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By Harry A. Lipsitt, Douglas Y. Wang

A fatigue study in completely reversed axial tension-compression has been perforried on high-purity titanium and on three high-purity alloys of titanium. The alloys each contain approxi7nately 0.75 at. pct of a single interstitial element; carbon, nitrogen, and oxygen, respectivley. The results corroborate a previously published theory which proposed that strain aging under alternating stress was responsible for the fatigue limit behavior of certain alloys. The present data indicate that in these alloys an increasing strain-talline aging effect under alternating stress is provided by oxygen, carbon, and nitrogen, respectively. CURRENT research on the nature of the fatigue limit in metals suggests that the presence of a fatigue limit in metallic materials is a manifestation of strain aging that occurs under alternating stress.lm5 A comprehensive theoretical model based on the above hypothesis has been developed to explain the existence of a fatigue limit.' This model also provides increased insight into several other fatigue phenomena as under stressing, overstressing, and coaxing effects. The theory, as well, provides equal understanding for those cases where no real fatigue limit is observed. Briefly, this theory assumes that the S-N curve for a pure metal is a smooth function of the applied stress, and the effect of adding an element that is soluble (or forms a precipitate) in the pure metal is simply to shift the S-N curve to the right. If the added element confers the power to strain age, the result is a further shift of the S-N curve, this time upward and to the right. Since strain aging is not expected to be a strong function of stress, and since damage per cycle is known to be quite stress dependent, it is to be expected that there will be some limiting lower stress at which the strengthening due to strain aging will balance the damage due to crack propagation. This stress is the fatigue limit. The position of the fatigue-limit knee was thought to be a function of the magnitude of the strain-aging effect on both the finite and infinite life portions of the S-N curve. Although the strain aging hypothesis seems to be reasonably valid for bcc materials,2'6 it needed to be tested for both fcc and cph metals. This report is the first of a series concerning the fatigue-limit behavior of titanium with varying amounts of the interstitial solutes (C, N,, and 4) that are known to cause static strain aging in titanium. Yield-point effects have been reported for polycrys-talline high-purity titanium alloys containing either carbon, nitrogen, or oxygen.7'9 These effects were observed at testing temperatures in the range 100 to 300'. In addition yield-point and strain-aging effects have been reported for single crystals of titanium containing 0.1 wt pct C plus N.' These yield points were observed over a wide temperature range, but no room-temperature aging occurred. Aging at 180' was required to cause the return of the yield point. The magnitude of the yield phenomena in titanium containing interstitials is not expected to be as large as is observed in bcc metals because of several factors. Titanium has a very high chemical affinity for oxygen and nitrogen. The thermodynamic stability of solutions of oxygen or nitrogen in titanium is recognized. Lattice parameter measurements of titanium containing arbon, oxygen,1° or nitrogen" show that the "c" parameter is expanded more than the "a" parameter, but that up to about 2 wt pct this results in an insignificant change of the axial ratio 'c/a." Ehrlich" has shown that the sites occupied by interstitial atoms in titanium are spherically symmetrical and therefore a lattice expansion, at a constant c/a ratio, results in a simple dilation of the interstitial site. Such a dilation involving no shear has been shown to react only with edge components of dislocations.13 This causes only a weak pinning action. Shear stresses would be anticipated locally when only one of the two interstitial positions was occupied. The carbon atom will cause a symmetrical distortion of the lattice whereas the oxygen and nitrogen atoms have, in addition, the previously mentioned chemical affinity of titanium for these elements. These factors will result in a considerably smaller reduction of free energy upon the association of interstitial atoms with dislocations, and therefore a much weaker pinning than has been observed for the bcc metals. These considerations would lead to the hypothesis that of the interstitial elements considered here carbon would cause the strongest pinning effect in titanium where the amount of interstitial in solution is constant. This hypothesis will be borne out in the analysis of the present results.

Jan 1, 1962

[ARIZONA Established July 10, 1915 CHARLES R. KUZELL, Chairman GILBERT C. DAVIS, First Vice-Chairman ALBERT MENDELSOHN, Second Vice-Chairman MORRIS G. FOWLER, Secretary-Treasurer Phelps Dodge Corporation, Douglas, Ariz. LYLE M. BARKER P. D. I. HONEYMAN A. T. BARR H. M. LAVENDER T. G. CHAPMAN WALTER C. LAWSON GEORGE M. COLVOCORESSES W. H. LOERPABEL EDWIN H. CRABTREE, JR. CARL F. MILLS WALTER I. GARMS P. M. MOSIER WESLEY P. Goss J. A. RICHARDS 11. C. HENRIE JOSEPH A. WILCOX C. F. WILLIS]

Jan 1, 1946

By B. W. Frazier

Jan 1, 1882

By M. D. Hassialis

THE object of a technical paper is to communicate new technical knowledge, the paper being the vehicle of communication and the existence of new knowledge its reason for being. It follows that the development of information worthy of communication, the criterion being novelty, is prerequisite to exercising the privilege of communication. The act of communication is achieved when the reader perceives the nature of the new knowledge, i.e., when he understands it. A paper achieving this objective is an acceptable technical paper. Development of new knowledge has as one of its purposes the increase of the existing state of knowledge and the enjoyment of the benefits derived therefrom. Technical knowledge is a collection of facts so ordered as to make apparent, relations existing between the facts. When the interrelations have been exposed the facts have been interpreted or explained Three broad, overlapping categories of technical papers may be recognized: papers consisting of (a) a report of facts, (b) an explanation of facts, or (c) a combination of a report and an interpretation. Ideally a technical paper should belong to one of the last two categories but current practice is to accept papers belonging to any of the three categories. Based on a small sample drawn from the scientific and engineering literature, the relative frequency of the three types is a: b: c:: 20:1:14. If the sample be limited to engineering literature, the ratios become a:c::2:1; type (b) being nonexistent. This large departure from the ideal is a consequent of the

Jan 1, 1948

By M. Bevis, A. F. Acton, P. C. Rowlands

Defor~nation twinning and transformation twinning modes most likely to be operative in Fe-Ni and Fe-Ni-C martensites have been determined using a new theory of the crystallography of deformation t~inning.~ This analysis shows that potentially important conventional and nonconventional twinning modes1 have been omitted in previous analyses. Discussion is given on the relevance of the predicted twinning modes to the lattice invariant shear associated with the martensite transformation in steels and to anomalous deformation twinning in Fe-Ni-C martensites. THE two most important criteria which appear to govern operative twinning modes in metallic structures1 are that the magnitude of the twinning shear should be small and that the twinning shear should restore the lattice or a multiple lattice in a twin orientation. The latter criterion ensures that the shuffle mechanism required to restore the structure in a twin orientation is simple. These criteria have been adhered to in the prediction of twinning modes2"6 in bcc and bct single-lattice structures with axial ratios in the range y = 1 to 1.09 as, for example, encountered in martensite occurring in steels. Refs. 2 and 3 in particular consider the martensite transformation in steels and the twinning modes in these cases relate to transformation twinning, and hence the lattice invariant shear associated with the martensite transformation. The list of twinning modes which can be compiled from these sources is incomplete and the ranges of magnitude of shear considered could be unrealistically small, particularly in the case of deformation twinning. The latter consideration is supported by the fact that twinning modes with magnitudes of shear large compared with the smallest shear consistent with a simple shuffle mechanism have been established in, for example, the single-lattice structure mercury7 and the multiple-lattice structure zirconium.&apos; In addition the anomalous deformation twins reported by Ftichrnan4 to occur in a range of Fe-Ni-C martensites still remain unexplained. It is clear that a comprehensive analysis of twinning modes likely to be operative in martensite In steels is required. The results of the application of a new theory of the crystallography of deformation twinningg to these structures are presented in this paper. The theory has been used to determine all shears which restore the lattice or a multiple lattice in a new orientation with magnitude of shear up to a required maximum. The orientation relationships between parent and twinned lattices are not restricted to the classical orientation relationships of reflection in the twin plane or a rotation of 180 deg about the shear direction. PREDICTED TWINNING MODES Twinning modes which restore all or one half of lattice points to their correct twin positions will be referred to as m = 1 and m = 2 modes, respectively. These modes are the most likely to describe operative modes in single lattice structures. The bcc m = 1 and m = 2 modes which have magnitudes of shear s in the range s < 2 and s < 1, respectively, have been given10 and are reproduced here in Tables I and 11. Detailed discussion of the crystallography of these modes and cubic modes in general will be discussed elsewhere (~evis and rocker, to be published). The four twinning elements Kl, &,ql,7)2 as well as the magnitude of shear s are given for each twinning mode, and the twinning modes are given in order of increasing shear. Two twinning modes are given in each row of the tables, the twinning mode Kl, Kz, ql, q2 and the reciprocal twinning mode with elements Kl = K,, Ki = Kl, q: = q2, and 17; = ql. The m = 1 and m = 2 twinning modes which describe twinning shears with small magnitudes of shear and simple shuffle mechanisms in bct crystals with -y = 1 to 1.09 are given in Tables I11 and IV, respectively. On increasing the symmetry of the tetragonal lattice to cubic, that is making y = 1, all modes listed in Tables 111 and IV must reduce to crystallographically equivalent variants of the modes given in Tables I and 11, respectively, or become twinning modes with both shear planes as symmetry planes in the cubic lattice and hence not considered in Tables I and 11. With the exception of this last type of mode only those tetragonal twinning modes which reduce to modes 1.1, 1.2, 2.1, and 2.2 of Tables I and I1 are considered in Tables 111 and IV. For values of y in the range -y = 1 to 1.09 the tetragonal modes and the corresponding cubic twinning modes have approximately the same magnitude of shear. The twinning modes listed in Tables 111 and IV are therefore by the criteria given above the most

Jan 1, 1969

The members of the Institute will recall the account given in the March Bulletin of the inauguration exercises of the Engineering Foundation which was inhibited by an initial gift of $200,000 by Mr. Ambrose Swasey, to be administered by the United Engineering Society as trustees. The Engineering Foundation Board is now constituted as follows: GANG DUNN, Chairman, EDWARD D. ADAMS, Vice-Chairman FREDERICK R. HUTTON, Secretary, JOSEPH STRUTHERS, Treasurer, American Society of Civil Engineers. J. WALDO SMITH, CHARLES WARREN HUNT.

Jan 12, 1915

By A. Gatti

Studies were made on the system iron plus alumina. Various methods of dispersing and various amounts of alumina were used. Powder metallurgy techniques were used to produce the final product. Microstructures and some mechanical properties are presented. Alloys containing up to 16 pct alumina by weight are ductile at all temperatures tested. The ivon-alumina materials have a higher yield stress and improved creep resistance over that of pure iron. SINCE the development of SAP&apos; an A1- Al2O3 powder metallurgy product, great interest has been shown in the development of a SAP-like structure in metals and alloys other than aluminum. The outstanding properties of this class of materials are: 1) Good creep resistance at high temperature. 2) High yield strengths and high hardness at high temperatures. 3) High recrystallization temperature. However, the lack of ductility and formability has thus far limited the applications of SAP-like materials. The following report deals with methods of dispersing A12O3 in Fe, processing of powders into rod, structures produced after processing, and mechanical properties of the iron-alumina material produced. Methods of dispersing the alumina and also the volume fraction of alumina added were varied. MATERIAL Powder Processing— Four methods of obtaining dispersions of alumina in iron were studied. 1) Oxidation-reduction of a Fe + 8 pct Al alloy. .2) Coprecipitation of Fe(OH)3 + Al(OH)3 from aqueous solution. 3) Colloidal mixing of Fe,O3 and Al2O3. 4) Colloidal mixing of Fe powder and A1,O3. Fig. 1 is a processing flowsheet which outlines the processing steps taken to produce a final extruded bar 1/4 in. in diameter and about 30 in. long. The - 100 mesh iron-aluminum alloy was oxidized by placing a thin layer of powder on an alumina plaque. The reduction step was modified to include 1/2 hr at 1000°C since the powders tended to become pyro-phoric unless sintered slightly after low-temperature reduction. Compacting was done in a 1-1/8-in.-diam pressing die. The slugs produced averaged 1 in. in length. The billets were encased in low-carbon steel cans shown schematically in Fig. 2. The blank is included for structure and property comparison purposes. TESTING PROCEDURE All tests were made on as-extruded material.

Jan 1, 1960

By Charles T. Holland, David A. Olsen

Considerable work has resulted in the development of a formula by which the strength of coal pillars for an L to T ratio of up to 12 may be estimated. One of the factors involved in this formula is the coefficient of friction between the coal pillar and the adjacent rock with which it is in contact. This paper presents the results of studies on sandstone, limestone, shale and coal and the coefficient of friction between coal and the other three under wet and dry conditions. With the coefficients of friction thus determined and the use of results obtained earlier by Meikle and Holland, it seems probable that coal pillar strength may be more closely estimated. Several investigators1-3 have found that the com-pressive strength of cubical coal specimens can be correlated by an equation such as

Jan 1, 1969

THERE is at least one concrete indication that Soviet Russia&apos;s two most important iron ore producing centers are seriously depleted. While keeping in mind Russia&apos;s penchant for reverse propaganda, one piece of evidence indicates that Magnitugorsk in the southern Urals and Krivoi Rog in the Ukraine have been mined to a point where lower grade ores are being recovered. An article in Pravda, Soviet newspaper, by I. P. Bardin. a Russian metallurgist, says that ore presently mined must undergo an expensive enriching cycle before it can be used in blast furnaces. Com- pounding Russian metallurgical troubles is the low quality of coking coals. High ash and sulphur content typifies the coal Badin talks about. Coal from the Ukraine, Eastern Siberia, Kazakhstan, and the Far East requires extensive treatment before it can be used, according to the article in Pravda.

Jan 7, 1953

By R. G. Weavind, R. S. Young, I. Wolf

ONE of the most important fields of investigation at the Diamond Research Laboratory in Johannesburg is concerned with improvements in metallurgical practices for the diamond mining companies, with particular reference to increased recoveries of the smaller industrial stones. Considerable work has been done on the possible application of flotation processes to the diamond industry. From the viewpoint of recovery processes, diamonds in their natural state may be grouped into two classes, the water-repellent diamonds, which adhere to a grease surface, and the water-avid diamonds, which, because of their wettability, will not adhere to a grease surface and must be recovered by means other than the grease tables used for water-repellent diamonds. Experiments in the flotation of small diamonds from both kimberlite and alluvial deposits indicate the following conclusions: Water-repellent diamonds: Satisfactory flotation of —16 mesh diamonds, which are naturally water-repellent, may be accomplished using either Aero-float 25 together with cresylic acid, or Du Pont B23 as frother together with kerosine as auxiliary oily conditioner or froth stiffener. The quantities of reagents required are of the order of 0.15 lb per ton Aerofloat and 0.18 lb per ton cresylic acid. The use of acid circuits is detrimental, and for best results a pH between 7 and 9 should be maintained. R. G. WEAVIND and I. WOLF are with the Diamond Research Laboratory, Johannesburg, South Africa, and R. S. YOUNG, Member AIME, is Director of Research, Diamond Research Laboratory. TN 76B. Manuscript, March 23, 1951. A flotation period of 5 to 10 min is necessary to insure that all floatable diamonds are removed. Diamonds larger than 16 mesh cannot be recovered satisfactorily by flotation. Xanthates do not act as collectors for diamonds, and this is probably associated with their inability to impart a water-repellent surface to this mineral. Water-repellent diamonds smaller than 28 mesh can be floated quite well by the addition of a frother alone, such as pine oil or Du Pont B23. Water-avid diamonds: Partial flotation of the smaller sizes of wettable diamonds can be achieved by preconditioning with fatty acid soaps, cationic amines, and similar reagents, which will impart a water-repellent film to diamonds. Washing to remove excess reagent, followed by flotation, will result in a fair recovery, but the latter is much lower than for water-repellent diamonds. Crushed boart: Recovery of crushed boart from the waste products of industrial uses is best accomplished by first conditioning the diamonds present in the mixture with fatty acids, cationic amines, etc., removing the conditioning agent by washing, and floating in a cell of the pneumatic type. Flotation reagents found to be most suitable are Du Pont B23, and Aerofloat 25 together with cresylic acid. The optimum quantities are 1.2 g Du Pont B23, and 0.55 g Aerofloat plus 1.4 g cresylic acid, per liter of pulp in the cell. A solids-to-water ratio of 1 to 4 is found to be the most suitable, and alkaline circuits are necessary for best results. Diamonds larger than 28 mesh are not recovered satisfactorily by this procedure, but for finer sizes flotation offers an excellent procedure for the reclamation of this strategic industrial material.

Jan 1, 1952

By I. S. Servi, N. F. Graves

THE etch-pit technique has long been used to reveal low-angle boundaries and, in general, the distribution of dislocations in high-purity metals. Often this technique is amenable to quantitative computations,&apos; but generally is affected by some degree of uncertainty because etch pits can be nucleated not only by dislocations, but also by inclusions and surface imperfections. In the case of high-purity zinc, Gilman&apos; reported that etch pits were produced only after adding 0.1 atomic per cent of cadmium to the crystals and aging at a proper temperature. In the course of a study of low-angle boundary behavior in zinc crystals, etch pits were produced in 99.999 pct zinc without resorting to intentional contamination, by etching in a 50:50 HNO3H2O solution. The technique consists of etching until the heat of reaction brings the solution to a boil, and in displacing the etchant rapidly with a stream of cold water, thus avoiding staining. The undesirable features of this technique are the heating effect and the removal of a considerable amount of material. A high polish is obtained if staining is controlled properly; therefore, the etch pits appear very clearly and with excellent contrast when observed under dark field illumination. This is especially helpful for cursory examinations at low magnifications. Several observations were made on zinc crystals of square cross section, having one face parallel to the basal plane and one edge parallel to a slip direction, Fig. l(a). When such a crystal was bent about 2" over a glass die and annealed at 390°C, a sharp boundary was formed only in the inner portion of the crystal. Near the two prismatic faces, perpendicular to the basal plane, the boundary was always branched into many lower-angle boundaries, Fig. 1(b). Attempts to move the main boundary by applying a shear stress to the specimen invariably resulted in curving the boundary, the branched ends remaining pinned in their original location, Fig. 1 (c). The prismatic face, when etched as indicated in the foregoing, revealed the existence of numerous (sometimes up to 30) fine boundaries, nearly parallel to each other. Pre-existing lineage boundaries, generally parallel to the direction of growth, were barriers to the formation of polygonization boundaries and interrupted the continuity of the substructure, Fig. 2. Twin

Jan 1, 1959

By William J. Coulter

WITHIN the past thirty years the United States has been involved in two tragic, vicious, and costly world wars. To make the world safe for democracy was the reason given for our participation, but the confusion and misunderstanding that prevails all over the world today suggests that war is not the proper approach to the attainment of that utopia. These conflicts were conceived and prosecuted by nations far advanced in civilization and culture. Their best manhood was sacrificed, a staggering tax burden was saddled on their peoples, huge financial losses were incurred, destruction of property was appalling, and cultural and peaceful scientific advancement received a setback that may require centuries to retrieve. Therefore, some basis is established for the conclusion that progress in the past fifty years has been most outstanding in the development of instruments used for death and destruction, and that progress in this direction between the two World Wars would indicate that the next war will go far toward total destruction of world civilization.

Jan 1, 1946

By A. J. Weinig

NEED for some simple method of determining tonnages in mill circuits has always been felt by operators and consultants alike. To meet this demand the following method was evolved and has been found accurate and practical after considerable testing on various mill flows. The essence of the method is to add a chemical at a uniform rate to a mill flow, such as a launder conveying pulp, and then determine the concentration of the added chemical in a sample of the pulp. From this procedure the tonnage can be calculated. Common table salt has proved the most satisfactory chemical for ordinary conditions. It has many decided advantages for use in tonnage determinations, among them being the following:

Jan 1, 1933

By Raymond L. Orr

Calorimetric measurements have been made of the heats of solution of gold axd indium in a number of liquid tin-rich alloys at a temperature of 705°K. Relative partial molar enthalpies of gold were determined as a function of dilute solute concentrations in the binary Au-Sn system and in the ternary Ag-Au-Sn and Au-In-Sn systems. Relative partial molar enthalpies of indium were determined for dilute solute concentrations in the In-Sn, Ag-In-Sn, and Au-In-Sn systems. Through application of the interaction coefficient concept introduced by Wagner and more recently extended by Lupis and Elliott, ualues have been obtained for the Au-Au, Ag-Au, Au-In, and Ag-In enthalpy interaction coefficients in liquid tin. The results are inte@reted in terms of solute atom distributions through comparisons with the predictions of dilute solution models. INTEREST in the thermodynamic behavior of dilute liquid alloys stems from two primary sources. From a practical viewpoint, it is often of importance to know or to be able to predict the effect that one solute will have on the thermodynamic properties of the other solutes in a multicomponent system. Studies of dilute solutions may also be rewarding from the theoretical point of view. Some of the difficulties arising from the more complex interactions possible in concentrated solutions are avoided, leading to easier interpretations in terms of solutibn models and bonding energies. For example, in a binary alloy the limiting values of the partial molar properties of the solute represent the case for which each solute atom is completely surrounded by atoms of the solvent, and no other interactions are possible. Solute - solute interactions in dilute solutions are conveniently treated by the interaction coefficient concept of ~agner.&apos; Using a Taylor series expansion for the logarithm of the activity coefficient, In yi, of a component, i, in a solution consisting of dilute solutes with atomic fractions xi, xj, xk, and so forth, in a solvent, s, and neglecting the second- and higher-order terms, Wagner obtained the expression: Where Wheyz is the limiting value of yi in the pure solvent, s. The interaction coefficients, e:, e:, and so forth, are defined by: Since yi is related to the excess partial molar Gibbs energy of component i by GfS = RT In yi, E: is re- ferred to as the "Gibbs energy interaction coefficient". Lupis and Elliott~ extended Wagner&apos;s treatment to the relative partial molar enthalpy, aHi, and the excess partial molar entropy, qS. They defined the enthalpy interaction coefficient as: and the excess entropy interaction coefficient as: leading to expressions similar to Eq. [I]: The three interaction coefficients are related by? The self-interaction coefficients, E:,qf,and at, represent the effects of interactions between atoms of component i in solvent s; €3, q{, and 03 represent the effects of interactions between i and j atoms in solvent s; and so forth. From the Maxwell-type relationships between partial molar quantities, it may be shown1&apos;2 that e{ = ej, r}\ =tj), and ai - crj. Experimental determination of the interaction coefficients requires extremely precise measurements of the appropriate properties as functions of solute concentrations in very dilute regions. Few such data exist for intermetallic alloys, even for binary systems, because of experimental difficulties. This is especially true with respect to enthalpy data for dilute alloys. Examination of the compilation of data for binary alloys by Hultgren, Orr, Anderson, and ~elle~~ reveals that determination of limiting values of &fii(Xi =0) often requires extrapolations to infinite dilution from xi = 0.05 to 0.10. Direct measurements of the enthalpy interaction coefficient, qi, for multicomponent systems are virtually nonexistent. This quantity is of course subject to direct calorimetric measurement, but its determination must be limited to cases where high experimental precision is possible. The heats of solution of gold and indium in liquid tin can be measured with relatively high precision, which makes determinations of 73 involving these metals as the measured solutes experimentally attractive. This paper presents the results of such determinations of the Au-Au, Ag-Au, Au-In, and Ag-In enthalpy interaction coefficients in liquid tin. MODELS FOR DILUTE-SOLUTION BEHAVIOR Random-Solution Behavior. In the quasi-chemical treatment of solutions, only nearest-neighbor bonds are considered, and a composition independent value

Jan 1, 1967

By N. J. Grant, D. S. Bloom

N recent reports, Sully&apos; and Beck and coworkers&apos; I have advanced hypotheses concerning the formation of the phase. Both of these hypotheses are based on Pauling&apos;s theories of the electronic configuration of the elements of the first transition group. Sully considered that the number of electrons which can be absorbed in filling electron "holes" is the factor which determines whether or not the structure can form. Beck suggested that the presence of a certain concentration of electron "holes" is the controlling value. It can be shown that a similar criterion can be developed without making reference to Pauling&apos;s theories. Table I shows the elements of the first transition group and the incidence of the a structure in the binary systems of these elements according to the data presently available. Also appended is the number of electrons considered to exist in the 3d-4s levels of these elements. If the atomic percentages for the phase are listed as shown in Table 11, and if the number of electrons in the 3d-4s levels per atom is calculated for the a boundary values, the results are as shown in the last column. It can be seen that the numerical values are all in the vicinity of 7 electrons per atom. This is true also for the ternary Cr-Mo-Ni IT phase, which occurs in a system in which none of the binary compositions are known to develop the phase. In the Fe-Mo binary, the high temperature a phase, which occurs at a composition of 50 atomic pct of each element, also yields a ,;1 e of 7 electrons per atom. From inspection of Tables I and 11, it develops that any series of sequential numbers which is assigned to the elements under consideration will result in the numbers pertaining to a compositions grouping themselves around one specific number. It does not follow, however, that this random number necessarily has physical significance. Such a point has already been discussed by Hume-Rothery." One interesting point develops from this study, however, and that is the position of manganese with reference to the other elements and to the phase. In the system used here, the formation of phase is associated approximately with the value of 7 electrons per atom, which is also the number of electrons per atom that manganese has. Manganese, it will be recalled, exists in three different crystal forms, none of which are the usual, simpler metallic forms; on the other hand, elements just to the left of manganese (in Table I) generally have lower coordination-number structures (body-centered cubic) than do elements to the right of manganese (face-centered cubic). The contribution to a complex crystal structure by the interalloying of elements from opposite sides of manganese is significant in that the a phase is formed in binary systems including one element from each side of manganese, with manganese capable of participating with both sides. It is indeed an interesting coincidence that manganese, with 7 electrons per atom, solidifies in complex crystal forms, and that when alloys of the transition elements are made which have seven 3d-4s electrons per atom, they, too, tend to assume a complex crystal form. From the above, it might be deduced that the study of the a phase might be advanced by a critical examination of the element manganese and how its structure is affected by small additions of elements which change the 3d-4s electrons per atom number. The role of atom size would also be of interest in formation. References &apos; A. H. Sully: The Sigma Phase in Binary Alloys of the Transition Elements. Journal Inst. Metals (1951) 80, Part 4, p. 173. 2 S. Rideout, W. D. Manly, E. L. Kamen, B. S. Lement, and P. A. Beck: Intermediate Phases in Ternary Alloy Systems of Transition Elements. Trans. AIME (1951) 191, p. 872; Journal of Metals (October 1951). "W. Hume-Rothery, H. M. Irving, and R. J. P. Williams: The Valencies of the Transition Elements in the Metallic State. Proc. Royal Soc. (September 1951) 208A. p. 431.

Jan 1, 1954

By K. E. Gray, A. Podio

ABSTRACT Berea and Bandera sandstone samples were impacted with both 3/4-in. and 1/2-in. long wedges, each having a 60° included angle and a 0.05-in. flat, at various confining pressures, with borehole and pore pressures held fixed at atmospheric pressure. Samples were saturated with air, water, glycerine-water, solirol, mineral oil and soltrol-mineral oil mixtures to obtain a wide range of pore fluid viscosity. Penetration depth was held constant at 0.1 in. Dry and soltrol-mineral oil-saturated Berea samples were impacted at depths of penetration from 0.01 to 0.04 in. under 1,000 psi confining pressure to study crater initiation. Results indicate that viscosity of the pore fluid is influential primarily during the early stages of crater formation. Differences in bit force, crater volume and blow energy for tests parallel and perpendicular to bedding were significant, but decreased as the stress state was elevated. Crater volume, blow energy and bit force were nonlinearly related with depth of penetration. Crater volume was nonlinear with energy of blow. Fixed-penetration tests on saturated Berea yielded greater crater volume than did similar tests on dry samples. Differences in the nature of deformation for low values of bit penetration were noted between saturated and unsaturated samples. INTRODUCTION Rock failure during bit-tooth impact and scouring action constitutes a vital part of the drilling process and a difficult problem for researchers. Much study has been devoted to various aspects of the problem, and much has been learned about mechanics of rock failure. However, analytical treatment of drilling at depth remains difficult, partly because there are so many factors involved and because valid simulation of downhole conditions is extremely difficult. Forming individual craters by a bit tooth or chisel impacting, or indenting, a rock mass has been studied by many investigators.1-18 Similarity between single-tooth chisel impact and the corresponding action of a rotary bit has been discussed by Appl and Gatley, Garner, Podio, and Gatlin l8 compared the similarity in single-blow impact tests with microbit drilling data reported by Cunningham and Eenink.l9 Maurerll has used single-tooth impact data to develop a "perfect cleaning" theory of rotary drilling. Individual roller cutter-tooth impact data have been reported by Young. 20 Single-tooth tests in all of the cited literature were carried out on dry rocks. Inasmuch as any subsurface rock of oilfield interest is saturated with some fluid, it seemed desirable to study crater formation in permeable rocks saturated with a viscous pore fluid as a step, however short, toward more realistic simulation of subsurface conditions. This paper presents results of single-blow chisel impact studies on Berea and Bandera sandstones, both dry and saturated with pore fluids of various viscosities at confining pressures to 10,000 psi. EXPERIMENTAL APPARATUS AND PROCEDURE EXPERIMENTAL APPARATUS The same basic apparatus for single-blow chisel impact at elevated stress states, described in earlier papers was used in this study. l6. l8 Fig. 1 shows the complete experimental system; Fig. 2 shows a cross section of the pressure cell, with a sample ready to be impacted. EXPERIMENTAL PROCEDURE Two different rocks, Berea and Bandera sandstones, were used in this study. Both rocks have been used extensively in research, and rock descriptions can be found in a paper by Gnirk and Cheatham.15 Permeability to air of Berea is about 300 md normal to bedding and 540 md parallel to bedding. Bandera had vertical and horizontal air permeabilities of 18 and 57 md, respectively.

Jan 1, 1966

By B. H. Caudle, A. R. Khan

The oil production performance of thin-oil-column type reservoirs producing entirely by natural water drive are discussed in this paper. The dimensionless production histories were obtained in a series of scaled porous-medium laboratory-model tests under varying effects of rate of production, mobility ratio across moving boundary, ratio of oil- and water-sand thickness and mobility ratio across fixed boundary including the effects of different residual oil saturations in the water-invaded regions. This scaled-model study of thin oil columns indicated that greater recovery of oil results for lower values of the following: rate of production, mobility ratio across the moving boundary, water-sand thickness relative to the oil-sand thickness, and mobility ratio across the fixed boundary or residual oil saturation in the water-invaded region of oil sand The results of the study are given as dimensionless production history plots which may be used to predict the performance of the field they represent. INTRODUCTION Oil fields producing under natural water drive can be classified into two major groups: (1) an "edge-water drive" reservoir group in which the water is encroaching from the reservoir periphery, and (2) the group of reservoirs in which the oil-sand is entirely underlain by an aquifer. Reservoirs in the second group are further subclassified as "bottom-water drive" reservoirs and "thin-oil-column" reservoirs. The latter reservoirs are characterized by their relatively equal oil- and water-sand thicknesses and by having both the oil and water zone relatively thin. When oil is produced from a water-drive reservoir by a partially penetrating well, water breaks through sooner or later before all of the displace-able oil is recovered. Many analyses of this general situation have been made with varying degrees of realism in their approaches, both theoretical and experimental5.6 in nature. Pertaining to the scaled laboratory model studies of natural water drives using porous media, detailed investigations have been made by Henley, et al.7 on bottom-water drive and by Caudle8 on edge-water drive reservoirs. No laboratory model studies, however, have been made to investigate the performance characteristics of thin-oil-column reservoirs. This paper presents the results of a study on scaled models of thin-oil-column reservoirs, operated under varying conditions corresponding to the actual field practices. SCALING PARAMETERS The object of scaling is to produce a one-to-one relationship between physical and dynamic parameters of the model -and prototype. The most comprehensive treatment of scaling techniques for oil reservoirs is given by Geertsma, et a1.,9 which covers two methods for arriving at dimensionless groups for scaling. Table 1 lists the scaling parameters suitable for creating kinematic and dynamic similarities between the model and the prototype in the variables considered for the thin-oil-column reservoirs. In order to achieve similarity it is essential that the dimensionless groups listed in Table 1 have equal values in the model and the protorype simulated. Since it has been established that the role of interfacial forces is neglible in gross fluid movement in a reservoir no attempt was made to scale capillary forces- Although there are reports describing Scaling criteria for these forces,10,ll consideration of the necessary but restrictive conditions for

Jan 1, 1970

By A. T. Chatas

A description of the geometrical characteristics of spherical reservoir systems, a discussion of unsteady-state flow of such systems and examples of engineering applications are presented as backgmund material. The fundamental differential equation, a description of average spherical permeability and the introduction of the Laplace transformation serve as theoretical foundations. Engineering concepts are investigated to indicate particular solutions of interest, which are analytically obtained with the aid of the Laplace transform. These are numerically evaluated by computer, and presented in tabular form. INTRODUCTION A tractable mathematical analysis of unsteady fluid flow through porous media generally requires incorporation of a geometrical symmetry. The simplest forms include the linear, cylindrical (radial) and spherical. Most analytical endeavors have concentrated on cylindrical symmetry because it occurs more often in petroleum reservoirs. Nevertheless, some reservoir systems do exist that are better approximated by spherical geometry. Review of technical literature revealed but a single reference to unsteady spherical flow in petroleum reservoirs.l The motive and purpose of the present work was to remove this gap in technical information, and to provide the practicing engineer with some useful analytical tools. The mathematical details associated with the particular solutions of interest involved use of the Laplace transformation. Hurst and van Everdingen previously demonstrated the efficacy of this operational technique, and in many respects the present treatment was patterned after their earlier work.2 PRELIMINARY CONSIDERATIONS GEOMETRICAL CHARACTERISTICS Geometrically, a spherical reservoir system is defined at any instant of time by two concentric hemispheres whose physical properties of interest vary only with the radial distance. Every physical property is thus restricted to be a space function of only one variable: the distance along a radius vector emanating from the center. Such a system is composed of an outer region and an inner region, separated by a defined internal boundary. The inner region simply extends inward from this boundary, whereas the outer region extends outward from it to an external boundary. The position of the internal boundary is presumed fixed, so that the size of the inner region remains constant. On the other hand, the position of the external boundary at any given instant of time is determined by the distance into the system that a sensible pressure reaction has occurred, Thus, the external boundary may change position with time. It initially emerges from the inner region and advances outward to its ultimate position. When this ultimate position coincides with a geometric limit, the reservoir system is said to be limited. When it coincides with points subject to pressure gradients furthest removed from the internal boundary, yet short of a geometric limit, the system is said to be unlimited. In this investigation two different boundary conditions are imposed at the ultimate boundaries of limited systems. The first requires that no fluid flow occur across this boundary; the second that the pressure remain fixed at this boundary.3-5 UNSTEADY-STATE FLOW In a strict sense virtually all flow phenomena associated with a reservoir system are unsteady-state. The transient behavior of these phenomena requires accounting, however, only when time must be introduced as an explicit variable. Otherwise, steady-state mechanics may be used. Analytically, steady-state conditions prevail in a reservoir system only over that portion of its history when this relation is satisfied:

Jan 1, 1967

By G. J. Wilson

Difficulties experienced in correlating vertical and lateral locations of subsurface features that are encountered in directional wells prompted critical review of the tangential method of computing directional surveys. Inherent discrepancies were indicated to cause small incremental but significantly large cumulative errors in computed vertical depth and horizontal departure. A radius of curvature method, developed for planning and analyzing directional wells, was studied as a means of more accurately calculating survey data. Errors incurred in the tangential method were not present in the radius of curvature method. Conflicting assumptions in calculating dog-leg severity by the tangential method were resolved by a new procedure that was derived from the radius of curvature method. Results of the investigation showed the radius of curvature method to be an improved method for computing directional surveys. Introduction Many improvements in directional drilling tools and techniques have been made in the past 10 years,&apos; but the method of computing survey data has remained virtually unchanged. While use of computers greatly aids the process of calculation&apos; and eliminates many human errors, manual and computer calculations are still made with the assumption that the wellbore consists of straight-line segments. This paper points out discrepancies in the method and presents an improved method in which the wellbore is assumed to be curved. Tangential Method The method presently used to calculate vertical depth, horizontal departure and direction coordinates with measured values of well depth, inclination angle and direction angle is termed the tangential method. This term stems from performing calculations with a series of straight-line segments, with each segment assumed to be tangent to the wellbore at a corresponding survey point. A segment is defined by inclination and direction angles measured at only the lower or deeper end. Consequently, a discrepancy or error is introduced for each segment. Errors are not of extreme magnitude, but cumulatively are significant due to the need to define as accurately as possible the vertical and lateral location of subsurface features such as pay tops, fluid contacts and fault cuts encountered in expensive directional well bores. In Fig. 1, the curved-line segment ab represents a portion of the actual borehole as viewed in the vertical plane. Points a and b are survey stations and +, is the inclination angle at point b. The curved-line segment ab is assumed to be the straight-line segment arb of a length equal to ab and tangent at point b to the curved-line segment. Lengths a&apos;c&apos; and c&apos;b are equal to a&apos;b cos +, and a&apos;b sin +,, respectively. Point a already has been fixed by calcillations performed with survey data obtained at point a, and calculated lengths m&apos;c&apos; and c&apos;b are projected as lengths from point a, rather than from point a&apos;. Point b1 is thus fixed and assumed to represent the actual point b. Calculated length ac" is shorter than actual length ac, and calculated length c"bl is longer than actual length cb. Since b1 is the point from which the next deeper segment will be projected, errors are cumulative. Cumulative error continues to increase as long as the inclination angle continues to increase. When the inclination angle decreases (Fig. 2), calculated length ac" is longer than actual length ac, and calculated length c"bl is shorter than actual length cb. These errors also are cumulative, but differences between calculated and actual lengths are opposite in mathematical sign to differences demonstrated in

Jan 1, 1969

By L. R. Raymond, J. L. Hudson

This paper proposes a comparatively short-term (8 to 10 hours) well test for detecting and characterizing well-bore damage and for measuring mean formation permeability. The proposed test is made by injecting fluid at constant pressure, recording injection rate as a function of injection time. After one to four hours of injection, the well is shut in and fall-off of bottom-hole pressure is obtained as a function of shut-in time. Formation permeability is estimated by an iterative technique. First, a value of formation permeability is assumed. Then, a plot of the recorded injection rate as a function of dimensionless time is made, using the assumed pertneability value. From the slope of the injection-rate curve. a new value of formation permeability is calculated. If the new value agrees with the original assumed value, the assumption was the correct formation permeability. If the values do not agree, the process is repeated using the new permeability value in the calculation. Convergence is rapid, and a reliable permeability value results. Pressure fall-off data are used to check the result. Graphs of pressure and injection rate us functions of time given in the paper show that changes in permeability of the formation in the neighborhood of the wellbore are disclosed by this technique. Thus, the short-term test can he used to detect formation damage. Also, a rough measure of the radial extent of damage can be inferred, which is helpful in designing stimulation treatments. The mathematical model used for this work was a single-zone, horizontal reservoir with a damaged zone in which permeability decreased continuously as radial distance to the wellbore decreased. This model is more realistic than the usual two-zone, discontinuous permeability model used in published works; calculations indicate the realistic model is valid. Vertical variations in horizontal permeability were studied with this model, and results indicate that the permeability measured by the short-term test is the mean horizontal permeability for the vertical interval tested. The proposed short-term test thus should be useful in detecting and characterizing formation damage and in measuring formation permeability needed in calculating reservoir transmissibility. INTRODUCTION To plan the most efficient production or injection schedule for a well and to design or evaluate the optimal stimu- lation treatment, it is necessary to know the properties of the reservoir adjacent to the well, particularly the reservoir transmissibility and characteristics of a damaged zone, if one exists. Several techniques for determining reservoir transmissi-bility from well tests have been presented in the literature. 1,2,3,4 All these techniques rely on conducting constant-rate well tests that often are difficult to execute. A constant-pressure well test is generally easier to carry Out. and this paper contains the first available method for the analysis of constant-pressure well tests. Determination of wellbore damage from transient well tests has been the subject of several papers."" From these studies it is apparent that information necessary for determination of the characteristics of a damaged zone is available shortly after the transient well test is initiated. Consequently, it may not be necessary to carry out an extensive well test (for example, a pressure build-up test) if the primary purpose of the test is to detect the existence of wellbore damage. All previous studies of well testing to determine wellbore damage have been based on the two-zone perrneability model. In this model the damaged zone has a permeability k,, extending to a radius r,,, and the formation permeability k obtains from r, to the drainage radius r,.. Consequently, there is a discontinuity in permeability at r = r,,. This discontinuity can be eliminated by assuming a continuous variation in permeability through the damaged zone. The effect of this assumption on transient well tests is discussed in following sections of this paper. In addition, all formations have within them vertical permeability variations associated with lithology changes throughout the zone of interest. This paper also considers the effect of these variations on transient well tests. ANALYSIS OF CONSTANT-PRESSURE WELL TESTS The mathematical analysis associated with the injection of fluid at constant wellbore pressure into a single-zone, horizontal reservoir completely filled with a fluid of small and constant compressibility and constant viscosity is given in Appendix A. In this analysis it is assumed that the well is located at the center of an undamaged, circular drainage area. From this analysis, the formation permeability can be obtained as follows. 1, Estimate a value for the formation permeability k. 2. Prepare a plot of injection rate q vs

Jan 1, 1967