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By E. L. Dougherty

A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonbomogeneities. Numer ical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parmeters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval's heterogeneity factor H. which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomo-geneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. INTRODUCTION It has been shownl,2,3 that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by oval! have taken two approaches: (1) development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing5,6 and (2) simultaneous application of Darcy's Law for flow and the diffusion equation with a convection term for mass transfer.7,8,9 We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of nonlinear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics. In our equations the mixing process is characterized by four parameters. Three of these, labeled ß, P1 and P2, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores. The purpose of this paper is (1) to present the details of the mathematical analysis, (2) to present the results of the calculations, (3) to consider what light the results shed on the mixing process in an unstable miscible displacement, and (4) to provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations. We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. The oil phase consists of oil containing dissolved

By John P. Hager, Igor A. Wilkomirsky

The thermodynamic properties of the Pb-Ag system have been determined between 775° and 950°C by the cell: Electrotransport measurements on silica-saturated PbO-SiO2 melts established that the conduction was entirely ionic and that lead is present only in the divalent state. The activities of lead and silver exhibit Positive deviations from ideal behavior. In dilute solutions the activities of lead and silver follow Henry's law. The values obtained for yhb and yig at 1200°K are 1.49 and 1.69, respectively. Determination of a portion of the liquidus curve agrees well with the established phase diagram. provides an accurate means for the thermodynamic study of liquid alloy systems. However, Wagner and wernerl have shown that cells of type I are limited to alloy systems for which the reaction at the alloy-electrolyte interface will be extremely small. The traditional electrolyte for cells of type I has been a low melting point mixture of group IA chlorides, to which a small amount of the compound ACIZa has been added. However, the choice of a chloride electrolyte may not always be practical, in that the Gibbs free energies of formation of the compounds ACIZ, and BCIZb may not be sufficiently different to minimize Reaction [I]. On the other hand, the Gibbs free energies of formation of the oxides of metals A and B may be sufficiently different to minimize Reaction [I]. In this case, the use of molten oxide electrolyte would be clearly advantageous. In the present study, the thermodynamic properties of the Pb-Ag system have been investigated using the cell: Previous galvanic cell studies on the Pb-Ag system2'= are not reliable due to the displacement reaction between the alloys and the chloride electrolyte. Wagner and ~erner,' using Laitinen and Liu's' value at 450°C for the standard electrode potential of Reaction 111, have estimated the percent error in the activity of lead bPb) when using a chloride electrolyte. At 1000°C the error for xpb = 0.10 is 12 pct. Taking the Gibbs free energies of formation for PbClz and Ag cI,' and the equations of Wagner and Werner,' the error in apb at 1000°C and Xpb =0.10 was calculated to be 140 pct. However, using the Gibbs free energies of formation for Pb O' and an estimated value for Ag 20, the error in apb when using a molten oxide electrolyte at 1000°C was estimated to be less than 1 pct for The virtual reaction of cell I1 for the passage of n Faradays of positive electricity from left to right in the cell is: where 5 is the Faraday equivalent (23,063 cal per v equivalent), E is the electromotive force of the cell in volts, and n is the number of Faradays of electricity required for the transfer of 1 g-atom of lead through the cell. The value of n should be equal to 2 since lead is generally divalent in oxide melts. However, the presence of either tetravalent lead ions or electronic conductivity through the molten oxide electrolyte will result in a value of n greater than 2. Bockris, Kitchener, and Davies' have determined the amount of ionic conductance in a liquid PbO-SiO2 mixture (xPbO= 0.50) at 920°C by measurement of the volumes of CO and C& evolved at a carbon anode during electrolysis. From their data a value of 2.13 * 0.16 was calculated for n. Although their measurements indicate the possible presence of multivalent lead ions and/or electronic conductivity, their measurements were not at silica saturation and no definite conclusions can be drawn. However, as a result of the electrotransport measurements described in the next section the ;due of n can be taken as equal to 2.

Jan 1, 1969

By Eugene F. Broome, Hugh A. Walls

Self-diffusion coefficients were measured using the modified shear cell technique over a temperature range from 31" to 401°C. These data agree within experimental error with those of Petit and Nachtrieb, which were determined from 30°to 99°C. LIQUID self-diffusion behavior in gallium has been studied previously by Petit and Nachtrieb&apos; using their shear cell technique.&apos; Data were obtained in that investigation over temperatures ranging from 30.6 to 98.7"C, and these comprise the only published data for liquid gallium. In the work reported here, diffusion data were obtained from 30.8 to 400-9.Cusing a shear cell technique different from that of Petit and Nachtrieb. This modified shear cell method and the mathematical analysis for diffusion in a finite capillary geometry have been previously described.3 PROCEDURES AND ANALYSIS The segments of the modified shear cell were fabricated from types 304 and 316 stainless steel. No corrosion problems with gallium were encountered until attempts were made to obtain data at 500°C. The diffusion capillary diameter was 1.59 mm and capillary lengths for the four sets of cell segments used are given in Table I. Gallium with a purity of 99.999 wt pct was obtained from Var-Lac-Oid Chemical Co. The gallium-72 isotope used to measure the self-diffusion coefficients was produced from this inert gallium by irradiation in The University of Texas Reactor Facility, and was checked for radiochemical purity. Following a period of isothermal diffusion controlled to within 0.0l°C, the contents of each capillary section were emptied into a counting planchet, weighed to assure that gallium had not been lost during handling, and the radioactivity determined by windowless gas-flow proportional counting. Great care was taken to obtain a reproducible counting geometry for the samples. Diffusion coefficients were obtained from the solu-tion3 to the diffusion equation for the modified shear cell problem, viz.: in which B2= C2(t)Li + L2)- CSL1-COL2 P* (C0-Cs)(L1+ L2) and L, and L2 are the capillary segment lengths. The step-function initial concentration distribution was expressed as C(x,O) = C, for -L1 = x < 0 and C(x,O) = Co for 0 < x 5 L?. Also, C2(0 = ^- fcix,t)dx Computation of the diffusion coefficients was done numerically as described in our earlier paper.3 Because of the short half-life of gallium-72 (14.1 hr) and the relatively long counting times taken to give a precise value of the diffusion coefficient, it was necessary to account for the radioactive decay both during the actual count and between counts for different samples (before and after diffusion). Thus, the average count rate Cz(t) for a second sample counted from times t3 to t4 can be made consistent with the average rate Co determined for a first sample counted from times t1 to t2 by the relationship: N(e-»i-e-M») , , C2(f) " &-«,)(*-«.-«-»«) [21 in which N is the total number of counts taken and is the decay constant. RESULTS AND DISCUSSION The self-diffusion coefficients determined in this investigation are listed in Table 11. Values of the parameters used to calculate the coefficients are given in the table, as are values of the random counting error &apos; for the concentration ratio pz and the corresponding expected random variation AD in the diffusion coefficient. The quantity is calculable from: &apos;Cg — C2(t)} , „ ,2 .-„¦, M co-csl(ACs)J W in which AC is the error in the individual count rate. The mean values of the diffusion coefficients within each temperature group are also given in Table 11. Such temperature groupings of data are reasonable because of the small variations between the temperature~.~

Jan 1, 1970

By R. Lagneborg, R. Gullberg

An X-ray method for determinig volume fractions of phases in textured materials has been developed. The method involves measurements of the integrated intensities of reflections of each phase for one single orientation of the sample. The method was checked by evaluating the phase contents in samples from two stainless Cr-Ni steels containing austenite and ferrite in known amounts. In the present case measurements of about five reflections from each phase were required. The agreement between calculated and known volume fractions was found to be very close. AN X-ray diffraction method is often employed for determining the amounts of two or more phases in a material. The details of the method have been described at several instances.&apos;" In short, the method is based upon the fact that the integrated intensity of a reflection is directly proportional to the volume fraction of the phase considered. In principle, the method only requires the measurement of the intensity of one reflection for each phase. The most severe shortcoming with this method is that it disregards influences from preferred orientation in the material. In a diffractometer, where this type of analysis is most conveniently carried out, the geometry is such that the diffracting planes for a specific Bragg peak are all parallel to the surface of the specimen. This implies that it must be required that the occurrence of the diffracting planes parallel to the specimen surface must be as frequent as for any arbitrarily oriented physical plane of the sample. This requirement will generally only be fulfilled for a material free of texture. Since all materials in reality always exhibit a preferred orientation to some extent. the deficiency of the method is quite serious. In cold-deformed material the texture is appreciable, but also annealed material will in many cases display a considerable texture. The problem of quantitative phase analysis in textured material is one of obtaining the integrated intensity averaged over all orientations of the specimen with respect to the X-ray beam. Lopata and ~ula~ have shown that this can be accomplished by integration of intensities over the whole pole figure, or by random rotation of the specimen in the X-ray beam, or by a combination of both. Hence, in this method the average integrated intensity for a specific reflection is obtained by directly determining the intensity for a sufficient number of physical orientations of the sample. However, since an excess of diffracting planes in a certain surface plane necessarily must be accompanied by a deficiency of another type of diffracting plane, it appears to be possible to obtain the correct average intensity for a specific diffracting plane by performing an appropriate averaging of intensities belonging to a large number of diffraction planes of different hkl when all intensities have been produced from one single orientation of the specimen surface. In the present work such a method has been attempted and tested experimentally for two stainless Cr-Ni steels containing austenite and ferrite. 1) THEORY The expression for the integrated intensity of a Bragg reflection diffracted from a phase in a polycrys-talline sample in a diffractometer is: where C is a constant only dependent on the incident X-ray power and the diffractometer geometry, v the volume of the unit cell, F the structure factor, m multiplicity of the diffracting plane, L Lorentz factor, P polarization factor, e-2 temperature factor, p average linear absorption coefficient of the irradiated vO1umej and V volume fraction of the phase &apos;Onsidered. Hence, the factor R in the abbreviated form of Eq. [I] can be calculated and depends only on 0 and the diffracting plane {hkl}. For an alloy containing two phases, a and y, we can write

Jan 1, 1967

By John Wulff, David A. Stevenson

The solubility of iron and cobalt in liquid lead, the solubility of chromium in liquid tin, and nickel in liquid silver were determined up to 1300°C in an atmosphere of hydrogen. Liquid samples were taken at different temperatures and analyzed. The data obtained were plotted to show the relationship between log mole fraction of solute and the inverse of the absolute temperature. Resulting values for the differential heat of solution (AH) and the excesspartial molar entropy (S)are: for the iron-lead system = _24,200 cal per mole and AT = 5.0 e.u. for the a phase, and AH = 18,300 and S = -0.1 e.u. for the y phase; for the cobalt-lead system AH = 16,500 cal per mole and AS =0.7 e.u.; for the chromium-tin system AH = 15,600 cal per mole and AS = 8.5 e.u.; for the nickel-silver system AH =18,000 cal per mole and AS = 4.0 e.u. RECENT developments in coating, brazing, and heat transfer have focused attention on specific cases of solid-liquid interaction in metal systems, particularly those involving dilute liquid solutions. One fundamental quantity of interest in such systems is the equilibrium phase distribution between solid and liquid phases. In any effort to fully understand such interactions, one must be able to describe the equilibrium state precisely. Furthermore, in order to develop genera! relations for such systems, one must know the equilibrium state in a number of different cases. This investigation was devoted to a study of the equilibrium phase distribution in four binary systems: solid iron-liquid lead; solid cobalt-liquid lead; solid chromium-liquid tin; solid nickel-liquid silver. The iron-lead system was previously studied by Shepard and parkman&apos; and later by Fleischer and Elliott2 with differing results. Both investigations were carried out by sampling the saturated liquid, and analyzing it chemically. The cobalt-lead system was previously reported by Pelzel,3 who noticed no discontinuity near the transformation. A limited investigation of the chromium-tin system was made by Wlodek and wulff4 using a weight loss method. This work was done in conjunction with the development of a process for coating molybdenum with chromium from tin solutions. To more fully under- stand the kinetics of the process, a more accurate determination of a solubility was desirable. No significant data were found in the literature on the nickel-silver system. Data on the latter system were, however, relevant to the investigation of the corrosion kinetics of copper-nickel alloys in liquid silver as carried out by Harrison and wagner,5 EXPERIMENTAL APPARATUS AND PROCEDURE Of the techniques available for the study of such systems the most effective appears to be that of liquid sampling,2,6,7 which is the method used in the present investigation. A schematic diagram of the sampling furnace is given in Fig. 1. Large pieces of solute metal, in excess of saturation solubility, were added to 200 g of the solvent metal, and the entire charge placed in an alundum crucible. Analytical reagent or materials of chemically pure grade were used in all investigations. The crucible was contained in a zircon muffle tube positioned vertically in the uniform hot zone of a Globar resistance furnace. The tube was provided with a number of ports which permitted sampling at temperature and in controlled atmospheres or vacuum; the ports were also useful for evacuation and introduction of gases as well as for thermocouple measurements. A chromel-alumel thermocouple Sheated in a porcelain tube was used for temperature measurements. A purified hydrogen atmosphere was employed in all experiments reported in this paper. The hydrogen was purified by passing it first over hot copper gauze to remove oxygen and then through a molecular sieve immersed in

Jan 1, 1962

By J. A. Musselman, P. F. Gnirk

A study was made of indexed penetrations by a single dull bit tooth under statically applied loads into rock subjected to confining pressures from atmospheric to 5,000 p.si and atmospheric pore pressure. Experimental results obtained with a 45" wedge tooth over the above range of pressures are presented for two limestones and a sandstone, a variely of indexing distances and two degrees of tooth dullness. The optimum distance between successive bit-tooth penetrations required for maximum rock damage and chip formation decreases substantially with increa.sing confining pressure above the brittle-to-ductile transition pressure of a particular rock. However, the distance remains approximately constant for a variation in confining pressure below the transition pressure. At a given confining pressure, the bit-tooth force required lor chip formation is constant for indexing distances greater than optimum, but generally decreases linearly with decreasing indexing distance for distances less than optimum. The chip-formation force data obtained at confining pressures for which the chip-generation mechanism is macroscopic-ally of a pseudoplastic nature compare favorably with previous theoretical results for indexed dull hit-tooth penetrntion into an idealized, rigid, perfectly plastic rock. INTRODUCTION To study the cutting action of a roller-cone bit, the interaction of a penetrating bit tooth with craters formed in a rock surfacc by the passage of previous bit teeth must be considered. Current knowledge of the basic mechanics of bit tooth-rock intcract:on under simulated borehole environmental conditions has been extensively reviewed.&apos;,&apos; Particularly of current interest are the effects of bit-tooth shape, distance between successive penetrations and differential pressure at the rock surface on the extent of the interaction. Pertinent to this paper are results of an experimental investigationb f the interaction between successive penetrations by sharp, wedge-shaped bit teeth. It was demonstrated that both bit-tooth angle and differential pressure influence the extent of rock damage between successive bit-tooth penetrations. Specifically, the optimum or minimum distance between successive penetrations required for maximum interact&apos;on or chip generation tends to decrease with decreasing bit-tooth angle and increasing differential pressure. In addition, at differential pressures on the order of 2,000 psi for four va- rieties of limestones and sandstones, the macroscopic mechanism of chip formation exhibits a transition from brittle to ductile. In this paper, experimental consideration is given to successive or indexed penetrat ons by wedge-shaped bit teeth. Since pore pressure in a rock sample is maintained at atmospheric pressure, the differential pressure at the fluid-rock interface is equal to the confining pressure. The degrees of bit-tooth dullness include teeth with flat and round apexes (Fig. 1). Of primary concern in this paper are the bit-tooth forces required for chip formation, the macroscopic mechanism of chip formation and the minimum distance between successive penetrations, i.e., optimum indexing distance required for maximum rock damage, as functions of differential pressure. Of further interest is a comparison of actual bit-tooth chip formation forces at elevated differential pressures with calculated forces from previous theoretical results4 for indexed dull bit tooth penetration into a rigid-plastic rock. EXPERIMENTAL APPARATUS AND PROCEDURE The experimental apparatus consists of a pressure vessel equipped with a piston through the side of the vessel (Fig. 2). A single bit tooth inserted in the lower end of the piston is forced at a desired rate into the rock when the ram pressure chamber is pressurized. Electrical instrumentation incorporated into the apparatus yields a graphical plot of force on the piston as a function of bit-tooth penetration or displacement into the rock. Since the piston and ram assembly are in force equilibrium for a constant confining pressure in the main vessel, the fluid volume in the vessel remains constant during bit-tooth penetration. Hence, the force resisting penetration of the tooth is independent of the force exerted on either end of the as-

By E. J. Harris

Mathematical solutions to complex mine ventilation problems are possible, but often the airway network is so complex that the mathematical solution becomes tedious and impractical. A fluid network analyzer, designed and built for analyzing mine ventilation problems has been in service at the Bureau of Mines&apos; Pittsburgh station for approximately nine years. Using this analogue as a model, the mine ventilation network is simulated electrically by a combination of series and parallel circruits laid out to conform with actual mine airways. A tungsten filament lamp, referred to as a Fluistor, is used to simulate mine airway resistance. With the analogue ventilation model established, voltages of the proper amplitude to represent ventilating pressures are impressed across the circuit at points where mine fans and airshafts are located. Comparison of mathematical solutions of complex systems against analogue results showed a maximum variance of 3% for pressures and 2% for quantities. An electrical fluid network analyzer, designed and built especially for analyzing mine ventilation distribution problems, has been in service at the Bureau of Mines, Pittsburgh, for approximately nine years. It is a nonlinear, low voltage, fluid network analyzer of the type developed by the late Malcolm S. McIlroy, Professor of Electrical Engineering, Cornell University, who cooperated with G. E. McElroy, of the Bureau of Mines, in adapting the instrument to mine ventilation systems. Several modifications have been made since the original installation, but a considerable part of this paper is drawn from G. E. McElroy&apos;s original description of the analogue.&apos; The analysis of water or gas distribution systems2,3 led to the development of this type of network analyzer. Several similar units are now employed by utility companies for this purpose; however, the Bureau of Mines unit is the only one designed specifically for mine airflow problems. Other airflow analogues employing a similar principle have been used at the Central Research Station of the Netherlands State Mines,4 in England,5 and in South Africa.6 Information on these devices indicated they were somewhat inflexible because commercial lamps with a sufficient range of resistance are difficult to obtain. Computers for mine ventilation analysis have been developed in Germany which instead of lamps use a variable resistance to adjust for turbulent flow laws. These units are expensive, but excellent results have been reported in their application. THE ANALYZER Theory of Application: As airflow generally follows the law of turbulent fluid flow, resistance to flow is nonlinear; consequently, the problem has been to find a nonlinear resistance element of suitable range that can be used for electrically simulated airflow. Tungsten filament lamps operated on alternating or direct current approximate the square-law resistance characteristics of mine airflow over a large range below maximum or rated voltage; that is, the voltage drop varies approximately as the square of the current. Consequently, the heart of the network analyzer is a nonlinear resistor known as a Fluistor, which is simply a custom-made low voltage, tungsten filament lamp that is available in a progressive series of relative resistance values ranging from 0.05 to 500 in nominal 5% steps. However, variations in manufacturing large groups result in differences of 1 to 3%, but series arrangements required for high-loss branches can be matched within about 1%. Utilizing a combination of Fluistors and load circuits, the mine ventilation system is duplicated electrically. Intake load circuits are connected from power intake to primary points of the circuit network; segments of unregulated flow along intakes and returns are represented by Fluistors, regulated splits and leakage paths are represented by load circuits and Fluistors of proper capacity; and mine exhausts are connected to ground from the last point of the network to complete the circuit. For the special purpose of representing booster fans or natural draft conditions, boosters or separate source circuits are provided that can be inserted between any two points of a network to increase voltage to the required value. Physical Layout: The analyzer consists of three 42

Jan 1, 1963

By Ulf S. Landergren

Diffusion coefficients and marker movements have been determined in brass using welded couples. Three different concentration ranges were employed at 750°C, while a fourth concentration range was measured at 500°, 600°, 700°, and 800°C. Marker displacements toward and porosity development in the high zinc side of the couple were observed in all cases. The results were interpreted as favoring a vacancy diffusion mechanism. IN the large amount of diffusion literature which has accumulated during the past half century, very few experimental data have been presented on body-centered-cubic metallic phases. The impressive combination of experimental and theoretical studies which has given the vacancy mechanism a fairly secure position as the preferred mechanism for most face-centered-cubic metals has no counterpart for body-centered-cubic phases, although the theoretical picture seems to be in a better state than the experimental work. The attempts to select diffusion mechanisms by the theoretical calculation of the activation energy for the various conceivable unit diffusion processes and the energy of formation of the type of lattice defect required have been based on models of two kinds. The first kind utilizes potential functions fitted for certain properties of pure crystalline copper; the second kind is fitted for sodium. The latter is an example of an open metal in which the metallic ion is small compared with interatomic distance,&apos; while the former is characteristic of the larger class of metals in which the ions have diameters about as large as the interatomic distance. brass should resemble copper in this fundamental property. It should be evident that results on the mechanism of diffusion obtained for one of these classes need not necessarily apply to the other. Huntington and Seitz, using a model of the copper type, showed that the activation energies to be expected for interstitial migration or a two-atom direct interchange were much higher than that for vacancy diffusion. Zener pointed out that a four-atom ring rotation would involve an activation energy considerably lower than the two unlikely mechanisms although still higher than the vacancy mechanism in the face-centered-cubic structure. Furthermore, he argued, the four-atom rotation would be relatively easier in a body-centered-cubic lattice and might be competitive with the vacancy mechanism. Paneth showed that a body-centered-cubic crystal-like sodium could form interstitial defects of special type, called a crowdion, by crowding an extra atom into < 111 > directions where the defects would affect a line of about eight atoms. The defect was constrained to move along the defining line. Unlike the face-centered-cubic case, therefore, the theoretical calculations for the body-centered-cubic mechanism do not provide a very clear-cut answer, and the absence of adequate experimental studies is the more serious. This investigation was undertaken for the purpose of obtaining useful information on diffusion in body-centered-cubic phases. brass was chosen for several reasons: 1—the phase field is sufficiently wide at high temperatures to permit the use of diffusion couples with adequate concentration ranges for satisfactory chemical analysis, 2-—thermodynamic activity data are available for the calculation of mobilities from diffusion coefficients, 3—the phase is as close to the theoretical model of the copper -type on which the calculations have been done as any body-centered-cubic metallic phase is likely to be. Measurements of the movements (if found) of inert markers during the diffusion process would indicate that a vacancy or Or mechanism played a major role in diffusion in brass. If no marker movement should be found, a ring mechanism would be indicated but not assured. Experimental Procedure The alloys used in these experiments, listed in Table I with analyses, were supplied by the Naval Research Laboratory. They were from ingots of 3x3 in. cross-section, heated to 760°C, reduced under a

Jan 1, 1957

By R. I. Jaffee, C. M. Craighead, G. A. Lenning

The effects of increasing hydrogen content, introducing a notch, and changing the strain rate on properties of titanium and one of its alloys were investigated over a range of testing temperatures from —196° to 200°C. Both high purity and commercial purity A-55 titanium were used as representative a materials, while a commercial Ti-8 pct Mn alloy was used for an a-P alloy. It was found possible to analyze the data, using the ductile-to-brittle transition temperature concept. Increasing hydrogen, the presence of a notch, and increasing the testing speed raised the transition temperature for the a materials. The presence of hydrogen and notches raised the transition temperature of the a-B alloy also. However, increasing the testing speed generally decreased the transition temperature of the a-p alloy. IN previous papers, the authors have shown that hydrogen is most detrimental to the notch-bend impact toughness of a-titanium&apos; and to the tensile ductility of a-B titanium alloys.&apos; These general effects have been confirmed by Kessler and co-workers," and by Kotfila and Erbin." Kessler showed that the slower strain rate in notch-rupture tests was a more sensitive measure of hydrogen embrittle-ment of a-B alloys than the tensile test. In the present paper the authors cover, with tensile and notch-bend tests, the effect of testing speed, notches, and testing temperature on hydrogen em-brittlement. High purity and commercial purity titanium, examples of u materials, and a commercial a-,f3 Ti-8 pct Mn alloy were investigated. The purpose of the investigation was to correlate the factors producing embrittlement. Materials The high purity titanium for this investigation was obtained by arc-melting crystal bar from Foote Mineral Co. into 1 Ib ingots. As-cast hardnesses for these ingots ranged from 60 to 90 Brinell. The arc-melted ingots were forged to % in. diam rods at 1470°F. These rods were swaged to & in. diam at room temperature prior to machining of the specimens for hydrogenation and testing. The commercial A-55 titanium and the Ti-8 pct Mn alloy were obtained from Rem-Cru Titanium Inc., as % in. diam rod. The A-55 titanium was hot swaged to 1/4 in. diam at 1300°F prior to machining of the specimens for hydrogenation and testing. The a-p C-11OM alloy was hydrogenated prior to hot swaging to 1/4 in. roc1 at 1300°F. Hydrogenation prior to fabrication permitted testing of the a-P alloy in the equilibrated and stabilized condition. The equilibration and stabilization treatment used was an air anneal for 1 hr at 1300°F, followed by furnace cooling to 1100°F and then air cooling. Hydrogenation was done in a Sieverts apparatus described previously.&apos; The hydrogenation treatment consisted of heating for 1/4 to 1/2 hr at 820 °C in purified hydrogen, slow cooling to 680"C, holding 1 hr for homogenization, and rapid cooling to room temperature. Intended hydrogen levels for the a-tita-nium materials were 0.05, 0.5, 1.0, 1.5, and 2.0 atomic pct—about 15 to 430 ppm. For the Ti-8 pct Mn alloy, the intended hydrogen levels were 0.05, 0.5, 1.0, 2.5, and 5.0 atomic pct—about 15 to 1100 ppm. The material for the 0.5 atomic pct level of hydrogen was vacuum annealed prior to hydrogenation to increase the accuracy of the addition. Vacuum annealing to remove hydrogen consisted of heating for 6 hr at 820°C, and resulted in a hydrogen content of about 10 to 15 ppm. When hydrogen contents were above 0.5 atomic pct—100 ppm—the hydrogen was added without prior vacuum annealing.

Jan 1, 1957

By H. J. Morel-Seytoux

Methods of predicting the influence of pattern geometry and mobility ratio on water flooding recovery predictions are discussed. Two methods of calculation are used separately or concurrently. The analytical method yields exact solutions in a convenient form for a unit mobility ratio piston-like displacement. A few typical pressure distributions, sweep efficiencies and oil recoveries are presented for various patterns. For non-unit mobility ratio, one may resort to a numerical method, such as that of Sheldon and Douherty. 1,2 Because the domains of applicability of the analytical and numerical techniques overlap, the exact solutions provide estimates of the errors in the numerical procedures. The advantages of the analytical and numerical methods can be combined. To develop a numerical technique as independent of geometry as possible, the physical space is transformed into a standard rectangle. The entire effect of geometry is rendered through one term, the "scale-factor", derived from mapping relations. The scale factor can be calcu-lated from the exact unit-mobility ratio solution for the particular pattern of interest. By this means recovery performances for arbitrary mobility ratio con be obtained for many patterns. A sample of tesults obtained in this manner is presented. INTRODUCTION Pattern geometry and mobility ratio are two major factors in making a waterflood recovery prediction. Because assisted recovery has become increasingly important to the oil industry, pattern configuration and mobility ratio also assume a greater significance in the assessment of the economic value of recovery projects. The influence of pattern geometry and mobility ratio in shaping a recovery curve and on the other quantities of interest to the reservoir engineer is the main subject of this paper. Much effort has already been spent on estimating quantitatively the influence of either pattern or mobility ratio or both on oil recovery. The literature reports many investigations of this nature. 3-9 However, many results or methods of recovery prediction presented in the literature cannot be considered fully satisfactory. Even for unit mobility ratio and piston-like displacement, where analytical solutions are available, the literature shows discrepancies. For non-unit mobility ratio, the divergence in the results is extreme. For infinite mobility ratio in a repeated five-spot, depending on the investigator, the sweep efficiency ranges from 0 per cent to 60 per cent. With respect to the influence of pattern on recovery, only the repeated five-spot has received much attention. Other confined patterns and pilot configurations have received very little attention. Two calculation methods are presented in this paper, either separately or concurrently: the analytical method of potential theory and the numerical method of finite-difference approximation. The analytical method is more restricted in scope than the finite-difference method, but it has the definite advantage of providing exact solutions within its range of applicability. If a unit-mobility ratio piston-like displacement is assumed, the analytical approach is possible. A few typical results are reported in this paper; the detailed description of the general method and of a great variety of results will be the subject of other articles. Fornon-unity mobility ratio, we must resort to a numerical scheme. The numerical technique is that which was described by Sheldon and Dougherty.l,2 It is not limited to piston-like displacement. However, mainly single interface results will be presented here. Because the respective domains of applicability of the analytical and the numerical method overlap, useful comparisons of exact and numerical solutions can be made for a variety of patterns. The advantages of the analytical and numerical approaches can be combined. The reason for the success of this analytical-numerical approach can be summarized in the following two points: 1. The numerical solution for arbitrary mobility ratio can be programmed most efficiently when the physical space in which the displacement actually takes place is transformed into a standard shape; and 2. This can be done with remarkable simplicity whenever an analytical expression for the pressure

Jan 1, 1966

Remote sensing, in general, is the recording of light and heat from a planet&apos;s surface within a certain range of the electromagnetic spectrum. For the Earth, systems capable of this recording are the MultiSpectral Scanner (MSS) and SLAR. The former is the recording system used in satellite and will be discussed in the next section. SLAR stands for Side Looking Airborne Radar. This device sends invisible radar waves which illuminate the Earth&apos;s surface. The reflected waves are subsequently recorded as images. The system can operate through darkness and dense cloud cover, and is particularly suited for the study of geological structures at both large and small scale (Wayland 1976). Remote sensing techniques are now widely being made use of in mineral exploration, especially for those last remote &apos;sanctuaries&apos; where geological data are meagre or non-existent. For places like Borneo, West Irian, the Amazon Basin etc. remote sensing, in the form of both satellite imagery and SLAR, is of considerable help, in fact more often than not the only help, to delineate geological provinces, geotectonic domains and meaningful lineaments. In the case of New Zealand, well made geological maps at scale 1:250&nbsp;000 by the Geological Survey are available to the public and these provide useful preliminary grounds for the selection of target areas. However, even in this case LANDSAT imagery can be of aid as will be shown later.

Jan 1, 1977

By Jacques Moraille

The public is asking for more aesthetic designs if they can be proven cost-effective at providing an appealing element to new dams. Lake Lenexa was designed and built around the idea of providing for basic dam functions such as flood control, enhanced water quality, recreation but also to provide an inviting community focal point for the residents to visit and enjoy; truly interact with the dam. The architecturally unique dam and ?one of a kind? spillway were designed to symbolize the water cycle as water moves from nature into the urban environment and the back to nature. A pedestrian bridge that spans the spillway offers visitors a good view of cascading pools and a fountain. The original Lake Lenexa dam layout incorporated relatively high, cast-in-place concrete retaining walls to form the spillway structure. The Black & Veatch project team performed a Value Engineering (VE) study to determine cost-effective means for implementing architectural features within the spillway, which resulted in innovative uses of construction materials not typically used in dam and reservoir construction. The VE study concluded that mechanically stabilized earth (MSE) retaining walls that are normally used for transportation projects would be a cost-effective alternative to the originally planned cast-in-place wall systems for the main spillway and stilling basins. The Black & Veatch study added value by mixing cement-kiln dust (CKD) with on-site clay soils to produce a stabilized material for use under the spillway. The CKD stabilized material properties include low compressibility, high strength and low permeability, which reduced seepage and uplift pressures under the spillway slabs. The cost savings provided by the VE alternatives reduced total costs and enabled architectural elements. The award winning dam design also used drilled caissons, expanded polystyrene (EPS) block forms, customized steel forms and external concrete vibrators to build the pedestrian bridge and upper spillway structures.

Jan 1, 2009

By James E. Parkes

The Silver Spring Transit Center is a new three-level transit center that will include bus loops for County, Metro and intercity buses, parking, and retail space. It replaces an existing bus station and connects to a busy metro rail station in downtown Silver Spring, Maryland. Significant site constraints in both plan and profile had to be dealt with in developing a design for support of the structure. Over 90 rock-socketed drilled shafts ranging in size from 3 to 7 foot in diameter were ultimately used to accommodate the limited space and large column loads, and to adapt to the variable rock surface at the site. Site access during design was limited due to the existing active bus station, so contract documents were adapted to include further explorations. Differences in anticipated and actual field conditions regarding the depth, quality, and variability of the rock had to be overcome in construction. Osterberg Load Cell testing during construction allowed for verification and optimization of the shaft design. Additional issues dealt with on this constrained site in an urban setting included construction staging issues, such as working around specialty contractors for tieback walls, blasting operations for rock excavation, productions issues for hard bedrock, as well as coordination issues with third parties, most notably the Washington Metro Area Transit Authority. Aspects of the foundation design and optimization, preparation of the contract documents to deal with the complicated nature of the project, and lessons learned from construction are also discussed.

Jan 1, 2011

By F. Agterberg

In his 1978 monograph ‘Lognormal-de Wijsian Geostatistics for Ore Evaluation’, Professor Danie Krige emphasized the scale-independence of gold and uranium determinations in the Witwatersrand goldfields. It was later established in nonlinear process theory that the original model of de Wijs used by Krige was the earliest example of a multifractal generated by a multiplicative cascade process. Its end product is an assemblage of chemical element concentration values for blocks that are both lognormally distributed and spatially correlated. Variants of de Wijsian geostatistics had already been used by Professor Georges Matheron to explain Krige’s original formula for the relationship between the block variances as well as permanence of frequency distributions for element concentration in blocks of different sizes. Further extensions of this basic approach are concerned with modelling the three-parameter lognormal distribution, the ‘sampling error’, as well as the ‘nugget effect’ and ‘range’ in variogram modelling. This paper is mainly a review of recent multifractal theory, which throws new light on the original findings by Professor Krige on self-similarity of gold and uranium patterns at different scales for blocks of ore by (a) generalizing the original model of de Wijs to account for random cuts; (b) using an accelerated dispersion model to explain the appearance of a third parameter in the lognormal distribution of Witwatersrand gold determinations; and (c) considering that Krige’s sampling error is caused by shape differences between single ore sections and reef areas.

Jan 1, 2015

By T. M. Garland

This report presents a more extensive perspective of the calculated profitability of developing and producing crude oil and associated natural gas by primary methods from selected onshore areas of the United States. Estimates were made for cost of drilling, completing, equipping, and producing oil wells at four depths in seven onshore producing areas. A computer program was developed for calculating the discounted cash flow rate of return for the 64 different models in each area resulting from varying the oil-producing rate and production decline rate. The results of these calculations provide data that vividly illustrate the change in rate of return to changes in well depth, initial producing rate, and production decline rate, as well as to variations in development cost and operating expense. Cost per barrel of oil produced in terms of annual cost and total cost is also discussed. Included in the report are explanations of the method of determining costs and the procedure used for profitability analysis. Summaries of all cost estimates and results of profitability analyses are presented in the appendix in tabular form for each of the seven producing areas.

Jan 1, 1972

By George S. Koch

A mathematical simulation model has been devised to guide the layout of underground mine workings, drill stations, and drill holes that are established in order to search for tabular ore bodies. Developed and tested for elliptical ore shoots in fissure veins in the Galena mine, Coeur d&apos;Alene district, Idaho, the model can also be applied to ore bodies contained within sedimentary beds (for instance, many types of uranium, copper, and gold ore bodies) or other tabular structures. Programed for a time-shared digital computer, the model contains both stochastic and deterministic variables. Stochastic or natural variables include the number of ore shoots and their sizes, orientations, locations, and values. Deterministic or controllable variables include (1) locations and costs of workings; (2) drill-station locations and costs; and (3) drill hole azimuths, inclinations, lengths, and deflections, if any. For various assumptions about the stochastic variables, the model is run while the controllable variables are changed deliberately. Thus, layouts are devised to determine the percentages of the total number of assumed ore shoots found at different costs. In order to choose among the various layouts, cost-effectiveness measures are calculated.

Jan 1, 1974

By K. H. Johnston

This guide was written to furnish the coal industry with a description of techniques, instruments, and clues on how to find abandoned oil and gas wells that have penetrated coal seams. The report includes specific information on searching techniques currently in use by several coal mining companies, gas-transmission companies, and waterflood operators, as well as information on State agencies responsible for the enforcement of laws and the preservation and distribution of data pertaining to the drilling, development, and abandonment of oil and gas wells. Comparative tests were performed with several commercial electronic metal detectors to determine the feasibility of using them to aid in the search for abandoned wells and to determine the instrument most suited for that particular use. The role of methane detectors to locate abandoned wells is described, including a case history. Tests were made to develop an efficient procedure to follow in systematically searching an area for metallic clues or hydrocarbon evidence to abandoned wells. The guide describes, in detail, a search sequence, including the collection of basic data, preparation of the selected area, and the physical search. Methods are given for evaluating the results.

Jan 1, 1973

By Ali Kazmi, Wern-ping N. Chen

A load rating procedure was performed to evaluate safe load capacity of the Port of Miami Tunnel (POMT), FDOT Tunnel No. 871071 SR 887. The rating procedure performed on a total of eleven stations beneath roadways and with fill depth less than the tunnel exterior diameter (42 ft). Calculations on tunnel sections passing beneath roadways were performed to evaluate the structural response of the sections subject to moving vehicular loads, dead load, and earth pressures. Ratings were performed in accordance with AASHTO and FDOT guidelines. The procedure considered two types of vehicles (HL-93 and FL-120) and two rating levels (Design level and Permit level). As part of HL-93 vehicle, Tandem load was also considered for rating, separately. For HL-93 and HL-93 Tandem, inventory and operating level ratings were performed. The results show rating factors are high. The minimum rating factor is 16.8 using Inventory truck HL-93. For Permit level using FDOT FL-120 truck the minimum rating factor is 6.9. As can be seen, rating factors are higher than comparable analysis for bridges. This paper explains how the procedure can be implemented for tunnels and evaluates the rating results.

Dec 1, 2022

By Robert W. Van Dolah

The prevention of fires and explosions involving the combustibles and oxidants likely to be found in flight vehicles requires a knowledge of the flammability and related characteristics of these materials. This circular is a compilation of the available charactersilics data for a series of combustibles and oxidants of current interest. Vapor pressure data are presented for fluorine, oxygen, chlorine trifluoride, nitrogen tetroxide, nitric acid, hydrogen peroxide, ethylene oxide, hydrogen, ammonia, pentaborane, unsymmetrical dimethylhydrazine, monomethylhydrazine, hydrazine, and a series of hydro-carbons including decalin, tetralin, bicyclohexyl and other high-density fuels. In addition, flammability characteristics diagrams are included for each of the fuels in contact with air and, where available, other oxidants (for example, oxygen and nitrogen tetroxide). To assist in understanding these data, sections on definitions and theory and applications have been included. Each section is complete in itself and can be used separately. For example, a reader who is familiar with the general theory of combustion and detonation may find the data sections more useful than the definitions and theory and the application sections. However, since pertinent data are included in these sections, they should also prove useful to the experienced engineer interested in preventing fires and explosions.

Jan 1, 1963

By A. Vilinska

The adhesion of Leptospirillum ferrooxidans bacterial cells onto the sulfide minerals pyrite and chalcopyrite was evaluated using two different physical-chemical approaches; thermodynamic and extended DLVO theory. For the parameters incorporated into calculations, the zeta potentials and contact angles of powdered solids and bacterial cells were acquired experimentally. The Hamaker constants essential for Lifshitz-van der Waals inter-action calculations were calculated following two different methods: macroscopic and microscopic. Adsorption tests were carried out at physiologic conditions to estimate the amount of cells adsorbed onto a mineral surface and the extent of alteration of that mineral surface in biobeneficiation. The free energy of adhesion was found to be negative for both minerals, indicating that the adhesion is energetically favored and preferred. The interaction energy diagrams of the total interacting force was also negative for the cases where the particles were charged oppositely; in the remaining cases, the total force was attractive after overcoming an energetic barrier caused by the repulsive electrostatic forces. Under the conditions of the adsorption test, the experimental results are in agreement with the theoretical; this suggests that the physical-chemical forces are crucial for bacterial adhesion.

Jan 1, 2011