1 of the War Production Board&apos;s critical list, along with such company as magnesium aluminum, and nickel. This is in sharp contrast with the position a year ago when the supply well exceeded demand, and tin was used when feasible in place of really scarce metals. The geographical sources of tin production in recent years are shown in Table 1. Preponderance of former production in southeastern Asia, particularly Malaya and the Netherlands Indies (but all now controlled by the Japanese). is entirely too marked to be funny. Of the 1940 known world production of 237,000 long tons nearly all was controlled by the United States, Great Britain, and their friends. Now their supply is from countries that produced only 28 per cent of that amount. This excludes China and Australia, which because of shipping difficulties and local consumption, cannot be expected to export much tin. In spite of some expected increase in production, therefore, the supply is, and will continue to stay for at least several years, way below that desired for even normal uses. Although deliveries to consumers in the United States alone

Jan 1, 1942

By R. P. King

Flotation plant simulation, a relatively recent methodology in mineral processing, is defined and corresponding uses are discussed. Typical simulation structures are compared. Current problem areas exist although these are not insurmountable. Following a brief state of the art discussion, the N. I. M. simulation program is reviewed. In general, digital plant simulation is expected to be of substantial benefit in the near future.

Jan 1, 1976

By L. C. Binon

Exploration budgets are commonly determined by rules of thumb, such as a percentage of earnings or other fiscal measure. An appropriate exploration budget is the amount needed to achieve company goals. It can be determined by discounting the income expected from achieved goals. Budgets for individual projects are determined in a similar manner except that risk of failure is included in the computation.

Jan 1, 1984

By William I. Rau

This presentation will examine the role commercial banks will be expected to assume in financing international minerals projects, including a discussion of various financing techniques such as project loans, production loans, and production payments. A discussion of the necessity for completion guarantees, finalized sales contracts, reserve evaluations, management contracts, and marketing undertakings in conjunction with financing availability are also included.

Jan 1, 1981

By A. Donald Kelmers, Forest G. Seeley, B. Zane Egan

INTRODUCTION Coal ash, presently the fifth most abundant of the solid minerals produced in the United States, is expected to become the fourth most abundant by the end of this decade (1). The production of fly ash from the combustion of pulverized coal amounted to a total of 44 million metric tons (Mt) in 1977 and is expected to Increase to 91 Mt by 1985. Coal ash, which results from the Inorganic clay and mineral content of the coal, contains several elements and thus can be considered as a mined and crushed mineral resource rather than a waste material Furthermore, potential problems associated with fly-ash disposal ponds and the leaching of potentially hazardous elements through groundwater infiltration and/or rainfall provide additional incentive for processing fly ash for environ- mental control as well as for the recovery of certain metal values. Fly ash could provide an abundant domestic source of aluminum and several other metals Aluminum is now recovered from bauxite, and over 90% of this ore is imported since domestic sources are limited and cannot meet the U.S. demand There is a close relationship between the aluminum content of fly ash and the domestic consumption of this metal (Table 1).

Jan 1, 1981

By Chikao Nishiwaki

INTRODUCTION The Japanese dependency for mineral raw materials from foreign sources increased rapidly within the 20 years since the Korean war. During this 20 year period Japan has attempted to industrialize and develop her economy while depending mostly on heavy import of nearly all kinds of mineral raw materials. She has fabricated them using energy generated mostly by mineral fuel that are also imported. Fabricated goods are either used domestically to accelerate more fabrication industry or exported after adding more refinement or fabrication. In this paper iron ore as a major raw material for the Iron and Steel industry, three major base metals, copper, zinc and lead, and petroleum as a major energy source have been selected as examples to represent the general features of various kinds of mineral raw materials that are imported. Among other important mineral commodities for which Japan dependa upon foreign sources are: Aluminium, nickel and cobalt, potash and phosphorous 100 percent dependent and tin, tungusten, chromium and molybdenum over 95 percent dependent. IRON ORE Statistics for the important iron and steel raw materials, namely iron ore, coal and scrap iron are shown in Tables 1, 2 and Fig. 1. Iron ore is by far the most important and basic among these three commodities. There has been practically no steel or iron imported as a metal into Japan during this period. Iron ore, including aggregate such as pellets, and metallurgical coal are mostly transported in large ore cargo boats to the port where very efficient port facilities unload them directly at the steel mill site. As a result

Jan 1, 1976

By Paul A. Beck, John Towers, W. D. Manly

Recent work on grain growth in high purity aluminum and in a solid solution type alloy of aluminum and magnesium1 showed that the isothermal increase of the average grain diameter D with time follows the equation D = K(tg + A)2 Eq 1 Here tg is that portion of the total annealing time 1, which is available for grain growth, that is the annealing time less the time necessary for complete recrystallization. The parameters A and n depend only on the temperature. A has the dimension of time, and is usually of the same order of magnitude as the time for recrystallization: R. In some instances R may be substituted for A in Eq I. This is the case for example at long periods of annealing or at high temperatures, where both A and R become small in comparison with t. In such instances Eq I is simplified to D = K, tn Eq 2 For high purity aluminum the exponent n increases in the ratio of about I to 5 in. the temperature range of 350&apos; to 6w°C. 70-30 brass has been long known to exhibit grain growth of the continuous type, such as occurs in pure metals. For this reason, it was of interest to determine whether grain growth in brass also follows Eq I and 2 as it does in aluminum. Isotherma1 grain growth data for 70-30 brass were published in recent years by R. S. French2 and by H. L. Walker.&apos; Fig I shows a log D vs. log t plot of French&apos;s data, together with the 500, 600 and 700°C data by Walker for 42.8 pct reduction by rolling. In such a log D vs. log t plot Eq 2 corresponds to a straight line with a slope of n. As seen in Fig I, the data of French and the 600°C data of Walker can be represented by straight lines. However, the 500 and 7c0°C data of Walker give curved lines and the average slope of his 500°C line is very different from the slope of the line representing French&apos;s data for the same temperature. Furthermore the curvature of the 700°C line suggests a tendency for grain growth to stop after 8 hr. If confirmed, this would constitute a definite deviation from Eq 2, not explainable on the basis of the specimen thickness effect found in high purity aluminum.&apos; Walker&apos;s specimens were 0.125 in., or 3.18 mm thick, while the deviation occurs at a grain size of approximately 0.4 mm. A further point of divergence arose recently, when J. E. Burke suggested4 on the basis of Walker&apos;s data, that, instead of Eq 2, grain growth in 70-30 brass follows the equation D - D, = K . tgn Eq 3 Here D, is the grain size as recrystallized at the temperature in question. Although it was possible to show5 that, for pure aluminum, for which isothermal grain growth has been carefully investigated, Eq 3 is incompatible with the experimental facts, the situation remained somewhat obscure with respect to 70-30 brass. In view of the discrepancies between the published data on brass from different

Jan 1, 1949

By John Towers, Paul A. Beck, W. D. Manly

Recent work on grain growth in high purity aluminum and in a solid solution type alloy of aluminum and magnesium1 showed that the isothermal increase of the average grain diameter D with time follows the equation D = K(tg + A)2 Eq 1 Here tg is that portion of the total annealing time 1, which is available for grain growth, that is the annealing time less the time necessary for complete recrystallization. The parameters A and n depend only on the temperature. A has the dimension of time, and is usually of the same order of magnitude as the time for recrystallization: R. In some instances R may be substituted for A in Eq I. This is the case for example at long periods of annealing or at high temperatures, where both A and R become small in comparison with t. In such instances Eq I is simplified to D = K, tn Eq 2 For high purity aluminum the exponent n increases in the ratio of about I to 5 in. the temperature range of 350&apos; to 6w°C. 70-30 brass has been long known to exhibit grain growth of the continuous type, such as occurs in pure metals. For this reason, it was of interest to determine whether grain growth in brass also follows Eq I and 2 as it does in aluminum. Isotherma1 grain growth data for 70-30 brass were published in recent years by R. S. French2 and by H. L. Walker.&apos; Fig I shows a log D vs. log t plot of French&apos;s data, together with the 500, 600 and 700°C data by Walker for 42.8 pct reduction by rolling. In such a log D vs. log t plot Eq 2 corresponds to a straight line with a slope of n. As seen in Fig I, the data of French and the 600°C data of Walker can be represented by straight lines. However, the 500 and 7c0°C data of Walker give curved lines and the average slope of his 500°C line is very different from the slope of the line representing French&apos;s data for the same temperature. Furthermore the curvature of the 700°C line suggests a tendency for grain growth to stop after 8 hr. If confirmed, this would constitute a definite deviation from Eq 2, not explainable on the basis of the specimen thickness effect found in high purity aluminum.&apos; Walker&apos;s specimens were 0.125 in., or 3.18 mm thick, while the deviation occurs at a grain size of approximately 0.4 mm. A further point of divergence arose recently, when J. E. Burke suggested4 on the basis of Walker&apos;s data, that, instead of Eq 2, grain growth in 70-30 brass follows the equation D - D, = K . tgn Eq 3 Here D, is the grain size as recrystallized at the temperature in question. Although it was possible to show5 that, for pure aluminum, for which isothermal grain growth has been carefully investigated, Eq 3 is incompatible with the experimental facts, the situation remained somewhat obscure with respect to 70-30 brass. In view of the discrepancies between the published data on brass from different

Jan 1, 1949

By H. D. Yoo, M. R. Tek, D. L. Katz

The behavior of gas-storage reservoirs subject to water drive is investigated through analog simulation on an electronic differential analyzer. The simulation technique developed on an LM-10 computer permits the prediction of reservoir volume or pressure resulting from the movement of water in the surrounding aquifer. The method developed on the analog computer consists of setting up an appropriate transfer-function circuit and feeding the arbitrary time-varying boundary conditions as an input signal. The input may be specified as gas reservoir pressure, pore volume or the water flux. Several cases studied include an isolated gas reservoir on a limited aquifer, interference among three reservoirs adjacent to a common aquifer and the growth of gas-storage volume on an aquifer. It is concluded that the method developed on an electronic differential analyzer provides an excellent technique to simulate and investigate the behavior of gas reservoirs subject to water drive. The agreement between the reservoir performance as predicted from the simulation technique and as measured from actual field data is found to be better than the range usually encountered in predicting water-drive behavior. INTRODUCTION It is generally known that some gas-storage reservoirs are located on top of blanket sands of large extent, saturated with brine called aquifers. Because the volume of the body of water associated with aquifers is usually very large and water is compressible, the cyclic pressure variations encountered in normal storage service inevitably cause unsteady, compressible flow conditions in the adjacent aquifers. The solution to radial diffusivity equation for a limited aquifer for constant terminal conditions has been know111 since the early 1930&apos;s. The solution for the constant terminal conditions for an infinite aquifer was puhlished in 1949.2 The proldem of handling the unsteady flow of water through a porous medium with time-varying boundary conditions has been studied by many investigators through the use of graphical,3 digital4 computing techniques or on an R-C type of electrical analog called a reservoir analyzer.5 The digital computer performs a series of arithmetic calculations to superimpose the solutions of constant terminal conditions, while the R-C type of analyzer permits the simulation of the continuous medium by means of "lumped-cell" electrical resistance and capacitance elements based on finite-difference approximations. The graphical method is based on the convolution integral solution of the partial differential equalion. The purpose of the present study was to simulate the behavior of an aquifer on a general-purpose, electronic differential analyzer to obtain the influx of water or the change in pressure at the reservoir continuous1r and quickly. The use of the electronic differential analyzer was based on well known solutions for the constant terminal conditions already available in the literature.2,6-8 THEORETICAL DEVELOPMENT MODEL. The gas reservoir (R) is described in relation to an aquifer in Fig. 1. The permeability and porosity of an aquifer sand, the viscosity of the brine, and the compressibility of the brine and the formation are assumed to be constant. It further is assumed that the blanket sand is not thick enough to give appreciable vertical pressure distribution. The model in consideration is circular with radial geometry. The aquifer radius can be of limited or infinite extent. The gas-water interface is assumed to be fully segregated, and the displacement of the gas by