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By J. D. Rice, S. C. Pitzer, C. E. Thomas

Interpretation of pressure build-up data obtained in the conventional manner has often been difficult because of the deviation from theoretical behavior. Major causes of this deviation have been attributed to damage and afterflow, and to fluid redistribution in the wellbore which, in extreme cases, can result in a pressure hump in the early portion of the build-up curve. Theoretical investigations show that bottom-hole pressure is definitely influenced by phase redistribution in the tubing column during surface shut-in tests, and that the magnitude of the effect is sensitive to the producing gas-oil ratio and stabilized rate of flow in the well. For field experiments a wire-line tubing packer, which can be run in the tubing against a stabilized flow rate, was developed for bottom-hole shut-in tests. By use of this bottom-hole .shut-in method, pressure humps previously observed in surface shut-in tests were completely eliminated and the effects of afterflow minimized. Analog and digital computer studies have been made to obtain theoretical curves for comparison with field curves, and remarkable agreement between the results of bottom-hole shut-in tests and theoretical curves has been obtained. INTRODUCTION Pressure build-up data from shut-in wells have been used by the petroleum industry to determine the permeability of the formation, to estimate wellbore damage, to evaluate the static reservoir pressure and to speculate reservoir volume. Calculation of these factors is based on methods of analysis developed for theoretical systems whose build-up curves have a charac- teristic shape when the wells are shut-in at the sand faCe.1,2,3,5,8,10 However, field curves obtained by conventional surface shut-in methods do not always exhibit this characteristic. Such factors as stratification, rock heterogeneities and irregular reservoir geometry can cause the character of a build-up curve to deviate from that predicted by theory for a simple system. In addition, all field build-up data are affected by the methods utilized in obtaining the measurements. Conventional surface shut-in techniques allow two effects to occur which contribute directly to the manner in which pressure builds up at the sand face. The first, afterflow, has been recognized for some time and methods are available for estimating the magnitude of its effect and for correcting its influence.' The second, phase segregation in the tubing column after shut-in, has been reported only recently and appears to exert a considerable influence on the character of field build-up curves.!' In extreme cases, phase segregation can produce "pressure humps" in the early portion of the build-up curve. Such curves have been considered anomalous and have defied analysis. It is the purpose of this paper to discuss the effect of phase segregation in the tubing string during build-up and to present a bottom-hole shut-in technique for obtaining field build-up data which minimizes the influence of afterflow and eliminates phase segregation effects. It will be shown that reliable reservoir information can be calculated from build-up measurements obtained using this method, even though conventional surface shut-in tests on the same wells yield anomalous data. DISCUSSION OF PHASE REDISTRIBUTION EFFECTS Some of the effects of phase redistribution on pressure build-up curves have been described previously by Matthews and Stegemeier" who have presented evidence that phase segregation is responsible for the pres-

By John Nunes, Frank R. Larson

Temperature-dependent functions of various ten-sile flour stress and fracture parameters were investigated on iron and low composition alloys of Fe-C, Fe-Cr, Fe-Mn, and Fe-Ni. Data were obtained over a range of test temperatures from 200" to -196"C at an initial strain rate of 0.01 min". It was found that the strain-hardening exponent, n, for the Fe-Ni alloys increased significantly at very low testing temperatures with increased alloy addition. Also, the stress and strain at fracture followed a predictable transitional type of behavior. The flour stress-temperature dependence was evaluated employing the relation: M where it is shown that composition can strongly influence the constant M. An empirical formula describing this effect is as follows: M = MI (equivalent at. pct Ni)-'" Some preliminay, tests were run on several commercial steels to test the generality of this relationship. One of the phenomenological explanations of the ductile-to-brittle transition encountered in bcc metals is based upon the difference in the temperature dependence of the flow and fracture stresses.' It states simply that the fracture stress is relatively insensitive to temperature and that the yield or flow stress rises rapidly with decreasing temperature so that, when the flow stress reaches the fracture stress, brittle fracture occurs without appreciable plastic deformation. This behavior is illustrated schematically in Fig. 1 where the ductile-to-brittle transition is shown to occur at two possible temperatures. The lowest temperature, TB, represents essentially completely brittle behavior while the higher temperature, TN, represents "notch" brittle behavior. Support for this theory is obtained when it is observed that fcc metals, which do not commonly have a ductile-to-brittle transition, also do not commonly exhibit any strong temperature de- pendence of the yield stress. This relationship of yield or flow stress behavior with the ductile-to-brittle transition has been generally observed for most metals representative of these two crystallo-graphic structures. One exception to this generalization appears in the case of tantalum where no apparent ductile-to-brittle transition has been observed. However, this may simply be an indication that this type of behavior is not directly related to the flow stress and that some other mechanism such as twinning must also be operative. A comparison of the typical temperature dependence of the yield stress of some representative metals is shown in Fig. 2. In the study of the temperature dependence of the strength of metallic materials, considerable ef-

Jan 1, 1963

By L. J. Health

Synthetic rock with predictable porosity and permeability has been Prepared from mixtures of sand, cement and water. Three series of mixes were investigated primarily for the relation between porosity and permeability for certain grain sizes and proportions. Synthetic rock prepared of 65 per cent large grains, 27 per cent small grains and 8 per cent Portland cement, gave measurable results ranging in porosity from 22.5 to 40 per cent and in permeability from 0.1 darcies to 6 darcies. This variation in porosity and permeability was caused by varying the amount of blending water. Drainage-cycle relative permeability characteristics of the synthetic rock were similar to those of natural reservoir rock. INTRODUCTION The fundamental behavior characteristics of fluids flowing through porous media have been described in the literature. Practical application of these flow characteristics to field conditions is too complicated except where assumptions are overly simplified. The use of dimensionally scaled models to simulate oil reservoirs has been described in the literature. 1-3 These and other papers have presented the theoretical and experimental justification for model design. Others have presented elements of model construction and their operation. In most investigations the porous media have consisted of either u ncon soli da ted sand, glass beads, broken glass or plastic-impregnated granular substances—materials in which the flow behavior is not identical to that in natural reservoir rock. The relative permeability curves for unconsoli-dated sands differ from those for consolidated sandstone. The effect of saturation history on relative permeability measurements is discussed by Geffen, et a1.4 Wyga15 has shown quite conclusively that a process of artificial cementation can be used to render un consolidated packs into synthetic sandstones having properties similar to those of natural rock. Many theoretical and experimental studies have been made in attempts to determine the structure and properties of unconsolidated sand, the most notable being by Naar and Wygal.6 Others have theorized and experimented with the fundamental characteristics of reservoir rocks. This study was conducted to determine if some general relationship could be established between the size of sand grains and the porosity and permeability in consolidated binary packs. This paper presents the results obtained by changing some of the factors which affect the porosity and permeability of synthetically prepared sandstone. In addition, drainage relative permeability curves are presented. EXPERIMENTAL PROCEDURE Mixtures of Portland cement with water and aggregate generally are designed to have certain characteristics, but essentially all are planned to be impervious to water or other liquids. Synthetic sandstone simulating oil reservoir rock, however, must be designed to have a given permeability (sometimes several darcies), a porosity which is primarily the effective porosity but quantitatively similar to natural rock, and other characteristics comparable to reservoir rock, such as wettability, pore geometry, tortuosity, etc. Unconsolidated ternary mixtures of spheres gave both a theoretically computed and an experimentally observed minimum porosity of about 25 per cent.7 By using a particle-distribution system, one-size particle packs had reproducible porosities in the reproducible range of 35 to 37 per cent.6 For model reservoir studies of the prototype system, a synthetic rock having a porosity of 25 per cent or less and a permeability of 2 darcies was required. The rock had to be uniform and competent enough to handle. Synthetic sandstone cores were prepared utilizing the technique developed by Wygal.5 Some slight variations in the procedure were incorporated. The sand was sieved through U. S. Standard sieves. A 18-20 sand denotes that the sand passed the Number

Jan 1, 1966

By A. J. Mcintosh

PRICE changes in competing fuels in the last three decades have reflected the changes in the consuming habits of the people of the United States. Prior to World War 11 the importance of fuel oil and fuel gas increased almost constantly while the relative importance of both bituminous and anthracite coal decreased. During this same prewar period coal prices increased to a much greater extent than oil prices. In fact, in many years, oil prices declined and in most cases are now no higher than they were back in 1925-26. During the war natural economic trends were entirely upset because of the tremendous petroleum requirements of the Army and Navy. Under these conditions many industrial plants were converted to the use of coal and the new installations in home heating and industrial plants of all kinds which might have used oil were practically eliminated. Although petroleum prices were rigidly controlled by OPA coal prices increased several times during the war. An over-all statement as to the rela-

Jan 1, 1947

By R. E. Gilchrist, R. F. Nielsen

When a gas is displaced by mother in a porous medium, and there is a relative immobile liquid present. there is a transition zone in which the gas composition varies from essentially that of the original gas to that of the injected gas. The change in extent of this zone with time may be governed by a mixing process in the direction of flow and by the rate of establishment of gas-liquid equilibrium, if the gases are appreciably soluble in the liquid. The relative importance of these two factors in deterri~ining the growth of the transition zone is discussed, with appropriate equations and experimental data. INTRODUCTION The various solution methods of oil recovery involve a transfer of the components of a mixture, whether within a single phase or between a liquid and gas. The similarity of a natural porous medium to systems used in separation and chromatographic processes makes it seem reasonable that certain concepts used by chemical engineers in "mass transfer" might be applicable to petroleum reservoirs. One approach, the HETP (height equivalent to a theoretical plate), involves a distance or length of time over which equilibrium might be con. sidered as established. Another approach involves direct use of a rate of mixing or rate of establishment of equilibrium. The latter approach has been preferred in relation to production problems. DISCUSSION AND PROCEDURE When a gas or liquid in a porous medium is displaced by one of different composition but miscible with it there will be set up a transition zone in which the composition varies from cssentially that of the original fluid to essentially that of the injected fluid. If the fluid being displaced is a gas, and there is a relatively immobile liquid present, the transition zone may be

By D. J. Coolidge, H. L. Sheakley

THIS paper does not deal with all sands used in the glass industry in Missouri; it covers only that used in the plate-glass factory at Crystal City. However, it is probably safe to say that other sands, pro- [ ] duced throughout the state for this purpose, are of identical nature. The glass sand used in Missouri is commonly called the St. Peter deposit, which is ascribed to the Ordovician Rock series in the form of sandstone. This St. Peter deposit, aside from a few small outliers, covers a large area of eastern Missouri. It forms, through a broad curve, the northeast margin of the typical Ozark region between Cape Girardeau on the southeast and Mineola, Montgomery County, on the northwest. The belt is extremely irregular, varying from one to ten miles in width; its length is 150 miles in a straight line. [ ] The outcrop near the entrance to the Crystal City mine appears in the form of a sandstone bluff approximately 30 ft. high, running along Plattin Creek (Fig. , I). Above the sand rock an overburden of Joachim limestone appears, which, thickens to nearly 300 ft. and forms the hill commonly called Buck Knob. Test holes, where drilled at various points and the drillers' log indicate that the St. Peter deposit ranges in thickness from 63 to 71 feet. PROPERTIES OT THE ST. PETER SAND From an analysis of the glass sands of the St. Peter formation in Missouri, the follow-

Jan 1, 1942

By K. E. Merklin, F. D. DeVaney

Students of the modern blast furnace seem unanimously agreed that they are observing a major revolution in practice. Rather than changing construction and operation of the furnaces, most of the great advances now under way deal with the raw materials feed. Prepared burdens have gained increasing significance during recent years. Sizing, concentration, and agglomeration have all become bywords to greater production and reduced operating costs. The remarkable results with test furnaces in which self-fluxing sinter makes up part or all of the ore charge foretell even greater improvements. Other investigators have reported many of these advances, and it is enough to predict here that more and more operators will turn to the use of self-fluxing sinter. This change in the operator's requirements comes at a time when one major section of the iron ore regions, the Mesabi, is finding it difficult to maintain, let alone improve, the tonnage and grade of its shipping product. To meet the new demands with respect to quality and structure, the iron ore producers of this area turned first to screening, crushing, and concentrating intermediate ores. More recently, declining higher-grade reserves have led to multimillion-dollar investments in plants to treat the low-grade magnetic taconites.1,2 To yield a suitable concentrate, the Minnesota magnetic taconites must be ground to about 80 pct through 325 mesh, too fine to be charged directly to the blast furnace or to make acceptable feed to the sinter strand. The pelletizing process was developed to meet the structure requirements laid down by the blast furnace operators. Taconite producers are succeeding in their efforts just when the attention of the blast furnace man is being drawn to the great advantages of self-fluxing sinter.3 The taconite operators are ready with an alternative. Why not produce sclf-flus ing pellets? At the Hibbing laboratory of Pickands Mather & Co., where much of the early work was done that led to Erie Mining's 7.5-million ton taconite plant at Hoyt Lakes, Minn., preliminary investigations have been made. Present Taconite Operations: Details of this work will be clarified by a brief review of agglomeration practice in commercial taconite plants. After the taconite has been ground to about 80 pct through 325 mesh to liberate the magnetite grains, the ore is concentrated on magnetic separators, thickened, and filtered to about 10 pct moisture. This structure and moisture fit in closely with the conditions required to produce good balls. It has been found with taconite concentrates that at least 60 pct of the feed to the balling drum must be —325 mesh to obtain good ball compaction within reasonable time. The filter cake moisture usually permits a slight water addition at the balling drum, and further balling control is obtained by adding about 12 Ib of bentonite and 1 1/2 lb of soda ash per dry short ton of concentrate. These additives, and occasionally small quantities of fine coal, are thoroughly mixed with the filter cake ahead of balling. The swelling property of bentonite improves the green and dry strength of the balls so they can be handled without breakage until they are fired. Soda ash is added for pH control to insure maximum performance of the bentonite, and coal is added for more heat in the firing process when required. The balls, normally 3/8 to l-in. diam, are brought to a temperature of 2350" to 2500°F in the indurating furnace. Heat for this process comes from three sources: 1) fuel burned in the combustion chamber, 2) oxidation of the magnetite concentrates to hematite, and 3) coal added to the balls. Pellet strength is developed by grain growth and bridging and, if enough slag-forming constituents are present, by slag bonding. Conversion to hematite is usually close to 100 pct in the fired pellets. Batch Test Procedures: Initial studies of self-fluxing pellets were made by producing balls on a batch basis under carefully controlled laboratory conditions. The l-in. balls, uniform in size, were fired in an oxidizing atmosphere in a standard laboratory muffle furnace. The firing procedure consisted of

Jan 1, 1961

By C. F. Lucks, W. D. Wood, H. W. Deem

Electrical ad thermal-conductivity measurements have been made on titanium and 6 titanium alloys. The following expression was derived for calculating thermal conductivity from electrical conductivity: K = 0.626 s T x 10-8 + 0.00497 where K = thermal conductivity, cal sec-1 cm-2 cm0C-1 s = electrical conductivity, ohm-]cm-1 T = temperature, deg Kelvin This expression gives calculated thermal conductivities that are not in error by more than 10 pct from the experimental values for A-55 titanium and the 6 alloys measured; namely, A-110AT, C-110M, C-130AM, Ti-6A1-4V, Ti-140A, and Ti-155A, which are representative of the presently available commercial a and a-ß titanium alloys. THERMAL conduction in a gas, liquid, or amorphous solid is accomplished by energy diffusion from molecule to molecule, a relatively slow process. For this reason, such materials have a low thermal conductivity. When a material is crystalline, there is in addition a heat transfer by a vibratory motion of the crystal lattice. It is the contribution of this lattice conduction that makes a crystal a much better conductor than a gas, liquid, or amorphous solid. Lattice conduction, however, does not account for the relatively enormous thermal conductivity of a metal. This is explained by the freedom of movement of valence electrons. These valence electrons drift in a metal in a direction toward a drop in electrical potential and, to a lesser degree, in the direction of a temperature drop in the metal. Since both the electrical and thermal conductivities of a metal depend upon the presence of free electrons, there should be some relatively simple relation between the two. Wiedemann and Franz in 1653 first discovered an approximate empirical relation between the electrical and thermal conductivities of metals at the same temperature. This ratio varies appreciably with temperature, and Lorenz later showed that by adding a temperature factor to the Wiedemann-Franz ratio the value of K/(s T) is constant, where K is the thermal conductivity, a the electrical conductivity, and T the absolute temperature. This Lorenz constant shows a greater variation for alloys than it does for pure metals, the ratio increasing slightly as the proportion of alloying elements increases. It has been found that a closer correlation between electrical conductivity and thermal conductivity can be obtained by means of an equation of the form K - A s T + B [1] where A and B are constants. In this equation the term AsT is the contribution of electronic conduction and B is the contribution of lattice conduction to the total thermal conductivity. EXPERIMENTAL MEASUREMENTS Electrical-resistivity and thermal-conductivity measurements on titanium and 6 titanium alloys serve as the basis for determining an equation of the K = AsT + B type for titanium alloys. Specimens—Table I shows nominal compositions of the 7 metals on which electrical and thermal conductivities were measured. The electrical and thermal-conductivity specimens for each alloy were taken from stock of the same heat and usually from adjacent sections of the same bar. All of the metals measured were in a mill-annealed condition. Methods—Electrical-resistivity measurements

Jan 1, 1959

By D. A. Elgillani, M. C. Fuerstenau, J. D. Miller

Adsorption of lead and ferric iron on quartz and alumina is presented as a function of pH. Only the hydrolyzed species of these metal ions, FeOH++ and PbOH+, adsorb significantly on each of these minerals. Zeta potentials of quartz were measured as a function of pH in the presence of various additions of aluminum, lead, and magnesium salts. Sign reversal occurs at the pH values where significant concentrations of hydroxy complexes are formed. Models of adsorption are presented in the absence and presence of collector. The mechanism of adsorption of metal and collector species in the activation of nonmetallic minerals is still the center of considerable discussion in spite of the extensive study given this system. Until recently, the view was widely held that hydrated metal ions were responsible for this phenomenon. This fact is surprising, since it had been shown that the pH range in which flotation is effected corresponds to that in which metal ion hydrolysis occurs.' Additional support of this concept was pro vided by the work of Wolstenholme and Schulman in another system.' Later work has shown that hydroxy complexes of metal ions are the active species. These studies have also indicated that basic aqueous complexes of metal-collector may be necessary for flotation.3-7 Depending on the molecular weight of the collector, formation of these complexes may occur before or after precipitation of the metal-collector salt has occurred. Ion pair formation can occur when low molecular weight collectors are involved because relatively high concentrations of metal hydroxy complex and collector can be present in solution before precipitation occurs. This is not the case when high molecular weight collectors are used. A model of aqueous complex adsorption has been presented6,7 in which it has been assumed that adsorption occurs by the formation of water from adsorbed hydroxyl and hydrogen of the hydroxyl contained in the complex. Other authors8 have suggested that hy-droxy complexes are involved in these systems but that collector adsorption occurs by replacement of the hydroxyl of the adsorbed metal hydroxy complex with a fatty acid anion. All of these investigations have involved mineral surfaces that were negatively charged so that it is not possible to state with certainty whether hydrated metal ions or hydroxy complexes are the active species in this system. Use of a positively charged mineral should be helpful, however, since the hydrated metal ion will be repelled from this surface. On the other hand, if the hydroxy complex adsorbs by splitting out water, surface charge should have no effect because of the free energy decrease that the system will experience when water is formed. In this regard, sapphire is well-suited for study, since its surface is positively charged until approximately pH 9. Electrokinetic studies of quartz in the presence of various metal ions should also be useful in establishing the mechanisms of adsorption in these systems. That is, if the hydroxy complexes adsorb by water formation, drastic changes in the zeta potential should occur in the pH range in which hydrolysis occurs. In this view, adsorption of ions of widely different hydrolysis characteristics on both sapphire and quartz was measured. In addition, zeta potentials of quartz were measured as a function of pH in the presence of various metal ions and compared with flotation responses obtained under similar conditions. Experimental Materials and Techniques Reagent-grade aluminum, ferric and magnesium chlorides, and lead nitrate were used in this investigation. Adjustments in pH were made with reagent-grade HCl or KOH. Conductivity water, made by passing distilled water through an ion exchange column, was used in all of the experiments.

Jan 1, 1971

By J. Geertsma, F. de Klerk

During the hydraulic fracturing treatment of an oil or gas well the liquid pressure in the borehole is increased until tensile stress in the surrounding rock exceeds tensile strength. Once a tensile fracture is initiated, it is penetrated by liquid from the borehole and fracture propagation under continuous hydraulic action takes place. The fracturing liquid carries a propping agent to ensure a highly permeable flow channel after pressure release. Field results range from failure to obtain increased production to outstanding success. In all cases, however, it unfortunately remains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact the ideal ones. Though experience provides a lead, a more satisfactory way to predict results would seem to be to subject the fracture propagation process to a theoretical analysis that (1) makes the maximum use of the relevant physical information and (2) so simplifies the resulting calculations that the field engineer gets practical data that he can handle comfortably. We are attempting here to do this in connection with the prediction of fracture width and areal extent before pressure release. What remains of the fracture afterwards depends on the distribution of the propping agent between the fracture walls, and that is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplify- ing assumptions have had to be made: 1. The formation is homogeneous and isotropic as regards those of its properties that influence the fracture-propagation process. 2. The deformations of the formation during fracture propagation can be derived from linear elastic stress-strain relations. 3. The fracturing fluid behaves like a purely viscous liquid; i.e., any peculiar flow behavior due to the addition of gelling agents or other additives is neglected. Moreover, the effect of the propping agent distribution on the distribution of fluid viscosity in the fracture is not taken into account. 4. Fluid flow in the fracture is everywhere laminar. 5. Simple geometric fracture-extension patterns are assumed — either radially symmetrical propagation from a point source (Fig. 1A) or rectilinear propagation originating from a line source (Fig. 1B). In the first case the periphery of the fracture is circular, in the second case it is rectangular. 6. A rectilinear propagation mode can be accomplished only by injection over a large perforated interval, thus forming a line source. Such a rectilinear fracture must therefore be located in the vertical plane. A circular propagation mode might be expected from injection through a narrow band of perforations. This forms a point source. Because gravity effects are excluded from our considerations, the fracture propagation plane may in this case assume any angle with respect to the wellbore as far as the

Jan 1, 1970

COUNCIL OF ECONOMICS OF AIME Formerly Mineral Economics Division Established as a Division December 15, 1948 Established as a Council February 26, 1957 Douglas Donald, Chairman Sheldon Wimpfen, Vice-Chairman (Mining) A J Phillips, Vice-Chairman (Metals) E Connaughton, Vice-Chairman (Petroleum) J S Vanick, Contact AIME Director A H Lindley, Jr Secretary-Treasurer Lehman Brothers 1 William Street New York 4, N Y COUNCIL OF EDUCATION Formerly Mineral Industry Education Division Established as a Division January 15, 1932 Established as a Council February 26, 1957 L E Shaffer, Chairman J D Forrester, Vice-Chairman O Cutler Shepard, Past Chairman , Contact AIME Director

Jan 1, 1959

By B. E. Warren

Jan 1, 1965

By F. W. Bowdish

A theoretical and experimental laboratory study has shown that the rate of breaking of oversized particles in a ball mill is proportional to 1) the concentration of such particles, and 2) the area of the balls, provided that the balls are larger than a certain size relative to the particles. If all undersized material were removed as formed, the rate of breaking would be almost independent of the quantity in the mill. Rate equations are given which are similar to those for zero, first, and second order reactions. Deviations of small balls from the equation for a second order phenomena are quantified by a factor called "nipping efficiency." Some data are correlated by a dimension-less equation, which is used to estimate nipping efficiencies from data not in the correlation. The investigation described here was undertaken after a literature survey revealed that little was known concerning the mechanism of breaking of particles within a ball mill and the effect of this mechanism upon grinding rates. One paper, by Roberts1 , offered a theory concerning the mechanism of breaking, and a rate equation for the breaking of particles larger than some size to particles smaller than that size. That paper provided the starting point for a theoretical and experimental investigation of grinding under carefully controlled conditions. THEORETICAL CONSIDERATIONS In his paper on the probability theory of ball mill grinding, Roberts theorized that "... a given expenditure of power leads either to a certain number of point to point blows per bp-hr or to a certain distance of line contact per hp-hr ..." He assumed that the balls touch each other during each blow or during moving contact. Then he said that a volume of pulp, dependent upon the size being considered, would be covered per minute within which all oversized particles would be crushed to particles smaller than that size. Naturally, the higher the concentration of oversized particles in the pulp, the higher the rate of which they would be broken. From this reasoning Roberts obtained the differential equation -dC/dt = k hp/ton C (1) where k is a constant for any size of particle, density of particle, and moisture content of pulp. C is the percentage of oversize in the material to be ground, t is the time, and hp/ton is the power input per ton of material in the mill. He then integrated the equation to log Co/Ct = k/2.3 hp/ton t , where Co and Ct are the percentage of oversize at time zero and t respectively. By always using the same quantity of material in a mill and assuming that it required constant power to run the mill, he was able to combine the horsepower per ton factor with the other constants to give an equation for a first order rate.

Jan 1, 1961

By L. C. Graton

The federal taxes on incomes and excess profits are of course heavy. In 1917, the value of the mineral production of the United States was a little in excess of $5,000,000,000. The total of federal taxes for that year, for the mineral producing companies, as computed by themselves, amounts, according to tentative compilations, to about $207,000,000, and the total for the comprehensive group of mineral and metal industries to about $766,000,000, which figures represent respectively 9.5 per cent. and 35.1 per cent. of the total tax paid by all corporations. Because of greater complexities in applying the revenue laws to mineral properties than to most other industries, opportunity is afforded for wide differences of view. The taxes indicated above, therefore, are not final and may conceivably be very materially increased. For 1918, the taxes are expected to be still greater, but no compilations are yet available. Taxes at a high rate are to continue indefinitely. The subject is clearly of gravest import to the mining industry in particular. The Commissioner of Internal Revenue, who is charged by law with the administration and collection of the taxes, is determined that these functions shall be performed in a just and businesslike way. Fairness and finality are to be the chief objectives. In view of the peculiar conditions that attach to the tax program as applied to mines and other wasting industries, like oil, gas, and timber, the Commissioner has resorted to professional advice and assistance by manning a Sub-division of Natural Resources with competent engineers, brought in from the several industries, into whose hands he has placed for solution the technical questions involved. These engineers have a two-fold duty: (1) to devote to the solution of these problems their own knowledge and experience; (2) through their acquaintance with their respective industries, and with the men engaged in those industries, to focus upon these problems, by conferences and otherwise, the best opinion of the country. The principal object of this paper is to acquaint the mining profession with the attitude of the

Jan 1, 1923

By L. C. Graton

The federal taxes on incomes and excess profits are of course heavy. In 1917, the value of the mineral production of the United States was a little in excess of $5,000,000,000. The total of federal taxes for that year, for the mineral producing companies, as computed by themselves, amounts, according to tentative compilations, to about $207,000,000, and the total for the comprehensive group of mineral and metal industries to about $766,000,000, which figures represent respectively 9.5 per cent. and 35.1 per cent. of the total tax paid by all corporations. Because of greater complexities in applying the revenue laws to mineral properties than to most other industries, opportunity is afforded for wide differences of view. The taxes indicated above, therefore, are not final and may conceivably be very materially increased. For 1918, the taxes are expected to be still greater, but no compilations are yet available. Taxes at a high rate are to continue indefinitely. The subject is clearly of gravest import to the mining industry in particular. The Commissioner of Internal Revenue, who is charged by law with the administration and collection of the taxes, is determined that these functions shall be performed in a just and businesslike way. Fairness and finality are to be the chief objectives. In view of the peculiar conditions that attach to the tax program as applied to mines and other wasting industries, like oil, gas, and timber, the Commissioner has resorted to professional advice and assistance by manning a Sub-division of Natural Resources with competent engineers, brought in from the several industries, into whose hands he has placed for solution the technical questions involved. These engineers have a two-fold duty: (1) to devote to the solution of these problems their own knowledge and experience; (2) through their acquaintance with their respective industries, and with the men engaged in those industries, to focus upon these problems, by conferences and otherwise, the best opinion of the country. The principal object of this paper is to acquaint the mining profession with the attitude of the

Jan 1, 1923

Albin. B . R Billings. Mont . '28 Amnter . Nathan L 26 Broad St.. New York . N . Y . '28 Bache . Jules S 42 Broadway. New York. N . Y . '28 Borrett . C . P . 5338 Harper Ave .. Chicago. I11 '28 Baum . Frank G. . Cons . Hydro-Electric Engr Camel'. Shasta Co. . Cal. '23 Baylean, William S Russ Bldg .. San Francisco. Cal . '28 Bean, Louis H .. V.P.. Dwight P . Robinson & Co.. lnc 126 E . 46th St New York. N . Y . '28 Beatty . Roes J . 1106 First National Bank' Bldg .. Chicago . Ill . '28 Benwell . Oswald F . 110 Gilpin St .. Denver. 1310 . '28 Beymer. Albert 9.. V.P .. Keystone. National Bank Pittsburgh. Pa . '28

Jan 1, 1929

By C. S. Samis, D. P. Seraphim

In the presence of oxygen, galena is oxidized in an aqueous medium containing ammonium acetate in accordance with the following reaction: PbS + 1/2 0, + 2 NH~Ac -» PbAc, + So + 2 NH: + H2O. This reaction was studied in an autoclave under oxygen pressure by polarographic measurement of the concentration of lead ion in solution. Oxidation rate is parabolic. The reaction products are lead acetote and elemental sulfur, the latter forming a film on the galena crystal. Reaction kinetics appear to be determined by the diffusion of lead from the galena phase to the solution interface through the film of sulfur. RECENT applications of pressure leaching on a commercial scale have emphasized the metallurgical importance of the oxidation of sulfide minerals in aqueous media by oxygen under pressure. Research experience has shown that sulfates, thio-nates, and metal oxides are the products of humid oxidation of sulfide minerals in basic solutions. The metal oxides may be solubilized in the presence of a complexing ion.' Certain oxide minerals are also amenable to treatment by this type of oxidation.' Several kinetic studies have been made of reactions of this type. Stenhouse' found that pyrite (FeS?) oxidized in a sodium hydroxide solution to produce a soluble sulfate and an insoluble layer of iron oxide and that the kinetics of the reaction were controlled by oxygen diffusion through the oxide layer. Andersen' studied the oxidation of galena (PbS) in a sodium hydroxide solution under oxygen pressure. He found the lead and sulfur to be simultaneously oxidized to produce plum bite ions and sulfate ions, and that the reaction rate was proportional to the surface area of the galena. The kinetics appeared to be determined by the reaction of oxygen and water with the galena surface. In each of the above reactions the metal and sulfur components of the mineral were oxidized simultaneously and at equal rates. In the present study the alkaline medium has been replaced by an approximately neutral solution of ammonium acetate in which lead sulfate is soluble. Under the conditions no sulfate was produced and no sulfur could be detected in the solution. The metal component of the mineral was solubilized and the liberated sulfur remained as a film of elemental sulfur on the surface of the galena crystal. A kinetic study of this reaction was undertaken to establish the kinetic mechanism and to determine the rate controlling step. Specific reaction rates were determined by oxidizing crystals of galena of measured surface areas in an autoclave maintained at the desired temperature and oxygen pressure. The rate of reaction was followed by measuring the concentration of lead in the ammonium acetate solution with a cathode ray polarograph, employing stationary platinum electrodes incorporated in the autoclave. Experimental Materials and Equipment Crystals of galena obtained from Violamac Mines, Retallack, B. C., were selected for oxidation because

Jan 1, 1957

By K. Leutwyler

The key to realistic casing stress analysis in thermal recovery installations is accurate knowledge of the temperatures involved. Much information leading to prediction of heat losses from tubing string to wellbore has been published. This .same information permits calculation of casing temperature under certain conditions. This paper reviews the basis for most of the published work, the line source solution to the diflusivity equation and examines some of its application criteria in the light of unsteady-state conditions. An alternate finite differences method is presented for correlation, and experimental data pertaining to the heat transfer mechanism in the annulus is reported. In the light of the information presented in the paper, it appears that the assumption of a line source for the tubing-wellbore system is valid even for reasonably short periods of heat flow, .such as "steam soak" operations. The empirically modified equation presented earlier matches computer derived results of the finite differences approach lor periods as short as 50 hours. Previously predicted cas ing temperatures and the associated stress levels are thus verified based on these correlative computations and the reported experimental information. Fall out from the computer output resulting in some studies of the influence of insulating cement properties on casing temperature, and experimentally studied effects of nitrogen placed in the annulus at various pressures., are described. INTRODUCTION Generally speaking, predictions of average casing temperatures have been based on an idealized model involving a centralized tubing string at uniform constant temperature radiating energy towards the casing under steady-state conditions.'. ' Heat is transferred away from the casing to the formation by unsteady-state conduction across thermal barriers consisting of cement and the mud sheath. Heat balances written on the casing permit prediction of instantaneous casing temperatures. During early periods of injection, casing temperature varies appreciably as a function of time; however, for long injection times this variation decays as heat flow from the wellbore to the formation stabilizes, and it becomes virtually negligible as conditions surrounding the wellbore become quasi-steady-state (Fig. 1). Carslaw and Jaeger -escribe a solution to the diffusivity equation for a line source (Fig. 2). A constant supply of heat is introduced into the medium from the line placed into the origin of the x-y coordinate system and parallel to the z-axis. Heat spreads outward in the infinite cylindrical solid and the temperature increase on a line going through point (x, y) parallel to the z-axis at a distance r can be predicted by: The following criterion must be considered: the Carslaw and Jaeger equation is obtained on the basis of a large

Jan 1, 1967

By F. H. Buchella, J. F. Buchanan

The San Manuel copper deposit is located about 45 miles northeast of Tucson. The concentrator, smelter, administration building, and other plant facilities are located about seven miles southeast of the ,nine area at the new town of Sari Manuel as shown on Figure 1 (Sketch).

Jan 1, 1961

Jan 1, 1902