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By R. W. Parsons

wben a displacement front encounters an isolated permeability heterogeneity, it will be perturbed. The details of this perturbation will depend on the beterogeneity size and shape, the Permeability contrast, and the mobility ratio. This paper deals with the displacement front behavior for one, simple, mathematically tractable model: a circular permeability discontinuity and unit mobility ratio. The progress of an initially planar front is shown for four permeability contrasts: k2/k1 = 0, 5/2, 2, m. The front distortion is more pronounced than streamline and isopotential distortion and it approaches a constant shape downstream from the discontinuity. INTRODUCTION The impact of reservoir heterogeneities on oil displacing processes depends upon the variation of the heterogeneous property (frequency distribution), its disposition (spatial distribution), and the inherent stability of the displacement mechanism.l The interplay of these factors plus the impracticability, if not impossibility, of describing a natural rock system in any detail makes exact displacement front movements difficult to determine. It is useful, however, to be able to qualitatively visualize what heterogeneities will do to a displacement front. In this respect certain simple models that can be treated analytically are of value. The following analysis will show the displacement front behavior for one such model. MODEL DESCRIPTION The flow field is two-dimensional and infinite in extent. The fluid flow is single phase, steady state and unidirectional at x, y = 2 m, or before insertion of the discontinuity. A circular permea- bility discontinuity is placed at the origin. Porosity and thickness are the same within and exterior to the heterogeneity. This is exactly the same model that was used by Greenkorn et al. to check analytically Streamlines as determined by Heie-Shaw flow models and finite difference computer techniques.2 FRONT POSITION CALCULATIONS The results of displacement front calculations are presented in Figs. 1 through 4 for four different permeability contrasts: k2/kl = O, %, 2, m. The times corresponding to the front locations are the Same for the 0 and cases! and for the 1/2 and 2 cases. The determination of front positions at various times is based on known analytical expressions for velocity potentials ().2 and stream functions ().2 These expressions are in terms of the x and y

Jan 1, 1969

By N. N. Breyer

A specially built "hard" tensile machine with characteristics permitting the precise detertnination of the drop of the load at the yield point has been used to study the magnitude of the yield-point phenotnenon in prestrained martensitic 4340 steel. A new phenonzenon, the appearance of a secondary yield point, has been observed by holding the specimen at constant strain in the plastic region. Furthermore, it has been found that a series of yield-point drops could be introduced by successive constant strain holds in the plastic region. The isothermal kinetics of the development of the secondary yielding point lave been studied at four temperatures: 24° 0° -18°, and -79°C. From the results of the kinetic investigation, equations for the In a previous investigation1 it was shown that, contrary to generally held opinion, steels of medium carbon content, such as 4340, 4140, and 86B30, in the as-quenched martensitic condition, can be cold-drawn through a die with reductions in area of up to 10 pct without cracking. Tensile specimens of 4340 machined from bars quenched and prestrained in this manner exhibited tensile strengths of about 400,000 psi coupled with 30 pct reductions in area. In addition, it was found that each sample of such steels exhibited a yield point in the quenched, cold-drawn condition. Since these studies were conducted on a commercial hydraulic testing machine of a type which is not well-suited to detailed study of yield-point behavior, it was decided to study this phenomenon more thoroughly on a rigid straining machine. In this new investigation, use of such a "hard" machine not only allowed study of the magnitude of the yield-point drop but also revealed a new phenomenon—secondary yielding of the martensite introduced by stopping crosshead motion after plastic deformation of the sample had begun. The present paper is a report of these findings. MATERIALS AND PROCESSING The material used was a commercial 4340 steel of the composition shown below: 0.41 0.80 0.013 0.019 0.31 0.85 1.76 0.28 1 0.42 0.77 0.015 0.024 0.30 0.84 1.69 0.28 0.08 2 1 = Ladle analysis. 2 = Laboratory analysis. Bars of this steel were processed in the following way: 1) machined to predetermined diameters; 2) austenitized at 870°C for 1 1/2 hr; 3) oil-quenched; 4) cooled to -115°C for 1/2 hr; onset and increase in magnitude of the secondary yielding in this temperature region have been found to fit the relationship ?Ys = Atn where ?Ys is the magnitude of the secondary yield Point in psi, t is the time in seconds, and A and n are parameter characteris-tics of the material. Although the occurrence of the primary and secondary yield points could be rationalized qualitatively on the basis of stress-induced ordering of carbon atoms in the stress fields of dislocations, as postulated in an earlier paper, the kinetics of the secondary-yield-point development were interpreted to indicate that the ordering involves more than just single jumps of carbon atoms from high-energy to neighboring low-energy sites. 5) pickled and lime-coated; 6) drawn through a carbide die. The predetermined diameters were chosen so that drawing through the same die gave the various reductions desired. Tensile specimens of 0.252 in. diam with a 1 1/4 in. gage length were then prepared from the drawn bars and tested. In order to study the stress-strain behavior at the yield point in detail, a rigid tensile machine with a high spring constant was constructed. Columns of large cross section (relative to the specimen cross section) constituted the machine frame. A dc motor was used to drive a screw via a gear reducing train and a "crane" thrust bearing. In this relatively simple device small deformations could be observed un-blurred by the slow response and lower spring constant inherent in hydraulic machines.' A strain-gage dynamometer permitted load changes as small as 8 lb to be read. RESULTS Tensile test samples machined from bars in the as-quenched condition with no subsequent drawing and samples from bars with 3.8 pct reduction after quenching gave stress-strain curves typified by those shown in Figs. I and 2. The time lapse between predrawing and tensile testing varied but usually ranged between 3 to 6 days at room temperature. The strain rate during testing was 0.003 in. per in. per min. The as-quenched curve is seen to have a broad serrated maximum whereas the stress on the specimen prestrained 3.8 pct rose linearly to point A, Fig. 2, fell abruptly to B, and then gradually to C. The abrupt drop to B was accompanied by evidence of incipient necking. The drop of the stress at the yield point in the prestrained samples (A to B in Fig. 2) changed with the percent prestrain, as illustrated on Fig. 3. Although the tensile strength increased continuously with the amount of previous cold drawing, the magnitude of the yield point drop first increased—up to about 6 pct prior reduction—and then decreased. Specimens from bars predrawn more than 8 pct broke in a brittle fashion in the elastic portion of the stress-strain curve.

Jan 1, 1967

The airplane, while not a product of the war, owes its present very prominent place to the war; if it had not been for the war its development would have been retarded many years. War planes were made for various purposes, but their most important use was for photographing the enemies' lines. The same methods; with some modifications, are now

Jan 6, 1919

By R. G. Treuting, W. C. Ellis

D. Whitwham, M. Mouflard, and P. Lacombe (British Council Research Fellow, Labratoire du Professor Chaudron, Vitry-sur-Seine; Inqenieur de Recherches, Labratoire de Vitry; and Maitre de Recherches, Labratoire de Vitry, Professeur Adjoint de Metallurgie, Ecole des Mines, Paris)—The authors' work is of great interest in bringing out the geometrical relations existing between twinned lattices, and for the notion of a coincidence super lattice developed from this. We should like to point out that a similar idea was put forward by Friedel8 in his book on the subject of lattice merohedrism "merihedrie réticulaire:"—When two crystals A and B are twinned with respect to a mirror plane, there exists a common superlattice, "réseau periode," which is independent of the contact surface between the two crystals. The volume V of this superlattice is a simple multiple of the volume v of the lattice of crystals A, or B, (Fig. 5). This "multiple cell" is defined by the twin plane (p q r) and a row of atoms [h k l] normal to this plane, the base being taken as the smallest unit (two-dimensional) of this plane. Two cases must be considered. First when the multiple cell, as defined, has no atom site at its center nor at the center of its faces other than (p q r), v the twinning index is defined by —. In the second v case, when one of the two above conditions does not v apply, then the twinning index is V 2v A more intuitive definition of the twinning index would be the proportion of atoms of C, which would coincide with those of C1 when the C, lattice is imagined to extend on the other side of the contact surface. In the case of cubic crystals, the twinning index

Jan 1, 1952

By R. I. Parsons, M. B. Standing, E. N. Lindblad

The recovery of the heavier components from a gas cap or retrograde pool is shown to be the greatest when the sand is cycled with a dry gas at a low pressure. This conclusion is in direct opposition to the belief that the most efficient production program is pressure maintenance and cycling at or near the dew point. The results are calculated from: (I) constant volume, variable composition pressure-volume-temperature tests on a mixture of trap gas and liquid from a producing well; (2) published equilibrium constant data and the measured composition of the dew-point material; and (3) the fact that in a sand section of homogeneous permeability, injected gas displaces reservoir gas nearly, quantitatively. The results are based on the simplifying assumption that variable permeability systems may be defined by the ratio of two statistical parameters, and that gas injected into an actual sand will behave as though the sand were composed of many layers, each of constant permeability. Introduction Pressure decline in gas-condensate type reservoirs is accompanied by the formation of a liquid phase throughout the reservoir. Over the past ten years the processing of the material from these types of reservoirs for the heavier hydrocarbon components and the return of the light fractions to the reservoir ("cycling") has become increasingly popular. It has often been stated that the purpose of such a program is to prevent the loss of the retrograde liquid phase formed in the reservoir. The purpose of this paper is to present the results of laboratory tests and computations concerned with several possible methods of producing a gas cap or condensate type of reservoir. The results show that the recovery of heavier hydrocarbons for this type of reservoir is not a maximum under conditions of cycling at or near the dew-point pressure. Instead, variations in permeability and the ability of the dry injected gas to revaporize condensate, point to cycling at a considerably reduced pressure as the optimum production-method. In addition the paper suggests a way of evaluating sands for their permeability variation. The calculations presented in the following sections of the paper are in terms of the production of the butanes and heavier fraction from the gas cap of a field which had an original pressure of approximately 3000 psi. Specifically, the calculations show: 1. To what extent the condensate formed in the reservoir after pressure decline can be recovered by the cycling of a dry absorber-plant gas through the sands. 2. Whether there would be greater recovery of hydrocarbons if cycling were instigated at the original reservoir pressure.

Jan 1, 1948

By M. B. Standing, R. I. Parsons, E. N. Lindblad

The recovery of the heavier components from a gas cap or retrograde pool is shown to be the greatest when the sand is cycled with a dry gas at a low pressure. This conclusion is in direct opposition to the belief that the most efficient production program is pressure maintenance and cycling at or near the dew point. The results are calculated from: (I) constant volume, variable composition pressure-volume-temperature tests on a mixture of trap gas and liquid from a producing well; (2) published equilibrium constant data and the measured composition of the dew-point material; and (3) the fact that in a sand section of homogeneous permeability, injected gas displaces reservoir gas nearly, quantitatively. The results are based on the simplifying assumption that variable permeability systems may be defined by the ratio of two statistical parameters, and that gas injected into an actual sand will behave as though the sand were composed of many layers, each of constant permeability. Introduction Pressure decline in gas-condensate type reservoirs is accompanied by the formation of a liquid phase throughout the reservoir. Over the past ten years the processing of the material from these types of reservoirs for the heavier hydrocarbon components and the return of the light fractions to the reservoir ("cycling") has become increasingly popular. It has often been stated that the purpose of such a program is to prevent the loss of the retrograde liquid phase formed in the reservoir. The purpose of this paper is to present the results of laboratory tests and computations concerned with several possible methods of producing a gas cap or condensate type of reservoir. The results show that the recovery of heavier hydrocarbons for this type of reservoir is not a maximum under conditions of cycling at or near the dew-point pressure. Instead, variations in permeability and the ability of the dry injected gas to revaporize condensate, point to cycling at a considerably reduced pressure as the optimum production-method. In addition the paper suggests a way of evaluating sands for their permeability variation. The calculations presented in the following sections of the paper are in terms of the production of the butanes and heavier fraction from the gas cap of a field which had an original pressure of approximately 3000 psi. Specifically, the calculations show: 1. To what extent the condensate formed in the reservoir after pressure decline can be recovered by the cycling of a dry absorber-plant gas through the sands. 2. Whether there would be greater recovery of hydrocarbons if cycling were instigated at the original reservoir pressure.

Jan 1, 1948

By AIME AIME

CORROSION of tanks, pipes and other equipment in the oil fields is becoming worse as the production of high- sulfur crudes in the Texas panhandle and west Texas areas increases. It has been estimated that .in certain fields of that State one tank out of every five has to be replaced every year because of the high sulfur content of the crude. One suggested method for combating tank corrosion is the use of .materials which have a high resistance to the corrosive action of hydrogen sulfide and high-sulfur crudes; aluminum is one of these materials. As a result, the United

Jan 1, 1929

By Ellsworth Daggett

Jan 1, 1879

By Byron W. Cheever

While engaged in experimenting with the usual methods for estimating phosphorus in iron and steel, it occurred to me that potassium chlorate might be used to oxidize the carbon, and thus avoid the tedious and vexatious evaporations necessary for successfully carrying out the usual methods. After many trials, the following plan was adopted : Take, for analysis, of Bessemer or other low-carbon steels, from 3 to 5 grammes; of crucible steel, 10 grammes; of pig-iron, 1 to 5 grammes, according to the percentage of phosphorus supposed to be present. Of iron, high in phosphorus (1 per cent.), take 1 gramme. Place in a No. 4 evaporating dish the amount of iron or steel decided upon, cover with a funnel which will just fit inside the dish, and then add gradually HNO3, (1.20 specific gravity), using 12 C.C. of acid for each gramme of steel or iron taken. (A larger quantity of acid will be required for small samples.) When the full amount of acid has been added, and the violent action has ceased, place the evaporating dish on a sand-bath, add 10 C.C. HNO3, (1.40 specific gravity), and boil till the bulk of the solution is reduced about onehalf. Then add 10 C.C. HNO3, (1.40 specific gravity), continue the boiling, and add from time to time, during the next 15 minutes, small portions of pulverized KCIO3, till about 2 grammes have been added. (If the solution shows signs of going dry, more strong acid must be added.) This will precipitate the manganese, with some iron. Sometimes it happens that the manganese does not come down readily, and more KCIO3, or further concentration, or both, will be required. The process is not complete till the manganese is precipitated, which may be known by the appearance of a dark, mirror-like deposit on the dish, at the edge of the solution. Boil the solution 5 minutes after the last addition of KCIO3, and then add cautiously (to prevent sudden explosions) 5 C.C. strong HCl. This will dissolve the precipitated manganese and iron. Continue the boiling till the chlorine is all expelled, adding from

Jan 1, 1885

By George W. Riter

Discussion of the paper of H. 0. Hofman and C. R. Hayward, presented at the New Haven Meeting, February, 1909, and printed in Bulletin No. 30, June, 1909, pp. 513 to 529. GEORGE W. RITER, Salt Lake City, Utah (communication to the Secretary*).-In their paper, Messrs. Hofman and Hayward deal with a branch of silver metallurgy that is on very uncertain ground, both as a commercial process and as a metallurgical science; moreover, its field is limited to few localities and to peculiar conditions. The literature on the subject is incomplete and full of conflicts. The paper under discussion clears u p no disputed points; on the contrary, because of hasty generalization, its tendency is towards further confusion. In Table I., the authors assume that each test-lot of 1,800 g. of ore contained exactly 5.499 g. of silver, that any variation in the quantity of silver recovered, however slight, should be ascribed to variation in the time of grinding. It is barely possible that the ore was mixed so uniformly as to justify this assumption; but those of us who know how difficult it is to get uniform samples of any ore in which silver mineral is present in rich particles will have a doubt on this point. The unlikelihood of getting absolutely uniform test-lots of ore also reflects on the data in Table II., on the effect of varying the amount of salt in a pan-charge. The authors say " The salt series was the last one that was investigated." This again raises a question as to whether the ore was split into test-lots at the time of sampling, or whether it was kept in bulk in such a way as to permit mechanical concentration of values before the end of the experiments. The conclusion following Table II.: " There is no reason, therefore, for going beyond six per cent. of salt," is hardly to the point. If we assume that salt is of benefit only when in solution, it follows that the relation between the quantity of salt

Mar 1, 1910

By Paul Averitt

In spite of recent trends in the United States toward construction of steam generating plants near mine mouths, and toward use of high-voltage direct current for long-distance transmission of electricity, coal in substantial amounts is being transported over relatively long distances to serve specific needs. As coal is a low-cost bulk commodity which is more suitable for use near the point of origin, some of these long hauls are of considerable interest because they show what can be done under the pressure for more and more coal to support industrial and economic growth. Japan has an Insatiable Appetite for Coal Perhaps the longest U.S. coal journey begins in the east Appalachian Basin of southern Pennsylvania, eastern West Virginia, and southwestern Virginia. High-quality coking coal mined in these areas is shipped by rail to Baltimore, Md., and to Hampton Roads, Va., where the coal is reloaded on freighters for shipment primarily to western Europe and Japan. In 1967, shipments of coal to western Europe totaled 19 million tons, and shipments to Japan totaled 12 million tons. Japan also imports coal from Australia, the U.S.S.R., Canada, Poland, the People's Republic of China, and to a lesser ex- tent from several other countries. In an effort to solve long-term needs, Japanese steel interests have contracted for the purchase from the Kaiser Steel Corp. of 51 million long tons of coking coal over the period 1970 to 1985. The coal will come from the Kaiser Steel Corp. mine near Fernie, British Columbia. This arrangement will reduce Japan's future dependence on Appalachian Basin coal.

Jan 10, 1969

By AIME AIME

AMONG the industrial motion pic¬tures released in the last year of possible interest to people in the mining industry are the following: "A New World Through Chemistry," made by the public relations department of E. I. du Pont de Nemours & Co., Wilmington, Del. This film, which is in sound and color, interprets in twenty minutes of narration and ingenious photography many of chemistry's newest developments. It may be borrowed either in 16-mm. size on an 800-ft. reel, or 35-mm. size on a 2000¬ft. reel, the only charge being the cost of returning the film. Douglas D. Rothacker, 729 Seventh Ave., New York City, is prepared to loan free of charge except for transportation each way several films prepared in the plants of the International Nickel Co., 16 mm. with sound. These include: "Nickel High Lights," 35 minutes; "Nickel Mining," 18 minutes; "Nickel Smelting," 18 minutes; "Nickel Refining," 9 minutes; and "Copper Refining," 6 minutes.

Jan 1, 1941

By J. B. Cheatham

Applications of the mathematical theory of plasticity promises to lead to the solution of many drilling and rock mechanics problems. ,Because of mathematical considerations, the inelastic behavior of rock has frequently been represented by a perfectly plastic model in conjunction with a yield criteria of the Coulomb or Mohr type. The totality of all stress states for which a solid ceases to behave elastically can be represented as a limit surface in stress space. ,Probing of such limit surfaces indicates details of strain hardening which are not provided by the standard triaxial testing procedure. Probing tests of the limit surfaces have been performed on Cardova Cream limestone to provide data for extending plasticity theory to cover situations in which consolidation and strain hardening are present. Test results indicate that this highly porous limestone undergoes a permanent volume decrease when it is subjected to hydrostatic pressures in excess of 3,500 psi. A virgin sample tested under a confining pressure of 1,500 psi has a yield strength of 1,700 psi; however, if the sample is subjected to a consolidation pressure of 5,000 psi, before testing at 1,500 psi, the yield strength is raised to 2,300 psi. Thus, both consolidation and strain hardening are important considerations in describing the mechanical behavior of this limestone. Tests conducted with the axis of the core having different orientations indicate that this rock is also anisotropic. Portions of the initial and subsequent limit surfaces are determined for samples loaded either perpendicular or parallel to the bedding planes. INTRODUCTION Previous experimental work in rock mechanics indicates that no mathematically tractable constitutive theory is inclusive enough to describe the mechanical behavior exhibited by all types of rocks under all conditions of stress and temperature. Indeed, the type of deformation encountered in a single type of rock is known to depend upon the stress and temperature conditions in the rock during deformation.l-5 Certain rocks and minerals, notably those minerals composed of ionic salts, have been shown to exhibit plastic deformation when tested under conditions of high confining pressure.2 Since the mathematical theory of plasticity provides simplifications over the theory of elasticity in certain types of problems, such as those in which limit analysis can be applied, it is of interest to know under what conditions plasticity theory may be applied to rock mechanics problems. The following factors determine the nature of the deformation a particular specimen will undergo: (1) the microscopic structure of the rock, i.e., the structure visible under an optical microscope, including number of phases, porosity, distribution of phases, (2) the mineralogical structure of the solid phases, (3) the conditions of stress and the rate of change of stress and (4) the temperature. Extensive experiments on Yule marble, Carthage marble, Solenhofen limestone and other calcerous rocks indicate that these relatively nonporous rocks deform plastically under certain conditions of loading, and creep under other conditions of loading.l-3 This study is concerned with the behavior of Cordova Cream limestone (Austin chalk) which is also composed almost entirely of calcite and thus has the same mineralogical composition but, because of a rather large porosity, it possesses a different microscopic structure. This investigation was undertaken to learn if Cordova Cream limestone deforms plastically despite the embrittling effect of the pore spaces, and to provide data which can be used to determine whether the mathematical theory of plasticity can describe the mechanical behavior of Cordova Cream limestone. A brief discussion is given of some of the underlying principles of plasticity theory concerning stress space and limit surfaces. Strain hardening is defined and a discussion is given of how the mechanical behavior of a material can depend on the previous history of the loading. This is followed by a description of the experimental procedures

By Edgar F. Cruft

INTRODUCTION It is sometimes said that "mines are made, and not found." I rather doubt that the exploration geologist would be overly sympathetic to that statement, and, of course, like most one-liners it is only partly true. Access to different financial markets are important at the mineral prospect stage. The modern mine financier has a much more complex, and interesting, job than the financiers of an earlier era, for example, the Canadian financiers of the 40's and 50's who had one simple set of options; i.e. float a company, promote it, and sell an equity stock issue, and then promote it some more. QUALITIES OF A FINANCIER Because technical people are seldom taught financing in their basic training, and because they are usually not involved in it until at quite a senior level in their careers, the whole field often acquires a certain mystique. The engineering professions have too often believed financing is the province of the accountant or financial executive and just as we in the technical world are often too quick to bristle if the latter try to tread on our domain, the opposite can just as easily be true. Unfortunately, this is another example of a compartmentalized individual, and that is one thing the successful financier cannot be. However, to be a successful financier one does not need extensive training or experience in accounting or finance. In fact it can sometimes be a disadvantage to get too buried in working only from the standpoint of discounted cash-flow analyses, ROI's, etc. It must be stressed, however, that one had better know how these analyses are made, and be knowledgeable in understanding a balance sheet, and have a good understanding of financial terminology. The difference between a simple project-type debt financing with a commercial bank and a more inventive and creative financial package comes from an intuition and an experience relating to risk-reward factors. The most important element is "common-sense", based on knowledge and experience. The goal is structure a financial package that fits the project, and in so doing it is important to recognize that it must fit within the limitations of the group supplying the money. I find insensitivity to recognize these constraints the most common mistake made in the field. Put yourself in the other person's place and understand his sources of funds and financing limitations. The engineer has an advantage in financing, as he or she has (or should have) a better idea than anyone of the value of the product, be it the mine, prospect, or company i.e. the intangible or potential worth which cannot be put on a pro-forma. He also knows, or should know, the risks involved. Two projects might look the same on paper, but a good financier must have a sense of when to take whatever deal he can get, and when to hold out based on his evaluation of future developments. It is essential to have a good sense of commodity values and trends, trends affecting the general economy (money supply, interest rates, effects of energy costs, etc.), and political considerations. He must also have a good understanding of the science and art of taxation as deals can often be financed using the government as a silent and unwitting partner by proper use of the tax laws. WHEN TO SEEK FINANCE The first critical decision to make in financing a mineral prospect is "when". At the exploration level, when it is only a dream in the geologist's eye, the alternatives are more limited than when it is a fully-engineered project. The "when" decision depends on how much in internal funds the company has to play with, and how desirable it is to invite financial participation to spread the risk. Assuming that decision is not taken out of lack of money, no one can categorically say when to do it. There is

Jan 1, 1985

By G. A. Croes, N. Schwarz

The dimensionless groups, to which the variables that govern the displacement of oil from reservoirs by liquids can be combined, are derived. Three types of displacement are considered, viz. cold-water drive, hot-water drive and solvent injection. The derivation of the dimerzsionless groups is carried out by means of the relevant basic equations (in-spectional analysis). The resulting sets of groups are afterwards completed by means of dimensional analysis. The form of the groups is given in such a way that they can be adapted to suit the various boundary conditions that are encountered in practice. The physical meaning of the groups is discussed. They have all been brought together on a chart, from which their mutual relation and their corresporzdence to related dimensionless groups in common use in other engineering sciences can be read off. The limitations of dimensionally scaled model experiments as a useful tool for studying liquid flow in porous media, as occurring in oil reservoirs, are discussed. The use of models to study fluid mechanics has an appeal for everyone endowed with natural curiosity. What active boy has not played with ship and airplane models, or crude models of dam and drainage systems Even in the most advanced technical engineering, such models play a fundamental and indispensable role. "And yet in few departments of the physical sciences is there a wider gap between theory and practice, between scientific knowledge and the state of art, than in the use of models to study hydrodynamic phenomena." Garrett Birkhoff1 INTRODUCTION Laboratory displacement experiments are extensively used to investigate, directly or indirectly, the production behavior of petroleum reservoirs. Such experiments are representative of the reservoirs as a whole, if they are carried out with models that are "properly scaled." The performance of oil reservoirs is governed by the values of a number of variables, which can be combined to dimensionless groups. Two general methods are available for the derivation of these groups. In the first of these, dimensional analysis, combination of the variables is done essentially by trial and error. Its only premise is knowledge of the complete set of relevant variables. In the second method, inspectional analysis, the dimensional homogeneity of the equations describing the behavior of the system to be studied is used. The resulting dimensionless groups can be divided into: (a) independent (variable) groups, such as dimensionless length, time, etc.; (b) dependent groups, giving the dimensionless form of the variables, such as recovery and pressure, that can, at least in principle, be measured during an experiment; (c) similarity groups, which are independent constant groups, such as ratio of length to height of the reservoir and ratio of

Jan 1, 1957

By Frederick C. Langenberg

A method is presented for computing the solubility of nitrogen in molten alloy steels. Examples are given to illustrate the procedure, and comparisons are made between predicted and measured nitrogen solubilities. THERE is an increasing use of nitrogen as a major alloying element in steels, or as a partial substitute for other alloying elements. Nitrogen is a potent austenite stabilizer, and Cr-Mn-low Ni-N steels, or even Cr-Mn-N steels, are being considered

Jan 1, 1957

By C. Laird, C. E. Feltner

An investigation into the effect of a material's slip character on its high strain fatigue properties has been carried out using copper and Cu-7.5 wt pct A1 as representative wavy and planar slip mode materials, respectively. In copper, the constant term and exponent in the Coffin-Manson equation, ?EpNf1/2 = const, are unaffected by the temperature of testing or the history of the metal. On the other hand, in Cu-7.5 wl pcl Al, while the exponent is invariant, the constant is increased with respect to copper and increased further with decrease in temperature. The life in Cu-7.5 wt pct A1 is double that of copper at room temperature and about four times at 78°K. Fractoflaphic studies indicate that these diffevences in life are associated with the early stages of cracking. In copper, severe surface rumpling provides crack nuclei at pain boundaries independent of' testing temperature or the history of the metal. In Cu-7.5 wt pct Al, the planar slip mode of deformation prevents grain boundary folding; crack nucleation is therefore mainly transgranular and the increase in life with respect to copper is associated with a prolonged linking-up stage of such transgranulay cracks. At the lower temperature the increased difficulty of cross slip inhibits multiplication of trans-granular cracks and retards the linking-up process, giving a further enhaancement in life. It is expected that such behavior will be found general in materials of wavy and planar slip mode, respectively. STAGE II crack propagation in high strain fatigue takes place by a repetitive process of crack tip blunting in the tension part of a fatigue cycle followed by resharpening of the crack in the compression part.1-3 This mechanism has come to be called the "plastic relaxation process".3 At very high strains (lives to failure less than 103 cycles), most of the life of a specimen is spent in crack propagation by the plastic relaxation process.4,5 Since the differences in the cyclic strain hardening behavior of metals and alloys are comparatively small in this strain range,6,7 the amount of blunting at a crack tip depends primarily on the applied strain amplitude. The rate of crack propagation in this life range is therefore nearly constant with respect to material and temperature of testing. In the longer life portion of the high strain fatigue range (l03 to 103 cycles to failure), a considerable fraction of the lives is spent in crack initiation and Stage I growth. Grain boundaries have frequently4,5,8 been found to be the sites for this growth which is also associated with a surface folding process.4'5 Such folding behavior may also be general in any material having a grain structure and capable of plastic deformation. It has therefore been suggested475 that the universality of the Coff in-Manson law,9'10 constant,* where ?Ep is the plastic strain range and Nf the number of cycles to failure, is reflected in the approximate invariance of both the crack initiation and propagation behavior. It happens that, in most investigations of the phenomena associated with failure,4,5,8 materials with a wavy slip mode have been used as vehicles for the studies, or else "normally" planar slip mode materials have been tested under conditions giving rise to wavy glide deformation, e.g., stainless steels cycled at high temperature.'' The purpose of the present investigation was to determine whether or not different cracking phenomena would occur when the slip mode of a material is planar and if the associated life to failure would be different than that of a wavy slip

Jan 1, 1968

By H. H. Evinger, M. Muskat

A method has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-prcssure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical prop-crties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.' Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of o to Ioo bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* Q ? u log r?/r? where k is the sand permeability, h its thickness, µ the liquid viscosity, ?p the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius re, and r? is the well radius. This gives the productivity factor: f= Q/kh?p ? 2p/µ log re/r? f=Q/ kh?p ? 2p/µ log re/r? which will have a numerical value for a

Jan 1, 1942

By M. Muskat, H. H. Evinger

A method has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-prcssure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. Introduction The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical prop-crties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.' Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of o to Ioo bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* Q ? u log r?/r? where k is the sand permeability, h its thickness, µ the liquid viscosity, ?p the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius re, and r? is the well radius. This gives the productivity factor: f= Q/kh?p ? 2p/µ log re/r? f=Q/ kh?p ? 2p/µ log re/r? which will have a numerical value for a

Jan 1, 1942

By A. T. Goldbeck

THE use of stone as a building material in relatively large blocks is recorded in ancient historical records but only within the past 200 years has broken stone in small sizes begun to have extensive use, principally in highway construction. Tresaguet, in 1764, describing his method for highway construction in France, required the top surface to be built of stone about the size of a walnut, broken by the use of a hammer. It is said that the Romans, in the top layer of their rather massive roads, used large stones bonded together with lime mortar and bedded in small stones mixed with mortar. Much of the early macadam as built by McAdam around 1815 in England was made with hand-sledged broken stone. In 1858, the use of crushed or broken stone received a great impetus from the invention in that year by Eli Whitney Blake of what is said to be the world's first stone crusher. As a consequence of that invention, stone could be crushed to small sizes with considerable ease and, as a natural result, the use of crushed stone in macadam roads and as railroad ballast increased at a great rate. Also, as portland cement came into use, machine-produced crushed stone furnished readily available aggregate. Rapidly, other uses developed, such as for fluxstone in the production of pig iron and for other metallurgical operations and chemical utilizations. These utilizations made for the rapid growth of the crushed-stone industry and this growth is still proceeding with the growth of population and the development of new uses, notably the employment of limestone for the improvement of soils for agricultural purposes. The industries of which the production of crushed stone is a part have a tonnage second only to that of mineral fuel in the mineral industries of this country.

Jan 1, 1949