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By L. Kaufman

An equation is derived relating AF a", the difference in free energy between austenite and martensite, to temperature and composition in the iron-chrmnium and iron-chromium -nickel systems. This equation is used to calculate at M,for low-carbon stainless steels. A method for utilizing the energetic equations to calculate M, in stainless steels is suggested. In addition, an explanation is given for the anomalous effect of chromium in forming a y loop concurrent with the lowering of M, in iron-base alloys. It has been demonstrated that the effect of alloying elements on the Ms temperature is strongly dependent upon the influence of the alloying element on the thermodynamic properties of the y and a phases. Notwithstanding the fact that alloying elements affect the Ms temperature by changing the lattice parameters, elastic constants, and inter-facial energies of the a and y phases, their primary role is a thermodynamic one. Thermodynamic analyses have been presented for the iron-carbon'-4 and iron-nickele systems in which equations are derived for Fa and FY, the free energies of the b.c.c. (or b.c.t.) and f.c.c. phases. These equations, which can be obtained with the aid of the equilibrium diagrams, can be used to help predict the Ms vs composition curves. This paper deals with a calculation of the thermodynamic properties necessary to compute AFffLY for iron-chromium alloys. In view of the lack of direct information concerning the activity of chromium in the a and y phases of iron, the regular solution approximationa,g was utilized to bridge the gap. After the necessary equations were derived for the iron-chromium system they were used to calculate AFff— Y for stainless steels by combining them with the previous results obtained for iron-nickel alloys. The results of these calculations offer a means of rationalizing the anomalous behavior of chromium in iron-base alloys. The latter depends on the regular solution approximation in contrast to the explanation offered by zener , which is based upon the "magnetic specific heat effect." THERMODYNAMICS OF THE IRON-CHROMIUM SYSTEM If y represents the atomic fraction of chromium in an iron-chromium alloy, then the free energy of the b.c.c. phase Fa, the f.c.c. phase FY, and the difference in free energy between the f.c.c. and b.c.c. phases of the same composition are given through [3] and Fmy represent the free energies of mixing of the a and y phases; while @era -' and uFea 4Y represent the difference in free energy between f.c.c. and b.c.c. chromium and iron respectively. The values of AEFe0ff4Y in the temperature range between 0" and 900K ( .

Jan 1, 1960

By R. M. Asimow

Both smith1 and wells2 have shown that the dif-fusivity of carbon in austenite increases rapidly with increasing carbon concentration. Smith has shown, in addition, that part but not all of this increase can be attributed to the concentration dependence of the activity coefficient of carbon in austenite. From the work of Eshelby', it is known that, because of the image displacements, there is a uniform dilatation of the material in a body containing random centers of dilatation. It is thus tempting to explain the enhanced diffusivity as resulting from this apparent negative pressure caused by the interstitial carbon atoms.* That is, the activation free energy for diffusion is not directly a function of concentration if we consider that the alloy is subjected to a concentration-dependent pressure. To proceed with a quantitative solution, it is necessary to determine the activation volume AV for the diffusion process. An exact calculation of AV is quite a difficult problem and does not appear to have been solved as yet. A simpler procedure is to use the semiempirical, macroscopic theory of seyes' which relates the activation free energy AG to AV. Keyes has shown that for many types of diffusion processes the following relationship is valid Where p is the Gruneisen constant and x the compressibility. This relationship is based on the assumption that AG can be identified with strain-energy terms. In general there will also be contributions to AG due to a change in the energy of the valence electrons of the metal; thus the relation must be considered largely empirical. Surprisingly, for self-diffusion where it is well-known that the electronic contribution is quite important,' the Keyes relation works quite well for many systems. For interstitial diffusion where it might be expected that the relationship is on a firmer theoretical basis, the limited experimental data available is not in particularly good agreement as can be seen from Table I. However, it must be remembered that besides the uncertain basis of the Keyes formula there is considerable uncertainty in some of the experimental values of AV. The only real justification for using the Keyes formula in the present analysis is that it gives a result which satisfactorily solves the problem at hand and, further, there are no more reliable procedures for calculating AV available. The coefficient 3 in Eq. [I] is determined such that the room-temperature value for x is to be used. The activation entropy AS is estimated as 8.95 x 10"3 kcal per OK mole using the values in Table I1 and the Zener" relation AS = PAHIT, where p is a dimensionless thermal coefficient of Young's modulus which is to be evaluated at low values of T/T,, aH is the activation enthalpy, and T, is the melting temperature of the alloy. The resulting value of AG at 1000°C is 25.6 kcal per mole. The Gruneisen constant (p = 3cup/XC,), where p is the density, is evaluated from the room-temperature data in Table I1 after calculating C, from the relation. A value of p = 8.32 g per cu cm based on the value of a. in Table I is used. The result is C, = 5.0 x lo6 erg per g, H = 2.32, and AV = 3.41 cu cm per mole at 1000°C and infinite carbon dilution. It is assumed that the activation volume is not a function of carbon concentration. The theory could be refined to consider AV a function of concentration, but due to the uncertainties in the parameters there seems little justification for this. Carbon dissolved in austenite forms a nonideal solid solution, so that in writing an equation for. the diffusivity of carbon it is necessary to take into account the change in activity coefficient with concentration. The resulting equation is16

Jan 1, 1964

By Barlow S

The Kelian Gold mine project won two excellence awards from the Victorian Division of the Institution of Engineers, Australia. It was a challenging project, fast tracked in a remote and inhospitable tropical environment. The creation of a profitable and efficient mine was a significant engineering and project management achievement. The difficulties encountered and the way they were managed provide valuable lessons. These include the importance of sufficiently detailed engineering in all aspects of the job to enable the best estimates possible to be prepared during feasibility studies, the need to prepare the project scope and execution plan with disciplined and rigorous attention to detail by a highly experienced team and the value of identifying, assessing and mitigating risk and uncertainty during execution. The practical benefits of applying these lessons were demonstrated in the successful management of technical uncertainty on the recent diversion of the Kelian River to allow the expansion of the Kelian mine.

Jan 1, 1997

By E. Ferguson

In evaluating refractory designs for cast house applications, thermal calculations are frequently performed to determine cold face shell temperatures, temperature profiles and metal freeze plane locations within the refractory layer, and heat loss in the steady state condition. A problem arises when looking at molten metal transport crucible designs in that these structures are usually operating under non-steady state conditions throughout their production cycle. Because the molten metal temperature varies with time, and material properties such as thermal conductivity are temperature dependant, mathematical solutions are at best... complicated. This paper presents a relatively simple, iterative solution, that can be set up on a standard computer spreadsheet program, to calculate heat transfer in non-steady state conditions. These calculations can provide curves for (1) molten metal temperature vs time and (2) cumulative heat loss vs time, given variable starting conditions, to aid in the evaluation of molten metal transfer crucible refractory designs.

Jan 1, 2004

(Under this heading will be published notes sent to the Secretary of the Institute by members or other persons introduced by members.) Member, graduate Columbia School of Mines, age 35, married, best of health, dependable, desires position as manager or scout for reliable interests. Experience covers responsible positions incident to the mining and milling of gold-silver, copper, lead, and zinc ores, and the examination of base and rare-metal deposits in United States and Mexico. Salary $3600. Available April 1. No. 453. Member, mining engineer, technical training, age 32, assayer, engineer and superintendent of porphyry copper development, churn drilling and shaft sinking. Examination of prospects and development of gold prospects. Considerable flotation experience. No. 454. Young Columbia graduate, conscientious worker, with experience in inorganic analysis, surveying, draughting, and wit. post-graduate training in geology, desires position wt. prospects. Minimum salary considered, $130 in U. S. and $150 in Mexico. At present employed. Draft exempt. No. 455.

Jan 5, 1918

By E. G. Davis

The Bureau of Mines investigated gaseous direct reduction of low-grade iron ore concentrates in a continuous fluid-bed reactor. These studies were made in a 4-inch diameter fluid-bed reactor using hydrogen alone, and oxygen-or air-reformed natural gas as the reductants. The percent reduction is directly dependent on the mole ratio of hydrogen in the reducing gas to the oxygen associated with the iron oxide in the ore. Two-and three-stage fluid bed tests were simulated by repeated continuous tests. The results showed that percent reduction of the final product was dependent on the mole ratio of the quantity of hydrogen in the gas of each stage to oxygen in the iron oxide of the initial ore feed. Reduction as high as 87 percent in the single stages and as high as 94 percent in the multistages was obtained when either hydrogen or reformed natural gas was used as the reducing gas. Magnetic separation and concentration of the highly reduced fluid-bed product yielded a high metallic iron concentrate analyzing 85 percent total iron and 80 percent metallic iron with total iron recovery as great as 90 percent. Agglomeration of the high-grade metallized concentrate produced hard pellets analyzing 85 percent total iron and 78 percent metallic iron. Green pellets, with good strength, were made without any binder in a drum pelletizer. Direct melting of the high-metallic fluid-bed product in a basic lined arc furnace produced a nearly pure iron which contained 0.09 C and 0.01 P with 95 percent recovery of the metallic iron in the metal.

Jan 1, 1972

By W. E. Foreman, A. Hayatdavoudi, A. Ghalambor

The objective of this investigation was to determine the sensitivity of three selected input parameters in the operational control of continuous bottom fed thickeners used for the treatment of coal refuse slurries. The three variable parameters were "Feed Flow Rate," "Feed pH," and "Feed Solids Concentration." These three input parameters were studied under three cationic-anionic polymeric conditions. For each polymeric condition, two mathematical models were developed, one for overflow response and the other for underflow response. The combination polymers produced the best quality of overflow and underflow. For this polymeric condition, change in the feed solids concentration was the most sensitive factor in the maintenance of the overflow quality, and the feed pH was the most sensitive factor for the maintenance of underflow quality. The mathematical models generated a set of plots that would allow an operator to control and/or adjust any of the three variables to achieve optimum conditions.

Jan 1, 1991

By G. W. Elger

The Bureau of Mines investigated the conversion, at both laboratory and pilot plant scale, of a low-grade ilmenite to chlorination-grade feedstock that could substitute for imported rutile used to produce titanium tetrachloride. The concentrate was derived from the Tahawus, NY, lode deposit of ilmenite-magnetite in rock that contains anorthosite and gabbro. Charges of the ilmenite concentrate, containing 46.6 wt pct Ti02 blended with soda ash, were carbothermically reduced in an electric arc furnace, which separated most of the iron and left a high-titanium slag. However, the slag contained Ca, Mg, and Mn constituents that rendered the material unsuitable for continuous chlorination by causing plugging problems. After being ground and pelletized, the slag was reacted with S02 and air at 7000 to 9000 C, which selectively converted the harmful impurities to soluble compounds that were removed in a subsequent water or dilute HCI leach. In laboratory tests, the combined levels of harmful impurities were decreased from 5 to as low as 0.5 wt pct in leached slags. In pilot plant tests, leached slags sulfated at a rate of 10 lb/h averaged 85.5 wt pct Ti02 with pertinent impurity levels averaging 1.86 wt pct. The leached slag was successfully chlorinated in a laboratory fluidized-bed reactor at 9500 C to extract titanium as TiCI4.

Jan 1, 1986

By RUSSELL S. DAVIES, Andrew Allan, John W. Buch

This is a progress report for the period February 1, 1949, to August 15, 1949, covering experiments with lightweight shearing machines for developing thin, steeply pitching anthracite beds. The over-all objective at the time an underground test section was established on July 30, 1946, was to improve mining above the gangway by developing methods for mechanization of pitch mining. Following the preliminary cutting tests in the gangway with the German machines, it became evident that the use of machines of this type indicated advantages for development work that could not be overlooked and warranted investigation. An agreement was reached with the cooperating company that this be done. Thus, the objectivo in the period covered by this report has been to obtain operating data to uso in comparing hand and machine methods of driving development openings. In obtaining the machine-mining data, 78 feet of gangway, 108 feet of heading, and 80 foot of chute work were driven. Hand-mining data are authentic for the mining condition. It has been shown that full mechanization is two and one-half times as fast as conventional hand methods on a lineal-feet- advance-per-shift basis and costs but little more than one-third as much. Tho machines are air-powered; there is less shattering of the coal bed by blasting; water sprays are used to allay' dust; coal is loaded by machine; no rock is taken; timber is not dislodgod by heavy blasting charges; and it may be said, except for the development of a means for transporting timber to the face, that the tasks for the miner are less arduous, and the working face equally as safe, or safer, than in driving by hand. Face timbering remains the greatest time- consuming cycle item, and steps are being taken to correct this. More than 50 percent of the cycle time is now usod for face-timbering work.

Jul 1, 1951

By G. E. Norman, A. L. Mckague

"The new smelting process commenced operation in 1978. The pelletizing and sinter plants were replaced with slurry-fed roasters and the blast furnaces with electric furnaces. The existing converter aisle and matte handling facilities remained unchanged.Process DescriptionNickel-copper concentrate is partially roasted in two slurry-fed fluid bed roasters. After gas cleaning, the sulphur dioxide gas is transferred to the acid plant. The roaster product is conveyed to two electric furnaces for smelting to produce a waste slag and furnace matte. The slag goes to the disposal area and furnace matte containing the metal values is processed in the converters for further removal of iron and sulphur.The final matte containing about 75 per cent metal values is shipped to the refinery in Norway.The commercial smelter was designed for 2135 tonnes per day of concentrate, with an availability of 85% . Roasters and electric furnaces were sized at 117 per cent of design, or 1250 tonnes per day on each of two lines. Concentrate storage capacity in the plant is sufficient for two to three days' plant operation.The new smelting process will be discussed under the following headings:Concentrate Slurry HandlingFeed PreparationRoaster OperationRoaster Gas CleaningCalcine TransferElectric Furnace Operation and Process Control Converting and Matte HandlingUnder these headings, process control , equipment changes, and plant performance after three years' operation is reviewed. A brief discussion of accident prevention , and working environment is also included ."

Jan 1, 1984

By T. A. Wright

THE SAMPLING of waste materials containing copper, lead and tin has taken on a new significance within recent years, and is of increasing importance, on account of the entry of some of the copper refineries into this field and the tendency towards consolidations among the smelters. In the past, such material was sold on the basis either of a rough or grab sample or of casual inspection of the lot. The two principal sources of this waste are the processes of fabrication and the scrapping of automobile, electrical, plumbing, railroad and other equipment. In both cases much material can be sorted, salvaged and sold by classification and grade to be melted "as is" or with the addition of new or virgin metal. The increasing care in classifying exercised in the large manufacturing plants tends to increase the proportion of this usable scrap; on the contrary, the increasing use of more complex and special non-ferrous alloys tends to make sorting and grading more difficult in turnings, borings, clippings, etc., and consequently is making sampling of more moment. In tin, lead, aluminum, and zinc furnace by-products such as ashes, drosses, skimmings, etc., the trade practice of evaluation has not varied much. For instance, tin drosses, battery lead, and aluminum skimmings are ordinarily sold on what is called' "metallic button" or "metallic recovery" or "metallic yield." Copper and lead waste, however, is being sold more and more on actual copper and lead contents based on sample and chemical analyses. This paper will be devoted chiefly to the sampling of materials suitable only for refining and recovery of one or more of the metals present. The methods described are often based on the fact that but one metal, such as copper, is to be paid for. The loss of volatile constituents in melting does not appreciably affect the final copper result, as the "after-melting" assay can be readily calculated to the "before-melting" basis, but if smelter efficiency continues to increase, so that in time zinc, for instance, may be recovered on a paying basis, the method of sampling dirty brass, for example, will have to be changed also.

Jan 1, 1928

By L. Arbore

Introduction Mine operators are interested in energy conversation in two ways. With our finite sources of energy, we are concerned for future generations. In addition, as mine operators, we want to minimize energy costs. Moving material represents a substantial amount of the energy used in mining operations. Wheeled vehicles are used extensively to move materials. And they derive all their energy from fuel. Energy is also required to overcome the vehicle's inertia, and internal and external frictional forces. Included in the vehicle's frictional forces is its suspension. Tires are an important part of this suspension. What influence do tires have on the overall fuel consumption of the vehicle? Does tire construction affect this influence? As far back as 1896, it was apparent that tires were a factor in fuel consumption. A test was devised in France using a coal-fueled steam-driven auto. The test measured whether there was any fuel savings with the new pneumatic tires rather than of the then commonly used solid tires. The result was a 28% savings in water and a 29% savings in coal on pneumatic tires. Today, the pneumatic tire is accepted, but there are differences in present constructions. Tire Construction: Bias vs Radial There are basically two types of tire construction, bias and radial. Bias tires have been around for about 60 years. Radial tires are more recent. They were developed to improve a tire's ability to withstand higher speeds and loads, as well as to improve tire life and vehicle handling. Another advantage of the radial tire is its lower rolling resistance. This characteristic results in lower fuel use by a vehicle. This has been demonstrated with passenger cars and over-the-road trucks. It is now being demonstrated with earthmoving equipment. A basic description of both types of tire construction should now be reviewed: The casing of a bias-ply tire is made up of crisscrossed textile plies or layers. The cords of these plies run on a bias, from bead to bead. The cords of each ply run on an angle relative to the cords of the adjacent plies. As the tire rolls and deflects, the angle between the cords changes, like the blades on scissors (Fig. 1). The cords of one ply pull one way, and the adjacent ply pulls another, straining each other. This movement generates heat. Since the same layers of cords wrap around under the tread, they

Jan 9, 1984

By Gerard C. Gambs

The electric utility industry is the largest customer of the U.S. coal industry, consuming nearly 50% of present coal production. By 1980, the electric utilities are expected to burn over 500 million tpy of coal or 75% of total coal production. When coal is burned in electric utility plants, ash is produced in one of several forms. These include fly ash, bottom ash and bottom slag. At the present time, approximately 20 million tons of these ashes are produced and must be disposed of by the utilities at a cost of 50[c] to $2 per ton. In 15 years, more than double this quantity will be produced. Only a small quantity of this ash is put to any practical use. Much remains to be done about expanding uses for fly ash and bottom slag.

Jan 1, 1967

The strategy of adjusting operating conditions to maintain optimum process performance as the feed quality varies - adaptive optimisation - is being investigated by computer simulation of chemical processes for the treatment of ores. Those ore-process systems that are most likely to yield substantial benefits from adaptive optimisation are being identified as a guide to the selection and development of systems for practical application. The generalised mathematical representation of the cost structure, ore quality variations, process kinetics, reactor characteristics and operating variables for ore-process systems is described. Results are summarised for temperature, reagent concentration or residence time as the manipulated variable. For almost all systems, adaptive optimisation was economically beneficial, although a few exceptions have been identified where there is a significant synergistic effect between poor-performance and good-performance materials in a blended feed. The sensitivity of the benefits of adaptive optimisation to a range of economic and technical factors is summarised.

Jan 1, 1985

By K. R. Vost

Calculations are given for the reduction in amplitude and change in phase of the diurnal variation in air temperature as the air flows through a mine. The concrete lining of a typical shaft was found to have a much greater effect than the steelwork. An increase in the conductivity of the concrete, or filling of the steelwork with water, did not have enough effect on the rise in air temperatures underground during the day to justify the costs involved. The steel temperature followed the air temperature much more closely than the concrete temperature did. Calculations are given for the heat stored in steel and concrete during the day.

Jan 1, 1980

By William M. Gleason

When SME’s 2006 Arizona Conference convened in December at the Hilton El Conquistador Resort in Tucson, AZ, there was considerable excitement among the 387 attendees. There was a noticeable buzz surrounding the progress of Phelps Dodge’s Safford copper mine in southern Arizona, one of the first new major copper mines to be permitted in more than 30 years in the United States. There were also plenty of good feelings about the mining industry in general. Commodity prices remained high and with no signs of a slowdown in the immediate future. Things were good in Arizona. But there were also cautionary tones at the conference and the Mining Foundation of the Southwest banquet that preceded it.

Jan 1, 2007

By A. M. Gaudin, D. W. Fuerstenau

By streaming potential techniques, the zeta potential of quartz has been measured as a function of the concentration of dodecylammonium salts at different pH values. These experiments indicate that adsorption of dodecylammonium ions takes place as individual aminium ions until a certain critical concentration is reached in the double layer, at which point the adsorbed collector ions begin to associate into patches of ions, called hemi-micelles. Because of its effect on the surface potential of quartz, pH controls the adsorption of dodecylammonium ions. The value of cooperating agents and nonionized constituents of flotation systems is discussed. A PREVIOUS investigation' of the role of pH in the flotation of quartz with anionic collectors is here extended to an inquiry of how the cationic collector, dodecylammonium acetate, is adsorbed at the quartz-solution interface. The equilibrium amount of this collector adsorbed by quartz has already been measured as a function of concentration and pH.2,3 The weight of prior evidence has suggested that two mechanisms are involved in the adsorption of this collector by quartz, but with existing adsorption measurements alone it is not possible to determine what the mechanisms are. Gaudin and Bloecher2 postulated that a polymolec-ular adsorption coating begins to form before the first monolayer has been completed. Gaudin and Morrow4 indicated that a similar situation might exist in the film of dodecylammonium ions on hematite. A study of electrokinetic potentials at the quartz-solution interface provides some detail toward a fuller understanding of the adsorption mechanism. Experimental Results The zeta potential at the quartz-solution interface was calculated from streaming potential data measured with the apparatus described in detail in a thesis by Fuerstenau5 and briefly in a paper by Gaudin and Fuerstenau.1 The quartz used in these experiments was a 48/65-mesh fraction prepared in the manner described previously.' Zeta potential of quartz was obtained for various amounts of the amine salt at pH 4, 7, 10, 11. In

Jan 1, 1956

By Morris Muskat

A theory is presented for calculating the performance history of complete water-drive systems producing from idealized stratified formations. The general equations are applied to systems where the permeability stratification is either of the exponential or linear type. Calculations were carried through for different degrees of permeability stratification, but with special emphasis on the effect of the mobility ratio between the produced oil and the invading water on the resultant performance. These results are also expressed graphically as curves for the initial water breakthrough recovery, for the different degrees of stratification, as a function of the mobility ratio, and of the composition of the produced fluid stream as a function of the cumulative oil recovery. For several typical cases the latter has also been plotted as a function of the cumulative oil and water throughflow. The general result is that when the mobility of the oil is lower than that of the invading water the channelling tendency resulting from the permeability stratification becomes aggravated as the higher permeability zones become flooded out. Situations of this type would obtain when producing low gravity or highly viscous oils. Conversely, if the mobility of the oil is high compared to that of the invading water, the flooding of the high permeability zones will lead to a retarding and choking effect, and the gross bypassing phenomena will be partially suppressed. These conditions would correspond to those of flooding high gravity or low viscosity oils. A discussion is given of the various basic assumptions made in the analysis, including that of ignoring the stripping phase of the production history as implied by relative permeability concepts. INTRODUCTION The physical ultimate recoveries from oil reservoirs are basically determined and limited by the physical oil displacement processes associated with the reservoir producing mechanism. In practice, however, the economic ultimate recoveries are further limited by the mobility of the reservoir fluids and the uniformity and continuity of the producing formation. In fact, it is the differential depletion between the component parts of the composite reservoir which ultimately determines the total recovery at the time of field abandonment. While this observation applies to both the solution gas drive and gravity drainage mechanisms, in which use is made only of the energy contained within the original oil-bearing reservoir, it is of even more paramount importance under operations wherein the energy associated with extraneous fluids provides the ultimate oil expulsion mechanism. Whether the invading fluid is the water from an edgewater drive, water injected for pressure maintenance, gas injected for pressure maintenance, or gas returned to the formation in a cycling program, it is often the continuity and uniformity of the producing section which will control the economic efficiency of the operations. The importance of the problem of reservoir non-uniformity does not, of course, lessen its complexity or the difficulties of its solution. In fact, these are inherently such that the concept of a "general" solution is virtually meaningless. About all that can be reasonably hoped for is the analysis of specific and well-defined types of non-uniformity which may give some degree of approximation to actual reservoir conditions. Since variations in the nature of the reservoir which depend only on the position along the streamlines will not lead directly to major differential depletion development within the reservoir, the types of non-uniformity considered thus far have involved stratification assumptions. That is, the producing section has been replaced by a multi-layer "sandwich," each uniform areally, and differing from the others only in its basic physical constants as to thickness, porosity and permeability. The fluid motion in the composite system is thus approximated by a parallel superposition of the independent fluid movements in the individual strata. For the specific application to cycling operations the theory of the effect of permeability stratification has been developed for both discontinuous' and continuous types of permeability stratification. Among the latter, treatments have been given of systems in which permeability distributions are governed by exponential, linear' or probability3 functions. In all these studies complete dynamical equivalence was assumed between the injected dry gas and the displaced wet gas. The overall effective permeability of each stratum was therefore considered as constant and independent of the degree of invasion of the injected fluid. In the case of the displacement of oil by water, the assumption of dynamical equivalence between the water and oil will be strictly valid only by accident. Even if the oil viscosity should be the same as that of the water, the effective permeability to the oil in the presence of the connate water will in general be quite different from that of the water behind the water-oil interface flowing past the trapped residual oil. As a result the effective permeability for the stratum as a whole and rate of water invasion will change with time as the intrusion continues. The differential fluid motion in the individual strata will thus also vary with time. Qualitatively, it is easy to predict the resultant effects. If the permeability to viscosity ratio of the invading fluid exceeds that of the fluid displaced, the stratification and bypassing effect of the perme-

Jan 1, 1950

By R. G. Agarwal, Ramey Jr. H. J., Al-Hussainy R.

Although it has long been realized that gas recovery from a water-drive gas reservoir may be poor because of high residual saturations under water drive, it appears that only limited infomlation on the subject has been available until recently. This study was performed to show the qiiantitative potential importance of water influx. Results indicate that gas recovery may be very low in some cases: perhaps as low as 45 per cent of the initial gas in place. Gas recovery under water drive appear to depend in an important was on: (I) the prodirction rate and manner of production; (2) the residual gas saturation; (3) aquifer propertie.); and (4) the volumetric displacement effciency of water invading the gas reservoir. The manner of estimating water-drive gas reservoir recovery can vary considerably. Examples are: the steady-state tnethorl. the Hurst modified steady-state method, and various unsteady-state methods such ac. those of van Ever-dingen-Hurst, Hurst, and Carter-Tracy. The Carter-Tracy water influx expression was used in this study. In certain cases, it appears that gas recovery can be increased significantly by controlling the production rate and manner of production. For this reason, the potential importance of water influx in particular gas reservoirs should he investigated early to permit adequtrtr planning lo optirtize the pay reserves. INTRODUCTION In recent years, the economic importance of natural gas production has become increasingly apparent. This has been evidenced by more intensive exploration efforts aimed at gas production, and exploitation of both deep, as well as low-permeability gas reservoirs. Technical developments such as deep-penetration fracturing have made development of such formations economically feasible. Unfortunately, water influx has forced abandonment of a number of gas reservoirs at extraordinarily high pressures. Although reservoir engineering methods for estimating water influx have long been available, it appears that application of these methods to the water-drive gas reservoir has been sporadic.'a Available methods for estimating water influx which can be applied to the water-drive gas reservoir problem include the steady-state method,1 the Hurst modified steady-state method and various unsteady-state methods such as those of van Everdingen-Hurst. Hurst, and Carter-Tracy. Interesting applications of these solu- tions to gas reservoir and the aquifer gas-storage problems have appeared recently.3,12,14 The experimental study of residual gas saturations under water drive by Geffen et al. in 1952 indicated that residual gas saturations could be extremely high. A value of 35 per cent of pore volume is often used in field practice when specific information is not available. The study of Geffen et al. showed that residual gas saturation might be much higher in some cases. Naar and Henderson concluded that the residual non-wetting phase saturation under imbibition should be about half of the initial non-wetting phase saturation. The Naar and Henderson result that residual gas saturation under water influx should be about half the original gas saturation is recommended as an estimate if laboratory measurements are not available. Thus, it is clear that a considerable portion of the initial gas in place might be trapped in a water-drive gas reservoir as residual gas at high pressure. A full water-drive would result in loss of residual gas trapped at initial reser.voir pressure. Consideration of transient aquifer behavior leads to the conclusion that high-rate production of water-drive gas reservoirs could result in improved gas recovery by reduction of the abandonment pressure. However, there appears to be little quantitative information on this possibility. One of the few advantages of water-drive gas production appears to be improved deliverability through water-drive support of the reservoir pressure. There may also be an advantage in higher condensate recovery caused by pressure maintenance for gas-condensate water-drive reservoirs. In view of the preceding, this study was made to assess the potential importance of water-drive in gas reservoir engineering. The Carter-Tracy approximate water-influx expression was used because this equation offers some advantages in hand-calculation which do not appear to have been generally recognized.' However, calculations were performed in the main with a high-speed digital computer to permit evaluation of the effect of water-drive under a large variety of conditions. CALCULATION METHOD Water-drive gas reservoir performance can be estimated in a manner completely analogous to oil reservoir calculations: a materials balance is written for the reservoir, and a water influx equation is written for the aquifer. Siniltaneous solution provides the cun~ulative water influx and the reservoir pressure. When reservoir performance data (gas produced and reservoir pressures) are available, it is usually possible to match performance data to determine the initial gas in place and the water influx parameters —

Jan 1, 1966

By T. A. Toney

With new lightweight designs, spirals have become standard equipment in coal preparation plants worldwide. To their credit, spirals typically show very low coal losses to the refuse stream under most operating conditions. However, spirals do tend to separate at cut points in excess of 1.80 S.G. Attempts to obtain lower cut points have typically resulted in coal losses to middlings. Middlings retreatment with secondary spirals is therefore becoming common place. Other forms of retreatment with water-only cyclones, hydrosizers, and recirculation have been attempted with some success. This paper reports on a novel (Patent Applied For) approach to retreating spiral middlings m a heavy-media-cyclone circuit.

Jan 1, 1998