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By G. E. Archie

The usefulness of the electrical resistivity log in determining reservoir characteristics is governed largely by: (I) the accuracy with which the true resistivity of the formation can be determined; (2) the scope of detailed data concerning the relation of resistivity measurements to formation characteristics; (3) the available information concerning the conductivity of connate or formation waters; (4) the extent of geologic knowledge regarding probable changes in facies within given horizons, both vertically and laterally, particularly in relation to the resultant effect on the electrical properties of the reservoir. Simple examples are given in the following pages to illustrate the use of resistivity logs in the solution of some problems dealing with oil and gas reservoirs. From the available information, it is apparent that much care must be exercised in applying to more complicated cases the methods suggested. It should be remembered that the equations given are not precise and represent only approximate relationships. It is believed, however, that under favorable conditions their application falls within useful limits of accuracy. Introduction The electrical log has been used extensively in a qualitative way to correlate formations penetrated by the drill in the exploitation of oil and gas reservoirs and to provide some indication of reservoir content. However, its use in a quantitative way has been limited because of various factors that tend to obscure the significance of the electrical readings obtained. Some of these factors are the borehole size, . the resistivity of the mud in the borehole, the effect of invasion of the mud filtrate into the formation, the relation of the recorded thickness of beds to electrode spacing, the heterogeneity of geologic formations, the salinity or conductivity of connate water, and, perhaps of greatest importance, the lack of data indicating the relationship of the resistivity of a formation in situ to its character and fluid content. On the Gulf Coast it is found that the effects of the size of the borehole and the mud resistivity are generally of little importance, except when dealing with high formational resistivities or extremely low mud resistivities. Fortunately, little practical significance need be attached to the exact values of the higher resistivities recorded. Low mud resistivities are not common, but when this condition is encountered it may be corrected by replacing the mud column. With the present advanced knowledge of mud control, invasion of mud filtrate into sands can be minimized, thereby increasing the dependability of the electrical log. The effect of electrode spacing on the recorded thickness of a bed is often subject to compensation or can be sufficiently accounted for to provide an acceptable approximation of the true resistivity of the formation. As development of a field or area progressively enhances the knowledge of the lithologic section, the resistivity values of the electrical log take on greater significance, ultimately affording acceptable interpretations. The salinity, and

Jan 1, 1942

By G. W. Healy, J. C. Schottmiller

Molten silicates were found to exist in the Cr-Si-0 system at temperatures above 1450°C. one atom of oxygen is readily removed from CrzOs in the presence of Si02 at 1700°C, forming a silicate melt. Steam-hydrogen ratio measurements made at this temperature indicate that the free energy of the reaction: Cr20s(c) + Hz = 2CrO (in Si02 -saturated melt) + H20 is approximately 5600 * 1500 cal. A deep-blue chromous silicate, probably Cr2Si04, forms from these melts at about 1400" to 1500°C, and is characterized by.its distinctive X-ray diffraction pattern and optical properties—distinct pleochroism and high refractive indices. THE question of the state of oxidation of chromium in slags has vexed metallurgists for many years The experiments of Koerber and Oelsenl suggested the probable presence of divalent chromium in silica-saturated slags equilibrated with high-chromium melts. Hilty and coworkers2 had also found chromium at lower valency, as Cr304, in inclusions formed from oxygen-saturated Fe-Cr melts with as little as 10 pct Cr. In both cases, disproportiona-tion of the lower oxide to CraO3 and chromium was found to occur to a greater or lesser extent, depending upon the rate of cooling from the high temperature. The work on Cr304 was sufficiently detailed for chipmans to derive its thermodynamic properties, but Oelsen's experiments in the silicate system were not extensive enough since most of his runs were made with slags containing large amounts of manganese oxide in addition to iron and chrome oxide and silica. The present study describes experiments carried out to map out an approximate liquidus diagram in the CrzOs, "CrO", SiOa portion of the Cr-Si-0 system, and to measure the partial free energy of solution of oxygen in the system. EXPERIMENTAL 1) Approximate Melting-Point Determinations. Preliminary trials showed that when an equimolar mixture of Cr20s and SiOa was treated with hydrogen in the temperature range 1500" to 1600°C, copious amounts of steam were evolved, and a low-melting liquid formed which could be quenched to a blue, crystalline, material having a distinctive X-ray diffraction pattern. It was found that the identical material could be produced by heating intimately mixed, finely divided Cra03, Cr, and SiOa, held in a tungsten crucible, under purified argon. Thus, it was possible to prepare mixtures containing any desired proportions of chromium, silicon, and oxygen, pel-letize them, heat to temperature in the furnace shown in Fig. 1, and observe, after cooling, whether the pellet remained unchanged or showed signs of incipient, partial, or complete melting. 2) Free Energy of Solution of Oxygen. This was studied by measurement of steam-hydrogen ratios for the reaction: H20 (gas) + O (dissolved in charge) + Ha (gas) The experimental method chosen was to prepare a

Jan 1, 1964

By David Turnbull

In most reactions involving solids the transformation kinetics may be represented by the combination of two processes —those of nucleation and of growth. For example, Mehl and his coiq-orker in their studies on the transformation of austenite to pearlite in steels have been able to describe the kinetics in terms of the rates of nucleation and of growth. By micrographic examination of their specimens they determined the nucleation rate (rate of appearance of pearlite colonies) as a function of time, of percent transformation, and of temperature. They observed that after an incubation period in which no nuclei are observed, the number of nuclei appearing per unit time per unit of untransformed grain boundary area, increases at an increasng rate with time. When recrystallization rates have been interpreted in terms of rates of nucleation and growth and the rate of nucleation determined, an incubation period followed by an increasing rate of nucleation has also been reported. Among the studies in which this phenomenon has been observed are those of Kornfeld and coworkers3 on cold-drawn aluminum wire, of Anderson and Mehl4 n the recrystallization of aluminum sheet, and of Stanlcy and Meh15 on the recrystallization of silicon ferrite sheet. The existence of an incubation period during which no nuclei are observed does not appear to have been reconciled with the generally accepted Volmer-Becker theory of nucleation in condensed systems. This theory ostensibly requires the rate of appearance of nuclei to be independent of time. Volmer-Becker Theory In order to form a stable nuclcus of a new phase B in a mother phase A, the molecules or atoms of the mother phase must surmount a free energy barrier whose height is determined by the volume free energy change accompanying the transformation and the energy of the surface separating the two phases. The free energy difference between nuclei of various sizes and the molecules or atoms of the mother phase is plotted schematically in Fig I as a function of the radius of the nucleus r. This free energy difference is plotted for two values of the change of free energy per atom, (Jb — ja) accompanying the transformation when the volumes of the two phases are infinite. One of these values of (Jb—Ja) corresponds to a temperature above the temperature To at which the phascs A and B are in equilibrium, and the other to a temperature below To. In order for a nucleus of phase B to be stable at a temperature T² < TO, its radius must be equal to or greater than the critical value r* for which the free energy of formatioil of the nucleus is a maximum, the of phase B having radii equal to or less than r* will be called embryos hfehl and Jetter," in discussing the kinetics of nucleation in solid systems, suppose that embryos of critical size are formed

Jan 1, 1949

By L. S. Darken

It has long been recognized that the driving force in an isothermal diffusion process may be regarded as the negative gradient of the chemical potential (partial molal free energy) of the diffusing substance. This equivalence is exactly analogous to the fact that a mechanical force is the negative gradient of the potential energy. Nernstl in 1888 expressed these driving forces in terms of osmotic pressure, which is directly related to the chemical potential and free energy. The relationship between the diffusivity, mobility and activity coefficient of electrolytes in aqueous solution has been developed in great detail by Onsager and FuossZ with results which have recently been confirmed experimentally by Harned and Nuttall. This interpretation of the driving force in isothermal diffusion has been discussed earlier by the author,4,5 who pointed out4 that "for a system of more than two components it.is no longer necessarily true that a given element tends to diffuse toward a region of lower concentration even within a single phase region"; departure from the behavior of an ideal solution may be so great that the concentration gradient and the chemical potential gradient, or activity gradient, may be of different sign, thus giving rise to "up hill" diffusion. Since, in the discussion of that paper,4 some skepti- cism as to the validity of this conclusion was expressed, it seemed desirable to adduce experimental evidence to support it. Evidence of such diffusion in nonmetallic systems has already been reported. For example, it was observed by Hartley" in a series of experiments in which sodium chloride diffused from a saturated solution in about 5 pct acetone in water into a solution virtually free of salt but with essentially the same acetone concentration. Specifically, a wine glass containing crystalline salt and saturated solution was totally immersed in a large glass cylinder containing the acetone-water solution without salt; the difference in specific gravity was such as to prevent convection. Diffusion of salt was accompanied by a marked depletion of acetone in the wine glass; after 3 days the acetone concentration decreased from 5.37 pct at the top of the glass, where the salt concentration was low (0.93 pct), to 1.84 pct at the bottom where the salt concentration was high (21.64 pct). This "uphill" diffusion was found to be such that the partial pressure (activity) of acetone was essentially equalized throughout the system when a steady state gradient of sodium chloride was maintained. In order to demonstrate the existence of such diffusion in metals, a series of four weld-diffusion experiments was made. In these measurements pairs of steel of virtually the same carbon content, but differing markedly in alloy content, were welded at the end and held at 10500 C for about two weeks. Subsequent analysis showed that carbon had diffused so as to produce an inequality

Jan 1, 1949

By G. E. Archie

The usefulness of the electrical resistivity log in determining reservoir characteristics is governed largely by: (I) the accuracy with which the true resistivity of the formation can be determined; (2) the scope of detailed data concerning the relation of resistivity measurements to formation characteristics; (3) the available information concerning the conductivity of connate or formation waters; (4) the extent of geologic knowledge regarding probable changes in facies within given horizons, both vertically and laterally, particularly in relation to the resultant effect on the electrical properties of the reservoir. Simple examples are given in the following pages to illustrate the use of resistivity logs in the solution of some problems dealing with oil and gas reservoirs. From the available information, it is apparent that much care must be exercised in applying to more complicated cases the methods suggested. It should be remembered that the equations given are not precise and represent only approximate relationships. It is believed, however, that under favorable conditions their application falls within useful limits of accuracy. Introduction The electrical log has been used extensively in a qualitative way to correlate formations penetrated by the drill in the exploitation of oil and gas reservoirs and to provide some indication of reservoir content. However, its use in a quantitative way has been limited because of various factors that tend to obscure the significance of the electrical readings obtained. Some of these factors are the borehole size, . the resistivity of the mud in the borehole, the effect of invasion of the mud filtrate into the formation, the relation of the recorded thickness of beds to electrode spacing, the heterogeneity of geologic formations, the salinity or conductivity of connate water, and, perhaps of greatest importance, the lack of data indicating the relationship of the resistivity of a formation in situ to its character and fluid content. On the Gulf Coast it is found that the effects of the size of the borehole and the mud resistivity are generally of little importance, except when dealing with high formational resistivities or extremely low mud resistivities. Fortunately, little practical significance need be attached to the exact values of the higher resistivities recorded. Low mud resistivities are not common, but when this condition is encountered it may be corrected by replacing the mud column. With the present advanced knowledge of mud control, invasion of mud filtrate into sands can be minimized, thereby increasing the dependability of the electrical log. The effect of electrode spacing on the recorded thickness of a bed is often subject to compensation or can be sufficiently accounted for to provide an acceptable approximation of the true resistivity of the formation. As development of a field or area progressively enhances the knowledge of the lithologic section, the resistivity values of the electrical log take on greater significance, ultimately affording acceptable interpretations. The salinity, and

Jan 1, 1942

By Irwin Roman

IN studying the possibilities of a continuously recording magnetometer for use along the surface of the earth and in an airplane, the Federal Bureau of Mines was led to a study of the theoretical resolving power of magnetic observations, both in the variation of the total magnetic intensity and in each of the two components ordinarily measured. Along with this general study, an attempt was made to determine the relative worth of the total intensity anomaly and the vertical anomaly in geophysical prospecting. General considerations led to three conclusions: I. In the northern magnetic hemisphere of the earth, the total intensity anomaly is offset to the south of the vertical anomaly, for a positive anomaly (see Appendix, note I). 2. The resolving power of magnetic observations decreases rapidly with distance from the disturbing body. 3. The horizontal anomaly has little value in prediction of the disturbing body but might be useful in making a choice between bodies suggested by the vertical or total anomaly. Some of the considerations leading to these conclusions were: I. The normal intensity and the anomalous intensity are vectorially additive; hence for a positive anomaly in the northern magnetic hemisphere the total intensity will be a maximum at some point south of the disturbing body and north of the point at which the line to the disturbing body is parallel to the normal earth&apos;s field. The anomaly itself has a maximum value directly above the body. For a positive anomaly of constant magnitude, the total intensity will be a maximum when the anomaly vector is parallel to the normal vector. This is shown schematically in Fig. I (not to scale) for a magnetic distribution not restricted to a relatively thin sheet in the magnetic meridian. The normal field has a magnitude Io with vertical component Vo and horizontal component H,. Six station points along a traverse&apos; across the body from south to north are shown at M to S. At each of these stations the normal magnetic field vector terminates at F. At each of these stations the magnetic field vector due to the disturbing body B terminates at A. The line through the station point and the point A passes through B. The magnitude of the anomaly, indicated by the length of the vector terminating at A, is proportional to some power of the distance from the station point to the disturbing body. If the&apos; disturbing body B is a concentrated point of magnetic material, the anomaly is proportional to the inverse second power of the distance. For a uniform magnetic distribution over a line perpendicular to the observed traverse, the anomaly is proportional to the inverse first power of the distance. For surface distributions, the law of intensity is more complicated. At each field point, the total magnetic intensity T is the vector sum of the

Jan 1, 1946

By J. D. Price, W. M. Bertholf

One of the chief difficulties with which the operator of a coal washing plant has been forced to contend is the handling of the very fine coal. First he has the problem of separating the fine coal from washery water. This is usually accomplished by the use of settling cones or Dorr thickeners: in either event the separated fine coal contains a high amount (40 to 80 pct) of water and, somewhat loosely, dependent upon the size of the coal particles present, may be known as sludge or slurry. His second problem is the satisfactory further dewatering of such separated sludge and/or slurry. At the coal washing plant of the Colorado Fuel and Iron Corp., washed coal from the Deister Plat-O tables is sluiced to a stationary inclined de-watering screen provided with 3/16 by 1-in. slots, and the coarse coal passing over this screen is conveyed by a Baum-type elevator and a flight-type distributing conveyor to a battery of Carpenter centrifugal driers. The fine coal and water passing through the openings of the primary dewatering screens, plus the fine coal passing through the screens of the centrifugal driers (and no small portion of which is the result of the disintegrating action of these driers) is pumped to two 30-ft Link Belt settling cones. The sludge recovered as underflow from these cones was formerly dewatered on stationary screens having 1/16 by 1-in. slots and discharged on top of the coarse washed coal in the Baum drainage conveyor; but after a relatively few hours of op eration the circulating load of fine coal on this conveyor built up to a point where it became necessary to reduce the quantity of feed to the washing tables. The original arrangement of our coal washing and dewatering equipment is shown in Fig 1. In order to regain the loss in active throughput which had been caused by this circulating load, an installation of six vibrating filters was made during the year of 1936. This resulted in an increase in normal tonnage of washed coal from 1430 to 1750 tons per 8-hr shift, a gain of slightly over 22 pct. This increase in throughput has made a very substantial decrease in the " conversion cost" per ton of washed coal. Since the vibrators were installed, we have gained about 2,000,000 tons in production, compared to what would have been produced in the same number of shifts at the former rate. Putting it in slightly different form, we have saved in the past 12 yr the cost of 1400 operating shifts in the washery. Fig 2 shows the location of the vibrating filters as applied to the original flowsheet. It will be noted that the sludge from the bottom of the settling cones is passed through a distributing box and thence to the filters. The de-watered coal from the filters is de-livered to the conveyor receiving the dried coal from the Carpenter driers.

Jan 1, 1950

By W. C. Ellis, E. S. Greiner

WHEN metallic materials are deformed plastically, the process may be considered as one in which hardening and recovery occur simultaneously. The net hardening is that produced by deformation in the absence of recovery lessened by recovery during and immediately following deformation. Strain hardening takes place through movements of large groups of atoms acting to a degree as an entity. A complex microstress system is developed. Recovery is a diffusive-type process involving single atoms or, at most, only a few atoms in concerted action. This is accompanied by elastic strain relaxation. Recovery is strongly temperature-dependent. The driving energy for the process resides in thermal fluctuations of the atoms augmented by the energy of the stress field producing the deformation, and by that produced by the deformation. At very low temperatures recovery is essentially absent, or very small. At high temperatures in the hot working range, recovery is so rapid that deformation results in no appreciable net hardening. The interplay of strain-hardening and recovery results in differing end structures depending on the temperature and the strain rate of the process. For example, there is a prominent difference in the spacing of the slip markings and in the detail of X-ray diffraction patterns. High temperatures and slow strain rates favor a wide spacing of slip markings and sharp reflections.&apos;,&apos; This suggests that change in rate of the recovery concurrent with deformation modifies to a degree the manner of the deformation. Different slip systems may operate. For very slow rates, the mechanism may, as has been suggested, differ from that of "classical slip." In the experimental work that follows the findings will be interpreted from the point of view developed in this section. Recovery and Electrical Conductivity Electrical conductivity is a sensitive indicator of the state of strain in a material3&apos; * and was used in this investigation. The materials studied in wire form were: OFHC copper, a high purity (99.99 pct) and 2s grade aluminum, and grade A nickel. Wire annealed and initially 0.050 in. in diam was drawn through diamond dies in a simple holder maintained at 25", —75°, or — 195°C. Precautions were taken that for each material all conditions of drawing were the same except the temperature. Electrical resistivity was measured for each condition at 20°C. This was done as soon as practical after drawing to minimize possible room temperature recovery. The data for the four materials are plotted in Fig. 1 in terms of the change in resistivity for drawing at the several temperatures. The effect of temperature of drawing on the increase in resistivity is most pronounced for copper. Drawing at 25°C to 80 pct reduction in area increases the resistivity approximately 2 pct; drawing at —195°C to the same reduction increases the resistivity about 6 pct. The increase in resistivity" & in this metal is due to extra scattering of conduction electrons originating in the lack of orderly arrangement of the atoms induced by the deformation process. It has been suggested

Jan 1, 1953

By F. X. Spiegel, D. Bardos, Paul A. Beck

Ti6NileSi7)G is known to be cubic, with 116 atoms in the unit cell. In the present work four new G sili-cides were found with other transition elements and five G germanides. The titanium-group elements are very efficient in forming G phases. The vanadium -group elements are somewhat less efficient, and the chromium-group elements do not form any. Cobalt can replace nickel in most cases, but it is somewhat less efficient. Iron was not found to form any G phases. Germanium is somewhat less efficient than silicon. The (TiNiSi)E phase has been previously identified by Westbrook. However, its crystal structure has not been determined. In the present work the E phase was found to have an orthorhombic unit cell with lattice parameters a. = 7.02, bo = 5.18, co = 11.11A. A large number of other E phases were found at the same stoicheometric ratio in ternary systems of silicon and germanium with transition elements. Lattice parameters similar to those for TiNiSi were measured. The number of atoms per unit cell is estimated at 30 to 36. The vanadium-group elements are somewhat more efficient in forming the E phase than the titanium-group elements. Chromium-group elements were not found to form any E phases. Cobalt is somewhat less efficient than nickel, and iron is less efficient than cobalt. Germanium is not as efficient as silicon. ThE ternary silicide designated as G-phase was first identified by Beattie and versnyder1 and by Beattie and Hagel2 at the approximate composition TiNi2Si. Westbrook et al.&apos; gave the composition as Ti2Ni7Sis. This phase was found to be fcc with a. = 11.201A and 116 atoms per unit cell. Beattie4 and more recently independently Hladishevskii, Kripyakevich, Kuzma, and Teslyuk5 were able to show that this structure is isotypic with MgeSi7CuLe and Th6Mn23. The latter structures had been determined by Florio, Rundle, and snow,&apos; Nagorsen and Witte,7 and Bergman and Waugh.8 According to the crystal structure, Ti8Ni6Si7 may be considered as the ideal composition. The Russian investigators5 identified six additional ternary phases isotypic with Ti6Ni6Si7, in which titanium is replaced by Mn, V, Nb, Ta, Zr, and Hf, and one, namely MneNil6Ge7, in which germanium replaces silicon. They also found that Cr6Ni6Si7, which does not occur as a ternary phase, can be stabilized by replacing 1 at. pct of the Cr by V, Mn, or Ta. Another ternary silicide was found by Westbrook et al.3 at the composition TiNiSi, and it was designated by them as the E phase. The crystal structure of this phase has not been deter-

Jan 1, 1963

By E. P. Valby

A method is presented in which the hydrocarbon weight fractional analyses of the well effluents from a true gas-tip-portion well and a true dark-oil-ring well furnish the basic data for determining the properties of any mixture of production from the two sources. The effect of injected gas on these properties can be computed. Comparison of similar properties of a given well effluent to the properties of mixtures of the basic well effluents will give the relative amounts of production from the two sources and injected gas. Presentation of Problem Oil fields having an area of gas-cap, or light-oil production, over the dark-oil area present a problem of increasing gas-oil ratios during the production of an oil well. The use of pressure maintenance in a field such as above, or a cycling project, wherein residue gas from an absorption plant is injected into the reservoir, adds to the problem, because a part of the increased gas-oil ratio may be due to the production of injected gas. The usefulness of a means to determine the amount of injected gas in a well effluent led to the development of a method in which well-effluent analyses of a true gas-cap-portion well and a true dark-oil-ring well furnish the basic data needed to determine whether injected gas of a known composition is present in a given well effluent. Development op Method The method presented herein is based upon the principle that if two fluids, or well effluents, having different properties are mixed in known proportions by weight, • the properties of their mixtures can be computed. Conversely, if these basic data are known, the properties of a mixed well effauent can be used to compute the relative amounts of each type of well effluent in the mixture. A convenient way of making these computations is to have the fractional analyses of the base well effluents and mixtures expressed in weight fractions The mathematical equations expressing the properties of mixtures will be developed for a two-component system consisting of the well effluents from the dark-oil ring and the gas-cap area. The added effect of injected gas, a third component, will also be developed. The following assumptions have been made in developing the method: 1. The gas-cap and dark-oil fluids exist initially in separate portions of the reservoir. 2. The fluids in each portion exist in a single phase at pressures above the saturation pressure for the dark-oil fluid. 3. The composition of each fluid is substantially constant throughout its respective portion of the reservoir. 4. Changes in reservoir pressure and temperature will not change the composition of the fluid entering the well bore. 5. The injected gas displaces original gas-cap fluid 100 per cent. •• 6. AS the injected gas travels through a

Jan 1, 1945

By H. W. Hitzrot, R. H. Limons, L. V. Fegan

The testing of a new method for measuring pellet-bed temperatures in the traveling-grate or shaft furnace is presented in this paper. This method, using silver-palladium alloy wires as indicators, overcomes disadvantages existing in the methods based on the use of thermocouples which are costly and time-consuming. The authors have developed and tested a new method for measuring pellet-bed temperatures in the traveling-grate or shaft turnace through the use of silver-palladium alloy wires as indicators. This method overcomes the disadvantages of existing methods, which, based on the use of thermocouples, are generally costly and time-consuming. For example, in the case of the traveling-grate furnace, the installation of an instrumented pellet, together with its attached thermocouples, requires stopping the furnace, with resulting loss of production time. As for temperature measurement in the shaft furnace by the existing method, the movement of the shuttle-car feeder seriously interferes with both the actual insertion and the resulting distribution of continuously fed thermocouples. The authors have overcome these difficulties by using, as temperature indicators, a range of silver-palladium alloy wires that can be easily recovered, after firing at any desired location in a pellet furnace. Silver-palladium wires having specific melting points from 2000°F to 2500°F are enclosed in ceramic capsules. Each capsule is placed in a ni-chrome wire basket filled with a sample of green pellets, the baskets being the means for recovering the capsule after firing. After the encapsulated wires have been exposed to the firing cycle, the alloy wires are examined to determine the maximum temperatures attained by the pellet sample. This method gives accurate, rapid determinations of maximum temperatures attained during pellet induration in either the traveling-grate or shaft furnace The new method has the following advantages over existing methods: 1) it is less expensive; 2) no furnace downtime is required; 3) the testing units can, be made in quantity in advance; 4) measurements can be made in rapid succession at all desired locations; 5) measurements of maximum firing temperatures are more accurate; 6) on the basis of points 4 and 5, the new method gives a more reliable picture of the correlation of pellet quality, petrographic textures and maximum temperatures, thus providing a more effective quality-control tool. A disadvantage of the method is, of course, that the measurements are not continuous and only maximum temperatures are determined. TEST PROGRAM Preparation of Materials: CALIBRATION OF ALLOYS - In the following discussion the term "bead point" (see Fig. 1) refers to the temperature at which each alloy begins to melt and form a bead. Fig. 2 gives the bead point curve for silver-palladium alloys. Before the alloys are used in plant tests, the bead point of each alloy should be determined in the laboratory to verify the alloy compositions. Once a given alloy has been calibrated, it can be

Jan 1, 1965

By P. B. Crawford, W. L. Huskey

A study has been made to determine the effects of random vertical fractures existing in a reservoir matrix on the effective matrix properties and producing characteristics of a well. The study indicated that short vertical fractures may distort the isopotentials by 1 percent in the vicinity of the fracture. A correlation was developed which showed the effect of fracture density on the producing capacity of a well. The correlation indicated that fracture shape had little effect on producing capacity, but that total fracture length was closely correlated with the producing capacity. Effective values of reservoir permeability were found to correlate closely with fracture density when measured parallel to the direction of flow. INTRODUCTION In reviewing the petroleum literature, it is found that in most analytical solutions of hydrocarbon reservoir behavior the assumption is made that the rock is uniform throughout although core analysis and well logging surveys indicate that substantially all reservoirs are heterogeneous and some are fractured. Only in recent years have investigators studied the effects of reservoir hetrogeneity. Russell1 discussed the effect of fractures in reservoirs. The literature indicates that fractures greatly affect the exploitation of man reservoirs. This is described by Elkins and Skov2 and Little-field et al. 3 Several types of reservoir heterogeneity have been studied by unsteady-state methods. In 1959, Landrum et al. 4 showed that transient phenomena in hydrocarbon reservoirs could be studied by thermal models. pickering5 studied the flow of heat in stratified linear reservoirs consisting of plates of different metals separated by sheets of rubber which were suddenly exposed to a low-temperature source at one end. Cotman6 studied both laterally and vertically heterogeneous thermal model reservoirs with special reference to cross flow. Another type of reservoir heterogeneity involves the presence of highly permeable, circular lenses around or near the wellbore which was studied by Miesch7 using a thermal and a steady-state model. Many studies have been made of the effects of induced hydraulic fractures on well performance. 8-10 Work regarding vertical fractures that exist initially in the reservoir was reported by Givens, et al.11 Since there appears to be little published work on the importance and influence on reservoir performance of fractures that exist out in the rock matrix, this study was conducted to determine the effects of vertical fractures on pressure distribution, producing capacity and the effective permeability of the reservoir rock. The analogy between the flow of electrical current through a conducting body and the flow of fluid in a porous medium provides a convenient method of studying various aspects of petroleum reservoirs. For electrical radial steady-state flow,12 For steady-state fluid flow, With the above analogy, it is only necessary to establish the ratio of the values of the electrical units in terms of the corresponding flow units to make the analogy quantitative. The ratios are shown below.

By Irwin Roman

In studying the possibilities of a continuously recording magnetometer for use along the surface of the earth and in an airplane, the Federal Bureau of Mines was led to a study of the theoretical resolving power of magnetic observations, both in the variation of the total magnetic intensity and in each of the two cornponents ordinarily measured. Along with this general study, an attempt was made to determine the relative worth of the total intensity anomaly and the vertical anomaly in geophysical prospecting. Genera1 considerations led to three conclusions: I. In the northern magnetic hemisphere of the earth, the total intensity anomaly is offset to the south of the vertical anomaly, for a positive anomaly (see Appendix, note 1). 2. The resolving power of magnetic observations decreases rapidly with distance from the disturbing body. 3. The horizontal anomaly has little value in prediction of the disturbing body but might be useful in making a choice between bodies suggested by the vertical or total anomaly. Some of the considerations leading to these conclusions were: I. The normal intensity and the anomalous intensity are vectorially additive; hence for a positive anomaly in the northern magnetic hemisphere the total intensity will be a maximum at some point south of the disturbing body and north of the point at which the line to the disturbing body is parallel to the normal earth&apos;s field. The anomaly itself has a maximum value directly above the body. For a positive anomaly of constant magnitude, the total intensity will be a maximum when the anomaly vector is parallel to the normal vector. This is shown schematically in Fig. I (not to scale) for a magnetic distribution not restricted to a relatively thin sheet in the magnetic meridian. The normal field has a magnitude 10 with vertical component V0 and horizontal component Ho. Six station points along a traverse across the body from south to north are shown at M to S. At each of these stations the normal magnetic field vector terminates at F. At each of these stations the magnetic field vector due to the disturbing body B terminates at A. The line through the station point and the point A passes through B. The magnitude of the anomaly, indicated by the length of the vector terminating at A, is proportional to some power of the distance from the station point to the disturbing body. If the disturbing body B is a concentrated point of magnetic material, the anomaly is proportional to the inverse second power of the distance. For a uniform magnetic distribution over a line perpendicular to the observed traverse, the anomaly is proportional to the inverse first power of the distance. For surface distributions, the law of intensity is more complicated. At each field point, the total magnetic intensity T is the vector sum of the

Jan 1, 1949

By A. W. D. Hills

This paper describes the development of a generalized integral-Wofile method for the analysis of heat transfer dwing solidification. The method is extremely flexible, and can be applied to a wide range of situations. This flexibility has been achieved by characterizing the solid metal layer in terms of two parameters, and by developing two simultaneous nonlinear differential equations for these parameters in terms of the heat fluxes crossing the boundaries of the solid layer. The use of these equations is illustrated in a series of examples which involve the solidification of pure metals at zero superheat cooling under different conditions. The simplicity with which the method can be extended to treat more complicated jwoblems is illustrated in a further example which involves natwal convection effects in the liquid metal. ThE rate at which molten metal solidifies in an industrial casting process, and the structure of the cast product, are both controlled by the rate at which heat can be removed from the casting. A knowledge of heat transfer rates is thus essential to the control of the process and to the control of the structure and soundness of the final casting. Heat transfer rates during real solidification processes cannot be predicted by formal mathematical techniques, however, because nonlinear boundary conditions are involved. Approximate methods are normally used, and these have included electrical and hydraulic analogue techniques, finite difference methods, and the integral-profile method. Considerable effort has been devoted to the development of the first two techniques, but the integral-profile method has been used very little so far. This is unfortunate because the method is capable of providing relatively accurate solutions for the heat transfer equation during solidification without involving large amounts of computer time. A further advantage of the method is its flexibility, although this is not apparent from the integral-profile solutions that have been developed to date. These solutions have been derived for the solidification of molten metal at zero super-heat under cooling conditions involving either a constant heat flux from the cooled surface;&apos; a constant heat transfer coefficient at the surface,&apos;-3 or a specified variation in the surface temperature.4,5 A generalized integral-profile method is presented in this paper which can be used to predict unidirectional solidification rates under a very wide range of more realistic cooling conditions. The use of the method is illustrated in a series of problems involving pure metals, or skin forming alloys, solidifying at zero super-heat. However, the principal advantage that this method has over the previous integral-profile methods is the ease with which it can be extended to treat more complicated solidification problems. This is illustrated by considering a problem in which super-heat is liberated from the liquid metal by natural convection during the solidification process. In the final section of the paper the generalized method is compared with previous methods used to predict solidification rates and its extension to more complicated solidification problems is briefly discussed.

Jan 1, 1970

By Maurice Rey, H. Brevers

THROUGH circumstances connected with the war, the senior author lost his records therefore it has been impossible to include numerical data in this paper. The arsenical quicksilver ore investigated had been roasted, with poor metallurgical results. The vapor-tension temperature curves of mercury and arsenious trioxide are similar, and the arsenical compound hampers the coalescence of mercury drops in the condenser and is the cause of large stack losses. The ore was a gray limestone carrying small amounts of carbon and mineralized with cinnabar and two arsenic minerals, realgar (As2S2) and arsenopyrite (FeAsS). The proportion of realgar often exceeded that of cinnabar; the proportion of arsenopyrite was smaller. The grade of the ore varied between 0.8 and 4 per cent Hg. The problem was to make a high-grade mercury concentrate, as free from arsenic as possible. The water used throughout the testing was hard, having a pH- of about 8. FLOTATION OF REALGAR Realgar showed a very strong tendency to float. It formed a film at the surface of the pulp and floated in abundance with only pine oil. Therefore an attempt was made to float the realgar before the cinnabar, but this was not very successful; the percentage of mercury in the realgar concentrate could never be brought below 2 or 3 per cent. Cinnabar slimed easily and floated with pine oil, so that some of it always accompanied the realgar. There was also the question of the cinnabar-arsenopyrite separation. On further investigation it was found that realgar can be floated not only with pine oil but even better with a combination of hydrocarbons and pine oil. Washing the ore with ether revealed that it contained hydrocarbons, which helped to float the realgar. In this connection it belongs to the same class as carbon, sulphur and talc. It can be floated also with a xanthate, when activated by a heavy-metal salt. The conditions favoring the two types of flotation are opposed, as activation by a copper salt facilitates xanthate flotation (in fact, is even necessary to it), whereas it hinders pine oil and petroleum flotation. One type of flotation can be termed nonpolar and the other polar, a distinction that has been stressed in a previous paper. DEPRESSION OF REALGAR AND FLOTATION OF CINNABAR Many chemicals were tested in an attempt to float the cinnabar and depress the realgar. Finally starch rendered soluble with caustic soda was tried, also several grades of commercial soluble starch, and dextrin was found to be the best and the most convenient reagent. Several of these starch preparations have a strong flocculating effect on the pulp, which is a distinct disadvantage. Dextrin, with its low flocculating power, is excellent. It is noteworthy that starch preparations are also depressants for carbon and talc, so that the fact apparently has a general

Jan 1, 1941

By William A. Johnson

The fundamental role of diffusion in many reactions occurring in solid metals has long been recognized, and there have been careful measurements of rates of diffusion in numerous alloy systems; but our understanding of the atomic mechanism by which diffusion occurs is scarcely in an advanced state.l-3 It is doubtful that this mechanism can ever be directly ascertained; rather, all imaginable mechanisms must be examined and the one that is in best accord with such data as can be obtained from suitably chosen experiments should be selected. Because of its relative simplicity, diffusion in a system containing only one kind of atomic species—commody called self-diffusion—is of considerable theoretical interest. It may be expected that diffusion theory will not be advanced appreciably until a wide variety of diffusion experiments—of which diffusion in a chemical concentration gradient and self-diffusion are two important types—are carefully performed and inter-compared. Aside from the purely theoretical interest in self-diffusion measurements, such studies will be of considerable engineering importance. The rate of any process in a pure metal requiring the movement of atoms, of which recrystallization and creep are two familiar examples, will be understood more readily with the aid of self-diffusion data.† Self-diffusion implies the diffusion of something into its exact counterpart; the detection of such a process is patently impossible, and it is necessary to substitute for it the diffusion of one isotope (in this case radioactive) into another isotope (in this case stable) of the same chemical element. There is, however, no reason to suppose that a radioactive atom will not diffuse at the same rate as its stable isotope, for all of the isotopes of the same element have exactly the same chemical properties; neither the difference in nuclear energy nor the difference in mass would be expected to exercise an important influence in this phenomenon. In this sense, self-diffusion may be thought of as the diffusion of radioactive atoms down a radioactivity concentration gradient, just as usual diffusion is the diffusion of one kind of atom down its chemical concentration gradient. The first measurements of self-difiusion were made by von Hevesy4-6 using the radioactive lead isotope thorium B in ordinary lead. The recent development of means for producing artificial radioactive elements has made possible similar measurements on gold,7, 8 copper,2, 9 and zinc.10, 11 Many of the data that have been obtained are rather poor, and no adequate reason has been given for their poorness; it appears, however, that the unsatisfactory results are characteristic of the particular experimental procedure employed, and not of self-diffusion measurements in themselves. The experimental technique that has yielded the poorer results is the deposition of a thin layer of radioactive atoms on the surface of a specimen and the determination of the rate of inward diffusion

Jan 1, 1941

By E. A. Nichols

The purpose of this paper is to present a contour map that shows the geographical variation in geothermal gradients in the Mid-Continent and Gulf Coast oil fields. Introduction Frequently there arises the need for an estimation of the temperature to be expected at a predetermined depth in working with a wildcat or in deepening old production into &apos;Ones that are relatively unknown. The study of geothermal gradients in oil fields has been made previously by many investigators. One of the pioneers in this work was C. E. Van Orstrand,&apos; who, as well as most of the other investigators, was primarily interested in the relation between temperature and depth in a given locality. Between 192r and 1929, American Petroleum Institute Research Project NO. 25 fostered a thorough study of earth temperatures.2 K. IV. French did some work in California, the results of which were published in 1939.3 In most of these studies, an attempt was made to correlate temperatures in a rather localized area. This paper will show the results of an attempt to correlate temperature gradients over rather large Portions of the Mid-Continent and Gulf Coast area. Method of Obtaining Data It has been found that for complete thermal equilibrium to be established in a well, the well must stand undisturbed for a period of several hours to several weeks, depending upon the way the well was produced prior to the shut-in period. The data in this paper were obtained in conjunction with running pressures in wells or in taking samples of reservoir fluid. Glass maximum recording thermometers were used in all but a few instances. The wells had been shut in from one hour up to I. or 12 days. Since the wells were normal producing wells, some of the shut-in times undoubtedly were insufficient for complete thermal equilibrium to have been established and the temperatures measured do not necessarily represent the true earth temperatures. They do represent the temperature conditions that will be encountered in a well that is producing oil. The data, therefore, can be useful in working with or in estimating the temperatures to be expected in producing reservoirs. In obtaining a thermal gradient by dividing the difference in temperature of the formation and the mean annual surface temperature by the depth of the formation, one is assuming the depth-temperature line to be straight. Depth-temperature curves are almost straight lines (Fig. I). However, on close examination of accurate data, a slight curvature usually is observed. Most wells yield curves with slopes increasing with increasing depth. These curves are believed to be from wells that are in and are underlain by sedimentary material. Some few curves have slopes that decrease with increasing depth. These curves are believed to be from wells that are underlain rather closely by granite or some other igneous rock. Most investigators

Jan 1, 1947

By L. L. McMurray

ILMENITE is the most important raw material for manufacture of titanium dioxide.1 Industrially, several other products are made from ilmenite, the most important of which are: ferrotitanium, ferro carbon-titanium, copper-titanium, titanium carbide and titanium nitride. The production of titanium metal is still in the laboratory stage because of the difficulty of extraction and as yet no important application for the metal has been found. Ilmenite has received considerable attention as an industrial raw material. Imports of ilmenite concentrates for the first nine months of 1941 were 156,737 short tons, the chief source being Travancore, India.2 Domestic production of ilmenite has here-tofore been confined to Amherst and Nelson Counties, Virginia, where a complex rutile, ilmenite, and apatite ore is mined and treated to utilize all three of these minerals. A recent report3 has described development of the large titaniferous magnetite ore body at Tahawas, New York, where it is expected that 800 tons of ilmenite concentrates, containing 48 per cent Ti02 will be produced daily. Additional domestic production is expected from a large ilmenite deposit recently opened in Caldwell County, North Carolina. Flotation tests indicate that a high-grade concentrate containing 53 per cent Ti02 can be made from the North Carolina ore. Prospecting of domestic ores in other areas has been reported.4 It appears that increased domestic production of ilmenite may well save considerable shipping space so vitally needed in these times. The composition and chemical structure of pure ilmenite is given by Dana as: FeO, TiO2; Ti, 31.6 per cent, Fe, 36.8 per cent, 02, 31.6 per cent. This composition is variable in that some iron or titanium may be replaced, giving a variable iron-titanium ratio. As an example, the iron-titanium weight ratio of ilmenite in Caldwell County, North Carolina, has been determined to be 0.94 (using 97.1 per cent ilmenite concentrate obtained by heavy liquids on minus 150-mesh ore) compared with theoretical 1.16. No rutile was noted in this ore to account for the low value. This North Carolina ore is free of magnetite, which is a common associate of ilmenite ores. In view of a large potential production from North Carolina, the Tennessee Valley Authority conducted a study of methods of concentration of that ore, of which the results are reported herein. THE ORE Five samples of ore were taken from the deposit at various exposed locations and were mixed for the study and testing. An attempt was made to proportion the amount of weathered and unweathered portions in making the composite sample, so as to approximate actual operating conditions. An examination of representative specimens of the sample showed the following general facts: I. The black mineral comprising nearly 70 per cent of the ore is ilmenite.

Jan 1, 1944

By G. G. Gunther, C. L. Boeke

(Any discussion resulting from presentation at the Los Angeles Extractive Metallurgy Division Meeting will appear in the November 1953 issue.) I. M. Symonds (Cia Minera de Penoles, Monterrey, N. L., Mexico)—This is a most interesting paper describing zinc deleading operations. Mr. Gunther was kind enough to show me his operation last fall. Outside of the excellent results, I was most impressed by the ease of control. I had expected a difficult operation requiring careful control and supervision, but found one requiring little attention. The only disappointing fact of the separation is the poor copper recovery in the concentrate of the deleading float. The final zinc concentrate still has about 3 pct chalcopyrite (assuming the copper is chalcopy-rite) which adversely affects the zinc grade. If the copper mineral is free, the poor recovery is probably due to the high cyanide concentration. Fortunately, about 75 pct of the copper is recovered before the pulp goes to the zinc circuit. Mr. Gunther&apos;s remarks about proper cyanide to zinc sulphate ratios cannot be overemphasized. Although our experience has been mostly confined to the conventional Pb-Zn separation, we have found these ratios most important, and more important in the mill than in the laboratory. The laboratory appears to give optimum results over a wider range of reagent control than the mill, especially in regard to the effect of cyanide. In the mill in handling relatively high grade ores, we usually find that ratios of cyanide to zinc sulphate of 1 to 10 or 20 or higher work best. Where there is a substantial amount of chalcopyrite present, it has been noted that cyanide in the range of 0.02 to 0.10 lb per ton of ore is often beneficial in zinc rejection and possibly in copper recovery in the lead concentrate, while larger amounts, say 0.20 to 0.25 lb per ton, will float more zinc and cause a serious rejection of chalcopyrite. On an ore with 15 to 20 pct Zn content, we have had to use 0.8 to 1.2 lb of zinc sulphate per ton of ore with the above cyanide to obtain optimum results. Sometime ago we made a laboratory study following Parral and Santa Barbara practice on an ore which never had a very satisfactory rejection of zinc in the lead concentrate. The results were not encouraging and a mill test was not run. Since then the study has been reopened using fresh zinc concentrate from the mill in the laboratory instead of one made in the laboratory. A reasonably clean lead float from the zinc concentrate was obtained. It has been checked several times and each time the zinc concentrate made in the mill responds and the one made in the laboratory does not. Although undoubtedly some reasonable explanations can be given, it is presented here only

Jan 1, 1953

By L. L. McMurray

Ilmenite is the most important raw material for manufacture of titanium dioxide.&apos; Industrially, several other products are made from ilmenite, the most important of which are: ferro titanium, ferro carbon-titanium, copper-titanium, titanium carbide and titanium nitride. The production of titanium metal is still in the laboratory stage because of the difficulty of extraction and as yet no important application for the metal has been found. Ilmenite has received considerable attention as an industrial raw material. Imports of ilmenite concentrates for the first nine months of 1941 were 156,737 short tons, the chief source being Travancore, India.2 Domestic produttion of ilmenite has heretofore been confined to Amherst and Nelson Counties, Virginia, where a complex rutile, ilmenite, and apatite ore is mined and treated to utilize all three of these minerals. A recent report3 has described development of the large titaniferous magnetite ore body at Tahawas, New York, where it is expected that 800 tons of ilmenite concentrates, containing 48 per cent TiO2 will be produced daily. Additional domestic production is expected from a large ilmenite deposit recently opened in caldwell county, North carolina. Flotation tests indicate that a high-grade concentrate containing 53 per cent TiO2 can be made from the North Carolina ore. Prospecting of domestic ores in other areas has been reported.&apos; It appears that increased domestic production of ilmenite may well save considerable shipping space so vitally needed in these times. The composition and chemical structure of pure ilmenite is given by Dana as: FeO, TiO2; Ti, 31.6 per cent, Fe, 36.8 per cent, O2, 31.6 per cent. This composition is variable in that some iron or titanium may be replaced, giving a variable iron-titanium ratio. As an example, the iron-titanium weight ratio of ilmenite in Caldwell County, North Carolina, has been determined to be 0.94 (using 97.1 per cent ilmenite concentrate obtained by heavy liquids on minus Iso-mesh ore) compared with theoretical 1.16. No rutile was noted in this ore to account for the low value. This North Carolina ore is free of magnetite, which is a common associate of ilmenite ores. In view of a large potential production from North Carolina, the Tennessee Valley Authority conducted a study of methods of concentration of that ore, of which the results are reported herein. The Ore Five samples of Ore were taken from the deposit at various exposed locations and were mixed for the study and testing. An attempt was made to proportion the amount of weathered and unweathered portions in making the composite sample, so as to approximate actual operating conditions. An examination of representative specimens of the sample showed the following general facts: 1. The black mineral comprising nearly 70 per cent of the ore is ilmenite.

Jan 1, 1948