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By R. E. Wagner

MISSOURI's famous lead area, in what is known as Southeast Missouri, is locally termed the "Lead Belt." These deposits are in the Bonne Terre dolomite of late Cambrian age which has a thickness of nearly 400 ft. Underlying this is the La Motte sandstone which varies in thickness from 0 to 400 ft. The La Motte beds are deposited directly on the ancient erosion surface of Pre-Cambrian porphyries and granites of probably Algonkian age. The buried igneous peaks extend up into the Bonne Terre in several areas within the Lead Belt. Overlying the Bonne Terre are shales and siliceous dolomites of late Cambrian and early Ordovician age. Within the Lead Belt these have a thickness of from 0 to 500 ft. The district is bounded in general on the southwest by the Sims Mountain fault, on the northwest and north by the Big River fault, and on the

Jan 1, 1947

By O. S. True, C. H. Herty

It is well known that manganese will desulfurize molten iron through the formation of manganese sulfide, which, being only slightly soluble in the metal, rises to and enters the slag where it remains as such (mixer slag) or is converted partly or wholly to calcium sulfide (basic open-hearth slag). The reaction by which manganese sulfide is formed is Mn + FeS = MnS + Fe. This reaction is generally considered to be reversible, although McCancel states that such is not the case. The experimental work was carried out to confirm the results of Roh12 as to the reversibility of the reaction. Six trials are herein considered. In each 200 gm. of electrolytic iron free from manganese and sulfur were melted in a pure zirconia crucible in a carbon resistance electric furnace. To the melted iron in runs 2, 3 and 4 metallic manganese and manganese sulfide were added to give 1, 2 and 4 per cent. manganese respectively, with 0.50 per cent, of sulfur in each. In runs 5, 6 and 7, metallic manganese and iron sulfide to give the same proportions of. manganese and sulphur as in runs 2, 3 and 4, were added. The melts were held molten in the furnace for an hour and then cast into small ingots. The results of these melts are as follows: Ingredients of Charge Analysis or InRot ManOaneBe, SulfUR, ManOaneBe. SULFUR, Run Material Charged PeR Cent. PeR Cent. Per Cent. PeR Cent. 2 MnS + Mn............... 1.0 0.452 0.636 0.367 3 MnS + Mn............... 2.0 0.50 1.57 0.310 4 MnS + Mn............... 4.0 0.50 2.81 0.230 5 FeS + Mn................ 1.0 0.50 0.647 0.397 6 FeS + Mn................ 2.0 0.50 1.45 0.374 7 FeS + Mn................ 4.0 0.50 2.73 0.195

Jan 1, 1925

By R. V. Ramani, G. W. Luxbacher

The approach proposed in this paper is, as stated by the authors, an update of methods well discussed in the literature. The authors are to be congratulated for their excellent effort in quantifying a difficult problem with realistic cost data. Economic analysis of the components of a mine ventilation system is complicated by both the dynamic nature of the system and the uncertainty as to the time when system changes occur. We wish to address three specific areas of this paper which require further consideration: shaft designed air capacity, shaft location, and economic criteria used within the analysis. With regard to ventilation shaft size optimization, the system complexities are illustrated in the quantity flow through the shaft. Obviously, the capacity chosen by the designer is a static parameter while the utilized capacity is usually a dynamic variable over the life of the shaft. The designed capacity may be used for a short or a long period, and this may occur during the beginning, middle, or near the end of the shaft life, leading to different operating costs at different times. Operating costs, as shown by the authors' Eq. 8 are more dependent on air quantity than any other single factor (quantity cubed as compared with other factors to the single power); hence, extreme accuracy in the assessment of some of the other factors discussed by the authors may be secondary to the quantity estimation. Incorporation of a variable usage factor for air quantity over the life of the shaft in this optimization problem deserves some consideration. Although the authors have chosen to examine optimum ventilation shaft sizing, it must be remembered that optimization of the whole system-is the primary objective of any optimization process; unit optimization of such items as shafts may not complement the overall process. We have discussed this subject in some detail in another paper in this Transactions volume (Luxbacher and Ramani, 1979). While the recommended process by Wang, et al. can be used in shaft sizing, the shaft operating conditions (pressure head and air quantity) are intertwined with the shaft location within the mine infrastructure:

Jan 1, 1980

By Basil B. Zavoico

ALTHOUGH the American petroleum industry was affected by the Second World War from its early beginning it was not until Dec. 7, 1941- that the industry was placed on full war footing. Even throughout most of 1942 the American overseas operations were limited and not until late in the year did expansion of military activities, more particularly the offensive in North Africa, affect the domestic supplies to such an extent that critical deficiencies developed locally in this country, particularly along the East Coast. The definite outlook for greatly expanded offensive operations by the United States on both Atlantic and Pacific fronts makes certain that during 1943 the domestic situation will. not be alleviated; rather it may become even more critical even though additional transportation facilities, now being built and planned. will be completed from the southwestern producing states to the East Coast.

Jan 1, 1943

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By A. J. Griest, P. D. Frost, J. R. Doig

During the past 5 years, research directed toward the development of titanium alloys having improved strength-ductility relationships and heat treatability has been carried out at Battelle for the U. S. Air Force.1"3 In the course of this work, a method of heat treating ß-stabilized titanium alloys was developed which produced a wide range of useful properties.4 The heat treatment consisted of two steps: a) solution treating at temperatures in the a-ß phase region, and b) overaging at a lower temperature in the range 800°to 1100°F. Corollary to the alloy development work, research was conducted on the mechanism of the heat-treatment reaction. The investigations of Frost and co-workers on isothermal transformation in Ti-Cr5 and Ti-Mn8 alloys disclosed the existence of the transition phase, w, during the course of the decomposition of metastable ß phase. Subsequent work at Battelle7,8 'and at Case Institute by Brotzen and co-workerss further clarified the nature of the decomposition process. Beta decomposition was found to proceed by the following series of reactions: 1 2 3 4 a + Ti, My (in eutectoid systems). ßo, ßr, and ßU refer to ß phase of original, enriched, and ultimate alloy contents, respectively. Omega is a transition phase having a complex structure. 10-13 Step 4, of course, occurs only in ß-eutectoid systems. This paper presents data correlating transformation behavior with mechanical properties for the following alloys: Ti-8Mn, Ti-8Mn-2A1, Ti-4Mn-4A1, Ti-6Al-4V, and Ti-4Fe. The isothermal decomposition of ß in titanium-manganese alloys of similar composition has been investigated by Frost and coworkers8 and the effect of various annealing treatments on alloys in this system has been studied by Holden, Ogden, and Jaffee.14 The compositions Ti-8Mn-2Al, Ti-4Mn-4A1, and Ti-6A1-4V, were studied in the present work in an effort to define more clearly the effect of aluminum on the response to solution and aging treatments. Ogden, Holden, and Jaffee15 have invesitgated the effect of aluminum on the response of a similar alloy (Ti-8.8Mn-2.46A1) to annealing treatments, and Luini and Lee16 have made an exploratory investigation of the heat-treatability of the Ti-4Mn-4Al alloy. The Ti-4Fe alloy was studied as an example of a moderate1y active eutectoid system. Holden, Ogden, and Jaffee 17 have studied Ti-Fe alloys and have presented some hardness data for aging at 400°C for alloys of Ti-2.56, 5.01, and 7.35 iron after quenching from the a-ß field (750°C). EXPERIMENTAL PROCEDURES The experimental procedures generally used in the precipitation-hardening study are outlined in the following sections. Departures from these techniques are noted in the discussions of the individual alloys. Table I presents the nominal and actual compositions of the alloys studied, together with the swaging and rolling temperatures. In all cases, these temperatures were in the a-ß field and the microstructures consisted of an equiaxed a-ß mixture. Melting and Fabrication—Except for the commer-

Jan 1, 1960

By W. A. Backofen, D. Lee

Titanium of commercial purity (RC-70) and two all-a (hcp) alloys (4Al-1/4O2 and 5Al-2.5Sn) were tested in sheet form under conditions of combined-stress loading. Plane-strain compression and plane -strain tension together with uniaxial compression and tension provided information for constructing the tension-tension and compression-compression quadvants of the plane-stress yield locus. Coordinate values were obtained from yield-strength measurements; the slope at each point was based on a plastic-strain ratio. The materials represented a wide range of plastic anisotropy, which was reflected in correspondingly varied departures of the yield locus from that for iso-tropy. The tension-tension and compression-compression quadrants were not identical. If the uniaxial yield strength is insensitive to direction and the sign of the applied stress, the Mises or perhaps the Tresca criterion is adequate for predicting the onset of yielding under combined-stress loading. The prediction is not so straightforward in plastically anisotropic material. Depending upon details of texture, combined-stress yielding resistance may be substantially different from that indicated by the usual criteria.' However. a continuum theory of yielding under such conditions is available for reasonably direct application.2,3 Whether or not it can be used successfully must, of course, depend upon how closely the conditions of the theory are satisfied in the material in question. In its present form the theory contains no provision for Bauschinger-type effects, nor does it allow for the consequences that might grow out of deformation by more than one mechanism, e.g., by slip and twinning.4 With those limitations, more importance must be attached to experimental information about the yield surface for anisotropic materials. Studies of the yield surface have generally been confined to states of plane stress (tension-tension and tension-compression) established in thin-wall tubes by externally applied forces and internal pressure. That approach would be entirely suitable for anisotropic materials if they were available in tube form or in sufficient bulk to be machined into test specimens. 6-9 It would not serve for the textured and anisotropic sheets of much current engineering interest, unless sheet could be formed into high-pressure tubing without structural change. Since there would seem to be little chance of the latter, practical alternatives are needed. One such alternative is the subject of this paper. It involves the use of a few selected but relatively simple uniaxial loading tests on sheet specimens. The underlying idea is presented here with some details relating to application and a few results bearing on how well it has worked. THE BASIS OF TESTING Conventional Measurements. Yielding for a general case of anisotropy is described by the plane-stress locus in Fig. 1. Reference directions in the sheet specimen are related to the stress coordinates as shown with the insert: x is the rolling direction, y the transverse direction, and z the through-thickness direction. The four reference-direction yield strengths (t, tension; c, compression), Xt, Xc, Yt, and Yc, are all different. Nine paths that can be followed in uniaxial loading experiments are identified. Paths 1, 2, 3, and 4 represent conventional tension and compression testing to establish Xt, Yt,.Xc, and Yc. Useful information also comes from the ratio of the transverse plastic-strain components associated with yielding and flow in conventional tension or compression. A condition to be satisfied in locus construction is that the plastic-strain vector be everywhere normal to the locus.10 The projection of the vector which would

Jan 1, 1967

By R. A. Burton, J. T. Hansford, D. A. T. Donohue

Substantial evidence indicates that many petroleum producing horizons contain naturally occurring, ordered fracture systems and that within a particular geologic zone, vertical fractures induced in wellbores often will be directed along a particular compass direction. Both conditions will seriously alter the fluid displacement behavior within reservoirs. In this study the effect of induced fracture orientation and length on sweep efficiency is determined for a five-spot pattern. In general, it is assumed that all wells are fractured and directed along the same compass direction. Using the electrical analog to steady state, two-dimensional fluid flow in porous media, boundary conditions are obtained from which flood fronts are tracked numerically. The numerical computations require a particle tracking routine for approximating flood front histories. It is shown that recovery is sensitive to the length and orientation of fractures for the pattern studied. with the proper design of fracture-pattern systems, recovery can be enhanced considerably. INTRODUCTION Hydraulic fracturing introduced in 1949l gave the industry a rather inexpensive means of increasing the fluid injection or production capacity of wells. It has been used with particular success to increase the production rate of wells completed in tight formations, such as in western pennsylvania2 where producers have fractured in depleted or near-depleted fields and observed economic responses. Once the natural energy declines in such a reservoir where all wells have been fractured, waterflooding is generally suggested as means of further increasing recovery. Of the dual objective sought in waterflooding — high injectivity and high breakthrough sweep efficiency — the former condition can be obtained if all wells in the flood pattern are fractured; the latter condition should depend on the nature of the fracture system. Considerable theoretical work has been published on the nature of fractures induced in boreholes.3-5 Although discussion persists concerning the possibility of forming a horizontal fracture at a given point within the wellbore, it is generally conceded that only vertical fractures will develop below a given depth, i.e., where the fracturing Pressure is less than the overburden load. Given the fact that fractures will be vertical in most cases of interest, it is also important to know whether there is order to fracture orientations within a given geological region. Kehle has suggested that in tectonically relaxed areas of uncomplicated geology, the stresses are fairly uniform and all fractures in the region should be parallel.5 Dunlap arrived at a similar conclusion in a theoretical investigation of localized stress conditions surrounding the borehole.6 He concluded that most vertical fractures are propagated in a preferred azimuthal direction. Fraser and Pettitt, in extending these theoretical suggestions to a specific field case, used an impression packer to record both a vertical fracture and the orientation of this fracture in the wellbore of a well in the Howard Glasscock field, Tex.7 Use of this information enhanced the waterflood recovery of the field. Anderson and Stahl also used impression packers on three fractured wells in the Allegheny field. N. Y.. and found that the fractures were oriented more or less along the same compass direction.8 Orientation of the fractures in this manner depends on the stress condition within the formation during fracturing. Elkins and Skov have demonstrated that a natural, oriented, vertical fracture system exists within the Spraberry field? Heck suggests

Jan 1, 1969

By D. J. Carney, E. Van Meter, J. J. Oravec

A study was made of combustion-air temperatures and factors affecting air temperatures in the open-hearth regenerative systems. Air-temperature surveys in the regenerative system revealed marked thermal gradients in the air above the checkers. The design of the fantail-uptake region plays a prominent part in increasing the heat recovery of the regenerative system. THE efficiency of the open-hearth regenerative system is one of the most important factors affecting open-hearth performance. Until recently, this factor has not received the attention in the literature given to many other items affecting performance, such as the type of charge, speed of charging, and the mechanical equipment of the open hearth. J. S. Marsh' emphasized the importance of the flame temperature and its dependence upon the combustion-air temperature. By means of measured air temperatures in open-hearth furnaces, data were presented which showed a remarkable degree of correlation between production rate and combustion-air temperature. This correlation was extremely good in view of the numerous factors, other than air temperature, which affect open-hearth production rates. In Marsh's work, a 100°F increase in air temperature reduced the heat time by approximately 45 min. Realizing the importance of combustion-air temperature, it is desirable to know which factors control the regenerative efficiency of the open-hearth furnace. B. M. Larsen recently discussed this subject.' The present paper illustrates a few of the more important items that affect regenerative efficiency and combustion-air temperature. In the latter part of 1951, a study of open-hearth combustion-air temperatures was begun at the South Works of the United States Steel Corp. In the initial work at open-hearth shop X, which produces low carbon steel products, temperatures were measured in the uptake in a manner similar to that used by Marsh' and the results obtained were very similar to the Bethlehem data. When it was decided to expand the study of combustion-air temperatures, open-hearth shop Y was selected because of the greater variety of furnace-design features, types of steel produced, and firing rates used. With the use of aspirating thermocouples, continuous gas analyzers, thermocouple and optical pyrometers, a study was made of: 1—effect of combustion-air temperature on open-hearth production rate, 2—thermal gradients present in various zones of the regenerative system, 3—effect of furnace-design variations on air temperature and heat recovery, 4-—effect of furnace-operating variables on heat recovery, and 5—variation in heat recovery with furnace age during the normal furnace campaign. Data collected on individual heats at 15 min intervals included air-flow rate, firing rate, checker temperature, combustion-air temperature, and furnace pressure. These data were collected on approximately 230 heats of steel. In addition, information was obtained at random on air infiltration and combustion-gas compositions. The data gathered have shown the desirability of closer control of open-hearth firing practices, a need for reducing air infiltration in the uptake zones, and a need for further study of design of checkers and of uptake-fantail areas. Equipment Air is practically a nonradiating medium. Consequently, in the measurement of air temperatures, the principle of heat conduction must be used rather than heat radiation. For this reason, aspirating-type thermocouple pyrometers normally are used to measure air temperatures. With these devices, air

Jan 1, 1956

By D. A. Flanagan, B. L. Landrum, P. B. Crawford, B. C. Norwood

Herern is described a heat conduction model which has been developed to predict the pressure distribution within a reservoir being subjected to rrnsteady-state depletion. Although potentiometric models have been widely used to study reservoir pressure distribution, their application is limited to the study of steady-state cases. Electrical analyzers may be used to study unsteady-state phenomena, but their application and simulation have certain limitations. Much of the now accepted theory of unsteady-state fluid flow in porous media has evolved from previous heat conduction knowledge. An analogy between the flow of fluid in an unsymmetrical reservoir and con-duct ion of heat in a similarly shaped unsymmetrical metal plate is made to show adaptability of the hear conduction principle to transient reservoir cases. A description of the model and necessary instrumenrarion is included. Data show influence of well location on pressure distribution during unsteady-state deple[ion. Application of results is made to a hypothetical reservoir and to a reservoir located in an irregular aquifer. INTRODUCTION Development of methods for predicting behavior of petroleum reservoirs has resulted partially from adaptation of electrical and thermal flow concepts to the flow of fluids through porous media. Extensive investigation of electrical and thermal flow problems has resulted in mathematical solutions applicable to many reservoir problems. The relative ease of measuring electrical flow has brought wide acceptance of the use of the potentiometric model to study certain field problems. Potentiometric models are restricted to the study of steady-state conditions because of the instantaneous response of electrical flow to changes in the applied potential. The electrical reservoir analyzer has been one of our most useful instruments for studying certain phases of unsteady-state behavior1. Other than approximation techniques, no method exists for determining pressure distribution in an irregular reservoir during primary depletion. Heat flow, like fluid flow, is inherently transient. The model described here was developed to use this transient nature of heat flow, measurable in the laboratory, to simulate transient flow of fluids in the porous medium of the reservoir above the bubble point. A metal plate shaped like the reservoir to be studied was heated by a "well" source. Temperature increase in the plate is analogous to pressure decline in the field if the field is being depleted, or pressure increase if fluid is being injected. This study is intended to determine the feasibility of using the transient nature of the heat flow to study the transient behavior of fluid flow. It is hoped that this new technique will aid in the understanding of one of the more complex phases of reservoir engineering. THE FLUID FLOW-HEAT CONDUCTION ANALOGY The similarity of the equations which describe the flow of fluids through a porous medium and the conduction of heat through a solid is well known2. Rate of flow of fluids is given by Darcy's law3. while the rate of flow of heat is given by Fourier', (I,, - KA 4T........(2) Combining Eq. 1 with the equation of continuity for a compressible liquid", i.e.,results in Expressing y in terms of the compressibility, i.e., pr = peey ,..........(5) and by expanding the exponential and neglecting higher orders of cp one can obtain

By H. H. Rachford, D. S. Howard

In the withdrawal of fluids from tilted aquifers it is of value to be able to predict pressure patterns during the course of the pressure decline. As an example of this, in the displacement of fluids from oil reservoirs being produced by water-drive, prediction of the reservoir pressure is an important factor in fixing production rate. The prediction of pressure patterns in the depletion of an inclined aquifer has conventionally been made by solving the well known flow equations for the pressure Patterns in a horizontal aquifer, and correcting these patterm for the pressure difference due to the hydrostatic head associated with the vertical distance between a point in the horizontal aquifer and the corresponding point in the tilted aquifer. Inasmuch as the equation describing flow in tilted strata is different from that for horizontal flow. there was question as to the validity of the simple corrective procedure current1y in use. To examine the magnitude of error made using this procedure, an inclined aquifer was chosen for which the error was expected to he large, and the equation for flow in this tilted stratum was solved numerically. The results of the conventional procedure of correcting the solution of the equation for horizontal flow was compared with the solution of the correct equation by studying the difference between predicted pressures by the two methods. Three forms of the hydrostatic head correction were studied. The results for all three forms of the head correction are similar. The error in the approximate solution is quite dependent on the position of the horizontal aquifer with respect to the inclined one. The error is greatest at the producing end ad increases with amount of fluid withdrawn. The magnitude of the errors is not large if a good choice is made for the position of the horizontal datum. The most satisfactory position for the datum in all cases is near or slightly about the mid-point of the inclined stratum. Use of the best approximate method studied with the best datum tested yielded predicted pressures in error no greater than 7 psi. INTRODUCTION The movement of water by expansion from an aquifer to displace fluids from a contiguous oil reservoir was first recognized over 20 years ago.9 Since that time much work has been done to relate this mechanism to reservoir behavior mathematically. The result of this effort on the part of many workers has led to an understanding of underground fluid movement which has enabled us to follow and predict the behavior of the water-drive reservoir. One reason that good progress has been made in the application of mathematics to the study of pressure patterns and water movements in aquifers has been that the differential equation which describes this process is of a relatively simple form. The equation for the isothermal, horizontal, viscous flow of water through homogeneous sandstone is identical with that for the diffusion of heat through homogeneous solids, and this equation and means of obtaining solutions for it with many types of boundary conditions have been studied extensively. That this work has been highly successful is clearly emphasized by the large number of solutions developed for problems of interest both by methods of formal mathemat-

Jan 1, 1957

By R. E. Holmes, T. W. Leland

The solution to the unsteady-state mass- and heat-transfer equations describing the adsorption of a dilute component from a gas stream flowing through a packed bed is readily applicable to the design of hydrocarbon recovery units. The solution to these equations depends on the assumption of a linear equilibrium equation to relate concentrations on the surface to concentrations in the gas. This assumption is shown to be justifiable for components which are very dilute in the gas stream. This approach permits the prediction of the effects of bed shape and size, cycle time, and gas mass velocity on the recovery of each component. It also allows the time and gas flow rate needed for regeneration to be determined. The equations involve a constant for each component and another constant characterized by the type of adsorbent. These constants must be evaluated from operating data. Values of these constants determined for silica gel are presented. This paper points out the type of experitrrental data needed for a thorough design of hydrocarbon adsorption units. INTRODUCTION The growing importance of adsorption processes to recover hydrocarbons from natural-gas streams has created an urgent need for better methods to design and predict the performance of these processes. Since the original use of solid adsorbents in natural-gas processing was for dehydration, most of the current design methods for hydrocarbon recovery re extensions of those developed earlier for dehydration. These methods are based on an adsorptivity or bed loading factor defined as the amount of a particular component adsorbed per unit weight or per unit volume of the packed bed. The recovery of a given component is then expressed as an empirical function of its adsorptivity on a given adsorbent. In spite of the simplicity and initial utility of these methods, they are not completely satisfactory in that they do not predict the effect of the dimensions of the bed in relation to flow rate and cycle time, and do not predict the distribution of various components along the length of the bed. It is possible, however, to make a considerable improvement in the design of these processes by applying the basic equations of mass and heat transfer applicable to gases containing small concentrations of adsorbing components flowing through granular beds. These equations have been developed and solved by Anzelius,' Furnas,% nd Hougen and Marshall." where G = mass velocity of the inert constituents (assumed to be methane), lb/hr-sq ft, y = weight of an adsorbing component in the gas per unit weight of inert, lb of a given constituent per lb of methane, x = bed length, ft, p, = packed bed density, lb/cu ft, P, = gas density, Ib/cu ft, f = void fraction in the bed, t = time, hours, and w = weight of a given component adsorbed per unit weight of adsorbate free solid, Ib/lb pure adsorbent. The term on the left side of Eq. 1 represents the flow rate per unit bed volume of a component entering less the flow rate per unit bed volume of that component leaving the differential bed length. The terms on the right side represent, respectively, the accumulation rates per unit bed volume on the solid and in the gas phase within the differential bed section. The last term is negligible for this application since pgfv is quite small in comparison with p, and G. The partial differential is determined by the mass-transfer rate between gas and solid in the differential section.

By M. A. Selim, W. H. Somerton

Thermal expansions and heats of reaction of three typical sandstones were measured in the temperature range of 25°to 1,000°C. The significance of these data in subsurface heat-transfer calculations is discussed. Linear thermal expansions were measured both parallel and perpendicular to the bedding planes. Volume expansions are reported as the perpendicular expansion plus two times the parallel expansion. Expansion behavior of the sandstones was found to be controlled by the expansion characteristics of the quartz content. Differential expansion of the quartz grains and other minerals included in the sandstones caused permanent deformation of the heated samples after they were cooled to room temperature. Structural damage resulting from heating is probably an important cause of the reduction of thermal conductivity of heated samples. Measurements of heats of reaction were based on the known heat required for a- quartz inversion. Thermal reactions, which probably include deby-droxylation of clay minerals and decomposition of carbonate minerals contained within the samples, were found to require more than one-fourth of the amount of heat necessary to raise the temperature of the rock alone. In shales and limestones, the reaction heat could be substantially greater than that required from specific heat considerations alone. INTRODUCTION In earlier work, l-3 methods of measuring thermal properties were developed and thermal data for several sedimentary-rock types were reported. Data included thermal conductivity, specific heat and thermal diffusivity. In addition, calculations of heat transfer in subsurface formations may require data on the thermal-expansion characteristics of rock and the heats of reaction of mineral constituents. Thermal expansion of rocks is relatively small in magnitucle and, from the standpoint of change in bulk density, has only minor effects on heat-transfer cliaracteristics. Thermal-expansion behavior, however, may have significant effects on the structure of rocks. Differential expansion of different minerals and along different crystal-lographic axes may result in structural damage which could effectively reduce the thermal conductivity of the rock. Many mineral constituents of sedimentary rocks undergo phase or related changes when heated to sufficiently high temperatures. Although some of these reactions (such as the a-ß quartz inversion) are reversible and the heat absorbed is returned to the system upon cooling, many of the major reactions are irreversible. Through certain temperature ranges, the additional heat energy required to complete the reactions may be nearly as great as that necessary to raise the temperature of the rock in the absence of thermal reactions. If the heat requirements for these reactions are not considered, serious errors in heat-transfer calculations may result. Thermal-tzxpansion and thermal-reaction data have been obtained for three typical sandstones. Methods of measurement and results obtained are reported and discussed in the following. THERMAL EXPANSION OF SANDSTONES The linear expansions of three outcrop sandstones (Bandera, Berea and Boise) have been measured in the temptbratue range of 25° to 1,000° C. Expansion measurements were made in the directions parallel and perpendicular to the bedding. The differential expansion apparatus used is that described by Mitoff and Pask.4 The test sample is heated in an electric furnace with a temperature rise of 6°C/minute. The lengthening of the samples upon heating is compared with the small and known expansion of a fused silica rod. The change in length is transmitted to an X-Y recorder by means of a Statham transducer. A maximum error of ± 1.5 per cent has been obtained with this apparatus

By E. R. Buchanan, R. E. Reed-Hill, F. W. Caldwell

Poly crystalline zirconium tensile specimens containing a sizable fraction of grains unfavorably oriented for slip were deformed at 77°K to strains as high as 9 pct. The contributions of the various twinning modes to the observed strain were deter~nlned quantitatively using measured twin volume fractions and Schrnid orientation factors. The results indicate that at very small strains twinning can account for almost all of the observed strain. At higher strains slip becomes the dominant means of deformation. The most significant form of twinning was {1121}. PLASTIC deformation in polycrystalline aggregates is poorly understood even today. This is primarily because slip cannot be easily observed or studied in the interior of a metal. On the other hand, twinning can be discerned inside a specimen after deformation. Twinning studies can therefore often yield quantitative information about polycrystalline deformation not otherwise obtainable. This investigation uses the above aspect of twinning in determining the contributions of twinning to the strain during tensile deformation at a cryogenic temperature (77°K). Polycrystalline zirconium was used as the object of study. There are several reasons why this information should be of value. In contrast to many metals, both the strength and ductility of zirconium increase with a corresponding decrease in temperature. This may be related to the fact that twinning becomes more profuse and complex with decreasing temperature. Secondly, it has been discovered that certain room-temperature properties of zirconium can be greatly improved by about 1 pct prestrain at 77°K. These include an increase in tensile elongation in critical directions by over 50 pctl and a large mechanical hysteresis effect.2 Both effects are believed to be related to twins formed by prestraining: plastic twin-boundary movements accounting for the increased ductility, and anelastic twin-boundary movements for the internal friction. Thirdly, hexagonal metals which twin primarily on only the (1012) mode (such as beryllium, zinc, and magnesium), unlike zirconium, are very limited in ductility at cryogenic temperatures. Therefore, the significance of the various types of twinning in zirconium at cryogenic temperatures is of more than academic interest. Three twinning mechanism-s have beenobserved in quantity at WOK, {1012), {1121), and {1122). Each must be considered as a unique deformation mechanism because of their markedly different twinning shears and basically different angles between twinning and basal planes, as shown in Table I. It is therefore necessary to separately consider the role of each of these twins during plastic deformation at 77°K. Fortunately, each twin possesses unique morphological features which makes its identification possible on a properly prepared metallographic section. The use of the polarized microscope3 can also greatly aid in identification of the various forms of twins. EXPERIMENTAL PROCEDURE Arc-melted sponge zirconium plate, previously describedY4 was machined into 1/8 by 1 1/4 in. threaded-end, round tensile test specimens. These specimens were deformed to the desired strains in a liquid-nitrogen cryostat mounted in an Instron testing machine. The tensile axis was the transverse plate direction. This specimen direction resulted in large numbers of grains in orientations unfavorable for deformation by prism or basal slip. Deformed specimens were sectioned, mounted in epoxy cold-mount resin, ground on metallographic papers, electropolished, and anodized to provide surfaces sensitive to polarized light. Standard quantitative metallographic procedures5

Jan 1, 1965

By Pramod C. Thakur

Introduction Methane is contained under pressure within the fractures and adsorbed on the surface of the coal seams and adjacent strata. It is released into the mine atmosphere during mining of the seam creating explosive gas-air mixtures. Large volumes of air, sometimes as high as 20 tons of air for each ton of coal mined, are circulated constantly to dilute and carry away methane from coal mines. Removal of methane from solid coal, wherever high methane emissions occur, has been discussed by Spindler and Poundstone (1960) and Thakur and Davis (1977). Methane control in longwall gobs is much more complicated. As longwall mining progresses, the overburden continually subsides, and the immediate roof caves behind the roof supports. Even the underlying strata heave and open up communication channels feeding gas to the longwall gobs. The pressure of gas in the underlying and overlying strata is usually higher than the ambient air pressure in the mine. Thus the mine workings become natural pressure sinks, into which gas flows from the entire disturbed zone. Winter (1975) defines this zone as the "gas emission space". Depending on the number of gas-bearing zones in the gas emission space and their gas contents, the total methane emission from longwall gobs could vary from a few to more than one hundred cubic meters of gas per ton of mined coal. Hence the ventilation of longwall faces demands a large quantity of air. This ventilation need is further enhanced by high air losses specially on caving faces (with no stowing of the gobs). The old system of longwall ventilation, the 'U' pattern, where all the air was brought down one gate road and exited through the other gate road, loses large quantities of air through gobs giving a high methane concentration at the return end of the face. The 'Y' ventilation pattern where intake air is brought down both head and tail gate roads relieves the situation to some extent but, on most longwalls, some kind of methane control is still needed. With the onset of longwall mining in Europe several decades ago, the initial work on methane control on longwall has naturally been done there. The basic principle of methane control has always been, and still remains, some means of "bypassing methane from the gas emission space without letting it mix with the mine air". In most cases the bypassing mechanism is either a strategically located borehole or a roadway. A successful methane control program depends on the following basic premises: a. Determination of the geometry of the gas emission space and location of gas bearing horizons therein. b. Estimation of the rate of methane influx into the longwall gob. c. A scheme to bypass the gas in the most economic and efficient manner and thus prevent it from entering the mine atmosphere. In successful methane drainage programs a high proportion, usually between 50 and 70 percent, of the total gas emissions in a working district is removed before it can enter the mine airways. Advantages of methane drainage can be summarized as: 1. Generally reduced methane levels in the mine leading to increased safety and productivity. 2. Reduced air requirements and corresponding savings in ventilation horsepower. 3. Faster rate of advance for development headings and economy in the size of headings. 4. Possible use of mine gas as an additional source of fuel. The purpose of this paper is to briefly review the geometry of gas emission space and methane influx therein and discuss more successful European and U.S. longwall gob gas control techniques.

Jan 1, 1981

The following discussion was held on August 2.2, 1927, during the meeting of the Institute at Salt Lake City. It. IIIatch, Garfield, Utah.—The object of the meeting, I belicve, is to determine the proper chemical composition to insure long wear of a ball in a mill. This might also apply to rods. I feel that there is only one way of determining accurately the wearing qualitites of balls in mills, and that is by actually wearing out 400 or 500 tolls of different kinds of balls. Two things add to the wearing qualities of a ball: (1) the tenacity, with which the particular particles of iron or steel are cemented together; (2) the individual hardness of each partiele. My cxperience is that a ball that has a Brincll of 550 to 650 will give comparatively long life. There is considerable difference of opinion as to the best steel and iron alloys neressary to produce a satisfactory grinding ball. Some favor chrome, somr manganese and some nickel. Personally, I believe cast iron alloyed with chrome makes the best ball for small sizes; for large sizes (31/2 in. arid up) steel alloyed with mangancse is best. L. O. Howard, Pullman, Wash.—How would this method apply to hning? A. Kissock, New York, N. Y.—I do not subcrribe to that exactly. As I am connected with the Climax Molybdenum Co. you would hardly expeet me to. We have been much interested in trying to work out this grinding-ball problem and have spent a, great deal of thought and effort on it. As we are associated with the American Metal Co. and have a number of Proprrties of our own, we are in poaition to try our ideas on ourselves first. We have tried different compositions, but, have not done anything very remarkable with them yet,, except that we have been able to say that the combination of chrome and molybdenum has given the best, wearing ball. Mr. Hatch feels that iron is the best. medium for grinding, hut since toughtiess as well as hardness is a factor in wearability we feel that a well made steel is better for this purpose. Another difficulty with cast, or chilled, iron is lack of uniformity front day to day or from heat to heat, and the impossibility of protlucing balls free from blow or shrinkage holes which matcrially affect their life. If cast iron is made hard it becomes brittle and lacks strctc11 or toughness. This prevents its use in the larger sizes, aS break:lgc, is a sorious hantlic:~p to efficiency. We have trirtl hard and brittle balls and softer but very tough balls and have proved that maximum hardness, with sufficient toughuess to prevent hrcakagv, is the most important factor. in resistarnce of a steel to abrasion. It is well known that. chromium is one of the best hardening agencies for cither iron or. steel; and molybdenum is recognized as an clerment capable of introducing tonghness. In other words, the proper combination of chromium and molybdenum permits unusual hadness with still sufficient touglmess to stand up under severest impact. It is yet too early to give any actual mill results of this new Combination and though we are proving our ideas at our own properties we have to depend on others to help us make the data more general and more worth while and would like to get some testa 206

Jan 1, 1928

By Arthur Taggart

Recent jig practice has shown such marked departures from the pronouncements of the textbooks, particularly as to particle size recovered and size range of feed, as to make it desirable to reexamine the mechanism of jig action. This paper presents the results of such a study. The general conclusions of the Paper are: I. A jig bed is a bi-functioned as well as bi-parted body. The upper layer comprises a plastic stream moving slowly in a substantially horizontal direction from feed lip to tail board. It serves to rough out tailing and light middling and to pick up heavy middling and lift it out 01 the jig box. The lower layer acts as the ultimate separating means by absorbing concentrate and rejecting heavy middling. 2. The separating function of the lower layer is performed in three definitely diflerent ways, depending upon the relative sizes of the grains presented to it and those composing it. Experimental The experimental work consisted of close and long-continued visual observations of operating beds in a plunger jig, eccentric driven, and in determinations of the settling rates of various metal spheres through a quartz bed under various conditions of operation. Falling velocities were measured by an ingenious method devised by A. 6. Dorenfeld, a student in the Mining Department at Colum- bia. Spheres of different metallic alloys, 3/8-in. diameter, were cast with a short piece of fine copper wire frozen in to Serve for suspension-A short piece of black cotton thread was looped to the top of the wire to serve as an indicator. The set-up for a test is shown in Fig. I. The thread should be boiled, if necessary, to make it freely water absorbent. The piece of clean plate glass D is supported rigidly at the proper height in a vertical position. The white scale E is similarly supported behind the glass. At the beginning of a test, D is filmed with water by holding it (best with clean rubber finger cots) under running tap water. It is then clamped in approximate position and C, already wet, is laid across it and drawn straight and vertical with the upper end at or near the top of D, and the ball A slightly above the top of the expanded bed. The water film holds the string to the glass. For a test the string is released, its upper end position noted just after the top of the ball becomes submerged, when the corresponding time is read, and thereafter simultaneous readings of position and time are taken as desired. Results of the visual studies of the bed are given at the pertinent places in the following discussion. Results of the settling tests are summarized in Figs- 2 and 3. Definitions The name bed as used herein refers to the entire mixture of solids and water filling the jig box. A layer is a stratum of a bed composed of particles of substantially the same specific gravities. A granular product is long-range when it approximates a crushed or ground product limited as to upper size only; a short-rafzge product is one closely sized. A bed is loaded when operating with continuous feed and discharge of products; it is unloaded when pulsating norma11y but neither being fed nor

Jan 1, 1943

By Arthur Taggart

Recent jig practice has shown such marked departures from the pronouncements of the textbooks, particularly as to particle size recovered and size range of feed, as to make it desirable to reexamine the mechanism of jig action. This paper presents the results of such a study. The general conclusions of the Paper are: I. A jig bed is a bi-functioned as well as bi-parted body. The upper layer comprises a plastic stream moving slowly in a substantially horizontal direction from feed lip to tail board. It serves to rough out tailing and light middling and to pick up heavy middling and lift it out 01 the jig box. The lower layer acts as the ultimate separating means by absorbing concentrate and rejecting heavy middling. 2. The separating function of the lower layer is performed in three definitely diflerent ways, depending upon the relative sizes of the grains presented to it and those composing it. Experimental The experimental work consisted of close and long-continued visual observations of operating beds in a plunger jig, eccentric driven, and in determinations of the settling rates of various metal spheres through a quartz bed under various conditions of operation. Falling velocities were measured by an ingenious method devised by A. 6. Dorenfeld, a student in the Mining Department at Colum- bia. Spheres of different metallic alloys, 3/8-in. diameter, were cast with a short piece of fine copper wire frozen in to Serve for suspension-A short piece of black cotton thread was looped to the top of the wire to serve as an indicator. The set-up for a test is shown in Fig. I. The thread should be boiled, if necessary, to make it freely water absorbent. The piece of clean plate glass D is supported rigidly at the proper height in a vertical position. The white scale E is similarly supported behind the glass. At the beginning of a test, D is filmed with water by holding it (best with clean rubber finger cots) under running tap water. It is then clamped in approximate position and C, already wet, is laid across it and drawn straight and vertical with the upper end at or near the top of D, and the ball A slightly above the top of the expanded bed. The water film holds the string to the glass. For a test the string is released, its upper end position noted just after the top of the ball becomes submerged, when the corresponding time is read, and thereafter simultaneous readings of position and time are taken as desired. Results of the visual studies of the bed are given at the pertinent places in the following discussion. Results of the settling tests are summarized in Figs- 2 and 3. Definitions The name bed as used herein refers to the entire mixture of solids and water filling the jig box. A layer is a stratum of a bed composed of particles of substantially the same specific gravities. A granular product is long-range when it approximates a crushed or ground product limited as to upper size only; a short-rafzge product is one closely sized. A bed is loaded when operating with continuous feed and discharge of products; it is unloaded when pulsating norma11y but neither being fed nor

Jan 1, 1943

By P. Hazebroek, M. Prats, E. E. Allen

Well locations in water floods frequently do not coincide with the ideal well locations associated with the flood pattern which is used. A question of importance is. "How much oil is lost because of this?". This is the problem treated in this paper. It is assumed that each pattern in a five-spot flood has the proper number of production and injection wells but that the wells may be off-pattern. The distance by which a well is off-patern is given in terms of the pattern spacing, defined as the length of one side of a five-spot. The influence of off-pattern wells on the performance of a five-spot flood has been investigated mathematically for unit mobility ratio. All production and injection rates are assumed to remain equal. The loss in recovery resulting from pattern irregularitie: has been calculated at a cumulative water injection corresponding to a 98 per cent water-cut in a regular five-spot. Displacing a single production or injection well by about one-third the pattern distance reduces the total field recovery by 4.4/N per cent of the recovery obtainable with regular spacing, where N is the number of five-spots in the flood (assumed large). When off-pattern wells are separated by at least one regular five-spot and are displaced by less than one-third the pattern distance, the total loss in recovery in a large-scale flood is, at most, 1 per cent of the recovery obtainable from that field with a regular five-spot pattern. However, much higher losses may occur if the off-pattern wells are not separated by a regular five-spot, if the rates are imbalanced, or if the mobility of the injected water is higher than that of the crude. Although the loss in oil recovery due to pattern irregularity often may be low, the off-pattern case will always require injection of more water to reach the same final water-cut. The volume of water injected per unit volume of oil displaced has been calculated for each five-spot adjacent to a five-spot containing a single 08-pattern well. The cumulative water injection at the time of 98 per cent water-cut may be increased by as much as 37 per cent when a production well is displaced one-third the pattern distance toward an injection well. The existence of differences between actual subsurface locations and the idealized well patterns used in secondary recovery operations is well recognized. However, the methods commonly used for predicting waterflood behavior ignore such differences, even when subsurface locations are known. The reason for this is simple. The idealized well patterns are highly symmetrical and, as such, the production history of the pattern (and even of the field) can be determined from that of a few production wells—usually from only one. Consideration of the many irregular well spacings found in a specific field would entail a large amount of work, and then the results would be applicable only to that specific field. In an attempt to provide an answer to the more general problem, this paper considers a water flood having an idealized well pattern, except for one well which is not at its regular location. When several off-pattern wells are present, their contributions are assumed to be additive unless the off-pattern wells are close to each other. Only four positions of the off-center well (at x, y. of Fig. 1) are considered in this paper. These are shown

This volume summarizes characteristics and the geological setting of porphyry copper deposits of the Western Hemisphere. Grouped by characteristics, porphyry copper deposits are described in six regions: Andean orogen, Appalachian orogen, Alaska, northern Cordilleran orogen, southern Cordilleran orogen, and the Caribbean. Each region has its own peculiarities of geologic setting, and those deposit characteristics that may be projected from one chapter to another will be used in reaching the conclusions from which to draw genetic models for porphyry copper deposits. The term porphyry in this volume denotes a type of ore deposit, rather than a rock classification. The classification of intrusive igneous rocks used in this volume is shown in Figs. 36a and 42 (pp. 103, 130). Some modern classifications suggest mineral-ratio definitions other than those used in this volume; however, most literature references cited are based on the classification shown in Figs. 36a and 42. The reader should be aware, therefore, that quartz monzonite in this volume contains from 35% to 65% potassuim feldspar and at least 10% quartz. A term used in this volume is defined where introduced within the context of a specific chapter. Distensional tectonic conditions are used in the sense of Cady (1972) in the Appalachian orogen, for example. Porphyry copper deposits are defined as large bodies of mineralized rock, usually including a porphyritic intrusive phase, that have copper sulfide minerals disseminated through them. The definition has no commercial connotation and is used strictly in a noneconomic sense to encompass the spectrum of copper mineralization associated with these deposits. Terms commonly accepted in the literature are not defined. Porphyry molybdenum and porphyry copper deposits commonly are distinguished by most economic geologists. The basis for the separation is summarized in one chapter of this volume. To permit the reader to more easily peruse the bibliography for any particular region, references will be found at the end of each chapter. The bibliography is not intended to be complete, but is designed to provide adequate minimum coverage for descriptions of deposits in the chapter concerned. Each entry is properly referenced in the text of that chapter to facilitate the reader's research into any particular topic. This volume is written from the point of view of the exploration geologist whose task it is to evaluate the structural, petrographic, mineralogic, and metallogenic characteristics of a porphyry copper deposit. The goal of the evaluation is to determine if, and where, concentrations of metals may exist in an igneous- hydrothermal system that includes the most complex set of geologic factors found in any of the many types of ore deposits. The successful porphyry copper geologist is simultaneously a petrographer, geochemist, structural geologist, and mineralogist. Some porphyry copper deposits have developed in volcanic arcs underlain by a Benioff seismic zone with a trench paralleling the arc. The most convincing example of a deposit known to have developed in an environment where subduction is an active process is the 3.3 m.y. (million years) old Dry Creek occurrence in the Aleutian arc (this volume). On the other hand, the younger deposits in the Cascades appear to have formed in a volcanic arc lacking both the Benioff zone and the offshore trench. Subduction is not widely accepted as an active mechanism for the period when the younger Cascade deposits formed. Subduction has also been questioned for deposits formed at a great distance from a plate boundary (e.g., Bingham). Regardless of the pros and cons regarding subduction, most deposits are associated with regional faults. Strike-slip

Jan 1, 1978