Search Documents

H. A. SCHWARTZ, ? Indianapolis, Inc. (written discussion§).-Re-ferring to the very interesting paper on the graphitization of white cast iron, the writer desires to present certain facts and conclusions, entirely, in harmony with those of the authors but which may he not without interest as furnishing additional evidence upon the same subject. The graphitization of white cast iron, being the basis of malleable

Jan 10, 1919

Executive SIDNEY J. JENNINGS, Chairman GEORGE D. BARRON J. E. JOHNSON, JR. EDWIN LUDLOW ROBERT M. RAYMOND Membership KARL FILERS, Chairman LEWIS W. FRANCIS J. E. JOHNSON, JR. LOUIS D. HUNTOON ARTHUR L. WALKER Finance GEORGE D. BARRON, Chairman CHARLES F. RAND BENJAMIN B. THAYER Library E. GYBBON SPILSBURY,1 Chairman ALEX C. HUMPHREYS3 GEORGE C. STONE 2 J. H. JANEWAY4 BRADLEY STOUGHTON

Jan 5, 1918

PRESIDENTS DAVID THOMAS 1871 R W RAYMOND 1872-1874 A L HOLLEY1875 ABRAM S HEWITT 1876 T STERRY HUNT 1877 ECKLEY B COXE 1878 - 1879 WILLIAM P SHINN 1880 WILLIAM METCALF 1881 RICHARD P ROTHWELL 1882 ROBERY W HUNT 1883 JAMES C, BAYLES 1884-1885 ROBERT H RICHARDS 1886 THOMAS EGLESTON 1887 WILLIAM B POTTER 1888 RICHARD PEARCE 1889 ADAM S HEWITT 1890

Jan 1, 1923

STANDING COMMITTEES. Executive. CHARLES F. BAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS, ALBERT R. LEDOUX, BENJAMIN B. THAYER. Membership. BENJAMIN B. THAYER, Chairman. WALTER R. INGALLS, JOHN H. JANEWAY, JR., JOHN D. IRVING, HERMAN A. PROSSER. Finance. EDWARD L. YOUNG, Chairman. KARL FILERS, JAMES GAYLEY. Library. JAM ES, F. KEMP, Chairman. JOHN HAYS HAMMOND,3 E. GYBBON SPILSBURY,2 ALEX. C. HUMPHREYS,4 BRADLEY STOUGHTON.

Jan 8, 1913

STANDING COMMITTEES. Executive. CHARLES F. RAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS, ALBERT R. LEDOUX, BENJAMIN B. THAYER. . Membership. BENJAMIN B. THAYER, Chairman. KARL EILERS, JOHN H. JANEWAY, JR., JOHN D. IRVING, HERMAN A. PROSSER. Finance. EDWARD L. YOUNG, Chairman. KARL EILERS, JAMES GAYLEY. Library. JAMES F. KEMP, Chairman1 JOHN HAYS HAMMOND,3 E. GYBBON SPILSBURY,2 ALEX. C. HUMPHREYS.4 BRADLEY STOUGHTON.

Jan 10, 1913

STANDING COMMITTEES. Executive. CHARLES F. RAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS, ALBERT R. LEDOUX, BENJAMIN B. THAYER. Membership.. BENJAMIN B. THAYER, Chairman. WALTER R. INGALLS, JOHN H. JANEWAY, JR., JOHN D. IRVING, HERMAN A. PROSSER. Finance. EDWARD L. YOUNG,Chairman. KARL EILERS, JAMES GAYLEY. Library. JAMES F. KEMP, Chairman. JOHN HAYS HAMMOND,3 E. GIBBON SPILSBURY,2 ALEX. C. HUMPHREYS,4 BRADLEY STOUGHTON.

Jan 7, 1913

David THOMAS 1871 R. W. RAYMOND 1872-1874 A. L. HOLLEY 1875 ABRAM S. HEWITT 1876 T. STERRY HURT 1877 ECKLEY B. COKE 1878-1879 WILLIAM P.SHINN 1880 WILLIAM METCALF 1881 RICHARD P. ROTHWELL 1882 ROBERT W. HUNT 1883 JAMES C. BAYLES 1884-1885 ROBERT H. RICHARDS 1886 THOMAS EGLESTON 1887 WILLIAM B. POTTER 1888 RICHARD PEARCE 1889 ABRAM S. HEWITT 1890 JOHN BIRKINBINE 1891-1892

Jan 1, 1929

STANDING COMMITTEES Executive CHARLES F. RAND, Chairman. JAMES F. KEMP, JOSEPH W. RICHARDS, ALBERT R. LEDOUX, BENJAMIN B. THAYER. Membership BENJAMIN B. THAYER, Chairman. KARL EILERS, JOHN H. JANEWAY, Jr., JOHN D. IRVING, HERMAN A. PROSSER. Finance EDWARD L. YOUNG, Chairman. KARL EILERS, JAMES GAYLEY. Library JAMES F. KEMP, Chairman.1 JOHN HAYS HAMMOND,3 E. GYBBON SPILSBURY,2 ALEX. C. HUMPHREYS,4 BRADLEY STOUGHTON.

Jan 1, 1914

By Henry J. Schwellenbach

Lack of a system in scheduling the replacement of capital equipment can result in emergency purchases of units which may later be found unsuitable for the job. New York Trap Rock Corp., which produces crushed stone for use as construction aggregate, was faced with just such a situation some years ago. The company replaced capital equipment only when machinery in use was no longer serviceable, or when there was an obvious need for different equipment. Operating and maintenance costs were generally neglected because an efficient method was lacking. New York Trap Rock has four plants located along the Hudson River, all within 70 miles of New York City. Crushed stone output-6 million tons a year-is moved to markets in metropolitan New York, New Jersey, and Long Island areas by water transport. Customers are contractors with ready-mix concrete and asphalt plants located on the water.

Jan 10, 1959

By T. E. Scott, O. G. Koepke

DURING research currently in progress the need arose for interplanar angles and planar spacings to analyze crystallographic data obtained from hcp yttrium. In the absence of such existing information, a program was written in Fortran-11 language and processed on an IBM 7074 computer. The program and results have been assembled in report form to make them generally available.' Of the possible combinations of, only those most frequently encountered were employed. The ranges of h, k, and 1 involved were: However, not all combinations and permutations of the above appear in the tabulation because redundancies occur in several cases. Nevertheless, fifteen types of planes and all their equivalent planes have been included, giving a total of 109 sets of Miller-Bravais indices.

Jan 1, 1967

By W. J. Keep

Cast-iron, or pig-iron, is iron which contains all the carbon that it could absorb during its reduction in the blast-furnace. As is well-known to chemists, carbon exists in cast-iron in two distinct forms. In chemical union, as "combined" carbon, it cannot be discerned, except as it may increase the whiteness of the fracture, in so-called white iron, or carburetted iron (sp. gr. about 7.72). Carbon mechanically mixed with the iron as graphite is visible, varying in color from gray to black, while the fracture of the iron, according to the color and amount of graphite it contains, ranges from a light to a very dark gray. The specific gravity of graphitic iron is about 7.40. Silicon in cast-iron is evidently to some extent combined with the iron and the carbon ; but whether it exists also in a form corresponding with graphitic carbon, mechanically mixed with the remaining mass, is a question still in dispute, which we have not in this paper endeavored to answer. It has been the opinion of many writers on metallurgy, and many foundry men, that silicon is in every way injurious to cast-iron. Yet

Jan 1, 1889

By W. J. Carlson, I. Iwasaki

A previous article reported a combination process for recovering both metallic iron and metallic manganese from the manganiferous iron ores of the Cuyuna Range in Minnesota.' In this process, the iron was recovered by direct reduction and magnetic separation and the manganese was recovered from the nonmagnetic tailing by leaching and electrolysis. The current efficiency during the electrolysis of manganese is quite low, in the range of 60 to 70%, due to the simultaneous plating of hydrogen.2,3 The parameters that affect the current efficiency are (1) the concentrations of the manganese ion and the ammonium sulfate buffer, (2) the effect of autoxidant, (3) temperature, (4) pH, and (5) current density. To study the plating characteristics of manganese metal.

Jan 1, 1969

By J. J. Sense

This paper deals with the Asarco method for the determination of equipment availability. It is apparent that no single availability equation will provide all of the information necessary for the complete record of equipment availability. In the Asarco system, three separate availability records are carried on major equipment. The first is mechanical availability, the second is operational availability, and the third is a historical record of equipment use. The derivation of the three items and the definitions of the time elements used in the various availability equations are presented and discussed. The Mission unit of American Smelting and Refining Co. is located in Pima County, Ariz., approximately twenty miles southwest of Tucson. The unit consists of an open pit copper mine and concentrator. The concentrate is shipped by rail to company smelters at Hayden, Ariz., or El Paso, Tex. Mine stripping began at Mission in the fall of 1959, and construction of the 15,000 tpd concentrator was started in the spring of 1960. The first ore was treated in midsummer of 1961 and full ore production was reached in August 1961. At that time over 46 million tons of material had been moved from the pit. Current production (ore and waste) averages over 100,000 tpd. Total production to date (ore and waste) is over 120 million tons. Major equipment currently in operation at the Mission pit is as follows: 3 P & H 1800 Electric Shovels - 9 cu yd dippers 1 P & H 1900 Electric Shovel - 9 cu yd dipper 2 B.E. 190-B Electric Shovels - 9 cu yd dippers 35 Euclid LLD Trucks - 60-ton capacity 6 KW-Dart 55-T Trucks - 55-ton capacity 1 KW-Dart D-2550 Truck - 65-ton capacity 1 LeTourneau Westinghouse 65 Haulpak - 65-ton capacity 3 Euclid S-18 Scrapers - 274011 capacity 4 Caterpillar D-8 Dozers 4 LeTourneau Westinghouse Tournadozers 1 Michigan 280 Dozer 2 Caterpillar Model 12 Motor Graders

Jan 1, 1964

A concept gaining attention among rock mechanics researchers in studies of soil-structure inter- action is the use of compressible packing between the structure such as tunnel lining and the soil or rock. Lester H. Gabriel, provided information about work on this concept at the II Symposium on Rapid Excavation, October 16-17, 1969, Sacramento State College, Sacramento, Calif. It is well-known that loads transmit their effects to those locations which deform least. Traditionally, the question to be answered by the structural engineer is how rigid the structure ought to be. The stronger the structure, the more resistant it becomes to deformation. If it is more rigid than the surrounding strata, the structure acts as a pillar, focusing load on itself. However, if the structure is less rigid than the surrounding strata, blocking or packing between the structure and the enclosing material facilitates the formation of soil or rock arch. The object then is to design and build structures such as tunnel linings, which harness the advantages of carefully planned small movements. Tests on plaster cylinders imbedded in granular sand and loaded were compared to those of plaster cylinders protected in sheathing of polyfoam rubber. The compressible sheath permitted support of up to ten times greater loads Gabriel, Lester H., "Principles of Soil-Structure Interaction Applied to Tunnel Linings." Hecla Mining Co. has successfully used shotcrete with substantial cost savings for ground support purpose. To date, the use of shotcrete in Hecla's operations has been limited to openings where long-term high quality support was required, in exceptionally difficult ground, and to a limited degree in stope support. Experience with both the wet and dry process indicated that the latter was better for their applications. The availability of effective accelerators which reduce losses from rebound, give high-early strength and permit placement in wet conditions, led to this conclusion. The gross cost under such conditions as those at Hecla, including rebound losses and overshooting, is estimated by Hecla to be $51 per cu yd.

Jan 12, 1969

By Douglas R. Shaw

Normal dodecyl mercaptan was evaluated as a collector for flotation of sulfide minerals and precious metals. The reagent is from the class of normal mercaptoalkanes (n-alkyl thiols), and is commercially available in the form of a mixture of n-dodecyl mercaptan, the primary constituent, and a water-soluble dispersant, under the trade name Pennfloat™ 3. * Reported are results of bench-scale flotation experiments on many commercially treated base metal and precious metal sulfide ores. Dosages, points of addition, and flotation pH were among the variables studied. Most notable results were increased copper, molybdenum, and precious metals recoveries. Dosages of dodecyl mercaptan on some ores were considerably lower than required for conventional collectors. The reagent was shown to be a highly effective and versatile collector on virtually all of the more than 30 sulfide ore types examined.

Jan 1, 1982

By R. G. Knickerbocker, R. R. Lloyd, W. T. Rawles

In July 1041, the Experiment Station of the Bureau of Mines at Boulder City, Nevada, began a study of methods of producing magnesium metal from magnesium oxide, with particular emphasis upon the direct use of magnesium oxide in a molten chloride electrolyte. The program was extended to include pilot-plant study of chemical methods for the preparation of pure magnesia from dolomites and magnesites. Preliminary work on the production of magnesia from dolomite was done with the cooperation of Kobert D. Pike and the Harbison-Walker Refractories Co. These investigatipns included a cooperative arrangement whereby the Bureau tested certain steps of the Harbison-Walker-Pike process. The process finally developed by the Bureau includes the precarbonation mixing step of the H.W.P. flowsheet prepared by Mr. Pike. Two magnesium-reduction plants using MgO as a source of magnesium were being constructed in the West, and they enormously stimulated interest in various dolomite deposits as possible sources of the magnesia needed by them. This paper describes one phase of this program—the operation of a pilot plant for producing cell-grade magnesia from dolomite from Sloan, Nevada. The process developed for this purpose is an adaptation of a well-known process first proposed by Clossonl and modified by others,2"1 involving the use of calcium chloride and carbon dioxide. It is based on the following chemical reactions: MgCl2 + Ca(OH)2 = CaCl2 + Mg(OH)2 [1] Mg(OH)4 + CaCU + CO2 = MgCl2 + CaCO, + H2O [2] The first reaction proceeds almost completely to the right because of the much greater solubility of calcium hydroxide as compared with magnesium hydroxide. Under equilibrium conditions, when only the four components shown in reaction I are involved, the ratio of magnesium to calcium in solution, according to solubility-product relationship, will be: This reaction is the basis of present commercial processes for recovering magnesium from sea water and dolomite. The second reaction is, in effect, a reversal of the first reaction produced by adding COz. This reaction also proceeds nearly to completion, the solubility relationship being: Ca where P indicates partial pressure of COz, in atmospheres.

Jan 1, 1944

By P. M. Robinson, J. S. LI. Leach

The heats of solution oj' indiurrr, tin, lend, nrzd tellurium have been calculated from the measured heat effects when mechanical mixtres of indium and telLuium tin and tellurium, and lead and tellurium were added to liquid bismuth. The results are in good agreement xith publislzed values.s for the separate sollction of each eleltzent in bismuth. The heats oj solution of cadmium and tellurium calculated from the rneasuved heat effects on adding trechanical mixtures of these elements do not ugree zc,itl the published values jbv the separate solution of each element. It is shown that at 623°K Ile interaction between cadmium and tellurium dissolved in liquid bismuth is strong enough to led lo preciPitation of solid CdTc. The heats oj- jor-mation of CdTe at 273" nd 623°K (1)-c crilculated fi-or the measured heat ejlfecls. The calcnlaled az'erage deviation from the Kopp-l\'ez?,zunrz rule fov solid CdTe is less than 0.06 cat per g-atom- C over this lertzperalure range. Tlze importance 0.f these oDserl.ations to the determination of heals of formation hy metal solution calorimetry is considered. LIQUID metal solution calorimetry is a convenient method for determining the heats of formation of solid compounds. In this technique the heat of formation is the difference between the measured heat effects on dissolution of the compounds and of mechanical mixtures of the components in the liquid metal.' The heat of solution of the mechanical mixture may be calculated from the measured heat effect. At infinite dilution of the solutes, this heat of solution is equal to the sum of the heats of solution of the separate components. If the heat of solution of one of the components is known, the value for the other can be derived; if both are known, they may be used to check the accuracy of the calorimetric technique. The heats of formation of the tellurides of cadmium, indium, tin, and lead have recently been measured by metal solution alorimetr. The heats of solution of indium, tin, lead, and tellurium at infinite dilution in liquid bismuth at 623"K, calculated from the measured heat effects on solution of the mechanical mixtures, are in good agreement with the published values. The heats of solution of cadmium and of tellurium calculated from the measured heat effect on solution in bismuth at 623'K of mechanical mixtures of cadmium and tellurium, however, do not agree with values estimated from the literature. 1) EXPERIMENTAL PROCEDURE AND RESULTS The Heats of Solution of Indium, Tin, Lead, and Tellurium in Bismuth. The heat effects were measured when mechanical mixtures corresponding to the compounds In,Te, InTe, In2Te3, In2Te5, SnTe, and PbTe were dissolved in bismuth. The calorimetric procedure and the method of calculation have been described elsewhere.' The heats of solution of the mechanical mixtures were obtained by subtracting the change in heat content per gram-atom of the sample between the addition temperature (273°K) and the bath temperature (623"K), (H623°K - H273°K)S, from the measured heat effects. The calorimeter was calibrated with pure bismuth. The reported values of the measured heat effects are based on (HGoK - ^273oK)Bi = 4.96 kcal per g-atom.3 The measured heat effects are found to be linear functions of the solute concentrations of the bath in the dilute solution range. The values, extrapolated to infinite dilution, are listed in Table I, together with the heats of solution of the mechanical mixtures calculated using the published values of (H 623°K - H273°k)s for indium, tin, lead,3 and tellrium. All the error limits quoted in this work represent the spread of values obtained. The heats of solution in liquid bismuth at 623°K of mechanical mixtures of indium and tellurium in four different proportions were determined. Values of the heats of solution of the two components were then calculated from the resulting four simultaneous equations: The heats of solution at infinite dilution of tin and lead in liquid bismuth at 623°K were calculated from the heats of solution of the mechanical mixtures of tin and tellurium and of lead and tellurium using the heat of solution of tellurium calculated above. These values of the heats of solution are listed in Table I1 together with some published values for comparison.

Jan 1, 1967

By R. A. Oriani

The partial molal volume of hydrogen is one of the parameters that describe the elastic interaction between the solute and the stress fields about inclusions, dislocations, and cracks. As such the partial molal volume is probably of importance in the elucidation of phenomena such as hydrogen embrittlement and hydrogen yield point. A knowledge of this quantity would also be helpful in thinking about the state of dissolved hydrogen in iron. However, because of the very low lattice solubility of hydrogen in iron the usual ways of determining the lattice expansion are not practicable. It is therefore of interest to apply the thermodynamics of stressed bodies to two sets of measurements of the effect of elastic stress upon the permeability of hydrogen in order to deduce a value of the partial molal volume, VH, of hydrogen dissolved in a iron. Beck ..' and previously de Kazinczy, observed that a uniaxial tensile stress increases the permeability of hydrogen in iron and in various steels. Beck et 01. employed Armco iron and A.I.S.I. 4340 steel, whereas de Kazinczy used a steel the composition of which was 0.13 C, 0.23 Si, 0.46 Mn, 0.006 P, and 0.038 S. Upon releasing the stress the permeability increment disappeared if the stress was below the elastic limit. Both investigators employed cathodic charging to introduce the hydrogen. de Kazinczy measured the permeation through a thin-walled tube by collecting the gas, whereas Beck et al. measured the permeation through sheets of various thicknesses by a very sensitive electrochemical technique. Both investigators measured the steady-state permeation at constant rate of hydrogen ion discharge, and Beck measured in addition the hydrogen diffusivity by a time-lag technique which is independent of the boundary conditions. Beck et al. and de Kazinczy found a linear relationship between log (J,/Jo) and the stress, where Ju/Jo is the ratio of the flux of hydrogen when the metal is under uniaxial tensile stress, a, to the flux under zero stress, for the same temperature and charging current. Beck et al. found in addition that the diffusivity of hydrogen is not changed by stress. Both investigators concluded that the observed change in permeability is due to an increase in hydrogen concentration, and furthermore that the increase in concentration is due directly to the thermodynamic effect of stress upon concentration. Accepting this assessment of the situation for reasons given below, one may use the equation3j4 in order to evaluate I/H, the partial molal volume of hydrogen. This equation is valid for the domain of a/E «¦ 1 (where E is the Young's modulus) and under the assumption that hydrogen expands the lattice isotrop-ically. From the data of Beck el al, one calculates V7H - 2.0 cu cm per g-atom, and from those of de Kazinczy one obtains 1.8 cu cm per g-atom. That the increase of concentration with stress is indeed of thermodynamic origin is attested to by the facts that the experimental results conform to the thermodynamic relation, Eq. [I], and that the results are the same whether a pure iron1 or each of two different steels172 is used. Neither of these facts wou1.d necessarily be expected if the effect of stress were, rather, to increase the ratio kn/k, of the kinetic factors of the following competing reactions: H(ads) — H (dissolved) Such a change of kinetics at the surface could be an alternative explanation of the effect of stress on the permeability. Although this writer does not deem this explanation to be the correct one for the reasons given above, it must be admitted that unambiguous proof that the phenomenon has a thermodynamic origin does not yet exist. Two kinds of experiments may be suggested. One is to plate a variety of metals on the input surface of the steel and repeat the stress experiment at a variety of hydrogen charging currents. The other is to employ somewhat thicker specimens in order to be able to apply uniaxial compressive stress. Eq. [I] shows that ln(c,/c,) depends on the sign of the stress, but it is difficult to see a physical basis for which k2/kl would depend on the sign of a. The present value of V^ in a iron agrees with phragmen's5 estimate, which he based on comparisons with the lattice expansion by hydrogen of titanium, zir-

Jan 1, 1967

By E. I. Alessandrini, A. U. Seybolt

Selective oxidation (preferential oxidation of a single alloy component) can be an important oxidation mode in the case of alloys such as Si-Fe, Al-Fe, and so on, when heat-treating in atmospheres of low oxygen potential. It was the purpose of this work to identify the oxide films formed on iron containing 31/4 pct Si at low oxygen potentials, and to make some observations on the H2O/H2 ratios required to form them. EXPERIMENTAL METHOD HYDROGEN of varying water content offers a very convenient method of establishing a wide range of oxidizing power, or oxygen potential. The method chosen to provide a desired H2O/H2 ratio was to nearly saturate hydrogen at room temperature by bubbling the gas through water at room temperature, and then to wring out the excess water by passing the wet gas through a long glass spiral immersed in a refrigerated liquid at a desired dew point. After oxidation, the samples were examined by electron diffraction in order to identify any film which might be present. PREPARATION AND TREATMENT OF SAMPLES The samples were prepared from a Si-Fe alloy made in the laboratory using electrolytic iron and 96 pct ferro-silico11, vacuum-induction melted, hot-rolled then cold-rolled to 0.015-in. thickness. After the cold-rolling the samples were annealed at 1000°C. Transmission Laue X-ray patterns showed very little evidence of preferred orientation, but it is likely that a weak texture could have escaped notice. The chemical analysis was as follows: 3.34 Si, 0.01 Al, 0.001 0, 0.006 C, 0.002 N. Before each sample was oxidized, it was polished through 4/0 emery paper, cleaned and dried using benzene, carbon tetrachloride, acetone, absolute alcohol, and ether. The method of oxidizing the samples was as follows: Samples about 1/2 by 1 by 0.015 in. were held in the upper, cool part of a vertical vacuum furnace until the desired temperature was established in the furnace, Fig. 1. The sample was then lowered into the uniform hot zone where it was heated quickly to the desired temperature, and subjected to hydrogen of controlled moisture content (dew point) as mentioned previously. Temperatures from 400" to 1000°C were used, and dew points from room temperature to —78°C were explored. In general, the runs lasted about 6 hr, but a few runs were of different duration, as will be indicated later. After the predetermined period of time had elapsed, the specimens were withdrawn by the hollow stainless steel-quartz holder to a cool zone at the top of the furnace. EXPERIMENTAL RESULTS The results are summarized in Table I. Most of the electron-diffraction patterns were obtained by glancing-angle reflection, but in a few cases it was possible to strip the oxide films from the surface by a total immersion in a 3 pct bromine-methanol solution. Some of the thinner stripped films yielded quite satisfactory transmission patterns. However, both diffraction techniques yielded the same results; the patterns while most frequently showing a (low) tridymite, also showed a (low) cristobalite in some cases. A few patterns showed evidence of both phases. Because of the known nonequilibrium behavior of silica, it is not surprising that both forms of silica could coexist on one sample. It was noted that at fairly low dew points such as —40°C, there was a tendency for diffuse diffraction rings, suggesting a very small crystallite size. Also some subsequent experiments to be reported later show that thin silica films can be amorphous.

Jan 1, 1959

By E. L. Dougherty

A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonbomogeneities. Numer ical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parmeters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval's heterogeneity factor H. which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomo-geneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. INTRODUCTION It has been shownl,2,3 that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by oval! have taken two approaches: (1) development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing5,6 and (2) simultaneous application of Darcy's Law for flow and the diffusion equation with a convection term for mass transfer.7,8,9 We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of nonlinear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics. In our equations the mixing process is characterized by four parameters. Three of these, labeled ß, P1 and P2, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores. The purpose of this paper is (1) to present the details of the mathematical analysis, (2) to present the results of the calculations, (3) to consider what light the results shed on the mixing process in an unstable miscible displacement, and (4) to provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations. We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. The oil phase consists of oil containing dissolved