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By C. S. Smith, L. W. Kempf, C. S. Taylor

The thermal conductivity of aluminum alloys is of considerable industrial importance. This is particularly true in such applications as internal-combustion engines where one of the principal reasons for the use of these alloys is their relatively higher thermal conductivity. In spite of this, relatively few data are available on this property of aluminum alloys. The reason is quite apparent to anyone concerned with the experimental determination of coefficients of thermal conductivity. This determination, in theory so simple, is extraordinarily difficult if any high degree of precision is desired. Fortunately, some .knowledge of the relationship between thermal and electrical conductivity has permitted the use of the latter physical property in deducing the relative approximate values of the thermal conductivities of metals. This fundamental relationship, first enunciated by Wiedemann and Franz' as applying to metallic elements and later shown by Lorenz2 to be applicable to alloys within a single metallic system, has been of service in the industrial application of metals. The electrical conductivity of metals is easily determined with a high degree of precision. It is, therefore, quite desirable that the relationship between electrical and thermal characteristics be determined with the greatest possible precision. This paper presents data on the electrical and thermal conductivities of a number of aluminum alloys of industrial importance. Literature on Thermal Conductivity of Aluminum Alloys Masumoto3 determined the electrical and thermal conductivities of 18 aluminum alloys. His results indicated a relatively constant relationship between thermal and electrical conductivity.

Jan 1, 1937

By B. L. Averbach, M. Cohen

THE PROBLEM MANY hardened steels contain significant quantities of retained austenite even in cases where the carbon and alloy contents are low. In fact austenite has been detected in plain carbon steels containing as little as 0.50 pct carbon.1 Although the austenite may not be visible metallographically it causes definite dilatometric and magnetic effects during subsequent tempering or subatmospheric cooling.1,2,3 Therefore if the reactions which hardened steels undergo during later treatment are to be understood in quantitative fashion it is most essential to have some kind of absolute analysis for the austenite content in hardened steels. Once this analysis has been made, the austenite transformations can be followed precisely by observing such sensitive phenomena as changes in length or in magnetization but the latter techniques can only determine differences in the amount of retained austenite and usually an independent method must be found to put these differences on an absolute basis. In certain instances the microscope can be used advantageously to determine the percentage of retained austenite. The quenched sample is tempered to "darken" the martensite with minimum decomposition of the coexisting austenite, and then is polished and etched in the usual fashion. If the austenite is clearly distinguishable from the tempered martensite and other possible constituents its volume percentage can be measured quantitatively by point counting or lineal analysis.4 Such microscopic methods, however, depend on the etch being sufficiently discriminatory. In fairly coarse structures, if the austenite content is greater than 10-15 pct, there is probably little smearing of the etch, and point counting or lineal analysis seems to be quite accurate. On the other hand if the structure is difficult to resolve, as in commercially treated fine-grained steels which contain less than 10-15 pct retained austenite, the latter may be completely obliterated by the dark etching martensite or it may appear disproportionately low as the interfaces between the two constituents become difficult to distinguish. Another disadvantage of the metallographic method is the need for "darkening" the martensite and hence the determination cannot be applied to as-hardened steels. The required tempering may spoil the structure for other tests or may even remove a small part of the austenite which is being sought. X ray methods hold more promise for covering the range under 15 pct retained austenite. Although austenite and martensite in the hardened steel may be chemically identical, their crystal structures and lattice parameters differ, and the intensity of an austenite diffraction line is some continuous function of the percentage of re-

Jan 1, 1948

By Charles Fulton

This paper describes experiments carried on at the Case School of Applied Science, together with their results. Their success led to the design of the larger furnace herein described, but which has not been built. A PREVIOUS article' by the authors contained a general description of the new roasting furnace herein described but it did not go into detail as to the metallurgical behavior or the results obtained. Believing that such information would be of great value, they have elaborated on the subject and have given many unpublished details. The furnace described applies the principle of roasting finely divided zinc-sulfide ores, now produced in large quantity by the flotation process, in gaseous suspension; that is, the ore particles are carried, in suspension, in a current of air and gaseous products of the roast. The relatively great fineness of flotation concentrate presents difficulties and problems of roasting in furnaces of the ordinary type; the fine ore is forwarded through the furnace in the form of a shallow bed and its very fineness leads to dense impervious bedding which prevents oxygen from reaching the interior of the bed, thus unduly lengthening the time of roasting and preventing the elimination of the last of the sulfur. The fineness of the concentrate, normally, should lead to a rapid and complete roast, for the speed of roasting is a function of the surface exposed to oxygen, which surface is greatest, per unit of weight, in very fine material. The difficulty in bed roasting is to get the oxygen to the particle. If the fine ore, during the roasting, could be freely suspended in oxidizing gases, full advantage could be taken of the great surface conferred by its fineness. This fundamental idea, of course, is not new, for the Stedtefelt furnace, familiar to the older metallurgists, is an example of it; but the manner in which this is accomplished may be new.

Jan 10, 1924

By M. A. Meyers, P. P. Meyers

The analysis of the phenomena involved in determining the compressive strength of iron-ore agglomerates leads to the identification of important parameters. It is shown mathematically that the pellet rupture strength is proportional to the cross-sectional area. Fracture is initiated at the center of the pellets by the tensile stresses developed by the compressive loads normally to the compressive axis. The variation in strength between individual pellets of identical composition and subjected to identical treatments u due to internal voids of varying sixes that act as stress-concentration sites. Two novel testing procedures are proposed. The first consults of testing the pellets between two plates having three steel spheres each. This configuration simulates much better the environment actually encountered by the pellets. The second procedure consists of a thick-walled cylinder in which a piston penetrates; a large group of pellets is tested simultaneously, as the stress versus strain plot is being recorded. This latter test presents vacant advantages over the conventional testing procedure; the main one is that one single test is sufficient to characterize the mechanical response of the pellets.

Jan 1, 1984

Secondary minerals are the result of a process of concentration and enrichment and are commonly richer than the primary minerals of the same deposit. Secondary ores that contain abundant sulphides are commonly distinguishable in the field from primary ores; this distinction is more difficult with ores that carry a small quantity only of sulphide minerals, and microscopical examination of the ore in thin section is advisable in all doubtful cases. It is frequently difficult, and in some cases impossible, to determine the primary or secondary character of quartzose gold ores. The safest guide is the presence or absence of gaseous or fluid inclusions in association with the ore minerals; such primary association coupled with a lack of traces of oxidation is indicative of primary origin. Any ore that carries traces of oxidation, such as iron stains, endritic oxides of manganese, kaolin and so forth must be considered to have been acted upon by surface agencies, and secondary enrichment must be suspected. Further examination, however, may indicate that the contained value is primary, and, therefore, persistent in its vertical distribution. The manner of occurrence of secondary minerals is frequently characteristic; secondary minerals, being due to the action of surface waters, are commonly found in cracks through earlier minerals, or as crusts lining vugs or surrounding nucleal masses, or in general, in some distribution later than and not conforming to the arrangement of the primary minerals. Secondary sulphides are often found as soft black pulverulent masses or coatings, although they frequently occur well crystallized or as

Jan 1, 1932

By C Gunther

Secondary minerals are the result of a process of concentration and enrichment and are commonly richer than the primary minerals of the same deposit. Secondary ores that contain abundant sulphides are commonly dibtinguishable in the field from primary ores; this distinction is more difficult with ores that carry a small quantity only of sulphide minerals, and microscopical examination of the ore in thin section is advisable in all doubtful cases. It is frequently difficult, and in some cases impossible, to determine the primary or secondary character of quartzose gold ores. The safest guide is the presence or absence of gaseous or fluid inclusions in association with the ore minerals; such primary association coupled with a lack of traces of oxidation is indicative of primary origin. Any ore that carries traces of oxidation, such as iron stains, dendritic oxides of manganese, kaolin and so forth must be considered to have been acted upon by surface agencies, and secondary enrichment must be suspected. Further examination, however, may indicate that the contained value is primary, and, therefore, persistent in its vertical distribution. The manner of occurrence of secondary minerals is frequently characteristic; secondary minerals, being due to the action of surface waters, are commonly found in cracks through earlier minerals, or as crusts lining vugs or surrounding nucleal masses, or in general, in some distribution later than and not conforming to the arrangement of the primary minerals. Secondary sulphides are often found as soft black pulverulent masses or coatings, although they frequently occur well crystallized or as

Jan 1, 1932

By H. F. Yancey

THE jig may be termed the standard coal-washing machine. Although exact figures on the relative tonnages of coal treated by the various coal-cleaning processes are not available, it is known that a large part of all the coal given special cleaning treatment is handled by jigs. This wide use of the jig warrants a special study of its performance. In this paper are presented the results of an analysis of work done by a three-compartment jig in treating bituminous coal from the Thick Freeport bed in Allegheny County, Pa. Certain systems of washing coal require sizing before washing, while others treat unsized coal. The prevailing practice, however, for the preparation of coking coal from the more easily washed coal is to treat an unsized or natural feed at about -1 in. size and smaller. Under such conditions, the minimum size of particle that is beneficiated has long been and is still a matter of discussion and conjecture. In a careful laboratory investigation Jüngst1 concluded that the practical limit of settling of fine coal is reached at from 0.02 to 0.008 in. On the other hand, Hancock2 has found that single-compartment jigs, used in preparing coal for the domestic market, usually allow most of the heavy (refuse) particles smaller than 1/4 in. to go into the washed coal. He also states that it is impossible with the ordinary coal jig to make any noticeable improvement in the quality of the coal finer than 20 mesh (about 1/30 in.). Because of its importance in coal cleaning, the work described in this paper was undertaken for the purpose of obtaining information on this subject, as a part of the general coal beneficiation program being carried out by the Bureau of Mines.

Jan 4, 1925

By Thomas Fraser, H. F. Yancey

The jig may be termed the standard coal-washing machine. Although exact figures on the relative tonnages of coal treated by the various coal-cleaning processes are not available, it is known that a large part of all the coal given special cleaning treatment is handled by jigs. This wide use of the jig warrants a special study of its performance. In this paper are presented the results of an analysis of work done by a three-compartment jig in treating bituminous coal from the Thick Freeport bed in Allegheny County, Pa. Certain systems of washing coal require sizing before washing, while others treat unsized coal. The prevailing practice, however, for the preparation of coking coal from the more easily washed coal is to treat an unsized or natural feed of about — 1 in. size and smaller. Under such conditions, the minimum size of particle that is beneficiated has long been and is still a matter of discussion and conjecture. In a careful laboratory investigation J?ngstl concluded that the practical limit of settling of fine coal is reached at from 0.02 to 0.008 in. On the other hand, Hancock2 has found that single-compartment jigs, used in preparing coal for the domestic market, usually allow most of the heavy (refuse) particles smaller than 1/4 in. to go into the washed coal. He also states that it is impossible with the ordinary coal jig to make any noticeable improvement in the quality of the coal finer than 20 mesh (about 1/30 in.). Because of its importance in coal cleaning, the work described in this paper was undertaken for the purpose of obtaining information on this subject, as a part of the general coal beneficiation program being carried out by the Bureau of Mines.

Jan 1, 1925

By S. R. B. Cooke, Iwao Iwasaki, Hyung Sup Choi

John Dasher (Materials and Processes Engineer, Crucible Steel Co. of America, Pittsburgh, Pa.) The authors are to be congratulated for their excellent work, dramatic results, and persuasive explanation on the neglected subject of the temperature variable in soap flotation. The explanation includes why heat is helpful in conditioning and why heat is helpful in flotation. This is a fine start, but I hope the work will be continued to show which is the major effect. In the work of Noman and Dash er(1) it was found that substantially all the benefit of heat came from the conditioning step, and that results were much better if a thick pulp was conditioned hot and then diluted with unheated (or less heated) water for flotation (or agglomerate tabling) than if the same quantity of heat was used to condition and float at some intermediate temperature. In other words, heat for conditioning gives a Rood return, but additional heat for dilution water is near or beyond the point of diminishing return. Strathmore R. B. Cooke, lwao lawsaki, and Hyung Su0p Choi (Authors' Reply) Mr. Dasher'skind comments on our paper are appreciated. In view of the relative simplicity of empirical investigationsof the temperature variable upon conditioning and flotation, it ispuzzling why the subject is so neglected. Our work, being sub sidiary to the main investigation of the effect of structure of fatty acid collectorsupon iron ore flotation, was quite restricted, but we intend to return to the subject as soon as possible. Mr. Dasher's point, that given a certain number of calories it is better to invest them for conditioning in a thick pulp rather than to spread them out for both conditioning and flotation operations, is well taken and cannot be argued. On the other hand there is no question that high temperature during the flotation of iron ores induces superior frothing characteristics, and, in particular, greatly augments the rate of flotation and markedly decreases the time required for "difficult" particles to float.

Jan 1, 1961

By E. G. Leonardon, C. Schlumberger, M. Schlumberger

The authors give a definition of the various types of corrosion that may affect a metallic conductor buried in the ground, namely: 1. The metallic conductor may be attacked by the surrounding soil. This phenomenon is purely local and is called by them soil corrosiveness. 2. The metallic conductor may connect two regions of the ground when the electrolytes have a different composition. An electrical current will then be generated and certain zones of the conductor will be oxidized. This is autogalvanic corrosion. 3. Stray current may flow in the ground and enter the conductor in certain sections and leave it in others, thus causing oxidization in certain zones; this is electrolytic corrosion. The soil corrosiveness has been studied extensively by the United States Bureau of Standards and the authors give a summary of the work carried out and results obtained along this line. In autogalvanic corrosion it has been shown, by the investigation of buried pipes, that the zones of corrosion are associated with the zones of egress of the electric current (anodic zones). The location of these zones can be determined by measuring at the surface of the ground the difference of potential that exists along the path of the pipe. This work is performed easily and quickly with the apparatus invented by the authors for the exploration of conductive orebodies. The problem of electrolytic corrosion is a difficult one because it is a question of stray current which may vary in direction and intemsity at every instant. Therefore the components of the electrical field must be known at a given station and compared with the components of the clectrical field at another station, at the same moment. This is achieved by a rccording apparatus that will register the variations of the intensity of the electrlc current along two rectangular directions, during several minutes

Jan 1, 1934

By Teder R. I., M. M. Protodyakonov

In order to find an empirical relation between a quantity F and (m) independent variables or factors, each of which take (n) different values or levels, it is necessary to conduct nm different experiments (all possible combinations of the factors), each of which has to be repeated a few times (usually five) due to the scattering of the data. The total number of such experiments is very large, thus for example, when m = 4 and n = 5, it is equal to 5.54 = 3125; and very rarely is it possible to conduct such a number of experiments. Various possible methods of planning partial experiments are illustrated in Fig. 1. Each method shows a large combinative square consisting of five columns and five rows of middle squares, each of which, in turn, is further divided into five columns and five rows of cells. Such a partition corresponds to a plan of an experiment with four factors, each of which takes five different levels. The blackened cells indicate the combination of factors in a partial experiment. The total number of experiments is reduced on the basis of the following considerations: a) The effect of only a few levels of some factors is studied (Fig. la). Such an investigation gives no information on the effect of some factors, therefore it cannot be accepted as satisfactory; b) By reducing the number of levels of each factor; in such a case it is not possible to obtain an empirical relationship, but only whether some factors have an effect. This is evidently inadequate;

Jan 1, 1971

By E. R. Morgan

A series of manganese-rich ferromagnetic alloys has been studied. The alloys are based upon an interstitial solution of carbon in manganese. In each of the systems investigated, the ferromagnetic phase was found to be face-centered-cubic in structure. This magnetic phase is based upon the composition (Mn, X)4C; where X is a metallic element which has both a positive size factor with respect to manganese and a high positive valence. Typical elements of this type are aluminum, indium, and tin. Preliminary magnetic measurements indicate that the effective magnetic moment of manganese in the alloys is at least 1.0 Bohr magneton per atom. It is emphasized that the critical atomic separation beyond which ferromagnetism can occur will be governed by the electronic configuration of the manganese atoms. Lattice parameter measurements show that the ferromagnetic condition in the present alloys is associated with an increased atomic separation of only 3 to 6 pct compared with a hypothetical face-centered-cubic lattice of pure manganese. MANGANESE which is paramagnetic and not ferromagnetic in the pure state can become ferromagnetic if suitably alloyed. Under favorable conditions manganese can have an effective ferromagnetic moment of the order of 3.41,2 or even 4.0 compared with a moment of 2.2 Bohr magnetons for iron. The incidence of ferromagnetism is believed to be controlled by the degree of atomic separation.4,5 This is consistent with the fact that the atomic separation, when considered in terms of the ratio of the atomic diameter R to the diameter r of the 3d-shell, is larger in the ferromagnetic metals. The values of R/r calculated by Slater,' for metals of the iron group are given in Table I, and Slater has suggested that the critical ratio of R/r is 1.5. Consideration of the criterion of atomic separation alone would suggest that there are three classes of possible ferromagnetic manganese alloys: 1— Ordered structures, of either solution or compound types, such that manganese atoms are not near neighbors; 2—Structures in which the separation of near-neighbor manganese atoms is sufficiently increased by the presence of suitable solute atoms; and 3—Dilute solutions of manganese. Typical ferro- magnetic alloys of types 1 and 2 are the Heusler alloys and Mn4N, respectively. There are no recognized ferromagnetic alloys of type 3. In view of the proximity of the ratio R/r for manganese to the critical ratio of 1.5, the present work was concentrated on manganese-rich alloys rather than on ferromagnetic alloys of low manganese content, several examples of which are already known. Calculation of the distance of closest approach of manganese atoms in each of its allotropic forms, Table 11, indicates that the high temperature ? phase provides the most suitable basis for ferromagnetic alloys of high manganese content. However the high temperature forms of pure manganese cannot be retained on quenching, although a face-centered-tetragonal form apparently can be produced by electrodeposition. Since the critical separation which must be exceeded in order to obtain ferromagnetism is dependent upon the number of electrons in the d-shell, no exact critical value of R/r can be assumed. Not only will this separation vary from one pure metal to another, but it will also vary with the valency of the given type of atom when it is in an alloy. Raynor8 has shown that metals of the iron group probably

Jan 1, 1955

By M. Cohen, B. L. Averbach

Many hardened steels contain significant quantities of retained austenite even in cases where the carbon and alloy contents are low. In fact austenite has been detected in plain carbon steels containing as little as 0.50 pct carbon.1 Although the austenite may not be visible metallographically it causes definite dilatometric and magnetic effects during subsequent tempering or sub-atmospheric coo1ing.l,2,3 Therefore if the reactions which hardened steels undergo during later treatment are to be understood in quantitative fashion it is most essential to have some kind of absolute analysis for the austenite content in hardened steels. Once this analysis has been made, the austenite transformations can be followed precisely by observing such sensitive phenomena as changes in length or in magnetization but the latter techniques can only determine differences in the amount of retained austenite and usually an independent method must be found to put these differences on an absolute basis. In certain instances the microscope can be used advantageously to determine the percentage of retained austenite. The quenched sample is tempered to "darken" the martensite with minimum decomposition of the coexisting austenite, and then is polished and etched in the usual fashion. If the austenite is clearly distinguishable from the tempered martensite and other possible constituents its volume percentage can be measured quantitatively by point counting or lineal analysis.4 Such microscopic methods, however, depend on the etch being sufficiently discriminatory. In fairly coarse structures, if the austenite content is greater than 10-15 pct, there is probably little smearing of the etch, and point counting or lineal analysis seems to be quite accurate. On the other hand if the structure is difficult to resolve, as in commercially treated fine-grained . steels which contain less than 10-15 pct retained austenite, the latter may be completely obliterated by the dark etching martensite or it may appear disproportionately low as the interfaces between the two constituents become difficult to distinguish. Another disadvantage of the metallographic method is the need for "darkening" the martensite and hence the determination cannot be applied to as-hardened steels. The required tempering may spoil the structure for other tests or may even remove a small part of the austenite which is being sought. X ray methods hold more promise for covering the range under 15 pct retained austenite. Although austenite and martensite in the hardened steel may be chemically identical, their crystal structures and lattice parameters differ, and the intensity of an austenite diffraction line is some continuous function of the percentage of re-

Jan 1, 1949

By B. L. Averbach, M. Cohen

Many hardened steels contain significant quantities of retained austenite even in cases where the carbon and alloy contents are low. In fact austenite has been detected in plain carbon steels containing as little as 0.50 pct carbon.1 Although the austenite may not be visible metallographically it causes definite dilatometric and magnetic effects during subsequent tempering or sub-atmospheric coo1ing.l,2,3 Therefore if the reactions which hardened steels undergo during later treatment are to be understood in quantitative fashion it is most essential to have some kind of absolute analysis for the austenite content in hardened steels. Once this analysis has been made, the austenite transformations can be followed precisely by observing such sensitive phenomena as changes in length or in magnetization but the latter techniques can only determine differences in the amount of retained austenite and usually an independent method must be found to put these differences on an absolute basis. In certain instances the microscope can be used advantageously to determine the percentage of retained austenite. The quenched sample is tempered to "darken" the martensite with minimum decomposition of the coexisting austenite, and then is polished and etched in the usual fashion. If the austenite is clearly distinguishable from the tempered martensite and other possible constituents its volume percentage can be measured quantitatively by point counting or lineal analysis.4 Such microscopic methods, however, depend on the etch being sufficiently discriminatory. In fairly coarse structures, if the austenite content is greater than 10-15 pct, there is probably little smearing of the etch, and point counting or lineal analysis seems to be quite accurate. On the other hand if the structure is difficult to resolve, as in commercially treated fine-grained . steels which contain less than 10-15 pct retained austenite, the latter may be completely obliterated by the dark etching martensite or it may appear disproportionately low as the interfaces between the two constituents become difficult to distinguish. Another disadvantage of the metallographic method is the need for "darkening" the martensite and hence the determination cannot be applied to as-hardened steels. The required tempering may spoil the structure for other tests or may even remove a small part of the austenite which is being sought. X ray methods hold more promise for covering the range under 15 pct retained austenite. Although austenite and martensite in the hardened steel may be chemically identical, their crystal structures and lattice parameters differ, and the intensity of an austenite diffraction line is some continuous function of the percentage of re-

Jan 1, 1949

By Chester A. Fulton

APATITE, the most abundant crystalline phosphate mineral, is found in igneous rocks and probably is the primary origin of all other phosphates, whether mineral or organic. Its chemical formula may be expressed as Ca5(Cl,F) (PO4) 3. The chlorine may be replaced almost entirely by the fluorine. It is found in large or small hexagonal prisms, usually of a vitreous luster and a green or red color, but also violet, white, or yellow. It is found largely as an accessory mineral in granitoid rocks. Its hardness is 4.5 to 5 and its specific gravity is about 3.2. There are many other phosphate minerals-for instance, amblygonite, autonite, collophane, lazulite, monazite, pyromorphite, torbenite, triphylite, turquoise, vivanite, wavellite-with base elements of calcium, magnesium, iron, aluminum, manganese, lead, cerium, lanthanum, lithium, or several of these in combination and with various amounts of water of crystallization. However, these phosphate minerals have but little value save as specimens for mineral collections, the exception perhaps being turquoise. While large deposits of igneous apatite are mined today for the production of fertilizers and chemicals, more than 90 pct of the world phosphate production is derived from secondary apatites, called phosphorites. These calcium (and magnesium, aluminum, and iron) phosphates have been formed in the alteration of sediments by solutions containing phosphoric acid. Such solutions have come from the weathering or leaching of igneous rocks containing apatite, bone deposits of prehistoric animals and marine life, or guano deposits (excreta of birds). These phosphorites are mostly alterations of phosphatic limestones that took place slowly over many years. Whether it is apatite or phosphorite that is being produced, it is known in the trade as "phosphate rock." The sedimentary phosphate deposits are of marine origin. Some, as laid down, were rich in phosphate or have become so by subsequent subaqueous action and have not been further enriched since emergence from the sea. Some were originally phosphatic limestones or marls from which calcium carbonate was dissolved away by waters containing carbon dioxide, in which calcium carbonate is much more soluble than

Jan 1, 1949

By Peter I. Brooker

Elementary estimation methods in which blocks are assigned values according to a geometrical area of influence concept are investigated for a tabular deposit. This quantitative assessment of the estimation technique is made using Matheron's geostatistics which allows the variance of the error between actual block values and estimated values to be found once the semi-variogram is known. For the deposit in question it is shown that the elementary technique makes poor use of the available information. There is a 20% relative error associated with it, whereas by using the optimal technique of kriging this can be reduced to 9%. An infill drilling program, which might have been suggested on area of influence results, would reduce the estimation variance only marginally over that of the current campaign; the relative error being lowered to 6%. Thus the geostatistical analysis shows this would be an unnecessary expense. The accuracy of an earlier drilling stage is also studied and it is shown that with the information available at the earlier stage block values could have been known with a relative error of 13%. Drilling could have stopped then if this were reckoned a tolerable error level. These results are all obtained for blocks whose size is dictated by the mining engineer and is set at the current grid size. In the area of influence approach smaller blocks are considered as the grid becomes finer and a study of the accuracy of area of influence estimates and kriged estimates for differing block sizes is presented. Between drilling stages more information from which the semi- variogram is calculated becomes available. The sensitivity of the estimation to changes in the semi-variogram parameters between earlier and current drilling programs is investigated.

Jan 1, 1977

By M. Prats

The effect of a sand-filled vertical fracture of limited radial extent and finite capacity (fracture capacity is the product of the permeability and width of the fracture) on the flow behavior of a cylindrical reservoir producing an incompressible fluid through a centrally located well has been investigated mathematically. The shape of the lines of equal pressure near the fracture is essentially independent of the size of the reservoir, provided that the field radius is of the order of the fracture length or larger. For reasonable values of production rates and of fluid, reservoir and fracture properties, the total pressure drop between the end of the fracture and the well is gelrerally negligible compared with the pressure drop in the reservoir. With regard to production response, the effect of vertical fractures can be represented by the production response of an equivalent or effective well radius. For a high-capacity fracture, the effective well radius is a quarter of the total fracture length, decreasing with the fracture capacity. When invasion effects are simulated by decreasing the width of the damaged zone with distance from the well, the effect of formation damage around a fracture on the production response is not so seriolls as indicated by the literature. This suggests that frac fluids with a conventional filter-loss response are better than high-spurt-loss frac fluids, provided the effective permeability of the damaged zone is the same. INTRODUCTION This paper considers the effect of the fracture capacity, as well as the formation damage which can result from fracture treatments, on the productive capacity of vertically fractured wells. Other publications, notably those of van Poollen,l,2 consider these same effects. In addition to providing more general results for vertical fractures than are available from the liter- ature, the present paper gives the equivalent well radius of fractures having different lengths and capacities and, also, includes pressure distributions in and around the fractures. The effect of a damaged zone around a fracture on the production response was not found to be so great as that reported by van Poollen. 2 This difference probably stems from the fact that we consider a damaged zone which is widest (but is still small) near the well and thins out toward the extremities of the fracture, whereas van Poollen considers a damaged zone having a uniform width for the entire fracture length. Simple, but adequate, equations which describe the effect of these variables on production response are presented (in Appendixes A and B). Thus, results can easily be extended to values of the variables not specifically considered here. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The liquid is incompressible. It is assumed that, after the well is fractured, the cylindrical outer "boundary" is at a uniform potential, provided that it is not too near the fracture. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir).3 Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir described above. If gravity effects are neglected, the flaw behavior in the reservoir will be independent of the vertical position ill the oil sand. This means that the flow behavior in the fractured reservoir can be described by the two-dimensional flow behavior shown in the horizontal cross section of the reservoir, Fig. 2. PARAMETERS The effect of a fracture on the pressure distribution in the fracture itself and in an otherwise undamaged (no skin) reservoir indicates that the pressure distribution is a function of three parameters.

By Roscoe C. Clark

In a previous technical note' by Walter Rose, evidence is offered in support of the contention that "the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely." It is not the purpose of this note to present further discussion of this possibility but rather to point out that the argument presented there does not appear to be generally valid. In the cited note' reference is made to the experiments of Welge2 wherein it was shown that when water was displaced by oil from a core the pressure in the water phase was less than in the oil phase but that when this oil was then produced by water drive the pressure in the water phase was greater than in the oil phase. Rose has concluded from these observations that conditions of static equilibrium did not obtain since the fluid saturations were such that phase discontinuities seemed unlikely. The argument from which this conclusion was drawn is based on the contention that "the pressure is always greatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase." This premise appears to have been reached from a consideration of capillary phenomena in cylindrical tubes, although it may a1so hold for other types of pore geometry, hut as will be shown below it does not hold for all pore shapes and hence is not generally applicable. Since the pore structure of porous media such as reservoir rocks i- in general so complex as to defy exact description. it is undoubtedly of great value to establish a model in terms of pore shapes of known geometry, provided of course that the limitations of the model are recognized. That the limitations of the capillary. or cylindrical, tube model have not always been fully recognized will be evident from the following discussion of a pore of different shape hut one which may a. logically he considered a.; the capillary tube. The pore space to be considered is that shown in Fig. 1, which may be thought of as the "hole in a doughnut."* Consider the interface, A-B-A', between two immiscible fluids, P, and P2, which interface meets the solid alone a line, A-C.A'-C'. The interface A-B-A' is the surface of a spherical segmen† while the line of mutual contact be-

Jan 1, 1950

By Leonard C. Grimshaw

Diffusion of carbon from gases into iron has been the object of much research, because of its long recognized importance in carburizing processes, but the direct diffusion of carbon from steel into iron has received relatively little attention. Because of the increasing use of clad metals in industry, direct diffusion from steel into iron is becoming of practical importance. Therefore, the object of this investigation was to study the diffusion of carbon from several different kinds of steel directly into relatively pure iron, realizing that elements in the steels other than carbon might influence the rate of carbon diffusion. The previous work on diffusion of carbon into iron has been considerable, and includes many reports in foreign languages. This work has recently been well reviewed by Mehll and Krynitsky12 and the reader is referred to their excellent bibliographies. Methods of Study There are two main methods by which the direct diffusion of carbon from steel into iron may be studied. In one method, steel is first decar-burized in part, and diffusion of carbon then allowed to take place from the steel into the decarburized steel. This method is open to two serious objections: (1) the decarburized steel is not iron, but contains elements such as manganese, silicon, chromium or tungsten, which may be an essential part of the steel under study, and which may seriously influence the diffusion of carbon into the decarburized area; (2) there is from the start of diffusion an unknown carbon-concentration gradient between the steel and the decarburized area. Another method, which possesses neither of these disadvantages, is to study diffusion from steel into a thick plating of electrolytic iron. Herc the chief difficulty is to secure an electrolytic deposit of iron upon steel without introducing an oxide film at the interface that will interfere with diffusion. The author is able to deposit iron upon any kind of steel without introducing an oxide film at the interface, so that diffusion of elements from the steel into the iron is free to proceed unhindered.

Jan 1, 1938

By Leonard C. Grimshaw

Diffusion of carbon from gases into iron has been the object of much research, because of its long recognized importance in carburizing processes, but the direct diffusion of carbon from steel into iron has received relatively little attention. Because of the increasing use of clad metals in industry, direct diffusion from steel into iron is becoming of practical importance. Therefore, the object of this investigation was to study the diffusion of carbon from several different kinds of steel directly into relatively pure iron, realizing that elements in the steels other than carbon might influence the rate of carbon diffusion. The previous work on diffusion of carbon into iron has been considerable, and includes many reports in foreign languages. This work has recently been well reviewed by Mehll and Krynitsky12 and the reader is referred to their excellent bibliographies. Methods of Study There are two main methods by which the direct diffusion of carbon from steel into iron may be studied. In one method, steel is first decar-burized in part, and diffusion of carbon then allowed to take place from the steel into the decarburized steel. This method is open to two serious objections: (1) the decarburized steel is not iron, but contains elements such as manganese, silicon, chromium or tungsten, which may be an essential part of the steel under study, and which may seriously influence the diffusion of carbon into the decarburized area; (2) there is from the start of diffusion an unknown carbon-concentration gradient between the steel and the decarburized area. Another method, which possesses neither of these disadvantages, is to study diffusion from steel into a thick plating of electrolytic iron. Herc the chief difficulty is to secure an electrolytic deposit of iron upon steel without introducing an oxide film at the interface that will interfere with diffusion. The author is able to deposit iron upon any kind of steel without introducing an oxide film at the interface, so that diffusion of elements from the steel into the iron is free to proceed unhindered.

Jan 1, 1938