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By J. B. Morrow

AMONG the most notable of Canada's many contributions to the personnel of the mining industry in the United States is J. B. Morrow, born in Halifax, Nova Scotia, April 9, 1886. Soon after completing his schooling at Dalhousie University in 1906 he emigrated to Arizona and Kew Mexico, via Cobalt and Larder Lake, Ontario. After preliminary experience in sampling and mucking he was employed by the Phelps Dodge Corp., first as chemist at the Copper Queen smelter, then, in 1908, with the Corporation's Stag Canyon coal branch at Dawson, N. M., in various capacities fro111 chemist to coke oven and coke department superintendent, and finally as general outside superintendent. While with Phelps he had some contact with the late Dr. Douglas, of whose industrial methods he has always been a great admirer.

Jan 1, 1937

By H. T. Byck

The plastering properties of six representative California drilling muds were studied over a temperature range of 70 to 175 F. at several mud weights, using a high-pressure circulating filter press with full size consolidated cores. In all tests, with untreated as well as with chemically treated muds, the filtration rates at elevated temperature were higher than at low temperatures and in nearly every case this increased filtration rate was notably larger than could be attributed alone to the decreased viscosity of water—the flowing medium—at elevated temperatures. It is concluded that no existing method will permit even an approximate determination of the filtration rate at high temperature from data at room temperature. It is necessary to measure filtration at the temperature actually anticipated in the well, or to make a sufficient number of tests at various lower temperatures so that a small extrapolation of these data to the anticipated well temperature may be applied. Such tests should be carried out on the mud as actually used in the well. The viscosity of each of the muds was determined over the same temperature range. While no relationship was observed between mud viscosity and plastering properties, it was found that chemical treatment of the muds for viscosity reduction shifted the temperature of minimum viscosity to appreciably higher values than for untreated muds. Importance of Plastering Properties A survey of the literature on rotary drilling muds clearly shows the growing realization of the importance of plastering properties,'-5 not only from the point of view of the successful completion of the mechanical operation of drilling the well but also from the point of view of minimum impairment of the natural flow possibilities of a given well. Poor plastering properties with attendant high filtration rate (large water loss to the formation) and thick mud sheath, lead to stuck drill

Jan 1, 1940

By A. G. Metcalfe, Koeneman

A study of the structure of chemically deposited nickel by Goldenstein, Rostoker, Scpssberger, and Gutzeit has been reported recently. In this work it was shown that the nickel deposit produced by the catalytic nickel-reduction process was an amorphous solid. Crystallization occurred at elevated temperatures when the original powder pattern which showed only a diffuse ring with a d-spacing of 2.01A became sharp, revealing nickel and nickel-phosphide lines. The phosphide was indexed provision%lly on a tetragonal lattice of parameters a = 9.01A and c = 4.42A, which is in reasonable agreement with the structure of Ni3P proposed by No-wotny and Henglein.3 The transformation from the amorphous to the solid state occurs abruptly (e.g., after 7 min holding at 400°C) with the evolution of considerably more than 1000 cal per gm-mole. A more detailed analysis of these effects requires a knowledge of the solubility of phosphorus in nickel. Konstanti-now3 mapped out the phase diagram in 1908 but did not determine the solid solubility. The eutectic was placed at 11 pct P and 880°C. The purity of typical catalytic nickel deposits is very high.' Spectrographic analysis for heavier elements showed only trace amounts of aluminum, calcium, iron, magnesium, lead, and silicon. The term "strace" is a qualitative definition for less than 0.1 pct and probably less than 0.01 pct. Analysis for the interstitial elements yielded 0.04 pct C, 0.0023 pct 0, 0.0005 pct N, and 0.0016 pct H. Some of this material with 7.5 pct P was used in the present work. EXPERIMENTAL METHODS Alloys were prepared from carbonyl-nickel shot and a master composition containing 7.5 pct P. Cold-crucible, nonconsumable-arc melting was used.

Jan 1, 1959

By D. B. Hobbs, H. O. Burrows, T. D. Stay

ALUMINUM which has lost its original identity as to source may be considered as secondary. This would include scrap originating in the fabrication of aluminum, which is not consumed at the plant of fabrication, and all material resulting from fabrication, which has lost its original identity regardless of whether it be consumed at the plant of fabrication or not. In general, secondary aluminum may be divided into two classes, commercially pure and alloyed. The chief impurities found in commercially pure aluminum are copper, iron, titanium and silicon; while in aluminum alloys, copper, iron, titanium, silicon, zinc, manganese, magnesium, nickel, or tin, may be present in varying proportions. Occasionally lead and antimony are found in secondary aluminum alloys, especially if the alloy results from remelting vender's automotive scrap. Such alloyed elements as are found in the scrap cannot be removed on remelting. In this, the remelting of secondary aluminum differs from the smelting of secondary copper or most other secondary metals. The majority of secondary materials reach the consumer in the form of remelt ingot or remelt No. 12 ingot. This ingot varies greatly in quality, depending upon the source of the material, and the manner in which it is refined and blended. The principal differences between primary and secondary ingot are: 1. The composition of secondary ingot may be more or less indefinite. 2. Secondary ingot may contain more dross and oxide. Secondary ingot may, however, be used successfully in a great many products. RELATION OF PRIMARY PRODUCTION TO SECONDARY PRODUCTION Table 1, compiled from data published by The American Metal Market, gives an approximate idea of the relation of primary to secondary production. Information obtained from other sources leads the authors to believe that the figures for secondary production are somewhat low.

Jan 1, 1928

By H. M. Wolflin

SOMEWHAT more than a year ago the writer collected some extensive notes on metal-mine fires and a paper on metal-mine fire prevention and fighting, a summary of these notes, was hastily pre-pared, with the assistance of G. Chester Brown, chief mining engineer, Industrial Accident Commission for the National Safety Council meeting. This summary, which is admittedly incomplete, is submitted in the hope that it will evoke some discussion that may result in a reduction in metal-mine fire hazard along the line. To accomplish such a reduction does not require the application of complicated scien-tific data. The use of just a little care, a small amount of thoughtfulness and a bit of common sense will work wonders. UNDERGROUND FIRE FIGHTING There may be some interest in a short list of con-clusions of a rather general nature that were reached in connection with some recent mine-fire fighting opera-tions. No effort has been made to cover the field; the items have been jotted down loosely, and very hastily, in the order in which they occurred to the writer. Originality is claimed for, only a few of them. 1. Temperature readings and analyses of mine-air samples, systematically taken, are invaluable aids to effective metal-mine fire fighting and recovery opera-tions. The analysis of the return-air samples fre-quently gives a surprisingly accurate indication of conditions existing underground. 2. Employees must be thoroughly trained in the use, of mine rescue apparatus, because a relatively slight difference in the amount of training makes a vast difference in the amount of work they can per-form under oxygen. In general, slender, wiry men make better apparatus men than those of heavy, more muscular physique, although there are frequent excep-tions to any such general statement. 3: Surprisingly high temperatures, up to 165° F. or 170° F. pan be endured for short periods by wearers of mine rescue apparatus if the air is dry, but lower temperatures, 135° to 140° F. are almost unbearable if the air is very moist.

Jan 2, 1922

By R. S. Rickard, B. Ball

INTRODUCTION Pyrite responds to the flotation reagents normally used in sulfide flotation systems. For example, it is well known that xanthates are good collectors for pyrite, and cyanide, sulfide and hydroxides are depressants. The particular response of pyrite to these and other reagents is used to advantage in several areas. By careful control of depressant and collector additions, pyrite can be separated from other sulfides by flotation. This is of obvious importance in base metal sulfide flotation where pyrite depression is often required to produce a marketable grade concentrate. Flotation of pyrite has long been employed in gold ore processing, and it appears that pyrite flotation from coal may become important in the future (1). It is probably a direct consequence of this relative ease of separation, plus the low economic value of pyrite, that detailed investigations on the chemistry of its flotation and depression are relatively limited. Gaudin (2, 3, 4) and others, in the mid-1950's published data on the flotation of pyrite, but detailed or consistent mechanisms were lacking. In 1955, Sutherland and Wark's book (5) was published, in which a large , amount of empirical information, especially earlier work of Wark and Cox, was presented. More recently, in 1968, significant contributions have been made by Fuerstenau et al. (6, 7) and Majima and Takeda (8). These papers introduced electrochemical explanations of the effects observed with xanthate and cyanide ions.

Jan 1, 1976

By E. G. Dean

A method of top slicing has been devised at the Miami Copper Co.'s mine at Miami, Aria., which differs radically in some ways from the customary methods of top slicing. The area of that section of the orebody in which top slicing is used is about 800 ft. square. The ore, while for the most part soft, is, nevertheless, considerably harder than the capping. The latter is siliceous, seldom containing any clay or other binding material, and breaks into fine particles so that it runs like sand if given the opportunity. Because of these facts, and because the ore is above the average grade of the mine ore, it has been mined by top slicing. Haulage levels are opened up 150 ft. apart, vertically, with two sub-levels between at 50-ft. intervals, to facilitate the putting up of ore chutes. These sublevels are used during slicing for distributing air in the ventilation system. On the haulage level the drifts are spaced on 50-ft. centers, and raises along these drifts are also spaced on 50-ft. centers, except the incline raises as hereafter noted. The raises are cribbed where necessary. Where the wear will be excessive, 1/4-in. iron plates are spiked to the top of every third set of cribbing, for its protection. When top slicing was first used, an attempt was made to carry a slicing face from fifty to several hundred feet long. Timber and other supplies were brought in through long drifts from an auxiliary shaft. Great difficulty was experienced in keeping these drifts open, the side pressure breaking the posts and the top weight breaking both caps and posts. Furthermore, the men could not work efficiently while these drifts were being repaired. The slicing faces advanced irregularly, due to varying conditions, and in many ways the results were not all that could be desired. It was then decided to divide the slicing area into blocks 200 ft. square and this was later changed to 250 ft. square. At the center of each block a two-compartment raise is put up as a supply raise, the compartments being 2 ft. 6 in. and 4 ft. by 4 ft. 4 in., the smaller being used as a manway. Station sets of 12 by 12 timber with

Jan 1, 1917

By J. H. Frye, D. L. McElroy, E. E. Stansbury

The rates of growth of pearlite in high-purity Fe-C alloys have been measured as a function of the transformation temperature. These and other data have been correlated in terms of a derived rate equation. Activation energies for the growth were found to be 24,200 cal per mol of austenite for the 0.78 pct C alloy and 27,600 cal per mol for the 0.93 pct C alloy. Theoretical implications are discussed. AN excellent review of the the theoretical and experimental studies on the mechanism and kinetics of the eutectoid reaction has been presented recently by Mehl and Dube.' They have pointed out that these investigations have followed two lines of approach: 1—experimental studies and derivations of expressions for the overall transformation characteristics, and 2—derivation of expressions for the nucleation and growth rates in terms of fundamental processes. Investigations of the latter type have been concerned for the most part with the nature of the growth at the austenite-pearlite interface in plain carbon and alloy eutectoid steels. They discuss two theories of the rate of growth of pearlite from aus-tenite—those of Brandt and of Zener. Both derive rate equations which are based on the assumption that carbon diffusion is the controlling mechanism. Mehl and Dube,' Zener,2 and Brandts. " have attempted to calculate growth rates by use of these equations together with thermodynamic and diffusion data. The results are encouraging, but agreement is not so good as to constitute verification of the theories. Furthermore, it Is not clear how these equations are to be used to study the effect of alloying elements which apparently exert little influence on carbon diffusion, but markedly decrease growth rates. It is not clear whether or not the addition to iron of an alloying element which does not diffuse during transformation can alter the rate of growth of body-centered from face-centered cubic iron. That it can greatly decrease the overall transformation rate has

Jan 1, 1954

By Fred Leighton, Wilson Blake

The microseismic method of detecting instability and high-stress zones in underground mines was developed by the U.S. Bureau of Mines (USBM) in the early 1940's.l,2 For about 25 years this method has been used throughout the world by mining and construction companies in assessing the stability of underground and surface excavations. Rock noises are the release of small amounts of stored strain energy propagating outward from their source as a seismic wave that can be detected with special geophysical equipment. This release of strain energy is caused by a rock mass undergoing load changes resulting in small-scale displacement adjustments such as microcracking, shearing, sliding, and crushing of crystal grains, some even as small as the elastic displacements themselves. No detailed field studies of any of these mechanisms have been made, and knowledge about the origin of rock noises is relatively incomplete. Laboratory tests have shown that when rocks are stressed in a testing machine, the rock noise rate-the number of rock noises generated per unit of time increases with increasing applied stress.3 This increase is most pronounced as the ultimate strength of the rock is approached. The standard field procedure has been to monitor a rock structure at intervals and plot rock noise rates vs. time, thus gaining a semiquantitative estimate of the behavior and stability of the structure. The success of such monitoring, however, has depended almost entirely on the experience and knowledge of the operator, his interpretation of the data, and his equipment. Very little study has been devoted to the basic properties of the vibration record of a rock noise. USBM decided that the microseismic method was being used sufficiently by various mining and construction companies

Jan 1, 1970

By H. T. Byck

The plastering properties of six representative California drilling muds were studied over a temperature range of 70 to 175 F. at several mud weights, using a high-pressure circulating filter press with full size consolidated cores. In all tests, with untreated as well as with chemically treated muds, the filtration rates at elevated temperature were higher than at low temperatures and in nearly every case this increased filtration rate was notably larger than could be attributed alone to the decreased viscosity of water—the flowing medium—at elevated temperatures. It is concluded that no existing method will permit even an approximate determination of the filtration rate at high temperature from data at room temperature. It is necessary to measure filtration at the temperature actually anticipated in the well, or to make a sufficient number of tests at various lower temperatures so that a small extrapolation of these data to the anticipated well temperature may be applied. Such tests should be carried out on the mud as actually used in the well. The viscosity of each of the muds was determined over the same temperature range. While no relationship was observed between mud viscosity and plastering properties, it was found that chemical treatment of the muds for viscosity reduction shifted the temperature of minimum viscosity to appreciably higher values than for untreated muds. Importance of Plastering Properties A survey of the literature on rotary drilling muds clearly shows the growing realization of the importance of plastering properties,'-5 not only from the point of view of the successful completion of the mechanical operation of drilling the well but also from the point of view of minimum impairment of the natural flow possibilities of a given well. Poor plastering properties with attendant high filtration rate (large water loss to the formation) and thick mud sheath, lead to stuck drill

Jan 1, 1940

By Edwin C. Holden

In making the original estimates for a report recommending the cyanidation of Ymir stamp-mill tailings, the writer was unable to find in any of the standard works on cyanide-practice certain data applicable to the local conditions; nor has he as yet seen quite the same practice recorded in the rapidly growing literature of cyanidation. To present these figures, together with a few novel features of local practice, the present paper is offered. The ore treated is obtained from a fissure-vein of steep dip, occurring in a slate country. The ore-body is lenticular in plan, swelling from 4 ft. in width at one end to a maximum of 42 ft., and tapering irregularly to less than 18 in., where payvalues cease. In the wider portions of the fissure the ore is mixed with more or less horse-matter from the walls. The clean ore is white, massive quartz, with from 8 to 12 per cent of sulphurets; the latter being pyrite, sphalerite and galena, the predominance being in the order given. The precious metal tenor is variable, the gold more closely following the pyrite, the silver the galena. The present mill-supply is practically all from below the oxidized zone. The unavoidable admixture of horse-matter and stope-filling with the ore as mined, affects more or less the character of the mill-feed, which sometimes contains from 10 to 25 per cent of slate. During the last three months of 1902, the mill-feed carried 0.3977 oz. gold and 1.903 oz. silver per ton of 2,000 lb., 2.65 per cent lead and 2.92 per cent zinc. The iron, unfortunately, was not determined. The Ymir mill and mine have been fully described elsewhere;* suffice it to say of the milling that the crushed ore,

Jan 1, 1904

By Fred Wright

IN A recent paper1 a detailed discussion is given of the possibilities. of using polarized light in the examination of opaque substances. The factors underlying the problem .are there treated from the viewpoint of the electromagnetic theory of light and the presentation is necessarily mathematical in form. The practical methods resulting from the discussion are, however, relatively simple and promise to be of value in the determination of certain ores and metals when studied in reflected light under the microscope. The results of the theoretical investigation referred to may be summarized by stating that in general the optical constants, such as refractive indices and absorption indices, cannot be satisfactorily ascertained on small, random, polished sections; that the use of polarized light enables. the observer ordinarily to determine whether the crystal plate is isotropic or anisotropic, and also to ascertain the degree of anisotropism; that for this purpose methods based either on the contrast in intensity between the two reflected components of non-polarized light, or on the amount of rotation of the plane of polarization, on reflection, of vertically incident, plane-polarized light, may be employed; that methods based on the phase difference between the two reflected components are in general of little value because of the small differences in phase which ordinarily result for a relatively large change in birefringence or biabsorption. The measurement of the optical properties of transparent minerals, even in minute irregular grains, is a simple task with modern petrographic microscope methods and is accomplished by petrologists as part of their ordinary routine work. But the determination of the optical constants of opaque substances is difficult and is rarely attempted; all observations are necessarily made in reflected light and are restricted commonly to the determination of color, of hardness, of the character of crystallization, and

Jan 2, 1920

By Grover J. Holt

Open-pit mining on the iron range has been in a stage of transition for several years from the standpoint of mechanization. The most radical change in open-pit mining methods was started in open-pit haulage in 1937 with the departure from the then standard system of locomotive and car transportation and the advent of the heavy duty truck as a replacement. The initial use of trucks was followed shortly by the first installation of a conveyor belt for open-pit ore haulage. The growth of the combination of trucks for gathering units delivering to a conveyor system for transportation out of the pit, has been rapid and this transition appears to have reached a peak in 1949 with locomotives and cars now being used in only a few of the largest open pits. One point which must be considered, if we assume that the maximum equipment change- over point has been reached, is that the largest pits have probably passed their peak of production. Future ore replacement must come from smaller pits wherein the truck conveyor system has done an outstanding job.

Jan 1, 1950

By C. S. Anderson

GEORGIA, since 1829, has produced nearly $18,000,000 from her gold mines, but in late years the output has dwindled to insignificance. In view of present universal efforts to increase gold production, it seems pertinent to record some recent observations in that field, briefly review its past and weigh probabilities of reviving gold mining there. Little in this paper can be claimed as new or original, and it does not present results of a detailed or profound investigation of the whole region. The Allatoona gold mine was reopened in January, 1932, and explored at greater depth during the period from January to June of that year. A number of other abandoned mines were visited, but since the workings, in common with most such mines in Georgia, were flooded or caved, underground conditions could not be examined. For a wider knowl-edge of the subject, a search was made through available pertinent literature and statistics, a bibliography of which is appended hereto. To all the sources obligations are gratefully acknowledged.

Jan 1, 1933

By E. S. Bardwell, Roy H. Miller

During the period extending from May, 1922, to September, 1923, the copper-refining furnaces of the Great Falls Reduction Department of the Anaconda Copper Mining Co. at Great Falls, Mont., were operated exclusively with pulverized coal as fuel. The installation was made first as an experiment. It proved successful from the start and was abandoned solely because fuel oil from the Sunburst field became available at a price sufficiently low to be more desirable from an economic standpoint. The equipment required for pulverized coal has, however, been kept intact and is available for immediate use should the oil supply fail. Inasmuch as pulverized coal had been used on two large reverbera-tory smelting furnaces and was, at the time we were considering its application-to the copper-refining furnaces, being used on the Wedge furnaces roasting zinc concentrate for the electrolytic zinc plant, we were equipped with a coal-pulverizing plant of ample capacity to supply pulverized coal for the furnace refinery. The only problem was to devise suitable means for transporting pulverized coal from the pulverizer plant, located in the smelter building, to the refinery about 3000 ft. distant and about 150 ft. above the level of the pulverizer plant. When studying this installation, it should be borne in mind that the layout represents an adaptation suited to the existing conditions at this particular plant. The installation was entirely satisfactory and uniformly dependable but might be modified to advantage from an operating point of view if an entirely new installation were being planned. Fuel Supply The use of the local coals, high in ash and sulfur, was abandoned some time before coal-dust firing was attempted. Local coals from the Great Falls field carrying an average of 4 per cent. sulfur and 22 per cent, ash were used with fair success in the small furnaces in use prior to 1916. In the 250-ton furnaces, however, the time lost in grating and removing clinker from the fireboxes, as well as the difficulties incident to the high-sulfur content of the fuel, became serious and recourse was had to the

Jan 1, 1927

By E. S. Fisher

GRAIN coarsening implies a discontinuous type of grain growth during which a few grains in a fine grained recrystallized matrix grow to large grain sizes at the expense of the matrix. Studies of this phenomenon in various metals1,2 indicate that grain coarsening may result when continuous grain growth in a fine grained matrix is inhibited by either a dispersion of very fine inclusions or by a strong texture. In the former case a period of annealing time exists prior to grain coarsening during which grain growth inhibition is gradually de- creased by dissolution or coalescence of the dispersed inclusions. This mechanism can be made to occur in uranium during anneals at high a phase temperatures. ' A study of some of the factors influencing the kinetics of grain coarsening and the coarse grain sizes in a uranium has led to a method for preparing a uranium single crystals. Previously such single crystals containing considerable substructure were prepared at this laboratory by a phase change method, similar to that described by Cahn.3 Attempts to prepare more perfect single crystals by strain-anneal techniques were unsuccessful. Cahn3- as reported his attempts to apply such techniques to uranium. He proposed that the failure of strain-anneal techniques is basically due to the many twins which

Jan 1, 1958

By R. Moldenke

Unlike the furnaces employed in the reduction of ores to mattes and metals, the foundry-cupola has only melting to do. This looks simple enough; and its development has progressed through centuries by cut-and-try methods; but there is still much to be learned concerning the causes which underlie the production of defective castings, even from first-rate materials. There are other differences between the smelter and the cupola. The former is usually, the latter rarely, run continuously. In the smelter there is some chance for experiment, since rich slags can be treated again; while in the cupola the metal must be good for casting from the first tap to the drop of the bottom ; otherwise, heavy damage will result. In the smelter, the object sought is the production of metal or matte with a minimum loss in the slag; whereas, in the foundry, a variety of castings of different compositions must often be run from the same heat, one after the other. Experience with the cupola has shown that the melting should take place, throughout the heat, in one zone, the zone of maximum temperature, which is clearly marked on the cupola-lining by the severe cutting action of the slag and iron oxide. The design and operation of the cupola must conform to this condition. This conformity having been secured, other considerations resolve themselves into those details of construction which will involve least trouble and cost of repairs. The very high temperatures required to melt iron and steel in the cupola, leaving the metal sufficiently superheated for casting, render the use of water-jackets inadvisable. It is always possible to patch up the lining at the melting-zone between daily heats; and the rest of the lining is seldom affected enough by abrasion and chemical action to require replacement oftener than once in nine months. The cupola is practically a shell of steel, lined with the proper refractory material, and provided with a sct of tuyeres for the admission of air to burn the fuel and melt the metallic

Jan 1, 1913

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951