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By D. Walton, W. C. Winegard, W. A. Tiller, J. W. Rutter

It is shown that the cellular substructure observed in binary alloy crystals grown from a melt of known concentration can be eliminated by the proper choice of growth conditions. For a given solute concentration, there exists a critical ratio of temperature gradient G in the melt to the rate of solidification R of the crystal, i.e., of G/R, which must be exceeded before the cellular structure can be eliminated. A secondary substructure is observed which is related to the cellular substructure. IN crystals grown from the melt, a prismatic substructure has been observed by Buerger,1 Pond and Kessler,2 and Rutter and Chalmers." This structure is columnar in the direction of growth and appears as a network of hexagonal cells in the plane of the solid-liquid interface. Rutter and Chalmers3 have shown that this substructure occurs as a result of the presence of a layer of high impurity concentration in the melt adjacent to the solid-liquid interface. The formation of the substructure is accompanied by a redistribution of this impurity in the neighborhood of the interface. The structure can be controlled by proper adjustment of the variables in the solidification process such as a rate of solidification and the temperature gradient in the liquid. The redistribution of solute during the solidification of metal crystals has been treated theoretically

Jan 1, 1956

By R. A. Cunningham, A. S. Murray

If a dense fluid such as mud or water is used for circulation, the formation drilled is influenced by a hydrostatic pressure. This pressure depends on hole depth arid drilling fluid density. Laboratory tests indicute that drilling rates in many forri~ations are decreased with increased pressure,—in some cases as much as 90 per cent. A comparison between laboratory and field tests indicates that drilling fluid head affects drilling rates in the field approximately the, same as in the laboratory. Drillirrg rates of many formations are increased by reducing drilling fluid head. INTRODUCTION For many years it has been noted that field and laboratory drilling rate tests did not agree even when the formations tested were the same. For instance, tests of some shales by the Hughes Tool Co. laboratory indicated drilling rates approximately 20 to 30 ft/hour, whereas in the ground this shale would drill only 3 to 5 ft/hour. A possible reason for this discrepancy is the effect of the high pressure which the drilling fluid exerts against the formation at the bottom of the hole. Consider a small element of rock (Fig. II that is to be removed by a rock bit. If the hole is filled with mud or water. the upper surface of the rock element is subjected to a pressure which depends on hole depth and fluid density. The mass of earth around this rock element presses against the circumferential surface and the lower surface. Because of the probability of shearing stresses between the rock element and the surrounding rock, this element is not under true hydrostatic stress. However, as a first approximation for test purposes the rock element was assumed to he under hydrostatic stress. The effect of hydrostatic pressure on some physical properties of rock has been studied.1,2,3 These tests show that the "differential" compres-sive stress:': necessary to cause rup- ture in rock cylinders is greater when tested under high hydrostatic pressure than when tested under atmospheric conditions. These tests were made with pressures greater than 20,000 psi which is in excess of those normally encountered in oil well drilling. Similar tests were made by the Bureau of Reclamation' using pressures equivalent to those encountered in oil well drilling. Again the "differential" compressive stress necessary to produce failure increased with increasing hydrostatic pressure. These tests indicated that drilling rates would probably decrease. Correlation between these tests and drilling tests was not practical. The purpose of this work is to study the effect of mud column pressure on drilling rate, assuming that the material drilled is in a state of hydrostatic strcss. This problem was initially investigated in the laboratory using variable bit loads and confining pressure;. Confirmation of laboratory results was obtained in the field from a series of carefully controlled drilling tests. Because of the necessity of testing many different types of formations. only results from representative formations will be presented here.

Jan 1, 1956

By Howard B. Bradley, Charles F. Weinaug

The phase behavior of a naturally occurring hydrocarbon system whose critical temperature is near the reservoir temperature has been described. The same volume per cent liquid was observed for the firkt time at three different pressures for isotherms immediately below the critical temperature. The shapes of the isothermal equilibrium constant curves necessary to predict this phenomena are discussed and illustrated. INTRODUCTION The phase behavior of a number of hydrocarbon systems has been reported; however, very little data are available on natural occurring hydrocarbon systems whose critical temperature is near the reservoir temperature. This appeared to be the case for the fluid studied here; therefore the pressure-volume-temperature data for this system were determined for preqentation. METHOD The PVT data were obtained with equipment similar to hat described by Weinaug and Katz,1 consisting principally of a two-section, double-windowed gauge mounted in a conktant temperature air bath. The procedure followed was essentially that used by Katz and Kurata5 except that a cathetom-eter, reading direct to 0.01 cm, was used to determine the height of each extreme phase limit. The system studied was formed by recombining -.vapor and liquid samples from the first stage separator of the well. Portions of these samples were displaced with mercury into the cell which had previously been filled with mercury. A predetermined amount of the liquid sample was introduced, while an excess of vapor was admitted. The resulting mixture was brought to equilibrium at the condition of the separator during sampling. By adding mercury to maintain the pressure, enough vapor was displaced to give a gas/oil ratio within the cell equal to that produced by the separator at the time of sampling. The remaining material was then considered to be equivalent to the reservoir fluid. An analysis of material in the cell, computed from analysis of vapor and liquid samples and the separator gas/oil ratio. is given in Table I. Table I — Composition of Hydrocarbon System Component Mole Per Cent Carbon Dioxide 0.13 Nitrogen 0.76 Methane 53.91 Ethane 14.20 Propane 9.64 Iso Butane 1.25 Normal Butane 4.29 Iso Pentane 1.12 Normal Pentane 1.87 Hexane 2.72 Heptanes + 10.11 hloleculal. Weight of Heptanes + 178.50

Jan 1, 1951

By Howard B. Bradley, Charles F. Weinaug

The phase behavior of a naturally occurring hydrocarbon system whose critical temperature is near the reservoir temperature has been described. The same volume per cent liquid was observed for the firkt time at three different pressures for isotherms immediately below the critical temperature. The shapes of the isothermal equilibrium constant curves necessary to predict this phenomena are discussed and illustrated. INTRODUCTION The phase behavior of a number of hydrocarbon systems has been reported; however, very little data are available on natural occurring hydrocarbon systems whose critical temperature is near the reservoir temperature. This appeared to be the case for the fluid studied here; therefore the pressure-volume-temperature data for this system were determined for preqentation. METHOD The PVT data were obtained with equipment similar to hat described by Weinaug and Katz,1 consisting principally of a two-section, double-windowed gauge mounted in a conktant temperature air bath. The procedure followed was essentially that used by Katz and Kurata5 except that a cathetom-eter, reading direct to 0.01 cm, was used to determine the height of each extreme phase limit. The system studied was formed by recombining -.vapor and liquid samples from the first stage separator of the well. Portions of these samples were displaced with mercury into the cell which had previously been filled with mercury. A predetermined amount of the liquid sample was introduced, while an excess of vapor was admitted. The resulting mixture was brought to equilibrium at the condition of the separator during sampling. By adding mercury to maintain the pressure, enough vapor was displaced to give a gas/oil ratio within the cell equal to that produced by the separator at the time of sampling. The remaining material was then considered to be equivalent to the reservoir fluid. An analysis of material in the cell, computed from analysis of vapor and liquid samples and the separator gas/oil ratio. is given in Table I. Table I — Composition of Hydrocarbon System Component Mole Per Cent Carbon Dioxide 0.13 Nitrogen 0.76 Methane 53.91 Ethane 14.20 Propane 9.64 Iso Butane 1.25 Normal Butane 4.29 Iso Pentane 1.12 Normal Pentane 1.87 Hexane 2.72 Heptanes + 10.11 hloleculal. Weight of Heptanes + 178.50

Jan 1, 1951

R. W. Raymond, New York, N. Y,:—Since the presentation of my note on this subject at the New York Meeting, Professor Louis has pointed out an error in my statement of his conception of " pitch "—namely, he understands the pitch, in the restricted sense which he proposes, to be the angle of inclination of the axis of an ore-body, measured on the vertical plane drawn through the body; whereas, I represented him as proposing to define " pitch " as the angle of inclination of an oblique body, measured on the plane of the dip, in the direction of the strike. The difference will appear upon consideration of the accompanying isometric projection, Fig. 1, in which ABCD represents the plane of the inclosing ore-deposit (vein or bed), and AC the axis of the oblique ore-shoot. ABE is the angle of the dip, as universally understood; and ACE

Jan 1, 1909

By Thomas Cox

The following compilations are made from a series of investigations and are used to present the subject in an unbiased manner, as the writer does not represent any company or financial interest. The present situation is complex. The producers are hard pressed by reason of the low price of crude, while the independent refiner is little better off, because of the corresponding cut in price of refined products, except on occasional contracts. If the real costs are analyzed, it will be seen that the land speculators and the lessors—royalty owners—make the larger profits and not the struggling legitimate operator or independent refiner. The present-day (October, 1922) posted prices per barrel for crudes are Kansas, Oklahoma, Mexia, Gulf Coast, and Louisiana..... $1.25 Healdton............................................. 0.75 Northern Texas and Central Texas...................... 1 . 50 Pennsylvania......................................... 3.00 Wyoming, Elk Basin.................................. 1.25 Wyoming, Salt Creek................................ 0.70 California Base..................................... 0.60 These prices are at the well. In addition, crudes must be gathered and transported to refinery (by pipe line or tank cars), refined, and the refined products marketed. These crudes are of various gravities, ranging within a narrow margin for each field or district, so that averages are not difficult to deduce, and it is these averages that really determine the average operating conditions. In order to show the present realizations, the prices and costs now obtaining are listed against the average yields; the figures are also adjusted VOL. urn.----71

Jan 1, 1923

By Thomas Cox

The following compilations are made from a series of investigations and are used to present the subject in an unbiased manner, as the writer does not represent any company or financial interest. The present situation is complex. The producers are hard pressed by reason of the low price of crude, while the independent refiner is little better off, because of the corresponding cut in price of refined products, except on occasional contracts. If the real costs are analyzed, it will be seen that the land speculators and the lessors—royalty owners—make the larger profits and not the struggling legitimate operator or independent refiner. The present-day (October, 1922) posted prices per barrel for crudes are Kansas, Oklahoma, Mexia, Gulf Coast, and Louisiana..... $1.25 Healdton............................................. 0.75 Northern Texas and Central Texas...................... 1 . 50 Pennsylvania......................................... 3.00 Wyoming, Elk Basin.................................. 1.25 Wyoming, Salt Creek................................ 0.70 California Base..................................... 0.60 These prices are at the well. In addition, crudes must be gathered and transported to refinery (by pipe line or tank cars), refined, and the refined products marketed. These crudes are of various gravities, ranging within a narrow margin for each field or district, so that averages are not difficult to deduce, and it is these averages that really determine the average operating conditions. In order to show the present realizations, the prices and costs now obtaining are listed against the average yields; the figures are also adjusted VOL. urn.----71

Jan 1, 1923

By Luther Lennox

DURING the last few years, one of the great problems in the milling of all ores has been that of crushing. This subject involves not merely the cost of the operation, but also the selection of the proper degree and character of crushing to yield the best metallurgical results on the given ore. Considering the diversity of machinery, one is led to wonder at the variety of crushing methods employed, even when realizing that metallurgy demands varying products. In an attempt to investigate the relative crushing resistances of a number of ores now being milled in this country and Alaska, the management of the Portland mills requested samples of average mill-run of ore from various companies. The request met with a ready response, indicating the desire of all operators to gain information on the subject. The difficulties involved in this investigation were numerous, lack of time for outside problems during this strenuous period being a serious one. Also, we were unable, in the time, to obtain a correct 150-mesh . screen; in the screen analyses tabulated and plotted herewith, the 150 mesh screen was used merely to protect the 200-mesh screen, not to ascertain points on the curves.

Jan 8, 1918

By M. G. F. Söhnlein

In the earlier clays, these ores were treated by chloridizing-roasting followed by amalgamation, with satisfactory results, according to the information now available. Material from old tailing dumps from ore treated by this process, which are found at several places in the vicinity of Oruro, seldom contains more than 5 to 6 oz. of silver per ton. As ore with less than 100 oz. per ton was not treated, the extraction of silver must have been good. Reports of the operating companies published about 1890 asserted that over 90 per cent. of the silver was recovered, but in these calculations, as a rule, no allowance was made for silver lost during roasting and the figure referred only to the extraction of silvcr by amalgamation from the roasted ore.

Jan 1, 1921

By P. A. Beck, A. Merlini

Quantitative texture determinations were made for rolled and for rolled and annealed strips of 3, 6, and 10 pct Zn brasses. The main components of the rolling texture gradually shift over a wide composition range from the orientation characteristic of copper to that of 70-30 brass. At least the main features of the corresponding gradual changes in the annealing texture may be accounted for qualitatively on the basis of the oriented growth theory of annealing textures. All the oriented nucleation-type theories are notably less successful in accounting for the observed textures. EARLIER investigations by von Goeler and Sachs,' Dahl and Pawlek,' and Brick, Martin, and Angier" suggested that the annealing texture of copper is more sensitive to the addition of solute elements than the rolling texture. It was reported3 that the cube texture changes over into a brass-type recrys-tallization texture on addition of about 1 pct Zn, while the deformation texture changes only at about 5 pct Zn. Such behavior would be difficult to reconcile with any theory of annealing texture formation that relates the annealing texture to the deformation texture. In particular, the oriented growth theory of the cube texture" is based on a certain orientation relationship between the cube texture and the main components of the deformation texture which could not be reconciled with the reported behavior of low brasses. It was, therefore, of interest to re-examine these textures by means of the quantitative methods now available. The deformation and annealing textures of rolled a brasses with approximately 3, 6, and 10 pct Zn have been determined in terms of (111) and (200) pole figures. Experimental Methods The chemical analyses of the Cu-Zn alloys of commercial purity used in the present work are given in Table I. Chill-cast bars of the tabulated compositions were rolled and annealed according to the following schedule: I—rolling from 1.2 to 1.02 in. thickness, 15 pct reduction area, annealing 15 min at 450°C; 2— rolling from 1.02 to 0.867 in. thickness, 15 pct reduction area, annealing 15 min at 450°C; 3—rolling from 0.867 to 0.600 in. thickness, 31 pct reduction area, annealing 2 hr at 540°C; 4—rolling from 0.600 to 0.400 in. thickness, 33 pct reduction area, annealing 2 hr at 480°C. In the final straight rolling of 96.25 pct reduction area, the strips were reversed end to end after each pass. The final annealing temperature was determined for each alloy by annealing specimens of the cold-rolled strips in salt bath for 5 min at varying temperatures. The results of the hardness measurements are given in Fig. 1, where the final annealing temperature used for each alloy in determining the annealing texture is indicated by a cross.

Jan 1, 1956

By John Hays Hammond

This is an era of " expansion; and, conformably with the change in commercial conditions, the function of the mining engineer, as well as that of his confreres in many other professions, has also expanded. From the position of an engineer, limited to the determination of technical questions, the engineer of to-day has come to assume an economic importance in those branches of industry dependent upon engineering skill for their development. He is indeed an engineer of limited usefulness who does not go further professionally than to submit a purely technical report on subjects presented for his consideration. While he has the same responsibility as formerly in the solution of the technical problems involved, he is further expected to supplement his report with advice on the financial and commercial aspects of these problems. For the great majority of problems presented to the engineer ultimately involve the determination of the pecuniary, relations of the propositions under consideration. The great corporation lawyer no longer earns his fee by merely submitting his opinion as to the legal issues involved in law-suits affecting the corporation; he now assumes charge of the entire legal work, including both the organization of the corporation and the maintenance of its legal status thereafter. In like manner, the engineer, whose report was, as I have said, formerly confined to the determination of the geological and other cognate features of a mining enterprise, is now expected, not. only to embody information on these subjects in his report, but also to give his opinion whether the property offered for sale in pursuance of such an enterprise is worth the price asked for it. Moreover, if he recommends the purchase of a property, he incurs a certain moral responsibility for its efficient manage-

Nov 1, 1908

By C. C. Bailey

Part I Problems of Mine Financing Directed primarily at the methods and problems of financing domestic mining ventures-projects involving one or more of the stages: exploration, development, commercial operation.

Jan 6, 1953

By Roswell H. Johnson, W. E. Bernard

To know the rate of declinc of oil wells is very important, yet ordinarily we are prevented from getting this rate because the oil from several wells is put into one or a few tanks as soon as the wells have been connected to the power. The object of doing this is economy of tanks, pipes, labor, and accounting. But we are making a great sacrifice for this small economy. The advantages of the individual records are that we would know better: 1. When the well has ceased to be profitable. 2. When a well has gotten into bad condition. 3. The real record of the yield per acre and the rate of decline of the wells. The lease total is too mixed as to age of the wells for existing records to have much significance. To obtain such individual well records and more accurate logs are the great desiderata of satisfactory management of oil properties. 4. Which wells show the slowest decline—information which is valuable in locating new wells or purchasing adjoining leases. The truth of this statement is evident, when we reflect upon the large number of purchases of producing property. Intelligent appraisal is of the utmost advantage and it is impossible without individual well-pro-

Jan 1, 1918

By David B. Scott

The Mogollon mining district, New Mexico, has received little public attention, although for 15 years it has been the leading silver producer of the state; it is situated in a region remote from the principal lines of travel, and its activities have usually been limited to the operations of two or three companies. The value of the total production of the district in the 44 years of its history has been estimated at $15,000,000. For the years 1904 to 1917, inclusive, the output was: gold, $4,370,000; silver, 10,042,000 oz.; copper, 874,862 lb.; total value, approximately $10,500,000. In 1913 the district contributed 80 per cent. of the total silver production of New Mexico, but in 1917 only 41 per cent., due to serious interruption in the operations of the leading producer. Since 1914 the silver output has diminished one-half, and the present high value of silver is nearly offset by the increase in cost of production. The output of gold has rarely exceeded 35 per cent. of the total for New Mexico. The ratio of silver to gold, by weight, has averaged 46:1 based on the whole output of the district. Location and Topography The town of Mogollon is 75 mi. (121 km.) by a poorly located highway ,. from the nearest railroad terminals, at Silver City and Tyrone. All supplies are transported by motor trucks and teams. The area, sometimes called the Cooney Mining District, lies on the western flank of the Mogollon Mountains, which occupy the western part of Socorro County. The elevations drop steeply on the west to the valley of the San Francisco River, adjacent to the Arizona boundary. The topography is very rugged, the whole area being sharply dissected; deep canyons with steep gradients and rugged walls are characteristic of the whole western slope of the Mogollon Range. The main canyons i run east and west, and usually maintain a flow of water during the entire year. As would be expected in a region of such deep dissection, the mines are generally dry. The mountain ridges between the canyons have altitudes varying from 7000 to 10,000 ft. (2130 to 3050 m.) and drop sharply, on their western face, to the floor of the San Francisco Valley at an elevation of 5000 ft. (1525 m.). Erosion has been rapid, and the

Jan 1, 1920

Jan 4, 1950

By Jack White

W. I. Garms-—The authors state that when they added 11 tons of balls to the 45 pct volume ball load, the power needle did not budge. The question arises as to whether any increase in capacity accompanied the 11-ton addition. It is hardly conceivable that all of the balls making up the l l-ton addition were sterile. However, as the work done in the ball mill is not by kilo-watthours per se or balls per se but by kilowatthour-balls, it is possible that the kilowatthourballs in the mill before the ll-ton addition had a different amperage, voltage or robustage than those in the mill after the addition and that the overall outcome was that equal work was done before and after the addition. The authors can keep the efficiency that they got with the 45 pct volume 1-in. ball charge and get additional capacity by putting more kilowatthourballs to work in the form of the addition of 11 tons of 2-in. balls to the present ball charge, and subsequent makeup additions by weight of 20 pct 2-in. balls and 80 pct 1-in. balls. J. F. Myers (authors' reply)-—Mr. Garms points his finger at the 11 tons of "sterile" balls added to the Tri-cone mill. A fact so interesting to us that we felt it should be reported. Clearly, ball slippage at the existing mill speed prevented any further transfer of power from the shell to the ball mass. We agree that the kilowatthourballs would increase, were we charging rough 2-in. balls as suggested by Mr. Garms. The assumption is, of course, that we would get a corresponding increase in work done. Our reported data (CIME meeting, Vancouver, 1946) shows a gain of work accomplished of 7.6 pct as we decreased the ball size from 2 in. to 1% in. and a further gain of work accomplished of 2.1 pct when we went from 1 % in. to 1 in. The small ball results reported by H. R. Banks at Chapman Camp are also very convincing. In the case of 2-in. balls they would take the conventional ball path and start cascading. They would thus destroy the classifying pool over the "foot" of the

Jan 1, 1951

By Jack White

W. I. Garms-—The authors state that when they added 11 tons of balls to the 45 pct volume ball load, the power needle did not budge. The question arises as to whether any increase in capacity accompanied the 11-ton addition. It is hardly conceivable that all of the balls making up the l l-ton addition were sterile. However, as the work done in the ball mill is not by kilo-watthours per se or balls per se but by kilowatthour-balls, it is possible that the kilowatthourballs in the mill before the ll-ton addition had a different amperage, voltage or robustage than those in the mill after the addition and that the overall outcome was that equal work was done before and after the addition. The authors can keep the efficiency that they got with the 45 pct volume 1-in. ball charge and get additional capacity by putting more kilowatthourballs to work in the form of the addition of 11 tons of 2-in. balls to the present ball charge, and subsequent makeup additions by weight of 20 pct 2-in. balls and 80 pct 1-in. balls. J. F. Myers (authors' reply)-—Mr. Garms points his finger at the 11 tons of "sterile" balls added to the Tri-cone mill. A fact so interesting to us that we felt it should be reported. Clearly, ball slippage at the existing mill speed prevented any further transfer of power from the shell to the ball mass. We agree that the kilowatthourballs would increase, were we charging rough 2-in. balls as suggested by Mr. Garms. The assumption is, of course, that we would get a corresponding increase in work done. Our reported data (CIME meeting, Vancouver, 1946) shows a gain of work accomplished of 7.6 pct as we decreased the ball size from 2 in. to 1% in. and a further gain of work accomplished of 2.1 pct when we went from 1 % in. to 1 in. The small ball results reported by H. R. Banks at Chapman Camp are also very convincing. In the case of 2-in. balls they would take the conventional ball path and start cascading. They would thus destroy the classifying pool over the "foot" of the

Jan 1, 1951

By H. B. Heller, T. J. LaChapelle

Phosphorus nitride has been used as a diffusant for introducing phosphorus into silicon under various conditions. It has a temperature -dependent rate of decomposition beginning in the 500°C range, increasing very rapidly above 1000 C, producing gas -eous phosphorus and nitrogen. Best control was obtained with a two-temperature arrangement, with silicon at the proper higher diffusion temperature. It is an easier compound to use than the usual P2O5 because it is nonhygroscopic and yields temperature-controlled surface concentrations together with excellent final surfaces. Surface doping nearly as high as that produced by phosphorus pentoxide has been observed for sources at 850" to 900°C. Reproducible high sheet resistances were obtained by using slow flow rates (1 linear in. per min) and staggered-baffle gas mixing with the nitride at 550°C. Both inert gas (argon, nitrogen) and oxidizing ambients have been examined. Oxygen reacts to produce anhydrous P2O5, consuming the source at a rapid rate. Nitrogen, except for short diffusion times, suppressed the dissociation reaction and sometimes produced inferior surfaces. Argon appears to be a more useful ambient. PHOSPHORUS is a common impurity atom which may be introduced into a semiconductor lattice to create a p-n junction or an nn contact region. Various investigators1-4 have described techniques which can be used with either elemental phosphorus or certain of its compounds. This paper discusses a newly available compound of phosphorus, phos- some processes silicon wafers are precoated with a phosphate glass which acts as the doping source. Although a nonoxidizing form like elemental phosphorus or a phosphine can be used, most diffusion methods usually involve the use of phosphorus pentoxide. Because of the rapid volatility of this compound, a two-step process is often used, combining a gaseous deposition to introduce a predetermined quantity of phosphorus into the silicon with a later redistribution to obtain the desired distribution and surface concentration. Such a process usually involves predepositing phosphorus at surface concentrations greater than 1020 cm-'. At such doping levels the phosphorus-diffusion coefficient appears to be strongly concentration-dependent.596 Distribution profiles5'9 for these high concentrations of phosphorus do not follow Fick's laws, having extended subsurface regions which appear electrically to be nearly uniformly doped with ionized impurity atoms. Radioactive-tracer experiments also show near-surface anomalies in the distribution profile. Additionally, it has been shown1' that the introduction of very high surface concentrations of impurity atoms into silicon (a step necessitated by the subsequent lowering of concentration during the redistribution) creates dislocations, even in material having no dislocations originally. For device fabrication the use of oxide masking introduces certain difficulties and limitations.7'8 The standard practice of using phosphorus pentoxide as an impurity source adds other problems to these because of the speed and ease with which this compound reacts with moisture present in any gas in contact with it. In fact, P2O5 is one of the fastest and most effective drying agents for gases. Because it is such an excellent desiccant, completely anhydrous phosphorus pentoxide is difficult to obtain and is even more difficult to keep dry. Adequately dry gloved boxes must be used for storage and transfer of the chemical. The presence of even traces of moisture will cause formation of phosphoric acids which, during the high-temperature diffusion, results in polyphosphoric acids of variable composition. Such reaction by-products end up as gradually accumulating viscous fluids in the cooler parts of the diffusion furnace. The calculation of the final solute distribution for

Jan 1, 1964

[†AARONSON, ALFRED E., Vice-Pres., Mid-Co. Petroleum Co., Mid-Co. Bldg. Tulsa, Okla. '18 ABADIE, EMILE R., Min. Engr Address wanted. '76 ¦ABADILLA, QUIRICO A. Geol. Dept. Cia. Mexicans de Petroleo "El Aguila," S. A., Edifico "El Aguila," Esq., Calles Aurora y Comercio,] [ ]

Jan 1, 1925

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