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By Morris Muskat

A general theory has been developed for the effect of permeability stratification on the efficiency of the gas-injection phase of cycling operations. It has been applied to three special types of permeability variation; namely, exponential, probability, and linear. In the case of the exponential permeability distribution the effect of areal pattern sweep efficiency was also taken into account. The exponential permeability distribution can be characterized by the ratio of the maximum to minimum permeability, which has been termed the stratification constant. Curves were calculated for the variation in total wet gas recovery and total gas throughflow, to give that recovery to various abandonment limits of the wet gas content in the produced gas, as a function of the stratification constant. The cumulative wet gas recovery decreases monotonically as the stratification constant increases and is generally higher at the lower values of the wet gas content abandonment limits. The total gas throughflow first rises to a maximum as the stratification increases, and then ultimately declines. The effect of the areal sweep pattern efficiency is relatively minor as compared to that of the stratification constant, except in the region of low values of the latter where the formation is substantially uniform. The probability distribution can be characterized by a "variation" parameter varying from o to I as the formation changes from strict uniformity to extreme variability. The curves of total wet gas recovery and total gas throughflow to different abandonment limits of wet gas content versus the variation parameter have the same general characteristics as for the exponential permeability distribution. In the linear permeability distribution the ratio of maximum to minimum permeability also serves as a stratification constant index defining the distribution. The curves of total wet gas recovery and gas throughflow to fixed abandonment limits versus the stratification constant are similar to those for the exponential permeability distribution. However, for the higher values of the stratification constant the recoveries and throughflows do not asymptotically fall to o as in the latter, but approach constant values determined by the abandonment limit of wet gas content in the produced gas. Introduction It is becoming generally recognized that one of the most important factors determining the economic feasibility of cycling operations is the areal continuity and permeability distribution of the producing formation. While the effects of areal variations in permeability, porosity, thickness, and well pattern on the sweep efficiency can be evaluated by electrical model studies,' those due to permeability stratification require separate treatment. Several studies have been reported2,3 on the' influence of permeability variations on the wet gas recovery by cycling. In these, however, discontinuous permeability variations either have been assumed explicitly, or the analysis has been carried through as if they were discontinuous. While, in fact, the actual permeability profiles will undoubtedly be discontinuous, recent develop-

Jan 1, 1949

By J. PARKCEH CHANNING

Discussion of the paper of Lewis T. Wright, presented at the New Haven meeting, February, 1909 (Trans., xl., 492 to 495). J. PARKE CHANNING, New York, N. Y. (communication to the Secretary*):-Mr. Wright, in his introductory paragraph, says: " It is commonly believed by metallurgists that in copper-smelting, the copper in the slags, which is irreducible by continued smelting, is retained in the form of 'prills' of matte." On a recent visit to Greenwood, B. C., I was discussing with J. E. McAllister, the general manager of the British Columbia Copper Co., and the former metallurgist of the Tennessee Copper Co., this very question; and he held strongly to the idea that the copper in slag was in two forms-one portion contained in occluded matte and the other as an oxide. He believed that this same rule would apply to the silver in the slag. From my experience I am strongly inclined to agree with Mr. McAllister; and it appears quite reasonable that in furnaces treating oxidized copper-ores, and to a less degree in furnaces treating sulphide ores, there is always bound to be present a certain amount of copper oxide and silver oxide, which will behave like any base and get into the slag as such. We all know that in Arizona, in the early days, when it was customary to produce black copper, because the ores were nearly all oxidized or carbonates, and sulphur was scarce, the slags as a rule carried 2.5 per cent. of copper and seldom ran less than 1.5 per cent. of copper. The economic point was determined by the extra coke necessary to produce the reducing action. In connection with the extra saving in copper, Arthur L. Walker, now professor of metallurgy at Columbia University, and formerly general manager of the Old Dominion Copper Mining Co., at Globe, told me that with coke at $60 per ton it never paid him to make slags containing less than 2.5 per cent. of copper. *Received Oct. 8, 1909.

Feb 1, 1911

By Albert D. Brokaw

THE accompanying chart was devised to provide a rapid and simple method of correcting for temperature and compressibility (deviation from Boyle's law) of gas under relatively high pressures and temperatures, such as are encountered in many deep reservoirs. The chart was prepared by interpolating for the desired values in the experimental data of Burke and Keyes1 and Kvalnes and Gaddy2 on the compressibility of methane, after adjusting their results from 0°C. to 60°F. and combining the correction factors for compressibility and temperature into a single multiplier, which, applied to the product of pressure and reservoir volume, gives at once the volume at one atmosphere (14.7 lb. per sq. in. abs.) and 60°F. The relationship 0f this multiplier to the compressibility factor Z, as used in most discussions, is simply: [Multiplier = 460° + 60°ZT –] where Z is the compressibility factor and T the absolute temperature (Rankine). Fahrenheit temperatures are shown on the vertical axis and pressures in pounds per square inch absolute on the horizontal axis. Correction factors or multipliers at intervals of 0.05 from 0.55 to 1.40 have been plotted on the chart and are calculated t0 give volume of gas at one atmosphere pressure (14.7 lb.) and 60°F. The operation is as follows: The reservoir volume, times the number of atmospheres pressure, times the multiplier, gives the volume of gas measured at one atmosphere (14.7 lb. per sq. in.) and 60°F. For example, a reservoir is estimated to have a volume of 10,000,000 cu. ft., bottom-hole pressure is 2940 lb. per sq. in. and temperature is 184°F To make the correction for methane, follow the 184° line horizontally to the 2940-lb. pressure line. The intersection lies between the 0.85 and 0.90 correction lines, and by interpolation we may estimate the multiplier at 0.863. The computation is simply: [ ] Using the chart for methane prepared by Prof. G. G. Brown3 and his associates, the multiplier is found to be 0.867. Details 0f computation are as follows: Correction factor to apply to PV to correct for deviation from Boyle's law and adjust to measurement basis of 60°F.: [ ]

Jan 1, 1941

By W. E. Bron, E. S. Machlin

GRAIN boundary migration in V-shaped thin specimens of high purity silver was studied. Each specimen contained two crystals having the relative orientation: (111)A/(111)B; (ll0)A/(101)B. The boundary between these two crystals varied between a continuous curved and an alternating two plane interface. The plane interfaces were oriented parallel to (101)A/(011B) and (121)A/(211)B. Traces of these planes are shown in Fig. 1. Evidently the two plane interface, although of higher area, comprises lower total interface energy than the average curved boundary it replaced. The plane boundaries were found to move at 650 °C to consume the broad segment of the V opposite to the direction of interface area and energy decrease. On investigation, using the thermal etching technique of Hendrickson and Machlin,1 it was found that the outer grain contained 8.3x108 more dislocations per cm" than the grain at the apex of the V. Consequently, the boundary moved to decrease the strain energy associated with the difference in dislocation density across the boundary. The rates of motion of specific {110} and {112} boundaries were measured during interrupted anneals at 650°C by referring the position of the boundaries to each other and a fiducial line on the specimen surface. The measured rates of motion are 0.075 and 0.025 mm per hr for the {110} and {112} boundaries, respectively. Plots of grain boundary motion vs time of annealing show straight lines with little deviation of data points from these lines.

Jan 1, 1957

SME Membership Directory Listings of record March 31, 1072 SOCIETY OF MINING ENGINEERS OF AIME

Jan 7, 1972

By Kalervo Rankama

UNTIL a few years ago, geological mapping, the study of ore boulders, and different geophysical methods were the principal means used in the systematic search for mineral deposits covered by a layer of disintegration products or soil. These methods have been developed to a high stage of perfection as far as the geometrical definition of the conductor is considered. Use of geophysical methods in prospecting is based on the fact that an ore body differs from the country rock not only geologically but also in its physical properties. The general drawbacks and complications included in the use of geophysical methods are well known to everyone who has been using them, so need not be entered into here in detail. One of the more important ones is the fact that geophysical methods are unable to furnish information concerning the chemical composition of the ore bodies responsible for the indications. Further, the ores of many metals, such as silver, gold, beryllium, zinc, mercury, tin, lead, vanadium, antimony, chromium. molybdenum, tungsten, manganese, cobalt, nickel, and the platinum metals cannot be directly located by known geophysical methods, owing to lack of physical characteristics suitable for distinguishing them from the country rock. Thus it is quite natural that efforts have been made to develop direct methods for prospecting and locating ore bodies of the elements named. Known as chemical, biogeo-chemical, and geobotanical methods of prospecting, these have been much improved during recent years. A brief review of these methods and of some results obtained with them will be presented in the following, on the basis of available information and my own experience.

Jan 1, 1947

By Shiou-Chuan Sun

DISCUSSION shiou-chuan sun (author's correction) - Too late for revision, the author realized that the data on stability of froth presented in this paper were not based on the same height of froth column. It is recommended herein that the stability of froth is better calculated by dividing the time elapsed until the froth disappeared by the volume (in cu cm per sq cm) or height of the froth column, and is expressed in sec per cm. The stability data in Tables I, II, and III of this paper were recalculated, in accordance with this recommendation, and the results are shown respectively in the accompanying Tables VII, VIII, and IX. Compared with Tables I, II, and III of the paper, the stability data of Tables VII, VIII, and IX are more reliable in disclosing the persistence of froth of various frothers having different frothabilities. For example, the conclusion given in the paper that the stability of froth is generally proportional to the volume of froth becomes invalid when the stability of froth is expressed in sec per cm, as shown in Tables VII, VIII, and IX. Table VII shows that both the stability and volume of froth increase with the addition of small amounts of n-hexyl alcohol, and that further additions of n-hexyl alcohol decrease the stability but increase the volume of froth. Table VIII indicates that the stability of different types of frothers is governed by their chemical composition and is difficult to predict from their frothability. Table IX shows that the stability of different frothers with similar nonpolar groups tends to increase with a decrease of the hydro- philic property of their polar groups, and consequently with the decrease of their solubilities. This is further substantiated by the fact that the stability of frothers, as listed in Table IX, is generally lowered by the solvent effect of absolute ethyl alcohol. Table IX shows also that the stability of froth tends to increase with the decrease of the volume of froth* provided the frothers used have similar nonpolar groups and dissimilar polar groups.

Jan 1, 1953

By Shiou-Chuan Sun

DISCUSSION shiou-chuan sun (author's correction) - Too late for revision, the author realized that the data on stability of froth presented in this paper were not based on the same height of froth column. It is recommended herein that the stability of froth is better calculated by dividing the time elapsed until the froth disappeared by the volume (in cu cm per sq cm) or height of the froth column, and is expressed in sec per cm. The stability data in Tables I, II, and III of this paper were recalculated, in accordance with this recommendation, and the results are shown respectively in the accompanying Tables VII, VIII, and IX. Compared with Tables I, II, and III of the paper, the stability data of Tables VII, VIII, and IX are more reliable in disclosing the persistence of froth of various frothers having different frothabilities. For example, the conclusion given in the paper that the stability of froth is generally proportional to the volume of froth becomes invalid when the stability of froth is expressed in sec per cm, as shown in Tables VII, VIII, and IX. Table VII shows that both the stability and volume of froth increase with the addition of small amounts of n-hexyl alcohol, and that further additions of n-hexyl alcohol decrease the stability but increase the volume of froth. Table VIII indicates that the stability of different types of frothers is governed by their chemical composition and is difficult to predict from their frothability. Table IX shows that the stability of different frothers with similar nonpolar groups tends to increase with a decrease of the hydro- philic property of their polar groups, and consequently with the decrease of their solubilities. This is further substantiated by the fact that the stability of frothers, as listed in Table IX, is generally lowered by the solvent effect of absolute ethyl alcohol. Table IX shows also that the stability of froth tends to increase with the decrease of the volume of froth* provided the frothers used have similar nonpolar groups and dissimilar polar groups.

Jan 1, 1953

By J. R. Martson

The arrangement of the larger furnace at the United Verde smelter, together with the boiler layout and connecting flues, is shown in Fig. 1. The important dimensions are given in the figure, and cross-sectional areas of combustion space, flues, etc., are recorded. The location and extent of the baffling in the boilers also are shown because of their importance in the interpretation of the data. Two boilers serve each reverberatory furnace. They are of the class M-26 Stirling type (rated at 713 boiler hp. each). Steam is generated at 178-lb. gage pressure at a total temperature of 528" F., from feed water at a temperature of 113" F. The feed water is condensate from turbogenerators plus make-up softened by the lime-soda process. The make-up is rather large in amount as it must match the amount of steam consumed in reciprocating blowing engines and the like, which are not served by surface condensers. As a result the boiler feed water has a hardness of 1.5 to 3.0 grains per gallon, but this results in the formation, during six months to one year of boiler operation, of scale only of "eggshell " thickness or less. The boilers are set at the same elevation as the tapping floor of the furnace, which results in the introduction of the waste-heat gases at the top of the front bank of tubes and necessitates the inversion of the usual baffling arrangements. The boilers are equipped with valve-in-the-head soot blowers, which keep most of the dust blown off the surface of the tubes, but it is necessary to supplement the soot blowers by high-pressure air lances, inserted by an attendant through side doors in the boiler setting. Deposits of coal ash and of dust from the furnace charge accumulate in the flues between the reverberatory furnaces and the boilers and this necessitates cleaning of these connecting flues by hand during the greater part of one of the three 8-hr. shifts during each 24 hr. This cleaning operation requires the opening of clean-out doors, which, of course, has some effect on the yield of steam. Revebberatory Furnace Practice The United Verde furnaces are fired with pulverized coal of sub-bituminous type of which the screen and chemical analyses are given in Table 1.

Jan 1, 1934

By H. Landssberg

Subsidence caused by mining operations has been a matter of interest for the mining engineer for just 111 years, since the Belgian committee for study of subsidence in the city of Liege submitted its first report in 1825. This interest is fairly expressed in the enormous amount of literature that has since appeared on this subject. A bibliography, probably far from being complete, which preceded this study as a preliminary survey, comprises more than 800 titles. In spite of this fact the problem remains today as acute as it has ever been. The questions of as good a recovery as possible of the national resources, the safety of the operations, and the protection of private and public property are the important angles from which to look at the problem. The Problem To systematize an investigation regarding the effects of mine excavations two different aspects have to be dealt with: (1) the subsidence of the immediate roof above the workings, affecting the safety of the workers and the progress and efficiency of the operations; (2) the subsidence of the surface, which is also, from the point of time, the second event. The immense importance of surface subsidence as regards the impairment of surface structures of every kind in a mining area is self-evident. Both effects result from reactions of the strata overlying the excavations and they depend mainly on the extent of the excavations and the structure and geological condition of the strata. It has been stressed repeatedly, in this country principally by G. S. Ricel,† that for the understanding of the phenomenon of subsidence accurate surveys are the most urgent necessity. In the past, however, at least in the normal course of mining operations, these surveys have been very crude. The control of the roof in the mine is left to the observation of the behavior of the timber, warning cracks and sounds in roof and walls and to the general judgment and experience of the worker and his supervisors. In any given case this may or may not be sufficient to prevent fatalities but certainly it does not give any accurate information as to what is happening in roof and strata. On the surface, principally in endangered areas, surveys have been conducted more frequently, but also in this case usually weeks or even

Jan 1, 1936

By H. Landssberg

Subsidence caused by mining operations has been a matter of interest for the mining engineer for just 111 years, since the Belgian committee for study of subsidence in the city of Liege submitted its first report in 1825. This interest is fairly expressed in the enormous amount of literature that has since appeared on this subject. A bibliography, probably far from being complete, which preceded this study as a preliminary survey, comprises more than 800 titles. In spite of this fact the problem remains today as acute as it has ever been. The questions of as good a recovery as possible of the national resources, the safety of the operations, and the protection of private and public property are the important angles from which to look at the problem. The Problem To systematize an investigation regarding the effects of mine excavations two different aspects have to be dealt with: (1) the subsidence of the immediate roof above the workings, affecting the safety of the workers and the progress and efficiency of the operations; (2) the subsidence of the surface, which is also, from the point of time, the second event. The immense importance of surface subsidence as regards the impairment of surface structures of every kind in a mining area is self-evident. Both effects result from reactions of the strata overlying the excavations and they depend mainly on the extent of the excavations and the structure and geological condition of the strata. It has been stressed repeatedly, in this country principally by G. S. Ricel,† that for the understanding of the phenomenon of subsidence accurate surveys are the most urgent necessity. In the past, however, at least in the normal course of mining operations, these surveys have been very crude. The control of the roof in the mine is left to the observation of the behavior of the timber, warning cracks and sounds in roof and walls and to the general judgment and experience of the worker and his supervisors. In any given case this may or may not be sufficient to prevent fatalities but certainly it does not give any accurate information as to what is happening in roof and strata. On the surface, principally in endangered areas, surveys have been conducted more frequently, but also in this case usually weeks or even

Jan 1, 1936

By W. F. Mattes

The manufacture of steel rails in the United States upon a large scale may be roughly dated from the years 1875-76, and the same years witnessed an active movement among the railroads toward the adoption of heavier and improved patterns. In this movement each road was a law unto itself, and the "personal equations " of some scores of engineers were so freely injected into the calculations that patterns were multiplied in the most absurd and mischievous manner, until at length the burden upon the mills became wellnigh unendurable, and called forth a vigorous protest in Mr. Holley's paper,* read before the Institute in February, 1881. There were then regularly manufactured in the various mills of the United States, no less than 119 different patterns of steel rails, subject to current order, of which 64 per cent. were embraced under five weights per yard. Commenting upon these and other figures there given, Mr. Holley stated as the primary object of his paper, " to show that,, while this multiplication of rail-patterns is an annoyance and an expense to rail-makers, it is a source of immense loss to railway companies." Since 1876 the increase in gross annual tonnage upon our leading lines has been very great, and has been accompanied by an increase of wheel-loads and running-speeds. As the average weight of the rails of 1876 was by no means excessive, the growing deman Is of traffic have slowly driven the roads toward stiffer sections, inaugurating a movement that now promises to become epidemic. In 1876 a 67-pound rail was a first-class equipment; to-day everything under 75 pounds is light, and many 80's are coming into use. European practice has long been heavier than ours; in part because the higher cost of sleepers has led to an average of 3-feet spacing, instead of two-feet as with us. The old 84-pound double-header, and Sandberg's 80- and 89-pound rails, respectively 51/4 inches and 591/2 inches high, are reported common on English roads; and he is strongly advocating the general adoption of the 100-pounder shown in Fig. 7, with what success I have not learned, except that the Belgian government has ordered a lot. Mr. Sandberg points out the undesirability of frequent changes of pattern, and the recent rapid growth in traffic-requirements; prognosticates a continuance of this

Jan 1, 1887

By R. H. Migliaccio, M. B. Kahle

The railroad haulage system was started at Kennecott's Bingham Mine in 1906 and has remained a prime mover of ore and waste for the succeeding sixty years. As the stripping ratios increased contract stripping on the upper levels of the mine was introduced employing truck and shovel methods. The ore production then was 90,000 tpd. Analysis of expanding the ore production to 108,000 tpd revealed that the increased ore production and continually rising stripping ratio would result in waste production requirements that exceeded the capacity of the rail haulage system above 6290 level. The advent of larger haulage trucks (65-100 tons) in the early 1960's made available to the Bing- ham Mine economic and operating factors which showed truck haul- age to be the best replacement for rail haulage on the upper levels of the mine. As part of that analysis it was concluded that company stripping would replace the contractor stripping in the top area of the mine.

Jan 7, 1973

By E. L. Claridge, K. S. Lee

Areal sweep efficiency of oil displacement by enhanced-viscosity water exhibiting pseudoplastic behavior was measured in a Hele-Shaw model representing one-quarter of a five-spot pattern. The pseudoplasticity of polymer solutions and the velocity distribution in the five-spot pattern produced a condition under which the mobility ratio between the displacing and the displaced fluid could not be assigned a single value. Instead, the movement of the displacement front is governed by local mobility ratios which are also time dependent. The areal sweep at breakthrough with polymer solutions was poorer than the sweep obtained with Newtonian fluids of comparable viscosity. However, the areal sweep at 1 PV throughput was greatly improved as compared to flood water without polymer. It was also demonstrated that, even after the oil-cut had declined to a low value during a regular waterflood, switching to polymer flood efficiently swept out the oil remaining in the model. INTRODUCTION The behavior of fluid displacements in isotropic porous media for various patterns of injection and production wells has been extensively investigated.1-7 These investigations all concerned Newtonian fluids, i.e., the viscosity of each fluid was constant regardless of flow rate. The generally unfavorable influence on areal sweep efficiency of higher mobility of the displacing fluid as compared to the mobility of the displaced fluid has been established for both miscible and immiscible fluids. The principle was also established that a close correspondence exists between miscible and immiscible flood front behavior,2, 3 although oil recovery in a waterflood at unfavorable mobility ratio may be less than that observed in a miscible displacement at the same mobility ratio. This is true even when oil recovery is expressed on the basis of movable oil. The reason is that oil saturation only slowly achieves its final value behind the water-flood front in accordance with the Buckley-Leverett8 simultaneous flow relations. It is convenient to use miscible displacements for laboratory simulation of waterflood frontal advance since the interfacial tension forces which are negligible in proportion to viscous forces on a reservoir scale9 are thus made nonoperative in the laboratory model. For miscible displacements, the Hele-Shaw type of model adequately represents a porous medium so long as the appropriate scaling rules5-10 are observed in its design and operation. During simulation of waterflood front behavior in the laboratory by using miscible displacements, the behavior of connate water may ordinarily be disregarded since it is usually indistinguishable from flood water in this process. However, when the flood water is deliberately thickened to improve the mobility ratio between water and oil. the effect on the sweep efficiency due to generation of a connate water bank during the process must be considered. In a uniform porous medium, such a bank is generated11 and efficiently displaced by injection of thickened water.l2 The oil originally in-place at the start of the waterflood is then displaced by connate water followed by thickened water. If the flood water must be thickened to obtain a favorable mobility ratio, the mobility of the oil phase is appreciably less than that of the connate water. Hence, the oil phase is inefficiently displaced by the connate water bank, and a considerable proportion of the oil comes in contact with and is displaced by the thickened waterflood front' A recent study 12 of five-spot displacements using miscible Newtonian fluids in which connate water banks of various sizes were simulated shows that, for connate water banks as large as 40 percent of 1 PV, major improvements in sweep efficiency resulted from use of a thickened

Jan 1, 1969

By C. D. Stahl, E. E. Templeton, R. F. Nielsen

It has been customary, in predicting saturation changes, to use the Leverett fractional flow formula", obtained by eliminating the unknown pressure gradient from the generalized Darcy equations for the separate phases. The formula presents difficulties in the case of counterflow, since the "fractional" flow may be negative, greater than unity, or, in the case of a closed system, infinite. Recently, it has been shown by several authors that the corresponding equations (with capillary pressure and gravity terms) for actual flow of the phase may be used just as well. These equations are in agreement with Pirson's1 statement that, if the two mobilities differ considerably from each other in a closed system, the flow is largely governed by the lower value. The present study was undertaken because of an apparent lack of experimental data on gravity counter-/low with which to test the theory. A 4-ft sand-packed tube in a vertical position was employed. Electrodes for determining saturations by resistivity were spaced along the tube, one phase being always an aqueous salt solution. Air, heptane, naphtha, or Bradford crude oil was used for the other phase. A reasonably uniform initial saturation was set up by pumping the phases through the system, alter which the tube was shut in and saturation profiles obtained at definite intervals. Cumulative flows over certain horizontal levels were obtained by integration of the distributions; hence, differentiation of the cumulative flows with respect to time gave instantaneous flow rates. To compare experimental and theoretical flow values, capillary pressures were assumed given by the final saturation-distribution curve. The upper part corresponds to the "drainage" region and the lower part to the "imbibition" region, where trapping of the nonwetting phase occurred. While calculations indicated that the capillary pressure saturation function and, probably, the relative permeability saturation functions changed during the segregation, the relation of the measured rates to saturation distributions are in general accord with the frontal-advance equation. It appears that the Darcy equations, as modified for the separate phases, are generally valid for counterflow due to density differences. The usual method of predicting saturation changes, which involves a continuity equation and the elimination of the unknown pressure gradient from the flow equations, should therefore be applicable. However, the need for advance knowledge of drainage and and imbibition "capillary pressures" and relative permeabilities during various stages presents difficulties. INTRODUCTION The present study was undertaken because of a seeming lack of experimental data relating to vertical counterflow of fluids of different densities in porous media. In particular, it was desired to determine whether data obtained from these laboratory tests were in accordance with certain mathematical treatments of counterflow which have been proposed. The gravity "correction" has been incorporated into the flow equations (and, hence, into displacement theory) nearly as long as both have been used. field4 and laboratory5 data have generally borne out the validity of the theory as applied, for instance, to downward displacement by gas, with all fluids moving downward. However, the modifications for counterflow have only recently been pointed out. 2-3 It has been customary to use fractional flow rates instead of actual flow rates in displacement calcuIations. In the case of counterflow, this results in negative values, values greater than unity and, when rates are equal and opposite, in infinite values. As pointed out by Sheldon, et a1,3 and by Fayers and sheldon,2 actual flow rates may be used just as well. The fact that these may be of opposite signs for the two fluids does not present any difficulty.

By Philip D. Anderson, Ralph Hultgren

Heat contents of extremely pure iron were measured over the range 300"to 1433"K, using a diphenyl ether calorimeter. Results from three samples containing widely differing impurities agreed with one another and with Previously reported results at higher temperatures (1184 ° to 1809°K) by Olette and Ferrier. From these data a table of heat contents of iron has been Prepared which is believed to be more accurate than those previously available. CP values have been derived which are consistent with these heat contents, with the best experimental Cp data, and with the thermodynamic conditions of equilibrium between bcc and fcc iron. The opinion is expressed that low-temperature extrapolations of presently known Cp values for y-Fe are not reliable. It would seem that the thermodynamic properties of iron, which is by far our most important metal, should have been well established long ago. This is not the case, however. As discussed by Olette and Ferrier,' there is objection to every earlier heat content measurement. While the best true Cp determinations agree well at temperatures below the Curie point, there is wide divergence at higher temperatures. Several investigators have examined available data and attempted to calculate thermodynamic functions for iron that are consistent with the two equilibrium temperatures of bcc and fcc iron. The two primary efforts were those of Austin' in 1930 and Darken and smith3 in 1948. The recommended values differ considerably; integration of Austin's Cp values leads to a heat content at 1100°K which is 300 cal per g-atom higher than the value recommended by Darken and Smith. The compilation of Fisher4 in 1949 was based on the selection of Austin. In 1956, Weiss and Tauer obtained yet another set of values by resolving Cp values into components due to dilation, lattice vibration, electronic excitation, and magnetism. The magnitude of contribution by each component and its dependence on temperature was estimated by semiempirical means. Their values are not self-consistent in that they do not form smooth curves when plotted vs temperature; moreover, their calculations cannot easily be repeated since they do not give the values of some of the parameters used. Clearly, experimental values for iron were in a most unsatisfactory state. The presently described measurements of the heat content of iron were therefore undertaken, covering temperatures as high as 1433°K. While the work was in progress, the high-temperature (1193" to 1789"K) heat content measurements of Olette and Ferrier' were published; in the region of temperature overlap the present results agree with Olette and Ferrier well within experimental accuracy. It is believed that the present results, combined with those of Olette and Ferrier, provide for the first time a reliable set of heat contents of iron from room temperature to the melting point. From these data, guided by available Cp measurements, it proved possible to derive Cp, entropy, and free energy function values for @-iron from room temperature to the melting point, and for y- iron in the temperature region of its stability. Exhaustive study led to the conclusion that extrapolations of y-iron functions to room temperature were not reliable enough to be useful; hence these have been omitted from the tables. EXPERIMENTAL Materials. Three samples of extremely high purity iron from different sources, containing widely different impurities, were measured. The first of these, designated "Chipman", was kindly supplied by Dr. K. K. Kelley of the U. S. Bureau of Mines from a lot which was made many years ago by Dr. John Chipman of the Massachusetts Institute of Technology. The second, designated6'Teddington", was supplied by the National Physical Laboratory, Teddington, England, from a lot zone-refined by them. The third sample, designated "Irsid", was supplied by the Institute de Recherches de la

Jan 1, 1962

By Frederic P. Dewey

(New York Meeting, February, 1912.) By the old method of determining platinum in ores and bullion, the silver-alloy first obtained in the regular course of assay is parted in strong sulphuric acid and the residual metal weighed. This is re-alloyed with silver by a second cupellation and parted in nitric acid, the residual metal being again weighed. Any difference shown between the two weighings is assumed to be, and is called; platinum. Sometimes it is so, and if any considerable amount of platinum be present, there will be a decided difference between the two weighings; but a slight difference is no real evidence whatever of the presence of platinum. On the other hand, the second weight may equal or possibly exceed the first, even when traces of platinum are present. Again, other members of the platinum group may go into solution in nitric acid more or less. If present, these would be called platinum and escape detection. The method does not provide any direct tests whatever as to the presence or absence of platinum. It is often indecisive, and sometimes jives erroneous results. It is, therefore, quite unsatisfactory. Being called upon many times to determine platinum in a wide variety of materials, particularly when present in very small amounts, I have realized the disadvantages and defects of this old method. In an article on the solubility of gold in nitric acid, 1 I have briefly outlined a method of gathering a little gold out of a solution containing much silver, which furnishes the basis of

Apr 1, 1912

By H. S. Price, J. C. Cavendish, R. S. Varga

This paper presents a new technique for solving some of the partial differential equations that are commonly used in simulating reservoir performance. The results of applying this technique to a simple problem show that one obtains accurate pressure values near wells, as well as accurate pressure pdients, which can be explicitly calculated. The method is completely rigorous in that convergence of the discrete numerical solution to the continuous solution for both pressure and pressure gradient is established. High-order, piecewise-polynomial approximations are used near the wells where pressure gradients are steep, while low-order, piecewise-polynomial approximations are used elsewhere to reduce greatly the calculation time. This combination is shown to give a uniformly good approximation to the solution. These approximations, obtained by using a Galerkin process with suitable Hermite subspaces, are shown to be theoretically and numerically superior to the usual approximations obtained from standard finite-difference techniques. Not only are much greater accuracies obtained, but computer times are also greatly reduced. The application of this technique to multiphase flow problems (e.g., single well coning problems) would have considerable practical interest, but such extensions of this technique with full mathematical rigor have not been made as yet. However, the numerical methods presented here are general, and in principle extend to multidimensional, multiphase flow. Moreover, the preliminary results given in this paper are sufficiently encouraging that we feel the effort in attempting these extensions is justified. INTRODUCTION The problem of obtaining accurate pressure distributions and pressure gradients around wells is of considerable importance in the numerical simulation of reservoir performance. The most common approach to solving this problem is to use finite difference techniques (see McCarty and Barfield9 or Peaceman and Rachfordl0). This approach, however, has many disadvantages, the major one being that many grid points are generally necessary for accurately describing the pressure distribution and the pressure gradient around wells. This need for a fine grid results in large computer times and often in prohibitively high costs. Besides investigating the method of finite differences, some authors, such as Welge and weber17 and Roper, Merchant and Duvall,13 have considered a combination of analytical and numerical techniques with some success. These approaches, however, are all nonrigorous and quite often cannot even be applied. In this paper, we present a numerical formulation of high-order accuracy, based on the Galerkin method, for solving this problem. We treat here only the partial differential equation that describes steady-state, single-phase flow. However, the methods presented are general and in principle extend to multidimensional, multiphase flow. Specifically we treat special cases of the problem in two dimensions described by: where G is a rectangle (with sides parallel to the coordinate axis) with boundary ?G, ?/?n denotes the outward normal, and y and B are non-negative constants such that y + B > 0.

Jan 1, 1970

By AIME AIME

The first Diesel-electric locomotives for the Mesabi iron range of the Lake Superior district were put into service last summer by the Oliver Iron Mining Co., U. S. Steel subsidiary. There were ten of these locomotives, rated 1000 hp. and weighing 125 tons each. They are designed for service from 16 to 24 hours per day to haul trains of loaded ore cars from open-pit mines, 200 to 400 ft. deep, on a two to eight-mile haul to the top of the pit. The locomotives push or pull the trains over switchbacks and up heavy grades with 5 per cent maximum against the load. High tractive effort, less smoke, and ability to negotiate sharp curves were among the reasons for the selection of Diesel-electric locomotives.

Jan 1, 1941

By Felix E. Wormser

REGISTRATION started bright and early Monday morning in the Silver Corridor at the Waldorf-Astoria with Mrs. W. H. Bassett as chairman. What a registration-over 200 ladies! Several joined us from as far away as California and Washington State. Apparently they enjoy our meetings so much that present travel inconveniences didn't discourage their coming. At noon the ladies joined the men at the All-Institute Luncheon and Monday evening we had our informal dance, which is separately reported. Tuesday morning was devoted to our annual meeting at which all Section annual reports were read. At noon we were all the guests of the W.A.A.I.M.E. at a luncheon at the Port Arthur Restaurant on Mott St. in Chinatown. Many of us rode down on the old 3d Ave. elevated railway-the last of four. It, too, is soon to be torn down. The luncheon was delightfully unusual, with huge dishes of delicious Chinese food on each table. Our chairman, Mrs. Read, who lived in China in her youth chose our menu, and she chose it well, for most of us indulged so heartily that as we arose from the table we felt we couldn't eat again for 24 hours. Someone donated sherry wine, and boxes of Chinese pencils as favors. We wonder who? All owe a big vote of thanks for this lovely party to Mrs. T. T. Read and Mrs. H. A. Prosser, chairmen, and Mrs. H. W. Hardinge, Mrs. R. Hursh, and Mrs. R. L. Lloyd, vice-chairmen.

Jan 1, 1944