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By R. C. Hassinger, D. V. von Rosenberg

Transverse dispersion has received considerably less treatment in the literature than has longitudinal dispersion. Different methods for determining transverse dispersion coefficients have been used in different investigations, and the results obtained have not been consistent enough to permit accurate generalizations as to the effect of various physical parameters on the magnitude of these coefficients. A numerical solution to the differential equation describing transverse dispersion in the absence of longitudinal dispersion was obtained to enable one to calculate the dispersion coefficient from experimental results. The more general dispersion equation including longitudinal dispersion also was solved numerically to give quantitative limits of a dimensionless group within which the assumption of negligible longitudinal dispersion is justified. Possible experimental procedures were examined, and one utilizing a cylindrical packed column was chosen for the determination of transverse dispersion coefficients. Values of these coefficients were determined for a system of two miscible organic fluids of equal density and viscosity, for two sizes of packing material over a wide range of flow rates in the laminar regime. The dispersion coefficient was found to decrease, for a constant value of the product of packing size and interstitial velocity, as the size of the packing material particles increased. INTRODUCTION Longitudinal dispersion has received extensive treatment in the literature, and consequently is better understood than its orthogonal counterpart, transverse dispersion. Many mathematical models of dispersion processes assume that transverse dispersion is rapid enough to damp out any radial** concentration gradients and therefore may be neglected. Laboratory and production results, however, indicate that this is a poor assumption.l,2 Various experimental procedures for determining transverse dispersion coefficients have been used in previous investigations, but the results have generally been expressed by similar correlations. The transverse dispersion coefficients obtained, however, have often varied considerably for given values of the correlation parameters. We feel that further experimental determinations of transverse dispersion coefficients will help alleviate some of the inconsistencies in these empirical correlations. One assumption implicit in all previous investigations is that of negligible longitudinal dispersion in the experimental system. An attempt to justify this assumption often is made using intuitive reasoning, but it is apparent that this reasoning must break down as the condition of zero flow rate is approached. A mathematical examination of the equations describing the system yields physical limits outside of which the assumption of negligible longitudinal dispersion is invalid. BACKGROUND In a porous medium, the "effective molecular diffusivity" De is less than the molecular diffusivity D measured in the absence of a porous medium, due to the tortuous path which a diffusing molecule must travel. Various authors3-5 have reported values of the ratio De/D in the range of 0.6 to 0.7. When there is fluid flow within the porous medium, mass transfer occurs by convective dispersion as well as by molecular diffusion. These are separate phenomena and can be treated as such on a microscopic scale. However, the mathematical complexity is such that only extremely simple geometries could be considered, and the results hardly would be applicable to the complex geometries existent in actual porous media. A more

Jan 1, 1969

By Herbert Clark Hoover, Lou Henry Hoover

PREVIOUSLY I have dealt with the methods of separating silver from copper. There now remains the portion which treats of solidified juices ; and whereas they might be considered as alien to things metallic, nevertheless, the reasons why they should not be separated from it I have explained in the second book. Solidified juices are either prepared from waters in which nature or art has infused them, or they are produced from the liquid juices themselves, or from stony minerals. Sagacious people, at first observing the waters of some lakes to be naturally full of juices which thickened on being dried up by the heat of the sun and thus became solidified juices, drew such waters into other places, or diverted them into low-lying places adjoining hills, so that the heat of the sun should likewise cause them to condense. Subsequently, because they observed that in this wise the solidified juices could be made only in summer, and then not in all countries, but only in hot and temperate regions in which it seldom rains in summer, they boiled them in vessels over a fire until they began to thicken. In this manner, at all times of the year, in all regions, even the coldest, solidified juices could be obtained from solutions of such juices, whether made by nature or by art. Afterward, when they saw juices drip from some roasted stones, they cooked these in pots in order to obtain solidified juices in this wise also. It is worth the trouble to learn the pro- portions and the methods by which these are made. I will therefore began with salt, which is made from water either salty by nature, or by the labour of man, or else from a solution of salt, or from lye, likewise salty. Water which is salty by nature, is condensed and converted into salt in salt-pits by the heat of the sun, or else by the heat of a fire in pans or pts or trenches. That which is made salty by art, is also condensed by fire and changed into salt. There should be as many salt-pits dug as the circumstance of the place permits, but there should not be more made than can be used, although we ought to make as much salt as we can sell. The depth of salt-pits should be moderate, and the bottom should be level, so that all the water is evaporated from the salt by the heat of the sun. The salt-pits should first be encrusted with salt, so that they may not suck up the water. The method of pouring or leading sea-water into salt-pits is very old, and is still in use in many places. The method is not less old, but less common, to pour well-water into salt-pits, as was done in Babylon, for which Pliny is the authority, and in Cappadocia, where they used not only well-water, but also spring-water. In all hot countries salt-water and lake-water are conducted, poured or carried into salt-pits, and, being dried by the heat of the sun, are converted into

Jan 1, 1950

RECENTLY seven Boy Scouts were chosen from all the troops in the United States for their all-around ability, excellence in' scouting, and special ability as writers. Two of the members of this selected group were sons of In-stitute members. In the accompanying illustration, Ber-nard Queneau, son of A. L. J. Queneau, of the U. S. Steel. Corp., can be seen at the extreme left, just behind Theo-dore Roosevelt, who is shaking hands with the boy next to. Carl Zapffe (standing in the middle with his hands behind him), the son of Carl Zapffe, manager of the iron ore prop-erties of the Northern Pacific Railroad.

Jan 6, 1928

By William B. Plank

STATISTICS just released by the American Society for Engineering Education and given in the table, show that the total current enrollment of 200,227 in the 220 engineering schools of the U. S. and Canada represents a gain of 9.8 pct over a year ago, while the mineral engineering enrollment in the U. S. of 9826 shows a gain of only 4 pct in that field. The spurt in the mineral group shown last year is thus slowed down to less than one half of that in the whole engineering student body. Last year, it was growing more rapidly than the whole engineering group.

Jan 5, 1954

Early production records are practically nonexistent, although the early geological survey reports mention a number of mines as being in operation at the dates of the field surveys. Reports of the Bureau of Statistics began in 1878, and as usual, the tonnages reported were undoubtedly small. County histories gave some production figures, but not many. The use of the Indiana block coal in blast furnaces furnished a substantial market for a number of years, which ended about the close of the Civil War. Some coke was made from Indiana coal for several years in the eighteen-forties, as is described in the chapter on Coke. (Chapter 35.)

Jan 1, 1942

WILDER D. BANCROFT,* Washington, D. C. (written discussion?).¬In two-phase systems there are three possibilities and Mr. Alexander has only considered two. We may have the first phase the internal one and the second the external one; we may have the first phase the external one and the second phase the internal one; and we may have both phases continuous. This last case occurs when we have a roll of wire fencing standing in the air; the wire is continuous and so is the air. It is quite probable that this case occurs very often in alloys and it it, therefore, important that it should not be overlooked. With gulch,

Jan 3, 1919

By J. M. Ohm, Carl M. Bunker

Two special tools for recovering gamma-ray probes and logging cable from drillholes have been designed by Ohm and Bunker and constructed by Ohm. Though intended specifically for U. S. Geological Survey equipment, they may be used with other equipment of the same general type. Fishing Tool for Probes: A fishing tool of the overshot type (Fig. 1) was designed to retrieve logging probes (sondes) that become disconnected from the logging cable and are trapped in the drillhole. When the tool slides over the top of the gamma-ray probe, studs on the bottom engage the shoulder near the top of the probe (Fig. 2), which is then pulled to surface.

Jan 10, 1959

The October meeting of the Mining and Geological Society, Lehigh University, was held in the Eckley B. Coxe Mining Laboratory, and was called to order at 8:15 p. m., by President R. L. McCann. After the reading of the minutes of the previous meeting, a short business session was held, for the purpose of electing a Vice-President to succeed G. S. Borden, who has left college. Nominees for the office were: H. J. Sloman, P. S. Justice, L. Sargeant. Dr. F. F. Hintze, of the Geology Department, was elected a member of the Advisory Committee, which now consists of the President-

Jan 12, 1916

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc., the Proceedings, and the papers revised for final publication. (In this revision, after the preliminary publication, authors are permitted to use the largest liberty; and the changes and additions made in papers are sometimes important. It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views. It should be added, however, that in the majority of cases there are no important changes.) These volumes are for sale as follows, in paper covers:

Jan 1, 1910

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc., the Proceedings, and the papers revised for final publication. (In this revision, after the preliminary publication, authors are permitted to use the largest liberty; and the changes and additions made in papers are sometimes important. It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views. It should be added, however, that in the majority of cases there are no important changes.) These volumes are for sale as follows, in paper covers:

Jan 1, 1917

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc., the Proceedings, and the papers revised for final publication. (In this revision, after the preliminary publication, authors are permitted to use the largest liberty; and the changes and additions made in papers are sometimes important. It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views. It should be added, however, that in the majority of cases there are no important changes.) These volumes are for sale as follows, in paper covers:

Jan 1, 1910

By William Loblowitz

A simplified system of flotation testing has been developed recently at the Bureau of Mineral Research of Rutgers University. The technique involves the known principle of skin flotation and can be used with minute quantities of sample and reagents in a beaker. A vessel containing the conditioned sample with added water and flotation reagents is held inclined and rotated slowly. Water-repellent particles come in contact with air and float on the surface of the liquid, while wettable particles are submerged. The float is poured off and filtered whereas the nonfloat remains in the beaker. The filtrate may be returned to repeat the process.

Jan 6, 1951

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc., the Proceedings, and the papers revised for final publication. (In this revision, after the preliminary publication, authors are permitted to use the largest liberty; and the changes and additions made in papers are sometimes important. It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views. It should be added, however, that in the majority of cases there are no important changes.) These volumes are for sale as follows, in paper covers:

Jan 1, 1910

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc., the Proceedings, and the papers revised for final publication. (In this revision, after the preliminary publication, authors are permitted to use the largest liberty; and the changes and additions made in papers are sometimes important. It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views. It should be added, however, that in the majority of cases there are no important changes.) These volumes are for sale as follows, in paper covers:

Jan 1, 1917

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc., the Proceedings, and the papers revised for final publication. (In this revision, after the preliminary publication, authors are permitted to use the largest liberty; and the changes and additions made in papers are sometimes important. It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views. It should be added, however, that in the majority of cases there are no important changes.) These volumes are for sale as follows, in paper covers:

Jan 1, 1910

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc., the Proceedings, and the papers revised for final publication. (In this revision, after the preliminary publication, authors are permitted to use the largest liberty; and the changes and additions made in papers are sometimes important. It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views. It should be added, however, that in the majority of cases there are no important changes.) These volumes are for sale as follows, in paper covers:

Jan 1, 1917

The volumes of Transactions, which are published annually, contain the list of officers, rules, etc., the Proceedings, and the papers revised for final publication. (In this revision, after the preliminary publication, authors are permitted to use the largest liberty; and the changes and additions made in papers are sometimes important. It should be borne in mind by those who study or quote a paper in the preliminary edition, that they may not have in that form the ultimate and deliberate expression of the author's views. It should be added, however, that in the majority of cases there are no important changes.) These volumes are for sale as follows, in paper covers:

Jan 1, 1917

By N. O. Johnson, R. A. Westin

Polychlorinated biphenyls were the basis of non-flammable askarel dielectric liquids wed in electrical equipment made between 1929 and 1978. Although PCBs were widely used in mine electrical equipment, the toxicity and environmental persistence of this chemical led Congress to ban its manufacture and use. Bureau of Mines Information Circular 8838 summarizes the regulations imposed by the EPA on the use and disposal of PCBs, and describes the limitations of available substitutes. Recent changes in the regulations will impose additional requirements on the use of PCBs by the mining industry. This paper is an update of the material presented in the Bureau of Mines information circular.

Jan 1, 1983

US 4,185,193-Method of assaying the vicinity of a borehole for uranium ore or thorium ore. A pulsed neutron source IS operated to irradiate the earth formations with fast neutrons. A detector responds to the delayed fission neutrons emitted by the ore as a measure of ore concentration and to the delayed neutrons from oxygen-17 as a measure of the neutron output of the source. The measurement of ore concentration is corrected In accordance with the measured changes in the neutron output of the source. R L. Caldwell, assigned to Mobil Oil Corp. Jan. 22, 1980 4 pp (250-269). Filed: 5-18-78 (906,907).

Jan 1, 1982

By Murray F. Hawkins, Marion L. Kimmel

sage' appears to have been the first (1933) to design a rolling ball viscosimeter for the express purpose of measuring the viscosity of oils with natural gas in solution, i.e., under reservoir conditions. In 1940 Hocott and Buckley' further refined the rolling ball instrument in both design and method of operation, and their instrument, known as the Humble type, was the forerunner of present day viscosimeters used in petroleum production and research laboratories. They also initiated the technique of charging the viscosimeter with a sample directly from a bottom hole sampler. In 1948 the committee on engineering research 01 the Petroleum Division of the AIME in Part 3 (1) of

Jan 1, 1955