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By Henry Emmett Gross

Two types of decline curves are considered and their applications are discussed. The first is the well-known semilogarithmic decline curve having the rate of production plotted on the logarithmic scale and the time on the horizontal scale. The other curve is the percentage of oil in the fluid versus cumulative production, and it is plotted on Cartesian coordinate paper. These curves are illustrated by carefully and adequately labeled graphs. Where conditions permit application of both types of curves for rationally determining the reserves of a well, both should be applied and the most conservative reserve should be chosen. Formulas are given for determining the economic limits. For a semi-l~~arithmic~decline curve the formula is: A = B X C X D X E X F or B = A/C ? D X E X F A = total monthly operating cost (average of past year), B = economic limit in barrels of oil per day, C = days in an average month = 30.4, D = market price of crude per barrel, E = 1-royalty, F = 1-gross production tax, G = water production in barrels per day at the economic limit, H =per cent oil in fluid at economic limit. The economic limit for a per cent oil in the fluid curve is: H = B/B+G X 100 The semilogarithmic decline curve is treated first. Straight-line extrapolations on semilogarithmic paper follow the compound interest compound discount law, hence the ensuing formulas derived from this law may be used in computing reserves for such extrapolations: [1___1/(1+Y)]

Jan 1, 1939

By Aureal T. Cross

THIS paper is a review of the published literature on research in coal geology, principally exclusive of resource studies, which appeared or became available during 1950 and the latter part of 1949. This report is not to be construed as being complete. The papers referred to in the bibliography are those among many more, which were read either in full or in abstract. Undoubtedly other papers were published' which either escaped the author's notice or were not available to him. Those which were seen in abstract only (about one fourth of those listed) were not available in time for the inclusion of more than a notice. An outline of all papers listed in the bibliography has been arranged by subjects and reasonable subdivisions with some papers cited under more than one subject. Most papers are indexed according to the principal subject of discussion or research only as to an unusual or noteworthy section of the entire report. There will likely be some disagreement as to the quality or merit of some of the papers selected and the specialist may be supercritical of the outline or organization of papers in his field. It may be that attention has occasionally been drawn to papers reporting old information or conclusions of questionable value. Conferences and Meetings One of the best indications of the growing interest in coal geology problems in the United States is the increasing number of times this- field has been the focus of attention at conferences and meetings. Notable among these are the joint meeting of the Society of Economic Geologists and the Geological Society of America at El Paso, November 1949, at which the principal thesis was concerned with low rank carbonaceous fuel deposits, especially of western United States. Among the papers given which are already available were those presented by Barghoorn,16 Parry,180 Roe,153 and Parks.162 At the annual meeting of the Botanical Society of America in New York, December 1949, a joint meeting of the Paleobotanical and Microbiological Sections was held for which a symposium on Microbiology in Relation to the Geologic Accumulation of Organic Complexes was 'organized. Publication of the six papers presented by Ralph G. H. Siu, Elso S. Barghoorn, Irving Breger, Claude E. ZoBell, James M. Schopf, and A. C. Thayson is anticipated. At the regular meetings of the Paleobotanical Section at the same time, several other papers of interest reported on coal ball studies, partial coalification of petrified wood, and floras. In Chicago, April 1950, a symposium on Applied Paleobotany was held by the Society of Economic Paleontologists and Mineralogists in conjunction with the American Association of Petroleum Geologists. The five papers presented at this meeting dealt with the use of Paleozoic plant microfossils for stratigraphic work, J: M. Schopf, Devonian-Mississippian fossils of the black shales, Aureal T. Cross, Mesozoic plants of stratigraphic value, Th. Just, plant microfossils of the Tertiary, L. R. Wilson, and studies of the Brandon lignite, Elso S. Barghoorn. Early publication of these in the Journal of Paleontology is expected. The Nova Scotia Research Foundation and the Nova Scotia Dept. of Mines sponsored an excellent 3-day conference in June 1950, which, dealt with several aspects of coal geology. Papers on coal classification, P. A. Hacquenbard, structure and sedimentation problems in Nova Scotia, T. B. Haites, new techniques of thermal analysis, W. L. Whitehead, geochemical investigations of Nova Scotia coals, Irving Breger, the role of fossil plant spores in coal correlation and the stratigraphy of the coal-bearing strata of the Appalachian Region, Aureal T. Cross, were given. Some discussions of these papers by those in attendance were recorded, and the entire proceedings is being prepared for publication. In September 1950, an unusual 3-day field conference was held by the Ohio and West Virginia Geological Surveys under the sponsorship of the Coal Geology Committee. This study of the stratigraphy sedimentation, and nomenclature of the Upper Pennsylvanian and Permian coal-bearing strata of southeastern Ohio, southwestern Pennsylvania, and northern West Virginia .was augmented by two discussions on associated rocks (clays and shales) and stratigraphic nomenclature at Wheeling, and Morgantown, West Va. An extensive guidebook was prepared, and transcriptions of the Morgantown meeting were made. As a follow-up of the September field conference, a round-table discussion 'was held on this general topic at a special open meeting of the Coal Research Committee in conjunction with the November meeting of the Geological Society in Washington. Short prepared statements to invite discussion were given on each of several topics by L. M. Cline, Carl O.

Jan 1, 1952

By E. T. Stephenson

Wert and Marx1 pointed out that a straight-line relationship exists between the activation energy of a relaxation process and the temperature at which the maximum relaxation occurs. The data available at the time indicated that this relationship held for a number of Snoek peaks, several grain boundary peaks, and pair relaxation in a brass. Theoretical justification for the observed relationship was found in the following equation, which Wert and Marx derived from the theory of interstitial atomic diffusion coefficients:' where AH is activation energy, R is the gas constant, T is the internal friction peak temperature, v is the interstitial atomic frequency, f is the frequency of the applied stress, S is entropy of activation. More accurate internal-friction data on interstitial diffusion in bcc metals have become available since Wert and Marx's paper. Table I gives activation energies calculated by several authors from a combination of elastic aftereffect data and the peak temperatures at several frequencies of measurement. (In the case of Fe-C and Fe-N, the referenced authors5'7'8'10 also used high-temperature diffusion data.) However, diffusion experiments at 150°C and above1'-13—rather than anelastic techniques—were used to determine the activation energy of hydrogen diffusion in Fe-H. In order to plot this recent data as a AH vs T graph we calculated the peak temperatures of the systems listed in Table I (with the exception of Fe-C, Fe-N, and Fe-H) by using published values3'' of AH and Do. These calculated peak temperatures varied by only a few degrees from experimentally determined peak temperatures. The calculated values were felt to represent the better average. A number of investigators have found the peak temperatures in Fe-C and Fe-N to be 38 to 40°C and 20° to 24°C, respectively. The values of 39" and 22°C (312° and 295°K in Table I) were determined by carefully executed experiments.6'8 The hydrogen peak temperature has been measured at 1 cps,12 20 cps,14 and 35,000 cps.15 All hydrogen peak temperatures were adjusted to 1 cps for Table I using AH = 3000 cal per mole. As Fig. 1 shows, the data of Table I fit a straight line at least as well as the earlier data used by Wert and Marx. Linear-regression analysis was applied to the data in Table I. The Fe-H data was omitted because the activation energy has not been experimentally determined in the temperature range of the peak. The analysis yields the equation: with a standard error of 860 cal per mole. The agreement of the data in Table I with the Wert-Marx equation is excellent. Strict application of Eq. [I] forces the linear regression analysis through the origin. In this case, the analysis gives a slope of 62.1 cal per mole per deg, and a standard error of *890 cal per mole. With this value, it follows from internal-friction theory that Hence, Do varies by only 30 pct among these bcc-interstitial systems. Thus, a concept suggested originally by Wert and Marx1 is confirmed by recently published data. The

Jan 1, 1965

By Aureal T. Cross

THIS paper is a review of the published literature on research in coal geology, principally exclusive of resource studies, which appeared or became available during 1950 and the latter part of 1949. This report is not to be construed as being complete. The papers referred to in the bibliography are those among many more, which were read either in full or in abstract. Undoubtedly other papers were published which either escaped the author's notice or were not available to him. Those which were seen in abstract only (about one fourth of those listed) were not available in time for the inclusion of more than a notice. An outline of all papers listed in the bibliography has been arranged by subjects and reasonable subdivisions with some papers cited under more than one subject. Most papers are indexed according to the principal subject of discussion or research only as to an unusual or noteworthy section of the entire report. There will likely be some disagreement as to the quality or merit of some of the papers selected and the specialist may be supercritical of the outline or organization of papers in his field. It may be that attention has occasionally been drawn to papers reporting old information or conclusions of questionable value. Conferences and Meetings One of the best indications of the growing interest in coal geology problems in the United States is the increasing number of times this field has been the focus of attention at conferences and meetings. Notable among these are the joint meeting of the Society of Economic Geologists and the Geological Society of America at El Paso, November 1949, at which the principal thesis was concerned with low rank carbonaceous fuel deposits, especially of western United States. Among the papers given which are already available were those presented by Barghoorn,'" Parry? Roe? and Parks."' At the annual meeting of the Botanical Society of America in New York, December 1949, a joint meeting of the Paleobotanical and Microbiological Sections was held for which a symposium on Microbiology in Relation to the Geologic Accumulation of Organic Complexes was organized. Publication of the six papers presented by Ralph G. H. Siu, Elso S. Barghoorn, Irving Breger, Claude E. ZoBell, James M. Schopf, and A. C. Thayson is anticipated. At the regular meetings of the Paleobotanical Section at the same time, several other papers of interest reported on coal ball studies, partial coalification of petrified wood, and floras. In Chicago, April 1950, a symposium on Applied Paleobotany was held by the Society of Economic Paleontologists and Mineralogists in conjunction with the American Association of Petroleum Geologists. The five papers presented at this meeting dealt with the use of Paleozoic plant microfossils for stratigraphic work, J. M. Schopf, Devonian-Missis-sippian fossils of the black shales, Aureal T. Cross, Mesozoic plants of stratigraphic value, Th. Just, plant microfossils of the Tertiary, L. R. Wilson, and studies of the Brandon lignite, Elso S. Barghoorn. Early publication of these in the Journal of Paleontology is expected. The Nova Scotia Research Foundation and the Nova Scotia Dept. of Mines sponsored an excellent 3-day conference in June 1950, which dealt with several aspects of coal geology. Papers on coal classification, P. A. Hacquenbard, structure and sedimentation problems in Nova Scotia, T. B. Haites, new techniques of thermal analysis, W. L. White-head, geochemical investigations of Nova Scotia coals, Irving Breger, the role of fossil plant spores in coal correlation and the stratigraphy of the coal-bearing strata of the Appalachian Region, Aureal T. Cross, were given. Some discussions of these papers by those in attendance were recorded, and the entire proceedings is being prepared for publication. In September 1950, an unusual 3-day field conference was held by the Ohio and West Virginia Geological Surveys under the sponsorship of the Coal Geology Committee. This study of the stratigraphy, sedimentation, and nomenclature of the Upper Pennsylvanian and Permian coal-bearing strata of southeastern Ohio, southwestern Pennsylvania, and northern West Virginia was augmented by two discussions on associated rocks (clays and shales) and stratigraphic nomenclature at Wheeling and Morgantown, West Va. An extensive guidebook was prepared, and transcriptions of the Morgantown meeting were made. As a follow-up of the September field conference, a round-table discussion was held on this general topic at a special open meeting of the Coal Research Committee in conjunction with the November meeting of the Geological Society in Washington. Short prepared statements to invite discussion were given on each of several topics by L. M. Cline, Carl 0.

Jan 1, 1953

By Aureal T. Cross

THIS paper is a review of the published literature on research in coal geology, principally exclusive of resource studies, which appeared or became available during 1950 and the latter part of 1949. This report is not to be construed as being complete. The papers referred to in the bibliography are those among many more, which were read either in full or in abstract. Undoubtedly other papers were published which either escaped the author's notice or were not available to him. Those which were seen in abstract only (about one fourth of those listed) were not available in time for the inclusion of more than a notice. An outline of all papers listed in the bibliography has been arranged by subjects and reasonable subdivisions with some papers cited under more than one subject. Most papers are indexed according to the principal subject of discussion or research only as to an unusual or noteworthy section of the entire report. There will likely be some disagreement as to the quality or merit of some of the papers selected and the specialist may be supercritical of the outline or organization of papers in his field. It may be that attention has occasionally been drawn to papers reporting old information or conclusions of questionable value. Conferences and Meetings One of the best indications of the growing interest in coal geology problems in the United States is the increasing number of times this field has been the focus of attention at conferences and meetings. Notable among these are the joint meeting of the Society of Economic Geologists and the Geological Society of America at El Paso, November 1949, at which the principal thesis was concerned with low rank carbonaceous fuel deposits, especially of western United States. Among the papers given which are already available were those presented by Barghoorn,'" Parry? Roe? and Parks."' At the annual meeting of the Botanical Society of America in New York, December 1949, a joint meeting of the Paleobotanical and Microbiological Sections was held for which a symposium on Microbiology in Relation to the Geologic Accumulation of Organic Complexes was organized. Publication of the six papers presented by Ralph G. H. Siu, Elso S. Barghoorn, Irving Breger, Claude E. ZoBell, James M. Schopf, and A. C. Thayson is anticipated. At the regular meetings of the Paleobotanical Section at the same time, several other papers of interest reported on coal ball studies, partial coalification of petrified wood, and floras. In Chicago, April 1950, a symposium on Applied Paleobotany was held by the Society of Economic Paleontologists and Mineralogists in conjunction with the American Association of Petroleum Geologists. The five papers presented at this meeting dealt with the use of Paleozoic plant microfossils for stratigraphic work, J. M. Schopf, Devonian-Missis-sippian fossils of the black shales, Aureal T. Cross, Mesozoic plants of stratigraphic value, Th. Just, plant microfossils of the Tertiary, L. R. Wilson, and studies of the Brandon lignite, Elso S. Barghoorn. Early publication of these in the Journal of Paleontology is expected. The Nova Scotia Research Foundation and the Nova Scotia Dept. of Mines sponsored an excellent 3-day conference in June 1950, which dealt with several aspects of coal geology. Papers on coal classification, P. A. Hacquenbard, structure and sedimentation problems in Nova Scotia, T. B. Haites, new techniques of thermal analysis, W. L. White-head, geochemical investigations of Nova Scotia coals, Irving Breger, the role of fossil plant spores in coal correlation and the stratigraphy of the coal-bearing strata of the Appalachian Region, Aureal T. Cross, were given. Some discussions of these papers by those in attendance were recorded, and the entire proceedings is being prepared for publication. In September 1950, an unusual 3-day field conference was held by the Ohio and West Virginia Geological Surveys under the sponsorship of the Coal Geology Committee. This study of the stratigraphy, sedimentation, and nomenclature of the Upper Pennsylvanian and Permian coal-bearing strata of southeastern Ohio, southwestern Pennsylvania, and northern West Virginia was augmented by two discussions on associated rocks (clays and shales) and stratigraphic nomenclature at Wheeling and Morgantown, West Va. An extensive guidebook was prepared, and transcriptions of the Morgantown meeting were made. As a follow-up of the September field conference, a round-table discussion was held on this general topic at a special open meeting of the Coal Research Committee in conjunction with the November meeting of the Geological Society in Washington. Short prepared statements to invite discussion were given on each of several topics by L. M. Cline, Carl 0.

Jan 1, 1953

By J. D. MacKenzie

THE world production of copper for the first eight months of 1927 shows an increase of 3 per cent over the same period in 1926. Since February of this year, however, production has been considerably curtailed. The United States reduction in the last four months has been offset by the increased South Ameri-can and Belgian Congo production. The United States is now producing 58 per cent of the world production, Chile and Peru 17.3 per cent, Belgian Congo 5 per cent. In 1926 the United States produced 54 per cent, Chile and Peru 16.3 per cent, Belgian Congo 6.3 per cent. Production, Tons 1917-largest war year 1,580,000 1925 1,581,000 1926-increase 3 per cent 1,628,000 1927-increase 3 per cent 1,670,000 Copper Producing Countries, 8 mo., 1927: Tons Per Cent United States 644,000 58.0 Chile and Peru 192,000 17.3 Europe 90,000 8.1 Belgian Congo 56,000 5.0 Japan 46,000 4.1 Mexico 30,000 2.7 Canada 23,000 2.1 Figures are not available for Spain and Portugal, which would probably precede Mexico.

Jan 12, 1927

By W. E. Bergman, P. G. Carpenter, H. B. Fisher

The conditions under which barium carbonate can be used to remove sulfates from drilling muds are limited The amount of sulfate remaining in solution in the system after treatment with barium carbonate is shown to be a function of the concentration of the carbonate and barium ions and the concentration of other electrolytes. Barium hydroxide may advantageously replace barium carbonate when the contamination is not entirely due to anhydrite (calcium in the system is then stoichiometrically less than sulfate) or when the carbonate concentration is high. The effect of substances such as quebracho, phosphates, and chromates, which form complexes or precipitates with barium, is discussed. INTRODUCTION As the complexity of the operations in drilling for oil has increased, more attention has of necessity been directed to the problems pertaining to the maintenance of good drilling mud properties. As a result, chemical treatment of muds has become an important factor in recent years. Some of these treatments have been designed to eliminate the deleterious effects of contaminants in aqueous mud systems by precipitation or other means. The most common of substances encountered during drilling include sodium chloride, cement, and calcium sulfate while various other contaminants: usually in small amounts, may be introduced from the water, clays, and other materials used in preparation of the mud. In certain cases, for example where continued salt-water flow is encountered or massive anhydrite is drilled, special muds may be used so that the physical properties of the mud will remain satisfactory for drilling. In other cases, it is desirable to remove the contaminants so that soluble electrolytes in the system are maintained at low values. For sulfate contamination, the conlmon practice in the field is to add barium carbonate to precipitate the sulfate as barium sulfate Ordinarily such a procedure gives satisfactory results. There have been important instances, however, where addition of barium carbonate was not effective in removal of soluble sulfates from drilling muds. and it is to these cases that the present paper is directed. While it is generally known that barium carbonate is not always effective in removing soluble sulfates from drilling muds, certain inconsistencies appear in the literature as to the limitations of its use, and little explanation for the limitations are given. Varnell and Kimbrel state that "the treatment (with barium carbonate for removal of sulfate) is simple and consists in maintaining a pH of 9 with caustic soda and quebracho." They caution that concentrations of quebracho greater than 1 lb./bbl. may inhibit the reaction. In another publication', a pH of 10.5 is considered "the maximum desirable," and the indication is that as much as 2.5 lb. quebracho per barrel may be present in the particular mud under discussion. Lancaster and Mitchell5 state that appreciable amounts of phosphates in the mud will inhibit the reaction with barium carbonate and that the phosphate treatment should be discontinued at least 24 hours before addition of the carbonate. Experimental work was initiated to ascertain the factors involved in using barium carbonate for the removal of sulfate contamination in drilling muds. While the experimental data herein reported are limited, they focus attention on the pertinent factors which must be considered for successful treatment. These factors are discussed from a practical and a theoretical view, the latter being supported by equilibrium data found in the literature. Further, it will be appreciated that the factors involved in this specific study will be closely analogous to those in certain of the other chemical treatments which involve a precipitation of the soluble contaminant. A thorough comprehension of these factors should result in a more fruitful application of this type of chemical reaction to the treatment of drilling muds. EXPERIMENTAL A. Reagents Two muds were used during this investigation. For one series of tests, bentonite suspensions were prepared by dilution of a stock suspension containing 8 per cent by weight of bentonite (Aquagel). For another series, a 6.4 per cent ben-tonitic mud weighted to 9.7 lb./gal. with barium sulfate (Mag-cobar) was used. Distilled water was used in all preparations. The quebracho (72% tannin extract) was obtained from the Thompson-Hayward Co. of Tulsa and contained 11.4 per cent moisture (105 C.). All other materials were reagent grade, and concentrations were corrected for water of crystallization, if any. All concentrations are expressed in pounds per barrel (42 gallons). B. Technique The systems — either mud or water — were contaminated with either sodium or calcium sulfate after treatment with the desired amounts of sodium hydroxide and quebracbo. For treatments with barium carbonate an approximately 3-fold excess (5 lb./bbl.) was used over that computed to be required to precipitate all the sulfate as barium sulfate. Barium hydroxide was used in concentrations of 2 lb./bbl. — about

Jan 1, 1949

By P. G. Carpenter, H. B. Fisher, W. E. Bergman

The conditions under which barium carbonate can be used to remove sulfates from drilling muds are limited The amount of sulfate remaining in solution in the system after treatment with barium carbonate is shown to be a function of the concentration of the carbonate and barium ions and the concentration of other electrolytes. Barium hydroxide may advantageously replace barium carbonate when the contamination is not entirely due to anhydrite (calcium in the system is then stoichiometrically less than sulfate) or when the carbonate concentration is high. The effect of substances such as quebracho, phosphates, and chromates, which form complexes or precipitates with barium, is discussed. INTRODUCTION As the complexity of the operations in drilling for oil has increased, more attention has of necessity been directed to the problems pertaining to the maintenance of good drilling mud properties. As a result, chemical treatment of muds has become an important factor in recent years. Some of these treatments have been designed to eliminate the deleterious effects of contaminants in aqueous mud systems by precipitation or other means. The most common of substances encountered during drilling include sodium chloride, cement, and calcium sulfate while various other contaminants: usually in small amounts, may be introduced from the water, clays, and other materials used in preparation of the mud. In certain cases, for example where continued salt-water flow is encountered or massive anhydrite is drilled, special muds may be used so that the physical properties of the mud will remain satisfactory for drilling. In other cases, it is desirable to remove the contaminants so that soluble electrolytes in the system are maintained at low values. For sulfate contamination, the conlmon practice in the field is to add barium carbonate to precipitate the sulfate as barium sulfate Ordinarily such a procedure gives satisfactory results. There have been important instances, however, where addition of barium carbonate was not effective in removal of soluble sulfates from drilling muds. and it is to these cases that the present paper is directed. While it is generally known that barium carbonate is not always effective in removing soluble sulfates from drilling muds, certain inconsistencies appear in the literature as to the limitations of its use, and little explanation for the limitations are given. Varnell and Kimbrel state that "the treatment (with barium carbonate for removal of sulfate) is simple and consists in maintaining a pH of 9 with caustic soda and quebracho." They caution that concentrations of quebracho greater than 1 lb./bbl. may inhibit the reaction. In another publication', a pH of 10.5 is considered "the maximum desirable," and the indication is that as much as 2.5 lb. quebracho per barrel may be present in the particular mud under discussion. Lancaster and Mitchell5 state that appreciable amounts of phosphates in the mud will inhibit the reaction with barium carbonate and that the phosphate treatment should be discontinued at least 24 hours before addition of the carbonate. Experimental work was initiated to ascertain the factors involved in using barium carbonate for the removal of sulfate contamination in drilling muds. While the experimental data herein reported are limited, they focus attention on the pertinent factors which must be considered for successful treatment. These factors are discussed from a practical and a theoretical view, the latter being supported by equilibrium data found in the literature. Further, it will be appreciated that the factors involved in this specific study will be closely analogous to those in certain of the other chemical treatments which involve a precipitation of the soluble contaminant. A thorough comprehension of these factors should result in a more fruitful application of this type of chemical reaction to the treatment of drilling muds. EXPERIMENTAL A. Reagents Two muds were used during this investigation. For one series of tests, bentonite suspensions were prepared by dilution of a stock suspension containing 8 per cent by weight of bentonite (Aquagel). For another series, a 6.4 per cent ben-tonitic mud weighted to 9.7 lb./gal. with barium sulfate (Mag-cobar) was used. Distilled water was used in all preparations. The quebracho (72% tannin extract) was obtained from the Thompson-Hayward Co. of Tulsa and contained 11.4 per cent moisture (105 C.). All other materials were reagent grade, and concentrations were corrected for water of crystallization, if any. All concentrations are expressed in pounds per barrel (42 gallons). B. Technique The systems — either mud or water — were contaminated with either sodium or calcium sulfate after treatment with the desired amounts of sodium hydroxide and quebracbo. For treatments with barium carbonate an approximately 3-fold excess (5 lb./bbl.) was used over that computed to be required to precipitate all the sulfate as barium sulfate. Barium hydroxide was used in concentrations of 2 lb./bbl. — about

Jan 1, 1949

By L. W. Davies

A problem often encountered is the provision of materials which have impurity contents below a certain specified level. This problem is in some cases solved by making use of the segregation of the impurity with respect to the liquid and solid states of the material: an ingot of the material is subjected to directional solidification and the ends of the ingot. which are richer in solutes which respectively raise and lower the melting point of the solvent, are removed. An important extension of this process is the zone-refining process invented by pfann,' in which molten zones are passed successively along the length of an ingot and displace solutes towards the ends. Pfann's process is particularly appropriate in cases for which the segregation coefficient k does not differ greatly from unity, or when the impurity content must be kept extremely low (-=,6 atom fraction); it is widely used, particularly in the purification of materials for use in semiconductor electronic devices. It is the purpose of this paper to investigate theoretically the efficiency of the above refining processes; that is! we determine the most economic method of attaining a given yield of solvent of specified purity, taking into account the variables of the process. One variable of interest is the effective value of the segregation coefficient. which depends on the rate of movement of the liquid-solid interface and on the degree of stirring in the liquid; in addition to this, in the zone-refining process we are also interested in the choice of zone length for most efficient operation. A mathematical determination is made here of the lengths of successive molten zones which give, for an initially uniform distribution, the most efficient removal of a solute of arbitrary distribution coefficient. In order to be able to give a quantitative treatment of efficiency, we first define figures of merit applicable to a given distribution of solute. FIGURE OF MERIT Let an ingot of length L contain a distribution y(x) of solute: we confine our discussion to mono-tonic distributions, in order to avoid inconsistencies in the subsequent analysis. The first moments of the distribution about the origin and x = L are respectively L F = hy{x)dx [I] G = f(L -x)y(x)dx = YoL2-F, [21 where yoL is the total amount of solute present. We shall see that the quantities F and G are useful figures of merit for a discussion of the efficiency of zone-refining processes. In the first place, it is

Jan 1, 1960

By L. W. Davies

A problem often encountered is the provision of materials which have impurity contents below a certain specified level. This problem is in some cases solved by making use of the segregation of the impurity with respect to the liquid and solid states of the material: an ingot of the material is subjected to directional solidification and the ends of the ingot. which are richer in solutes which respectively raise and lower the melting point of the solvent, are removed. An important extension of this process is the zone-refining process invented by Pfann,' in which molten zones are passed successively along the length of an ingot and displace solutes towards the ends. Pfann's process is particularly appropriate in cases for which the segregation coefficient k does not differ greatly from unity, or when the impurity content must be kept extremely low (=10-6 atom fraction); it is widely used, particularly in the purification of materials for use in semiconductor electronic devices. It is the purpose of this paper to investigate theoretically the efficiency of the above refining processes; that is! we determine the most economic method of attaining a given yield of solvent of specified purity, taking into account the variables of the process. One variable of interest is the effective value of the segregation coefficient. which depends on the rate of movement of the liquid-solid interface and on the degree of stirring in the liquid; in addition to this, in the zone-refining process we are also interested in the choice of zone length for most efficient operation. A mathematical determination is made here of the lengths of successive molten zones which give, for an initially uniform distribution, the most efficient removal of a solute of arbitrary distribution coefficient. In order to be able to give a quantitative treatment of efficiency, we first define figures of merit applicable to a given distribution of solute. FIGURE OF MERIT Let an ingot of length L contain a distribution y(x) of solute: we confine our discussion to mono-tonic distributions, in order to avoid inconsistencies in the subsequent analysis. The first moments of the distribution about the origin and x = L are respectively L F = hy{x)dx [I] G = f(L -x)y(x)dx = YoL2-F, [21 where yoL is the total amount of solute present. We shall see that the quantities F and G are useful figures of merit for a discussion of the efficiency of zone-refining processes. In the first place, it is

Jan 1, 1960

By A. F. Crowley, D. W. G. White

AS part of a continuing program of liquid metals research, the densities of liquid lead, tin, zinc, cadmium, and indium have been measured by a pycnometric method. The pycnometers are made of high-density graphite to the design illustrated in Fig. l(a). In pursuing this research program, emphasis has been placed on detailed experimental care. As a result, claims are made for densities accurate to within ± 0.05 pct over temperature ranges varying from about 100° to 200°C above the melting point. A paper reporting the densities of tin, lead, and Pn-Sn alloys has recently been published,' while papers dealing with

Jan 1, 1969

By C. P. Kempter

AS part of a continuing program of liquid metals research, the densities of liquid lead, tin, zinc, cadmium, and indium have been measured by a pycnometric method. The pycnometers are made of high-density graphite to the design illustrated in Fig. l(a). In pursuing this research program, emphasis has been placed on detailed experimental care. As a result, claims are made for densities accurate to within ± 0.05 pct over temperature ranges varying from about 100± to 200°C above the melting point. A paper reporting the densities of tin, lead, and Pn-Sn alloys has recently been published,' while papers dealing with

Jan 1, 1969

By Frederick N. Rhines, Robert F. Mehl

It has been shown elsewhere1 that the data on the rates of diffusion in solid metals are fragmentary and in many cases unacceptable. As a result, relatively little is known concerning the factors determining rates of diffusion and the variations in these rates with temperature. The first form of Fick's law (equation 1 below), in which the diffusion coefficient D is assumed invariant with composition, has been recognized for many years as only an approximation. The differential equation representing the second form of Fick's law (equation 4 below) has only recently been integrated by Matano,2 and unfortunately only in cases where a full diffusion-penetration curve (concentration-distance curve) has been obtained can the Matano solution be applied. The proper analysis of diffusion data is thus confined to the data of Grube and Jedele and of Jedele. 8 These data are essentially for one temperature alone and do not furnish any information on the variation of the activation heat of diffusion, Q, with concentration: no information exists on the variation of Q with concentration within a single solid solution field. 11 Much of the argument concerning the properties of metals that determine D and Q has been drawn from data in which variations of the quantities with concentration are unknown, for these data have been taken from experiments that could not furnish this information. Speculation concerning the properties of metals that may be effective in determining D and Q on the basis of data in which the chosen D and Q values are averages over wide concentration ranges of values at particular concentrations, ranges often of 100 per cent, is likely not to be fruitful.

Jan 1, 1938

By Frederick N. Rhines, Robert F. Mehl

It has been shown elsewhere1 that the data on the rates of diffusion in solid metals are fragmentary and in many cases unacceptable. As a result, relatively little is known concerning the factors determining rates of diffusion and the variations in these rates with temperature. The first form of Fick's law (equation 1 below), in which the diffusion coefficient D is assumed invariant with composition, has been recognized for many years as only an approximation. The differential equation representing the second form of Fick's law (equation 4 below) has only recently been integrated by Matano,2 and unfortunately only in cases where a full diffusion-penetration curve (concentration-distance curve) has been obtained can the Matano solution be applied. The proper analysis of diffusion data is thus confined to the data of Grube and Jedele and of Jedele. 8 These data are essentially for one temperature alone and do not furnish any information on the variation of the activation heat of diffusion, Q, with concentration: no information exists on the variation of Q with concentration within a single solid solution field. 11 Much of the argument concerning the properties of metals that determine D and Q has been drawn from data in which variations of the quantities with concentration are unknown, for these data have been taken from experiments that could not furnish this information. Speculation concerning the properties of metals that may be effective in determining D and Q on the basis of data in which the chosen D and Q values are averages over wide concentration ranges of values at particular concentrations, ranges often of 100 per cent, is likely not to be fruitful.

Jan 1, 1938

By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy's law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By Walter Rose

Theoretical expressions are presented to describe wetting and non-wetting phase relative premeability relations. These expressions have then been compared with existing published data, the conformance noted being sufficiently good to satisfy the requirements of some engineering use. As a consequence, it may be supposed that relative permeability characteristics of porous media now can be inferred from basic core analysis data, in a manner more convenient (although less direct) than presently available methods of experimental evaluation. INTRODUCTION This paper presents a new approach to the problem of relative permeability evaluation. A classification of published discussions of relative permeability concepts which have appeared in the petroleum literature will show that previously emphasis has been placed on methods of experimental measurement, on the interpretation of the data so obtained with respect to the variable properties of the system, and on theoretical and practical considerations which relate relative permeability to gross fluid behavior in petroleum reservoirs. Essentially, no detailed examination has appeared which treats the fundamental factors controlling the quantitative features of the relative permeability relation*, although cer- tain references can be Cited where a qualitative awareness of their existence and nature is indicated. This condition is explainable in terms of the recognized complexity of the problem, and in order to provide some basis for theoretical development, the general emphasis has been placed in the past on experimental procedures of evaluation, the validity of which, in principle, could be confirmed by the analysis of well and reservoir performance. However, because of the experimental difficulties which have been encountered (notably, difficulties due to the so-called "end effects"), and because of the general unreliability of field performance tests required to study the applicability of the data, relative permeability phenomena continue to be incompletely understood and described.? In this paper is examined the possibility of predicting relative permeabilities entirely from fundamental considerations. In addition, attention is called to certain important factors, previously unemphasized in the published literature, which now can serve as a basis for the eventual experimental confirmation of this and similar theoretical approaches, as well as the experimental solution of the problem in general. Therefore, the analysis presented herein has the dual purpose both of orienting future experimental activity and also of providing an immediate solution for the relative permeability porblem, sufficiently adequate for some engineering use. It will be seen that the conclusions reached are supported by theoretical and intuitive considerations, and they are not contradicted insofar as gross features are concerned by existing concepts and interpretations of published experimental data, except as specifically noted. Darcy's law, expressed simply as: k dp q = k/u dp/dx .......(1) where q is linear rate of flow (assumed horizontal), k is the † The poor comparison usually obtained between laboratory and field gas-oil ratios (c.f.. Fig. 4 of paper by L. E. Elkins) is illustrative of conditions which dimcourage unqualified acceptance of the results of previous studies except as presently useful approximations. In this connection, Evinger and Muskat have discussed in detail the discrepancy observed between field well productivity values and values obtained from the analysis of laboratory flow data.

Jan 1, 1949

By W. E. Forsythe

WHEN measuring ordinary temperatures, the instrument is generally placed in very close contact with the body the temperature of which is desired. However, if the temperature of the source is continually raised, a point is soon reached where no known substance will, in general, remain constant in any of its temperature-measuring properties if placed in direct contact with the source. Also, it is occasionally necessary to measure the temperature of a source that 'is so small or so situated that it would be very hard to bring the measuring instrument into direct contact with the source. When these conditions exist, advantage is taken of the well-known fact that all bodies, when at sufficiently high temperatures, send out radiation in amounts readily measurable. This radiation has been found to be related to the temperature. The temperatures of very hot bodies have probably always been judged by the color, or the brightness, of the light given off. With practice, one can estimate probably within 50° to 100° C. of the correct value. However, if judgment is left to the eye alone, very much larger errors are sometimes made, due to

Jan 9, 1919

By Emile Gyss

THE speed of drilling rock has become an impor-tant factor in mining operations, while the place-ment of holes, kind, and quantity of explosive used. are equally important. These are a function of the rock hardness and toughness. Both of these fac-tors must be considered in compiling a table that will enable a mine operator or engineer to estimate drilling speeds in a given rock, knowing its hardness, and from its toughness, the dynamite required. The hardness of a homogeneous rock may be defined as its resistance to a penetrating medium, such as a drill-steel bit, and toughness, its resistance to with-stand rupture by the tearing apart of its minerals or parts of the same mineral. Rock hardness, as it has here been defined, is a function of the hardness of the component grains composing it, as well as grain size, shape, arrangement, and binding minerals. Rock tough-ness depends on substantially the same factors, but is measured by a totally different method. The units in which rock hardness is usually ex-pressed are either relative values or alphabetical desig-nations which carry no definite quantitative meaning. R. M. Raymond has suggested the measurement of com-posite rock hardness, based on mineral hardness as ob-tained by the Moh scale. This is done by multiplying the percentage of each mineral in a rock by the Moh mineral hardness and dividing by 100. These values convey a clearer conception in the minds of men in-terested in rock work -and are the basis of the units used in Tables 1 and 2. The hardness of rocks as it has been variously de-fined may be determined by different methods. The first method is one in which the proportionate average of the hardness of minerals making up a rock is the basis for classification. The other factors of grain size, shape, arrangement, and binding power are not considered.

Jan 6, 1927

By J. M. GLEDHILL

IT would doubtless have been felt by many but a few years back that there was little left to be said on the subject of crucible tool-steel, and that something akin to finality had been arrived at in its manufacture and general treatment. Probably such feeling was justifiable when it is remembered that the making of steel in crucibles is by far the oldest method known, dating back from time immemorial, it being indeed impossible to accurately trace its origin and earliest development; but it seems certain that carbon-steel was made and used thousands of years ago for cutting-tools. Proof of this may be seen by the marvelous carvings and workings on the intensely hard stone-work of the ancients, for it would be difficult to conceive by what means, other than with steel tools, such work could have been executed; and it is wonderful to contemplate that steel cutting-tools should have been used so long ago, whilst the principle of manufacturing them-that is, by fusion of iron and charcoal in crucibles-was then in a measure on the sane lines as we work on at the present day. Archaeologists have discovered that the Chinese made steel in crucibles long before the Christian era. " Wootz " steel fabricated in India centuries ago was crucible steel, as was also the celebrated Damascus steel, produced at the forges of Toledo, and, curiously, this latter steel furnishes' yet another proof that "There is nothing new under the Sun," for it is recorded that Damascus steel contained certain percentages of tungsten, nickel, manganese, etc., some of the very elements, in fact, contained in the present modern high-speed steel, so that a latent high-speed steel may be said to have existed

Mar 1, 1905

By N. Christensen, B. Augland, T. H. Johansen

Samples of an Fe-Nb alloy were brought to equilibriurtr with hydrogen-methane mixtures in the temperature range from 950° to 1050°C, and subsequently analyzed on their carbon contents. The solubility pvoduct L = [%Nb] [%C] may be represented by the equation Approximate solubilities indirectly assessed through hardness measurements have been included from a previous report. These data are shown to be in a fair agreement with the present solubility measurements. IN an investigation based on hardness measurements by de Kazinczy, Ms, and pachleitnerl the molal heat of solution of NbC was estimated to 11.5 kcal per mole. This value was considered rather small, and an investigation using a similar technique was carried out. The results indicated a heat of solution about 35 kcal per mole.2 At this stage it was decided to determine the solubility under conditions of true equilibrium . During the course of this work a similar investigation was published by Smith. 3 His heat of solution, 41.6 kcal per mole, is not very different from the value resulting from the present work (42.5 kcal per mole). Our solubility product, on the other hand, is at considerable variance with that reported by Smith. Possible reasons for these differences are discussed below. Mori, Tokizane, and saheki 7 have studied the behavior of niobium in commercial steels, with special attention to the formation of niobium carbide, nitride, and sulfide. Assuming a carbide composition Nbco.87 based on X-ray diffraction and chemical analysis of residues extracted from Fe-Nb-C-S alloys, the molal heat of solution of niobium carbide was estimated to 35.2 kcal per mole. MATERIALS AND EQUIPMENT The chemical analysis of the materials is given in Table I. Electrolytic iron* was used in the preparation of

Jan 1, 1968