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By J. G. Y. Chow, S. B. McRickard

The tensi1e properties of Ferrovac iron have been studied from 4° to 300°K. The stress required for macroscopic yielding was found to he constant below approximately 50°K. The effect of mechanical twinning on this low -temperature stress plateau was investigated. The onset of twinning occurs in this iron between 130° and 150°K and depending on its previous thermal history the twinning-stress curue may drop below or remain above the vield-stress curves as the temperature is lowered. Twinning has been shown to initiate slip in quenclzed iron at low temperatures. In no instances, however, did the onset of twinning alter the continuity of the yield stress -tempwature curve. Our data shows that carbon inhibits twinning and slip at low tem-peratures. This observation nay be used to explain the ductile-to-brittle transition in iron. The effect of fast neutron irradiation on yielding and embrittlement in iron and Fe-C alloys is offered as supporting evidence for this viewpoint. THE mode of yielding in iron at low temperatures was studied in an attempt to find an expression based on a single mechanism to describe the thermal dependence of the yield stress of iron. There are two types of inflections observed in the variation of the yield stress with temperature in iron and Fe-C alloys. The first is associated with ductile behavior and consists of a region extending 50" to 100°K above absolute zero in which the yield stress is independent of temperature. The second is observed in more brittle materials such as Fe-C alloys and irradiated iron and consists of an abrupt discontinuity in the yield curve as the temperature is lowered through a ductile-to-brittle transition point. The temperature dependence of the yield stress for iron with four grain diameters as found in this study is shown in Fig. 1. To varying degrees all the curves appear to flatten or approach an asymptotic value as the temperature is lowered below 50°K. Several other investigators1,2 have observed a plateau in the yield stress of iron and steel at low temperatures and in 1956 Louat3 presented a theory which contained an explanation for this behavior. In a subsequent exchange with Erickson and Low4'5 who attributed the plateau to the onset of mechanical twinning Louat8 showed that twinning first occurs in iron and steel tested in tension at temperatures as high as 140°K which is well above the observed plateau in yield stress. Furthermore he pointed out that both twinning and slip are basically dislocation processes and that with modified parameters his original theory still applied when deformation is initiated by twinning. Variables which affect the ductile-to-brittle transition in iron are test temperature, strain rate, composition and grain size.7 LOW,8 Hahn et al.,9 and Hull10 have provided evidence which links brittle fracture at a given temperature with the specimen grain size and the onset of twinning. In fact, Hull equates the brittle fracture stress to the twinning stress. On the other hand brittle fracture has been observed in the absence of twinning and priestnerl1 has given a fracture criterion which is valid whether or not fracture is preceded by extensive twinning. The data presented here clarify the role of twinning in the low-temperature deformation of iron. Strong evidence is given that the amount and distribution of interstitial impurities such as carbon are of

Jan 1, 1965

By P. P. Reichert, L. S. Gournay, N. T. Burdine

An investigation of equivalent pore entry radii in typical samples of petroleum reservoir rock and the pore volume associated with each value of pore entry radius has been made. Theoretical discussions together with experimental procedures for obtaining pore entry radii and the distribution of pore volume with pore entry radii are presented. Experimental results on a number of core samples, along with typical distribution curves, are shown. Data on the per cent of the pore volume filled by mercury at a pressure of 1500 psi are included. The results of re-runs of samples, made possible by regenerative apparatus, show the repeatability of the data and indicate the amount of physical change in the samples by mercury penetration. Theoretical equations for calculating permeability from pore size distribution data were derived and the results of such calculations are compared with measured gas permeability data. The effect of the shape, surface area, and weight of the sample on the pore size distribution of reservoir rocks was investigated experimentally. Mercury capillary pressure curves are compared with those obtained by the porous diaphragm method using pas to displace water. Standard core analysis techniques, in general, lead to quantities which are statistical averages of the varying properties of the samples under examination. Although such statistical information has real value in predicting the gross performance of porous bodies. it fails to provide fundamental information concerning the properties of the porous medium itself or any processes which may be occurring in it. For example, a gas permeability measurement on a core sample is an indirect way of determining an average pore radius for that particular sample. Since there are many combinations of pore radii that will give the same radius. and, hence, the same permeability, no information is obtained on the pore size distribution. Furthermore, similar values in permeability do not imply similarity in other properties of a porous medium. For instance, it is possible to have two core samples with identical permeability which would have different residual oil contents at the end of an air-oil drive, or even different amounts of interstitial water. It has been recognized for some time by the petroleum industry that a determination of pore size distribution for porous reservoir rocks offered promise of increased understanding of fundamental flow processes in the porous matrix. and therefore of petroleum res- ervoir performance in general. There have recently been published several methods for determination of pore size distribution in porous materials. A report is given here of the modifications in equipment and technique required to adapt one of these methods to measurements on petroleum reservoir core samples. Although only a few correlations or applications of the method are available for presentation at this time, the technique is brought to the attention of the industry so that the opinions and experience of others with this or similar techniques may be exchanged. It seems possible that the method will have wide application in the future. METHOD There are three general methods which may be employed to measure the pore size distribution in naturally occurring rock formations. One method1 is based on experimentally determined adsorption isotherms for calculating the surface area of the porous medium. Knowing the surface area and the pore volume, a rough estimate of the pore radius can be made. Since this method depends on the thickness and uniformity of the adsorbed layer, the validity of the results would be highly questionable. A second method utilizes capillary pressure data obtained by static dis-

Jan 1, 1950

By W. O. Philbrook, K. Natesan

A mathematical model was derived for the temperature change in a particle undergoing heterogeneous chemical reaction and heal exchange with a stream of fluid. The model has been applied specifically to the exothermic oxidation of spherical particles of zinc sulfide. Very good agreement was obtained between the theoretical prediclion and experimental observation. It was found that at no stage of the reaction was the particle subjected to a state of thermal instability. In studies of gas-solid reactions, it is generally assumed that the gaseous and the solid phases are at the same temperature throughout the reaction period. This is not strictly true since most of the reactions are either exothermic or endothermic in nature. This paper deals only with heterogeneous gas-solid reactions of noncatalytic type. In the case of exothermic reactions (e.g., roasting of sulfides), there may result an increase in temperature of the particle due to the release of the heat of reaction, and this increase in temperature may enhance the reaction rate and thus cause further release of heat. Such a "spiralling" effect may lead to a thermally unstable situation within the particle. On the other hand, in the case of endothermic reactions (e.g., calcination of limestone), there may occur a decrease in temperature of the particle as the reaction proceeds, leading to a virtual "quenching" of the reaction front. A general discussion of autothermic processes with emphasis on properties and reactor design is given by Van Heerden. 1 Levesque and cubicciotti 2 observed self heating of the sample in the oxidation of thorium. Anous et al. 3 observed self cooling of the sample in their dehydration studies on chrome alum. Cannon and Denbigh, 4 and Ong et al.5 reported self heating of the sample in their studies of the kinetics of oxidation of zinc sulfide. A typical plot of heat generation and heat loss rates with reaction temperature is shown in Fig. 1.'14 The Sigmoid curve represents the heat generation rate while the straight lines represent the heat loss rate. The main objectives of this analysis are to estimate the temperature increase of a single particle undergoing an exothermic reaction and to study the possibility of a thermally unstable situation within the particle. Also, a study of the dependence of the tempera- ture increase on different process variables has been attempted. A "she ll-by-shell" method has been proposed to analyze the problem. The shells may be made as small as necessary, and equations may be set up for heat transfer by various mechanisms. Such equations will have to be solved for each shell, with the boundary conditions for ith shell being obtained from the (i - 1)th shell, using a high speed digital computer. The oxidation of spherical particles of zinc sulfide is considered for this analysis, but the treatment is general enough to be applicable to other reactions and particle shapes. The oxidation reaction can be written as AH =« -115 kcal/mole ZnS [1] Such a reaction has been found to proceed in a topo-chemical manner; i.e., as the reaction proceeds, a progressively thicker outer shell of zinc oxide is formed, while the inner core of unreacted sulfide decreases. It has been found experimentally, both in the present work and in the previous investigations,4-6 that the particle retains its original dimensions. Therefore, at any given time, the particle may be

Jan 1, 1970

By C. H. Li, J. Washburn, E. R. Parker

Yield stress in single crystals of zinc was shown to be dependent on prior annealing temperature and rate of cooling after annealing. Rate of strain hardening beyond the yield was not sensitive to annealing procedure. A tentative mechanism for the effect was discussed. COMPARATIVE mechanical tests of metal single crystals generally show a large scatter of results. Many factors may contribute to this variation. The present investigation was undertaken to evaluate the influence of two factors not ordinarily considered of major importance—annealing temperature and cooling rate after annealing. Since plastic properties of crystals are thought to depend on the presence of lattice imperfections, it follows that a variation in properties should result from differences in the distribution and density of these imperfections. Furthermore, in the light of current theories of interaction between edge dislocations and lattice vacancies,' it seems possible that annealing temperature and subsequent rate of cooling might play a part in this distribution. Analysis of the effect of these variables on plastic properties may lead to a better understanding of the annealed state. Single crystals of zinc which have been strained in simple shear undergo complete recovery of mechanical properties upon subsequent annealing. This behavior is useful because a single specimen can be used repeatedly, thus eliminating the uncontrollable variables introduced by the use of many crystals. The test section of the crystals used for these experiments was a cylinder 1/8 in. thick with a cross-sectional area of about 1/3 sq in. The specimens were acid-machined from spherical single crystals 1 in. in diameter in such a way that the slip plane (0001) was at right angles to the axis of the cylinder. In testing, a shear stress was applied along one of the slip directions, [2110] in the (0001) plane.' All crystals, unless otherwise noted, were grown in a helium atmosphere from molten 99.99 pct pure Horse Head Special Zinc. Fig. 1 is a family of curves obtained from one crystal. Each curve was obtained by deforming the crystal to 10 pct strain at a rate of 3 pct per min, following an anneal of 1 hr at 260°C. The strain direction was reversed every other time so that no progressive change in shape of the specimen took place during the series of tests. Since the stress-strain curve was reproducible within a fairly narrow range under the same conditions of annealing, it was then possible to determine the effect of changes in annealing conditions. A crystal was tested repeatedly as previously described but the annealing temperature and rate of cooling preceding each test were varied (Fig. 2). Two cooling rates were used, approximately 30°C per min and 3°C per min. Annealing was conducted at three temperatures, 200°, 300°, and 400°C. For a given annealing time and rate of cooling the room temperature flow stress was higher the higher the annealing temperature. The increase in flow stress was small as the annealing temperature was increased from 200° to 300°C but rose rapidly when the annealing temperature was raised from 300" to 400°C. Faster cooling from the high temperature produced an even greater strengthening of the crystal. The curves were obtained in the order indicated by the numbers. The stress level associated with a certain annealing treatment was, within the limits of scatter, always the same regardless of the

Jan 1, 1954

By J. Skrove, C. R. Boardman

In situ permeability of the rock outside the Hardhat chimney was determined by pressurization of long holes with air. Experimental data indicated a remarkable difference between fracture permeability of the rock near the chimney and that at a considerable distance. Although permeable fault zones were known to exist in the granite stock, the measurements of background permeability were quite low, on the order of tenths to several millidarcies. The observed difference is about two or three orders of magnitude above this background in the region 125 to 215 ft radially from the shot point, or 80 to 165 ft radially from the vertical axis of the chimney. The presence of a collapsed drift immediately beyond this region precluded measurements which could have defined the maximum extent of the zone of high permeabilily. INTRODUCTION Previous exploration has revealed that contained nu-clear explosions create cavities which generally collapse, resulting in rubble-filled chimneys and annular fractured zones. These geometries have been shown to result in complex flow regimes which should increase the production rate from hydrocarbon reservoirs.' Empirical scaling equations have been developed for estimatina chimney radii and heights for a variet; of rock media.' The exten; of the annular fractured zone has been documented and associated permeability changes have been observed qualitatively for several explosions. This study was begun to establish the nature and magnitude of the permeability of the latter region. It is anticipated that results will be useful in estimating permeability changes and consequent production stimulation which might ensue from a contained explosion in a hydrocarbon reservoir. The post-shot environment of the Hardhat event (a 5-kt contained nuclear explosion in granitic rock) was c'hosen for the experimental measurements. The Hardhat device was detonated at a depth of 939 ft, and subsequent exploration revealed a chimney of broken rock with a radius of 65 to 70 ft and a height above shot point of 281 ft.' BeFore the explosion, the Hardhat medium was highly jointed and fractured (Fig. I). Jt was expected that differential rock motion along these and other weaknesses induced during cavity growth and collapse would significantly alter the permeability of the rock mass. EXPERIMENTAL METHOD Initially, three 2-in. diameter holes (Nos. 10, 12 and 19) were drilled about 25 ft outward through the walls of the 500-ft level drift (elevation 4,253 ft, Fig. 2). One was drilled near the chimney and two holes, one vertical and the other horizontal, were drilled near the shaft. Order-of-magnitude differences in permeability obtained by pressurization measurements indicated further: investigation was warranted. A series of 3-in. diameter holes was then drilled with water as a coolant into the walls and roof of the drift (Fig. 2). An 11-in. long packer was set from 1 to 8 Et inside each hole and air was injected at measured Row rates. Hole pressures were monitored at the collar. Permeability was low enough in the holes near the access shaft that pressure could be maintained long enough to obtain good pressure decay rates. In the vicinity of the chimney, however, permeability was so high that this was not possible and air was injected under steady-state conditions. About one year later, these same holes were retested to

Jan 1, 1967

By T. P. Papazoglou, N. A. D. Parlee, W. C. Phelps

PRACTICAL designs for good "home made" molybdenum furnaces are hard to find in the literature. The one described briefly below left something to be desired but was good enough to operate as a rather long (30 in.) two-zone furnace for periods of over 2 months at temperature (1400° to 1600°C) without shutdown. The principal problem in our application was to establish a temperature profile with two distinct constant-temperature zones and no dip between the zones. This and other problems mentioned below would not arise, however, if both zones were operated at the same temperature and if a shorter furnace were acceptable. Since molybdenum windings oxidize very rapidly when heated in air, impervious refractory tubes were used for both the furnace core and the outer jacket tube shown in the accompanying figures. A protective atmosphere of forming gas (10 pct H2, 90 pct N2) was continuously passed through the gas-tight annular volume between the core and outer jacket. The water-cooled copper ends shown in Figs. 1 to 3 sealed the ends of the tubes. Annealed molybdenum wire (40 mil) was wound on the recrys-tallized alumina core (35.5 mm OD by 28.5 mm ID by 30 in.) at a spacing of 0.36 in. The spacing was reduced to 0.29 in. close to the ends to partially compensate for end heat losses. Fig. 2 shows two molybdenum-ground lead taps off the center of the winding to produce the two independect temperature zones. The ground lead was insulated with 1/4-in. alumina tubing and connected to the grounded copper end by passing the wires through the gas port tube and crimping each wire into notches cut at the mouth. To prevent sagging of the core at high temperatures, refractory "troughs" were cut from alumina and mullite tubing to cradle the core. The support "troughs" which were 6 in. long and located about 5 in. from each end of the annular volume also served as radiation shields. In view of the different expansion coefficients and operating temperatures of the core and outer jacket (3.5 in. OD by 3 in. ID by 30 in.), the ends of the tubes were smoothed and squared to produce good sealing surfaces, and the core was ground 1/32 in. shorter than the outer tube. The power terminals were passed through their respective conductor ports which were internally lined with alumina tubing and sealed with Armstrong adhesive A-6 leaving about 1 in. of protruding lead wire for external connections. (Adhesive A-6 is a two-component system consisting of an epoxy-type resin with a mineral fibrous filler and an amine catalyst.) Figs. 1 and 3 show the entire assembly of concentric refractory tubes, copper ends, and sealing o rings, held together with two brass flanges and 3/8-in. bolts with heavy springs for dimensional flexibility. The furnace shell (19 by 19 by 30 in.) consisted of a steel frame with sheets of transite forming a box. The copper ends protruded through two 3.75-in. circular holes cut at the center of each transite square end. Thermal insulation next to the transite exterior was effected by K-23 B&W bricks alld in a central volume of approximately 9 by 9 by 30 in. a row of K-30 bricks was lined up to support the hot assembly. The rest of the volume around the outer

Jan 1, 1965

By E. D. Gardner, E. M. Sipprelle

The Synthetic Liquid Fuels Act (58 Stat., 190; 30 U.S.C. Sup., Secs. 321-325) was approved by Congress April 5, 1944; it directed the Bureau of Mines to build demonstration plants to produce synthetic liquid fuels from coal, oil shale, and agricultural products. The most important oil-shale deposits in the United States are in the Green River formation of Colorado, Utah, and Wyoming. The oil shale of western Colorado generally is more amenable to exploitation, more persistent, and apparently richer than elsewhere in the Rocky Mountain Region. It occurs at the top of a high plateau surrounded by bold, nearly vertical escarpments 500 to 600 ft in height. The top 400 to 500 ft of these escarpments comprises an oil-shale measure that averages 15 gal of shale oil per ton; the bottom 70 90 100 ft of the measure, called the Mahogany Ledge, averages over 30 gal per ton. The full measure in a 1000-square-mile area is estimated to contain 300 billion barrels of shale oil;' the Mahogany Ledge is estimated to contain 100 billion barrels of oil. These estimates are based on numerous surfac,e samples and on core-drill holes drilled by the Government and by private enterprise. The oil-shale beds are undisturbed and lie nearly horizontal. The name "oil shale" is unfortunate, as the rock is a tough, strong marlstone. Organic matter named "kerogen" is a constituent of the rock. The oil-shale demonstration mine is on Naval Oil-Shale Reserve No. 1; it is about 5 1/2miles by mountain road from the plant site, which, in turn, is 2 miles from U.S. Highway 6 and 10 miles west from Rifle, Colo. The highway parallels the Colorado River, the Denver and Rio Grande Western Railroad, and a 66,000-volt public-utility power line. Early in the program it was realized that an oil-shale enterprise would have to be on a large scale to be commercial, and that unusually low mining costs would be necessary. The physical characteristics of the Mahogany Ledge and an overlying roof stone are unusually favorable both for large-scale operation and low mining costs. Quarry practices largely will be followed underground to mine the Mahogany Ledge. The aim has been toward complete mechanization of all mining operations. A mining unit would comprise a square mile containing 100,000,000 tons of oil shale with allowance for mining losses. An investment of $1,000,000 would be $0.01 a ton; such an expenditure, therefore, could be made to save, say, $0.015 per ton daily operating cost. A goal of a mining cost of $0.50 per ton was set up in 1945. Open-cut mining costs then were about $0.25 per ton of material handled; it was hoped that a cost double this amount could be obtained in mining the Mahogany Ledge. Costs of labor and supplies have increased since 1945 and so has the selling price of petroleum products. To those unacquainted with the character of the Green River deposits, the name "shale" suggested high mining costs. Others assumed that coalmining costs of $2 to $5 per ton would apply. To many, the expected mining costs appeared the principal handicap to the establishment of an oil-shale industry. The purpose of the Bureau of Mines is to demonstrate methods and to establish costs for mining the oil shale on a large scale. It is hoped this work will lead to the establishment of a large-scale, commercial oil-shale enterprise.

Jan 1, 1950

By L. A. Panek

Research on roof bolting has developed significant information with respect to the functions that can be performed by properly installed bolts and the methods that can be used to ensure that effective installation has been achieved. The present paper brings together results that are pertinent to the design of a bolting system for reinforcing horizontally stratified mine roof with vertical bolts. The design approach is based on the use of bolts to decrease the maximum bending stress within an arbitrary sequence of roof strata (see Fig. 2) in which the only loads are the weights of the individual beds. The use of rock bolts to achieve other objectives, such as to stabilize a fractured rock mass on the periphery of a mine opening,3 is excluded from consideration herein. Reinforcing effect of bolts consists of a friction effect and a suspension effect in combination. "Friction effect" refers to reduction of bending in a stratified roof due to clamping action of tensioned bolts, which compress the strata, thereby creating frictional resistance to displacement along planes of stratification. (The flexure of a sequence of strata is necessarily accompanied by horizontal displacement of each bed with respect to its neighbor, along mutual surfaces of contact.) Although the sliding of the beds tends to exert a shearing effect on the bolts, tests show that this has negligible influence on the bending stresses, probably because the bolts are so far apart. "Suspension effect" refers to the transfer of part of the weight of the weaker or thinner strata to one or more thick strata, which occurs when strata with differing tendencies to deflect are constrained to have equal deflection. The term "suspension" is used irrespective of whether the thin strata are above or below the thick strata, because tests show that the supporting effect of the flexurally more rigid roof strata is for practical purposes independent of their position in a bolted sequence of strata. An earlier paper4 dealt with a bolted unit in which all strata had equal flexural rigidity; bolting could develop a friction effect but no suspension effect. The present paper deals primarily with a bolted unit in which all strata do not have equal flexural rigidity, so that bolting can develop both a friction effect and a suspension effect. The reinforcing effect of the bolts was determined by a combination of experimental and theoretical stress analysis.4'6'7 The experimental method consisted of loading a model by rotating it in a centrifuge to simulate the gravity forces exerted about an underground excavation. Models were made from two different limestones, although the results are independent of the material because the elastic constants were taken into account in the data analysis. Electric resistance strain gages were bonded to the highest and lowest members of the bolted unit to determine the outer-fiber bending strains at the center and at the supports. The quantitative results presented herein are based on tests of 56 different models, which included a range of values for the structural parameters. Each model was tested several times, with different combinations of spacing and tension of the bolts. DESIGN EQUATIONS The effects of friction and suspension on the flexure of a bolted stratified roof can be expressed by the following equations, which give the maximum bending stress, the deflection, the friction effect, the suspension effect and the transferred load for any (the i-th) member of the bolted unit in terms of the structural parameters:

Jan 1, 1964

By G. P. Marino

The "conductivity ", Kr, of a spherical void in a linear temperature gradient due to radiation is calculated by integration of the general expression for diffuse radiation between two gray surfaces of arbitrary orientation. The spherical geometry allows an exact evaluation of the phenomenon without resorting to up-proximate expressions for the radiant heat flux. The resulting expression for Kr is three quarters of the approximate value obtained by Loeb. IN the determination of the thermal conductivity of porous materials such as sintered UO2 and ThO2 fuel pellets, the magnitude of the thermal conductivity in the pores due to radiative heat transfer across the pore, Kr, may be important in assessing the total conductivity of the pellets. Loeb' has calculated Kr for various pore geometries by approximating the net flux of heat between two surfaces of temperature difference AT as 4eT~AT and obtained: K,=4yoet3odp [1] where a is the Stefan-Boltzmann constant, E is the emissivity of the radiating surface, To is the average absolute temperature of the region across which radiation occurs, dp is the largest dimension of the gap in the direction of heat flow, and y is a geometric factor. That is: y = 1 for laminar pores and cylindrical pores with axes parallel to the heat flow direction, y = 2/3 for spherical pores, y = /4 for cylindrical pores with axes perpendicular to heat flow direction. It was the purpose of this work to obtain an exact expression for K, in spherical pores by integration of the general expression for the net heat transfer between two incremental areas on the surface of a spherical pore. This procedure yields a value of Kr 3/4 of that obtained by Loeb. I) CALCULATION OF Kr Fig. 1 illustrates the general geometry which defines the problem. The total emissive power for a gray body is given by: E = EoT4 [2] where E is the radiated energy per unit area of the radiation surface per unit time, T is the absolute temperature, o is the Stefan-Boltzmann constant (o = 5.67 X lo- '' watt per sq cm-"K1), and E is the emissivity of the surface. Although Eq. [2] gives the exact expression for the total emissive power of any gray body, all practical problems involve the net exchange of thermal radiation between a body and surrounding bodies. The two major considerations in the solution of such problems are a) shape and relative position of the surfaces and b) the emissivities of the surfaces. In this work it shall be assumed that all incremental areas on a pore have the same emissivity and, further, that little or no reflection occurs (i.e., the radiation hitting a surface is either absorbed or transmitted). Thus, the solution of the stated problem requires only that consideration a be satisfied. Consider two incremental surface areas dA 1 and dA2 of the same material in a general orientation to one another. Let dAl be at temperature TI and dAz be at T2. Fig. 2 illustrates the geometrical parameters involved. That is, 71, is the normal of dA, n2 the normal of dA2, r the line connecting the centers of each area, 81 the angle between nl and r, and Q2 the angle between 7,2 and r. Using Eq. [2] and the Lambert cosine law of diffuse radiation it is easily shown that:293 WdAf- dA, = ecr T*------^fpi------" dAidA2 [ 3a 1 and

Jan 1, 1970

By E. C. Skinner

Cardox, which consists essentially of a steel tube containing carbon dioxide compressed to the liquid state, is a trade name designating a device used principally in coal mines to break down coal. The use of Cardox to break down coal was developed in the Middle Western coal fields around 1927 or 1928. At first, a large, heavy tube was used, requiring many parts. Through experimentation and technologic improvement, the weight of the tube has been brought down from 88 lb. to 20 lb. and the new, light tube makes use of larger volumes of CO2 at lower pressures than formerly was thought possible. This blasting method is extensively used today in coal mines and probably one tenth of the bituminous coal produced in the United States is prepared with Cardox. Construction and Application As used in the coal mine, Cardox looks like a piece of steel pipe 2 to 3 in. in diameter and 3 to 5 ft. long. When it is necessary to fire a shot, the tube is wired with two leg wires that are long enough so that when the tube is pushed the desired distance into the hole the wires will protrude 5 to 6 in. It has been found that No. 18 insulated copper annunciator wire is the best material for leg wires. A two-conductor rubber-covered shot-firing cable of sufficient length is then attached to the leg wires. A 2 to 6-volt current is applied, either by means of shot-firing batteries or the standard type of shot-firing generator. Upon the application of the current, the charge in the cartridge is set off. Because the breaking action upon the coal is supplied by the relatively slow physical expansion of the carbon dioxide gas rather than by the rapid chemical formation of gases as in more familiar explosives, the result is a slow heaving action, somewhat similar to that produced by black powder, rather than a shap detonating effect. Permissible powder does its work at roughly ten times the pressures in use with Cardox. The escaped gas from a Cardox shot apparently works along the planes of weakness in the coal face, such as the coal cleats, the edges of the cut, and along the top of the seam, breaking off the coal toward the free faces and heaving the mass of coal outward. Cardox tubes are manufactured in various sizes to take care of variable conditions of seam size, undercut depth, cleatage, coal hardness, and so forth. The tubes range in diameter from 2 to 3 in. (Table I) and the normal CO2 charge is from 24 to 96 oz. For any one tube size, several sizes of shear disks are available, thus excellent control of the type of shooting desired is possible. In general, local experience and experimentation dictate the size of tube chosen for any particular job. For high coal, and deeper or wider cuts, a larger size is chosen to start with, and the opposite is true for low coal, softer coal, or small cuts. After the tube size has been experimentally selected, tests are run in the mine to determine how many shot holes are needed and where the holes should be placed. The size of the disk,

Jan 1, 1944

By J. J. Mulligan

Introduction Coal is found in every major geographic region through-out Alaska and in two offshore areas. Since about 1852, more than 100 small mines have opened and closed. In 1981 and 1982 production was almost entirely from one mine in central Alaska. Clearly, the utilization of Alaska's abundant coal resources presents political, economic, and technical problems that are far from solution. Location and Physical Features Figure 1 illustrates the geographical and geological similarity between Alaska and the western US. Alaska's Arctic region generally resembles Wyoming and the Dakotas. The Brooks Range is an extension of the Rocky Mountains. The central region of Alaska between the Brooks Range and the Alaska Range bears a general resemblance to the basin and range country of the western US. The southcentral and southeastern regions have a similar resemblance to the Sierra Nevadas and the West Coast. The Arctic, the central, and the southcentral regions have major coal fields. The southeast region has scattered occurrences. The topographic, climatic, and economic characteristics of each are different. These differences have a large effect on practical mining methods. Description of Alaskan Coal Coal deposits known in Alaska are almost all of Cretaceous or Tertiary age, much younger than the Carboniferous coal deposits of eastern and midwestern states. Consequently, most Alaskan coals have a higher moisture content and a lower heat value. Most Alaskan coals also have a much lower sulfur content. Low volatile bituminous, and anthracite coals occur in Alaska, but most Alaskan coals range downward in rank from high volatile bituminous to subbituminous and lignite. Alaskan coals are similar to coals of the northern Great Plains and the Rocky Mountains. Arctic Region Northern Alaska Coal Fields Northern Alaska coal fields are by far the largest group of coal deposits in Alaska (Fig. 2). Coal-bearing rocks extend from the foothills of the Brooks Range about 160 km (100 miles) northward to within about 80 km (50 miles) of the Arctic coast. The principal known occurrences are between the Colville River and the western coast. However, coal has been found eastward almost to the Canning River and westward under the Arctic Ocean. The northern Alaska coal fields are in a series of Cretaceous rocks that suggest a deltaic depositional environment. The beds tend to occur in series of up to eight or nine beds totaling 6-9 m (20-30 ft) of coal. However, beds 6-12 m (20-40 ft) thick have been reported, and beds 1-3 m (3-10 ft) thick seem to be relatively common. Including thin seams, coal in some places makes up about 10% of the stratigraphic section. However, no area has been explored in sufficient detail to block out any large body of reserves or to make reliable estimates of the total resource. Observation points in drill holes and along river and stream banks are few and far between. Coals in northern Alaskan fields tend to range in rank from bituminous, where moderately folded and faulted in the foothills, to subbittuminous in the gently folded rocks under the coastal plain. Coals toward the eastern extremities of the coal fields may be of Tertiary age and lower in rank, but the same general correlation between degree of folding and increase in rank can be expected. Some higher rank coals in the foothills belt are known to have coking properties but most, and possibly all, require

Jan 1, 1984

By H. R. Thresh, A. F. Crawley

THIS paper reports the results of viscosity measurements on cadmium and indium undertaken as part of a continuing program of liquid metals research at the Mines Branch, Department of Energy, Mines and Resources, Ottawa, Canada. For several years this work has continued with support from the Canadian Zinc and Lead Research Committee and the International Lead and Zinc Research Organization. In the literature, existing viscosity data for cadmium are conflicting and for indium are scarce. To achieve reliable viscosity values, further work was deemed desirable. Viscosities were measured using an absolute technique applied to an oscillating closed right cylinder of liquid metal. The apparatus, constructed in this laboratory, and the techniques involved in its use have been described in an earlier paper.' In calculating viscosity coefficients from the experimental data. Roscoe's2 mathematical analysis was used. Because accurate viscosity determinations are dependent on accurate density data, and since the available data in the literature are conflicting, the densities of liquid cadmium and indium were also determined in this laboratory by a pycnometric technique. This increased the control exercised over all the variables contributing to the accuracy of viscosity measurements. For both density and viscosity determinations, cadmium and indium of 99.999 pct purity were used. These materials were obtained from Cominco Ltd. In order to suppress excessive evaporation losses and help prevent oxidation, a technique developed in measuring the viscosity of zinc' was used for cadmium. This involved maintaining an atmosphere of purified hydrogen in the viscosimeter during the rela- tively long periods while the experimental temperature was changed and stabilized between individual determinations of the logarithmic decrement. Then, immediately prior to a decrement measurement. the viscosimeter was rapidly evacuated to a pressure of about 2 X 10-6 torr. On the other hand. with indium. no difficulties arise from vaporization or oxidation. In this case. therefore. the apparatus was held under a constant vacuum of about 2 x 10-6 torr. When all sources of random and systematic error have been evaluated, the technique is considered to yield data accurate within 10.5 pct. The viscosity of cadmium was measured to a maximum temperature of 451.8°C and that of indium to 346.5°C. These temperatures are. respectively. 130° and 190°C above the melting points. Two separate runs were made on indium. The results are given in Table I and, when plotted. yield the smooth curves evident in Figs. 1 and 2. Values of A and C to fit the well-known Andrade1 equation were determined by a regression analysis. The equation is: where n = coefficient of viscosity. i = specific volume. T = temperature in °K Despite its empirical nature. Andrade's equation has been shown by many workers to describe accurately the temperature dependence of viscosity. During the current research program, this equation has been found to fit the data precisely for all the metals and alloys that have been studied.5,6 The A and C' values for cadmium and indium are given in Table 11. Comparing the magnitude of the present data with those of previous workers,7-10 as has been done in Fig. 1, it is evident that the results of Fisher and Phillips10 deviate markedly from the rest. With the exception of one point from Gering and Sauerwald,7 all other data agree within ±2.5 pct. However, the agreement between the present results and the work of Menz and sauerwald9 is especially good over the entire experimental temperature range. Such agreement may be expected since Menz and Sauerwald's

Jan 1, 1970

By P. Ramachandraraa, T. R. Anantharaman

THE technique developed by Duwez, Willens and Kle-ment' for rapid solidification of molten alloys in small quantities by ejecting them on to a highly conducting substrate with the aid of a shock wave has come to be known as "liquid quenching" or "splat cooling" in literature and has already been applied to alloys of many binary systems.' The very high cooling rates of the order of l060 to 1080 per sec obtained in this technique and the consequent drastic undercooling of the melt have led to such striking results as formation of new amorphous and crystalline metastable phases and extension of solid-solubility limits in many alloy systems. The cooling rates in these experiments can, however, be neither accurately measured nor effectively controlled and hence the occurrence of either more than one metastable phase or appreciable differences in constitution in splat-cooled alloys of the same composition cannot be ruled out.3 In fact, workers in two laboratories have reported formation of two different cubic metastable phases in liquid-quenched Au-Si alloys containing 17 to 20 at. pct si.4,5 The present note deals with some new and interesting results obtained in a Ag-21 at. pct Ge alloy and a Au-27 at. pct Ge alloy subjected to the liquid-quenching treatment at different cooling rates. Two alloys of nearly the same composition had earlier been rapidly solidified by the standard "gun technique" in the same laboratory and shown to solidify in nonequilibrium structures, viz., an hcp phase (a = 2.987Å;c =4.718Å) in the Ag-Ge system6,7 and both hcp (a = 2.885Å; c = 4.754Å) and tetragonal (a = 11.627A; c = 22.491Å) phases in the Au-Ge system.3 Apart from different substrates (copper and stainless steel), different melt temperatures (50º to 500°C above the liquidus), and different capillary sizes (0.4 to 1.5 mm diam) in the "gun technique", slower cooling rates of the order of l050C per sec were also obtained in the present work by replacing the substrate by water at room temperature in a modification of the technique due to Olsen and Hultgren.8 No attempt was made to measure the cooling rate in any experiment. The products varied from fine powder (>40 pct by wt—200 mesh) obtained by quenching in water to thin flakes and foils (11.0 sq mm to 4.0 sq cm) produced by splat cooling. They were subjected to the Debye-Scherrer method of X-ray examination in each case. In case of the Ag-Ge alloy, in addition to the expected metastable hcp phase,6 a coexistent tetragonal phase (a = 5.093,Å; c = 7.009Å) was detected in some experiments. Eight weak X-ray reflections from this phase could be identified, two of them being the same as reported earlier.7 With increase in the cooling rate, the dominant hcp phase seems to be first accompanied by traces of silver or germanium and then either homogeneous or mixed with traces of this new tetragonal phase. The splat-cooled Au-Ge alloy showed generally the expected hcp and tetragonal phases,3 but sometimes traces of germanium were also present. Further, two new tetragonal phases with the following lattice param ters could be clearly identified in samples quenched

Jan 1, 1970

By James T. Waber, Allen C. Larson, Karl Gschneidner, Margaret Y. Prince

The original graphical method proposed by Darken and Gurry for predicting which elements are soluble in a given element was slightly modified and was used to predict terminal solubilities in 1455 known binary combinations. it was found that the modified Darken and Gurry method had a reliability of 61.7 pct in predicting extensive solid solubility (greater than 5 at. pct) and of 84.8pct in predicting limited solid solubility (less than 5 at. pct), an over-all reliability percentage of 76.6. Using the same experimental data, it was found that using only the simple Hume-Rothery size-effect criterion was 50.1 pct reliable in predicting extensive solid solubility, only slightly better than a purely random choice. and 90.3 pct reliable for predicting limited solid solubility, an over-all reliability percentage of 67.6. THE first rational rules for determining a priori whether two metals are not freely soluble in the solid state were announced by Hume-Rothery and coworkers.1,2 These well-known rules have been accorded a special place in metallurgical literature. Since the "electronegative" and "relative valence effect" rules of Hume-Rothery were only qualitative in nature it was difficult to use them in a quantitative analysis. The next major step was made by Darken and gurry3 and apparently went unexplored for a number of years. They prepared graphs illustrating the influence of both electronegativity and size difference on the solubility of elements in silver, magnesium, and aluminum, and they drew elliptical figures, whose maximum width was ±15 pct of the solvent radius and the maximum height was ±0.4 electronegativity units. The purpose of the present paper is to assess and compare the effectiveness of using the simple size-factor and the Darken-Gurry criteria to predict which elements will be soluble and insoluble in a given solute. In 1957, waber4 prepared Darken-Gurry plots for determining the solutes that were likely to be soluble in 6 and plutonium and introduced an inner ellipse as an aid to determining which elements should be soluble to a considerable extent. As illustrated in Fig. 1, the major axis of the outer ellipse corresponded to ±0.4 electronegativity units (OD) while the minor axis corresponded to ±15 pct of the radius of the solvent phase (OB). This simultaneous "action" of the two Hume-Rothery criteria was used to indicate which elements would have little or no solubility in the host lattice, namely those elements whose points lay outside this ellipse. An inner ellipse, "centered" over the same point of the solvent was drawn with ±0.2 electronegativity units (OC) and ±8 pct (OA) as the major and minor axes. Solutes with points lying within the inner ellipse were expected to be capable of forming extensive solid solutions with the host element. Use of this method of applying the earlier Hume-Rothery criteria was moderately successful for plutonium. For 6-phase plutonium, only one element out of the eight predicted to be extensively soluble was known to be almost insoluble, and of the sixteen elements predicted to have more restricted solubility, five were known to be essentially insoluble. The success of discerning solubility in the E phase by this method was comparable. One prediction made on the basis of this analysis was that the heavier rare earth metals, such as holmium, erbium, and thulium, should be soluble in the 6 phase, whereas the lighter rare earth elements, such as lanthanum or

Jan 1, 1963

By M. W. Legatski, D. L. Katz

The best currently available description of the longitudinal mixing properties of a porous medium is an equation of the form which relates the effective longitudinal dispersion coefficient Dp to the molecular diffusion coefficient Do, the electrical resistivity factor F, the porosity <f> and a Peclet number. If the parameters dpa and m are determined for a porous medium of known porosity and electrical resistivity factor, then a dispersion coefficient may be estimated for a given flow rate and a given gas pair. A new method, featuring on-line gas analysis by thermal conductivity and on-line data reduction by analog computation, was developed and used to determine these mixing parameters for eight naturally occurring sandstones and two dolomite samples. The exponent m of the above equation was found to vary between 1.0 and 1.5. The characteristic length dpa in the above equation was found to vary between 0.25 and 1.9 cm, with an average value of 0.4 cm for sandstones. Measurements were made on two cores in which paraffin wax had been deposited by evaporation from a pentane solution. They indicated that the presence of an immobile phase such as connate water could increase the dispersion coefficients significantly. INTRODUCTION While the petroleum and chemical industries have studied the mixing of miscible liquids flowing in consolidated porous media and of miscible gases flowing in unconsolidated porous media, relatively little data have been presented to describe the mixing of gases flowing through consolidated porous media. Such data are of particular interest to the gas storage industry. For instance, the U. S. Bureau of Mines is storing large quantities of a rich helium-nitrogen gas in contact with a natural gas in a dolomite reservoir. Since the rich gas occupies only 15 percent of the total reservoir volume, it is essential that the extent of rich gas-natural gas mixing be predicted and understood as a function of rock properties, pressure and rate of movement. This investigation was concerned only with the determination of longitudinal dispersion coefficients. It is understood that a transverse dispersion coefficient, which characterizes mixing perpendicular to the direction of flow, may be an order of magnitude less than the coefficient characterizing mixing in the direction of bulk flow.5719 It should also be recognized that the use of any dispersion coefficient is in itself a simplification. It is necessary to assume that mixing in a porous medium may be characterized by the equation for flow in a single direction. A number of authors1 l8,19 have pursued the mixing problem, not in terms of the so-called "dispersion model" described by Eq. 1, but in terms of a "mixing cell model". This model supposes that a porous medium is constructed of a large number of small mixing chambers and that the concentration of the diffusing component within each mixing chamber is uniform. Fick&apos;s law (Eq. 1) assumes that there is no gross by-passing of one fluid by another, and that there are not stagnant pockets of gas in the system under consideration as discussed by Coats and Smith.8 These assumptions are not always valid for flow through porous media and it is important to recognize the limitations upon Eq. 1. The most serious limitation upon the assumption of Fick&apos;s law mixing in a porous medium is

By J. Lemish

Considerable research has been conducted in Iowa in recent years on carbonate aggregate reactions in concrete. Groups outside the state have become active in the past few years after recognizing that certain carbonate aggregates are reactive in concrete. The paper reviews the nature and extent of the problem and a summary is given of research by the author and his associates. In recent years considerable research has been conducted in Iowa on carbonate aggregate reactions in concrete. The research is part of a general study on the behavior of carbonate rocks as concrete aggregates sponsored by the Iowa State Highway Commission. Research on carbonate aggregates has not been extensive in the past. Laughlin1 published one of the first papers on carbonate aggregates in 1928 and was followed by others, notably H. S. sweet,&apos; B. Mather et al.,3 and K. Mather4 who emphasized the petrographic and physical aspects of carbonate aggregates. The recognition that certain carbonate aggregates are reactive in concrete has led to increased participation in research in the past few years by groups outside of Iowa. Significant contributions have been made by Swenson and Gillot,5 Hadley,6 and Chaiken and Halstead7 in work which emphasizes the expansion of carbonate rocks in alkaline environments and the reaction of carbonate minerals or dedolomitization with alkalies. It is the purpose of this paper to review briefly the nature and extent of the problem and present a summary of the research by the author and his associates. EXTENT AND NATURE OF THE PROBLEM The problem is the deleterious behavior of certain carbonate aggregates in concrete. It was first recognized in Iowa over 20 years ago when poor service records of certain highways were correlated with aggregates produced from the Glory and LeGrand quarries. Deleterious behavior of carbonate aggregates have been reported in Canada and, more recently, in New York and Virginia. As more knowledge is gained concerning the problem, distress in concrete related to carbonate aggregates may be recognized over a widespread area. The problem may potentially exist in the Midwest, the Northeast, and other parts of the country underlain by thick sections of carbonate rocks readily available for utilization as aggregates. The nature of distress in Iowa highways is a general weakening and deterioration of concrete characterized by progressive cracking and spalling away from joints and edges (Fig. 1). The distress generally occurs after 15 years of service and becomes progressively worse. Specimens of such concrete lack the toughness of sound concrete and break easily under the hammer in the manner of a soft brick. The matrix is generally highly carbonated and dark borders, or reaction shells or rims outline the argillaceous carbonate aggregate fragments (Fig. 2). Cracks observed in cores cut across the aggregates and concrete matrix. Although localized volume change (expansion) is associated with spalling, there is no definite field evidence in Iowa that excessive growth of concrete slabs has occurred. The experience with carbonate aggregates in Iowa indicates that the concrete deterioration is not the same as that induced by the alkali-aggregate reaction associated with siliceous aggregates. The principal difference is that in Iowa the distressed concrete is weakened throughout the slab. In concrete affected by the alkali aggregate reaction, the

Jan 1, 1961

By J. Phillip Neal, Kefton H. Teague, Carroll P. Rogers

Feldspars, the most abundant minerals of the igneous rocks, occur in numerous forms and mixtures. The feldspars of commercial significance are found in widely distributed pegmatites as large crystals usually free of iron-bearing impurities and thus suitable for hand-cobbing, and also in larger bodies where the ore contains various types of feldspar intermingled with quartz and relatively free of iron-bearing impurities, or at least readily unlocked from impurities present at relatively coarse mesh. The latter type of ore includes some pegmatites, and the "alaskite" bodies so common in the Spruce Pine district of North Carolina. On the west coast of the US and in Oklahoma there is-or has been-commercial recovery of natural feldspathic sand as a source of alumina in glass and ceramics. "Aplite" in commercial terminology is a light-colored igneous rock with a granitic composition and a fine sugary texture, often banded with readily removable iron impurities. Only one area in Virginia produces aplite for the glass industry; it is located near Montpelier in Hanover County. According to Deer et al. (1966) the word feldspar derives from the Swedish feldt or jolt (field) and "spath:" chunks of rock appearing in tilled ground overlying granite. Castle and Gillson (1960) indicate a Germanic origin, citing "spat," which is said to refer to any transparent or translucent material which is readily cleavable. The term "spar" has in the past been applied to minerals other than feldspar, such as barite, calcite, and fluorite. It is correct to call the latter "fluorspar." There is a true barium feldspar, but it is rare and of no present economic importance. What is recognized as feldspar or "spar" by present producers and consumers consists of three silicate minerals which, if pure, would have the formulas KA1Si3O8 (microcline or orthoclase), NaAlSi3O8 (albite), and CaAl2Si2O8 (anorthite). These are almost never found in pure form in nature, but occur together in great abundance in a three-component system. A considerable number of different combined ratios of these three exists, with the exception that isomorphism between potassium spar and calcium spar is very limited. User specifications for feldspar products are largely built around the prevalent naturally occurring ratios. Passages following will refer to "K-spar," "Naspar," or "Ca-spar." Nomenclature and Descriptive Terms Relating to both the mineralogy and the economics of feldspar are certain terms whose coverage it is useful to specify. Commercially, aplite is a feldspathic rock mined and beneficiated in one location in Virginia, in which both titanium and feldspar minerals are present-the latter now being the major, if not the only, economic product. Technically, the term aplite when applied to this rock is of questionable accuracy. But, in light of accepted commercial usage, the term will be here used to designate it. Regarding the Virginia rock, Ross (1941) is cited. Alaskite is another term requiring understanding if not precise use. A distinctive rock type customarily called by this name is found near Spruce Pine, Mitchell County, North Carolina. An important major feldspar source, it contains somewhat higher levels of plagioclase feldspar and quartz than alaskite as defined in the Glossary of Geology and Related Sciences, which states that `orthoclase, microcline, and subordinate quartz are the principal

Jan 1, 1983

By L. G. Austin

My first contact with industrial milling was during the time I worked in the electricity generating industry in the United Kingdom. In visits to power stations to investigate either deposits in the boiler furnaces or polluting deposits settling around the stacks. I had to check the performance of the vertical coal pulverizers, since poor pulverization aggravated both problems. Naturally, then, when I came to the USA in 1957 to take a PhD in fuel technology at Penn State, I was put to work to review the science of coal pulverization. After this reviewing, I was completely confused. On one hand, there was a well-developed understanding of stress-strain equations, and a rapidly developing knowledge of how stressed, brittle solids fractured, based on the Grifith crack theory. On the other hand, reading in the grinding literature gave me: -Kick&apos;s Law, which was clearly not correct in the light of modem fracture theory; -Rittinger&apos;s Law, which was also clearly not correct; -Bond&apos;s Third Law of Comminution, which was claimed to have something to do with the Grifith crack theory, but where the connection between the two was made by intuitive pseudo-scientific reasoning I could not accept; -the choice of mill motor power for the most common type of coal mill, the Raymond pulverizer, was calculated from the fan power required to move air through the mill. Although I could accept the empirical connection between the two, it made no sense from the point of view of fracture energy. Even today, most books or review chapters on size reduction start from these laws. Incorrect statements abound in the literature, such as "the Hardgrove Index is based on Rittinger&apos;s Law," which it is not, "The Bond theory states that work input is proportional to new crack tip length produced in particle breakage," which is not true, etc. My own test work showed that these "laws" did not fit the data for grinding of coal. At about this time, Epstein (1948) and Broadbent and Callcott (1956), following the original work by R.L. Brown (1941) at the British Coal Utilization Research Association, proposed describing breakage as a series of fracture stages. I took their concepts and developed the basic differential equation for a batch grinding process continuous in time, analogous to a batch chemical reactor. Robin Gardner then joined the project and did his PhD on treating batch grinding in the same way as a batch chemical reactor. He found that the basic equation had already been partially derived by Sedlatschek and Bass (1953) in Ger- many. We confirmed experimentally the validity of the equations for describing batch grinding (1962) and formulated the equation describing steady-state continuous grinding in a fully-mixed mill. At about the time this work was published, Gaudin and Meloy (1962) and Filippov (1961) independently published essentially the same equations, but without experimental proof of the validity of the concepts. I will give a brief overview of what these beginnings had led to in the design of mills for size and power, and show some of the results of this more detailed understanding of grinding processes. Concepts of Fracture Mills such as tumbling ball, rod, pebble and autogenous mills and vertical mills such as the Raymond, and E-type, apply compressive stress to lumps or particles relatively slowly. Compressive stress applied to a particle of an elastic brittle solid imparts overall strain energy to the solid and produces local regions of tensile stress, [(Fig. 1)] (Berenbaum and Brodie, 1959).

Jan 1, 1985

By H. R. Brannon, F. M. Perkins, Weldon O. Winsauer

Both the abnormal resistivity exhibited by shaly reservoir materials and their potential are due to adsorption of ions. Interrelationships between the two have been derived and verified by laboratory results. These relations which have resulted from this work may be used in a qualitative manner to estimate whether or not a particular shaly reservoir contains hydrocarbons, and also to estimate the porosity of shaly sands. INTRODUCTION In spite of the progress which has been made in the last decade toward a better understanding and utilization of the electric log, there remain a number of problems in the interpretation of the log. One of these which is often troublesome is that of divining the nature of the fluids in sandstones or carbonate rocks which contain appreciable amounts of shale. It was shown by Patnode and Wylliel in 1949 that shaly rocks exhibit an abnormally low resistivity when saturated with solutions of low ionic concentrations. This phenomenon has been demonstrated to be due to the adsorptive properties of shale or clay in the rock.&apos; In estimating the fluid content of shaly sands or carbonates from the electric log, it is desirable and sometimes necessary to correct for the abnormally low resistivity. A similar correction is likewise often necessary if attempts are made to estimate the porosity of a stratum from resistivity measurements. The correction may be made from data obtained on core samples and from information on salinity of interstitial water. Cores, however, are not always available. Moreover, even if cores are at hand, their examination is time-consuming. It would be most desirable, therefore, to make corrections of this nature from the log itself. Since both the abnormal resistivity and the potential&apos; are consequences of the adsorption of ions on shale, it should be possible to utilize the potential curve to give better interpretation of resistivity data obtained in logging shaly materials. The work described in following sections was directed toward this end. THEORY Relation of Resistivity of Shaly Reservoir Rock to Adsorpttve Properties In discussing the effect which the presence of shale or clay exerts on the resistivity of a reservoir rock, it is convenient to make use of the resistivity factor.4,5 This quantity has been defined as the ratio of the resistivity of the rock when it is completely saturated with an electrolyte to the resistivity of the electrolyte itself. When the rock, such as a clean sand or carbonate, is free of shale the resistivity factor is virtually independent of the ionic concentration of the electrolyte used to saturate the sample, so that F = R0/Rw = constant for a clean rock . . (1) where F is the resistivity factor, R0 is the resistivity of the rock saturated with electrolyte, and Rw is the resistivity of the electrolyte. When the rock contains argillaceous material, the resistivity factor as defined above is no longer independent of the concentration of the electrolyte used to saturate the rock, but decreases as the ionic concentration of the electrolyte decreases. In explanation of this behavior, it is instructive to consider a sample of shaly porous rock placed in contact with a large volume of a dilute electrolyte. The sample is considered to become saturated with the electrolyte, and to attain equilibrium with it. As a result of adsorption by the shale surfaces within the rock, there is a greater concentration of ions in the solution adjacent to the shale particles in the interstices of the sample than there is in the external solution with which the

Jan 1, 1955

By M. Muskat, M. O. Taylor

Theoretical calculations have been made on the performance to be expected of gas-drive reservoirs for various characteristics of the oil and gas and the producing rock. Such performante has been expressed graphically as curves for the reservoir pressure and gas-oil ratios of the production as functions of the cumulative oil recovery. The latter has been expressed in terms of percentage of pore space of the reservoir rock. Such curves automatically give values for the ultimate physical recovery, if the latter is interpreted as the recovery obtained when the reservoir pressure has declined to atmospheric, or to any other pressure chosen as defining the state of practical complete depletion. Calculations of these pressure and gas-oil ratio histories have been made for conditions in which the oil viscosity, the gas solubility and shrinkage, the size of an overlying gas cap, if present, the permeability-saturation characteristics of the rock, and the amount of connate water, have been individually varied, The results serve to show the extent to which the ultimate recoveries are sensitive to the important physical parameters characterizing the oil reservoir. As is to be expected, the ultimate recoveries are found to decrease with increasing oil viscosity. Because of the predominant effect of the oil shrinkage associated with the liberation of the gas in solution, the ultimate recovery will decrease with increasing gas solubility. Increasing gas-cap volumes lead to higher recoveries, although the contribution made by the gas-cap gas is small as compared with the oil expulsion by the equivalent amount of solution gas. As a whole, the oil recovery when expressed in percentage of the pore space is not very sensitive to the details of the permeability-saturation relationship. However, if the rocks possess an equilibrium free-gas saturation, the rise in gas-oil ratio will be retarded, and the &apos;ultimate recovery somewhat increased&apos; The oil shrinkage associated with the liberation of the dissolved gas also leads to the result that as long as the connate water is immobile and the permeability ratio curve for the rock is a function only of the total liquid saturation, the stock-tank oil recovery will be less for a sand containing no connate water than for One with an Original water content as high as 3&apos; per cent. The space voidage in the former case will be somewhat greater, but the effect of oil shrinkage will lead to smaller values for the equivalent stock-tank recovery. These calculations also give data showing how the productivity indexes for the producing wells will vary during the reservoir history. Because of decreasing Permeability to the oil and increasing oil viscosity, the productivity index will fall continuously as Production proceeds, and may finally reach values as low as 10 per cent of the initial productivity index. Introduction In a previous paper1 was developed the basic theory for the prediction of the production histories of gas-drive reservoirs. The data required for the application of this theory included the characteristics of the petroleum fluids, such as the viscosity of the Oil and gas phases, the solubility of the gas in the oil, and the oil shrinkage— all expressed as functions of the reservoir pressure—and the permeability-saturation characteristics of the producing rock, as

Jan 1, 1946