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By R. G. Bentsen, D. A. T. Donohue

The cyclic steam injection process has become the most widely applied and most successful thermal recovery technique in use today.1-4 Normally, steam stimulation is repeated several times during the life of a project. The problem is to select the optimum number and size of steam treatments so that the profits realized over the entire life of the project are maximum. Obviously, operating costs rise directly with the frequency and amount of steam injection. Operating efficiency, on the other hand, can be adversely affected if the amount and frequency of stimulation are insufficient. Thus arises a multistage decision problem; that is, a decision must be made at each sub-period (day, for example), as to whether steam should be injected, and, if so, how much. It is desirable that these decisions be made in such a way as to secure maximum net profit before taxes. This can be achieved by dynamic programming. To use dynamic programming, we must be able to predict not only the production rate-time curve resulting from a given stimulation, but also how changes in stimulation policy will affect this curve. In this study, the effect of steam injection on well performance is estimated on the basis of a simple model that takes into account both steady-state and transient flow. Oil production rate is calculated for both types of flow, and the larger of the two values is used. This allows the calculation to change to radial steady-state flow at such time as this mechanism becomes more effective than the transient mechanism. We propose to show how dynamic programming can be used to optimize the steam soak process with respect to net profit. For this, a mathematical representation of the steam soak technique is necessary. A further objective, therefore, is the formulation of a mathematical model capable of realistically simulating the physical process. Oil Production Response Model The advantage of using a mathematical model is its generality and ease of manipulation. However, the model must be an accurate representation of the physical process, for a solution derived from a model can be no better than the model itself. The question now arises as to how well the model should be expected to simulate reality. In general, the simplest model should be tried first, for additional accuracy is apt to require additional cost and time. Also, the search for a high degree of accuracy may yield only greater complexity and difficulty without yielding significantly better results. With this in mind, we kept our model as simple as possible, yet generally representative of the actual physical process. The number of state variables is limited to three, and stochastic variations in the parameters are ignored. As a consequence, use of this model should be restricted to cases in which the underlying assumptions are not severely violated. In

Jan 1, 1970

By S. R. Balajee, I. Iwasaki

The interaction between British gum 9084 and dode-cylammonium chloride (DAC) at quartz and hematite surfaces was established from coadsorption studies and streaming potential measurements. The cationic DAC interacts with the somewhat anionic British gum 9084, leading to the formation and adsorption of a binary complex of DAC-British Gum 9084 at the interface. The parallel ability to depress quartz along with hematite as a result of the interaction between DAC and British gum appears to be the main reason for the ineffective depressant action of starches and starch derivatives in the cationic flotation of iron ores. Amines are not particularly selective collectors for the flotation' of siliceous gangue from iron ores and, therefore, a suitable iron oxide depressant is needed for a satisfactory separation. Various starches and their derivatives have been extensively tested with oxidized iron ores,'-3 and it has been empirically established that British gums and dextrins are preferable. However, for the flotation upgrading of magnetite-taconite concentrates from 8 or 8.5% Si O2 to about 5% Si 02, British gums, which have been used so successfully on oxidized iron ores, have been found to have no effect and oftentimes are actually deleterious.4 In previous articles,5-7, starches were shown by adsorption measurements, flotation tests, and floccula-tion tests to interact with calcium ions in solution, and it was thought that a study on the interaction between starches and dodecylammonium ions would be able to shed some light on the anomalous flotation behavior described above. In fact, starches are known to interact markedly with paraffin-chain-type surface active agents and, thereby, to precipitate the starch or inhibit the iodine-starch reaction.8 From X-ray diffraction studies and viscosity measurements, the formation of a helical complex between mylose and a surface active agent has been postulated.9 The interaction with other types of hydrophilic colloids, such as synthetic polymers and proteins, has also been investigated and is usually explained in terms of van der Waals' force interaction and/or ion-ion interaction. In the present investigation, the interaction of British gum and dode cylammonium chloride on quartz and hematite was studied by adsorption and streaming potential measurements in an attempt to establish the mutual adsorption behavior of British gum and dode-cylammonium chloride on mineral surfaces and to clarify the anomalous depressant activity of British gum in the cationic flotation of iron ores. All the measurements were carried out at a natural pH of near 7 because dodecylammonium chloride gives maximum selectivity of flotation separation at this pH2 and to avoid any third parameter in the system. EXPERIMENTAL MATERIALS AND METHODS Minerals: The quartz and hematite samples used for the adsorption tests were prepared as described in a previous paper,"J except that the specific surfaces of the samples were increased to 5,860 and 16,000 Sq cm per gm, respectively. For the streaming potential measurements, the 48165-mesh fractions screened out of the original samples were etched with hydrochloric acid, washed repeatedly with water, and stored under water in Pyrex bottles. Reagents:DodecyIammonium chloride (DAC) was prepared1 1 by bubbling dry hydrogen chloride gas through a benzene solution of high-purity dodecylamine supplied by Armour and Co. British gum 9084, received from Corn Products Co., was solubilized by first dispersing it in water to produce a 0.05% solution and then homogenizing it in a blender for 5 min. Distilled water was used in the preparation of the samples and the solutions and for all test work. Adsorption Measurements: The procedure for the adsorption density determinations was also the same as that described in the previous paper.1° The residual concentrations of the British gum and the DAC in the supernatant solution were analyzed colorimetrically by the phenol-sulf uric-acid and amine-picrate methods, respectively. The validity of the mine-picrate method for the colorimetric analysis of DAC in the presence of British gum and the analysis of British gum in presence of DAC were checked by establishing calibration curves between optical density and concentration. Streaming Potential Measurements: The cell assembly for the streaming potential measurements was similar to that described by Fuerstenau.' The streaming potential

Jan 1, 1970

By R. F. Ashton, D. S. Thompson

In reporting results of precipitation hardening experiments, it is customary to include such conditions as solution heat-treatment temperature, specimen size, and quench medium as well as the aging time and temperature. One portion of thermal history that is often overlooked is the effect of the heating rate employed to achieve the aging temperature. It is the intent of this note to demonstrate the importance of the rate of heating to aging temperatures. This work was carried out on the aluminum alloy 7075 aged at 162oC, a temperature commonly used to obtain stress corrosion resistant tempers. A 2 in. thick plate of 7075 was quenched into 24°C water after solution heat-treatment for 2 hr at 470°C. Approximately 13 in. around the periphery of the plate was discarded to minimize quench rate variations, and the remainder was divided into 0.5 by 1.8 by 2.0 in. blocks which were held at room temperature, 24oC, for 4 days. This aging, or incubation period, at room temperature allowed a copious supply of GP-zones to form. Blocks were then heated at various rates to 162oC using the practices shown in Table I. Both single- and two-step aging practices were employed for each heating rate. The single step consisted of heating directly to temperature at the indicated rate while the two-stage practice included an interruption of heating for 7 hr at 107°C. In the case of the two-stage 100°C per min heating rate experiment, the specimens were returned to room temperature after 7 hr at 107°C where they were held for 16 hr be-fore finally heating at this rate to 162°C. This devia-tion in practice is not considered to be significant. Blocks were removed after various times at 162oC, and aging curves were determined from duplicate R. F. ASHTON and D. S. THOMPSON,Member AIME, are Senior Scientists, Metallurgical Research Division, Reynolds Metals Company, Richmond. Va. Manuscript submitted December 2. 1968. IMD Table I. Aging Practices Two-step Single-Step Heating Rate* Aging Aging Heating Method oC per Min A B Programmed Air Oven 0.23 * 0.01 C D Programmed Air Oven 0.93 ? 0.03 E F Air Oven at Temp -10 G H Oil Bath at Temp ˜100 *Heating rate was measured with a thermocouple at the center of a specimen. An average value between the starting temperature and 3°C below the aging temperature is reported for practices E-H. PRACTICES 70 — A B C E and G 50 - 2 4 6 810 20 40 60 HRS.AT 162°C Fig. 1—The influence of processing variables on 7075 aging curves. Fig. 2—7075 aged according to practice H (single-step aged, fast heating rate) for 3 hr. Magnification 100,000 times.

Jan 1, 1970

By N. S. Stoloff, K. R. Jordan

The temperatwe and grain size dependence of the mechanical avoperties of ordered and disordered Fe-49 pct Co-2 Pct V were investigated. The yield and flow stresses obeyed the Hall-Petch relationship u = ai + kd-&apos;I2. Ohdering reduced the intercept stress cjj and raised the Petch slope, k, at all temperatures. Ordering also increased the temperatwe dependence of k. The ductile to brittle transition temperature increased with order and grair~ size. Cleavage fracture was nucleation limited and the fracture stress did not zlary linearly with d-&apos;". A quantitative test of the Cottrell-Petch fracture theory (and recent modifications which consider the influence of slip mode), demonstvated that this theory is not applicable to FeCo-V. COTTRELL&apos; and etch&apos; independently suggested that a criterion for cleavage failure at the yield point, a,, based on dislocation pileups at a grain boundary or other obstacle to dislocat.ion motion, is: aYYkd&apos;I2 1 opy [ll or, equivalently, aikz,d112 +k:)bpy [2] where a, and ky are the Hall-Petch intercept and slope, respectively, 2d is the grain diameter, P is a geometric factor dependent on the macroscopic ratio between shear and tensile stress, p is the shear modulus, and y is the true elastic surface energy. When the product of quantities on the left side of the equation is equal to or exceeds that on the right, cracks should be able to nucleate and propagate at the yield stress, as shown schematically in Fig. 1. Therefore a high intercept stress, high Petch slope, or coarse grain size favors brittleness. petch3 associated the existence of a ductile to brittle transition in ferrous alloys with the temperature dependence of ai. One of the earliest modifications of the Cottrell-Petch theory was presented by ~rmstrong,~ who derived an expression for transition temperature in terms of several measurable flow and fracture parameters. The latter paper was able to rationalize situations in which the transition temperature increases with decl-easing grain size, as in the case of molybdenum,&apos; and also suggested that Ppy should be a function of grain size as well as temperature. More recently Johnston et a1.6 and Smith and worthington7 have suggested that the temperature or composition dependence ol&apos; ky must also be taken into account if there is any cha.nge in deformation mode, as from wavy to planar slip, or wavy slip to twinning, with change in temperature or solute content. Armstrong %as suggested that for hcp metals changes in o;k,dw> o;k,d1/2< / is / ^^^^ / / y_______________________________________ d-"2 Fig. l—Schematic representation of grain size dependence of yield stress, cry, and fracture stress, CTF. Intersection defined by Cottrell-Petch equation. slip mode should be incorporated in the theory through changes in the critical resolved shear stress for the slip system which controls ky. The purpose of the present investigation was to critically test the modified677 Cottrell-Petch theory of fracture in the superlattice alloy Fe-49 pct Co-2 pct V, by studying the grain size dependence of the yield and fracture stresses over a range of temperatures, in conjunction with an investigation of slip mode and fracture behavior. Previous work has shown that long range order results in a sharp decrease in flow stress, a small increase in work hardening rate and a drastic upward shift in the ductile-brittle transition temperature of F~CO-V.~&apos;~ The only comprehensive study of slip character in this alloy has been reported in a preliminary account of the present investigation.10 EXPERIMENTAL PROCEDURE The experimental work was carried out on material produced from a 10 lb vacuum melted ingot, of composition 49.32 wt pct Co, 2.09 wt pct V, balance Fe. 30-mil thick sheet samples with a 1; in. gage section were machined from cold rolled stock. The degree of cold work ranged from 85 pct for the finest grained samples to 5 pct for the coarsest grain size. Details of ingot fabrication are reported elsewhere." Equi-axed grain sizes in the range 12.7 to 75.4 p were obtained by annealing for varying times at 850°C. (Re-crystallization annealing time, rather than temperature , was varied to control grain size to insure that samples of all grain sizes contained equivalent quenched-in vacancy and interstitial concentrations.) Grain sizes were measured by the line intercept method on several specimens of each grain size. Following recrystallization, all samples were disordered by quenching into iced brine.

Jan 1, 1970

By W. O. Philbrook, R. S. Kaplan

Rates of oxidation were studied for levitation-melted samples of Fe-C, Fe-Si, Fe-C-Si, Fe-C-P, Fe-C-Mn, and Fe-C-S alloys oxidized by mixtures of either 5 or 10 pct O2, in helium at several temperatures in the range 1850o to 2050°C. The concentrations of the oxidized elements decreased linearly with time. Mass transport in the gas phase was found to be the rate-controlling step. Ilowever, a mulliple -film model was necessary to account for the flux of iron and manganese vapor counter to the oxygen flow. THE advent of the basic oxygen and spray-refining processes of steelmaking has generated considerable interest in the kinetics of reactions between oxygen-bearing gases and liquid iron alloys. The object of this research was the determination of the role of mass transport in the gas and metal phases and of surface chemical reactions in the overall oxidation process. Of the reactions for elimination of elements dissolved in liquid iron, the oxidation of carbon has been investigated most extensively. Studies by Fuji and Ura,1 Fuji,&apos; and Gunji et a1.,3 done with pilot-scale basic oxygen furnaces, indicated that mass transport of gaseous oxygen was rate controlling when the metal carbon content was greater than 0.15 to 0.30 pct. When the carbon content was less than this critical amount, diffusion of carbon dissolved in the iron was thought to be rate limiting. L. A. Baker et a1.4,5 levitated samples of iron-carbon alloys and oxidized them in CO-CO2, CO-C02-He, and O2-He atmospheres at 1660°C. These investigators found that the metal carbon concentration decreased linearly with time and their samples exploded when the carbon content fell below about 0.8 pct. They concluded that the rate-limiting step was the transfer of oxidant to the gas-metal interface. A model based on this rate-limiting step predicted decarburization rates within a factor of two of those experimentally observed. The explosion of the samples was attributed to a shift in rate-controlling step from gas-phase mass transport to transport of carbon dissolved in the metal. L. A. Baker and R. G. ward6 and R. Baker7 used freely falling droplets to investigate oxidation kinetics. In both papers, the authors speculated that flame fronts may have been partially responsible for the lack of better agreement between experiment and theory. Swisher and Turkdogan8 oxidized liquid iron having an initial carbon content of 0.97 pct with CO-CO2 and CO-C02-Ar mixtures at 1580°C. They concluded that a surface reaction was the rate controlling step. Iron-silicon alloys have been oxidized by R. Baker7 and Filipov and Martynov.9 R. Baker 7 also studied iron-carbon-silicon alloys falling as liquid droplets through oxygen. He found that the rate of both carbon and silicon oxidation varied inversely with the drop radius. When the initial silicon concentration was greater than 6 pct, the samples cooled during their fall. Manganese oxidation has been studied by R. Baker,7 and by Filipov and Martynov.9 ward10 investigated the loss of manganese from liquid iron under vacuum. He found that mass transport of manganese vapor was rate limiting in argon atmospheres of 0.02 torr to 700 torr pressure. Iron-sulfur alloys were desulfurized with H2-He and H2-Ar mixtures by Peters et al.11 A model based on the transport of H2S from the gas-metal interface into the bulk gas gave fair agreement between the predictions of the model and the experimental results. EXPERIMENTAL TECHNIQUE Essentially, the technique consisted of using helium-oxygen gas mixtures to oxidize levitated samples of liquid binary and ternary iron-base alloys. The fused silica reaction tube is shown in Fig. 1. The coil design is similar to that of L. A. Baker et al.4&apos;5 A Tef-lon-sheathed, ferritic stainless steel lifter (B) and an alumina pedestal (C) were used to support the sample in the coil prior to levitation and for the recovery of the sample. Samples were inserted into

Jan 1, 1970

By J. C. M. Li

A dislocation model is constructed for a cylindrical tilt boundary of which the axis of tilt is parallel to the axis of the cylinder. The strain energy per unit area calculated from this model agrees with thut of an infinite vertical wall of edge dislocations. Based on this model, a dislocation mechanism for the shrinking of such a cylindrical boundary is proposed. The power relation between the grain boundary velocity and the driving force is accounted fm by the stress dependence of dislocation velocity. The activation area for grain boundary motion is found to correlate with that .for Creep in aluminum. In the preceding paper&apos; the velocity of a curved grain boundary is found to be a power function of the driving force, [1] where M is the velocity at unit driving force, y is the grain boundary energy, and p is the radius of curvature. This finding adds another nonlinear rate equation to metallurgical phenomena. While a macroscopic theory for the steady state as just presented2 can be used to understand the shape of the moving boundary, such theory usually does not provide any information about the atomistics of the process. It is attempted in this paper to discuss the nonlinear rate equation in terms of a dislocation mechanism. A DISLOCATION MODEL FOR A CYLINDRICAL TILT BOUNDARY Before a dislocation mechanism can be proposed for the motion of a cylindrical tilt boundary, it is necessary to construct a dislocation model for the boundary. For simplicity, a tilt boundary in a simple cubic lattice will be examined. Although this does not represent the situation in aluminum, it is expected that the general features will be similar. The details of the model in the fcc lattice can be constructed when a refinement of the simple model is called for. A cylindrical low angle tilt boundary in a simple cubic lattice is shown in Fig. 1. Two sets of edge dislocations are needed as shown. A schematic representation is shown in Fig. 2(a). In terms of a continuous distribution of dislocations, the density of dislocations n, of Burgers vector b, in the small segment ds of the grain boundary is Similarly the density of dislocations n, of Burgers vector bz in the same segment ds is where is the tilt angle of the grain boundary. Based on this continuous distribution of dislocations in the grain boundary, it can be shown that the interaction between a small segment of the boundary and the rest of it is zero. Furthermore, the stress produced at any point inside or outside the cylinder is also zero. This shows that the model is acceptable in the sense that the boundary has no long-range stresses. Since the model of continuous distribution of dislocations in the grain boundary does not reveal the interactions among individual dislocations, a discrete dislocation model has to be used for such purpose. For simplicity, an equivalent model is shown in Fig. 3. This arises because the total Burgers vector is, from

Jan 1, 1970

By G. W. Housner

The series of earthquakes in the vicinity of Koyna Dam in south- western India, which included a very damaging magnitude 6.5 shock on Dec. 11, 1967 (Dec. 10 GMT), is of much interest. The events are exceptionally well documented, which is a tribute to Indian geologists, seismologists, and engineers. To help in disseminating the information in the United States, this chapter presents a brief summary of the pertinent data and lists references. Koynanagar (Koynatown), which began as the construction camp for the dam, is located about 140 miles southeast of Bombay and 70 miles south of Poona at 17.4ºN and 73.7ºE, about 40 miles inland from the Arabian Sea. Koyna River flows almost due south from its source a distance of about 38 miles and then makes an abrupt turn to the east and travels some 480 miles to empty into the Bay of Bengal. Koyna Dam is located about 3 miles north of this turn. The approximately north-south trending continental divide is a few miles west of Koyna and the terrain drops steeply about 1700 ft to where the hydroelectric generating station is located. The reservoir behind Koyna Dam forms a long, narrow lake (Shiva- jisagar Lake) with mean water level (MWL) at 2160-ft elevation. The 345-sq-mile watershed receives an annual rainfall of about 200 in., most of which falls between mid-June and mid-October. The peak storage is 99 x l09 cu ft. A controlled flow passes under the continental divide in a tunnel and then down to the electric generating station about 5 miles WNW of the dam. The inflow not used for power generation is released to Koyna River. The Koyna project is a major source of electric power for Bombay and produces 540 MW at peak load.

Jan 1, 1970

By B. T. Brady

Rock mechanics, like all engineering disciplines, must have a theoretical foundation. The subject of this chapter is the formulation of analytical methods that may aid in the rational design and determination of the stability of engineering structures in competent brittle rock materials. By an engineering structure in rock, we mean any (1) excavated sub- surface opening, (2) open surface structure, or (3) system of openings in rock that is virtually self-supporting-that is, not requiring artificial systems to carry structural stresses. One factor necessary for designing or evaluating a structure&apos;s stability is knowledge of the material&apos;s mechanical properties, such as stress-strain behavior and fracturing characteristics. The composition of most structural materials such as metals and concrete is uniform and reproducible to the degree that their mechanical properties in service are nearly the same as those measured in the laboratory. Consequently, a rational design can be made on the basis of published mechanical property values. The same equivalence does not exist for rock materials for two reasons: (1) the composition of even the most common rock types is highly variable, and (2) the problem of the size effect is present. Mechanical property tests not conducted at a scale that includes these effects in normal proportion will not be representive of the in-situ rock mass. Of course, the alternative is to perform the test in-situ. Comparatively few mechanical property tests have been performed in-situ because of the physical limitations of test equipment and the prohibitive cost. The current procedure is to design a structure based on small-scale laboratory measurements, with a safety factor usually determined by the experience of the design engineer. While this procedure is somewhat unsatisfactory, laboratory measurements can and do provide a useful basis for the initial design.

Jan 1, 1970

By Gordon H. Geiger, John M. Svoboda

One mechanism of metal penetration into mold aggregates by cast steels is vapor state mass transport. In order to further understand and quantify this mechanism, the steady-state diffusion of metallic vapors was studied at 1250" to 1600°C in controlled oxygen pressure atmospheres by measuring the weight loss from a metal bath whose vapors were allowed to diffuse through a porous aggregate compact held at constant temperature. Mass transport rates substantially greater than those predicted from the assumption that the vaporizing species was the elemental metal vapor were observed. Vaporization rates were found to increase with an increase in the oxygen partial pressure in the gas atmosphere with maximum vaporization occurring at oxygen partial pressures just below those in equilibrium with a liquid oxide layer at the given temperature. When the liquid oxide layer was present, no vaporization was observed. Metal carbonyls were ruled out as the vapor species involved because of their thermodynamic properties. The species with the enhanced volatility were deduced to be gaseous metal-oxygen molecules, probably the polynuclear oxides (FeO)2 and (Mn0)2. Diffusion followed the ordinary diffusion mode, and Knudsen diffusion is not important in normal foundry molds. The interdiffusivities of the metallic vapors and the mold atmosphere, through the porous aggregates, were measured. The effective interdif-fusivity of the vapor species and mold atmosphere through the aggregate may be expressed as follows: Deff,12 - — where E is the void fraction of the aggregate and 7 is the "tortuosity factor". Aggregate material had no effect on diffusion rates, and the only relevant parameter was the void fraction. Values for 7 ranged from 3 to 6 for normal foundry aggregates with 4 being considered a good representative value. An area of interest in high-temperature metallurgical processes which has received little attention in the past is the diffusion of metal vapor species in porous aggregates. Research into the metal penetration phenomenon&apos; in foundry molds has shown that a major penetration mechanism is the vapor transport of metallic species into the porous foundry sand molds, followed by condensation of metallic films on the sand grains. Considerable study of the vaporization of metallic species has been reported in the literature, and the vapor transport properties of many metallic species have been determined.2&apos;3 Many instances have been observed where the vaporization behavior could only be explained by the existence of a metallic species with a vapor pressure greater than the elemental metallic species. These species were identified or, in some cases, presumed to be carbonyls,4,5 hydroxides,6-9 or vaporous oxides.10-16 The diffusion of gases through porous aggregates has received considerable attention in the literature pertaining to catalysis, although primarily at low temperature, and more recently in the literature concerned with ore reduction.17-22 The following experiments were devised and carried out in order to determine the nature of the metallic species involved in the metal penetration phenomenon, and the effective diffusivities involved. EXPERIMENTAL APPROACH Steady-state diffusion was selected for experimental convenience. The experimental systems used, shown in Figs. 1 and 2, consisted of a porous aggregate specimen contained in an impermeable alumina tube held above, and just separate from a metal bath. The entire system was held at constant temperature and pressure in a furnace with a controlled oxygen partial pressure atmosphere. After a brief period of nonsteady state behavior, a steady flux of metal vapor through the porous aggregate will develop due to the concentration gradient of metallic vapor in the gas phase. The flux of metallic vapor from pressure may be neglected because there is no pressure gradient. There is no flux from convection because there is no net flow of gas within the metal-aggregate system, and thermal diffusion is negligible compared to the flux from ordinary diffusion. If the material being studied is allowed to vaporize until steady-state behavior is attained, the experimental results may be analyzed using Fick&apos;s First Law.

Jan 1, 1970

Jan 1, 1970

By John F. Abel

A good mining engineer is supposed to make a good mine. What then makes a good mining engineer? There certainly are a lot of answers to that question. The answers depend on whether you are one, work for one, or employ one. There are several cliches about mining engineers, and there is some truth in them-as there usually is in any stereotype. Hollywood chose Jeff Chandler to portray a mining engineer in Foxfire. The image here was of an almost one-man mining operation. When Chandler picked up a jackhammer, cradled it in his gut and started drilling out a tunnel round, it gave one the hives. I would have liked to see him finish just one round that way. There are limits to what even the most hairy-chested of us will try. We can assume that Hollywood feels it needs to over- draw any profession to add impact.

Jan 1, 1970

By E. J. Bonet, P. B. Crawford

It is fairly common practice to reinject water into the aquifer near the oil-water interface in water-drive reservoirs. There have been many studies of aquifer behavior without reinjection,l-5 but apparently no analytical studies have been made to indicate performance when injection wells are present in the aquifer. The diffusivity equation may be used to describe the pressure behavior in an aquifer. When sources are present it can be written as A general solution of Eq. 1 may be obtained as the sum of two solutions. One is a general solution of the homogeneous equation, obtained by dropping the source term in Eq. 1 and still satisfying the required boundary conditions. Another is a general solution of Eq. 1 satisfying homogeneous boundary conditions.1° The first solution, which corresponds to the aquifer without reinjection, has been given quantitative and qualitative treatment in the literature.l-5,8,9 The latter solution will be treated here. Solutions with variable injection rates are obtained by superimposing solutions with constant rates, so we have considered only the latter. Five cases have been treated here: 1. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The pressure along the line x = 0 is maintained at zero pressure. (See Fig. 1.) Equations showing the pressure distribution, rates, velocity and cumulative influx have been developed. Certain numerical results are shown. 2. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The rate of production along the oil-water water contact is maintained constant. Equations showing the pressure distribution inside the aquifer are presented. 3. A linear aquifer of finite width and extent. Constant pressures are maintained at opposite ends of the aquifer. Water is injected at constant rates at point xo, yo. Equations showing the pressure distribution are shown. 4. A linear aquifer of finite width and infinite extent. The pressure is maintained constant at the oil-water contact. Water is injected at a constant rate at point xo, YO. 5. A linear aquifer of finite width and finite extent. The pressure at the oil-water contact is maintained constant. Water is injected at constant rate per unit length along a line x,. The Linear Aquifer The linear closed aquifer, performing at constant terminal pressure was selected as the first case to be analyzed. The development of the equations is based on uniform injection per unit of thickness, and gravity effects are neglected. In practical application this condition is probably most closely achieved when the

Jan 1, 1970

By L. T. Larson

The spectral reflectivity of zirconium in light of 441 to 668 nanometers (nm) wavelengths and air immersion has been determined. Bireflectance and apparent-angle -of-rotation measurements show zirconium to be optically isotropic when examined in light of approximately 484 nm wavelength. There is a direct relationship between bireflectance and the tilt of the basal pole of zirconium from the surface normal. This relationship allows the determination of the spatial orientation of the basal pole of an individual single crystal within a coarse-grained poly crystalline section to within± 2 to 3 deg for angles of basal pole tilt from 0 to 90 deg. In recent years considerable attention has been given to the quantitative determination of optical properties of opaque minerals by use of vertically incident, plane-polarized light. In particular, Cameron&apos; and Cameron et a1.2 have developed criteria for the identification of a large number of anisotropic ore minerals based upon measurement of the apparent angle of rotation and the ellipticity or phase difference of the reflected light. It was shown by Larson and Pickle-simer3 that apparent-angle-of-rotation measurements may also be used to determine crystallographic orientations of grains of noncubic metals. In particular, it was shown that the basa.1 pole orientation in space of zirconium grains can be determined to ±3 deg for those grains with basal pole tilts of 10 to 90 deg from the plane of the section. Another, even more widely studied, optical property is reflectivity. cameron4 has commented upon measurement of the reflectance of plane-polarized, vertically incident light and Bowie and Taylor5 have made such measurements an integral part of their system of ore-mineral identification. Leow6 has reported on the spectral reflectivity of molybdenite and has used reflectivity values to calculate refractive indices and absorption coefficients. Cameron7 has made use of reflectivity values to ascertain aniso-tropic ore mineral symmetry and Piller and v. Gehlen8 have evaluated sources and importance of errors in reflectivity measurements as applied to calculation of optical constants. cambon9 has shown that reflectivity measurements using vertically incident, plane-polarized light are useful in the investigation of metals and in the identification of phases present in alloys. Bronson10 has made preliminary measurements on the optical anisotropy of beryIlium and Mott and Haines11 have published qualitative data on the intensity of light reflected from sections of bismuth, tin, and aluminum when these metals are microscopically examined under crossed polarizing plates. Koritnig12 has correlated the reflectivity of homogeneous solid solutions with their chemical compositions. From the above work and investigations in progress by this author, it is apparent that accurately determined values for the reflectance of vertically incident, plane-polarized monochromatic light from carefully polished surfaces of noncubic metals can prove useful in identification, composition determinations, and crystallographic orientation applications. Finally, reflectivity values, when measured in two media of differing refraction index and related to standards whose spectral reflectivities in these media are known, can be used to calculate optical constants such as refractive index and absorption coefficient. These constants may prove of use to those concerned with problems of electron band configuration. This paper reports the spectral reflectivity of zirconium measured in light of 441 to 668 nanometers (nm) wavelengths and air immersion. It also gives maximum bireflectance values for a prism section of zirconium in these wavelengths and shows how bire-flectance may be used to determine the crystallographic orientation of zirconium single crystals. Because of the lack of information on the reflectivities of the standards in oil immersion, no attempt is made to calculate the refractive indices or absorption coefficients although it is recognized that such values may be of fundamental importance. METHOD Single crystals of zirconium were cut by electro-discharge machining from a single-crystal rod grown from iodide bar by an electron-beam zone-melting process.13 The crystal sections were mounted in cold-setting epoxy resin and mechanically polished to a plane, uniform, bright surface. Each crystal was then chemically polished in a 26/26/43/5 mixture (by vol) of water, nitric, lactic, and hydrofluoric acids to remove the mechanically damaged and smeared surface layer. Final polish was obtained by electropolishing at 30 v in a bath of methyl alcohol and perchloric acid (98/2 by vol) at -70oc.14 Reflectivity measurements were made using a photometer system designed and developed at Oak Ridge National Laboratory and described in detail by Larson.15 Briefly, the reflectivity measuring system consists of a reflecting microscope; a double-beam, null-balancing photometer array; a mechanically driven microscope stage; and a direct X-Y readout of the reflectivity of the specimen relative to its orientation on the microscope stage. The measuring photometer receives its signal from the specimen through a slotted Wright occular placed on top of the photovisual head of the microscope. The reference photometer receives light through a flexible glass "light pipe" from a mirror in the reflecting system of the microscope. Monochromatic light is attained through use of interference filters (15-nm half-peak width pass bands) placed in front of a stabilized Vickers 12 v, 100 w, tungsten-filament, quartz-iodide lamp.

Jan 1, 1970

By Freeman Bishop

The tight electric power supply is one of the most dramatic problems facing the mining industry in 1971. This is caused by rising demands for energy. Clean-fuel and air-pollution controls have contributed to the problems of producing energy from sulfur oil and coal. Coking coal has become scarce. One stimulating development is that coal is no longer the cinder in the mining industry&apos;s eye. In fact, it may be the favorite candidate as a base for fuel within a few years. Synthetic gas from coal is the watchword. In dedicating a multi-million- dollar project aimed at converting coal into oil and gas, Hollis M. Dole, Assistant Secretary of the Interior, recently made it clear that coal, which has been taking a back seat to nuclear fission research and study grants, is now coming into its own. Conversion pilot plants are being activated in all parts of the nation.

Jan 1, 1970

Jan 1, 1970

By Allen L. Hatch

A survey of all phases of the world&apos;s lead and zinc production in 1968 from ore through to refined metal was conducted by sending questionnaires to individual companies and the results of this survey are tabulated at the end of the paper. The paper goes on to review changes in the geographical distribution of the world&apos;s lead and zinc mine and metal production and in the trading patterns of raw materials, present and future utilization of metal production capacity, developments in metal smelting and refining processes and the growing importance of marketing, product development and research in the 1950&apos;s and 1960&apos;s.

Jan 1, 1970

By Karl A. Bauer, Cornelis Bezemer

The deposition of calcium carbonate scale on surface and subsurface production equipment creates an operation problem in many oil fields. The formation water in which the carbonate-scale-forming components are initially dissolved becomes supersaturated with calcium carbonate as a result of the drop in pressure during production. The continuous flow of a supersaturated solution through the production equipment results in the growth of a dense layer of calcium-carbonate crystals. For a scale layer to be built up, the supersaturated formation water should contact the walls of the production equipment. The tendency for scale to be deposited, therefore, will be low, if the crude has a low water cut and if the water is finely dispersed in the oil. A scale problem will occur, if at a high water cut part of the water is present as free water. The rate of scale deposition will then be approximately proportional to the rate of free water production. Depending upon where the formation water becomes supersaturated, scale may be deposited in the flow line only, in both flow line and tubing, and in some cases even in the perforations and in the formation near the wellbore. In the South Sumatran fields (Indonesia) the main difficulties encountered due to the deposition of calcium-carbonate scale have been restriction of flow through tubings and flow lines, wear and abrasion of plungers and liners, and stuck plungers or wellhead valves. So far, the only methods of combating the *Presently associated with Brunei Shell Petroleum Co., Ltd.. Seria. scale problem have been routine acidizing and additional well pulling. As for the pumping wells, it was estimated that some 50 percent of the total well-pulling effort was directly attributable to scale deposition. The most promising alternative was to prevent the deposition of calcium carbonate scale by means of chemicals. Inorganic polyphosphates such as sodium hexametaphosphate and trisodium polyphosphate are known to retard the formation of scale by the "threshold action". They are adsorbed on specific faces of the crystal nuclei and thus prevent crystal growth, thereby stabilizing supersaturation. Polyphosphates are effective at very low concentrations ( a few ppm), and far less than stoichiometric quantities are required to keep the scaling ions in solution. Recent investigations on barium sulfate scale1 have confirmed this mechanism. The types of polyphosphate mentioned can be applied as concentrated aqueous solutions either squeezed into the formation, lubricated down the annulus or injected via macaroni string. Several squeeze jobs with polyphosphate solutions have been carried out in the South Sumatran fields, however, with disappointing results. Lubrication down the annulus and injection through a macaroni string were not considered attractive in this area because of the kind of equipment and the degree of supervision these techniques require. Polyphosphates are also available in a granular, glassy form, which, in contrast with the readily soluble types already mentioned, show an extremely low

Jan 1, 1970

By J. Szekely

A rrlethod is presented for the estitnation of oxygen pickup by teettzed molten steel streams. Of the mechanisrt~s considered for oxygen absorption, physical entrainment appeared to be the most significant. The estent of this physical entrainment may be calculated by the application of boundary layer theory. It was found that the values of oxygen pickup thus predicted were in wry good agreement with data reported in the literature, in the case of short, well-defined metal streams. This entrainment model does not provide an adequate description of oxygen pickup by long streams, exoosed to external winds and where breakup of the streatn is likely. WheN molten steel is teemed into a mold or tundish it will absorb oxygen contained in its environment. Recently interest has been expressed in the measurement and possible prediction of the extent of this oxygen absorption: this interest owes its existence to two principal factors: a) the desirability of providing a quantitative assessment of the role played by the absorbed oxygen in impairing the quality of (vacuum degassed. stainless, or continuously cast) steel; b) the need for providing guidelines for stream protection methods. The purpose of this communication is to suggest a simple method for the prediction of oxygen absorption by continuous metal streams and to compare the predicted values with the data available in the literature. It is hoped that this method may provide at least an initial framework for the interpretation of additional data that might become available. FORMULATION Consider a continuous metal stream falling into a molten metal pool as depicted in Fig. 1. This system may absorb oxygen due to the following two mechanisms: 1) physical entrainment of gases (including oxygen) into the molten pool where reactions. thus absorption, will occur; 2) mass transfer (convec:tive diffusion) of oxygen to the metal stream. 1) Physical Entrainment. The physical entrainment may be calculated by using the concept of the diaplace-ttzent tlzickness of the laminar boundary layer, which will be stated briefly in the following.&apos; When a fluid flows past a solid surface, a portion of the fluid close to the surface is retarded due to fric-tional forces. This region in which the velocity of the fluid differs from that in the main stream is called the boundary layer. An illustration of this is given in Fig. 2 where it is seen that the thickness of the boundary layer increases as we move along in the x direction. In the laminar region, when Re, < 10&apos; the thickness of the boundary layer is given by the following relationship: f =4.64 Re;1" [1] where 61 is the boundary layer thickness, x is the length along the leading edge, Us is the velocity of the free stream, (i is the viscosity of the fluid (gas in this instance).

Jan 1, 1970

By G. S. Cole, G. F. Bolling

A series of Al-Cu alloys has been cast from constant superheat to solidify either with a hot top or with a free liquid/air interface. All the other variables which affect relative fluid motions were kept constant except the imposition of slow rotations m oscillations of the mold. Depending upon the exact circumstances, evi-dence could be found for the nucleation of equiaxed grains from dendrite bits detached from the columnar zone, or from the free surface, or from solid bits induced at pouring; a special experiment showed the solute buildup during ingot solidification and by inference the reality of constitutional supercooling. All methods of grain nucleation are thus supported. When solidification is arranged in a static mold the columnar- to-equiaxed transition occurs by one of these nucleation paths, subject to the natural decay of temperature gradients which promotes nucleation or the survival of nuclei. But when solidification is forced under special fluid flows it may display odd transitions. In one of these the equiaxed zone is synihesized from. dendrite bits detached from the solid/liquid interface. These survive under the concurrent lowering of temperature gradients and eventually cause transition by impeding columnar growth. GRAIN structure control is desired because real experience shows that specific properties are associated with specific cast grain structures. But since control is thus a matter of need and does not require understanding, much of casting remains art. For example, the manipulation of relative fluid motions in simple ingots provides a control of grain structure development,1-4 but theoretical insight is not required in order to broaden its potential applicability. Fortunately, however, once a variable like fluid flow is recognized it can also provide paths toward new insight. New observations using this variable have provided an insight which is curious. All the theories or descriptions of the columnar-to-equiaxed transition (CET) seem to be supported as long as the appropriate experiment is carried out. In order to develop this idea, let us ignore segregation, the chill zone (until a later section of this paper), and the origin and development of the columnar zone.= The details of questioning how equiaxed material forms in a casting may be divided in two. The first part is simply a questioning of the origin for equi-axed grains: are there fresh nuclei from heterogeneous nucleation, or dendrite bits broken off or melted from the columnar zone or elsewhere,6 or other solid bits surviving from the outset of freezing? The second is more complex, a questioning of the CET: does columnar growth slow down and allow the dominance of equiaxed grains, however they are formed, or do equi-axed grains take over and force columnar growth to stop? This "chicken-or-the-egg" second question can be quite useful, especially because it allows us to delineate the ordinary or NATURAL EQUIAXED ZONE and the induced or SYNTHETIC EQUIAXED ZONE. A natural equiaxed zone occurs if solidification proceeds in the absence of disturbances or extraneous forces such as ultrasonics, stirrings, and so forth. Both the CET theory proposed by Winegard and Chal-mers, 7requiring constitutional supercooling, and the CET theory suggested by Chalmers,8 requiring nuclea-tion only on pouring, pertain to the natural equiaxed zone. The best collating evidence to date for both these theories is contained in the work by Biloni and Chal-mers;9,10 the former theory7 is supported by special versions of the unidirectional growth experiment performed by Plaskett and winegardl1 and the latter theory&apos; is supported in detail for the solidification of small ingots. An equiaxed zone can be synthesized when disturbances caused by forced fluid flows2-4 or other artificial means9,10 break off or melt off dendrite tips from an advancing solid/liquid interface,* if (and only if) temperature gradients in the melt are (forcibly) reduced enough to ensure the survival of these bits of dendrites, 2&apos;3 Willful disturbances even so trivial as those produced by rapping a mold might be included here; as will be shown for example, this follows Southin&apos;s suggestion that the free liquid/air interface

Jan 1, 1970

By M. J. Langley

The American Zinc Company’s mining operations in East Tennessee are located in Knox and Jefferson Counties. Mineralization occurs, intermittently, through a strike length of more than 30 miles, from near the eastern edge of Knoxville northeastward to a few miles beyond Jefferson City. The presence of zinc in these Counties has been known for well over 100 years. In 1910 it was brought to the attention of American Zinc Company that zinc sulphide deposits in the Mascot area might be attractive. Following an examination and some surface prospect drilling, the American Zinc Company of Tennessee was organized and acquired the Mascot properties in 1911. Operations began in 1913 on the basis of 1,000 tons per day mill capacity. With the successful operation of the Mascot mines, the Company undertook explorations in the area from Jefferson City southwest through Friends Station to Mascot. The efforts resulted in development of substantial tonnages of zinc ore and enabled the Company to expand the Mascot and New Market milling operations to their present capacity of 11,100 tons per day. Folded and faulted Paleozoic sedimentary rocks under- lie the mining district. The principal zinc mineralization occurs in a group of strata known as the Knox

Jan 1, 1970