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By E. P. Miesch, P. B. Crawford

A study was made of the effect of permeable and impermeable lenses in a reservoir on the production capacity of a well. Both steady-state and unsteady-state data were obtained. An electrical resistivity model was used to obtain the steady-state data and thermal models. were constructed to obtain the unsteady-state data. The productivity of a well is affected very greatly only when the lenses are close to the well. The effect of circular lenses on the productivity ratio can be correlated with the distance from the center of the lens to the center of the well divided by the radius of the lens. When this dimensionless distance is equal to six or greater, the effect of the lenses on production capacity will be negligible. The pseudo steady-state productivity of a heterogeneous reservoir can be predicted using steady-state data. INTRODUCTION Many analytical solutions of reservoir behavior assume that reservoir rock is uniform and homogeneous. Although this assumption is used, all of the data from core analyses and well logging indicate that the reservoirs are heterogeneous. Very little work has been done on the performance of heterogeneous reservoirs. The work of Landrum,l et al. showed that transient phenomena in oil reservoirs could be studied with thermal models. Pickering and Cotman2 used thermal models to study flow in stratified reservoirs and investigated the effect of inhomo-geneities in oil reservoirs on transient flow performance. Loucks3 made a mathematical study of the pressure build-up in a system composed of two concentric regions of different permeability. Root, Silberberg and Pirson4 studied the effect of the growth of the flooded region on water influx predictions using a thermal model consisting of three concentric cylindrical regions of different thermal properties which simulated the aquifer, the flooded region and the unflooded portion of the original hydrocarbon region. Tomme, et a1.5 made a mathematical study of vertical fractures. The object of this investigation was to study the effect of highly permeable and impermeable lenses in the vicinity of the wellbore on the pressure depletion history of the well. Steady-state data were obtained for both conductive and nonconductive lenses that completely penetrated the formation. The lenses were symmetrically located at various distances from the wellbore. The unsteady-state data were obtained on seven thermal models. EXPERIMENTAL EQUIPMENT AND PROCEDURE STEADY-STATE DATA The steady-state data were obtained from an electrical resistivity model 30 in. in diameter and approximately 11/2 in. deep. The outside of the model was lined with a 30-in. diameter copper strip, which served as the outer boundary of the reservoir. The bottom was covered with a sheet of plexiglass so that it would be nonconductive. The model was filled with a slightly saline solution. The well size was varied from an 0.064-in. diameter copper wire to a 10-in. diameter copper cylinder. Readings were taken with an impedance bridge using AC current to prevent polarization at the contacts. Copper and wax lenses were used to represent infinitely conductive and nonconductive lenses, respectively. The resistance was first measured for each well diameter with no lenses in the reservoir. Then the conductive and nonconductive lenses were spaced symmetrically at various distances from the well and the resistance read from each lens location. The diameters of the conductive lenses were 3, 1.022 and 0.624 in., and those of the nonconductive lenses were 3, 2.25 and 1.563 in. The ratio of each resistance reading to the resistance reading with no lenses in the reservoir

Jan 1, 1965

By N. A. Gokcen, M. N. Dastur

In metallurgical process industries a knowledge of true melting and casting temperatures is very essential for increasing the operating efficiency as well as improving the quality of the finished product. Optical pyrometers are widely used for the purpose because of their cheapness and ease of operation. It is an unfortunate fact, however, that this mode of measuring temperature entails a source of severe error inasmuch as with all non-black bodies, the temperature observed is always below the true temperature owing to deficient emissive power. Hence, the need for emissivity correction arises. In 1913 Bidwell1 obtained emissivity values of 0.36-0.48 for a temperature range of 1520-1800°C. He measured the true temperature of molten iron by sighting into a carbon cavity immersed in the iron under an atmosphere of hydrogen. In 1914 Burgess2 determined the emissivity of a smooth surface of liquid iron free from oxide to be 0.37 under an atmosphere of hydrogen. He claimed to have attained an accuracy of within 5°C at 1500°C with an optical pyrometer using monochromatic light. He reported that no difference appeared to exist between the emissivities of pure iron and of steels containing considerable percentages of carbon, nickel or manganese; nor was there any appreciable variation of emissivity with temperature from 1530 to 1571°C. Wensel and Roeser3 found an elnissivity value of 0.4 for temperatures above 1375°C for cast iron. The average emissivity value for carbon steels reported by Leiber,4 odd,5 Hase6 and Umino7 range from 0.4 to 0.45. Knowles and Sarjant8 made an extensive study of emissivity of molten iron and steel over a wide range of workshop and laboratory conditions. Observations of true temperature were made with immersion thermocouples, and correlated with apparent temperatures indicated by optical pyrorneter readings taken on the pouring stream as it passed over the lip of the crucible. The emissivity of Armco iron was shown to be of the order of 0.4, rising slightly with increasing temperature. But for plain carbon steels containing up to 1.0 pct carbon the emissivity was shown to fall slightly with increasing temperatures. The results of their investigation are in agreement with those of Guthmann.9 Naeser,10 Spencer," Todd5 and Hase6 in regard to the relation between emissivity and temperature for plain carbon steels. However, Goller12 has found a rise of emissivity with increasing temperature for the same steels. Results of several investigations are given in Fig 1. Measurement of True and Apparent Temperatures The necessity for an accurate optical temperature scale for liquid iron in studies of gas-metal equilibria led to this investigation. Experimental measurements were carried out in the induction furnace used by Dastur and Chipman13 in their studies of the reaction of hydrogen with oxygen in liquid iron. The furnace as modified for this work is shown in Fig 2. The atmosphere of the furnace was a mixture of purified argon with hydrogen containing a small controlled amount of water vapor. Gases were preheated by means of a platinum-10 pct rhodium resistance coil. The stream of hydrogen sweeping across the surface of niolten iron vir-

Jan 1, 1950

By R. M. Rose, D. P. Ferriss, J. Wulff

Single crystals of tantalum were grown by multipass zone melting in an electron beam apparatus. Tension tests of these crystals at 4.2 x 10&apos;* per sec-gave a resolved louler yield stress of 7300 psi at with a chisel edge; total uniform deformation increased from 1 to 2 pct at 77°K to over 20 pct at 300°K. This, and slip traces, indicated that deformation is more inhomogeneous at lower temperatures. Deformation occurred exclusively by slip in <III> directions, on planes in the <111> zones. Cross slip was frequent, particularly for those orientations where the resolved shear stress on the cross system was comparable with that on the primary plane. The existence and magnitude of the upper yield point were found to be sensitive to orientation. This effect was related to the circumvention of dislocations which were "locked" by interstitial atoms, by double cross slip, or composite slip, of screw dislocations. Prestrainirg at 300°K did not remove the upper yield point in subsequent tension at 77°K. Also, this treatment was found to cause yield points, where none existed for the unprestrained material. This behavior was also rationalized in terms of the circumvention mechanism. The mechanical properties of polycrystalline tantalum have been investigated by several workers,1"4 and may be summarized by pointing out the following features: a) Sharp rise of yield stress with decreasing temperature below room temperature. b) Response to strain aging at 300" to 400"C. c) Yielding with upper and lower yield-point phenomenon at and below room temperature. d) Low strain hardening below room temperature. e) Reluctance to twin except at very high strain rate. Furthermore, tantalum is ductile at ordinary strain rates as low as 4.2"K.&apos; This feature, in particular, makes tantalum unique among the high melting point, bee transition metals of Groups V and VI in the periodic system. Therefore, a more fundamental and detailed knowledge of the low-tempera- ture deformation of tantalum is required. Since high purity and the absence of grain boundary effects make such a study most productive and unambiguous, the method of electron beam zone melting was selected for the preparation of test specimens. This technique has the further advantage that crystals may be seeded in order to obtain any desired orientation. EXPERIMENTAL The electron beam zone-melting equipment was constructed as a modification of that described by Calverley, Davis, and Lever? All crystals were made by three passes of the molten zone at 4 mm per min to achieve an optimum purity commensurate with economy of time and material. Table I reports the chemical analyses of the starting and refined metal. It will be noted that there remain some 50 to 70 wt ppm of interstitial elements, while all substi-tutional elements have been removed by evaporation. Tungsten is picked up by evaporation of the cathode filament wire. Crystal seeding was normally successful within 3 deg, and the orientation of all crystals are given in the standard stereographic triangle in Fig. 1. Tensile bars were prepared from the crystals by centerless grinding to the shape in Fig. 2. Specimens were then electropolished to remove 10 pct of the diameter in order to remove worked material and to prepare a metallographic surface for subsequent deformation trace observations. All specimens were held in the split bushing grips as indicated in the cross section view of Fig. 2. All tests were made at a strain rate of 2 112 pct per min in an Instron testing machine.

Jan 1, 1962

By H. R. Thresh, A. F. Crawley

THIS paper reports the results of viscosity measurements on cadmium and indium undertaken as part of a continuing program of liquid metals research at the Mines Branch, Department of Energy, Mines and Resources, Ottawa, Canada. For several years this work has continued with support from the Canadian Zinc and Lead Research Committee and the International Lead and Zinc Research Organization. In the literature, existing viscosity data for cadmium are conflicting and for indium are scarce. To achieve reliable viscosity values, further work was deemed desirable. Viscosities were measured using an absolute technique applied to an oscillating closed right cylinder of liquid metal. The apparatus, constructed in this laboratory, and the techniques involved in its use have been described in an earlier paper.&apos; In calculating viscosity coefficients from the experimental data. Roscoe&apos;s2 mathematical analysis was used. Because accurate viscosity determinations are dependent on accurate density data, and since the available data in the literature are conflicting, the densities of liquid cadmium and indium were also determined in this laboratory by a pycnometric technique. This increased the control exercised over all the variables contributing to the accuracy of viscosity measurements. For both density and viscosity determinations, cadmium and indium of 99.999 pct purity were used. These materials were obtained from Cominco Ltd. In order to suppress excessive evaporation losses and help prevent oxidation, a technique developed in measuring the viscosity of zinc&apos; was used for cadmium. This involved maintaining an atmosphere of purified hydrogen in the viscosimeter during the rela- tively long periods while the experimental temperature was changed and stabilized between individual determinations of the logarithmic decrement. Then, immediately prior to a decrement measurement. the viscosimeter was rapidly evacuated to a pressure of about 2 X 10-6 torr. On the other hand. with indium. no difficulties arise from vaporization or oxidation. In this case. therefore. the apparatus was held under a constant vacuum of about 2 x 10-6 torr. When all sources of random and systematic error have been evaluated, the technique is considered to yield data accurate within 10.5 pct. The viscosity of cadmium was measured to a maximum temperature of 451.8°C and that of indium to 346.5°C. These temperatures are. respectively. 130° and 190°C above the melting points. Two separate runs were made on indium. The results are given in Table I and, when plotted. yield the smooth curves evident in Figs. 1 and 2. Values of A and C to fit the well-known Andrade1 equation were determined by a regression analysis. The equation is: where n = coefficient of viscosity. i = specific volume. T = temperature in °K Despite its empirical nature. Andrade&apos;s equation has been shown by many workers to describe accurately the temperature dependence of viscosity. During the current research program, this equation has been found to fit the data precisely for all the metals and alloys that have been studied.5,6 The A and C&apos; values for cadmium and indium are given in Table 11. Comparing the magnitude of the present data with those of previous workers,7-10 as has been done in Fig. 1, it is evident that the results of Fisher and Phillips10 deviate markedly from the rest. With the exception of one point from Gering and Sauerwald,7 all other data agree within ±2.5 pct. However, the agreement between the present results and the work of Menz and sauerwald9 is especially good over the entire experimental temperature range. Such agreement may be expected since Menz and Sauerwald&apos;s

Jan 1, 1970

By T. L. Berger, M. C. lnman, M. F. Rose

AFTER shock loading, mechanical twinning has been observed by several authors1-4 for a variety of fcc metals and alloys. It has been shown2,3 that low stacking fault energy materials deform primarily by the formation of mechanical twins and stacking faults during dynamic loading. Further, Inman, Murr, and Rose2 have shown that a correlation exists between the average hardness and the volume percent of mechanically twinned material in stainless steel. It has been observed in nickel&apos; that mechanical twins are produced during shock deformation if the peak pressure associated with the shock wave is greater than 350kbar. It is the purpose of this work to discuss shock-hardening mechanisms in nickel and to determine to what extent the initial condition influences the final response. The "flying plate technique" was used to generate planar shock waves with peak pressures as high as 710 kbar. The details of the technique5" have been discussed elsewhere and will not be repeated here. The material used in this study was polycrystalline nickel of 99.98 pct purity and had an initial grain size of 0.18 mm. Prior to any deformation, all samples were given a stress-relief anneal of 6 hr at 600°C in a vacuum furnace. After annealing, the initial condition of the samples was changed by cold rolling individual samples from 0 pct to a maximum of 80 pct reduction in thickness. This provided samples with controlled initial histories for shock deformation. Immediately after shock loading, the specimens were slowed and quenched by suitable arrangement of buffer material and water bath. This technique minimized specimen damage and the effects of shock heating on the samples. Since deformation twins in high stacking fault energy fcc metals are only produced at high stress levels, the initial defect configuration prior to mechanical twinning should greatly influence the number of twins formed. In fact, Zukas and Fowler7 have found that prestraining in iron and steel greatly suppresses the formation of mechanical twins during the shock deformation process. Following the methods of Warren and warekois8 and Cohen and Wagner,9 X-ray diffraction profile analysis was performed to determine the incidence of stacking faults and mechanical twins in the deformed nickel. Analysis was made on samples in the annealed, cold-rolled, shock-loaded, and cold-rolled—shock-loaded states. The estimated accuracy of the peak position measurements is *0.01 deg in 2?. Therefore the accuracy in the measurement of the relative peak shifts between the (400) and (222) diffraction line profiles is on the order of *0.04 deg in 2?. None of our measurements indicated peak shifts greater than 0.04 in 28. This would correspond to a fault density of -1 pct and sets the limit on the sensitivity of our instrument. Similarly, analysis of the shift in the center of gravity of the diffraction line profiles yields the minimum measurable value of the twin fault probabilitya to be -0.002. Fig. 1 shows mechanical twinning in nickel shock-loaded to 400 kbar. In this photograph, fault intersections are clearly visible. The thickness of the individual fault lamellae was determined from the image widths of their lines of intersections by the

Jan 1, 1968

By M. E. Learmont, R. J. Lipp, I. Iwasaki

In the selective flocculation of iron ores, the concentration of alkaline earth ions in pulp solutions plays a critical role. Sodium silicate, alone or with sodium tripolyphosphate, has been used as a dispersant. When Ca+ + concentration exceeds 15 to 20 ppm, however, only a strong complexing agent, such as ethylenediaminetetraacetate (EDTA) was found to be effective (Heerema, Lipp, and Iwasaki, 1979). Some iron ores release Ca+ + in excess of 20 ppm. With ores that contain gypsum, the Ca+ + concentration may reach several hundred ppm. The purpose of this investigation was to compare the effectiveness of EDTA with nitrilotriacetate (NTA) in countering the adverse effects of Ca+ +, particularly at high Ca+ + concentrations. Emphasis was placed on the use of NTA since it is more cost-effective than EDTA. It is also used in detergents in some countries (Malaiyandi, Williams, and O&apos;Grady, 1979). NTA, like EDTA, forms a soluble complex with Ca+ + with a 1:1 molar ratio. Its structure and the value of log Kca are given below together with EDTA (Shibata, 1963). [ ] For experimental materials, an equal weight mixture of Lac Jeannine hematite and a high-purity quartzite from Thompson, MN, both ground to - 30 µm (- 560 mesh) was used. Selective flocculation test conditions and procedures were identical to those used in previous investigations (Heerema, Lipp, and Iwasaki, 1979). The optimum level of starch addition for the above mixture was determined to be at 300 g/t (0.6 lb per st). Initially, a series of selective flocculation tests were performed on the mixture pulped with 10-3M CaC12 (40 ppm Ca + +) at pH 11. With no NTA present, flocculation of the entire suspension resulted. The selectivities achieved in tests with 90, 100, and 150% of the stoichiometric amount of NTA were virtually identical to each other and also to the selectivity of separation obtained in the absence of Ca+ + Such an observation could have been expected since Ca+ + concentrations up to a few ppm may be tolerated in selective flocculation (Krishnan and Iwasaki, 1982). A similar series of tests were performed at 10-2M CaC12 (400 ppm Ca+ +). The results are shown in Fig. 1 as grade¬recovery curves. For comparison, the results obtained in the absence of Ca++ are included. At 90% of the stoichiometric amount of NTA, a large enough concentration of uncomplexed Ca+ + was left in solution to cause indiscriminate flocculation. Note in this figure that NTA is capable of countering the adverse effect of Ca+ + even at this high concentration when it is used in excess of stoichiometric amounts. The free Ca+ + concentrations at 100 and 150% are calculated to be 2.5 and 0 ppm, respectively. [ ] The relative effectiveness of NTA and EDTA was then compared at 100% of the stoichiometric amount using 10-2M and 10-3M CaCI2 (Fig. 2). EDTA appears to be slightly more effective than NTA. The free Ca++ of 0.02 ppm in 10-2M CaC12 with EDTA compared to 2.5 ppm free Ca+ + with NTA might account for the difference. As evident, prohibitively high additions of EDTA and NTA were required to complex high concentrations of calcium ion. The use of both of these agents would result in the accumulation of complexed Ca+ + in recycle water.

Jan 1, 1985

By J. B. Cohen

In an investigation of the microstructure of shock-loaded metal specimens1 C. S. Smith found that there was little distortion of grain boundaries or change in external dimensions, although the hardness corresponded to that produced by severe rolling. Furthermore, the hardness of individual grains was independent of the deformation structures present; grains with no markings were as hard as those heavily populated with markings. These markings which resemble twins do not appear in copper until high shock-loads of the order of 200 kb are applied. It appears that due to the high velocity of a shock wave and its sharp front, heavy deformation takes place on a submicroscopic scale. In this work an attempt was made to examine this deformation, particularly at a load below which macroecopic markings appear. The broadening of 200 and 400 diffraction peaks was examined from the face of a poly crystalline sample normal to the direction of the shock wave. These peaks were chosen because the elastic constants in copper are such that residual strains would be greatest in the <100> directions; hence, the strain-broadening contribution to these peaks would be large in comparison to other sets. Also the broadening due to stacking faults and microtwins would be greatest with this set.2 A complete Fourier analysis of these peaks was made, as described by warren,&apos; using the Stokes correction with peaks from an annealed sample.3 With the aid of the U. S. Army Ordnance Corps EDVAC computer and a curve matching program, sixty sine and sixty cosine coefficients were obtained for each peak. The last of these was about 1.5 pct or less of the largest coefficient, indicating good representation. Transverse sections from a 1.5 in. rod of as-drawn electrolytic tough-pitch copper were reduced in cross-sectional area about 50 pct by cross rolling. Disks 1.5 in. in diam were recrystallized at 275 °C for 30 min and then at 300°C for the same time. The faces were polished and deeply etched in nitric acid to remove 25 mils. The grain size was 0.02 mm. Laue back-reflection patterns indicated the sample was well recrystallized. The two diffraction peaks from this sample were recorded on a Norelco diffractometer using filtered copper radiation. Peak intensities were kept less than 600 cps to assure linearity of the counter and circuitry. This sample was then placed between two rods of the same material and diameter. The top rod was 2.25 in. long and the bottom rod 1 in. long. (In

Jan 1, 1961

By John P. Bryant, Samuel Kincheloe

Plant nutrients are obtained by plants from both the air and the soil. Carbon dioxide, a gaseous form of carbon and oxygen, supplies the carbon which usually makes up 50% or more of plant structure. Plants are capable of absorbing carbon dioxide directly from the air. Most of this nutrient comes from the air, although some carbon dioxide is absorbed by soil water and taken into the plant as liquid. Growing plants use more water than any other substance. Plant nutrients in the soil dissolve in soil water; soil water entering the plant carries nutrients into the plant structure. Water is then given off into the air as the plant breathes or transpires. Inorganic or mineral nutrients essential to plants are supplied through the soil. Inorganic or mineral composition of plants usually is less than 5% of their weight. In most crop-growing areas, much of this nutrition is inadequately supplied from the soil and must be provided by fertilizers. Proper fertilization of a soil to improve its mineral level and productivity is the role of the fertilizer industry. The 13 essential plant nutrients which often must be added to soils or plants and are generally considered fertilizer minerals are categorized as primary minerals (nitrogen, phosphorus, and potassium); secondary minerals (calcium, magnesium, and sulfur); and micronutrients, or trace minerals (boron, iron, manganese, copper, zinc, molybdenum, and chlorine). These classifications are based on quantity of nutrients utilized by plants and have no implication as to function or degree of necessity. One point of major significance to the fertilizer industry is that not all nutrient carriers supply that nutrient in a chemical form which will be available to the plant. Thus, a product which may be considered a fertilizer mineral may require substantial processing or may require substantial processing or treatment before it becomes useful as a nutrient carrier. Fertilizer Industry Scope Until about 1900 demands for higher crop yields were met simply by bringing new agricultural lands into cultivation. Since that time great progress has been made in increasing yields through fertilization and improved varieties and cultural practices. The importance of the fertilizer industry to the economy and welfare of the US is widely recognized. Fig. 1 illustrates the relationship of lime and fertilizers to crop yields. In terms of tons of fertilizer products, the growth of the industry has been phenomenal, particularly between 1950 and 1980. Table 1 shows the increase in fertilizer usage. Primary Plant Nutrients in Fertilizers Primary minerals (nitrogen, phosphorus, and potassium) are designated as such because [ ]

Jan 1, 1983

By Frank L. Nason

The complete statistics of zinc-ore production in the United States for 1916 are not yet available. The following figures are, therefore, only approximate. The total production of concentrates for this year, including New Jersey and Tennessee, amounts to 1,280,000 tons. Of this tonnage, five mines produced approximately 536,000 tons, or about 42 per cent. The remaining concentrates came mainly from the "Valley States," Missouri, Wisconsin, Kansas, Oklahoma, and Arkansas. The 1,280,000 tons of concentrates represent about 25,000,000 tons of crude or run-of-mine ore. Of the five mines producing the 42 per cent., the dimensions of three are approximately 25 by 1500 by 2000 ft. (7.6 by 457 by 610 m.) or more: Four of the five mines are undoubtedly veins in the common acceptance of the term. They are located in great vein systems. The mines of "Valley States" have not, so far, been classed as veins; simply as "secondary deposits." The origin of these secondary deposits has been a warmly debated subject. Many geologists contend that they are the results of leaching from overlying and adjacent rocks carrying but traces of zinc, these traces leached out and deposited in favorable places. If this theory is correct, deposition is strictly limited to shallow depths. No volume of ore comparable to that of "true fissure veins" is to be expeeted. Just what this means to the future of zinc mining in these States is here indicated. The total zinc-bearing areas of these States amount to about 9124 sq. miles (23,631 sq. km.). Assuming that 10 per cent. of this total will be more or less productive, there are 912 sq. miles (2,362 sq. km.) of "mineral" ground. The average depth of the operated mines is something like 100 ft. or less. In Bulletin 606, U. S. Geological Survey (1915), p. 202, Siebenthal makes the following statement: "The writer is informed by William Waugh, one of the drillers of the Stone City well, that cuttings from other wells which he drilled in the vicinity of Pittsburgh, Kan., have shown galena and sphalerite taken from a depth of 591 ft. (180.14 m.) and that the showing of ore at some places would be considered good enough to justify the sinking of a shaft had it been found in the Joplin district and at shallower depths." Leaving out of the question the prohibitive cost of such a shaft, there is

Jan 1, 1918

By J. Stuart Warner

The reaction COSO4(c)?CoO(c) + So3(g)was investigated from 950° to 1170OK by two different methods. The sulfate was decomposed in a previously evacuated space and Pso3 calculated from the measured total pressure on the assumption that Pso2 = 2P02. The sulfate was also decomposed under conditions of controlled oxygen pressure. The difference in the results obtained by these experimental techniques is attributed to the effects of thermal diffusion. The standard free energy change for the reaction is given by ?F° = 66,292 + 17.273T log T — 102.57 T (±300 cal/mole). It was found by DTA and X-ray diffraction studies that CoS04 undergoes a transformation at 617°± 4°C. THE metal sulfates may decompose directly to the oxide or pass through one or more intermediate basic sulfates. Provided the oxidation state of the cation does not change in the course of the reaction, the decompositions may be described in general as follows: One of the major objectives of this work was to determine the validity of Eq. [3] as much of the existing sulfate data has been calculated from decomposition pressures by Eq. [5]. The type of apparatus generally used for these measurements consists of a reaction vessel at high temperature which communicates with a manometer at room temperature. A temperature gradient is thus imposed on the gas phase causing thermal diffusion which brings about a partial separation of the different gaseous species present in an initially uniform mixture. The basic theory and experimental facts associated with this phenomenon are summarized elsewhere1 and it will suffice to state here that the heavier gaseous species diffuses down the temperature gradient. Since thermal diffusion destroys the homogeneity of the gas phase, it is not necessarily true that Pso2 = 2Po2 in any particular volume element of the gas phase even though there are twice as many molecules of SO, as of 0, in the gas phase considered as a whole. Under these conditions, the decomposing sulfate gives off SO, which dissociates to SO, and 0, and all three species are distributed throughout the system by thermal diffusion. However, the sulfate will continue to dissociate until the equilibrium value of PSo3 is established on the hot zone. Thermal diffusion may distribute SO2 and O2 throughout the gas phase in any way so long as Eq. [2b] is satisfied in the hot zone; i.e. Pso2(Po2)1/2=K3pso3. When a steady state is reached, we can characterize Pso2 in that

Jan 1, 1962

By J. L. Swedlow, M. L. Williams

Two standard techniques for assessing fracture initiatlon in sheet specimens involve measurements of 1) the applied load of fracture which, via linear fuacture mechanics, is used to find the fracture tough/less SC (or SIC), and 2) the velative displacement of fracture of the opposite free faces of the crack (COD). In the past, the quantitative association between these two parameters has not been determined in detail, owing to the mathematical difficulties of computing. the stress and strain fields in the combined elasto-plastic flow near the crack. Using a numerical technique Irecently developed and applied to a 7075- TO&apos; aluminum plane stress specimern, the two parameters noted have been determined and associated quantitatirely. CONSIDERABLE effort has been expended in selecting a rigorous yet practical manner for predicting fracture. The usual point of departure is the modified Griffith criterion in which the mechanism of energy dissipation is reflected in Sc (or SIC), the parameter of "fracture toughness". Sc. differs from the surface energy used by Griffith in perfectly brittle fracture in that it includes the effect of plastic flow in the vicinity of the crack tip. Because plastic flow alters the stresses and displacements predicted from the usual linear theory of fracture mechanics, and because analysis of the nonlinear stress-strain field has presented great obstacles: only estimates of several pertinent quantities have heretofore been available. Nevertheless, two parameters have often been measured experimentally althougll usually just at the point of fracture. These are the energy release rate, or fracture toughness 9, (or I,), and the crack-opening displacement (COD). Such observations have been used in connection with frarture criteria and have been most helpful in design, although their application requires care with respect to changes in geometrical configuration from that upon which the criteria were based 1,2 Recently, however, a reasonably accurate and comprehensive method for analyzing the elasto-plastic flow has been devised and applied to plane stress specimens having arbitrary octahedral stress-strain curves.3 It thus becomes feasible to compute, albeit numerically, both the fracture toughness and crack opening as functions of the applied tensile loading on a typical specimen geometry. As a result, it is now possible to associate these two parameters quantitatively, and thereby to associate data obtained by one method with data pertaining to the other. ELASTIC ANALYSIS For the case of linear elasticity, it is relatively easy to deduce the connection between various measures of crack deformation. Using, for example, the singularity analysis, it is found that the leading term of the Airy stress function x f°r symmetrically applied loadings on an isotropic medium is

Jan 1, 1968

By Harlan W. Nelson, James B. Purdy

The great majority of stokers used in residential heating installations are of the clinkering type. Because of inherent characteristics of the underfeed combustion process as it occurs in these small stokers, and because of the wide range of operating conditions encountered in residential heating schedules, not all bituminous coals can be used successfully in residential underfeed units. The problem of providing consumer satisfaction has been attacked by the joint efforts of the stoker manufacturers and the coal industry; the stoker manufacturers have been concerned with improving their product to permit the use of a wider range of coals, and coal operators have made every effort to market selected and better prepared coals. In view of the wide range of physical characteristics and chemical properties of bituminous coals, the problems are real and are receiving increased attention. Some twelve years ago a laboratory method was developed at Battelle Memorial Institute for the relative evaluation of coals for use in residential underfeed stokers. The method was developed in conjunction with work being done at that time for Bituminous Coal Research, Inc., and for individual coal producers, to obtain information on the characteristics of coal that determined the successful performance of the small stoker. Details of the equipment and test procedure were given by R. A. Sherman1 in a paper presented at the University of Illinois Fifth Short Course in Coal Utilization. During the past several years, the evaluation of over forty different coals has been determined by investigations sponsored at Battelle by coal operators in the eastern producing districts. The purpose of this paper is to compare the results and conclusions derived from the various tests with marketing experiences of the operators, and to discuss briefly the relationship of test results to standard laboratory determinations. Equipment Used in Tests Fig 1 shows schematically the equipment used in the evaluation tests. The stoker is a commercial model of conventional design, having a nominal feed rate of 30 Ib per hr. A special laboratory furnace is used, which is tightly sealed to prevent the entrance of secondary air. The complete stoker-furnace assembly is mounted on platform scales which permits the measurement of combustible weight losses occurring during the test. The furnace stack, in which are a thermocouple, flue-gas sampling tube, and smoke meter, is connected to the laboratory exhaust breeching through a friction-less connection. Through use of an auxiliary blower system, provision is made for the measurement of the air delivered by the stoker fan to the windbox. A water seal in the duct work eliminates inter-

Jan 1, 1950

By D. Van Winkle, C. Zener, H. Nielsen

THe internal friction of metals has been studied frequently at elevated temperatures.1-4 In most cases it rises rapidly with increasing temperature. The notable exceptions are ferromagnetic materials, and lead.2 This paper describes an investigation of the general features of the high-temperature internal friction of 70-30 alpha brass. Experimental Method The internal friction of a metal is a measure of the rate at which it dissipates energy of vibration. The measure adopted here, I/Q, is (I/2p) times the specific damping capacity, a measure commonly used by engineers. In the measurements of this investigation, the stress level was kept so low that the observations were independent of the stress, The general method of making such measurements, and of observing temperature of a specimen during a measurement, has been described.5.6 The driver and detector coils were wound with wire insulated with glass thread, in order to withstand the high temperatures used. In previous work electrical eddy currents in the specimen served as the coupling between the mechanical vibration of the specimen and the electrical circuits of the driver and detector. The high values of the internal friction in the present investigation rendered this coupling insufficient. In order to increase this coupling, pole pieces cut from ordinary telephone diaphragms were attached to the specimen. A mixture of French chalk and water glass proved a satisfactory cement. All measurements were made at the fundamental frequency for transverse vibration, which lay between 600 and goo cycles per second. Specimens The measurements described herein were made upon a single cylindrical rod of brass, kindly furnished by Dr. Cyril Stanley Smith, of the American Brass Co. This rod was the specimen E of the set of alpha-brass rods described in an earlier paper.6 Successively larger grain sizes were obtained by annealing at .successively higher temperatures. A slice was cut off one end after each set of measurements. Grain counts were made on each slice by W. E. Lindlief, of the American Brass Co. Nine fields were viewed on each piece, located as shown in Fig. I. Results are given in Table I. The grain size is defined in the usual way; namely, Grain size = I/n1/2 where n is the mean number of grains per square millimeter. Experimental Results This paper is concerned exclusively with the part of the internal friction that be. comes dominant at high temperatures. It is thus desirable to separate this part of the internal friction from the part that is

Jan 1, 1942

By C. Zener, H. Nielsen, D. Van Winkle

THe internal friction of metals has been studied frequently at elevated temperatures.1-4 In most cases it rises rapidly with increasing temperature. The notable exceptions are ferromagnetic materials, and lead.2 This paper describes an investigation of the general features of the high-temperature internal friction of 70-30 alpha brass. Experimental Method The internal friction of a metal is a measure of the rate at which it dissipates energy of vibration. The measure adopted here, I/Q, is (I/2p) times the specific damping capacity, a measure commonly used by engineers. In the measurements of this investigation, the stress level was kept so low that the observations were independent of the stress, The general method of making such measurements, and of observing temperature of a specimen during a measurement, has been described.5.6 The driver and detector coils were wound with wire insulated with glass thread, in order to withstand the high temperatures used. In previous work electrical eddy currents in the specimen served as the coupling between the mechanical vibration of the specimen and the electrical circuits of the driver and detector. The high values of the internal friction in the present investigation rendered this coupling insufficient. In order to increase this coupling, pole pieces cut from ordinary telephone diaphragms were attached to the specimen. A mixture of French chalk and water glass proved a satisfactory cement. All measurements were made at the fundamental frequency for transverse vibration, which lay between 600 and goo cycles per second. Specimens The measurements described herein were made upon a single cylindrical rod of brass, kindly furnished by Dr. Cyril Stanley Smith, of the American Brass Co. This rod was the specimen E of the set of alpha-brass rods described in an earlier paper.6 Successively larger grain sizes were obtained by annealing at .successively higher temperatures. A slice was cut off one end after each set of measurements. Grain counts were made on each slice by W. E. Lindlief, of the American Brass Co. Nine fields were viewed on each piece, located as shown in Fig. I. Results are given in Table I. The grain size is defined in the usual way; namely, Grain size = I/n1/2 where n is the mean number of grains per square millimeter. Experimental Results This paper is concerned exclusively with the part of the internal friction that be. comes dominant at high temperatures. It is thus desirable to separate this part of the internal friction from the part that is

Jan 1, 1942

By Keith Leonard Sutherland

THIS paper is a study of the differential flotation of the sulphide minerals in the presence of salts of silver, lead and zinc. In practice, accidental activation due to these salts is more important than their use as reagents to replace copper sulphate. The general method of investigation has been based upon contact tests, the temperature of 35°C. being chosen in conformity with earlier work. Potassium ethyl xanthate and potassium amyl xanthate were selected as collectors and pure sulphide minerals were used. The experimental procedure has been outlined in earlier papers and all solutions were kept carbonate -free.1,4 Contact, or spreading of an air bubble, at a mineral surface indicates the presence of an adsorbed collector film. PURITY OF REAGENTS The xanthates were purified in the usual manner.1 Neither the cyanide nor the sodium hydroxide solutions contained sufficient carbonate to give a precipitate with barium chloride solution. The silver sulphate was prepared from pure silver nitrate by evaporation with concentrated sulphuric acid until there was no evidence of brown fumes. This solution was diluted and the difficultly soluble sulphate washed with water so that unchanged nitrate was dissolved. The resultant crystalline powder was pure white. The lead and zinc salts were prepared by dissolving especially pure lead and zinc in C.P. nitric and sulphuric acid solution and the crystals drained. The standard solutions were checked by titration. It was felt desirable to use the sulphate radical wherever possible, but since lead sulphate was insufficiently soluble for the purpose of the experiments, it was necessary to use some other lead salt. A.R. copper sulphate was used without further purification. RESULTS The results are presented in the accompanying figures; the areas of noncontact (nonflotation) are shaded in Figs. 8, 9, 10 and 11; in the remainder they lie to the right of the curve. Zinc Sulphate The curves in Fig. I are to be compared with those for Fig. 2, for which zinc sulphate is absent. This comparison shows that the influence of the zinc ion is usually small. Its influence is more marked, however, for chalcopyrite in the absence of cyanide. The influence of zinc sulphate is also marked for copper-activated sphalerite, for which tests were made only in the absence of cyanide. The results are of importance in the separation of pyrite from copper-activated sphalerite when, zinc sulphate is added in the lead flotation section (p. 204 of ref. I). Sphalerite does not adsorb the collector (i.e., become floatable) under the conditions chosen.

Jan 1, 1942

By Paul A. Schafer

BALATOC mine, the principal gold-producing mine in the Philippines, is 10 miles southeast of Baguio, in the Cordillera Central of northern Luzon.1 The region is a deeply dissected plateau, ranging in altitude from 3000 t0 5000 ft. above sea level. The rocks consist chiefly of granodiorite, diorite, and remnants of metamorphosed sediments, cut by dikes of andesite porphyry and quartz-diorite porphyry. All are intruded by a volcanic breccia plug, oval in horizontal section, about 3200 ft. long and 2300 ft. wide, which is the north central part of the mineralized area. Three main vein systems have been developed (Fig. 1): q6, 231 and 364, which strike about N.70°E. and dip 5o to 90°S. Each system is a braided zone consisting of many individual components. They are disturbed by a series of premineral faults or shear zones striking about N.45°E. Twelve of these produce important effects on the persistence, character, and quality of veins. From west to east the faults are named (after claims): Hog, Big Gun, Bull, Pine, Lolita, Bar No. I, Bar No. 2, Curt, Sun, Helen, Itoe, and Frog. They are early breaks formed prior to the N.70°E. vein fractures. Mineralization occurs on them but, with several prominent exceptions, they are too low grade to mine. A number of northwesterly striking faults complete the structural pattern. Although they are relatively abundant, the effect on the veins is so small that they do not present any problems in mining or development. All of these faults that have been observed are later than the N.70°E. veins and offset them to the left. NORTHEAST FAULTS The early northeast faults* are notably continuous in spite of their small displacements, 20 to 100 ft. Frequently they appear so weak that their importance is masked and their identity clouded. The gouge along any of these faults may vary from exceedingly weak at one point to very strong at another point only a short distance away. In other words, the amount of gouge depends on the changes of attitude of the fault plane, and is no indication of the extent of the movement. Places where walls are spread apart are filled with gouge squeezed from tight places. Also, mineralization sometimes obscures fault gouges by replacement. The mineralization of northeast faults has produced several important ore bodies; namely, 231 west on Pine fault and q6 vein on the same fault. To a smaller extent, Lolita, Curt, Bull, Bar No. I, and Sun

Jan 1, 1942

By Dan Crackel, G. G. Ramos, Mark Heisel

INTRODUCTION Feasibility studies indicated that a cratering type stoping method was best suited to the character of the first ore block at Carr Fork. This method known as vertical crater retreat (VCR) has since been modified to a combination cratering and deck blasting using VCR drop raises for initial undercut development . The modified form retains many of the advantages of VCR while allowing high tonnage production blasts which have offset many of the disadvantages. FIRST CONCEPTS AND PREMISES Geologic Considerations The Steep Highland Boy (SHB) skarn orebody, the first of several blocks being developed, is a steeply dipping 70° to 90° limb of a syncline, with a width averaging 25 m (82 ft). The bed has a consistent east-west strike length of over 400 m (1300 ft) and extends from the surface to depths of over 1000 m (3300 ft). The footwall is highly fractured quartzite and the hanging wall grades from garneti te to limes tone and hornfe 1s. Because of the limestone in the hanging wall, the hanging wall appears more competent than the footwall. The ore is garnetite with lenses of massive sulphide and magnetite. The quartzite footwall is highly fractured not only because of the bedding but also due to the folding and intrusion of the quartz monzonite. This irregular footwall outline of some stopes in- creases the likelihood of excessive dilution. The principal ore mineral is chalcopyrite with some bornite. The garnetite ore is quite variable in terms of compressive strength and drillability. In addition to the sulphide and magnetite lenses, it is transected by clay- altered dikes and major and minor north-east faults. TABLE (1) gives the range and mean strengths of the rocks. Investigating Mining Methods Initial consideration of a suitable mining method centered around maximum safety and efficiency with minimum potential dilution. The following major methods were considered and investigated. Cut and fill mining was eliminated because of low productivity, the cost and problems associated with providing fill, and the relatively unsafe nature of the method. Sublevel caving was rejected due to the unpredictable cavability of the waste and the geometry of the ore body. Conventional sublevel or blasthole methods require excessive development, as fan and ring drills are limited to efficient drilling in the 18 to 25 m range (60 to 80 ft). Mining downdip with equipment drilling small diameter holes would have required eight separate extraction/drill horizons with crosscuts and associated excavation in the main ore block. The use of down the hole (DTH) machines cap- able of drilling 165 m (6g in) diameter holes

Jan 1, 1981

JOHN W. BELL, *Montreal, Quebec, Canada (communication to the Secretary?). The test results in Mr. Taggart&apos;s paper will, I am sure, be recognized as a notable contribution, and of great assistance in the study of the performance of the Hardinge mill. I regret, however, being obliged to note that Mr. Taggart still retains. such confidence in the Kick-Stadler method of computing the ?relative mechanical efficiency" of crushing machines. The Rittinger-Kick graph submitted by Mr. Gates and the tests made at McGill University disclosed precisely the same fundamental defect in the Kick-Stadler theory. Consequently, I have been obliged to recalculate in terms of Rittinger surface units the results obtained in the 28 rock-crushing tests cited by Mr. Taggart, in order to find- out what the relative efficiencies really were. In order to show the large discrepancies between the Stadler and Rittinger R. M. R&apos;s, the most, efficient result disclosed by each method is represented by the number 100, and the R.. M. E.&apos;s for the other tests have been recalculated on this basis. The results will be found in Table 1. Personally, I look forward to the time when we shall cease to talk about "relative mechanical efficiency" and merely refer to the "efficiency" of a crusher. All that is required to accomplish this is to agree on a standard method for determining the "crushing constant" of a given rock and a standard method for calculating the efficiency. The figures in the fourth column of Table 1 have been derived by assuming a constant of 2,000 for the quartzite crushed in the Yale tests. The Stadler method sometimes indicates changes in efficiency produced by, changes in operating conditions, as I pointed out in a paper describing rock-crushing tests made at McGill University. It is, however, not enough to determine that certain changes increase or decrease efficiency; surely it is equally important to determine the magnitude of these variations. By examination of Mr. Taggart&apos;s results, I have been obliged to conclude that the size of feed and amount of reduction greatly influence the Stadler R. M. E. figures, that they are positively misleading. It should be mentioned that since the majority of the tests have been made at the least efficient feed rates, and since, moreover, it is one of the evidently very important factors affecting efficiency, it is possible that different results might be obtained by a high-tonnage feed series, and that

Jan 8, 1917

By John L. Lamont, Walter Crafts

SELECTION of an alloy steel for a heat-treated article has been facilitated by methods for the calculation of hardenability,1 as-quenched hardness,2,3 and tempered tensile strength.4 Ductility and toughness may also be estimated if the steel is completely hardened on quenching,5,6 and the present study was carried out in order to develop a basis for estimating the Izod impact strength of partially hardened steel. The investigation was directed toward the prediction of Izod impact strength in steels of normal commercial quality without consideration of special compositions or heat-treatments that might produce abnormal brittleness. It was found that Izod impact strength of alloy steel is controlled by hardness, degree of hardening on quenching, and grain size. In fine-grained steels the impact strength for any given degree of hardening is inversely proportional to the tempered Rockwell C hardness, and the relation of impact strength to hardness is lowered by incomplete hardening. Calculation of the tensile strength and impact strength of heat-treating steels has shown that, except at very high strengths, tensile strength is raised by alloys without loss of impact strength whereas the tensile strength gained by higher carbon contents tends to be accompanied by a disproportionate loss of toughness. Plain carbon steels give relatively low and unpredictable impact strength. The calculation is sufficiently accurate to be helpful in the selection of alloy steel, and common grades of alloy steel have been evaluated with respect to combinations of tensile strength and impact strength attainable after heat-treatment in sections from I to 4 in. in diameter. PROCEDURE The study of the relation of hardness to impact strength was based on test data derived from 24 heats from four producers. The steels included the following SAE and AISI compositions: 1020, 1o30, 1040, 1340, 3310, 3316, 4320, 4330, 4340, 8620, 8630, 8640, 8720, 8730, 8740, 9310, 9317, 9440, 9917 and three high-alloy chromium-nickel-molybdenum steels. As far as is known, the steels tested were of normal commercial quality. They were supplied in 4-in. sections, which were forged to smaller sizes, prenormalized, and machined to final dimensions. Heat-treatment was carried out by heating to the usual austenitizing temperature for the grade of steel, holding for one hour per inch of thickness and quenching in still oil at room temperature. Previous work had indicated that this quenching treatment approximates a severity of H = 0.35. The bars were tempered as follows: ½ in., I in., and I 5/8 in., 2 hr; 2 ½ in., 3 hr; 4 in., 5 hr. All bars were air-cooled from the tempering tem-

Jan 1, 1947

By M. R. Tek, F. H. Poettmann, M. L. Grove

The general problem of single-phase natural gas flow through porous media has been considered both by mathematical analysis and field experiments. Theoretical studies on the fluid dynamics of natural gas wells resulted in derivations of expressions which permit a ber-ter understanding of the flow mechanism for conditions under which Darcy&apos;s law is no longer valid. In applying these results to natural gas production and testing technology, special emphasis war placed on the study of low permeability, slowly stabilizing formations. These applications resulted in a method of predicting the performance coefficients of tight natural gas wells. The calculation of the performance coefficient requires the determination of the "test-index", pkh/µ, the drain- age radius, R, and the effective wellbore radius, rw. Methods for estimating these parameters from field data were also developed. Field data from 15 wells were collected and analyzed. The measured values of the performance coefficients were compared with the predicted values. This statistical evaluation gave a bias of 7.14 per cent and a standard deviation of 11.6 per cent. INTRODUCTION The performance of a natural gas well is determined by the physical properties of the reservoir rock, the extent and the geometry of the drainage area, the properties of the flowing fluid, and the conditions of pressure distribution within the drainage matrix. The relation between the quantity of gas delivered and the pressure drop within the reservoir is characteristic of the behavior of each well and is often referred to as the back-pressure behavior of the well. It is well established that for normal, single-phase gas wells the relationship between the gas delivery rates and the bottom-hole pressure take, in general, the form, Q = c(P3 8 -P2 1)n. ,.......(1) where C is the performance coefficient, and n is the exponent corresponding to the slope of the straight-line relationship between Q and (P2 s, — P2 l) plotted on logarithmic coordinates. The determination of a well&apos;s performance by the back-pressure behavior not only permits the production engineers to analyze many operating problems, but also provides necessary information useful and essential to predict the future development of the field.&apos; Important engineering and production problems such as calculation of gas deliverability into a pipeline at a predetermined line pressure, design and analysis of gas-gathering lines, determinations of spacing and number of wells to be drilled during field development to meet future market or contract obligations, etc., all depend, at least in part, on the availability and use of reliable back-pressure curves.&apos; In the past the behavior of gas wells was evaluated

Jan 1, 1958