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By A. Andreas

New Mexico established an annual record by producing 38,897,741 bbl. of oil during 1940. This was approximately 6 per cent greater than the 1939 production of 36,746,840 bbl. The daily average produc-tion was 106,569 bbl. New Mexico retained its position as the seventh oil-producing state. The recommendations of the United States Bureau of Mines were followed by the Oil Conservation Commission in setting the monthly state allowable. At the beginning of the year the average top allowable for each qc-acre unit was 40 bbl. and at the close of the year it was 36 bbl. Remedial work by the operators has been extremely beneficial and satisfactory in reducing the gas-oil ratios in various fields. Gas formerly blown into the air is now being processed by numerous casinghead plants. The Oil Conservation Commission, with the full cooperation of the Proration Office and operators, has taken bottom-hole pressure surveys and has done considerable remedial work in various fields. Two new oil fields and one gas field were discovered in New Mexico during 1940. Numerous extensions to the existing fields were made. Some of these were definitely wildcats in the same townships designated as fields and some, although called extensions, were more than 3 miles from production. Lea County continued to be the largest oil-producing county in the state, with a production of 33,976,394 bbl. It had the largest number of completions during 1940, with 303 oil wells, 9 gas wells and 13 dry holes—a total of 325 wells. Eddy County was the next most active county, with 239 completions, of which 163 were oil wells, 8 gas wells and 68 dry holes. It produced 4,405,158 bbl. of oil during the year. The increased activity in Eddy County and the completion of a large number of producing oil wells have created a transportation problem that can be solved only by additional pipe-line facilities. During the year Eddy County was unable to produce 1,500,000 bbl. of its allowable oil, because there was no pipe-line outlet. There were 601 wells completed in New Mexico in 1940, of which 478 were oil wells, 22 gas wells and IOI dry holes. This was a decline of approximately 9.5 per cent in the number of completions compared with 1939, when 659 wells were drilled. Southeastern New Mexico Lea County.—The largest producing field in Lea County was the Monument field, with 6,894,475 bbl.; followed by Eunice with 6,559,348 bbl. and Vacuum with 4,743,065 bbl. The Hobbs pool, which for years was the largest producing field in the state of New Mexico, was fourth with 3,790,477 bbl. The Vacuum pool was the most active area, having 68 completions, of which 67 were oil wells and one was a dry hole. Only one new field was discovered in Lea County during 1940; the discovery well was in the Caprock area, the Livermore State No. I, in the SE. 1/4 SE. 1/4 sec. 30, T. 12 S, R. 32 E. This well was drilled to a

Jan 1, 1941

By A. Andreas

New Mexico established an annual record by producing 38,897,741 bbl. of oil during 1940. This was approximately 6 per cent greater than the 1939 production of 36,746,840 bbl. The daily average produc-tion was 106,569 bbl. New Mexico retained its position as the seventh oil-producing state. The recommendations of the United States Bureau of Mines were followed by the Oil Conservation Commission in setting the monthly state allowable. At the beginning of the year the average top allowable for each qc-acre unit was 40 bbl. and at the close of the year it was 36 bbl. Remedial work by the operators has been extremely beneficial and satisfactory in reducing the gas-oil ratios in various fields. Gas formerly blown into the air is now being processed by numerous casinghead plants. The Oil Conservation Commission, with the full cooperation of the Proration Office and operators, has taken bottom-hole pressure surveys and has done considerable remedial work in various fields. Two new oil fields and one gas field were discovered in New Mexico during 1940. Numerous extensions to the existing fields were made. Some of these were definitely wildcats in the same townships designated as fields and some, although called extensions, were more than 3 miles from production. Lea County continued to be the largest oil-producing county in the state, with a production of 33,976,394 bbl. It had the largest number of completions during 1940, with 303 oil wells, 9 gas wells and 13 dry holes—a total of 325 wells. Eddy County was the next most active county, with 239 completions, of which 163 were oil wells, 8 gas wells and 68 dry holes. It produced 4,405,158 bbl. of oil during the year. The increased activity in Eddy County and the completion of a large number of producing oil wells have created a transportation problem that can be solved only by additional pipe-line facilities. During the year Eddy County was unable to produce 1,500,000 bbl. of its allowable oil, because there was no pipe-line outlet. There were 601 wells completed in New Mexico in 1940, of which 478 were oil wells, 22 gas wells and IOI dry holes. This was a decline of approximately 9.5 per cent in the number of completions compared with 1939, when 659 wells were drilled. Southeastern New Mexico Lea County.—The largest producing field in Lea County was the Monument field, with 6,894,475 bbl.; followed by Eunice with 6,559,348 bbl. and Vacuum with 4,743,065 bbl. The Hobbs pool, which for years was the largest producing field in the state of New Mexico, was fourth with 3,790,477 bbl. The Vacuum pool was the most active area, having 68 completions, of which 67 were oil wells and one was a dry hole. Only one new field was discovered in Lea County during 1940; the discovery well was in the Caprock area, the Livermore State No. I, in the SE. 1/4 SE. 1/4 sec. 30, T. 12 S, R. 32 E. This well was drilled to a

Jan 1, 1941

By W. R. Shimer, F. O. Kichline

The investigation herein described was carried out for the purpose of studying, both by chemical and metallographical means, the extent of over-oxidation of steel that can be accomplished by excessive overblowing in a Bessemer converter. 111 addition there are appended some results of basic open-hearth and crucible steels. Remarks on Chemical Methods. The test block used was hemispherical in shape, 4.5 in. in diameter and 2 in. thick. Drillings for analysis were obtained by drilling through the entire solid part of the block, carefully avoiding all cracks and blow-holes and mixing these drillings thoroughly. Drillinga were carefully examined for scale and the finest were gone over with a microscope to be sure all scale from whatever source had been removed. Oxygen was determined by the well-known method of Ledebur, modified according to Cushman,1 with, however, the removal of the preheating tube, which was found unnecessary. This method has been found to give concordant results. Blanks run from 0.0003 to 0.0006 g. Duplicate determinations varied not more than 0.001 to 0.003 per cent. It seems to be generally supposed that the hydrogen method gives only that oxygen which is combined with iron. Whether this be true or not, the content of oxygen existing as iron oxide no doubt predominates sufficiently, so that the result obtained is sufficient to indicate whether the steel is over-oxidized or not. We are well aware that the oxides of manganese and chromium, when existing alone, are not reduced by hydrogen at a red heat. To learn of their action in steel the following work was carried out: A sample of ferro-manganese and of ferro-chrome were each exposed

Jan 1, 1914

BASIC open-hearth slags have no obviously unique features when compared with slags from other metallurgical operations. Open-hearth slags form and exist at temperatures ranging from 2500 to 3100 F (1370 to 1700 C). In the course of an open-hearth heat, the liquid slag changes slowly and continuously in chemical analysis-the changes reflecting changes in temperature, changes in metal analysis, solution of charged materials, solution of feed additions, and solution of refractories. Through- out the process, the slag performs specific primary functions that are responsible for a large measure of the technical and economic importance of basic open-hearth steelmaking. It is intended in this chapter to present the chemical reactions by which the primary functions of basic open-hearth slags are carried out, to describe the physical and chemical principles governing the extent to which these reactions proceed and can be regulated, and finally to indicate the limitations imposed on other features of the process by the fulfillment of the primary functions. Basic open-hearth slags perform three primary functions. First and foremost, the slag provides a means of removing phosphorus from the liquid metal. The ability to remove phosphorus is largely responsible for the widespread use of the basic open- hearth process. Second, the slag serves as a controlling factor in transferring the oxygen required for the other oxidizing reactions. Third, the slag provides a means of eliminating some sulfur from the open-hearth bath. While the extent of sulfur removal is not comparable to that of phosphorus, the ability to remove some sulfur contributes much to the value of the process. The effectiveness with which the slag fulfills its functions varies with temperature and composition. Since operating temperatures are fixed largely by the specified nature of the product and the equipment, the speed and extent to which the functions of the slag are carried out depend largely on its composition. The necessity for regulating slag composition to accomplish the re-

Jan 1, 1951

By D. H. Gray, G. Bergamini, I. Fatt

A method developed by soil scientists for measuring permeability anisotropy of soils has been adapted for use in studies of sandstone permeability aniso-tmpy. Studies on Berea and Bandera sandstone show that permeability of these materials decreases upon application of simulated overburden pressure. Permeability reduction of Berea and Grubb sandstone cores subjected to simulated overburden pressure is shown to be a function of the ratio of radial to axial stress. INTRODUCTION The effects of mechanical stress on reservoir rock parameters are now generally accepted as being important in reservoir engineering calculations. In several oil fields the unique behavior of the reservoir has been attributed to the influence of overburden pressure or internal fluid pressure on rock permeability or fluid content. l Although the gross effects of overburden pressure on permeability, porosity, waterflood efficiency, electrical resistance and sonic velocity have now been established,3-9 there are some very interesting, and perhaps important, details of rock behavior under stress that have not heretofore been studied. In this paper we will show that permeability anistropy of several sandstones is a function of overburden pressure. We will also show that permeability reduction of cylindrical samples of two sandstones, when subjected to mechanical stress, is a function of the ratio of radial to axial stress. Most studies of overburden pressure effects made in the past have attempted to duplicate reservoir conditions by applying hydrostatic external pressure on all surfaces of the sample. Assuming perfect elasticity, that is, no viscoelastic flow during geological time, reservoir rock in situ cannot be under hydrostatic stress as is apparent from the value of 0.25 for Poisson's ratio for most rock. In the absence of tectonic forces the horizontal stress component If there are directional permeability effects, as has been reported from field and laboratory studies, l0,11 then one would expect hydrostatic stress as used in the laboratory to give a different permeability reduction from that occurring under reservoir stress conditions. The influence of stress on directional permeability was measured by a modification of the method first described by Maasland and Kirkham for use on soil samples.12 Their method permits calculation of the permeabilities along each of the three mutually perpendicular axes of a cubic sample. The modification reported in this paper extends the method to observing these permeabilities when the sample is under hydrostatic stress. The Hassler sleeve type of core holder is satisfactory for studying overburden pressure effects on permeability if a known force is applied to the end plugs. Wyble6 used a sleeve core holder but did not load the end plugs. In this paper we combine sleeve pressure and axial force to give permeability changes which we believe are close to those occurring in reservoirs when reservoir pressure changes. The combination of sleeve pressure and axial force assumes, however, that the sleeve pressure simulates both vertical stress and horizontal stress in one direction. METHOD PERMEABILITY ANISOTROPY The Maasland and Kirkhaml2 method of measuring permeability anisotropy uses a cube of porous material which is Open On three faces and has discs with a Center hole for an air inlet cemented to the other three mutually perpendicular faces (Fig. 1). The rate at which air pressure falls in a bottle of known volume, and pressure slightly above atmospheric, when the bottle discharges through each disc, is

By M. C. Flemings, T. S. Piwonka

Pore formation is examined analytically in cellu-larly solidified single crystals, in cylindrical castings of pure metals and alloys, and in unidirectionally solidified castings. Effects are considered of fluid flow. dissolved gas, and surface tension. Experimental results show that flow through a partially solid "mushy" aluminum alloy obeys relations similar to those applicable for flow through other types of porous beds. Flow rate is proportional to the square of the fraction liquid (fL) for fL less than 0.3. Results indicate models chosen for mathematical description of pore formation in alloy solidification are valid. ONE of the solidification variables which is influential in determining mechanical properties of castings and of wrought material produced from cast ingots is porosity. This porosity may result from shrinkage, dissolved gases, or a combination of both, and may take the form of either macroscopic pores in localized areas of the casting or microporosity evenly distributed throughout large areas of the casting. In alloys which freeze over a range of temperatures some microporosity is generally found after solidification. There has been much discussion as to whether the micropores are caused primarily by shrinkage, by gas, or by a combination of both.'-3 There has, however, been little experimental or analytical work performed to delineate the relative contributions of shrinkage and gas in causing microporosity or to quantitatively describe the influence of processing variables on microporosity. Porosity other than microporosity (e.g., center line shrinkage) has also received only limited quantitative treatment.495 The aim of this work is to examine analytically the general problem of pore formation in solidification and to perform limited confirmatory experiments. Consideration is first given to shrinkage porosity in pure and nearly pure metals (shrinkage in cellular growth, centerline shrinkage in cylinders). Next, a discussion is given of formation of shrinkage-caused microporosity in unidirectional solidification and in "mushy" solidification. Finally, influences of dissolved gas and surface tension on microporosity are examined. Numerical results are given for aluminum and an aluminum alloy. Typical examples of microporosity are shown in Figs. 1 to 3, for 1) cellularly solidified aluminum, 2) sand-cast aluminum alloy, and 3) low alloy steel. SHRINKAGE POROSITY IN PURE AND NEARLY PURE METALS 1) Cellular Growth. In cellular freezing of an impure liquid, liquid grooves may exist over a considerable length of the growing crystal.6 The cross-sectional area of the grooves decreases with increasing distance from the cell tips; the root of the groove is blunt if the liquid at this point reaches eutectic composition. As a result of volume contraction during solidification, flow occurs down the groove, parallel to the growth direction; hence, there must be a pressure drop from the groove entrance to points within the groove. The geometry of the groove is simplified to that of a circular cylinder of radius r and length L, Fig. 4, L » r, and a simple and useful limiting case is obtained. This is that, in the circular cylinder freezing at constant velocity, the pressure at the root of the groove is lower than that pressure at radius r in grooves of other geometries where r decreases continuously to a lower limit at L. As discussed below, a pore resulting from a given pressure difference

Jan 1, 1967

THE foundation established by the partners of the late Robert W. Hunt provides for both a medal and a prize. The latter has not been given before this year, and the first award is to C. H. Herty, Jr., for his several papers on the physical chemistry of the open-hearth process.. He is the son of the well known chemist of the same name. He was born at Athens, Ga., on Oct. G 1896, graduated from the University of North Carolina in 1918, and went into war service as foreman of U. S. Chemical Plant No. 4, at Saltsville, Va. In 1919 he went to Massachusetts Institute of Technology, where he was successively instructor, research assistant, and research associate in the School of Chemical En-gineering practice receiving his master's degree in 1921 and his Ph.D. in 1924. He continued his brilliant work on the physical chemistry of the open-hearth process, much of it being done in cooperation with the Bethlehem Steel Co. at its Lackawanna plant, and dealing with the elimination of sulfur. In 1926 he joined the staff of the U. S. Bureau of Mines, in charge of its ferrous metallur-gical work at Pittsburgh, and continues to be active in research work on the physical chemistry and metallurgy of the open-hearth process. His Institute publications are: Some Factors Affecting the Elimination of Sulfur in the Basic Open-hearth Process," "Chemical Equilibrium of Manganese, Carbon and Phosphorus in the Basic Open-hearth Process" and "Desulfurizing Action of Manganese and Iron," and he will present a paper on ?Effect of Temperature on the Solubility of Iron Oxide in Iron" at the annual meeting.

Jan 2, 1928

G. W. TRAER (author's reply to discussion*).-Prof. Parr's discussion develops two points, upon which it seems desirable to comment. First, as to putting through a large enough tonnage to secure economic operation. At each manipulation of each oven 1500 1b. (680 kg.) of coal will be charged and the resultant coke discharged from a like amount of coal. . Sixteen slabs will be discharged at each manipulation, each approximately 5 ½ in. by 11 in. by 6 ft. (14 cm. by 28 cm. by 1.8 m.). The operating schedule of a commercial plant, based upon our observations and calculations, indicates a "through put" of at least 12 tons of coal per day for each oven. We have made these figures conservatively and feel confident of materially exceeding them in a fully developed operating system. Our oven plant, with containers, will not cost as much as high-temperature plants of the same capacity. They do not require container equipment; but this is much more than offset by the cost of the great basal heat regenerative flues. Our operating requirements are quite susceptible to the application of mechanical devices and we believe our labor cost will be well within the necessary limit. Second, as to Fig. 1 in my paper, showing the specific gravity' of the tar. It Was not intended to show that the specific- gravity of -the tar rises With decreasing heat, since of course the contrary is the fact. One of the curves shows the relation between temperature and specific gravity and the other the relation between temperature and- yield. Our consulting engineer prepared the chart according to his customary method for showing two dimensions.

Jan 1, 1919

By K. E. Gray, M. S. Seth

Equations of elasticity for transversely isotropic, axisymmetric, homogeneous, porous media exhibiting pore fluid pressure were formulated. Using an analogy between thermal and porous body stresses, it was shown that the solution for a transversely isotropic porous body may be obtained by incorporating body forces and the stresses due to a boundary load into the corresponding solution for the thermal stress problem. Equations of elasticity ad the thermal analogy method were used to determine transient horizontal, tangential, and vertical stresses and radial displacement in a semi-infinite cylindrical region when either a constant pressure or a constant rate of flow is maintained at the wellbore. The vertical and tangential displacements are zero from the conditions of the problem. A numerical analysis was made of the solutions obtained by using a digital computer to determine the relative influence of each system variable. Considering rock as a porous body with internal fluid pressure generally gives results significantly different than considering the rock to be nonporous; the directional character of rocks leads to significant differences as compared to results based upon the common assumption of isotropy. Stress gradients are high near the wellbore but die out away from the well. Radial stresses are compressive or neutral, whereas tangential stresses are tensile, neutral or compressive, depending upon the boundary conditions and physical properties of the system Vertical stresses are compressive for an unbounded system. For constant wellbore injection rate, the vertical stress is proportional to the rate of fluid injection and decreases with time, whereas the radial and tangential stresses increase with time. At a given location, the radial displacement generally is very dependent upon time. INTRODUCTION A realistic appraisal of the state of stress in subsurface rock formations would be of considerable interest and use to the petroleum industry. For example, knowing the state of stress in proximity to a wellbore would be of fundamental importance in designing a fracturing operation or, more important, of clearly understanding the conditions necessary to produce rock failure of desired dimensions and geometry. Understanding conditions necessary for rock failure at the wellbore would also be of utility in a preventive sense. For example, borehole stability is an important consideration for many rock formations, and knowledge of the stress state at and near the wellbore under conditions of substantial pressure gradient due to fluid flow would be of great value. When fluid flows through a porous body which is initially at some uniform stress level, the following forces generate stresses at any point in the body. (1) Forces due to nonuniform pressure distribution. With increasing pressure the elements of a body are compressed. Such compression cannot proceed freely in a continuum when the pressure is not uniform throughout, and thus, stresses due to flow of fluid are set up. (2) Pore fluid pressure. This gives rise to normal stresses whose value at any point is the product of areal porosity and the fluid pressure. Although the fluid exerts uniform pressure, the stresses it creates in an anisotropic body may not be the same in all directions since the areal porosity in an anisotropic porous body is a direction-dependent quantity. This consideration leads to the concept of directional porosity. (3) Body Forces. The flow of the moving fluid imparts a force to the rock matrix, the magnitude of which depends upon the pressure

Jan 1, 1969

By R. R. Wilson

THE Cassidy Colliery operated by the Granby Consolidated Mining, Smelting & Power Co., Ltd., is situated about 9 miles in a southerly direction from the city of Nanaimo on Vancouver Island. The coal seam worked, which is called the Douglas bed, outcrops in the western part of the property, clipping easteyrl, and is opened by a slope 7 by 14 ft. in the clear, and is timbered by 12 to 14-in. framed sets of timber, 4 ft. center to center. A separate manway provides for a traveling road and at the same time forms an intake airway. The general average of the dip of the seam at Cassidy is 18°, and varies in thickness from 1 to 25 ft., averaging about 8 ft. The main slopes follow straight down the dip a distance of 4545 ft. At the bottom of the main slope two rock tunnels were driven a distance of 1500 ft. to the south, cutting through a fault, and opening up an area in the same seam which is known as No. 7 South Section. The coal is found in this section at a vertical depth of 1560 ft., and is very soft and friable. The immediate roof is a strong, sandy shale overlain by massive sandstone while the floor is a light-colored shale, hard when freshly exposed. It does not soften materially oil exposure. In the folding of the coal measures a great thrust caused a movement along the coal seam as indicated by the slickensided nature of the coal. The floor has buckled and this has rolled and squeezed the coal-so that with rare exceptions it shows no normal bedding but curved slip planes, which frequently start at right angles to the floor, curving upward and then in the direction of the dip. As such planes are slickensided it is probable that there is a coating of clay which is more or less impervious to gas.

Jan 1, 1927

By William Hurst

Muskat's depletion performance equation is here derived considering the expansion behavior of the reservoir hydrocarbon system and a simple fractional-flow equation. This nietkod of derivation leads logically to the two extensions that follow. The first of these is concerned with gravity segregation in a depletion-drive reservoir. The second is concerned with including an empirically determined tern? for water influx in the performance equation. The more general equation for gravity segregation when there is a primary gas cap and empirically-determined water influx is stated for completeness. These equations have been found useful in reservoir performance calculations in Eastern Venezuela. A discussion on the methods of solving these equations follows, and considers firstly the effect of taking finite intervals in the numerical integration, and sec-ondly, methods of incorporating the time functions involved in segregation in with the expansion behavior. The paper concludes with a brief general discussion on further extensions to the depletion performance equation. INTRODUCTION The two fundamental sources of energy by which oil is produced from a reservoir result from pressure depletion inside the boundaries of the reservoir and fluid encroachment across the boundaries of the reservoir. The wells in either case form low pressure outlets through which oil and gas may be produced by the expansive force of the reservoir fluids and associated encroaching fluids. When the reservoir pressure is higher than the bubble-point pressure of the oil, so that there is no free gas in the reservoir, these expansive forces are the only ones available for the production of oil. However, when the reservoir pressure is less than the bubble-point pressure of the oil, free gas is vaporized as the pressure falls. With both oil and free-gas phases present, the additional forces of gravity and capillarity may operate on the gas-oil system, as they have previously operated on the oil-interstitial water system. Gravity tends to segregate the free gas from the oil due to their density difference. Capillarity opposes and eventually balances gravity as the more extreme free gas and oil saturations are reached, preventing the independent move- ment of free gas until it is above a certain saturation, and the independent movement of oil when it is below a certain saturation. The type of depletion performance equation chosen for predicting the future performance of a reservoir depends on the amount of past history available. When the reservoir is somewhere past the halfway mark in depletion, some form of decline curve is often used. With less past history, material balance equations which incorporate empirical factors based on the past performance are often used. When, however, the amount of past history is small, the Muskat depletion performance equation will usually be used. The distinguishing feature of this type of equation is that empirical factors based on the over-all or macroscopic reservoir behavior are almost or entirely absent. Each parameter affecting the reservoir performance is ascribed an independent set of values based on measurements made on laboratory samples; that is, incorporating microscopic empirical factors. In establishing Muskat-type depletion performance equations, it is necessary to consider the reservoir as consisting of a number of associated blocks, in each of which the saturations and pressures may be considered uniform, and in each of which all substances have uniform pressure-volume characteristics. Thus, a primary gas cap can usually be considered as one block and an aquifer as another. Gravity segregation may be negligible for practical purposes when the rock and oil properties are adverse and/or the dip or thickness of the reservoir is too small. In this case the whole oil leg may be considered as one block, except in very large reservoirs. In very large reservoirs the fluid and rock properties may vary enough, particularly in the dip direction, for it to be necessary to divide the oil leg into a number of blocks, in each of which the relevant quantities may be considered uniform. When gravity segregation of the oil and free gas is not negligible, it is necessary to consider the space occupied by the initial oil leg as divided into two blocks, a secondary gas cap and an effective oil leg, in each of which saturations may be considered to be uniform. The total volume of these two blocks is thus constant, but the secondary gas cap grows continuously at the expense of the oil leg. Muskat1 derived depletion performance equations for the basic case of an oil reservoir with closed boundaries and without segregation, and for the case of an oil

By P. M. Blair, D. W. Peaceman

The shape and position of the gas-oil transition zone during downdip displacement of oil by gas has been calculated using flow equations which include the effects of gravity, relative permeability, capillary pressure and compressibility of the fluids. The calculations treat the problem in two space dimensions, and results are compared with data from a laboratory model tilted at 30° and 60° from the horizontal on displacements near and above the maximum rate at which gravity segregation prevents channeling of the gas along the top of the stratum. The good agreement between calculated and experimental results demonstrates the validity of the tecbnique as well as that of the flow equations. INTRODUCTION Knowledge of the fluid distribution and movement in an oil reservoir is important in producing operations and estimation of reserves. The history of the oil industry has included steady progress in improving the accuracy of calculations which provide the required knowledge. The earliest method of calculating reservoir performance consisted of material-balance equations based on the assumption that all properties were uniform throughout a reservoir.l For many reservoirs such a simple formulation is still the most useful. However, when large pressure and saturation gradients exist in a reservoir, the assumption of uniform values throughout may lead to significant error. To reduce these errors, Buckley and Leverett2 introduced a displacement eqation which considers pressure and saturation gradients. Methods available at that time permitted solutions to the Buckley-Leverett equation in one space dimension; these solutions have been very useful in solving many problems related to the production of oil. However, the one-dimensional methods are not adequate for systems in which saturations vary in directions other than the direction of flow. An example of such a system is the case of gas displacing oil down a dipping stratum in which the gas-oil contact becomes significantly tilted. Of course, the Buckley-Leverett displacement method cannot predict the tilt of the gas-oil contact. Recent improvements3,4 of the one-dimensional Buckley-Leverett method achieve some success in predicting the tilt of the gas-oil contact at sufficiently low flow rates. However, at rates high enough that the viscous pressye gradient nearly equals or exceeds the gravity gradient, even these improved one-dimen,sional methods incorrectly predict the shape and velocity of the contact. Further progress in estimating such fluid movements in a reservoir appears to require consideration of the problem in more than one space dimension. The recent two-dimensional method of Douglas, Peaceman and Rachford5 appears adaptable to calculate changes with time of the saturation distribution in a vertical cross-section of a reservoir. The movement of saturation contours should represent the moving fluid contacts and include the effects of crossflow due to gravity, as well as variations in the rock and fluid properties. The nonlinear nature of the equations used in the method has prevented proof of the validity of the solutions. Douglas, Peaceman and Rachford made some comparisons with experiment but did not include cases in which gravity was important nor cases involving displacement by the nonwetting phase.For these reasons, a test of the two-dimensional method for a case in which these factors are included would be very desirable. The test selected was a comparison of calculated results with those from a carefully controlled laboratory experiment on a model with measured physical properties. The model selected was one in which gas displaced oil down a tilted, rectangular sand pack. The model can be thought of as representing a vertical cross-section taken parallel to the dip of a reservoir. The displacement thus simulates gas displacing oil downdip that might result from gas-cap expansion or gas injection. This report outlines the calculation method used

By G. P. Bowman, D. F. Howard, R. K. Saxer, J. R. Myers

This study was undertaken to redetermine the phase diagram of the lead molybdate-bismuth molyb-date salt system. A portion of this diagram was originally determined by Zambonini in 1920, and more recently by Beale. Thermal analysis and X-ray methods were used to define this system. The diagram was found to be a simple eutectic type with an eutectic at 11 mol pet lead molybdate and 634OC. A maximum solid solubility of 6 mol pet was found at the lead molybdate end of the diagram. Solid solubility at the bismuth molybdate end of' the diagram appeared to be quite limited and possibly nonexistent. These results generally agree with those of Beale, but differ significantly from those of Zambonini. MOLTEN salt systems have been vigorously investigated since World War 11. Much of this work has been performed as pure research; however, consideration has recently been given to their possible use as coolants in nuclear reactors. Because of this application and other potential applications, it was decided to reinvestigate the lead molybdate-bismuth molybdate phase diagram. This diagram was originally determined by Professor F. Zambonini of the University of Turin in 1920.' In 1961, a portion of this diagram was redetermined by Beale.2 With the quality equipment and high-purity materials available today, it was expected that discrepancies between the results of this present investigation and Zambonini's work would be obtained. This investigation was conducted in two parts. First, the general shape of the phase diagram was determined by cooling-curve analysis. Next, the primary solid-solution phase at the lead molybdate end of the diagram was investigated by means of X-ray diffraction techniques. EXPERIMENTAL PROCEDURE High-purity lead molybdate, assaying 99.993 pet, and high-purity bismuth molybdate, assaying 99.989 pet, were employed during this investigation.* The results of a spectrographic analysis of the two salts are presented in Table I. Twenty-two experimental compositions were prepared for cooling-curve analysis. Compositions selected are presented in Table 11. Several randomly selected samples were analyzed chemically to check that the compositions of the prepared specimens were within the limit of

Jan 1, 1964

By G. R. St. Pierre, M. J. Pool, R. Speiser

The activities of chromium in solid Cr-Ti solulions contaitning from 10 to 90 at, pct Cr were measured over the temperatutre range 1250" to 1380°C. The Knzudsen effusion technique with direct weighing of the Knudsen cell was used. This was possible because the vapor pressure 0f chromium is about 600 times greater than the capor pressure of titanium so that the amount 0f titanium effusing could be neg-Lected. the activities of titanium were determined by g-raphical integration of the Gibbs-Duhertz equatiotz. The solutio~ls sllcdied exhibited positive deviations from Raoult's law, but they approached ideality as the temperature was raised from 125 to 138t C. The integral free energy of mixing was calclated from the activity values. AF has a maximum value of - 1.66 kcal a1 1390°C and a composition oj 55 at. pcl Cv. The free energy of formation of 'TiCr, is —0.76' lzcal a1 1250°C. The heats and entropies of mixing usere determined using the second law and thus tile mlues could be in error by a considerable amount. The Cv-Ti system is not a regular solution. ThE increasing emphasis on application of various models to alloy formation and solution behavior has led to an intensified interest in the thermochemistry of alloys. In a majority of the cases where different models have been applied the alloy system used was a simple one. However, the amount of data available on more complicated systems is small and in order to fully understand the behavior of metallic solutions more experimental work has to be carried out on these systems. The Cr-Ti system is reasonably complex and even though this system was being investigated as early as 1937 by Kroll,' no previous work has been done on the thermodynamic properties of either the liquid or solid state. This research was undertaken to determine the thermodynamic properties of solid Cr-Ti alloys. EXPERIMENTAL PROCEDURE The experiments on the Cr-Ti system were carried out in a water-cooled metal vacuum system. This system is composed of a brass vaporization chamber wound with copper tubing for cooling purposes, a brass liquid-nitrogen trap, an oil diffusion pump, and a Duo-Seal forepump. The pressure in the system is measured with an ionization gage. The interior of the vaporization chamber is shown schematically in Fig. 1. The Knudsen cell is supported by the molybdenum tripod, and a magnetically operated shutter is provided to protect the Pyrex sighting glass against deposition of metallic vapors in the intervals between temperature measurements. Heating is accomplished by means of a 20-kw 450-kc Westinghouse oscillator. The susceptor in this case is 10-mil tantalum seamless tubing which also forms the outside of the sample container. The remainder of the sample container consists Of an im~ervims re-crystallized alumina crucible and a 10-mil-thick tantalum lid. Two holes are drilled in the lid. The diameters of these holes were measured with the calibrated stage of a "Tukon" microhardness tester. The thicknesses were measured with a micrometer. A Leeds and Northrup disappear ing-filament optical pyrometer was used to measure the temperature. This is sighted through the smaller of the two holes in the lid and corrections for the emissivity of the sample were not necessary since the ratio bf cell length to hole diameter was large enough to insure a hohlraum. The pyrometer was calibrated at the ~~t~~~l Bureau of Standards, and the correction for the Pyrex sighting window was determined in the laboratory. The titanium used in this investigation was obtained from Mallory-Sharon and the chromium from The Union Carbide Metals Co. The reported purities were

Jan 1, 1968

By Robert E. Snow, Douglas J. Cosler

The application and development of computer models for simulation of transient ground water inflow to underground mines can assist in mine planning and operation as well as environmental impact assessment. Applications include planning for water handling, treatment, and disposal operations based on predicted mine inflow rates, determination of mining impacts on ground water movement and potentiometric surfaces in neighboring aquifers, evaluation of methods for minimizing ground water inflow, and determination of ground water inflow quality. The potential ground water inflow components to a mine consist of direct inflow from an adjacent aquifer and infiltration through intervening geologic formations. The rates of inflow are controlled by the geologic conditions, the potentiometric surface of the aquifer, and the hydrogeologic characteristics of the water-bearing and confining formations. The capabilities and potential use of a computer model for simulation of mine inflow are illustrated through an example problem.

Jan 1, 1983

By Herman F. Kaiser, Charles S. Barrett, Robert F. Mehl

The copper-silver system presents several points of special interest in the study of segregate structures. The system is simple eutectic, with limited solid solutions terminal with the pure component metals. The extent of solid solubility decreases with decreasing temperature for both the copper-rich and the silver-rich alloys, thus offering a possibility for the formation of Widmanstätten figures and also a possibility for aging after quenching. In contrast to the structures studied previously the structures in this system are unique in their origin, for one terminal solid solution will precipitate the other, and vice versa. In most of the other systems for which crystallographic data on the precipitation (or transformation) process arc available, either intermetallic compounds or intermediate phases partake in the decomposition process; the absence of such phases thus distinguishes this system. The lattice structures of the two solid solutions are identical in type, differing in lattice spacing by approximately 10 per cent; because of this it seems difficult if not impossible to predict on the basis of present theory either the outward form of the precipitate or the lattice orientation relationships between matrix and precipitate. The eutectic temperature in the copper-silver system' is 779" C. At this temperature copper dissolves 4.3 atomic per cent (7.0 weight per cent) of silver in solid solution; this solid solubility decreases to zero at room temperature.² Silver at the eutectic temperature rctains 14.0

Jan 1, 1935

By Charles S. Barrett, Herman F. Kaiser, Robert F. Mehl

The copper-silver system presents several points of special interest in the study of segregate structures. The system is simple eutectic, with limited solid solutions terminal with the pure component metals. The extent of solid solubility decreases with decreasing temperature for both the copper-rich and the silver-rich alloys, thus offering a possibility for the formation of Widmanstätten figures and also a possibility for aging after quenching. In contrast to the structures studied previously the structures in this system are unique in their origin, for one terminal solid solution will precipitate the other, and vice versa. In most of the other systems for which crystallographic data on the precipitation (or transformation) process arc available, either intermetallic compounds or intermediate phases partake in the decomposition process; the absence of such phases thus distinguishes this system. The lattice structures of the two solid solutions are identical in type, differing in lattice spacing by approximately 10 per cent; because of this it seems difficult if not impossible to predict on the basis of present theory either the outward form of the precipitate or the lattice orientation relationships between matrix and precipitate. The eutectic temperature in the copper-silver system' is 779" C. At this temperature copper dissolves 4.3 atomic per cent (7.0 weight per cent) of silver in solid solution; this solid solubility decreases to zero at room temperature.² Silver at the eutectic temperature rctains 14.0

Jan 1, 1935

By G. N. Goldberg, Robert A. Rapp

The steady-state kinetics and microstructures of simultaneous internal oxidation and external scale formation were investigated for the oxidation of Cb-Zr and Ch-Zr-Re alloys in pure oxygen at 1000°C. For each binary alloy, a constant rate of scale formation was observed at steady state; the internal oxidatton zone reached a steady-state, time-independent thickness. The dependence of the scaling rate on zirconium content exhibited a maximum at a low zirconium colttent; more concentrated alloys oxidized at a slower rate than pure columbium. This composition dependence of the scaling rate may be partially attributed to the effect of the internal oxidation process as an intenla1 sink for oxygen, with the formation of voluminous, and relatively impermeable ZrO2 precipitates. However, the morphologies of the ZrO2 internal oxide precipitates also affected the scaling rate. The internal oxide precipitates were distributed uniformly in the external scale. The steady-state thicknesses of the internal oxidation zones were not in agreement with those predicted theoretically from an idealized simple model. However, in this particular alloy systen1 the ideal model is not satisfied experitmentally. For ternary Cb- Zr - Re alloys with Nr10e = 0.02 or 0.05, the steady-state thicknesses of the internal oxidation zones were less than those for the corresponding binary Cb-Zr alloys. For ternary alloys with NRe(0) - 0.05, a more adherent and much less porous external scale was formed, and a reduction in the kinetics of scale formation was observed. A number of authors'-7 have reported linear oxidation kinetics for the reaction of pure columbium at 1000°C in air or in oxygen of about 1 atm pressure. A thin and tightly adherent oxide layer is found at the metal/oxide interface beneath a porous external layer of scale. Although the suboxides CbO and CbO2 represent thermodynamically stable phases at 100O°C, generally only Cb2O5* is identified as a reaction product in quenched specimens. Studies at 1000°C at lower oxygen pressures8,10 (Po2 - 10-4 Torr) show that both CbO and CbO2 do form and that CbO2 is a protective oxide. The growth of CbO2 results in parabolic kinetics until Cb2O5 is nucleated and grows. Apparently because of the large volume change associated with its formation, Cb2O5 is porous and does not serve as a diffusion barrier; linear kinetics prevail after the surface is covered with Cb2o5. On the basis of these observations, several authors5,9,10 have suggested that the linear oxidation of pure columbium at 1000°C in air or oxygen of 1 atm is limited by a Loriers-type mechanism,11 whereby the total rate or reaction is controlled by ionic diffusion through a thin layer of CbO2 which is maintained at a constant thickness throughout the linear oxidation. However, the concept of a Loriers model for a three-phase CbOlCbO2 Cb2O5 scale, with the only oxygen activity gradient across the NbO2 phase, is not self-consistent. Further, the suboxides CbO and CbO2 were not observed in the high-temperature X-ray diffraction study of columbium oxidation by Goldschmidt.8 From investigations in which the large PO2, dependence of the linear scaling rate was demonstrated, the importance of an oxygen adsorption or dissolution step has been suggested.4,5,7,10,12 Thus the mechanism for the linear oxidation of pure columbium remains quite controversial. Since further insight into the oxidation mechanism of pure columbium is not provided by this investigation, the authors wish to emphasize at the outset that their experimental results are not interpreted in terms of a particular rate controlling step for the oxidation of pure columbium. Previous investigations13-18 of the oxidation of Cb-Zr solid-solution alloys in air or oxygen at 1000°C suggest a remarkable dependence upon zirconium content. For an alloy of bulk zirconium mole fraction, N2r(0) equal to 0.05 or 0.10, the oxygen uptake is reported to be as high as four times greater than that for pure columbium;13,14 for alloys with NZr(0) 0.05 or 0.10 the oxygen uptake is reported to decrease with increasing NZr(0); to a minimum uptake of about one quarter that for pure columbium at NZr(0): = 0.50.13-15Since zirconium forms a more stable oxide (ZrO2) than the lowest columbium oxide (CbO), and since columbium exhibits a high solubility19,20 and diffusivity21,23 for oxygen, the internal oxidation of the zirconium component to ZrO2 is expected at a reaction front ahead of the advancing metal/scale interface. The external scale is then formed at the metal/scale interface by the inward migration of oxygen through the scale, probably through a series combination of molecular and ionic diffusion. Internal oxidation in conjunction with external scale formation has been investigated by Maak24 for the oxidation of dilute Cu-Be alloys in pure oxygen at 850°C. For cu-Be and many other binary alloys,24-27 very small, essentially uniaxial internal oxide particles are formed in the most dilute compositions; for somewhat more concentrated alloys. the internal oxide particles precipitate as platelets or needles. From pertinent solutions to the diffusion equation, Maak28

Jan 1, 1967

By R. C. Hassinger, D. V. von Rosenberg

Transverse dispersion has received considerably less treatment in the literature than has longitudinal dispersion. Different methods for determining transverse dispersion coefficients have been used in different investigations, and the results obtained have not been consistent enough to permit accurate generalizations as to the effect of various physical parameters on the magnitude of these coefficients. A numerical solution to the differential equation describing transverse dispersion in the absence of longitudinal dispersion was obtained to enable one to calculate the dispersion coefficient from experimental results. The more general dispersion equation including longitudinal dispersion also was solved numerically to give quantitative limits of a dimensionless group within which the assumption of negligible longitudinal dispersion is justified. Possible experimental procedures were examined, and one utilizing a cylindrical packed column was chosen for the determination of transverse dispersion coefficients. Values of these coefficients were determined for a system of two miscible organic fluids of equal density and viscosity, for two sizes of packing material over a wide range of flow rates in the laminar regime. The dispersion coefficient was found to decrease, for a constant value of the product of packing size and interstitial velocity, as the size of the packing material particles increased. INTRODUCTION Longitudinal dispersion has received extensive treatment in the literature, and consequently is better understood than its orthogonal counterpart, transverse dispersion. Many mathematical models of dispersion processes assume that transverse dispersion is rapid enough to damp out any radial** concentration gradients and therefore may be neglected. Laboratory and production results, however, indicate that this is a poor assumption.l,2 Various experimental procedures for determining transverse dispersion coefficients have been used in previous investigations, but the results have generally been expressed by similar correlations. The transverse dispersion coefficients obtained, however, have often varied considerably for given values of the correlation parameters. We feel that further experimental determinations of transverse dispersion coefficients will help alleviate some of the inconsistencies in these empirical correlations. One assumption implicit in all previous investigations is that of negligible longitudinal dispersion in the experimental system. An attempt to justify this assumption often is made using intuitive reasoning, but it is apparent that this reasoning must break down as the condition of zero flow rate is approached. A mathematical examination of the equations describing the system yields physical limits outside of which the assumption of negligible longitudinal dispersion is invalid. BACKGROUND In a porous medium, the "effective molecular diffusivity" De is less than the molecular diffusivity D measured in the absence of a porous medium, due to the tortuous path which a diffusing molecule must travel. Various authors3-5 have reported values of the ratio De/D in the range of 0.6 to 0.7. When there is fluid flow within the porous medium, mass transfer occurs by convective dispersion as well as by molecular diffusion. These are separate phenomena and can be treated as such on a microscopic scale. However, the mathematical complexity is such that only extremely simple geometries could be considered, and the results hardly would be applicable to the complex geometries existent in actual porous media. A more

Jan 1, 1969

By K. F. Veith, R. L. Marovelli, T. S. Chen

An analytical study is made of thermal stress distribution in a thin circular disc subjected to a peripheral thermal shock at various rates of heat transfer. The problem is of importance in predicting the thermal shock response of a rock body of finite size. The theoretical analysis is based on radial heat flow by conduction in the disc and heat exchange by convection between the disc and the surroundings. The case of constant properties and plane stress is treated. Solutions of the stress distribution are presented for both cooling and heating shocks and an average stress theory is formulated. Preliminary experimental verification was obtained from the results of shock tests on thin rock discs insulated on both flat end faces so that heat exchange took place through the exposed peripheral surface. Physical properties vital to the analysis are Young's modulus, tensile strength, coefficient of linear thermal expansion, thermal diffusivity and thermal conductivity. Plots of these properties are presented. Historically, thermal energy has been used for primary rock removal throughout the ages. Although it is not widely known, the fire-setting method of thermal rock fragmentation was still in use 100 years ago in systematic underground mining operations in Scandinavia.' There, the availability of cheap labor and abundant wood fuel made the method competitive with the early blasting powders. By 1880, as high explosives replaced powder, use of the method declined and it was finally abandoned about 1885. Only 40 years ago, some experimental fire-setting methods were used for rock removal underground at Pribram and Zinnwald in Central Europe.2 Compressed air-oil burners replaced the earlier wood fuels. About 15 years ago, gaseous oxygen-oil burners were introduced in the United States and gained acceptance for difficult blasthole drilling and some quarry opera- tions. At present, there is renewed interest in the compressed air-oil burner designs. The literature included information on thermal secondary processes for rock weakening or particle liberation3,4,5,6,7,8 on thermal spallation of rock 9,10,11,12,13 and on the thermal fracture of materials other than rock. The 1955 Symposium on Thermal Fracture14 and the later work of Hassel-man, cover recent developments in thermal shock investigations on brittle ceramics. Although the number of published analytical and experimental investigations conducted on ceramic and refractory materials is large, the literature reveals that there is a lack of information on both the theoretical and actual response of rock to thermal shock. Many of the thermal shock studies on ceramic and refractory bodies are based on the case of heat transfer at the solid's surface by convection in either liquid or air. A similar heat transfer situation was adopted for a theoretical analysis of the thermal stresses in a thin circular disc subjected to a peripheral thermal shock. Experimental thermal shock tests were then conducted on rock specimens to check the analytical results. Specially insulated quartzite, basalt and taconite discs were shocked in either liquid or still air bath at various rates of heat transfer. The work was done in order to resolve the question as to whether theoretically determined tensile stresses are actually realized in a finite rock body undergoing thermal shock. Specifically, if theory predicts that the tensile strength of a rock should be exceeded in a particular type of controlled thermal shock, will fracture occur? This information is needed by Bureau researchers working on thermal and electrical rock fragmentation methods. The object of this paper is to present the main features of the theory and procedure being used in the authors' approach to quantitative prediction of rock response to a thermal shock. THEORETICAL ANALYSIS In the analysis to follow, simple geometry of a thin circular disc is considered. The disc is assumed to be isotropic, homogeneous and perfectly elastic, and to have constant thermal and mechanical properties. The effect of radiation is neglected so that heat is transferred by conduction inside the disc and by convection with its surrounding. In addition, the end

Jan 1, 1967