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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 N. E. Grosvenor

The present and future activity of western coking coals is discussed. A general description of location, quantity, and quality is used as a basis for discussing development, mining, and marketing problems facing these reserves. As the need for coke from the West increases, solutions to the present mining and transportation problems will be forthcoming. Improved mining and blending technology, coupled with a more economical transportation solution, must precede a rapid development of the West's coke reserves. Ever increasing demands on coke production enhance the prospects of an accelerated development of these reserves.

Jan 1, 1976

By E. Escobar Pallares

Footnotes to column heads and explanation of symbols are given on page 239. H.C.T. means the deep zone for High Cold Test crude oil. L.C.T. means the shallow zone for Low Cold Test crude oil. They occur in the same area. In the same area there are many shallow pits and some wells. In the column showing total oil production to the end of 1939 are included 355,997 bbl. from shallow pits before 1939. During the last year there was no production from shallow pita.

Jan 1, 1940

By E. Escobar Pallares

Footnotes to column heads and explanation of symbols are given on page 239. H.C.T. means the deep zone for High Cold Test crude oil. L.C.T. means the shallow zone for Low Cold Test crude oil. They occur in the same area. In the same area there are many shallow pits and some wells. In the column showing total oil production to the end of 1939 are included 355,997 bbl. from shallow pits before 1939. During the last year there was no production from shallow pita.

Jan 1, 1940

By H. E. Mauck

The many factors that control bumping must be carefully studied for each coal seam where bumps occur, and specifications known to exclude bumping should be incorporated in the mining plans. This calls for complete knowledge of the seam's characteristics and its adjacent strata, and in many instances these characteristics are not revealed until the seam is actually mined. Pressure and shock bumps, the two general types, occur jointly and separately. In this discussion no differentiation will be made. Whether pressure or shock, they are treated as bumps, and both must be eliminated.

Jan 9, 1958

By William B. Plank

For the first time in four years the number of mineral engineering students in the 228 engineering colleges of the U. S. and Canada exceeds 10,000. According to figures just released by the American Society for Engineering Education, the current enrollment of all engineering students is 222,178. The total of 10,274 mineral engineering students, undergraduate and graduate, is a 4% pct increase over a year ago. Total engineering is 11 pct larger than last year, about the same as in 1949-50, and 24 pct above 1950-51.

Jan 4, 1955

There is a basic need for the health and safety manager to know what work he or she is to do and how to do it in a more professional way. Peter F. Drucker in The Practice of Management said, "The ignorance of the function of management, of its work, of its standards and its responsibilities is one of the most serious weaknesses of an industrial society-and it is almost universal." The biggest need in mining today is for its managers to have a thorough understanding of the management control activity.

Jan 11, 1979

By George F. Sowers

THE geophysical methods of exploration employed so extensively in mining and petroleum investigations are now being used in civil engineering. Requirements differ from those of mineral ex- ploration and therefore modified techniques have been developed. The civil engineer is primarily interested in the uppermost soil and rock strata. In highway engineering the materials affecting design and construction may be found within 15 or 20 ft of ground surface, and data on soils and rocks is seldom needed for more than a depth of 100 ft even for the heaviest structures.

Jan 1, 1954

By H. W. Imholz

This report covers most of the counties in North Central Texas in which oil is being produced in commercial quantities. The exceptions are McCulloch and Runnels, which were omitted because the production is small and the detailed information necessary for a report is not available to the writer. Complete information was not available regarding the number of wells drilled in this district during the year. The writer wishes to thank Mr. T. F. Petty, of the Humble Oil and Refining Co., Wichita Falls, Texas, for information used in compiling Table 2.

Jan 1, 1937

By Howland Bancroft

THE writer has observed that some confusion is experienced by many mining engineers in making vertical sections of ore deposits in mining properties which they have examined. Having much examination work calling for the correct interpretation of vein structure and the subsequent platting of the same on sections, it has occurred to the writer that the accompanying diagram may be of use to others who at times may be called upon to prepare numerous sections. For example, a great mass of data on-strike and dip of ore bodies is collected underground in separate

Jan 7, 1914

By J. S. Mitchell

Cobalt recovery from arsenical concentrates by pressure leaching and reduction involves special methods and operating problems. Principal steps in the process are auto-oxidation acid leaching under pressure, filtration of the tailings, purification of the solution, hydrogen reduction of the ammoniacal solution, and electrical furnacing for sulfur removal and granulating the metal. Extracting cobalt metal from arsenical ores has presented a major metallurgical problem for many years. In acquiring the Blackbird mine near Salmon City, Idaho in 1943 Calera Mining Co. accepted the challenge to solve this problem.

Nov 1, 1956

By J. J. Scott, L. Adler3

L. Adler (Assoc. Professor, Department of Mining Engineering, Virginia Polytechnic Institute, Blacks-burg, Va.) - Dr. Scott is to be commended for undertaking the arduous and specialized task of applying three-dimensional photoelastic techniques to a mining problem. However, 1 feel his analysis suffers seriously from a lack of clarification on one important matter, among several others; and that the paper as a whole lacks balance and thus tends to confuse the reader. 1) The major technical criticism refers to the fact that nowhere are the boundary conditions for his mod-

Jan 1, 1964

By Merlyn B. Buhle

FOR the past 20 years electrical earth resistivity exploration has been used in Illinois in many phases of study undertaken by the State Geological Survey, chiefly in locating and outlining deposits of water-bearing sand and gravel from which to obtain ground water for municipal and industrial supplies. At least 43 municipalities in the state derive their total water supply from deposits of sand and gravel discovered by resistivity methods. These deposits occur in both Quaternary and preglacial valleys and within much of the glacial drift which covers .a large portion of the state

Jan 4, 1953

By J. S. Li, J. C. Edwards

A prediction is made of the airflow at the Bureau of Mines Lake Lynn Laboratory with a ventilation computer program that accounts for fan-driven forced ventilation and temperature-induced natural ventilation. There was substantial agreement between measured and predicted airflow rates. The capability of the program is demonstrated as a planning aid for ventilation under emergency conditions in a multilevel coal mine. Smoke spread in a multilevel mine is analyzed following the occurrence of two events, the failure of the main exhaust fan and the development of a fuel-rich fire in a passageway.

Jan 1, 1983

By D. E. Munson, P. R. Dawson

An empirical model is developed that predicts accurately the transient response of salt creep to incremental and decremental changes in stress and temperature. Even though the model is empirical, it is derived from a firm theoretical framework for the micromechanical deformation processes of both steady-state and transient creep. In the model, the transient creep functions modify the steady-state creep behavior, which in turn is based upon creep mechanisms and the def ormation-mechanism map. The model is applied successfully to experimental stress-drop results obtained for salt.

Jan 1, 1982

By W. S. Hungerford

As several papers on the subject of mining in soft ore-bodies have recently appeared in the Transactions and in the Engineering and Mining Journal, the following brief account of the method introduced by the writer at Low Moor, Va., may be of interest. It is in some respects similar to the system at Longdale, Va., referred to in Mr. Rothwell's paper, though differing in many of its details. That system has been employed by the Longdale Iron Company for many years, and to that company the writer is indebted for many

Jan 1, 1889

By Dennis Z. Mraz

An engineering procedure for designing the minimum separation between solution mined caverns in bedded salt deposit is described. The procedure is based on data obtained by in-situ and laboratory test methods. The formulae utilize the concept that salt rock under high pressure in a deep salt rock deposit would behave as a perfectly plastic substance, and that the active opening surrounding a typical cavern could be described by a circular ellipsoid. The paper describes the calculations required for the safe design of a solution mined salt cavern field.

Jan 1, 1984

By C. G. Fink, G. L. Putnam

The dissolution of gold by cyanide solutions was studied by determining the time required for the solvents to dissolve gold leaf. Minute traces, even 0.5 ppm, of sulphide ion retard the dissolution of gold, and this behavior cannot be accounted for by the presently accepted hypotheses involving oxygen-depletion or thiocyanate formation. On the other hand, traces of the salts of lead, bismuth, mercury, and thallium considerably accelerate the dissolution. The beneficial effect of lead is dependent upon the pH and cyanide ion concentration of the solution.

Jan 9, 1950

By Robert C. Bates

Published information on costs of radon daughter control in uranium mines was analyzed to develop estimates of the cost per ton for any level of radiation exposure control. All data were converted to 1967 cost of living index to provide a common analysis base. Re- of the analysis show that the cost per ton increases exponentially as the radiation level is lowered. A linear relationship with the cost of living index is assumed, and equations and graphs are provided to estimate control cost per ton for any exposure control level and cost of living index.

Jan 1, 1982

By William E. Messner

California’s Monterey Peninsula, noted for its beaches, resort hotels, and beautiful homes, also harbors a pioneering beneficiation operation. Here for more than 35 years the Del Monte Properties Co. has provided sand products from large dunes, some over 300 ft high, located in the Del Monte Forest. Raw material-the dunes derived by wave action from Santa Lucia granite of Jurassic age-has unusually consistent chemical and physical composition. Coarse crystalline feldspar is the principal constituent, followed in abundance by quartz, with some biotite, ilmenite, garnet, zircon, and monazite.

Jan 2, 1955