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By John V. Beall

BROMO Seltzer blue has gone to war. The blue of the Bromo Seltzer bottle is a product of cobalt, the Nation's No. 1 strategic metal. When the National Production Authority, on Nov. 21, 1950, ordered a 70 pct cutback in domestic use of cobalt, a stab of pain was felt in the hearts of the glass, porcelain enamel, steel, paint, pottery, and electrical and electronic equipment industries. The reason: A full-scale wartime economy with astronomical requirements for jet engines, high velocity projectiles, armor plate, electronic equipment, and the many products needed to win a war. There is little potential comfort for cobalt users in nonessential manufacturing, and the military will be pinched for optimum supplies of the metal. However, if proper measures are taken immediately and current plans are completed, in two years there will be far more cobalt available than ever before. When normal times return, cobalt supplies should be sufficient to meet peacetime military requirements, and greatly expanded domestic requirements that will result from new technological development for wartime but adaptable to peacetime products. The pres-

Jan 1, 1951

By James E. York

AT a meeting of the American Society for Testing Materials at Atlantic City, June, 1908, Dr.. C. B. Dudley, in his presidential address,' showed the vital necessity of not only making a steel rail as good as in the past, but of making it considerably better in order to meet the present and prospective require¬ments of railroads. Doctor Dudley requested the co-operation of all who from personal experience could give information that would result in bringing about the production of a steel rail that could be relied upon to meet the present requirements. I have had considerable experience in the practical manufacture of steel of almost every grade, during the past 40 years, and I shall suggest changes that will bring about the results desired. Doctor Dudley has had a long experience as chemical and metallurgical expert for the Pennsylvania railroad, but he frankly admits that up to the present time both he and other metallurgical experts lack the practical knowledge of steel-making that is necessary to state correctly the reasons for the unreliability of the steel rails now produced. The necessity is self-evident for more positive practical knowledge on the part of these experts of what is possible and what is impossible regarding the practical manufacturing of steel rails from the ingot to the, finished product. Chemical knowledge in steel-making is far in advance of what it was years ago, and might be said to cover every requirement (in that department) for producing reliable steel. The study of the metallography of steel has been of great value, also the physical testing of steel, but this knowledge will only de-

May 1, 1909

By T. B. Counselman

WHEN one thinks of Minnesota iron ore, one thinks of big open pits, where high- grade ore is simply scooped up with a power shovel, loaded into cars, and hauled away for shipment to the blast furnace. On the western end of the Mesabi range, however, are large tonnages of iron ore which contain too much silica to be used directly in the blast furnace, and these ores must first be concentrated to a purer form. The Mesabi range is about 100 miles long and a maximum of 3 miles wide. The iron formation, which in its unaltered form is called taconite: consists of a banded iron- bearing chert. Where the high-grade ore bodies occur, these have resulted from folding and cracking with sub- sequent leaching out of the silica, leaving the iron oxide behind. The big open pits and the underground mines are situated in these concentrations.

Jan 1, 1941

By S. A., Taylor

IT is very difficult to arrive at exact figures for the cost of maintaining excess capacity of coal mines, but we can approximate the various items. To do this, I will take the Pittsburgh district of Pennsylvania and the other districts can be compared to this one. I believe we can take the depreciation item of plant ac- count as a whole and discount it over a period of 20 years; while this is high for some items it is low for others and I believe it is not far from a safe basis. This equals 5 per cent per year, and this depreciation will take place about as rapidly when not in use as when in operation. A fair value in the Pittsburgh district to- day for plant and houses is close to $4 per ton per annum. At 5 per cent this will equal 20 cents per ton per year. The item of keeping the mine in condition, free from water, etc., will be close to an average of 2y2 cents per ton per annum.

Jan 1, 1928

By W. P. Blake

One of the most remarkable iron-ore districts of the world is found in Southern Utah, in Iron County, about 270 miles south of Salt Lake City, and 10 miles west of Cedar City. This region has long been known in a general way; but, being at present somewhat difficult of access, it has been rarely visited by 'any of our members. Professor Newberry has published somewhere a short description. Last year, by the invitation of J. R. Walker, Esq., of Salt Lake City, one of our associate members, I formed one of a party, including Professor G. W. Maynard and W. S. Keyes, to visit and inspect the region. A special car was placed at our disposal by the courtesy of Hon. John Sharp, Superintendent of the Utah Central Railway. From the present southern terminus of the road at Milford, a drive of 55 miles took us to Cedar City, about 10 miles east of the iron region. The ores outcrop in a low range of hills or mountains, and stand out in such bold relief from the general surface, and are so massive and jet black, that they may be seen for miles before they are reached. These outcrops extend in long lines over the hills, and mark very . clearly the course of the beds, conforming generally to the inclosing stratified formations, probably of Palaeozoic age. These rocks are somewhat obscure, but there are large outcrops of limestone without much alteration. This, in places, appears to be the adjoining rock, at others the wall-rocks are porphyry, and at others apparently a quartzite and a fine-grained felsite. The beds of iron-ore are from 10 to 100 feet and more in thick ness, and some of the outcrops extend unbroken continuously for 1000 feet and more. It consists chiefly of magnetite and hematite,

Jan 1, 1886

By James Gayley

(Wilkes-Barre Meeting, June, 1911.) THE paper presented to the Institute in 1910, by H. 0. Hofman, on Recent Progress in Blast Roasting,1 has called the attention of the iron industry to the adaptability of these processes to the reclamation of by-products such as flue-dust and blue billy, and the better preparation of concentrates and fine ores for use in blast-furnaces. The waste of valuable iron-ore through the production of flue-dust has increased at an enormous rate, and much of it has in reality been wasted as far as future recovery is concerned. Only in recent years has a possible future value been recognized, and the material stored. The increased use of Mesabi ores, which carry considerable fine ore, is principally responsible for the great increase in the production of flue-dust. The amount of fine material that is carried over depends on the fineness of the material and the velocity of the gases, and also to a very great extent on the regularity or irregularity of the working of the furnace. Attempts to recover a part of this loss have been made by recharging a portion of the production into the furnace, but as this material has been once carried out from the furnace, it is naturally in good shape to be carried out again. A recent practice at some works, is to soak the flue-dust thoroughly with water to give it more cohesiveness, but by many this is considered of doubtful advantage in the furnace, and the gases are in consequence heavily laden with moisture. There are vast deposits of magnetic iron-ores in the United States and Canada that are too low in iron for use at the present time, but which can be economically concentrated into very rich material ; in many cases the fineness of crushing necessary to secure proper concentration has prevented their

Aug 1, 1911

For the seventh consecutive year, the value of nonfuel mineral raw ma¬terials produced in the US set a new record, reaching almost $20 billion-up 12.7% from the previous year, according to the US Bureau of Mines. The Bureau reported that this mineral production was the basis for about $200 billion worth of processed materials of mineral origin.

Jan 5, 1979

By W. A. Backofen, A. T. English

The kinetics of re crystallization were determined metallographically for a 3-1/4 pcl Si-Fe rapidly compressed at temperatures of 710° to 911°C, and held for various times at the working temperature. As in re crystallization following cold wwk, the time for re crystallization was reduced by increased temperature and strain. Nucleation occurred chiefly at grain edges, although other pre-existing interfaces, notably inclusions, also served as nucleation sites. The importance of intragranular nucleation to grain refinement in hot working is pointed out, together with some possible techniques by which nucleation might be induced within the grains. The observed isothermal growth rates are quite accurately described by the equation G = 4 x 10-'/t (cm per sec), independent of temperature and strain at all but the shortest times. Changes in G during recrystalliza-tion can exceed two orders of magnitude. It is argued that release of stored energy associated with lattice defects cannot adequately explain the time dependence. A suggested alternative involves processes of solute segregation and desegregation in the unrecrystallized matrix and at the moving boundary, respectively. EFFORTS to improve hot-working practice are hampered by an incomplete understanding of the fundamental metallurgy involved. Research directed at establishing the required basic foundation falls into two categories, the first concerned with measurement of mechanical properties under the conditions of high temperature and strain rate which characterize such processing, the second focused on structure and its relation to the deformation conditions. Rossard,' Rossard and Blain,2 and Hardwick and Tegart have conducted many high-speed, high-temperature torsion tests on various metals. One of their objectives was interpretation of stress-strain curves in terms of the structures of specimens rapidly quenched following interruption of twisting. They showed that appreciable hardening occurred in the early part of the test, and that this hardening reflected the concurrent development of an increasingly dense substructure within the grains. The detailed nature of this substructure was observed to depend on the ease of polygonization which, at least in fcc metals, varies with the stacking-fault energy.= By holding specimens after interruption but before quenching, the nucleation and growth of new grains could also be studied. Some success has been realized in relating the microstructure of hot-rolled steel to its temperature:strain rate:strain history with such testing.' The same general observations have been made by others investigating rolling4f5 and drop-hammer forging.~-~ Incident to these experiments, some efforts were made to determine the kinetics of re-crystallization as well as the velocity of the migrating boundaries. The results have been largely qualitative, owing to difficulties of interpreting hardness measurements5 and microstructures. The work described here was undertaken to obtain more quantitative information from tests on a material having suitable metallographic properties, and, in this way, to provide further insight into the fundamentals of this practically most important kind of deformation processing. I) MATERIALS AND EXPERIMENTAL TECHNIQUES Materials. Electrolytic etching of a Si-Fe alloy reveals dislocations and substructure in unrecrystallized grains.8'9 This unique characteristic makes possible a precise determination of the extent of recrystallization. For that reason, it was the material selected for all experiments in the present work. The two particular alloys that were used are identified in Table I. A major difference between "A" and "B" is the number of inclusions, as noted in the table. Most of the experiments were made with material "A". It was received as hot-rolled plate 1 in. thick, sawed to 2-in. widths, hot-forged at 1200°C to 5/8-in. rounds, and finally annealed in a mechanical vacuum at 1000°C for 24 hr. The result was substructure-free grains of mean diameter 0.05 cm.*

Jan 1, 1964

R. Dawson Hall, who has long been a member of the editorial staff of Coal Age, has been appointed managing editor. Increase the Promise of the future. Buy W. S. S.

Jan 7, 1919

By Richard J. Lund

Stock piling-and by that I mean well-organized stock piling on a substantial scale-is almost as old as the hills themselves. It was back in early Biblical times, as recounted in the Book of Genesis, that Joseph was charged by Pharaoh with the responsibility of stock piling food during the seven years of plenty to guard against the seven subsequent years of famine that were revealed by the Pharaoh's dream. And this same policy of storing up food or materials to provide for future anticipated emergencies can be traced repeatedly down through the ages. So our own efforts are anything but new. Our modern concept of stock piling-the purchase and storage of strategic materials to assure supplies needed in time of some future war- stems from our experience in World War I. In 1920, the War Department was charged by Congress with the responsibility of procuring all War Department supplies and mobilizing industry in the event of another war. During the two decades that followed there were many authoritative studies made of our deficient mineral problem, all of which pointed out the urgent necessity of stock piling certain strategic materials as a reserve against future war. One such study, made in 1925 through the combined efforts of the Mining and Metallurgical Society and the AIME, was done at the ex- press request of the War Department. Eight years later another more de-

Jan 1, 1949

By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By W. I. Duvall, L. D. Sadwin

Three explosives with different detonation characteristics were tested by studying their cratering ability in a granite-gneiss. The strain wave generating characteristics of these explosives were also studied in the same rock medium. Correlations between the relative performance of three explosives as evaluated by crater studies and other methods of evaluation are indicated. Numerous test methods have been employed to evaluate the output performance of explosives; for example, the underwater explosion method, the airblast method and the ballistic pendulum method.'*' For blasting applications, the study of explosion produced craters and explosion generated strain waves are the most meaningful. This laboratory has employed these techniques extensively for many years and has shown that the detonation properties of explosives and their ability to generate strain waves in rock are related and that the amplitude and shape of the strain wave is related to some of the crater parameters such as slab thickness and fly rock velocity.3'11 However, a good comparison between the relative performance of explosives as determined by the crater and strain wave methods had not been made. The purpose of this investigation was to determine if the relative performance of three explosives as determined by the crater method shows a correlation with the relative performance as determined by the strain wave method. If a good correlation exists between these two sets of relative performance, it should then be possible to relate the detonation properties of an explosive to its ability to break rock in a crater test. In most commercial blasting operations, the diameter of the blast hole remains constant even though the type of explosive may change. In general, it is the explosive volume rather than the weight which remains constant when two or more explosives of different density are compared. Therefore all tests in this investigation were conducted on a constant volume basis rather than on a constant weight basis. TEST SITE AND ROCK PROPERTIES The tests described in this paper were conducted at a granite quarry owned and operated by the Consolidated Quarries Div. of the Georgia Marble Co. at Lithonia, Ga. The tests were performed in an area where the exposed rock surface was nearly horizontal and where the general rock mass had few joints or faults. The rock has an apparent sp gr of 2.6 and a longitudinal propagation velocity of 18,000 fps. The characteristic impedance of Lithonia granite gneiss is 53(lb - sec/in3). EXPERIMENTAL PROCEDURE There are many parameters which must be considered in the study of explosion-produced craters. The role played by each variable in the explosive-rock-crater system can be determined by experimental techniques in which one parameter is varied while others are maintained constant. In this investigation, the crater geometry was studied as the depth was varied for each of three explosives. The explosive volume and rock-type were held constant for all crater tests. The experimental arrangement used in performing the crater tests is illustrated schematically in Fig. 1.

Jan 1, 1965

By E. L. Jr. Spain

This study was undertaken primarily to determine the reasons for certain varia-tions in the soundness of gravel aggregate taken from a number of widely separated points on the Tennessee River. Under laboratory tests, concrete made with these various aggregates it some cases exhibited marked differences in specific gravity, crushing strength and durability. Gravel was studied in detail from Chattanooga to the mouth of the river and to a lesser extent from Chattanooga to Knoxville. The causes of variation were determined, and variational curves were constructed, which accurately predict the composition of aggregate at any point on the river and therefore its relative suitability for use in concrete. The aggregate at any point is suited for making sound concrete; the variance of suitability is due to varying percentages of sandstone and weathered material, which are less sound than other constituents.

Jan 1, 1937

By AIME AIME

A DOCUMENT of progress and of great interest to engineers is the report of the Military Affairs Committee of 'the Engineering Council, which has just been accepted and sent to the secretary of War. It provides .a plan whereby civilian engineers holding commissions in the Reserve Corps may; with their con- sent, be called into service of the army during peace at any time, either with troops in the field or in a consulting capacity on any government engineering work. The Military Affairs Committee finds ample authority in the military bill passed by Congress on June 4, 1920, for this arrangement and also for extending the privilege to military engineer, officer-s of the regular army to engage in civilian work during times of peace. It is hoped that the Secretary of War will adopt the suggestions and put the program outlined into effect. This is a constructive piece of work comparable to the efforts of the military Committee before the war which developed so much in the way of preparedness, particularly in the program of military lectures which, held in the auditorium in the Engineering Societies Building, became so popular that each lecture had

Jan 1, 1920

By G. G. Brown

Enthalpy-entropy diagrams are presented for natural gases of 0.6, 0.7, 0.8, 0.9, and 1.0 gravity over the pressure range of 5 to 10,000 Ib. per sq. in. and temperature range of 32º to 700°F. The charts indicate directly the work requirement and temperature rise for adiabatic compression or temperature change for free emansion of natural eases. Computation and Uses of Charts The Mollier diagram (Fig. 4), in which the enthalpy (heat content) is plotted against the entropy with lines of constant temperature, pressure,, and in some cases volume, has been found most convenient when dealing with the compression, expansion, and flow of fluids. In dealing with the flow of fluids, the sum of the increase in the enthalpy, AH, plus the increase in kinetic energy, AM —, plus the increase in potential energy, ?MZ, representing the total increase in energy of the fluid in flow, is equal to the sum of the heat q, and work added, —w, to the fluid while flowing between the entrance and exit of the flow system. AH + AM— + ?MZ = q-w [1] In cases where there is no significant change in potential energy or in kinetic energy (velocity), it follows that the increase in enthalpy is equal to the total energy supplied to the fluid. Under such conditions' the changes in the property of the fluid as it flows through a throttling valve, choke, or any other similar arrangement, may be read directly from the enthalpy-entropy diagram by following a horizolltal line between the known pressures' When compressing Or expanding a gas by means of a Or or engine in which no heat is added to or subtracted from the gas, but only work done, the changes in the properties of the gas may be determined along a vertical line of constant entropy between the entering and exit pressures. The power required for the compression of the gas may be readily determined by converting the increase in enthalpy into the desired units. The enthalpy-entropy diagram for natural gases is to the gas engineer what the steam diagram is to the steam-power engineer. For this reason it would be extremely convenient if a reasonably satisfactory enthalpy-entropy diagram could be prepared as a function of the gravity of the gas. A careful study of the known properties of natural gas indicate that this is possible. The effect of temperature upon the enthalpy at constant pressure is expressed as the "heat capacity" or "specific heat" of the gas. The best available data for natural and petroleum refinery gases indicates the relationship shown in Fig. I. From this it is clear that the specific heat of natural gases is a function only of the gas gravity and the temperature at atmospheric pressure. The effect of pressure on the enthalpy of natural gases is dependent upon the pressure-volume-temperature relationships,

Jan 1, 1945

By Robert Mehl

THE purpose of this investigation was to prepare high-purity iron-carbon alloys, to determine as precisely as possible the A3(GOS), the Acm(SE), and the A1(PSK) transformation temperatures in the meta-stable iron-iron carbide system (up to 1.4 per cent C), and to study the influence of carefully controlled and constant rates of heating and cooling (1/8 to 2° C. per minute) upon the transformation temperature and upon the resulting microstructure. Apart from the general metallurgical importance attending the completion of such a task, it will be noted that highly precise transformation temperatures are of interest and importance in the thermodynamic study of this system1. Several determinations of the iron-iron carbide diagram have been made. These suffer generally from the low purity of the alloys used, and from the application of methods of investigation of low sensitivity. Attempts to compare and weight the many data available in an effort to construct as accurate a diagram as possible have, in the main, been unsuccessful. In general, the wide differences in the results of different workers, the lack of complete analytical data, the omission of important details relating to the heat-treatment of the alloys, and the meager description of the methods of investigation applied, render such a process of averaging nearly meaningless. It may be seen from the summaries by Epstein2 and Körber and Oelsen1 that variations as great as 30° C. exist in the reported data on the A3 temperatures in iron-carbon alloys. For-tunately, the A3 temperature in pure iron is now known to be 910° C. ± 1° C.3 The best recent work on iron-carbon alloys is that of Esser4 on hypoeutectoid steels and that of Sato' on both hypoeutectoid and hyper-eutectoid steels.

Jan 1, 1937

By E. L. Jr. Spain

THE deposits described in this paper occur over much of Wayne County and in the southeast portion of Hardin County, Tennessee, and in the northeast and northwest portions of Mississippi and Alabama respec-tively. The presence of tripoli in this region has been known for some time and descriptions of various occurrences in Tennessee have been made by Jewell1 and Miser2, while Hilgard3, Lowe4 and Logan5 have treated the deposits that occur in the adjacent portions of Alabama and Mississippi, but there has not been a general survey of the entire field summarizing completely the geology of the deposits with respect to their origin and stratigraphic relationships. During 1934, while engaged in surveys of mineral resources through this region for the Tennessee Valley Authority, the writer collected data with this in mind, and has assembled them in this report. He is indebted to H. S. Rankin and N. A. Rose, of the Tennessee Valley Authority Geology Division, for field assistance.

Jan 1, 1936

By Arthur C. Spencer

ThRee great deposits of iron-ore, in Camaguey and Oriente Provinces, Cuba, are well known to me through careful field-examinations executed in the years 1901 and 1907. In 1901 I visited the Cubitas iron-ore district, which lies about 12 miles distant from the city of Camaguey in a northerly direction, and the Mayari district, which includes the Sierra Nipe, lying opposite Nipe bay on the north side of Oriente Province. In 1907 I again visited the Cubitas district, and also made a sojourn of several days in the Moa district, where the extensive deposits of iron-ore were observed and studied. The observations of 1901 were made under the auspices of the then Military Governor of Cuba, Gen. Leonard Wood, and my conclusions concerning the value of these deposits were incorporated in a report.' The examination of certain denouncements of iron-ore in the Moa district in 1907 was made in behalf of iron-masters operating in the United States, to whom I reported the existence of large amounts of easily-workable limonitic iron-ore, properly designated " brown iron-ore " in the terminology now current among iron-ore producers in the United States. In 1908 I published a paper entitled, Three Deposits of Iron Ore in Cuba, outlining the occurrence and origin of the surfi-cia1 ores existing in the Cubitas, Mayari, and Moa districts.2

Jan 1, 1912

By Michael J. Messel

OF the various minerals that occur in fibrous form known as asbestos, chrysotile is the variety most in demand for commercial uses, and, last year, over 683,000 tons of the various grades were produced in Canada and United States, exclusive of African and Russian production, which figures are uncertain. Production has not been able to keep up with the increased demand, and an acute shortage exists. Canada, Russia, and Africa are still the most important producers. However, Russia consumes most of its production at home and exports very little. The United States consumes over 60 pct of the total production and produces only about 4 pct of the total from deposits in Vermont and small quantities from Arizona. This paper will review mainly, some of the more recent developments concerned with the extraction and processing of this fibrous mineral for various industrial uses, such as textiles, insulation, building materials and brake linings.

Jan 1, 1949

By Owen Thornton

Recently equations have been presented by Rose and Bruce' and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"' multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately': — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949