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By John C. Franklin

INTRODUCTION Alpha-emitting radon daughter products are a recognized health hazard contributing to the development of lung cancer in persons exposed to excessive concentrations over an extended period. The primary control technique used by the mining industry is dilution with fresh air. Because the uranium is deposited in porous sandstone in most U.S. mines, the control of this hazard with dilution requires excessive volumes of air. As the mines become larger and deeper, the cost for ventilation becomes a major expenditure for the mining industry Most mines are maintaining levels of radon daughters lower than required by law but to maintain these present levels the mining companies are going to be drilling more vent holes or using other control techniques as the mine expands. These control techniques are being investigated by the U.S. Bureau of Mines to determine their effectiveness, cost, and safety for underground use. [Instrumentation] The Bureau's early research used batch sampling of both radon and radon daughters for determining the concentrations. In both cases it was determined that batch sampling did not give a complete understanding of what was happening to the concentrations. Therefore, continuous monitoring systems were developed for both. A continuous flow-through radon monitor was developed by the Bureau (Franklin, et al.., 1976) using a modified Lucas flask mounted on a photo-multiplier-tube (PMT). The air was filtered twice prior to entering the flask to remove dust, diesel smoke, moisture, and radon daughters. The signal from the PMT was then inverted, shaped, and driven to a data acquisition system (DAS) which accumulated the signals. The DAS has two comparators for setting the scan time and interval, a 24-hour clock with Julian date, a printer, and a perforated paper tape punch. Sampling time is determined by the type of experiment being conducted. Our normal sampling time is one 10-minute scan every 15 minutes, but could be set as low as one scan every minute or as long as a 16-minute scan every 167 minutes. There are two models of the DAS. One is a 10-channel system and the other a 30-channel system. On a 10channel system normally 6 channels are used for radon and radon daughters and the other four channels are used for temperature, absolute pressure, air velocity, and relative humidity as described by McVey (1977). Figure 1 shows a scan of five channels monitoring the radon concentration from intake to exhaust in a stope for a non-work day. If the radon concentration stayed this constant during work days, then continuous monitoring would not be necessary. [ ] Droullard (1977) developed a continuous alpha-beta monitor. This monitor has been modified so that it can be used with the DAS previously mentioned. Control Techniques The U.S. Bureau of Mines has conducted research in controlling airborne radon/radon daughter for 10 years. Major efforts have been conducted in sealing the rock to prevent the release of radon, bulkheading to seal nonproductive areas, backfilling with classified mill tailings, and positive pressure ventilation. Also, tests have been conducted to determine the mining cycles contribution to the radon problem. Surveys One stope with two intakes and one exhaust was continuously monitored to determine the effects of blasting, mucking, and drilling on the airborne radon concentrations (Franklin, et al., 1976). Two other detectors were located inside the stope which were close to the mining activity. In this stope no appreciable change in radon was observed during drilling holes for blasting and roofbolts. This study showed increases up to 40 percent in radon for slushing in the exhaust drift. The radon remained high and very eratic during slushing, as can

Jan 1, 1981

By R. Schuhmann, E. J. Michal

Experimental measurements are reported for the oxygen pressures of iron-silicate slags in equilibrium with solid silica. CO2-CO mixtures were bubbled through the slags in silica crucibles to find equilibrium values of p co2/p co over the entire composition range of silica-saturated slags at 1250°, 1300°, and 1350°C. From the data, the activity vs. composition relationships were calculated for O, FeO, and Fe. SLAGS composed primarily of silica and iron oxides have particular practical importance in copper smelting,' in acid steelmaking, and in accounting for the service behavior of silica refractories. These slags all contain both ferrous and ferric iron, so that, strictly speaking, they are ternary or three-component liquid solutions. For convenience, the components may be taken as the three oxides, FeO, Fe2O3, and SiO2. The constitution of the FeO-Fe,O,-SiO, system at slagmaking temperatures has been studied in a recent investigation described in a separate paper.' This work showed the compositional ranges of iron-silicate melts at temperatures up to 1450°C and also the temperature-composition relationships for melts in equilibrium with various solid phases, including iron, wüstite, magnetite, and silica. Broadly speaking, the compositions of iron-silicate melts at a given temperature should be thought of as varying over a two-dimensional field. In the first place, the silica/total iron oxide relationship varies from maximum silica for silica-saturated melts to minimum silica for wüstite-saturated melts or, at higher temperatures, to zero silica for straight iron oxide melts. In copper smelting, for example, the converter slags approach the low silica limits while the reverberatory-furnace slags have intermediate silica contents, perhaps approaching silica saturation in some circumstances. Liquids formed in the pores of silica refractories presumably are close to silica saturation. The second type of composition variation is in the ferric/ferrous relationship, which depends on how oxidizing or how reducing the process conditions are. Relatively reducing slags, such as acid-steelmaking slags, are lower in ferric oxide and ap- proach saturation with metallic iron. Oxidized slags, such as copper-smelting slags, contain larger percentages of ferric oxides and approach or reach saturation with magnetite. Since these two kinds of compositional variations are closely related to two general properties of interest for all metallurgical slags, basicity, and oxidizing power, it is hoped that the thermodynamic study of iron-silicate slags eventually will throw further light on the significance and nature of these long-recognized but as yet poorly understood slag properties. Measurements of oxygen activity as a function of slag composition, using CO-CO2 gas mixture to fix oxygen activities, afford an experimentally convenient approach to the study of the thermodynamic properties of iron-silicate slags. In a preceding investigation,³ his approach was used in a systematic study of iron-silicate slags in equilibrium with solid iron. The present paper gives the results of a similar study of the iron-silicate slags in equilibrium with solid silica. The experimental work consisted in the determination of CO2: CO ratios in gas mixtures at equilibrium in the system: gas: liquid slag: silica Determinations were made at temperatures from 1250° to 1350°C for slags ranging in composition from iron saturation to magnetite saturation. Also, equilibrium CO,: CO ratios and slag compositions were determined for the univariant systems: gas: liquid slag: silica: iron gas: liquid slag: silica: magnetite Experimental Methods The experimental procedure was essentially the same as that used in the previous study of iron-silicate slags saturated with solid iron," but in order to work with the silica-saturated slags an all-silica crucible assembly was used. A liquid slag was prepared from pure prefused stock materials and brought to equilibrium with the silica crucible at the desired temperature. Then a mixture of CO2 and CO was continuously bubbled through the melt

Jan 1, 1953

By L. C. E. FEIO, R. RAMSDEN

In many parts of the world deep level mining relies heavily on the use of refrigeration for providing safe thermal underground conditions. The trend in South Africa in recent years has been to locate the refrigeration plants on surface and to use these plants to chill water that is then distributed throughout the mine. The surface cooling installation normally consists of a pre-cooling tower in which water is first chilled before it is sent to one or more refrigeration plants for further cooling. Presently, the majority of these refrigeration plants use CFC refrigerants; however, to conform with the Montreal Protocol, these plants will have to be replaced or converted for use with alternative refrigerants. The optimum design criteria for installations using the new generation of refrigerants will be affected by their characteristics and are likely to be different from those currently in use. In light of these developments the industry is examining a number of alternative systems for future installations including water vapour refrigeration. Factors that affect the decision on the type of refrigeration system to be used in mine installations are reviewed. INTRODUCTION Gold mining has been carried out in South Africa for over 100 years and most of the reserves close to surface have been mined out; this has led to mining taking place at greater depths, approaching 4000 m below surface. One of the consequences of operating at these greater depths is that it is necessary to install refrigeration plants to cool the ventilation air so as to provide safe and healthy working conditions. With the current low precious metal prices there is pressure on mines to cut costs and in recent years there has been considerable effort devoted to the design of more cost effective and efficient refrigeration plants and cooling systems. In the last 10 years there have been many studies into the use of ice for specific applications (Eschenburg et al., 1986; Hemp, 1988 and Ramsden and Lloyd, 1992) and at present there are three ice making plants in operation on South African mines, each of which produces ice in different processes. In addition, detailed design studies have been carried out on the "split ammonia system" (Napier and Patterson, 1992). In this refrigeration system the evaporator is located underground close to where the cooling is needed, whilst the condenser and heat rejection system is on surface. As far as refrigeration plants are concerned the trend has been to move away from standard package units to custom built refrigeration installations. This has given the design engineer greater flexibility in the choice of key components for refrigeration installations. For example both screw and centrifugal compressors are used, the heat exchangers for the evaporators and condensers may be either plate or shell and tube, and in a number of installations evaporative condensers are used. In addition, the following refrigerants are in use, R12, R22 and ammonia. The acceptance of the Montreal Protocol and its amendments by the South African government will restrict the use of CFC refrigerants and it will be necessary to re-evaluate various refrigeration systems, including those that do not use conventional refrigerants, such as air cycle and water vapour systems, for new surface installations. Although new systems and refrigerants are being developed, only the following refrigeration installations will be compared in this paper: - a refrigeration system using R134a which has properties similar to R12 - refrigeration system using R22 or a new alternative refrigerant with very similar properties - an ammonia refrigeration system - a water vapour refrigeration system The benefits of new cooling systems are not discussed in detail, since they are largely mine specific and outside the scope of the present paper. Since the optimum design for an air cycle system (del Castillo, 1988) is dependent on the mine layout, this system is also not included.

Jan 1, 1993

By J. J. Jonas, J. L. Uvira

Equipment was constructed which permitted the hot compression of 99.8 pct Armco iron and 2.8 pct Si steel at constant true strain rates of 0.05 to 1 per sec over the temperature range 600" to 1000°C. A maximum true strain of 1.9 could be attained, followed by immediate quenching or by isothermal annealing. True stress-true strain curves were obtained, and the steady-state flout stress, a, strain rate, i, and temperature, T, were found to fit the following expression: The constants A, a, n', and AH were determined for the two ,materials. The activation energies obtained for Arrnco iron and silicon steel are 66 and 80 kcal per mole, respectively, and approximate those for seu- diffusion and for creep. This indicates that hot compression is a diffusion-controlled thermally activated process. THE hot compression of iron and steel is usually carried out in the austenite temperature range,1"7 as this is the one of greatest interest with respect to industrial hot working. However, a disadvantage of testing in the austenite range is that the hot-worked structure is destroyed by the phase transformations taking place during cooling. The present study was therefore carried out in the ferritic temperature range, and the hot-worked substructures were preserved by rapid quenching after deformation. The substructural results will be described in a separate paper, and the present communication is restricted to the strain rate/stress/temperature relationship observed during hot working. The results of hot-compression testing are usually given in the form of true stress/true strain curves, with a different curve for each temperature/strain rate ~ornbination.',~,~ Sometimes simple algebraic equations are fitted to the curves, so that certain extrapolations or interpolations can be performed.1'2'5 These equations are, however, devoid of mechanistic interpretations. The present study was undertaken to show that hot compression can be described by an equation of the type used in creep studies. That is, it will be shown that the temperature dependence of the strain rate in hot working is well-represented by an Arrhenius term, with an activation energy similar to that for creep. Also it will be seen that the stress dependence of the strain rate is similar to that for creep EXPERIMENTAL METHOD AND MATERIALS The investigation was carried out with the following three ferrous materials: 1) Armco iron; 2) Armco iron with 0.26 pct Mn; 3) 2.8 pct Si steel. The first two materials were utilized for investigations performed in the temperature range 600" to 800°C; the last one was used for tests at temperatures from 600" to 1000°C. The materials were of commercial purity,* as shown in Table I. Cylinders of five different sizes were prepared by strain annealing. The resulting mean grain diameter was 3 mm in the 1-in. Armco iron and 2 mm in the other sizes and grades. Different ratios of diameter/height were used to enable the determination of the coefficient of friction. The specimen faces were provided with concentric grooves, which acted as lubricant holders during compression, as recommended by English and ~ackofen' and others.2'9 Powdered glass lubricants were applied to the samples before hot compression to decrease friction and barreling, following the practice of previous investigator~.~~~~~~~~ Different mixtures of glass powder were used for each temperature, after the determination of suitable compositions by experiment.'' Equipment for Hot Compression. Hot-compression tests were carried out on an adapted 150-ton vertical hydraulic extrusion press and also on a modified high-temperature creep machine. The modified extrusion press was used for temperatures up to 800°C. The following items were added to the press: a) a high-temperature furnace with built-in upper and lower platens; and b) a transmission assembly, which permitted the attainment of logarithmically decreasing crosshead speeds. These accessories are described in detail in Ref. 11.

Jan 1, 1969

By James N. Grassby

Metal production has traditionally been a cyclical industry. 1977 in the base metals industry has highlighted that fact with a steady decline in the market place for base metals. Corporate aggregate planning is based on good forecasting and when changing conditions make that forecasting inaccurate, alternate analysis of schedules must be accomplished quickly. The computer is the only medium powerful enough to answer management's questions within an acceptable time frame. Worldwide communications networks now make it possible for the many multinational mining companies to arrive at coordinated corporate production plans based on similar basic data from several producing divisions. The Ontario Div. of Inco Metals Co., a unit of Inco Ltd., encompassed during 1977 14 producing mines, 2 nonproducing mines, 1 nonproducing open pit, 5 flotation mills, I smelter, 2 nickel refineries, 1 copper refinery, and an iron ore recovery plant. Several new mines are under development. Mine production approximates 63 500 tpd (70,000 stpd) from some 1000 workplaces. The need for longrange mine planning and scheduling is obvious and until recently has been satisfied by manual methods. However, while manual methods are often quite practical for a small number of mines, or for mines with relatively short lives, or for mines with only one mining method, the situation in the Ontario Div. is too complex and long-term to allow effective, timely planning by such methods. In 1967, a year after the first computer was installed in the division, work was begun on the computerization of the more than 30,000 borehole logs kept in the mines exploration files with a view to speeding up the assessment of mineral resources. Also in 1967 one of the first substantial systems developed on the main business systems computer was the monthly scheduling of development and production for all mines. This system encompassed tons productions per workplace, feet development per workplace, auxiliary and service activities and the requisite labor for each of these. These two dates are mentioned to show that concurrently with the acquisition of computers in the division there was an early understanding of the importance of automating mine scheduling and planning and of the potential for effective and useful computerization of such activities. In 1970, a pilot program was developed in one of the mines containing a large number of workplaces (350) to schedule the production on a network basis. Varying degrees of interest were shown by the individual mine engineers based on the complexity of the production planning problem at each mine. In an evolutionary process, mines were added to the system as its value became obvious in terms of time saving, flexibility, and accuracy. In 1975, the central mine engineering department decided that the system should be extended to all mines so that a complete division-wide long-range scheduling system would be available upon which to base development and production planning. This system would use basic ore data, allow the addition of scheduling commands, and calculate a schedule for the life of the mine. Many reports could be produced for each mine and all-mine summaries would also be available. The significance of the system can be stated in one phrase-speed, accuracy, and flexibility. Whereas in the past a long-range all mines schedule might have been done once a year, taking from two to three months, now it can be done in a day. The chief mines engineer can incorporate changes in input data and external constraints and call for a "new look" at the long-range schedule to assist him and mines production management in their decision-making processes. Using previous manual methods this could not be done quickly enough to be useful.

Jan 1, 1979

By R. V. Smith

The theory for unsteady radial flow of gas, as simplified by Aronofsky and Jenkins, has been reviewed and compared with actual well performance. This study indicated that the theory should be modified by the introduction of an empirical "rate of flow" function "Y(q)". The expansion of the theory on the flow of gas to include a Y(q) term bridges the gap between the theory of unsteady-state flow of gas and actual gas-well behavior. Apparently, the Y(q) term is a function only of the rate of flow for a given well. The completion factor or skin effect is associated with the Y(q) function in such a manner that at least two or more sets of drawdown or pressure build-up tests are needed to separate the Y(q) function and the completion factor. Since the Y(q) function used in this report represents an energy loss dependent on rate of flow near the well-bore of a gas well which is in addition to the loss required by Darcy's law, the Y(q) function is related to the exponent of the back-pressure curve for a gas well. Techniques and equations are presented which permit the estimation of stabilized and "short-time" deliver-abilities. INTRODUCTION The published theory of radial unsteady-state flow of gas through porous media may be divided into papers1-" which use Darcy's law as a premise and other papers4-7,16-10 which recognize that Darcy's law may not hold for flow into gas wells. Miller8 compared theory based on Darcy's law with actual gas-well behavior and concluded that flow into gas wells deviates from Darcy's law. Houpeurt4,5 in a thorough investigation of flow into gas wells concluded that the flow rate into a gas well is proportional to the difference between the squares of upstream and downstream pressures elevated to a power between 1.0 and 0.5. Houpeurt also concluded that the deviation from Darcy's law is caused by irreversible, kinetic energy exchange between the flowing gas and the porous media. Tek9 presented a complete evaluation of the flow problem in gas wells. Several investigators state that the inclusion of gas compressibility into flow equations based on Darcy's law does not begin to explain the flow problems suggested by gas-well behavior. For many years, natural-gas engineers have realized that gas wells by actual test exhibit behavior which cannot be explained entirely by Darcy's law. Many tests on gas wells have indicated that a value of 0.85 for the exponent in the back-pressure equation is a fair average for many wells. However, Darcy's law either for steady or unsteady-state conditions indicates that the exponent should be 1.0. The purpose of this paper has been to examine this deviation from Darcy's law and to present a reasonable mathematical means of evaluating the deviation. The method presented in this paper combines previous theory with an empirical function to provide a description of gas-well behavior. All equations in this report are for constant terminal-rate-of-flow conditions. While present methods of testing wells usually are not based on this concept, they are believed to approach the constant terminal-rate conditions closely in many tests. However, several gas wells were tested by holding the rates of flow constant in order to approach more closely the constant terminal rate of flow; the results confirm the concepts presented in this paper. REVIEW OF THEORY FOR UNSTEADY-STATE FLOW OF GAS The basic partial differential equation for the flow of natural gas has been given in technical literature; the equation for a cylindrical reservoir with the well in the center is

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas'-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller's results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By Gary Beerkirkcher

INTRODUCTION The mine hoisting equipment that is selected and installed at a mine is for the lifetime of the mine and, therefore, it is extremely important that a proper choice be made. Several types of mine hoist designs, including double drum hoists, single drum hoists, friction hoists, and various special designs of these, are available to¬day. Each has advantages and disadvantages and they should only be used in suitable applications. Drive systems for mine hoists must be evaluated together with the mechanical systems for each hoist application. It does not make sense to properly select the hoist mechanical system and then choose a drive system that turns out to be a bottleneck. MINE HOIST TYPES There are two basic types of mine hoists available in the world today: the drum hoist, on which the hoist rope is actually stored during the hoisting cycle, and the friction (Koepe) hoist, which merely passes the rope over the wheel during the hoisting process. Drum Hoists Single Drum Hoist: A single drum hoist (shown diagrammatically in Fig. 1) can be used as a service or production hoist with the cage or skip in balance with a counterweight (Figs. 2 and 3). It can efficiently service one or more levels, since the location of the counterweight at any time is not important. As a pro¬duction hoist with skips in balance, the single drum hoist is best used for single level hoisting. All rope adjustments for proper spotting must be done manually for the single drum hoist. This has to be done periodi¬cally to compensate for rope stretch. A variation of the single drum hoist is the divided drum hoist. If multilayer winding is necessary, the single drum hoist must have a divider to allow a sep¬arate compartment for each rope. If a counterweight is used with a divided drum application, the counter¬ weight rope can be wound on a smaller diameter (Fig. 4). Consequently, it moves a lesser distance than the main conveyance and rope adjustment problems are re¬duced. Double Drum Hoist: A double drum hoist in oper¬ation is shown in Fig. 5. Double Drum Hoist With One Drum Clutched: As a service hoist with cage and counterweight, a double drum hoist with one drum clutched (Fig. 6) can serve several levels efficiently. The advantage of having the clutched drum is that it allows rapid adjustment of ropes due to initial stretch. Some users may prefer the single drum hoist with manual rope adjustment, while others consider the added expense of the second drum and clutch is justified to make rope adjustments quickly. The value of this feature for a particular application should be discussed with the hoist manufacturer. As a production hoist with skips in balance for a multi¬level operation, the clutch can be adjusted for efficient hoisting from any level. Double Drum Hoists with Both Drums Clutched: There are also double drum hoists that have both drums clutched (Fig. 7). The main advantage claimed for this type of hoist is that if something happens in one of the two compartments, the hoist can operate in the other compartment to raise and lower men and sup¬plies. This feature is particularly favorable if there is only one shaft entrance to the mine. Multiple Drum Hoist: The multiple drum hoist, a South African innovation, is a type of drum hoist about which everyone should be aware. Basically, it uses two hoist ropes per conveyance which at great depths per¬mits use of smaller ropes and smaller drums. There are none in use in the United States today. However, they should be considered in very deep mines. Friction (Koepe) Hoists This hoist (Fig. 8) was introduced to the mining world by Frederick Koepe in 1877. The basic prin¬ciple of the friction hoist is that the hoist rope passing

Jan 1, 1982

By Robert E. Green, Edmund G. Henneke

Expressions are derived for the orientation factors associated with dislocation damping due to dislocation motion in the basal slip plane. The results of the calculation of these factors for zinc crystals aye pvesepzted and the relevance of these results to ultvasonic-attenuation measuvements is discussed. In this paper expressions are derived for the orientation factors associated with damping of sound waves due to dislocation motion in the basal slip plane of hexagonal crystals. For zinc crystals, the orientation factors for dislocation motion in one slip direction only, as well as for simultaneous motion in all three basal slip directions, have been calculated at 1-deg intervals. The results of these calculations are presented in the form of contour diagrams in a sector of a standard polar coordinate graph. The calculations have been carried out for both the traveling- and the standing-wave conditions. The relevance of these results to ultra sonic-attenuation measurements is discussed. Associated with the calculation of the orientation factors, the modes of elastic-wave calculation were also evaluated, according to the procedure previously employed by Hinton and Green.' The results of these calculations are not presented here since similar results have been reported earlier by Mus-grave.2 However, it should be mentioned that, although the qualitative features of Musgrave's results are preserved, the quantitative values are somewhat altered since different values for the elastic constants of zinc were used. ORIENTATION FACTORS It is convenient to refer to three different sets of coordinate axes, Fig. 1, in the following calculations. First, there are the Miller-Bravais axes which are used in describing the Miller-Bravais indices of planes and directions in a hexagonal crystal. These axes are denoted in the conventional manner by a,, a,, a,, and c. The second set of axes used is a rectangular Cartesian coordinate system located as shown in Fig. 1. Note that the x axis coincides with the close-packed direction al [2110], the z axis coincides with the c axis [0001], and the y axis is orthogonal to these two lying in the [0110 ] direction. Finally, a form of Eulerian angles is used to locate the position of the specimen axis. The angle between the specimen axis and the c axis is denoted by 0 and the angle between the projection of the specimen axis on the basal plane and the a, direction is denoted by ø. The majority of observations on plastic deformation of metal crystals indicates that such deformation is caused by the motion of dislocations on a limited number of crystalline planes and in a close-packed direction. In crystals with hexagonal symmetry the most prominent slip plane is the basal plane (0001) and the slip directiops- are one of the close-packed directions, [2110], [ 12101, or [ 1120]. To properly set the stage for the following work, several points must be clarified. First, we want to consider the contribution to the attenuation of elastic waves by dislocations only. While the Granato-Lucke, model for dislocation damping is presently the one most quoted, it is not necessary to refer the present work to it. The only assumption that need be made is that the motion of dislocations absorbs energy from the elastic wave and therefore attenuates it. It is immaterial here how this energy absorption occurs. However, because dislocations have been observed to move most freely on the (0001) plane for hexagonal crystals undergoing plastic deformation, it will be assumed that it is the dislocation motion on this plane which attributes to the observed attenuation. The basic orientation factor, Ok, is essentially the same as that used by Green and Hinton for fee crystals,4 defined by the equation

Jan 1, 1968

By A. N. Crownover, H. T. Kennedy, E. P. Miesch, C. H. Bowman

The paper presents correlations of (l) molar volume of gaseous hydrocarbon mixtures with pressure, temperature, composition and properties of the C,-plus fraction; (2) shrinkage of oils during flash and differential liberation of gas, including the calculation of formation volume factor under various conditions; and (3) bubble-point pressure with temperature, composition and characteristics of C, plus. The data on which the correlations are based comprise 1,615 measurements on 900 hydrocarbon systems, including numerous systems containing nitrogen, hydrogen sul-fide and carbon dioxide. In each correlation, the number of data points covered and the accuracy is substantially greater than in previously available work. Thus, the equation yielding molar volumes of gases has an average deviation of 2.04 per cent, applied to mixtures having temperatures up to 313F and pressures up to 9,800 psis, compared to 2.37 per cent for the Benedict-Webb-Rubin equation applied to the same data, and 4.53 per cent for the method based on the law of corresponding states. he equations resented are all explicit in the dependent variable, and require no iteration on the digital cow puter. INTRODUCTION The ease and accuracy of determining the composition of hydrocarbon mixtures, compared to the difficulty of measuring their properties under reservoir conditions, makes it desirable to utilize composition as the key to physical behavior to the greatest possible extent. As a result, there are available correlations between composition, or easily measured characteristics dependent on composition, and practically every important engineering property of reservoir fluids. The task confronting us is one of finding more exact relationships between important variables rather than extending correlations to new properties. This paper describes new correlations of molar volumes of gases, formation volume factors, and bubble-point pressures with composition, temperature and where possible, pressure. Each correlation is obtained by employing a sufficiently large amount of data so the calculated properties are probably as least as accurate as the measurement on which they are based. MOLAR VOLUME OF GASES Although many equations of state have been proposed for pure gases, only a few methods are applicable to hydrocarbons at conditions comparable to those in petroleum reservoirs. Still fewer arc useful in describing the behavior of mixtures, with which the petroleum engineer is largely concerned. The correlation presented here involves procedures similar to those of Alani and Kennedy The van der Waals equation is modified to make a and b functions of temperature instead of being constants for each material.This is a cubic equation, which may have either one or three real roots. The lowest root corresponds to liquid volume, while the highest applies to gas. When the procedure was applied to 703 pressure-temperature points of 164 gases of known composition and volume, the average deviation was 12.08 per cent, and the standard deviation 8.15. The above calculations were made using the constants derived for liquids by Alani and Kennedy and the mixture equation developed by them. A closer approximation to measured molar volumes is obtained by employing different sets of constants for different areas on the pressure-temperature chart, and by changing the relationship between a,,, and b,,, for mixtures and the a, and b, for individual hydrocarbons. The various sets are shown in Table 1, and the areas for which they are recommended are plotted in Figs. 1 through 7. In these figures, the area designated by zero is in the critical region for pure materials, and the values obtained for them may be unreliable. For normal mixtures, however, the area may be added to any of the bounding areas without substantial error. The new relationships employed are

Jan 1, 1966

By William C. Hagel

Oxygen-18 exchange between gaseous oxygen, held at a pressure of 125 mm Hg in a PL-IORh chamber, and splzeres of a Fe2O3 containing three or less grains was determined from 9000 to 1250°C. Isotope equilibrum on crystal surfaces appears to be quickly established, and the rate-determining factor is self-difiusion confbvrning to the relation D = 2.04 esp(- 77,900/RT) sq cin sec-'. Changing sphere diameters caused no detectable variation in diffusion coefficients. Oxygen ions diffuse faster than cations at low temperatures, but a crossover may occur at about 1150°C. INVESTIGATIONS by Davies et al.' and Himmel et al2 have suggested that the mechanism of iron oxidation above 600°C involves a predominance of cation migration in the wüstite (FeO) and magnetite (Fe301) layers and oxygen-ion migration in the hematite (a Fe2O3) layer. Evidence for little cation migration during hematite growth consists of: 1) the disappearance of radioactive-silver markers, presumed to vaporize from the oxide-gas interface, and 2) a large discrepancy between parabolic rate constants for magnetite oxidation and those calculated from Lindner's3 data for cation self-diffusion, D:, using Wagner's theory.4 Reversing the calculations gave anticipated self-diffusion coefficients, D:, for oxygen ions of 3.6 x 10-9 sq cm sec-1 at 1100°C and 5.9 x 10-10 sq cm sec-1 at 1000°C. Since then Kingery et a1.5 reported three values for oxygen-ion diffusion in polycrystalline, sintered hematite. These were obtained near 1200°C, at an oxygen pressure of approximately 150 mm Hg, and could be represented by the Arrhenius expression, Dg = 1 x 10 11 exp(-146,000/RT) sq cm sec-1. Extrapolation to temperatures below 1100°C infers that oxygen ions are less mobile than cations. This contradicts the aforementioned oxidation evidence and also coble7s study of the initial sintering of hematite. From the latter, apparent diffusion coefficients for the slowest rate-controlling species could be calculated, and fair agreement was found with an extension of Lindner's data for cation diffusion. Fig. 1 depicts such comparisons graphically. Three points have been included for the determinations of Himmel et al. on cation diffusion in large, natural hematite crystals surrounded by pure oxygen at atmospheric pressure. No dependence on crystal log raphic direction was noted. Since the value of 10-l4 sq cm sec-' at 1000°C actually represents an upper limit, one might interpret that there is a small decrease in D: when single crystals are employed. On the whole, however, cation diffusion appears relatively well-defined,* while the few results tension to lower temperatures. After having gained experience measuring oxygen-ion diffusion in certain glasses7 and in the corundum oxide, a Cr2O3, the purpose of this work was to determine D; values for hematite and thus possibly assist a mechanistic understanding of the kinetics of the oxidation and reduction of solid iron oxides. I) EXPERIMENTAL PROCEDURE A) Material. Hematite powder of moderately high purity was received from the Columbian Carbon Co. An accompanying lot analysis listed 0.03 H2O, 0.008 weight percents, with the remainder Fe2O3. Subsequent treatments were ball milling, drying, prepressing, and hot-pressing for 60 min at 1350°C under 5000 psi. Since graphite dies coated with a slurry of alumina were used for hot-pressing, the surrounding atmosphere at temperature was sufficiently reducing to form some magnetite on the outer surface of each cylinder. After removing any attached alumina, a stabilizing anneal of 50 hr at 1300°C in oxygen was added. The final product was nonmagnetic and exceeded 97 pct of the density (5.24 g cm-3) usually given for FezO3. On polishing cylindrical ends, counts were made of the number of grain boundary intercepts per

Jan 1, 1967

By C. van der Poel, R. L. Chuoke P. van Meurs

When an initially planar interface between two im-ttitcihle liquids is displaced at constant rate, U, nor-mat to the front, instability will occur for all rates greater than a critical rate. U, given by provided the Fourier decomposition of the spatial pertmrbcrtiott or deformation of the moving displacetment front contains modes with wavelengths. A, greater than a critical wavelength, given by tit there expressions, p, p and k, with the subscripts I and 2 distinguishing the two 1iquids under consideration, are density, viscosity and effective pemeability coefficients respectively; g is the absolute value of the acceleration due to gravity; and cos (zz') is the direction cosit7e between the vertical carlesian coordinate z' (positive upward) and the z coordinate norma1 to the initially plane macroscopic interface taken positive in the direction from Liquid I to Liquid 2. U is the average volumetric velocity (injected volume of liquid pet. unit time per unit of area normal to Z) and is positive for Liquid I displacing Liquid 2, negative for the reversc displacement and r2 is an effective inter-fucial tension (for displacements between parrallel plates, t0= s the ordinary bulk interfacial tension). further, there is a wavelength of maximum instability given by For natural perturbations, this wavelength will preclotninate and characterize the form of the instability as a quasi-sinusoidal deformation, i.e., viscous fitzgers of peak-to-peak separatiotr, A,,. Comparison of experitient with theory rei'eals tltat these considerations are recsonably valid for displacements in hoth parallel plate chantzels and nnconsoli-clutt'd glass ptnvder packs. These results are. tij particular interest for interpretation of data from laboratory experiments with regard to fielil applica/iotz.s. It is quite possible for A,, although st7zall relative to the large lateral dimension of the reservoir, to rxceed the greatr.st lateral extent of the lahoratory sample or model. If it does, frontal displace- ment occurs in the laboratory experiments, and oil INTRODUCTION Thc puposes of this paper are to present theoretical and experimental evidence for occurrence of macroscopic instabilities in displacement of one viscous fluid by another immiscible with it through a uniform porous medium and to compare available experimental data with some predictions of a theory of instability developed by the first author. The instabilities are referred to as macroscopic in the sense that spatially quasi-sinusoidal, growing fingers of the displacing liquid are formed, the width and peak-to-peak separation (wavelength) of which is large relative to a characteristic length of the particular permeable medium such as grain size. Visual models of two kinds have been used to obtain observations: displacement of oil by water-glycerine solutions through the flow channel formed by closely spaced parallel plates and displacement of oil by water with and without initial interstitial water through unconsolidated glass powder packs, employing the technique of matching indices of refraction. In all cases we have observed macroscopic instabilities or fingers under conditions predicted by the theory to be favorable for their occurrence. The phenomenon discussed here is not the production of streamers due to gross inhomogeneities such as permeability stratification of the porous medium. It is our object to show, on the contrary, that a quantitative prediction of finger spacing is possible in a porous medium known to be macroscopically homogeneous and isotropic throughout. The importance of the phenomenon in its influence on the configuration of oil and water with respect to oil production behavior was noted earlier by Engel-berts and Klinkenberg' who coined the term "viscous fingering". THEORY Necessary and Sufficient Conditions ior Instability anc Initial Kinematics There are several levels of increasing complexity in the theoretical description of instabiIity of fluid displacements in permeable media. Of these, the simplest description, ;tdapted to low permeability systems, is selected for presentation.' More inclusivc tlescriptions are reserved for separate publication.

By W. van der Knapp

A theoretical and experimental ana1ysis is given of the change in volume of a porous medium due to changes in external and internal pressures. The result enable one to deduce directly the effect of large increlents in stresses. It is shown that the three-dimensional representation of the volume of a nonlinear porous system is a cylindrical rules surface, the generating lines of Which have a slope according to the solid rock compressibility. Analytical expression for such a ,surface is very simple. It follows that the bulk and pore compressihilities depend only on the difference between pore fluid and external hydrostatic pressure, i.e., the effective rock frame pressure. From measurements on a number of sandstones as well as limestones it can be conduded that for practical values of this effective frame pressure the pore compressibility falls in the range between the compressibility of water and that of undersaturated crude oil. In general, pore compressibility is found to be higher the lower the porosity. For a particular limestone reservoir pore compressibility and porosity could he related by means of a simple empirical formula. Results from the described study find a direct applicxtion in material balance calculations and in prob1ems of liquid flow through porous media. Since the elastic constants of the rock bulk material enter into equatiorls for velocity of acoustic waves, the results are also of importance for calculating rates of wave propagation in these media. It is shown for sandstones with 1.5 to -10 prr cent porosity that laboratory measured porosities may differ from those lender reservoir conditions by about I per cent of their value. The difference for low porosity limestotnes can be of the order of 10 per cent. The subsidence caused by elastic deformation of reservoir rock is shown to he very small. General formulas relating pore and bulk volume to external and internal pressure can be derived, as has been shown by Biot1, Gassmann2 and Geertsma.2 Their theories describe the differential change in volume caused by a variation in pore fluid tension and external hydrostatic tension. It has been known for a long timei that the stress-strain relations of a packing of spheres are essentially noninear. Our experiments show that for almost all reservoir rocks which arc elastically deformable the relation between volume and loading is also a nonlinear one, resembling that of a packing of spheres very closely. The behavior of these media is often described by using the linear stress-strain relations for small incremental stresses and strains in the vicinity of a pre-stressed condition." The present study differs from these considerations in that it enables one to deduce the effect of large increments in the stresses directly. In analogy to the stress tensor for a homogeneous body the stress tensor for a porous body can be written in the conventional way: where the tensor components, o, and t, represent the total forces acting on the faces of a unit cube of porous material. This tensor can be split into two parts. a hydrostatic and a deviatoric part, as follows2,3,1 where the component of the hydrostatic stress system, a. equals The hydrostatic stress causes a change in volume whereas the deviatoric stress system gives rise to a change in shape only. One of the difficulties in describing changes of volume occurring in reservoir rocks is that the relations connecting these volume changes with external and internal stresses are essentially non-linear. A complete description requires the bulk volume, V,,, as well as the pore volume,V,,. to be known as a function of both the changes in pore fluid tension (v) and the hydrostatic tension on the outer boundary.

By N. Jaffe, J. E. Dorn

This investigation is concerned with the possibility that the creep resistance of metals might be reduced as a result of recovery at the creep temperature when the applied stress is reduced. For this purpose the effect of stress on the recovery of the creep behavior of pure polycrys talline aluminum was investigated in the cross-slip temperature range where the activation energy for creep is 28.000 cal per mole. Before recovery all specimens were given the same substructure by creeping them under a stress of 7800psi to a strain of 0.218. Recovery was then accomplished by holding the specimens at the creep temperatures of 327" and 337°K under a series of reduced stresses for various periods of time. When the original stress was reapplied the specimens crept more rapidly than when the original stress was first removed, illustrating that recovery did take place. The extent of recovery could be indexed in terms of the UNDER certain conditions of test, the creep rate decreases over the primary stage of creep often by as much as a factor of 10~B. Since the external variables of stress and temperature are held constant, such pronounced and significant changes in the creep rate must be attributed to various substructural modifications that are introduced as a result of creep itself. At the secondary stage of creep, over which the creep rate remains constant and the substructure no longer changes, a balance must be achieved between the rate of increase in creep resistance due to creep straining and the rate of recovery of the substructural modifications. The general validity of these concepts on substructural changes has already been shown,' including the corollary that a more creep-resistant substructure is introduced under a more rapid creep rate arising from a higher applied stress.' In spite of these well-documented facts, very little progress has been additional strain undertaken by the recovered specimen to achieve the same strain rate as the unrecovered specimen. It is significant that the higher recovery stresses gave the most rapid rates of recovery. Over the high range of reduced stresses, where some creq took place during recovery, the activation energy for recovery equaled that for creep, namely 28,000 cal per mole. But for stresses during recovery below 0.80 of the original creep stress, no creep was detected during recovery and an activation energy for recovery of about 72,000 cal per mole was obtained. Whereas the activation energy of 28,000 cal per mole suggests that cross-slip of dislocations is responsible for this recovery, the mechanism for the 72,000 cal per mole process is not known. This activation energy, however, is about twice that for self-difhsion. made in determining, in satisfactory detail, precisely what substructural changes so effectively modify the creep rate.' Up to the present, electron microscopy has failed to uncover, in a satisfactory quantitative manner, the mechanistic processes involved. Since, however, creep, at least at moderate and high temperatures, arises from one or more types of dynamic recovery processes, it should be possible to shed additional light on the total problem by investigating the recovery of creep resistance. The importance of such an investigation becomes apparent when the fact is recognized that there has yet been no direct experimental proof that the rate of softening due to substructural changes as a result of recovery equals the rate of hardening due to creep-induced substructural strengthening over the secondary stages of creep. Furthermore the problem of what happens to the creep-strain induced strengthening when the material recovers either at zero or some reduced operating stress has significant engineering consequences. It was for these reasons that the present investigation on the recovery of creep behavior was initiated. Inasmuch as a substantial background has now developed on the creep of high-purity aluminum, this material was again selected for the current investigation. Furthermore extensive evidence is now

Jan 1, 1963

By C. D. Thompson, D. C. Violetta, C. A. Czako

The mechanics of the continuous sintering process are briefly reviewed and the application of this process for the beneficiation of principal minerals used in making cement is shown. Pilot plant tests using pyrobeneficiation techniques were conducted with mixtures of limestone and shale in various ratios. Results are illustrated and show the percentage removal of carbon, carbonates, sulfur, alkalies, and volatiles as a function of the limestone-shale ratio. Tests with varying quantities of solid fwls, added to mixtures containing limestone and shale in a 4 to 1 ratio, were made to attain optimum elimination of the volatile constituents. Experimental results show that 90 pct of these constituents were removed during the calcination sintem'ng process. The advantages of using the beneficiated material for making cement are discussed with regard to prepam'ng, handling, and clinkering operations. A sintering process for treating raw materials or kiln waste products which contain high amounts of alkaline materials is described. Tests were performed with a high alkaline waste dust mixed in a 1 to 1 ratio with raw cement meal. The data from these tests and others using different halides for aiding alkali removal are evaluated by the alkali content of the cement clinker. Test results showed that the Dwight-Lloyd process could be applied with facility in beneficiating raw materials for cement making. Substantial quantities of deleterious volutile constituents were removed by calcining and sintering techniques. The continuous sintering process has been applied for a number of years as a means of beneficiating minerals for subsequent conversion to merchantable products. The process was developed and first used for nonferrous metallurgical applicatfons. However, it has risen to prominence for ferrous metallurgical applications where last year in the U.S. and Canada nearly 40 million tons of iron ore were treated by grate firing processes. Through the years of process development many investigators have realized the versatility of the sintering process and have directed experiments toward the use of it for applications with nonmetallic minerals. These have included calcining limestone, carbonizing coal, expanding shale, and burning cement raw meal. Today commercial sintering plants produce cement clinker from mixtures of limestone and shale, lightweight aggregate from shale or clay, and calcined products from phosphate shale. The mechanics of the downdraft sintering process have been presented by many authors. In general practice the materials to be agglomated are mixed as moistened fines with a solid fuel and this mixture is spread uniformly on the grates of the sintering machine. The charge is then momentarily directed under an ignition furnace. After ignition a continuous downdraft of air promotes combustion of the fuel and through heat transfer particles become partially fused into a coherent mass. This is cooled from continued draft induced after combustion. Many investigators have shown that distinct zones are formed during the process of sintering iron ores. At the midway point of the sintering process these are prominent and are, respectively, from the top of the bed to the bottom, comprised of a cooling zone of sintered material, a combustion zone of sinter formation, a calcination zone, a drying zone, and a zone of unreacted materials. Completion of sintering occurs near the discharge end of the machine where the firing zone approaches either the grates or grate dressing material called hearth layer. Here the peak draft temperature usually can be noted in the windboxes. The zonal pattern has been illustrated with the use of graphs which show thermal gradients as they progress through the bed of materials during sintering. Fig. 1 shows, in simplified form, thermal gradients existing when clinkering cement on a sintering machine. The thermal gradients illustrated are for periods of initiation, midway and completion of the clinkering process. The occurrence of these zones has importance for the beneficiation of cement raw materials. A research program was performed at the Dwight-

Jan 1, 1961

By B. C. Allen

Grain-boundary gvoocing was studied irz chronziu?n. molybdenum, tungsten, and the solid-solution alloys, Cr-35Re. Mo-33Re, and W-25Re at 0.6 to 0.9 of the absolute liquidus temperature under an inevt atmosphere , foveign nzetal zlapor, and liquid metal. The controlling mechanism of matter transport was deduced frolr groove size and shape. kinetics of growth, and cotnparisoz with theoretical relatiotzships derived by Mullins. Grooves in chowzizon formed prittzarily by volume diffusion tkrongk kelium or argon at 1 atm pressure and by e1)apovation-condensatiotz in a static vacuum. Groozles in the other nzetals and alloys forrned priniarily by sirface diffusion, the coefficients of which were calculated. Carbon was found to decrease the acti7:ation energy for surface diffusion on molybdenun. Sitrface diffusizities weve sinzilav for iWo-0.0ZC and Mo-33Re. The presence of about 1 -?nm pressure of silver or tin vapor did not affect the neckanis)n of grooz;e formation. In liquid titz or silz:er, pain bolindary gvooves formed by zolume diffusion in the liquid. BASED on theories of ullins," the mechanisms of grain-boundary grooving have been determined for low-melting metals such as copper in an inert atmospheres or in liquid lead.4 The purpose of this investigation was to study grain-boundary grooving in the refractory Group VI-A metals, chromium, molybdenum, and tungsten, and the bcc solid-solution alloys, r-35e, 0-33e,= and -25e,' at 0.6 to 0.9 of included to see whether Mullins' theories were applicable to them as well. EXPERIMENTAL WORK The materials chromium, molybdenum, tungsten, Cr-35Re, Mo-33Re, and W-25Re were in the form of 0.050-cm-thick sheet assaying 99.98 pct or better. The nominal carbon level was generally 30 ppm. The oxygen + nitrogen + hydrogen content was -50 ppm. Mo-33Re and W-25Re were prepared by powder-metallurgy methods and supplied by Chase Brass and Copper Co. The remaining materials were arc-cast. Chromium and Cr-35Re were prepared at Battelle by arc melting, extruding, swaging, and rolling. Mo-0.003C was supplied by Climax Molybdenum Co., and Mo-0.02C and tungsten by Universal Cyclops Corp. As a source of liquid metals, tin and silver granules assaying 99.98 pct were used. Spectrographic analyses indicated the presence of -100 ppm each of iron and silicon. Vacuum melting reduced the combined gas content to c5 ppm (2.60,, 0.9N2, 0.4H2 in tin and l.602, 0.7N2, and c0.04H2 in silver). Specimens were prepared for grain-boundary grooving. Coupons 0.5 by 1.5 cm with a small hole in one end, or substrates 1.5 by 1.5 cm, were cut from sheet. The specimens were annealed in containers of the same material to provide a vapor-solid equilibrium as well as to protect them from gaseous impurities. Outgassing was done at 2 x 10"5 mm for 15 to 30 min at 1150°C for chromium and Cr-35Re, 1750°C for molybdenum and Mo-33Re, and 2600°C for tungsten and W-25Re. Then recrystallization to a stable grain size of about 0.5 mm was accomplished by annealing at least 1 hr at 1600°C for chromium, 1800°C for Cr-35Re, 2350°C for molybdenum, and 2300°C for Mo-33Re in a rhenium-element resistance furnace under 1 atm of static argon or helium. The atmosphere was gettered by tantalum radiation shielding. Tungsten and

Jan 1, 1967

By S. Pearson, L. Rotherham

Measurements have been made of the variation of internal friction with temperature for spectroscopically pure silver, and for o series of solid solutions of silver with cadmium, indium, and tin, using a Ke-type torsion pendulum apparatus. Some experiments have also been made to investigate the effect of nonmetallic impurity on grain boundary relaxation in silver. The effect of the alloying elements is to increase the grain boundary viscosity, and to raise the activation energy for grain boundary relaxation from 22,000 cal per mol for pure silver to 43,000 cal per mol for the solid solutions; the same value being obtained, within the limits of experimental error, for all the alloying elements and solute concentrations investigated. Results of the experiments show exactly the same trend as those obtained previously for a similar series of copper solid solutions. They are in agreement with the general theory of grain boundary relaxation developed by Zener and Ke, but do not seem to be in agreement with either of the mechanisms so far put forward to explain grain boundary slip. EXPERIMENTS described in this paper were made as part of an investigation into the effect of alloying elements in substitutional solid solution on grain boundary viscosity, measured by the internal friction method developed by Ke.&apos; The apparatus and experimental procedure have already been described.&apos; Preliminary work was done with spectro-scopically pure silver. Experimental Work Materials Used—All the materials were supplied in the form of % mm diam wire by Messrs. Johnson Matthey and Co. Ltd. The silver and all the alloying elements used were spectroscopically pure. Composition of the alloys is given in Table I. They were all melted and chill cast under the same conditions as the copper alloys. The ingots were rolled to 1/4 in. sq rod with intermediate annealing at 600°C in an atmosphere of cracked ammonia when necessary. These rods were then drawn to wire by standard procedure with intermediate bright anneals at suitable steps in the drawing operations. Specimens from the annealed wires were sectioned longitudinally. mechanically polished, and examined under the microscope. They were then etched and reexamined. Grain sizes were reasonably uniform for all wires, and no traces of a second constituent were observed. The wires were weighed before and after testing so as to measure any loss of the alloying element due to evaporation. The loss was less than the accuracy of measurement—< 0.1 pct of the total weight— for the Ag-In and Ag-Sn alloys, but appreciable loss of weight occurred in the case of the Ag-Cd alloys. The percentage loss is given in Table 11. X-ray diffraction photographs were taken of all thc wires after test to determine whether there was any marked preferred orientation. Results of the examination are given in Table 111. Experiments on Spectroscopically Pure Silver-— Experiments were made on specimens in which the grain diameter was small relative to that of the wire, and on one specimen in which the grains were grown by the usual strain-anneal method to extend across the full diameter of the wire. These large grained specimens will be referred to as single crystal specimens. The wires were annealed for 11/2 hr at 700°C, and experiments were made at two frequencies of vibration, 1.5 and 0.4 vibrations per sec. The variation of internal friction with temperature is shown in Fig. 1. Experiments on a second small grain specimen gave approximately the same results as for the first wire. It will be seen from Fig. 1 that the peak in the curve for the small grained wire, which is presum-

Jan 1, 1957

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"&apos; and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

By J. D. de V. Louw

Introduction Zircon is a natural occurring mineral and may exhibit natural low level radioactivity. It contains trace levels (90 to120 pCi/g and 110 to 115 pCi/g respectively or 3.3 to 4.4Bq/g and 4.1 to 4.3 Bq/g) of naturally occurring radioactive uranium and thorium. This mineral is often found in a suiteof minerals (rutile, ilmenite and monazite) Due to the overlap in physical properties of monazite (containing 4–7% thorium) with some of the zircon (slight magnetic susceptibility) it often contaminates the zircon, adding to the levels of thorium in the product. Hazards associated with the products from zircon and its processing is inhalation of respirable dust (generated by milling) containing radioactive uranium and thorium which may cause cancer of the lungs. Legislature regulates the transport, use, workplace environment exposure and storage of radioactive material. In America the general regulation for the unlicensed use of low levels of radioactive materials limits the concentration to 500 ppm (U plus Th). Europe (IAEA) specifies a limit of10 Bg/g (Bequerels per gram) on the parents for transport only which is a higher level of U+Th. Companies selling into these markets need to comply with these regulations and certification is therefore required, not only of the major constituents determining the price, but of the U and Th levels as well. Exceeding the limits for U and Th may result in material being returned to the country of origin. However, for the analyst the requirement is to analyse for these elements throughout the production process as well as the analysis of the ‘tails’ that is returned to the mine area. This requires a wide range of concentration to be analysed. Methods of analysis A wide variety of methods exist for the analysis of U and Th in a range of matrices. (Table I) All these methods have been used with varying degrees of success in terms of accuracy. Overall precision for the different techniques varies from 5 to 25% relative. Time to produce results from these methods vary from a few minutes to several days. The Production Chemist is expected to produce between5 and 10 analyses per hour for process control purposes. A suitable technique that fits this requirement is X-Ray Fluorescence. Both Wavelength Dispersive (WDXRF) and Energy Dispersive X-Ray (EDX) instruments are suitable. X-Ray analysis in general has a few major advantages over competitive techniques. •It is fairly simple to set up and interferences are known and easy to correct •It has multi-element analysis capabilities •Clean spectral lines for U and Th (in zircon specifically) •Uncomplicated and easy to measure background •Low detection limits (3 to 5 ppm) •A very high degree of precision •Sample preparation is uncomplicated and fast (pressed powders and fused beads). In Zircon (ZrSiO4) processed sands the matrix is constant(>99% ZrSiO4) and the background is thus essentially constant. A typical set up for the analysis of U and Th by WDXRFis given below: X-Ray Tube Tungsten (W) Target, 2.5 to 3kW operated at 50mA/50kV Crystal LiF200 (or LIF220 for higher resolution) Analytical Lines (2?)U La1,226.14Th La1,227.47 Detector Scintillation Counter Analysis time, depending on the concentration can vary from as little as 20 seconds up to 5 minutes. Standards As with any other comparative technique XRF analysis relies heavily on the quality of the standards used. Assuming proper set-up and operation of the instrumentation as well as consistent sample preparation, accuracy is determined by the quality of the initial calibration standards. A search for the available zircon certified reference materials (CRMs) shows that there are only a few CRMs

Jan 1, 2003

By W. J. Boone

The Bureau of Mines has programmed for publication a series of Reports of Investigations of studies it has undertaken on low-temperature phase equilibria of several helium-bearing natural gases. This report is the second of a series of papers of the same general title; it is anticipated that additional reports of this series will be published. The advent of a helium conservation program and the prospect of production of helium by private industry, make it especially desirable to publish these data. This report describes phase equilibria related to a natural gas that is processed for helium at the Bureau&apos;s Exell Helium Plant (located about 35 miles north of Amarillo, Tex.). Carbon dioxide and water in the gas were removed before making the study; hence the data obtained are representative of the gas stream immediately after similar preliminary treatment in the plant process. Phase equilibrium data were obtained for conditions from -50° to -275° F. and from 100 to 500 p.s.i.a. Analyses of samples were made as follows: For a given run at a selected temperature and pressure, samples of the vapor and liquid phases were analyzed by mass spectrometer, and an additional sample of the liquid phase was analyzed for helium by means of special apparatus (7). 4

Jan 1, 1962