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By H. H. Rachford

This work presents a first-order analysis of the instability underlying viscous fingering in adverse viscosity-ratio water floods. It extends previous analyses of frontal instabilities, which were carried out with equations for parallel plate models, by including effects of the saturation transition zone observed behind the front in water floods in water wet systems. This zone tends to insulate incipient fingers from the high-mobility watet;. thus conditions for the onset of fingering differ from those in the parallel plate theory. Finite-difference solutions of the two-dimensional equations of displacement in porous media exhibited the predicted stability characteristics in six hypothetical field- and laboratory-scale floods in rectangular reservoirs. In contrast to results with parallel plate systems, this paper concludes that for waterwet reservoirs, laboratory models scaled by the usual criteria are also correctly scaled for frontal instability. Further, fingering in the systems studied can occur in any saturation range behind the front, and may occur at an intermediate saturation even though stability obtains both at the saturation corresponding to the Buckley-Leverett front and near residual oil saturation. Other points of contrast are that the likelihood of occurrence of fingering may not increase as flow rate or viscosity difference increases, but my be sensitive to changes in he relative permealdlity and capillary pressure functions. INTRODUCTION The recovery of oil by water flooding frequently involves displacing the oil by water of a lower viscosity. Displacement of a fluid by a less viscous one may lead to gross channeling or fingering like that observed in solvent floods, in which it severely lowers recovery efficiency.1 In addition to adverse effects on recovery, it has been suggested that the unstable move- ment causing fingering may interfere with interpretation of scaled model studies of proposed water floods, since the instability in the model might not be faithfully scaled to that in the reservoir prototype. In view of the serious implications of this possible breakdown of widely used scaled model techniques4-6 it is the purpose of this paper to examine the question further. Instabilities in the solutions of systems of differential equations imply a loss of smooth dependence on initial and boundary conditions. Thus, the possibility exists that in using models whose scaling is based on the differential system there may arise size- and rate-dependent factors which are not properly scaled. This possibility was examined in detail by Chouke et al., who analyzed the instability of frontal advance in a related problem, water-oil displacement in parallel plate models,2 in which a moving interface separates two regions of constant, unequal mobilities. First-order perturbation theory predicts the existence of a critical wave length for the growth of perturbations: and a wave length of maximum instability of A, = The interpretation is that wave lengths in a perturbation which are longer than A, will grow. Thus, if the width of a two-dimensional channel is greater than A,, fingers will grow, and the spacing of the fingers which grow at the maximum rate will be approximately It is important that the higher the velocity and/or the difference in flow resistance, the lower is A,, and thus the greater the number of fingers that can grow in a given model. In applying these conclusions to porous media, a pseudo-interfacial tension, , was assumed for the invasion front. Since this would not necessarily be equal to the liquid-liquid interfacial tension, an unknown constant was substituted for the foregoing expression for A, This was determined

Jan 1, 1965

By D. T. Peterson, F. A. Schmidt, J. D. Verhoeven

The velocity of mig-ration of these solutes in thorium metal due to a high amperage dc current was measured at several temperatures. All three solutes migrated in the same direction as the electron flow. Diffusion coefficients were combined with the migration velocities to predict the steady-state concentration profile. Electrotransport was shown to be an effective method of removing carbon, oxygen, and nitrogen from thorium and resistance ratios several times larger than for crystal bar thorium were achieved. However, the maxirnum attained purification was well below the predicted values, apparently due to some form of contamination. THE migration of solutes in metals when a high current density dc current is passed has been known for many years. This phenomenon has been the subject of a number of reviews published in recent years.l~* Many of the earlier investigators of electromigration of interstitial solutes interpreted the direction and velocity of migration on the basis of a charge on the solute particle. This interpretation is unclear because, in a given experiment, one cannot separate the contributions to the force moving the solute which arise from the charge on the solute in an electric field gradient and the momentum transfer from the scattering of the electrons or holes. There have been only a few quantitative measurements of interstitial migration velocities and some of these have been characterized by poor accuracy or by errors in the analysis of the experiment. The electrotransport mobilities of carbon, nitrogen, and oxygen in thorium were determined by observing the rate of movement of a discontinuity in the concentration profile. This method was used by Carlson el a~.~ to determine the mobilities of interstitial solutes in yttrium and its advantages are discussed in that paper. The specimen is essentially a pair of semi-infinite, bar-type diffusion couples. The electro-transport velocity was measured by observing the displacement of the mean concentration point in a measured length of time. The diffusion coefficients were calculated by the Grube method from the concentration profile. The transport mobilities and diffusion coefficients can be used to predict the concentration profile in an electrotransport experiment of a given time, current density, and specimen length. At long times a steady state will be reached such that the natural logarithm of the concentration of each solute varies linearly along the bar with a slope which is equal to the velocity of the migrating solute divided by its diffusion coefficient. The estimation of the purification potential of electrotransport is discussed by ~erhoeven.' A comparison of the concentration profile and the purification which should be expected from known solute velocities and diffusion coefficients with that which is obtained in an experiment can be very useful in indicating whether the maximum possible purification has been achieved. EXPERIMENTAL METHOD The apparatus used in this study consisted of a sample chamber which was equipped with two electrodes, a sight glass, and a flange for mounting to a high-vacuum system capable of obtaining pressure of 2 x lo-? Torr. The chamber was made of stainless steel and was 4 in. in diam and 6 in. long. The seal between the electrodes and the chamber was made with "0" rings and compression bushings. The thorium specimens were threaded and screwed into tantalum "U"-shaped adapters attached to the ends of the electrodes. This arrangement is shown in Fig. 1

Jan 1, 1967

By R. A. Greenkorn, R. C. Smith

Hele-Shaw cells are used to model creeping flow through porous media (where Darcy&apos;s law is valid). The effects of inertia on flow about obstructions in a Hele-Shaw cell can be calculated by a perturbation method if one can determine a solution to Laplace&apos;s equation. Results of a computer solution for flow about circular, square and elliptical obstructions are presented. These results show that or a modified Reynolds number of less than I, the inertia terms are small; and for values of less than 3, the average streamline predicts the ideal flow. Therefore, the analogy might be used for studying flow in porous media up to a modified Reynolds number of at least 3. INTRODUCTION The nature of fluid flow in porous media is of interest in the fields of soil mechanics, ground water flow, petroleum production, filtration and flow in packed beds. Because it is very difficult to study the phenomenological behavior of flow in porous media, homologs and analogs are used to study flow characteristics. A Hele-Shaw model, made of two closely spaced plates - usually glass — is often used as an analogy to two-dimensional flow in porous media. Hele-Shaw2 showed experimentally that the streamline configuration for creeping flow around an obstacle located between two closely spaced parallel plates is the same as for two-dimensional, ideal flow about the same obstacle. Stokes7 verified these observations mathematically. The usual equation of motion for flow in porous media is Darcy&apos;s law. The form of the mathematical statement of Darcy&apos;s law is identical, within a multiplicative constant, to the expression for the average velocity over the plate gap in the plane of a Hele-Shaw model. These models may be used to describe flow in both homogeneous and heterogeneous porous media. In the mathematical proof of the Hele-Shaw analogy it is assumed that the convective terms in the Navier-Stokes equations are negligible and that the equations of motion degenerate to Laplace&apos;s equation, with pressure the dependent variable. Whenever a Hele-Shaw model is used as an analogy to flow in porous media, .the validity of this assumption is in question. Riegels5 showed that if convection is not neglected, the velocity distribution around a cylindrical obstruction in the flow field depends on a Reynolds number, the plate spacing, and a dimension characteristic of the obstacle. Riegels&apos; solution, a perturbation solution, uses the boundary condition that the flow rate into the obstacle averaged over the plate gap at any point on the obstacle is zero. The method requires that a solution to Poisson&apos;s equation for the perturbation pressure be found. Riegels evaluated this solution for the case of the cylindrical obstruction. His method may be simplified by eliminating the need for solving Poisson&apos;s equation for the perturbation pressure. Instead, an analytic expression for the perturbation pressure gradient is obtained (valid for arbitrary shapes) and used to eliminate pressure from the equations for the perturbation velocities. The results show, for symmetrical shapes, that if NRe < 1, the convective acceleration terms are small, and that the average velocities represent ideal flow up to at least NRe = 3, where: L is a characteristic dimension of the obstacle perpendicular to flow, b is the plate spacing, u is viscosity, v, is velocity of approach and p is density. THEORY* Incompressible fluid flow through a Hele-Shaw model and a porous medium are analogous because the equations for the average velocity components in two-dimensional flow are identical if:

Jan 1, 1970

P. L. Pratt (University of Birmingham, Birmingham, England)—The author has measured the hardening effect of isolated edge and screw dislocation boundaries in a remarkably elegant manner, and he proposes that the detailed structure of the boundary determines its effectiveness as a barrier to slip although "there are still unknown details of the distribution which may be extremely important." On p. 678 the author states "that for a good crystal (one having a yield of about 30 psi) a change in annealing temperature from 300" to 400 °C resulted in a negligible shift in the level of the stress-strain curve." Is this in agreement with the results of the earlier paper by Li, Washburn, and Parker8 in which such a change of temperature produced notable hardening in crystals with a yield of about 30 psi? Or were these earlier crystals, of the same nominal purity, less perfect than those used in this work? The experiment illustrated in Fig. 15, p. 681, shows that the boundary has sharpened after annealing at 400 °C, the temperature at which the hardening effect first becomes apparent. Did the author verify that no sharpening of the boundary occurred at, say, 300 °C where no hardening was found? This would seem to be an important check on the proposed mechanism, especially since zinc of this purity should polygonize at temperatures well below 400 °C within the annealing times used here. There seem to be at least two alternative explanations which could fit these facts: 1—The boundary may sharpen at 300 °C or even lower temperatures but be unable to contribute greatly to the hardening until jogged by thermal vacancies and other impurity atoms after 400 °C anneal. This mechan- ism, discussed in the earlier paper,&apos; is believed to account for the thermal hardening observed by Blank&apos;" in NaCl, as stated elsewhere: and by results from recent experiments which tend to confirm this view. 2—The dislocations in the diffuse boundary may be locked by impurity atoms at 300 °C and thus only sharpen the boundary at 400 °C with the aid of thermal vacancies. In this case it would be difficult to distinguish between the two sources of hardening (sharpening or jogging), using metal of this purity. Jack Washburn (author&apos;s reply)—The author wishes to thank Dr. Pratt for his discussion. In connection with his first comment, it should be pointed out that the temperature of testing in the present series of experiments was —196°C, whereas, in the earlier experiments he referred to,&apos; it was 20°C. Therefore, the yield values should not be directly compared. It is likely that the crystals used in the present work were initially more perfect macroscopically than the large shear specimens used previously. The small size of the test section in the kink specimens made it possible to select regions of the large crystals, from which they were acid-cut, that were free of observable small angle boundaries. The sharpening of a microscopically diffuse boundary such as that in Fig. 15 begins in zinc of this purity well below 300°C. However, it is probably not justified to conclude that because a boundary looks sharp under the microscope it has attained the ideal structure. The author agrees with Dr. Pratt that jogging of dislocation lines is one of the structural features of a small angle boundary that should be important in determining its strengthening effect. More detailed information concerning the changes in boundary structure as a

Jan 1, 1956

By W. D. Robertson, A. S. Tetelman

The technique of decorating dislocations was employed to investigate deformation and fracture resulting from Precipitation of hydrogen in Fe-3 pet Si single crystals. It is shown that cracks are produced on (100) planes inside crystals, as a consequence of the precipitation of hydrogen gas, either when crystals are quenched from a hydrogen atmosphere at elevated temperatures or cathodically charged with hydrogen at room temperature. Plastic deformation in the vicinity of cracks, observed as arrays of decorated dislocations, is in conformity with the calculated stress distribution about a crack containing an internal pressure, and the observations provide information permitting a detailed analysis of the mechanics of crack growth. The fracture characteristics of crystals containing internal cracks were evaluated at 25o and -196°C and the results are related to the mechanism of hydrogen embrittlement in terms of the growth of preexisting cracks. HYDROGEN in bee iron or steel produces two characteristic changes in mechanical properties: I), a decrease in ductility (macroscopic strain at fracture) that depends on temperature and strain rate, and 2), spontaneous fracture under static load that depends on time and apparent stress. Resolution of these phenomena into the microscopic processes that combine to produce the macroscopic effects is especially difficult in the Fe-H system in which the active component cannot be directly observed and only maintained in equilibrium with great difficulty in the temperature and pressure range in which embrittlement phenomena appear. As a result of these complications, verification of the numerous hypotheses&apos;-5 that have been proposed to explain the microscopic mechanism of embrittlement depends on self-consistency with measured changes in macroscopic properties that are averaged over the volume of a specimen. It is obviously important to obtain a more direct evaluation of the microscopic processes that combine to produce embrittlement. Accordingly, the present investigation was designed to identify and observe, as directly as possible, the microscopic effects of introducting hydrogen into a bee crystal. It was concluded from a previous investigation6 of X-ray line broadening, produced by introducing hydrogen into pure iron at room temperature, that the only effect that could be associated with the introduction of hydrogen was plastic deformation; in particular, dilation of the lattice was not observed, within ± 0.01 pet, and no evidence was found that could be interpreted to support the idea7&apos;* that hydrogen occupies tetrahedral interstitial sites in the iron lattice. The absence of lattice dilation is consistent with the extremely small solubility of hydrogen in bee iron9,10 (0.015 at. pet at 900oC and 1 atm pressure), and the evidence of plastic deformation is consistent with the fact that hydrogen, introduced by cathodic charging, eliminates the carbon yield point.11-13 Following this investigation, the immediate problem was to devise a method by which plastic deformation could be observed directly. The technique employed by Hibbard and Dunn14 to observe the movement of dislocations during bending and subsequent polygonization of Fe-3 pet Si single crystals was adopted and modified for the present purpose to include the observation of dislocation arrays in the volume of the crystal, and their association with the fracture process. EXPERIMENTAL PROCEDURE Single crystals of a high purity Fe-3 pet Si alloy, containing 0.007 pet C, were grown in vacuum by

Jan 1, 1962

By S. J. Rothman, L. T. Lloyd

S. J. Rothman and L. T. Lloyd (Argonne National Laboratory)— Hagel&apos;s paperz0 discusses the question of the mechanism for self-diffusion in bcc transition metals. Recent work21"23 has led us to agree with him in reabandoning the ring mechanism in favor of a defect mechanism, most likely vacancies. On the other hand, we think that Hagel&apos;s attempt to group together all self-diffusion in bcc transition metals is wrong. We prefer the scheme of Peart, Graham, and omlin," who separate them into two groups. One group contains the anomalously behaved metals P titanium,&apos;, y uranium, and perhaps zirconim.&apos; The other group contains a iron," this alloy was held at 1800°C for 2 hr before quenching, its structure was all a. B. C. Giessen, I. Rump, and N. J. Grant (Authors&apos; reply)—We very much appreciate the discussion by Deardorff and Kato regarding the a to /3 transformation temperature of hafnium. In the W-Hf program, as well as in a current study of the system Cr-Hf, standard precautions were exercised against contamination, including vacua of less than 10"5 mm Hg and a weight control check of all specimens to insure an impurity rise of less than 100 ppm. Following receipt of the above discussion, a revision was made in the annealing process. Arc-cast specimens were etched with a 10 pct HF-90 pct HNO solution until 1 mm of surface, including a possible oxide film, was removed. Annealing was done in a hafnium container which provided a long diffusion path for gaseous contaminants. Finally, the heat treating time was shortened. Structural changes were noted to occur quite slowly. A 99.5 at. pct Hf alloy showed 70 pct /3 after 30 min at 1700°C and was 100 pct /3 after 10 min at 1715°C. After 24 hr at 1740C, the alloy was found to be 10 pct/3. This change is due to contamination; it was estimated that it corresponds to an increase of 60°C in the transformation temperature over a 24 hr period. The corresponding change in 30 rnin would be slight. Using the same hafnium as in the above publication, and three new alloys at 98, 99, and 99.5 at. pct Hf, the transformation temperature was indicated to be 1715" 15°C. Since this hafnium contained 4.4 at. pct Zr, a correction of 40 5C, based on an assumed approximately linear transformation temperature curve, must be made for pure hafnium. This yields a value of 1755 20°C in good agreement with Deardorff and Kato&apos;s value. Because the slope of the boundary is small, this permits a good extrapolation, and we regard the W-Hf alloys as well suited to check the Hf transformation temperature. niobirn,&apos;&apos; and molybdenum,22 whose activation energies correlate with the melting temperature and whose Do values follow Zener&apos;s predictions.28 We have no quarrel with Hagel&apos;s placing chromium into the second group; we disagree with his interpreting our data to make uranium fit into that group. Hagel considers that the measurements of self-diffusion in uranium below about 950°C represent combined volume and grain boundary diffusion. This contention is based on the curvature of the penetration plot for our 891°C run,4 which also has a nearly straight line plot of log c vs x. Hagel has extrapolated these characteristics to our 803.5C run and fitted his Arrhenius plot for self-diffusion in y uranium to our four highest temperature points only. We think this is wrong for the following reasons.

Jan 1, 1963

By L. C. Armstrong

Twice in the past two years and in two widely separated localities—ane near Williamsville, Mo., and the other in the Allard Lake district of Quebec— the Contract Drilling Division of the Longyear Company has experienced perplexing difficulties in drilling granitoid igneous rocks. The rocks in both places are characterized by appreciable amounts of feldspar intimately inter-grown with quartz particles of microscopic dimensions. The disappointingly slow rate of advance and the exceptionally high bortz loss, obtaining during the life of these two projects, are ascribed largely to the resistance to abrasion of these two minerals when arranged in this intergrown pattern. Whether all intergrowth-bearing igneous rocks would offer extraordinary resistance to bit progress cannot be stated with assurance on the strength of these experiences alone. More data on diamond drilling this sort of material in a number of localities are needed before any generalizations can be made safely. It should be pointed out that the lack of time and funds made it impossible for the writer, or other persons interested in correlating the details of bit histories with the kinds of rocks drilled, to be present during the performance of the contracts. However, the records kept in the normal course of drilling are deemed complete enough to be reportworthy. This information is presented here together with the findings made in studies of the rocks involved, with the thought that it may attract the comments of others who may have encountered similar refractory drilling conditions. A pooling of knowledge on the problem would be of material aid in devising more efficient cutting tools and procedures for penetrating this kind of rock. Drilling Blastholes in the Williamsville Granite Due to the unsatisfactory perform- ance of pneumatic percussion drills in boring blastholes on a construction contract near Williamsville, Mo., tests were made with a diamond drill. The poor progress achieved and the excessive loss of diamonds, however, soon led to the abandonment of these trials. The diamonds, in all of the bits tried, lost their cutting edges and acquired a polish after being in service for distances ranging from a few inches to a few feet. Coring bits containing surface-set, whole-stone bortz in a tungsten powder matrix were employed. The cost assignable to bortz wear averaged $7.17 per foot. This item of expense is several times the amount normally expended in diamond drilling in firm, unfractured, granitic rocks. Diamond-impregnated, tungsten carbide bits also were used without success. The diamond wear was at the rate of $0.98 per foot, but the diamond chips became too polished for further duty in less than a foot of drilling. The Williamsville granite is pink and medium-grained. In the hand specimen, it has a fresh, sound appearance; it is seemingly composed almost entirely of interlocking grains of feldspar and quartz and has no discernible features suggesting a greater durability than is usually found in rocks with this composition and texture. Microscopic examination, however, reveals a predominance of feldspar grains with more or less regularly distributed and sharply angular masses of quartz (see Fig 1). The pattern assumed by the two minerals in this mode of occurrence is referred to as a "graphic intergrowth," as it bears some resemblance to the cuneiform characters of ancient Persian writing. The other principal constituents are quartz-free feldspars (microcline and orthoclase) and quartz. All of these constituents are in nearly equidimensional grains, ranging up to about 3 mm in length. There are also

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Jan 1, 1936

By Waldemar Lingren

CONTENTS. PART I.-GENERAL FEATURES. [ ]

Jan 1, 1902

By Elmer R. Kaiser

COMBUSTION of coal and transfer of heat from flames and gases to boiler surfaces continue to be of great interest to engineers here and abroad. Numerous investigations have been in progress to improve furnace and boiler performance and economy. The importance of better understanding of the processes and opportunities for improvement is apparent when it is remembered that heat from at least 500 million tons of coal a year the world over is being transferred to boiler water at efficiencies ranging mostly between 50 and 90 pct. Even slight gains in efficiency, economy, and labor saving become very significant when multiplied by the enormous quantity of fuel consumed. Also the competitive position of the large coal, oil, and gas industries in satisfying the fuel consumers is greatly affected by the achievements made through technical progress with each fuel. This paper is part of a continuing activity of Bituminous Coal Research, Inc., to extend the knowledge of coal utilization for steam generation and to seek promising directions for future research and development in cooperation with others. Particularly in the latter regard, numerous interviews were held during the last three years to seek the experience and advice of boiler and combustion-equipment manufacturers, electric-utility executives, and fuel engineers. A wealth of published information was also reviewed, which together with the interviews pointed to the advisability of further work on ash and sulphur control. For the present purpose a number of factors important to efficient heat liberation and recovery have been grouped as follows: 1—combustion, temperatures, and rates of heat liberation; 2—radiation, convection, and furnace and boiler configuration; 3—sponge ash, slag, and hard-bonded deposits; 4— low-temperature deposits and corrosion (cooling flue gas below dew point and air-pollution control); 5—the limitations of coal cleaning and boiler size and cost as related to fuel characteristics; 6—future possibilities and conclusions. The development of combustion apparatus for power boilers is progressing at a lively pace. There has been no letup in improvements in design of pulverized-coal-fired boilers, and there is a strong trend at present toward improving dry-bottom units. Spreader stokers with overfire jets and dust collectors as standard equipment are gaining favor. Less than 10 years in commercial use, cyclone burners are going into numerous installations here&apos; and abroad.&apos; Underfeed and traveling-grate stokers have long since been developed for heavy-duty operation, yet new developments in overfire jets and humidification of air blast have improved their performance. A water-cooled vibrating-grate stoker of German origin is being introduced into the United States and Canada." The primary objectives of an ideal coal combustion device are: capacity to burn the variety and sizes of coals likely to be economically available during the life of the unit; capacity to burn the coals automatically for a wide load range and rapid load fluctuations and to burn the coals completely to CO2, H2O, and SO2, which means without smoke and cinders, or carbon in the refuse; capacity to control and discharge all the ash in final granular form without ash adhesion to walls or tubes, and without flue dust; minimum furnace volume; minimum labor and maintenance; low initial and operating cost. Regardless of the method of burning, the gaseous products of coal combustion are N2, CO2, O2, H20, and SO?. By way of illustration, the coal analyses in Table I is assumed from an installation described by E. McCarthy.&apos; When coal is burned with 20 pct excess air (theoretical air, 9.23 lb per lb of coal), the quantities of combustion gas shown in Table II are produced. In addition, the gases carry particles of fly ash, unconsumed cinders, soot particles, and small but significant amounts of vaporized oxides and sulphates of sodium, potassium, lithium, phosghorous, iron, and other metals. In recent years, germanium, one of the rare metals found in coal, has been shown to oxidize and vaporize at combustion temperatures and to be concentrated by reconden-sation at lower temperatures." Pulverized coal and cyclone flames" have peak temperatures of 3000&apos; to 3500°F. Temperatures in fuel beds of large underfeed stokers reach maxima of 3000°F, sufficient to fuse almost any ash and to volatilize some of it. These peak temperatures are above the optimum necessary for rapid combustion, but they hasten heat transfer for ignition as well as boiler heat absorption. Furnace and gas temperatures increase with combustion air preheat. Low excess air has the same effect. Fine coal pulverization and highly turbulent combustion shorten the distance for fuel burnout, increase flame temperature, and speed up heat transfer. Rates of combustion of pulverized coal exceeding 200,000 Btu per cu ft per hr have been demonstrated in atmospheric gas-turbine combusters,

Jan 1, 1955

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