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By Stanley L. Lopata, Eric B. Kula

The problem of preferred orientation has been considered in quantitative phase analysis by X-ray diffraction techniques. The average intensity of a diffraction peak can be obtained by integration over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. For rod or wire, where the pole figure shows rotational symmetry, the intensity is measured along a radius of the pole figure. Where no symmetry is present, rotational symmetry is imparted by rapid rotation of the sheet around its surface normal during measurement. These methods are applied to the determination of aus-tenite in an Fe-31 pct Ni rod and Fe-28 pct Ni sheet. X-RAY diffraction techniques are frequently used for quantitatively determining the relative amounts of two or more phases present in a structure.1,2 Briefly, the method requires a measurement of the intensity of a Bragg reflection for each phase. The method is based on the principle that the intensity of a Bragg reflection, IA, is directly proportional to the volume fraction of the given phase present, CA: T KRACA/2µ [1] where K is a constant independent of the diffracting phase, RA can be calculated and depends on the Bragg angle ? and the particular reflection measured, and µ is the linear absorption coefficient of the mixture.' For a mixture of two phases A and B, IA = RAcA [2] IA/IB=RAcA/Rbcb and CA+ CB = 1 [3] This allows the volume fraction of a phase to be calculated directly from the measured integrated intensities of the two phases present. This method is frequently used for quantitatively determining retained austenite in steels, but can be used for the quantitative determination of in titanium alloys, as well as phases in other alloy systems. The intensities are generally measured by diffracting only from planes whose normals are perpendicular to the specimen surface, with the implicit assumption being made that this intensity is typical of reflections from planes whose normals lie at other angles to the surface. If the specimen contains a texture or preferred orientation of the crys- tallographic planes by virtue of previous mechanical working, however, this measured intensity is correct only if the intensity level fortuitously is one times random. Examination of pole figures for actual rolled sheet shows that the intensity level at the center of the figure is seldom at the random level, and can very easily differ by a factor of five or more, leading to a commensurate error in the calculated amount of the phases. Textures have been commonly found in materials which are cold-rolled or recrystallized after cold rolling. This problem is becoming of greater importance since structural materials in use today, such as the high-strength stainless steels, frequently are further strengthened by cold rolling, and hence contain textures. Although high-strength carbon-containing alloy steels generally do not contain textures, some of the newer thermomechani-cal treatments will impart a texture even in these cases. In the case of hexagonal metals, such as titanium, probably every wrought sample will show some anisotropy. Since the standard X-ray techniques are inapplicable in all these cases, there is a clear need for some method of taking this anisotropy into account. The specific problem is to obtain the integrated intensity of a Bragg reflection for each phase, averaged over all orientations of the sample with respect to the X-ray beam. This can be done either by purely mechanical means or by a mathematical averaging. Mechanically, a small spherical speci-

Jan 1, 1965

By W. C. Hagel, H. J. Beattie

Phases present at 2200° and 1500°F (1204° and 816°C) were identified in sixty wrought developmental austenitic alloys possessing wide compositional variations. The bases were iron-, cobalt-, and nickel-rich as well as a base with equal parts of each. There are only two structure types previously not found in similar alloys, viz .-the Co3 W and the Fe3Al types. A molybdenum-rich monocarbide decorates dislocations with unusual clarity. Other results provide correlations between alloy composition and phas e precipitation. Grouping intermetal -lic phases into three general classes : I) geometrically close-packed, 2) topologically close-packed, and 3) bcc derivatives, the nickel base prefers the first, the iron base the second, and the cobalt base the third—each base tending to shun the other two classes. Thus, a crystal-chemistry effect previously noted by Laves and Wallbaum can he expanded for these Group VIII elemental bases. There appear to he no quaternary or higher -order structure types requiring more than three atomic species. AFTER studying aging reactions in many diverse commercial austenitic alloys1-4 as a function of detailed time-temperature variations in heat treatment, it became apparent that matrix composition influenced structure types and morphologies to a large extent. These tendencies were related4 to a crystal-chemistry effect uncovered by Laves and Wallbaum.5,6 We have now directed our efforts to exploration of the whole ternary field, covering the standard base elements—iron, cobalt. and nickel— with 10 to 20 pct Cr and moderate amounts, up to 10 pct, of the usual alloy additions. Solutioning and aging treatments were held constant with major emphasis on X-ray identification of microconstituents. The possible existence of exceptions to the Laves-Wallbaum effect, or any new phases, was sought. Phases appearing in austenitic alloys can be classified as geometrically close-packed (gcp), octahedral or nonoctahedral interstitial compounds, topologically close-packed (tcp), semicarbides, and bcc derivatives. Crystal structures of the first four classifications can be visualized as a dense packing of semirigid spheres of different sizes, while the bcc derivatives represent a less efficient packing of spheres. The Laves-Wallbaum effect involves the gcp and tcp phases. Gcp phases possess both tetrahedral and large octahedral interstices; examples are Ni3Ti(n), NiSAl(y'), Co3W(E), and other ordered AB3 compounds where B atoms are smaller than A. Their precipitation is primarily intragranular, presumably coherent with an austenitic matrix, and a chief source of strengthening. Most octahedral interstitial compounds (e.g., CbC, Tic, TiN, Mo2C) have a gcp lattice of large metal atoms which accommodate small carbon or nitrogen atoms in the octahedral interstices. The compound Ti2SC, previously designated Y phase or T phase, can, with some reservation due to its partial co-valency, be placed in this category.7 The nonoctahedral interstitials (e.g., M7C3, Fe3C) represent close-packings of spheres in structures that provide larger triangular-prism interstices for carbon, since the octahedral interstices formed by chromium and iron atoms are too small. Tcp phases possess only tetrahedral interstices; examples are Laves (Fe2Ti, Fe2Cb, Fe2W...AB2), p(Fe7MO6, Co7W8.... A8B7), and (FeCr, Co2Cr3)

Jan 1, 1965

By R. Frenkel, O. D. Sherby, J. E. Dorn, J. Nadeau

A method is shown for the study of the creep rate dependence of metals on the applied stress under the condition of constant structure. The method was applied to pure aluminum and to dilute solid solution alloys of magnesium, copper, germanium, zinc, and silver in aluminum. A linear relationship was found to exist between the true stress and the logarithm of the creep rate. ALTHOUGH extensive creep data are now avail-Aable, the fundamentals of the creep phenomena are as yet only vaguely understood. Many attempts have been made to formulate theories for creep. Eut their agreement with fact has been disappointing. It appears that merely pyramiding more of the same type of data that is now available will not provide the essential aid toward formulating a better understanding of the complicated process of creep. Perhaps attempts to construct better models for the mechanism of creep might have to be tentatively abandoned until new types of definitive creep data are uncovered. The question therefore arises regarding what type of data might be needed to provide the essential knowledge for formulating better and more realistic theories of creep. Perhaps one source of the failure to uncover an adequate theory arises from the fact that practically all theories for creep and nearly all analyses of experimental data on creep disregard the well-known fact that the structure of metals changes during creep. For example, it is customary in evaluating the effect of stress on the creep rate to correlate the secondary creep rate with the applied stress. But, as has been demonstrated recently,' the structures obtained during secondary creep tend to exhibit deformation banding at high stresses and polygoniza- tion at the lower stresses. Consequently the stress-secondary creep rate relationships found in this way are not fundamental, inasmuch as they reveal not only the effect of stress but also the effect of differences in structure on the secondary creep rates. It is the purpose of the study reported here to isolate the effect of stress alone on the creep rate in an attempt to provide new data for possible formulation of a better theory of creep. In addition an attempt will also be made to ascertain how structure, temperature, and alloying might affect the stress-creep rate relationship. The procedure that was adopted was simple: A specimen was precrept at a given engineering stress U, (initial engineering stress during creep under constant load, namely the load divided by the initial area of the specimen) and temperature T to a selected engineering strain, e (engineering strain, namely, the instantaneous gage length minus the initial gage length divided by the initial gage length), at which time the true stress was reduced to some lower value of the true stress, ^ (the true instantaneous stress, namely, the load divided by the instantaneous area). The instantaneous true creep rate, i, (the true strain rate; with E, the true strain, namely, the natural logarithm of the instantaneous over the initial gage length) following reduction of the true stress to U, was then determined. Second, third, etc., tests were conducted under identical conditions except the stress was reduced to yet lower values, us, u,, yielding yet lower instantaneous creep rates, ;, and i,. Inasmuch as the precreep conditions were identical in each series of tests, the instantaneous structures obtained immediately after reducing the stress were presumed to be identical.

Jan 1, 1955

By R. V. Colligan

[CONTENTS PACE Educating and Training Economic Geologists of the Future. By C. H. BEHRE, JR. (TP 2278, Min. Tech., Nov. 1948. Discussions by R. V. COLLIGAN and EVAN JUST) ....... I Mercury Industry in Italy. By EDWIN B. ECKEL. (TP 2292, Min. Tech., Jan. 1948. Discussion .............................. by C. N. SCHUETTE) 3 Chert in the Kingsport Formation at Mascot, Tennessee. By ARTHUR T. ALLEN. (TP 2299, ............... Min. Tech., Jan. 1948. Discussion by M. M. BUTLER) 5 Wall Rock Alteration at Butte, Montana. By RENO H. SALES and CHARLES MEYER. (TP 2400, Min. Tech., May 1948. Djscussions by C. D. HULIN, W. D. JOHNSTON, JR., and L. C. ................................... GRATON) 5] Educating and Training Economic Geologists of the Future R. V. COLLIGAN*-I can best illustrate my opinions by drafting another five year plan (Table 2). This plan is set up following the same stipulations outlined by Dr. Behre, namely: (I) the student is preparing himself for commercial work as a mining geologist; (2) he is attending an institution with a sufficiently broad curriculum (that is, engineering school and mining school as well as liberal arts college) to furnish the courses listed; and (3) he is not planning to continue his studies through to a doctor's degree before going into commercial work. A comparison of my study plan (Table 2) and that submitted by Dr. Behre (Table I) will at once point up the basic similarity, due to the obvious fact that there are so many essential courses which must be included in any outline of study. However, a more detailed analysis will show up certain differences, which, in fact, are only certain refinements on Dr. Behre's program. These I plan to discuss in order of their importance. The first and most important change is the addition of 12 hr of optional subjects, making a total of 24 hr of optional subjects as against a total of 12 hr under Dr. Behre's schedule. This of course entails the elimination of certain courses, which I shall discuss later. However, I wish to make it clear that I suggest eliminating these courses not because I feel that they are unnecessary, but rather because I feel the optional courses are more necessary to the complete education of the individual. I appreciate that Dr. Behre recognizes the importance of the cultural side of education, but I take issue with his thesis that the student will get it without credit and in his spare time. I do not think that the average college student, and certainly not the college freshman, is mature enough to know what he needs and where to get it in his spare time. I think it must be "spoon-fed"; he must be oriented through specific courses. University life (or should I say "college life") is too full of athletics, fraternity activities, dances, "bull sessions," and countless other enjoyable distractions, all of which contribute to the "full man." I fail to see how the average young American male can possibly sandwich in a necessary complement of "cultural activities" in his spare time. Since these latter activities do not fall within the pattern set by the "group," and show less promise of immediate return in enjoyment, or increased social status on the campus, they are bound to suffer in competition with the more popular, "group" activities. No doubt much of the criticism levelled against arts colleges, namely, that the cultural courses are useless, is well taken, for the culture

Jan 1, 1947

By J. W. Cunningham, W. A. Tiller, D. H. Lane

The effect of ultrasonic vibrations on ingot solidification has been considered both theoretically and experimentally. The theoretical section elucidates the mechanisms by which the ultrasonic vibrations might refine the ingot structure. The experimental section describes a very efficient means of introducing the ultrasonic vibrations to the freezing interface. The application of this technique to the consumable-electrode arc melting process shows that the columnar mode of freezing may be effectively suppressed yielding an ingot structure consisting predominantly of equiaxed grains. The results support the contention that the ultrasonic vibrations increase the nucleation frequency in the layer of liquid adjacent to the freezing interface. CERTAIN structural characteristics of as-cast ingots are undesirable since they create considerable difficulty for subsequent processing and often produce defects in the finished product. These structural defects are illustrated in Fig. 1(a), and are: 1) planes of weakness where columnar grains growing from the different mold faces meet, 2) strength anisotropy due to the preferred orientation of the columnar grains and 3) inhomogeneity due to segregation at dendrite boundaries within the columnar grains and at the columnar grain boundaries. The type of ingot structure that eliminates 1) and 2) and diminishes 3) is the fine-grained equiaxed structure illustrated in Fig. 1(c). Many attempts have been made to produce the desirable ingot structure illustrated in Fig. 1(c) by inoculating, casting with varying superheats, vibrating or stirring, or by irradiation with ultrasonic vibrations. These attempts have met with various degrees of success, the ingots generally having the structure illustrated in Fig. 1(b). All four methods have been the subject of numerous investigations,1"4 the latter producing the most erratic behavior and inconsistent success. The method of ultrasonic irradiation during ingot solidification has shown considerable promise on small-scale ingots (diam 2 in.) but has not yet been successfully adapted to large-scale operation. The present paper considers the application of ultrasonic radiation to ingot solidification both theoretically and experimentally. The purpose of the paper is to elucidate the mechanism by which ultrasonic energy refines the ingot structure and to describe a method for producing the desirable ingot structure in both laboratory scale experiments and in ingots of commercial size. THEORY Conventional Casting—Before discussing the possible effects of ultrasonic radiation upon ingot structure let us first briefly review the reasons for the breakdown of columnar crystallization to equiaxed crystallization during ingot solidification. The following is a slightly oversimplified description. In the conventional method of casting, the alloy having a certain degree of superheat, T, is poured to fill a cold mold which is at room temperature, Tc,. Due to conduction of heat through the mold wall the outer rim of liquid metal cools rapidly to the liquidus temperature and begins to supercool. At some degree of supercooling, nuclei of solid form at random in this supercooled layer at the mold surface. The grains in this chill layer begin to grow inwards producing a solute build-up, thus lowering the freezing temperature at the interface as illustrated in Fig. 2. As growth proceeds, the temperature gradient in the solid conducts away not only the latent heat of fusion evolved during growth but it also conducts away some of the superheat of the melt so that the temperature

Jan 1, 1961

By Frederik W. de Klerk

INTRODUCTION During the past 40 years, there has been in the United States of America and other industrialised Western countries a distinct displacement in the procurement of minerals from domestic sources towards an increased dependence on imported minerals. This was caused in part by one or each of the following: a lack of local supply of particular minerals, domestic source depletion or exhaustion and the relative ease and inexpensiveness of obtaining minerals from comparatively unexploited sources in underdeveloped and some developing countries, notably in the Middle East, South America, Southern Africa, and Australasia. Governments of the industrialised nations, concerned about the reliance of their economies on imported raw minerals examined both the degree of reliability and the extent of mineral resources in the countries and regions supplying the essential minerals. This brought a painful awareness of the vulnerability of industrialised countries as a result of the possible interruption of their mineral imports. In this regard, the United States of America may be quoted as a case in point: a report by a House of Representatives Subcommittee on Mines and Mining (Santini Subcommittee)1 revealed that the United States in 1980 was dependent on foreign sources for more than 50 per cent for 24 of the 32 minerals essential for national survival. The Subcommittee also acknowledged that although the United States may develop its own alternative energy sources, there are in many cases no substitutes for the strategic + minerals imported from foreign sources, from countries which are often unstable at best, hostile at worst. This resulted in various policy responses as well as contingency measures, amongst other, renewed emphasis on the utilisation of domestic mineral resources, an intensified search for substitutes of critical minerals and increased stockpiling programmes. Increased attention was devoted to analyses of the political and economic conditions prevailing in the regions from which strategic and other minerals are exported to the industrialised countries, and the formulation of policy measures vis-a-vis those regions. One region which attracted a considerable degree of attention has been Southern Africa, and in particular South Africa.2 The Santini Subcommittee affirmed that while the bulk of the minerals imported by the United States is supplied by a number of source countries, a host of critical[t] minerals vital to the well-being of that country (and this includes all the Western industrialised countries) originates from Southern Africa, a region, deservedly referred to as the "Persian Gulf of Minerals". Apart from the Republic of South Africa the mineral-rich countries concerned are Angola (diamonds, iron ore, oil), Botswana (diamonds, coal), South West Africa/Namibia (diamonds, uranium), Zambia (copper, cobalt), Zaire (industrial diamonds, copper, cobalt) and Zimbabwe (gold, nickel, chromium, asbestos). The Subcommittee however noted that, with the exception of cobalt, the greatest portion of the reserves of the critical minerals listed, lies within the borders of South Africa. SOUTH AFRICA A RELIABLE PURVEYOR OF MINERALS In view of the continual instability and political risk, along with the nationalisation of mineral industries in third world countries, importing industrialised nations have in recent years become more and more concerned about security of long-term supply, and have in consequence begun to diversify their mineral enquiries to areas where the following conditions prevail: • Long-standing record of consistency of supply; • An economic system of private enterprise; • Political stability; • A well integrated infrastructure, with a maintenance of transportation and development costs at realistic levels, and • Attractive investment opportunities, with security of the return of profits.

Jan 1, 1982

By D. W. Akins

The case history of a combination gas and water flood instituted early in the life of a field is described. It was recognized from the beginning that recovery would be low, under normal production methods, from the several separate, thin beds of porous limestone which had such poor native permeability that the wells would not produce without acidizing. It is thought that the combination flood gives excellent recovery efficiencies for this type of reservoir. The chief function of the gas flood now is to maintain bottom hole pressure in that part of the reservoir which will not be affected by the water injection program until later. Present estimates are that ultimate recovery will be approximately double the recovery expected under the original solution gas drive mechanism. Wide (80-acre) spacing has enhanced the economics of the over-all field program by the elimination of more than $5,000,000 worth of unnecessary wells. INTRODUCTION The Haynesville Pettit Field was discovered in November, 1941, with the completion of T. L. James Co.'s Callie Akin No. 1, located in the W 1/2 of the NE 1/4 Section 27-23N-8W, Claiborne Parish, La., at an approximate depth of 5,300 ft. The center of the field is about two miles north and a mile west of the town of Haynesville, La. A total of 189 producing wells have been drilled on 14,500 acres. An additional nine dry holes were drilled. The Louisiana-Arkansas state line divides the field so that 34 wells are in Arkansas and 155 are in Louisiana. Governmental sections are divided equally to contain eight production units making 80-acre spacing where the sections are regular. Along the state line in Louisiana there is an irregular tier of sections, each of which contains approximately 456 acres. When divided equally into eight production units the spacing is 57 acres per well for these three and a fraction productive sections. All Haynesville Pettit wells are identified by their section number followed by their position in the section as determined by numbering the production units counterclockwise beginning in the upper right corner of the section. All of the producing wells in the field except two are unit-ized and operated by the Haynesville Operators Committee. These two wells are located in the extreme northern part of the field in Arkansas. Efforts to bring them into the Unit are being continued. The Pettit operators organized the Haynesville Operators Committee and the field became a unit operation May 1: 1944. GEOLOGY The Pettit is Lower Cretaceous in age and is defined as the uppermost porosity in the Sligo formation. The unitized area known as the Haynesville Pettit Field is composed of two separate zones of porosity approximately 40 ft apart and without connection between the two, except in wells. These zones are known as the Upper Pettit and the Lower Pettit. The Upper Pettit is separated into two sections throughout most of its area by a relatively thin but quite impervious shale streak. These are called the "A" and "B" sections of the Upper Pettit. All of these lenticular zones are composed of coquina limestone and a small percentage of normal oolites. The large

Jan 1, 1951

By D. W. Akins

The case history of a combination gas and water flood instituted early in the life of a field is described. It was recognized from the beginning that recovery would be low, under normal production methods, from the several separate, thin beds of porous limestone which had such poor native permeability that the wells would not produce without acidizing. It is thought that the combination flood gives excellent recovery efficiencies for this type of reservoir. The chief function of the gas flood now is to maintain bottom hole pressure in that part of the reservoir which will not be affected by the water injection program until later. Present estimates are that ultimate recovery will be approximately double the recovery expected under the original solution gas drive mechanism. Wide (80-acre) spacing has enhanced the economics of the over-all field program by the elimination of more than $5,000,000 worth of unnecessary wells. INTRODUCTION The Haynesville Pettit Field was discovered in November, 1941, with the completion of T. L. James Co.'s Callie Akin No. 1, located in the W 1/2 of the NE 1/4 Section 27-23N-8W, Claiborne Parish, La., at an approximate depth of 5,300 ft. The center of the field is about two miles north and a mile west of the town of Haynesville, La. A total of 189 producing wells have been drilled on 14,500 acres. An additional nine dry holes were drilled. The Louisiana-Arkansas state line divides the field so that 34 wells are in Arkansas and 155 are in Louisiana. Governmental sections are divided equally to contain eight production units making 80-acre spacing where the sections are regular. Along the state line in Louisiana there is an irregular tier of sections, each of which contains approximately 456 acres. When divided equally into eight production units the spacing is 57 acres per well for these three and a fraction productive sections. All Haynesville Pettit wells are identified by their section number followed by their position in the section as determined by numbering the production units counterclockwise beginning in the upper right corner of the section. All of the producing wells in the field except two are unit-ized and operated by the Haynesville Operators Committee. These two wells are located in the extreme northern part of the field in Arkansas. Efforts to bring them into the Unit are being continued. The Pettit operators organized the Haynesville Operators Committee and the field became a unit operation May 1: 1944. GEOLOGY The Pettit is Lower Cretaceous in age and is defined as the uppermost porosity in the Sligo formation. The unitized area known as the Haynesville Pettit Field is composed of two separate zones of porosity approximately 40 ft apart and without connection between the two, except in wells. These zones are known as the Upper Pettit and the Lower Pettit. The Upper Pettit is separated into two sections throughout most of its area by a relatively thin but quite impervious shale streak. These are called the "A" and "B" sections of the Upper Pettit. All of these lenticular zones are composed of coquina limestone and a small percentage of normal oolites. The large

Jan 1, 1951

By Thomas L. Kesler

Present Raw Materials The lithium industry has had exceptional growth since publication of the last edition of this volume, and the present scale of mining and consumption of raw materials is a great many times that of 1949. The materials of present economic importance consist of four pegmatite minerals and lithium-bearing brine. Spodumene, a lithium pyroxene, occurs in greatest abundance, and is the chief source. It has the formula LiAlSi2O6 and theoretically may contain 8.03 pct Li2O, but in the more important deposits the content is 6.5 to 7.5 pct. The hardness is 6.5, the specific gravity 3.1 to 3.2, and the color mostly pale green to white although deep green, lilac, and yellow varieties exist. The crystals are prisms with strongly developed longitudinal cleavages, and crushing characteristically produces lath-shaped particles. Giant crystals up to 47 ft long are known, but in most occurrences the predominant size range is 0.5 to 12 in. long and 0.1 to 2 in. wide. Hypogene* alteration has formed lithia-bearing sericite and coarser muscovite and rarely eucryptite, while supergene* alteration yields kaolinite and hydrous mica. Lepidolite, of second importance, is a mica of varying composition approximating K2Li3-A14Si7O21(OH,F)3. It has lamellate cleavage, book structure, and a specific gravity of 2.8 to 3. The books range in size from microscopic to a diameter of several inches. The color is mostly violet, but other colors include pink, gray, yellow, and white. Most commercial lepidolite contains 3 to 4 pct Li20 and chemically is in the higher grade range of a series of lithium micas that includes polylithionite, zinnwaldite, and protolithionite. In this series, the content of Li2O is exceptionally as high as 7 pct. Petalite and amblygonite are also of economic importance, but are used in smaller amounts. Petalite has the formula LiA1Si4O10 and is white, gray, or pink. The hardness is 6, the specific gravity 2.4, the cleavage in two planes 114° apart, and the Li2O content commonly 3 to 4.7 pct with a maximum of 4.88. Amblygonite has the formula LiA1FPO4 in which OH may substitute for F to form montebrasite. It is white and has polysynthetic twinning in two directions at 90°. Amblygonite superficially resembles potash feldspar, but has a bluish or grayish tint unlike the cream or salmon tint of the feldspar.[t] The hardness is 6 and the specific gravity 3 to 3.1, and the content of Li2O is the highest among lithium minerals that occur in significant quantity, ranging mostly from 7.5 to 9 pct with a maximum of 10.2. The brine of Searles Lake in California30 has been a commercial source of lithium since 1938. See Chap. 7, p. 108. The "lake" is a saline evaporite deposit, and the exposed part has an area of 12 sq mi. To an average depth of 71 ft, this part of the deposit consists of crystalline salts with 50 pct interstitial voids. The voids are filled with brine that contains mainly sodium and potassium compounds, but the brine also contains 0.015 pct Li2O, which is recovered as dilithium sodium phosphate containing 21 pct Li20. This deposit overlies a

Jan 1, 1960

By Jack L. Taylor

Single crystals of tungsten grown from powder -metallurgy swaged rod by high-temperative annealing were deformed in tetzsion at temperatures from 2500 to 5000 OF. Orientation of specittzen tensile axis, strained ratrix, and defortnation bands was determined optically by reflections from {110} etch pits. Slip traces meve analyzed and slip directiorz determined. Results indicate that {110}(111) , {112){111}. and {123}{111} type slip occur in tungsten over the terpe,atuve rutge investigated. Slip is orientation-dependent occuvring on tCuzt cowzbitzation oj slip plane and direction which has the highest critical resolved shear stvess. Overshooting appears to be a general occurrence between 2500' and 5000°F. Dejornatiotz bands show rotation in a directiorz opposite to the yotation of tire tensile axis. DEFORMATION in bcc metals has been reviewed by Maddin and Chen,' Keh and eissman,' and most recently by Nabarro, Basinski, and olt. From these reviews it is apparent that some disagreement exists concerning the crystallography of plastic deformation in bcc metals. There is evidence of noncrystallo-graphic slip, the crystal slipping on or near a noncrys-tallographic plane in the (111) zone for which the resolved shear stress is greatest. There is also evidence to indicate that crystallographic slip occurs in the planes of the same zone. On the other hand, there is agreement that the close-packed direction ( 111) is the slip direction in bcc metals. Further, in pure bcc metals4 and alloys the operative crystallographic slip systems are strongly dependent on temperature. Both crystallographic and noncrystallographic slip have been reportede8 in tungsten, a group VIA bcc metal. The number of slip families which operate in the case of crystallographic slip, however, has been in question. The earliest study by oucher' of single-crystal tungsten tested at temperatures of 1800 to 5000°F led to the conclusion that only {112)( 111) type slip operated. Raymond and eumann recently reached the same conclusion studying deformation by rolling of plasma-flame single crystals at 1800°F; however, only [loo] and [110] orientations were studied. Work at high temperatures by Leber and Pughs on tungsten and Chen and Maddin9 on molybdenum suggests that conjugate slip on nonparallel (110) planes may account for the slip on (112) and (123) planes found by others working with bcc metals. The present paper presents evidence of three families or modes of slip in tungsten in the temperature EXPERIMENTAL PROCEDURE Material. Standard microtensile specimens, 0.160 in. diam by 0.640 in. gage length, were ground from commercial powder-metallurgy swaged tungsten rod, type MK. Specimens were heated for 10 min at 5150°F or 6 hr at 5400°F in vacuum of 1 x 105 Torr or less to produce single crystals. At the lower temperature an average of two out of seven specimens heated in a group developed single crystals throughout the specimen length as shown in Fig. 1, the rest remaining wholly poly crystalline. At the higher temperature, three or four out of seven specimens became single crystal. Other than to note that Laue X-ray photographs generally showed sharp, well-defined spots, no attempt was made to assess crystal perfection or measure dislocation density. Two tungsten single crystals grown from the melt by the plasma-arc process were also used for this study.

Jan 1, 1967

Discussion of the paper of DORSET A. LYON and ROBERT M. KEENEY, presented at the Salt Lake meeting, August, 1914, and printed in Bulletin. No. 92, August, 1914, pp. 1791 to 1800. LAWRENCE ADDICKS, Chrome, N. J.-I read this paper for the first time this afternoon, and it is really worthy of a much more careful reply than I can make with such a short time to consider it, but I just want to say that I differ with Dr. Lyon in his premises and conception of what happens in a refining furnace. He cites steel as an instance where the production of special grades justifies the high cost of power in an electric furnace, and goes on to say the same will be true in the case of copper, for the reason that you will get a better quality of product. I don't think you will get a higher grade of copper,. or a better conductivity, as I will explain in a moment. The cost of fuel in the Eastern plants is somewhere between 30c. and 40c. per ton of copper refined, and, if my memory serves me correctly, in an open-hearth steel furnace it is something like $1.25, so it is evident that steel could be handled to better advantage than copper on the basis of fuel. Now, taking the Great Falls plant to compare with is not quite fair, because that plant operates under peculiar conditions. The furnaces are relatively small; the coal is very bad and is very high in sulphur. No one would think of using a coal with 3.6 per cent. sulphur were anything better available. Due to these conditions, the amount of slag is inordinate, it being quoted as 3.5 per cent., and it is necessary to use lime, as there is a tendency to have troubles from arsenic owing to the very high current density used. I think he has taken about as hard a case as he could pick out. Now as to the conductivity of copper, my own idea about the reason that melted copper does not give as high a conductivity as pieces drawn directly from a cathode, or native copper, is that in the latter case the impurities are present as a mechanical mixture, while after melting they are chemically combined with the copper, which is a very different condition. Further, it is necessary to take the sample from a relatively smooth and consequently pure part of the cathode, as otherwise it would not draw. The same with the mass of copper; you pick out a good solid part of the copper, which is not representative. In fact, the refiners have all found they could not take fair samples of cathodes for a chemical analysis. It is always customary to use wire-bar copper -for the purpose of sampling, and the impurities are several times as great as shown by samples taken from .the cathodes. I think if we examine all of the examples he has given of cases where copper is higher in conductivity, it will fit with that explanation. For example, the Elmore process is a direct electrolytic deposit. Incidentally, at the present time there are a number of ex-

Jan 12, 1914

By Ralph E. Esarey, Robert G. Reno

DriLLing activity and prospecting for oil and gas increascd in Indiana in 1941 over the previous year. The greater part of the drilling and development continued to centralize in the Indiana portion of the Interior Coal Basin, in the southwestern part of the state, but other parts of the state were not neglected. Many wildcat wells were drilled, including a series of core tests through the mantle of drift on the southern flank of the Michigan Basin. These core tests have been followed by several unsuccessful production tests. Production tests were made also along the axis of the Logansport-Kankakec branch of the Cincinnati Arch. In all, 411 field locations and 141 wildcat wells were completed in Indiana during 1941; that is, a total of 552 wells, an increase of 3 2 wells over the previous year. The field tests resulted in 260 oil wells, 57 gas wells, and 94 dry holes; wildcats included 16 oil wells, 3 gas wells and 122 dry holes. At the end of the year, 53 field wells and 34 wildcats were drilling. Gibson and Posey Counties led the state, with 154 and 155 wells drilled, respectively. However, 125 wells produced oil in Gibson County, while 98 produced oil in Posey County. Twenty-five per cent of all wells drilled were wildcat; II per cent of these produced oil and 5 per cent produced gas. Grifin field continued to lead in drilling activity, with 157 successful wells and 20 dry holes (including important wells defining the field). Production is found in five pay zones (Tar Springs, Waltersburg, Elwren, Aux Vases and McClosky). It produced a major part of Indiana's estimated 7,200,000 bbl. of oil during the year. Heusler field, Posey County, expanded with 11 oil ells and 4 dry holes in the Waltersburg and Tar Springs. Vienna field, Posey County, completed four oil producers in the Mansfield sandstone, between 1200 and 1250 ft. The College field, discovered late in 1940, received three oil producers and two dry holes in the Aux Vases. Two new fields were discovered in Posey County during the year: Lamott pool, in the Tar Springs, at 1950 ft., had initial production of 55 bbl. on discovery. One producer and one dry hole have been drilled since. Mt. Vernon pool found saturation in both the Waltersburg and Cypress formations. The discovery well tested about 1000 bbl. per day; it tested the McClosky at 2764 ft. Seven producers have been drilled since the October discovery. Welborne-Switch pool found oil in the Cypress sand at approximately 2500 ft., with an initial production of 33 bbl. One more well in the area proved a dry hole. Gibson County had the following discoveries in 1941: The Patoka field was opened by a McClosky producer of 300 bbl. Another producing well has been drilled. An attempt was made to extend the Illinois Mt. Carmel field into Gibson County, Ind., and one producer of 24 bbl, was completed on the Indiana side. A dry hole has since been drilled, one location south. One small well was completed in the Mans. field at 1105 ft. in sec. 31, T.2 S., R.12 W., Gibson County promising a new field

Jan 1, 1942

The papers discussed in the following pages were presented during two sessions of the Geophysics Education Committee of the Mineral Industry Education Division on Feb. 17 and 18, 1941. At the first meeting, to consider the "Influence of Geophysics upon Geology Curricula," this Committee was joined by the Geophysics and Mining Geology Committees of the A.I.M.E., the Society of Economic Geologists, representatives of the American Geophysical Union, and delegates from the Committees on College Curricula and on Applications of Geology of the American Association of Petroleum Geologists. Quentin D. Singewald and Sherwin F. Kelly presided. At the ensuing session, especially emphasizing the integration of geology, physics and chemistry for the solution of earth problems, the joint participants with the Geophysics Education Committee were the Geophysics Committee, and representatives of the American Geophysical Union and of the Committee on College Curricula of the American Association of Petroleum Geologists. Richard M. Field and W. R. Chedsey presided. In the following summary of the discussion at the two meetings, written discussion submitted subsequently is not differentiated from that offered orally at the session. A provisional report of the Geophysics Education Committee was presented at the second session, and some of the following discussion refers to it. This report has not been printed (it is anticipated that a more comprehensive, final one will be rendered at the 1942 annual meeting), but a few mimeographed copies of this provisional report are at the A.I.M.E. headquarters and will be mailed on request. . Dr. W. P. HAYNES presented some notes prepared by Dr. F. H. LAHEE, Chairman of the American Association of Petroleum Geologists' Committee on College Curricula. This Committee's inquiries reveal the general opinion that a four-year academic preparation is inadequate, five or six being advisable. The fundamentals, mathematics, physics, chemistry, and English composition, should be stressed in the first three years, with specialization in the last two or three years. Some companies provide an apprenticeship period, and themselves give additional training.. During academic years more attention needs to be given to engineering training, to field mapping, and in geology to stratigraphy and sedimentation. The amount of mere memory work should be cut, and men trained to observe and reason. Dr. Lahee emphasized the need of more adequate preparation in English composition, because of the inability of many graduates to compose acceptable reports. SHERWIN F. KELLY pointed out that much time in university training, which ought to be devoted to technical subjects, was taken up with English courses. He emphasized that it is the part of the universities to demand of the high schools that the students they send to the university be properly trained to speak and write English. Prof. W. T. THOM protested against the crowding of high-school material into already overcrowded college curricula. C. E. DOBBIN, chairman of the Committee on Applications of Geology of the American Association of Petroleum Geologists, described briefly the work of his committee in publicizing geology, and said that it found a widespread popular interest in the subject but a lack of appreciation of its importance. He recommended that attempts to coordinate the works of geologists and geophysicists be expanded somewhat, toward the further developing and encouraging of a "species of geopolitician" capable of assisting the progress of geology and geophysics by more vigorous advertising of

Jan 1, 1941

By Robert G. Reno, Ralph E. Esarey

DriLLing activity and prospecting for oil and gas increascd in Indiana in 1941 over the previous year. The greater part of the drilling and development continued to centralize in the Indiana portion of the Interior Coal Basin, in the southwestern part of the state, but other parts of the state were not neglected. Many wildcat wells were drilled, including a series of core tests through the mantle of drift on the southern flank of the Michigan Basin. These core tests have been followed by several unsuccessful production tests. Production tests were made also along the axis of the Logansport-Kankakec branch of the Cincinnati Arch. In all, 411 field locations and 141 wildcat wells were completed in Indiana during 1941; that is, a total of 552 wells, an increase of 3 2 wells over the previous year. The field tests resulted in 260 oil wells, 57 gas wells, and 94 dry holes; wildcats included 16 oil wells, 3 gas wells and 122 dry holes. At the end of the year, 53 field wells and 34 wildcats were drilling. Gibson and Posey Counties led the state, with 154 and 155 wells drilled, respectively. However, 125 wells produced oil in Gibson County, while 98 produced oil in Posey County. Twenty-five per cent of all wells drilled were wildcat; II per cent of these produced oil and 5 per cent produced gas. Grifin field continued to lead in drilling activity, with 157 successful wells and 20 dry holes (including important wells defining the field). Production is found in five pay zones (Tar Springs, Waltersburg, Elwren, Aux Vases and McClosky). It produced a major part of Indiana's estimated 7,200,000 bbl. of oil during the year. Heusler field, Posey County, expanded with 11 oil ells and 4 dry holes in the Waltersburg and Tar Springs. Vienna field, Posey County, completed four oil producers in the Mansfield sandstone, between 1200 and 1250 ft. The College field, discovered late in 1940, received three oil producers and two dry holes in the Aux Vases. Two new fields were discovered in Posey County during the year: Lamott pool, in the Tar Springs, at 1950 ft., had initial production of 55 bbl. on discovery. One producer and one dry hole have been drilled since. Mt. Vernon pool found saturation in both the Waltersburg and Cypress formations. The discovery well tested about 1000 bbl. per day; it tested the McClosky at 2764 ft. Seven producers have been drilled since the October discovery. Welborne-Switch pool found oil in the Cypress sand at approximately 2500 ft., with an initial production of 33 bbl. One more well in the area proved a dry hole. Gibson County had the following discoveries in 1941: The Patoka field was opened by a McClosky producer of 300 bbl. Another producing well has been drilled. An attempt was made to extend the Illinois Mt. Carmel field into Gibson County, Ind., and one producer of 24 bbl, was completed on the Indiana side. A dry hole has since been drilled, one location south. One small well was completed in the Mans. field at 1105 ft. in sec. 31, T.2 S., R.12 W., Gibson County promising a new field

Jan 1, 1942

By M. E. Learmont, R. J. Lipp, I. Iwasaki

In the selective flocculation of iron ores, the concentration of alkaline earth ions in pulp solutions plays a critical role. Sodium silicate, alone or with sodium tripolyphosphate, has been used as a dispersant. When Ca+ + concentration exceeds 15 to 20 ppm, however, only a strong complexing agent, such as ethylenediaminetetraacetate (EDTA) was found to be effective (Heerema, Lipp, and Iwasaki, 1979). Some iron ores release Ca+ + in excess of 20 ppm. With ores that contain gypsum, the Ca+ + concentration may reach several hundred ppm. The purpose of this investigation was to compare the effectiveness of EDTA with nitrilotriacetate (NTA) in countering the adverse effects of Ca+ +, particularly at high Ca+ + concentrations. Emphasis was placed on the use of NTA since it is more cost-effective than EDTA. It is also used in detergents in some countries (Malaiyandi, Williams, and O'Grady, 1979). NTA, like EDTA, forms a soluble complex with Ca+ + with a 1:1 molar ratio. Its structure and the value of log Kca are given below together with EDTA (Shibata, 1963). [ ] For experimental materials, an equal weight mixture of Lac Jeannine hematite and a high-purity quartzite from Thompson, MN, both ground to - 30 µm (- 560 mesh) was used. Selective flocculation test conditions and procedures were identical to those used in previous investigations (Heerema, Lipp, and Iwasaki, 1979). The optimum level of starch addition for the above mixture was determined to be at 300 g/t (0.6 lb per st). Initially, a series of selective flocculation tests were performed on the mixture pulped with 10-3M CaC12 (40 ppm Ca + +) at pH 11. With no NTA present, flocculation of the entire suspension resulted. The selectivities achieved in tests with 90, 100, and 150% of the stoichiometric amount of NTA were virtually identical to each other and also to the selectivity of separation obtained in the absence of Ca+ + Such an observation could have been expected since Ca+ + concentrations up to a few ppm may be tolerated in selective flocculation (Krishnan and Iwasaki, 1982). A similar series of tests were performed at 10-2M CaC12 (400 ppm Ca+ +). The results are shown in Fig. 1 as grade¬recovery curves. For comparison, the results obtained in the absence of Ca++ are included. At 90% of the stoichiometric amount of NTA, a large enough concentration of uncomplexed Ca+ + was left in solution to cause indiscriminate flocculation. Note in this figure that NTA is capable of countering the adverse effect of Ca+ + even at this high concentration when it is used in excess of stoichiometric amounts. The free Ca+ + concentrations at 100 and 150% are calculated to be 2.5 and 0 ppm, respectively. [ ] The relative effectiveness of NTA and EDTA was then compared at 100% of the stoichiometric amount using 10-2M and 10-3M CaCI2 (Fig. 2). EDTA appears to be slightly more effective than NTA. The free Ca++ of 0.02 ppm in 10-2M CaC12 with EDTA compared to 2.5 ppm free Ca+ + with NTA might account for the difference. As evident, prohibitively high additions of EDTA and NTA were required to complex high concentrations of calcium ion. The use of both of these agents would result in the accumulation of complexed Ca+ + in recycle water.

Jan 1, 1985

By Irving B. Cadoff, Ernest Levine

The fracture path in a Cu-4 pct Ag alloy wet with mercury was found to he dependent on the heat treatment used prior to tensile testing. Both quenched and slow-cooled alloys were embrittled by the mercury.. For quenched alloys, which were single -phase, the crack path was intergranular. Slowly cooled alloys, which contained precipitate platelets, exhibited transgranular fracture. By comparing stress-strain data for these alloys with similar data on mercury -embyittled solid-solution alloys, it was found that the role of the precipitate and that of the grain boundary in the fracture process were equivalent . THE fracture path which results when metals are strained in a liquid environment appears to be dependent upon the nature of the specific system. Mixed transgranular and intergranular cracking has been observed in the 2024 T4 aluminum alloy when wet with a Hg-Zn amalgam.' Transgranular fracture was induced in an A1-4 pct Cu alloy by masking off the grain boundaries from the liquid Hg-Zn amalgam.' The embrittlement of solid-solution alloys of copper in mercury results in intergranular fracture.' The effect of a precipitated phase on the fracture path in copper alloys is the subject of the present investigation. Cu-4 pct Ag was chosen so that its behavior could be compared with previous work on embrittlement of copper alloys. PROCEDURE High-purity copper (99.999 pct) was used as a base metal, along with 99.999 pct purity silver. Melting was carried out in graphite crucibles with manual agitation to get adequate mixing. The ingots were homogenized by means of vacuum annealing, chemically cleaned, and cold-rolled with intermediate vacuum anneals, to the desired thickness of 0.025 in. The rolled sheets were sheared to the final specimen size of 1 by 0.025 by 0.1 in. The specimens were then electropolished in phosphoric acid (concentrated) and heat-treated in an evacuated capsule at the solution temperature of 770°C. One batch was slow-cooled and the other quenched in water. The thermal etching which occurred during heat treatment was sufficient to permit grain boundary and precipitate delineation. Tensile tests were carried out in air and in mercury on a Table-Model Instron at a pulling speed of 0.2 in. per min. Wetting was accomplished by electro-polishing in phosphoric acid, rinsing in alcohol, and immersing in a pool of mercury. Once wet the coating was stable throughout the mechanical tests. In our studies it was found that wetting the surface or total immersion in mercury produced identical results. For convenience, the wetting technique was used for the experiments described. The crack pattern was observed directly on the surface by removing the mercury after testing. De-wetting was accomplished by flame heating the samples in a vacuum after testing and before observation of the surface. No etchant or polishing was used so as not to obscure the crack pattern on the surface. The mercury removal, however, resulted in a pitted surface but otherwise left the pertinent features visible. Photomicrographs were taken in this condition so as not to disturb the structure associated with the crack pattern. The average precipitate spacing was measured previous to coating the sample with mercury by use of an optical eyepiece micrometer. RESULTS The microstructure of the quenched specimens was single-phase while that of the slow-cooled specimens contained thin platelets of a second

Jan 1, 1964

By M. R. Annis

Drilling mud rheological and gel property changes due to elevated temperatures frequently cause problems in drilling deep wells. A laboratory investigation of the effects of time, temperatures up to 3001; and mud composition on these properties was made with concentric-cylinder, rotational viscometers of the Farm type. The viscometers were sealed from the atmosphere to prevent dehydration of the sample. Gel strengths were found to be more sensitive than viscosities to changes in temperature and mud cornposition. The high-temperature gel strengths of bentonitic clay drilling fluids were not predictable from low-temper.atl4t-e measurements. At high temperatures, [lie clay flocculates. The floccu-lation temperature depends on the concentration and type of solids in the mud and the degree of chemical defloccula-tion. As the bentonite content of a mud increases, floccrrla-tion temperature decreases. Lignosulfonnte treatment raises the flocculation temperature. To minimize adverse high-temperatrrre effects on mud properties, the mud should be maintainted at minimum solids content, properly treated with. a defloccullant which is stable at the maximum ten?perature encountered and maintained at a pH high enough to insure activation of the deflocculant for the duration required. The Methylene Blue Test for cation exchange cnpacity of a clay was found to be a useful guide in deter.niinirig when a mud contains a dangerously high clay conWnt. INTRODUCTION In drilling a well it is desirable, for several reasons, to know the effects of time and temperature on the rheological and gel properties of the drilling fluid in the hole. Problems associated with drilling fluids normally occur down-hole: so it is reasonable to be interested in the properties of drilling fluids at the conditions which exist down-hole. It has long been observed that high pump pressures are often needed to start circulation after a trip and that the "bottom-up" mud that is circulated back to the surface is usually more viscous than it was before "cooking" at the bottom of the hole for several hours. Burk-hardt' showed that a knowledge of rheological proper-ties of muds under down-hole conditions is necessary to predict pressure surges. He showed that the viscosity of a mud greatly influences the magnitude of pressure surges and the likelihood of lost returns. McLean et aL~ showed that the rheological properties of a mud under down-hole conditions are very important to cementing operations. This paper presents data showing the effects of time and temperature on rheological and gel properties of water-base drilling fluids. Measurements of gel strengths and rheological properties were made with two different concentric-cylinder rotational viscometers of the Fann type. One was the conventional six-speed viscometer modified to operate at temperatures up to 350F and at the vapor pressure of the liquid at test temperature. The other viscometer was newly designed to operate at temperatures up to 500F and pressures up to 1,000 psi. Tests with both instruments were made under essentially the same operating conditions. The new viscometer is shown in Fig. I. In this investigation, great emphasis has been placed on the rheological properties of clay suspensions, since clays are largely responsible for a mud's thixotropic and gel-

By M. A. Dayananda, R. E. Grace, P. F. Kirsch

Ternary diffusion experiments were carried out at 750°C with vapor-solid diffusion couples in single-phase copper-rich Cu-Zn-Sn alloys. The Philibert-Guy method was used to calculate intrinsic diffusion coefficients at compositions corresponding to the plane of inert markers imbedded in the diffusion couples. Inter diffusion coefficients were determined at common composition points of intersecting diffusion paths. Intevdiffusion coefficients were also obtained at compositions corresponding to maxima in the tin concentration pvofiles Relations between the interdiffusion coefficients and the expansion of vapor-solid diffusion couples are described in detail. Such relations permit the calculation of constant interdiffusion coefficients in binary couples from expansion data directly. In ternary couples expansion data provide an additional constraint on the interdiffusion coefficzents. ThE phenomenological analysis of diffusion in ternary solid solutions has been developed extensively, and various approaches taken in the determination of diffusion coefficients have been reviewed recently by Guy et al.' Finite,' semi-infinite,3 and infinite4 diffusion couples have been used in studies of ternary diffusion, but most of the work has been done with infinite diffusion couples. Semi-infinite diffusion couples3 (vapor-solid couples) have been used to determine both intrinsic and interdiffusion coefficients in the Cu-Zn-Mn system, in which two diffusing species, zinc and manganese, were supplied from the vapor phase. If only one component has a sufficiently high vapor pressure to be supplied from a vapor source, vapor-solid diffusion couples may still be used. In this case the boundary conditions at the gas/solid interface may be governed by partial equilibria rather than by virtually complete equilibrium between the phases. In the present work diffusion measurements were carried out at 750°C with vapor-solid couples of Cu-Zn-Sn alloys. Only zinc was transported between the vapor source and the diffusion disks, because the vapor pressures of both copper and tin are at least 108 lower than that of zinc. Both intrinsic and interdiffusion measurements were made at several compositions. A secondary objective was to relate expansion of the diffusion couples with the interdiffusion process. Such measurements for binary couples yield average values of the interdiffusion coefficients over composition increments. In ternary diffusion couples ex- pansion data provide an additional constraint on the interdiffusion coefficients. COMPOSITION-DEPENDENT INTRINSIC AND INTERDIFFUSION COEFFICIENTS As shown by Philibert and GUy5 the determination of intrinsic diffusion coefficients in a ternary system requires two independent diffusion couples containing marker planes with identical composition. In the case of vapor-solid couples such a requirement torresponds to two couples set up with the same vapor source exposed to two diffusion disks of different composition. Inert markers placed initially on the disk surfaces become imbedded during diffusion. If the pair of couples exhibits appreciable marker burial with marker planes of virtually the same composition, the intrinsic diffusion coefficient may be evaluated at the composition of the marker planes. Fig. 1 is a schematic diagram of the concentration of of a Cu-Zn-Sn ternary vapor-solid couple after diffusion of zinc from a vapor source into a binary Cu-Sn alloy. The areas, Ai correspond to the cumulative intrinsic fluxes of the three diffusing species across the marker plane:5 where Ji is the intrinsic flux of component i, t is the diffusion time, and D3i are the intrinsic diffusion coefficients. For the determination of interdiffusion coefficients a pair of diffusion couples with intersecting diffusion paths is needed. At the composition point of intersection (C1, C2) the coefficients are evaluated from the equation:3

Jan 1, 1969

By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by

By J. F. Evers, S. Sadiq, F. W. Preston, G. W. Swift

Proper scaling of unsteady-state flow in laboratory gas reservoir models can be achieved if the permeability/fractional porosity ratio is less than 0.5 md. Porous media meeting this specification can be obtained from mixtures of sand and Portland cement provided (1) the water/cement ratio is in the range of 0.35 to 0.40, (2) the sand/cement ratio is in the range of 1/1 to 2/1, (3) the sand grain size is in the range of 48-100 to 18-28 mesh, (4) the mortar curing time is 7 days or more and (5) the cured mortar is dried under vacuum to reduce the temperature level employed during the drying process. The areal homogeneity of the mortars tested is reasonably good, although significant trends in vertical permeability were noted. The Klinkenberg and non-Darcy coefficients of mortar are such that proper scaling of these effects in the laboratory model could be expected. INTRODUCTION A long term deliverability prediction for a gas well is generally based on data determined from flow tests that are of short duration relative to the producing life of the well. These data, together with an estimate of gas reserves in place, form the basis for establishing the parameters of the mathematical model used to predict performance at future times. Results obtained from a mathematical model represent only an interpretation of the physical process being modeled. Experimental verification of the production process from discovery to abandonment is needed where production occurs under carefully controlled conditions. Ideally, one might consider such an experiment to be conducted in the field. Even if the cost of such an experiment could be justified, the time required would make it impractical to consider. However, if the time scaling problem could be handled properly, an experimental model of the gas reservoir production process could provide the necessary data to study the mechanisms of the production process in a reasonable time period. An experimental model has been designed and constructed using the data of this study as a basis. The model reservoir system consists of one producing well located at the center of a right-circular cylinder of porous material. Ten to 15 observation wells are located at strategic offset positions from the producing well. These wells, and the producing well, are fitted with pressure transducers so that the pressure-time history can be recorded at various radial and azimuthal positions in the drainage area during the entire production life of the system. Time is scaled in the model so that the time required to produce gas from discovery pressure to abandonment pressure is about 2 hours. This compares with a 20-year producing life in the model's field counterpart and gives a time scale factor of approximately 1:100,000. DESIGN CRITERIA To establish design criteria for the experimental model, the reservoir is considered to be a finite right-circular cylinder of radius rr, and height h with a producing well of radius rw located at the center and completed through the producing formation. This reservoir consists of a porous medium which has a uniform permeability k and gas porosity and the gas contained in the reservoir has density p, viscosity µ and molecular weight M. Initially, the pressure at all points within the reservoir is uniform at po. and the reservoir temperature is T. Since the reservoir production process has been demonstrated to occur in two distinct transient modes for either Darcy or non-Darcy flow,l it is