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By N. Jaffe, J. E. Dorn

This investigation is concerned with the possibility that the creep resistance of metals might be reduced as a result of recovery at the creep temperature when the applied stress is reduced. For this purpose the effect of stress on the recovery of the creep behavior of pure polycrys talline aluminum was investigated in the cross-slip temperature range where the activation energy for creep is 28.000 cal per mole. Before recovery all specimens were given the same substructure by creeping them under a stress of 7800psi to a strain of 0.218. Recovery was then accomplished by holding the specimens at the creep temperatures of 327" and 337°K under a series of reduced stresses for various periods of time. When the original stress was reapplied the specimens crept more rapidly than when the original stress was first removed, illustrating that recovery did take place. The extent of recovery could be indexed in terms of the UNDER certain conditions of test, the creep rate decreases over the primary stage of creep often by as much as a factor of 10~B. Since the external variables of stress and temperature are held constant, such pronounced and significant changes in the creep rate must be attributed to various substructural modifications that are introduced as a result of creep itself. At the secondary stage of creep, over which the creep rate remains constant and the substructure no longer changes, a balance must be achieved between the rate of increase in creep resistance due to creep straining and the rate of recovery of the substructural modifications. The general validity of these concepts on substructural changes has already been shown,' including the corollary that a more creep-resistant substructure is introduced under a more rapid creep rate arising from a higher applied stress.' In spite of these well-documented facts, very little progress has been additional strain undertaken by the recovered specimen to achieve the same strain rate as the unrecovered specimen. It is significant that the higher recovery stresses gave the most rapid rates of recovery. Over the high range of reduced stresses, where some creq took place during recovery, the activation energy for recovery equaled that for creep, namely 28,000 cal per mole. But for stresses during recovery below 0.80 of the original creep stress, no creep was detected during recovery and an activation energy for recovery of about 72,000 cal per mole was obtained. Whereas the activation energy of 28,000 cal per mole suggests that cross-slip of dislocations is responsible for this recovery, the mechanism for the 72,000 cal per mole process is not known. This activation energy, however, is about twice that for self-difhsion. made in determining, in satisfactory detail, precisely what substructural changes so effectively modify the creep rate.' Up to the present, electron microscopy has failed to uncover, in a satisfactory quantitative manner, the mechanistic processes involved. Since, however, creep, at least at moderate and high temperatures, arises from one or more types of dynamic recovery processes, it should be possible to shed additional light on the total problem by investigating the recovery of creep resistance. The importance of such an investigation becomes apparent when the fact is recognized that there has yet been no direct experimental proof that the rate of softening due to substructural changes as a result of recovery equals the rate of hardening due to creep-induced substructural strengthening over the secondary stages of creep. Furthermore the problem of what happens to the creep-strain induced strengthening when the material recovers either at zero or some reduced operating stress has significant engineering consequences. It was for these reasons that the present investigation on the recovery of creep behavior was initiated. Inasmuch as a substantial background has now developed on the creep of high-purity aluminum, this material was again selected for the current investigation. Furthermore extensive evidence is now

Jan 1, 1963

By B. C. Allen

Grain-boundary gvoocing was studied irz chronziu?n. molybdenum, tungsten, and the solid-solution alloys, Cr-35Re. Mo-33Re, and W-25Re at 0.6 to 0.9 of the absolute liquidus temperature under an inevt atmosphere , foveign nzetal zlapor, and liquid metal. The controlling mechanism of matter transport was deduced frolr groove size and shape. kinetics of growth, and cotnparisoz with theoretical relatiotzships derived by Mullins. Grooves in chowzizon formed prittzarily by volume diffusion tkrongk kelium or argon at 1 atm pressure and by e1)apovation-condensatiotz in a static vacuum. Groozles in the other nzetals and alloys forrned priniarily by sirface diffusion, the coefficients of which were calculated. Carbon was found to decrease the acti7:ation energy for surface diffusion on molybdenun. Sitrface diffusizities weve sinzilav for iWo-0.0ZC and Mo-33Re. The presence of about 1 -?nm pressure of silver or tin vapor did not affect the neckanis)n of grooz;e formation. In liquid titz or silz:er, pain bolindary gvooves formed by zolume diffusion in the liquid. BASED on theories of ullins," the mechanisms of grain-boundary grooving have been determined for low-melting metals such as copper in an inert atmospheres or in liquid lead.4 The purpose of this investigation was to study grain-boundary grooving in the refractory Group VI-A metals, chromium, molybdenum, and tungsten, and the bcc solid-solution alloys, r-35e, 0-33e,= and -25e,' at 0.6 to 0.9 of included to see whether Mullins' theories were applicable to them as well. EXPERIMENTAL WORK The materials chromium, molybdenum, tungsten, Cr-35Re, Mo-33Re, and W-25Re were in the form of 0.050-cm-thick sheet assaying 99.98 pct or better. The nominal carbon level was generally 30 ppm. The oxygen + nitrogen + hydrogen content was -50 ppm. Mo-33Re and W-25Re were prepared by powder-metallurgy methods and supplied by Chase Brass and Copper Co. The remaining materials were arc-cast. Chromium and Cr-35Re were prepared at Battelle by arc melting, extruding, swaging, and rolling. Mo-0.003C was supplied by Climax Molybdenum Co., and Mo-0.02C and tungsten by Universal Cyclops Corp. As a source of liquid metals, tin and silver granules assaying 99.98 pct were used. Spectrographic analyses indicated the presence of -100 ppm each of iron and silicon. Vacuum melting reduced the combined gas content to c5 ppm (2.60,, 0.9N2, 0.4H2 in tin and l.602, 0.7N2, and c0.04H2 in silver). Specimens were prepared for grain-boundary grooving. Coupons 0.5 by 1.5 cm with a small hole in one end, or substrates 1.5 by 1.5 cm, were cut from sheet. The specimens were annealed in containers of the same material to provide a vapor-solid equilibrium as well as to protect them from gaseous impurities. Outgassing was done at 2 x 10"5 mm for 15 to 30 min at 1150°C for chromium and Cr-35Re, 1750°C for molybdenum and Mo-33Re, and 2600°C for tungsten and W-25Re. Then recrystallization to a stable grain size of about 0.5 mm was accomplished by annealing at least 1 hr at 1600°C for chromium, 1800°C for Cr-35Re, 2350°C for molybdenum, and 2300°C for Mo-33Re in a rhenium-element resistance furnace under 1 atm of static argon or helium. The atmosphere was gettered by tantalum radiation shielding. Tungsten and

Jan 1, 1967

By S. Pearson, L. Rotherham

Measurements have been made of the variation of internal friction with temperature for spectroscopically pure silver, and for o series of solid solutions of silver with cadmium, indium, and tin, using a Ke-type torsion pendulum apparatus. Some experiments have also been made to investigate the effect of nonmetallic impurity on grain boundary relaxation in silver. The effect of the alloying elements is to increase the grain boundary viscosity, and to raise the activation energy for grain boundary relaxation from 22,000 cal per mol for pure silver to 43,000 cal per mol for the solid solutions; the same value being obtained, within the limits of experimental error, for all the alloying elements and solute concentrations investigated. Results of the experiments show exactly the same trend as those obtained previously for a similar series of copper solid solutions. They are in agreement with the general theory of grain boundary relaxation developed by Zener and Ke, but do not seem to be in agreement with either of the mechanisms so far put forward to explain grain boundary slip. EXPERIMENTS described in this paper were made as part of an investigation into the effect of alloying elements in substitutional solid solution on grain boundary viscosity, measured by the internal friction method developed by Ke.&apos; The apparatus and experimental procedure have already been described.&apos; Preliminary work was done with spectro-scopically pure silver. Experimental Work Materials Used—All the materials were supplied in the form of % mm diam wire by Messrs. Johnson Matthey and Co. Ltd. The silver and all the alloying elements used were spectroscopically pure. Composition of the alloys is given in Table I. They were all melted and chill cast under the same conditions as the copper alloys. The ingots were rolled to 1/4 in. sq rod with intermediate annealing at 600°C in an atmosphere of cracked ammonia when necessary. These rods were then drawn to wire by standard procedure with intermediate bright anneals at suitable steps in the drawing operations. Specimens from the annealed wires were sectioned longitudinally. mechanically polished, and examined under the microscope. They were then etched and reexamined. Grain sizes were reasonably uniform for all wires, and no traces of a second constituent were observed. The wires were weighed before and after testing so as to measure any loss of the alloying element due to evaporation. The loss was less than the accuracy of measurement—< 0.1 pct of the total weight— for the Ag-In and Ag-Sn alloys, but appreciable loss of weight occurred in the case of the Ag-Cd alloys. The percentage loss is given in Table 11. X-ray diffraction photographs were taken of all thc wires after test to determine whether there was any marked preferred orientation. Results of the examination are given in Table 111. Experiments on Spectroscopically Pure Silver-— Experiments were made on specimens in which the grain diameter was small relative to that of the wire, and on one specimen in which the grains were grown by the usual strain-anneal method to extend across the full diameter of the wire. These large grained specimens will be referred to as single crystal specimens. The wires were annealed for 11/2 hr at 700°C, and experiments were made at two frequencies of vibration, 1.5 and 0.4 vibrations per sec. The variation of internal friction with temperature is shown in Fig. 1. Experiments on a second small grain specimen gave approximately the same results as for the first wire. It will be seen from Fig. 1 that the peak in the curve for the small grained wire, which is presum-

Jan 1, 1957

By B. K. Larkin, H. R. Bailey

A model Of heat flow in an underground combustion process is studied. This model includes convection effects and thus is more general than previous studies which considered conduction as the only mechanistn for heat transfer. Both linear (tube run) and radial (field application) geometries are considered. The effects of ignition heaters, vertical losses and finite source width are considered for the linear case. The results are in the form of equations and are presented in graphical form for a number of cases. Convection effects increase frontal temperatures about 25 per cent over those computed for conductive transfer for typical field operating conditions. This increase in temperature is a result of heat being transported toward the front by the injection gas. Even greater temperature increases are realized as the per cent oxygen in the injection gas decreases. It is well known that compression costs are of considerable importance in estimating the economic feasibility of underground combustion. By assuming an ignition temperature for the combustion fuel, predictions of limiting conditions on fuel density and injection rate necessary to sustain the combustion zone are made. For typical field conditions, at least 0.75 lb/cu ft of fuel are needed with air as the injection gas. If the injection gas is 10 per cent oxygen and 90 per cent nitrogen, this figure is 0.69 lb/cu ft. INTRODUCTION The possibility of increasing oil recovery by underground combustion has been considered for many years. Recent field tests indicate that the underground combustion process is technically feasible. The economic feasibility depends to a large extent on the amount of air which must be injected to sustain combustion. Prediction of the success of employing underground combustion in a particular reservoir must be based on existing field tests, laboratory tube runs"&apos; and solutions of mathematical or analog models. Vogel and Krueger5 devised an electrical analog of the heat transfer problem in an underground combus-ion process. They considered the problem of heat conduction from a cylindrical source with increasing radius assuming no vertical losses. Bailey and Larkin and Ramey solved the corresponding problem including vertical losses by considering a mathematical model of the conduction process. Ref. 9, 10 and 11 also present information related to the subject study. The present paper generalizes these results to include both conduction and convection mechanisms for heat flow. A model of the conduction-convection process is described. The partial differential equations governing this model are written and solved for a number of cases of interest. The formulas are evaluated and the results are presented graphically. A CONDUCTION-CONVECTION MODEL Description of the Model A number of models are employed in this paper, each of which approximate a particular physical situation depending on the geometry, i.e., linear or radial flow, the type of vertical heat losses, the nature of the source, etc. The geometry for both the linear and radial case is shown in Fig. 1. A particular linear model is described in this section, and variations from this model are described in later sections of the paper. Consider a homogeneous, semi-infinite porous prism with lateral sides insulated as shown in Fig. 1. The left end, x = 0, is heated for a time t, with a plane heater supplying a constant heat flux and during this time; gas (nitrogen) is passed through the pores of the prism at a constant mass flux. At time t, the heater is turned off and air is injected in place of the nitrogen. This causes combustion to take place, and a uniform source of width 1 is formed which moves at a constant velocity v, to the right. The frontal velocity v, is related to the gas velocity v,, through stoichiometric considerations

LEAD and tin mixed together make an alloy through an attachment of natural affinity which they have with each other, so that when they are mixed it is difficult to recognize by the sight which one it is, if the essences of their qualities are not surpassed by more than half. If, indeed, one can be recognized, it is the tin which gives off a certain sharp odor to the sense of smell, besides having a greater hardness and whiteness. The best of these is the one that is the purest in its kind. In the alloy of tin it is the one that is the whitest and hardest, or, when it is bent or some thin end of it is held tightly by the teeth, is heard to crackle as frozen water does. Because this happens more with this than with other metals, I do not wish now to inquire into it. It is enough that it be a sign for recognizing when tin is pure or mixed. Pewterers say that it should be joined in alloy with lead and that it is better for working when it contains four or six pounds to the hundred because it makes it softer to the hammer and more fluid in casting. But I do not like to hear this, even if all they say is true, for I see that the tin that comes from England, when worked as well as in cakes that show it to be pure, is much more beautiful and better in all works than is that made in Venice. And I believe that it is not better for any work when mixed than when pure, except for the advantage of the master who, if he does nothing else, sells lead that is worth little for tin that is worth much. I find that when mixed it serves in only two things. One is when it is wished to make a solder for copper, for use when it is not worth while to solder the bottoms and large pieces of vessels with low-grade silver as should be done. The other is when master potters calcine it in order to make glazes and to apply white to their vases. I consider lead to be useless in all other works of any kind of metal, since it unites with none of the other metals of good company except tin.

Jan 1, 1942

By J. T. Norton, A. L. Mowry

S. J. SINDEBAND*—(1) Discussing the properties of the powders used, Mr. Rostoker mentioned a silicon powder as being between 150 and 325 mesh. We always had much difficulty in measuring particle size of silicon powder by screen analysis, because of its tendency to agglomerate. I would be interested in the method used to measure these particle sizes. (2) Mr. Rostoker maintains that the measurement of magnetic properties is more accurate in determining complete homogenization of an alloy, than is the X ray diffraction technique. I wonder whether this is really true. Even when diffusion is complete, magnetic properties will change during continuation of the heat treatment, due to change in density and pore shapes, as has been demonstrated by Mr. Rostoker himself. Which effect is faster, the diffusion of the alloy components or the attainment of final density, will, in my opinion, depend very much on initial material and sintering conditions used. For magnetic applications, of course, the magnetic measurements are most suited for determining the point at which equilibrium conditions are reached. (3) I was glad to see that Mr. Rostoker had used sample sizes which are similar to those I had used previously, and I believe that ring samples of about 2 in. od will become more or less standard samples for the determination of magnetic properties of powder metallurgy products. I should like to ask how the density was changed for the samples on which the effect of porosity was investi- gated, and, further, why the sintering temperature used for this series of experiments was so low. It is somewhat surprising that a 24-hr treatment at 850°C acts so much more to spheroidize the pores than a treatment for 1 hr at 1100°C. But the effect seems to be indisputable. I have made an investigation of the influence of sintering temperature for longer times on the maximum permeabilities of iron powder compacts which was presented at the International Powder Metallurgy Conference in Graz, in 1948, and I hope that these results will be published here within a short time. The results of this investigation are confirmed by Mr. Rostoker&apos;s findings that the change of time from 1 to 24 hr changes the permeability behavior considerably in the direction as indicated by Polder and Van Santen for spheroidiza-tion of pores. I do not quite understand Mr. Rostoker&apos;s explanation of the influ-

Jan 1, 1950

By John Henry Harden

THIS shaft, located in the northern anthracite coal-field about 2300 feet southwest from the court-house at Wilkes-Barre, in the County of Luzerne, Pa., is the property of the Lehigh & Wilkes¬Barre Coal Company. The sinking and cribbing to the solid rock (see isometrical view on Plate IX) was conducted by Mr. W. W. Kenrick. Dimensions of the earthwork to the foundation of the cribbing, 51&apos; 1/2" long, 17&apos; 4" wide, 31&apos; deep. Total amount of excavation in cubic yards, 998.5. Dimensions within the permanent cribbing, 45&apos; 4" long, 11&apos; 16" wide, 31&apos; deep, divided into six parts by buttons 8" x 12", each division, 7&apos; x 11’ 16". Permanent cribbing 12" x 12"; temporary cribbing 8" x 10"; backing, 3" thick ; clay puddle to ex¬clude surface water, 12" thick; conductors, 8" x 5"; lining, 1" thick from top to bottom of the shaft. In the latter part of the year 1871, Mr. H. Murray & Son contracted with the company for the continuation of the work at the rate of four hundred dollars per yard in depth, to a point 100 feet below the Hillman seam of coal ; for the succeeding 100 feet the price to be increased twenty-five dollars per yard, and so on until the bottom rock of the Baltimore seam of coal was found. The size of the shaft within the cribbing timbers is 45 feet 4 inches by 11 feet 6 inches, having six divisions of equal dimensions, 7 feet by 11 feet 6 inches, giving room for what is known as the" standard diamond" car, whose capacity when level full is 100 cubic feet, but when loaded by the miner 4 inches above the top contains 112 cubic feet.* Two divisions of this shaft are intended for hoisting coal from the Hillman seam, two from the Baltimore seam, one for ventilation, and one for pumps. The works were planned for two pairs of direct-acting, high-pres¬sure engines, twenty-four boilers, and for an estimated output of 2500 tons of coal per day from the two seams. * Size of the "standard diamond" car, 8&apos; 10” x 4&apos; 3" x 2’ 8” = 100.1.4; loaded 4 inches above the top, 8&apos; 10” x 4’ 3” x 3’ “0"= 112.7.6.

Jan 1, 1877

By N. A. Gokcen, S. Fujishiro

THE pressures of Mn(g) in equilibrium with Mn7C3 and graphite have been measured by McCabe and Hudson&apos; and Butler, McCabe, and paxton2 by means of graphite, zirconia, and Ta-Mo Knudsen cells. The details of corrections in their measurements were somewhat different from those of the authors;3&apos;4 hence, further independent results at higher temperatures seemed to be warranted. The stoichiom-etry of Mn7C3 in equilibrium with graphite and its stability up to the vicinity of 1373 °K have been satisfactorily established by Kuo and persson5 (See also Hansen and Anderko).&apos; The method of investigation has been described elsewhere in detail.3&apos;4 The carbide was prepared in the manner described by McCabe and Hudson. In order to avoid possible reactions with refractory oxides, only graphite cells were used for the effusion experiments. The authors&apos; results are the runs M-1, M-2 and M-3 listed in Table I, together with those of McCabe and co-workers. The heat capacity, c;, of Mn7C3 is not known; therefore McCable et al. plotted their data as log P vs 1/T and the results were only expressed first&apos; as, and later2 as logP=- -14220+6.06 without further thermodynamic calculations. However, it is possible to estimate closely the necessary heat capacity as follows: When H; - &98 of CrC, or MnO, is plotted vs x, corresponding to various compounds, with temperature as the parameter, it is seen that the relationship is represented by a line of very small curvature. This relationship is also followed by other compounds which do not exhibit solid state phase transformations. In view of the fact that chromium and manganese have the atomic numbers of 24 and 25 respectively, it is reasonable to assume that H; - H;ae vs x for MnC, follows the same type of lines as those for CrC, for which adequate data are available.7 Similar correlations appear to be valid for oxides of two neighboring metals for which reliable data are available. The procedure is thus to move the lines for CrC, vertically (parallel to the axis of HT - H298) until they coincide with the points for MnC1/3, the only carbide of manganese whose H; - HO298 has been

Jan 1, 1963

By L. F. Stutzman, George Thodos

The friction factor plot presented by Cornell and Katz4 and developed for the flow of fluids through consolidated formations has been directly adapted for handling fluid flow problems involvitrg both linear and radial flow. In this adaptation the friction factor plot is used directly for the solution of problems and thereby eliminates the use of conventional equations which are specific to laminar (Darcy) or turbutent flow. This upproach overcomes the disadvantages inherent in the use of these conventional equations. It eliminates the necessity of checking the type of flow occurring in order to identify the specific equation which must be used. In radial flow problems, because of the increasing mass velocity of the fluids as they approach the wellbore. the type of flow may no longer remain laminar. Consequently, it is necessary to use more than one equation in a problem and to identify the range over which each equation should be applied. Finally, in practice it has been found that much of the flow of gases through consolidated media occurs in a range that is neither laminar or turbulent. For this transitional region, no convenient equations are available. The method and presented friction factor plot are appficahle to both liquids and gases. INTRODUCTION The flow of fluids through unconsolidated media in packed beds has been treated extensively by a number of investigatorsl,2,3,5,7,8 Most of these studies present friction factors as a function of modified Reynolds number similar to those developed for conventional fluid flow through pipes. These friction factor plots are presented for linear flow; however, Elenbaas and Katz have extended these concepts to apply to radial flow. All of these studies on unconsolidated materials require a knowledge of packing properties such as sphericity. porosity, and particle diameter. Sphericity and particle diameter cannot be defined at the present time for consolidated formations such as those commonly found in gas or oil reservoirs. As a result many investigators have not utilized friction factors and Reynolds number in the study of fluid flow through consolidated media. However, Cornell and Katz4 present a plot (Fig. 1) for the flow of fluids through consolidated porous media, in which the friction factor defined as: The turbulence coefficient, P, is related to the formation permeability, K, as presented in Fig. 2. Three different types of flow may exist in the flow ot

Jan 1, 1957

By R. J. Wygal, J. Naar

An equation for three-phase (water, oil, gas) imbibition oil permeability is developed, assuming the water to be the dominant wetting fluid. Oil isoperms are obtained for consolidated sandstones characterized by 1/pc2 = CS*. The evolution of an oil-gas system imbibing water from Swi to(Sw,imb )max is shown to proceed along a line of constant oil saturation with increasing oil permeability and decreasing gas saturation. When the gas satuation cannot be reduced further, the system evolves along a line of constant Sg with decreasing oil saturation and permeability. The initial gas saturation is shown to reduce markedly the effect of complete wetting by either oil or water on flow performance. INTRODUCTION Imbibition oil isoperms are required for performance prediction when a well is producing water, oil and gas. This situation occurs in multiphase displacements such as underground combustion, steam injection and the water flooding of highly depleted reservoirs. In a recent paper,1 a model was presented for the prediction of two-phase imbibition characteristics. This paper extends the imbibition model to the case of three phases by assuming that the water is the dominant wetting fluid. The following results were obtained from the model: (1) an analytical expression of oil isoperms; (2) oil isoperrns as functions of reduced water, oil and gas saturations, valid for all sandstones having a capillary pressure curve which can be approximated by 1/PC = CS*; and (3) evaluation of the three-phase flow performance as dictated by complete wetting by either oil or water. The agreement between predicted and observed oil recovery in the presence of a gas phase, reported in Ref. 1, is a partial support for the present development. However, experimental data are not available at this time to check fully the model predictions. Perhaps this paper will stimulate the collection of such data. The imbibition model of a porous medium has been described previously, and the reader is referred to the paper of Naar and Henderson1 for details. In brief, the model is formed by the random interconnection of straight capillaries, with a provision for the blocking of the non-wetting phase by the invading wetting fluid. The following expressions were derived from the model. 1. The amount of oil blocked by the invading water is

By L. Zwell, H. A. Wriedt

In describing their procedure for measuring the lattice parameters of solid solutions, Abrahamson and Lopata report (p. 77) the final heat treatment of their alloy specimens as "700°C for 100 hr, followed by a furnace cool". The isothermal part of this treatment may be expected to precipitate solute in excess of the stable a solid-solution limit at 700°C; the subsequent slow cooling is likely to reduce the dissolved solute still further. Fig. 1 (upper) presents the data for titanium alloys so he;rt-treated and shows the lattice parameters of solid solutions containing up to 3.5 at. pct Ti; Fig. 17 (lower) shows 2 at. pct Ti as the solubility limit in a iron at 700°C. Figs. 1 and 17 are thus incompatible. The paper contains comparable incon~patibilities for zirconium alloys, for niobium alloys, and for tantalum alloys. The final heat treatment at 700°C may also be responsible for the anomalous "knee" in the lattice-parameter data for nickel alloys, Fig. 3. The "knee" composition is located near the 700°C limit of the stable a solid-solution field;37 alloys of the experimental composition range with more nickel than the "knee" composition are two-phase at 700 C and prolonged heat treatment of them at 700°C would tend to produce inhomogeneity rather than homogeneity. In Figs. 4 and 7, the composition ranges of the zirconium, hafnium, and niobium alloys examined terminate at alloy concentrations of 0.1 to 0.2 at. pct. These metals form very stable oxides and their partial removal from solid solution in iron by impurity oxygen may be expected. We believe that the authors should have reported the procedure by which they distinguished the amounts of alloying elements in solution and in oxide. The diagrams pertaining to copper in Figs. 3 and 18 (lower) are almost certainly incorrect. Three recent investigations of this system38-40 all substantially agree on the solubility of copper in a iron, finding it to be much larger than that reported by Abrahamson and Lopata. The change of the lattice parameter with composition reported by Abrahamson and Lopata is too large by a factor of three to five, as seen by comparison with the findings of other investigators.41738 Moreover, the authors violate, in Fig. 18, the accepted Fe-Cu constitution diagram37 by ignoring the eutectoid at about 850°C.

Jan 1, 1967

By P. S. Rudman

Laves phases, AB2, are considered as Izerrzisub-stitutional solutions m1hich are defined by a one-for-truo replacement scheme. Atomic-size tnisfit is considered in terms of deviations of the ratio 2V°b/V°A from unity, where v° = atomic volume. A simple elastic model has been used to calculated deviations from "Vegard&apos;s law of atomic vol-umes". Comparison has been made between calculated and observed atomic-volume deviations fov 222 Laves phases. Agreement is generally very good although there ave some few exceptions which appear to be excusable in terms of electronic changes that ore beyond the scope of the present model. We can consider the formation of a binary sub-stitutional solution A-B from an A solvent as one-for-one replacements of A atoms by B atoms. As the atomic-size ratio deviates from unity, the solution becomes thermodynamically less stable and hence more restricted because of atomic-misfit strain energy. In accordance with our previously presented conclusion1 that the atomic volume, v, is in general the most appropriate measure of atomic size, the ideal size ratio for a binary sub-stitutional solution is vg/vA = 1. The Laves phases have been described by Berry and Raynor2 in terms of various stacking sequences of hexagonal layers of B atoms for the three structures MgZn2(C14), MgCu2(C15), and MgNi2(C36). To form the Laves phase of ideal composition AB, we start with complete hexagonal layers of B atoms in the appropriate stacking sequence and we remove, according to an appropriate scheme for each structure, two out of every four B atoms and replace the two removed atoms by one A atom. We thus might expect to find that the ideal size ratio for the Laves phases is 2v/B/ VA= 1. From this point of view, then, we call Laves phases hemi-substitutional solutions since we employ one-for-two replacements. By analogy with substitutional solutions we can expect for Laves phases that as the ratio 2VB/Va deviates from unity the phase occurrence will be more restricted. Laves3 has plotted the distribution of Laves phases as a function of the radius ratio, ?A/rB, and found that, while the distribution extended from 1.05 < rA/B < 1.50, the

Jan 1, 1965

By L. L. Newman

PUBLIC UTILITY GAS PRODUCTION IN 1802, William Murdock first used retort coal gas to light his house and the Boulton and Watt plant where he was employed. For the next three quarters of a century coal served as the principal raw material for the manufacture of city gas for general distribution. Coal continued to hold its predominant position for another half century after Prof. Thaddeus C. Lowe developed the first practical method of enriching water gas with cracked-oil vapors in an integrated operation. This position, however, was no longer maintained through the medium of direct carbonization of coal in retorts but as a result of using anthracite or coke as the generator fuel in carburretted water-gas machines. The early water-gas machines were extremely crude and the consumption of both oil and generator fuel was very high. However, the cost of installation was considerably lower than for any coal-gas system having the equivalent gas-making capacity, the labor involved was small, and the water-gas machine could be started up and shut down quickly. It thus proved very useful as standby equipment and in taking peak loads from the coal-gas plants. The flexibility of the water-gas machine, furthermore, made it possible to change the candlepower of the gas readily to suit the required conditions. Later, when calorific value replaced candlepower as the standard of gas quality, the water-gas machine was found to be equally flexible in keeping the city gas under complete and convenient control. No basic improvements were made in the Lowe carburetted water-gas process until 1898, when means were added to provide for regular reversals of the flow of steam through the fuel bed. By judicious proportioning of the quantities of up-run and down-run steam, it became possible for the operator to control the hardness and position of the clinker to a degree that previously had been unattainable. Also in 1898, the first by-product coke plant in America to supply city gas was built at Everett, Massachusetts. Later many other by-product plants, of greatly improved design and capacity, were built, but not primarily for city-gas production, chiefly because of the relatively high investment cost per unit of gas made. Cheaper plant construction has been the subject of serious study, and some progress is expected, but other factors, such as plant life,

Jan 1, 1953

By M. Garfinkle

LITERATURE data1&apos;3 have suggested that the resolved shear stress necessary to initiate slip in a particular slip system in tungsten single crystals is strongly dependent on the tensile orientation of the crystals. This orientation dependence is contrary to the critical resolved shear stress criterion. Because the Schmid factors for slip on particular {110}( I l l), {112}(Ill), or {123}(111) slip systems in a (100) oriented tungsten crystal are virtually identical to the respective Schmid factors for a (110) oriented crystal, slip should initiate on the same system in both orientations, independent of the values of the critical resolved shear stresses. Thus, it would be expected that, for a critical resolved shear stress model to hold, the proportional-limit stress for these two orientations must be similar. The expectation of similar proportional -limit stresses has not been borne out by reported experimental observations. Rose et nl.&apos; reported that the proportional-limit stress for crystals near the (110) orientation was 92,000 psi, approximately three times that of (100) oriented crystals (31,000 psi). Garlick and probst2 reported greater than a fourfold difference. Most recently, Beardmore and ~ull~ examined tungsten crystals with orientations along the edge of the standard stereographic triangle and showed a gradual increase in proportional-limit stress from 28,000 psi for the (100) orientation to 93,000 psi for the (110) orientation. Again, the difference was more than threefold. As has been emphasized by these investigators, the apparent gross variation of proportional-limit stress with orientation precludes any meaningful analysis of slip mechanics using a simple critical resolved shear stress relation. The purpose of the present communication is to report that, by use of refined strain-measuring techniques, the proportional-limit stresses for the (100) and (110) orientations are quite similar. Obviously, to determine accurately the value of the proportional-limit stress, which is by definition the stress at which nonlinear stress-strain behavior first occurs, the method of measuring strain must be capable of high accuracy. The investigators cited used as the measured elongation the crosshead displacement of the tensile machine. This method, however, introduces extraneous strain contributions from the load train. Because these extraneous contributions are considerable in the initial portions of loading (as has been well-documented in the literature) the proportional-limit stress measurement, dependent on the deviation of a line from linearity, can be significantly affected. During the course of a recent study, room-temperature strain was measured directly on several (100)-and (110)-oriented tensile specimens axially oriented within 5 deg of the desired direction. Each specimen was fitted with two foil strain gages mounted on opposite sides of the 0.08-in.-diam reduced section. The tensile specimens were loaded at a crosshead speed of 0.01 in. per min on an Instron Universal Testing Machine. Strain was monitored through an external bridge circuit in which the specimen strain gages comprised two arms. The bridge output was recorded against the applied load. A strain of 2 x 10"" could be readily detected by this method. Some specimens were subjected to conventional loading while the load for others was cycled between zero and continually increasing values until the first deviation from linearity was observed. The results of these methods were similar, and the stress at which nonlinear behavior occurred was considered the proportional-limit stress. The proportional-limit stresses measured in this study are approximately 5000 and 6500 psi for the ( 100) - and ( 110) -oriented crystals, respectively, a range of values almost a magnitude less than those reported previously. Representative curves are presented in Fig. 1. Because of the nature of the measurements made, the point of departure of a line from linearity is often debatable. While the load-strain curve for the (100) -oriented crystals made a relatively abrupt deviation from linearity, the curve for the (110) -oriented crystal was more gradual, so that the actual point of tangency may be at a lower load than reported. Thus, the difference in values for the proportional-

Jan 1, 1967

By George M. Humphrey

It is indeed a pleasure for me to have this opportunity to discuss with you a subject which I find infinitely interesting and intriguing - namely, world-wide iron ore supply and demand. We will be examining the following: (i) current iron ore production and requirements; (ii) the major ore producing countries; (iii) the seaborne iron ore trade; (iv) ore grades or types; and (v) future requirements. For those who may not be familiar with the iron ore mining industry, it may be useful to know at the outset that our industry has been plagued with overcapacity for the past seven years. The optimism which prompted substantial expansion of productive capacity in the early to mid-1970&apos;s has unfortunately proved to have been unfounded. I shall begin by describing where we are today as well as a little about how we got there. In the latter regard, it&apos;s not so much that historical knowledge will solve any of the industry&apos;s problems or provide clairvoyance with regard to the future. Rather it&apos;s a feeling on my part that some knowledge of the past will provide a useful perspective capable of enhancing our analysis of future trends. At the time of writing, the most recent year for which we have definitive world-wide iron ore production and consumption statistics is 1980. In that year the world consumed approximately 859 million metric tons of iron ore to produce approximately 510 million metric tons of primary iron consisting of 502 million tons of pig iron and 8 million tons of sponge iron. Crude steel production for the same period attained a level of 719 million metric tons. Because it is possible in today&apos;s world to produce steel without consuming iron ore simply by melting scrap, the key statistic insofar as iron ore demand is concerned is primary iron production. In 1980 the ratio of iron ore consumption to primary iron production was 1.68:1.00. The comparable ratio over the past seven years has varied from 1.63 to 1.87 and averaged 1.72:1.00. All the same, as a practical matter crude steel production and iron ore consumption tend to parallel one another closely, and for the time being a good rule of thumb is that to produce an average ton of crude steel requires 1.20 tons of iron ore. Let&apos;s turn our attention now to the regions where the 859 million tons of iron ore necessary to support 1980 world-wide iron and steel production were produced. Not surprisingly, most of the ore was produced in the same region where it was smelted. In round numbers 65% of the world&apos;s iron ore production is currently consumed in the same general region as it is produced, while 35% enters the seaborne trade and is transported in ocean vessels to a more remote consuming area. Approximately 85% of the world&apos;s seaborne iron ore trade is directed to the Western European and Japanese markets, both of which are almost entirely dependent on off-shore sources for their mammoth iron ore requirements. The following tabulation lists, in order, the twelve leading iron ore producing countries in 1980 as well as their percentages of total and free-world production; in addition their export potentials are presented. As a group these countries accounted in that year for 89% of world-wide production which stood at 871 million tons. Leading World Iron Ore Producing Countries [ ] One will first note that world iron ore production is dominated by the top four producers - namely, the U.S.S.R., Brazil, Australia and the U.S.A. - which together accounted for nearly 60% of total 1980 production. Of these four major producers the U.S.A. and the U.S.S.R. produce almost exclusively for consumption in their own regions, whereas Australia and Brazil produce primarily for the seaborne export trade. In fact Australia and Brazil accounted for about 50% of all seaborne iron ore trade in 1980! It is also interesting to note that Australia, Brazil, the U.S.A. and Canada accounted for nearly 60% of free world iron ore production in 1980. Once again the importance of Australia and Brazil shows itself, with their share alone of free world production reaching 35%. As has already been noted, a significant 35% of the world&apos;s iron ore production in the year 1980 was

Jan 1, 1982

By K. E. Manchester, A. H. Clark

Hall measurements have been made on three groups of silicon samples, which were implanted with boron, aluininunz, and phosphorus ions. Boron and phosphorus implants show essentially bulk properties when annealed under previously determined conditions, i.e., 15 min at 80O°C for boron and 10 mirz at 600°C for phosphorus. Bulk properties were also observed in alu?rrilzum-implanted samples when ion concentrations were below 1015 cm-&apos;; however, strange low- terrzperalure behavior and a falloff in cavrier concenlralion was observed for sarnples with ion concenlration abozle loL5 ern-&apos;. This can be attributed to solid-solubility effects since the average bulk concentration f0.r the sample exhibiting bulk properties was below the reported solubility limit for aluminum, while the other samples were above the limit. A detailed study of the annealirzg process indicates that mobilities reach bulk c~alues in phosphorus implants at 250DC, in alutninurn ivnplanls a1 500°C, and in boron implants at 700°C. A simple rnodel has been proposed to fit the annealing data. THE technique of semiconductor doping by direct injection of energetic ions is being actively investigated at this Center. Previously published results from this laboratory have been concerned with the investigation of implanted profiles in silicon and the electrical properties of the resultant p-n structures.1&apos;2 Diode properties have been reported for junctions produced by implantation of boron ions and aluminum ions in n-type silicon and phosphorus ions in p-type silicon. Reverse current characteristics, as well as electron diffraction data, have indicated that the damage to the structure produced by the energetic ions during the stopping process can be minimized by a gentle anneal. The time-temperature conditions for this process have been determined by sheet resistivity studies.3 Electrical profiles of implanted phosphorus ions which have been determined by a differential sheet conductivity technique are based on the assumption that the carrier mobilities and activation energies for ionization are the same as in bulk silicon. These assumptions have been substantiated experimentally by measurement of Hall constants and resistivities of these implanted structures and the results are presented herein. After establishing the bulk property equivalence of the annealed layers, a more detailed examination of the annealing process was undertaken. The sheet resistivity technique initially used to determine anneal conditions has been broadened to include Hall constants and mobility behavior with anneal conditions. PROCEDURE The three groups of samples prepared for Hall measurements were implanted with mass-separated beams of boron, aluminum, and phosphorus ions. Ion concentrations are equivalent surface concentration and they have been determined from beam current measurements during implantation. Implant conditions for the samples are shown in Table I. In all cases, the samples had previously been angle-lapped on one edge and the junction delineated with an HF-copper sulfate solution. The surfaces of the implanted regions of the samples were exposed to the delineating solution and in the case of the "n"-type phosphorus-implanted areas it was later discovered that a finite amount of surface could be etched by this solution. This is discussed in the section on results. The implanted samples were ultrasonically cut into the conventional six-probe configuration shown in Fig. l.* In the annealing studies, for which the meas- urements were taken at room temperature, the sample holder was a Bakelite jig incorporating tungsten mechanical probes. The other measurements were taken using a conventional liquid-nitrogen cryostat, in which the temperature could be varied from 77" to about 400°K. For these measurements, 10-mil aluminum dots were evaporated onto the samples and alloyed with the silicon at 530°C for 15 min. The samples were then mounted in flat-packs, and gold wires were bonded to the aluminum dots. The electrical measurements were made with either a Leeds & Northrup K-5 Potentiometer, a Keithley 147 Nanovolt Null Detector, or a Keithley 601 Electrometer. No external bias was applied to the substrate. There is an inherent self-biasing arrangement at one or the other of the current contacts (depending upon the polarity), and this suffices to limit the current flow to the implanted layer. The magnetic field was generated by an A. D. Little electromagnet. Except for occasional checks of linearity of the Hall voltage with

Jan 1, 1969

By R. W. Snyder, H. J. Ramey

This paper presents the results of applying the Buckley-Leverett&apos; displacement theory to petroleum reservoirs consisting of a finite number of layers. The layers are assumed to communicate only in the wellbores, and the reservoir may be represented as a linear system. Most previous investigations of this nature were limited by assumptions and by inconsistent calculation techniques. This study improves on previous work by applying the Buckley-Lev-erett displacement theory to a noncommunicating layered system where permeability, porosity, initial saturation, residual saturation and relative permeability vary from layer to layer in a logical and consistent manner. Gravity and capillary-pressure effects are neglected. A modification of the Higgins-Leighton calculation method was used in this study. Waterflood predictions were made with all properties varying, and then with only permeability varying using several inability ratios. These results were compared with the Stiles and Dykstra-Parsons predictions. It is shown that the latter methods generally give poor values for the breakthrough recovery and pessimistic predictions for the performance after breakthrough. Similar results were obtained for a gas-displacement case. lNTRODUCTION Field experience with immiscible displacement usually shows constant producing conditions until breakthrough of the displacing fluid. Then oil production continues at increasing displacing-to-displaced fluid ratios until the economic limit is reached. Three different ideal mechanisms are known that will produce this behavior: (1) relative permeability effects as described by Buckley-Leverett frontal advance theory,&apos; (2) vertical stratification as considered by Stiles,2 Dykstra and Parsons5 and others and (3) different path lengths involved in areal (two-dimensional) flow between wells as described by Dyes et al.4 Without question, a combination of these factors modified by formation heterogeneity and other known and unknown factors actually does control the behavior of real systems. This paper presents results of an investigation of certain factors that should affect performance but which have received little attention to date. In 1944, Law5 demonstrated that porosity and perme- ability are often found to have normal and logarithmic-normal distributions, respectively. throughout cored intervals in natural formations. This led to the concept of the noncommunicating, multilayered reservoir model for immiscible displacement. This model assumes that the reservoir is composed of a number of layers that communicate only at the wellbores. Each layer is individually homogeneous, but may be different from every other layer. Stiles&apos; presented one of the earliest applications of this model to waterflood performance. In addition, Stiles assumed that the initial saturations and relative permeabilities were the same for each layer, porosity was the same. displacement was piston-like, fluids were incompressible and injection into each layer was proportional to that layer&apos;s permeability capacity (permeability-thickness product). The last assumption would be true if the mobility ratio for the displacement were unity.21 Dykstra and Parsons" used the same model as Stiles, but rigorously included mobility ratios other than unity for piston-like displacement. Dykstra and Parsons used their general result to produce charts for log-normal permeability distributions between layers. Similarly, Muskat6 Pub1ished analytical solutions for linear and exponential permeability distributions. In 1959, Roberts&apos; described a scheme for calculating water-drive performance for the noncommunicating, layered reservoir model which considered two-phase flow in the displaced region. Roberts used the same model and assumed that the injection rate into a layer was proportional to that layer&apos;s permeability capacity, but that flood front locations could be evaluated from the Dykstra-Parsons results. These assumptions are inconsistent, and a material balance cannot be maintained except for a mobility ratio of unity. At the same time, Kufus and Lynch8 coupled Buckley-Leverett displacement theory with the layered model to provide an improvement of the Dykstra-Parsons method that was consistent. In 1960, Higgins and Leighton9 resented a numerical method for calculating waterflood performance also considering two-phase flow in the displaced region. The result was used to investigate variation in absolute permeability and oil viscosity. An excellent, detailed history of using the noncomrnunicating, layered reservoir model was presented by Nielsen.&apos;" The preceding techniques (and many related ones) were similar in that differences in initial saturations, residual saturations and relative permeabilities from layer to layer were neglected. It is well known that the irreducible water saturation is an important function of absolute permeability. Calhoun11 showed that the irreducible water saturation

By J. J. Gilman, T. A. Read

S URFACE effects in the cleavage of brittle crystals have been known for some oftime,1, 2 but our knowledge of surface effects in the plastic deformation of crystals is of relatively recent origin. In 1936, Roscoe9 eported his observations comparing oxidized and clean cadmium crystals. He found that cadmium crystals 1/2 mm in diam when covered by an oxide film less than 1200 atoms thick had critical shear stresses about twice those for clean crystals. This effect is anomalous in that it cannot be caused by the inherent shear strength of a normal oxide film. Either an interaction between the film and the crystal causes the large increase in strength, or the oxide film has an abnormal mechanical strength. Several authors since Roscoe have studied surface effects in crystal plasticity. A complete review of the literature will not be presented, but most of the results may be summarized as follows: 1—The critical shear stress for slip is increased markedly by very thin oxide films on zinc4 and cadmium crystals;" &apos; also, the entire stress-strain curve is raised by an oxide coating;3,4 both effects increase with decreasing specimen radius. 2—Surface active substances such as oleic acid destroy the hardening effect of oxide films.4, 6-8 The time required for the reduction of the hardening effect to begin increases with the viscosity of the solvent4~ 3—There has been dispute in recent years about the effects of surface active substances themselves on plastic deformation. Rehbinder, Lichtmann, and Maslenikov9 state that surface active substances reduce the strength of metal monocrystals markedly and increase the number of slip lines per unit length at a given strain. The effect varies with orientation for tin crystals being smallest for x, = 0, largest for x, = 45", and intermediate as x, + 90°.10 Several workers claim to have disproved the results of Rehbinder&apos;)"." but Rehbinder and Lichtmann9 have defended themselves and Masing with his collaborators" has confirmed some of Rehbinder&apos;s results. 4—Immersion of metal specimens in electrolytes such as sodium chloride reduces their strength12,13&apos; and subsequent cathodic polarization increases the strength reduction. For noble metals, the strength reduction occurs for both anodic and cathodic polarization," increasing with increasing polarizing voltage. 5—Electroplated copper coatings effect the creep rates of zinc monocrystals. Poly crystals are not affected." 6—Immersion in dilute acid destroys the hardening effect of an hydroxide film. When an acid solution is applied to a steadily creeping crystal, the creep rate jumps to a very high value and then drops gradually to a steady value which is higher than the initial steady rate.*&apos; " If the hydroxide film to be removed is very thin (about 100A thick), the creep rate does not change measurably, but a small rapid strain-increment is observed when dilute acid is applied." 7—Crystal plasticity depends on specimen dimensions. This was observed by Lichtmann and Ven-stroml" for monocrystalline tin and by Andrade and Kennedy" for polycrystalline lead. 8—Immerson of copper crystals in mercury has no effect on their stress-strain curves.&apos;" 9—Bombardment of creeping cadmium crystals with a particles which penetrate the surface to only 0.005 mm may increase their creep rates as much as five times.&apos;&apos;&apos; The experiments which will be described in this paper pertain to: (a) the effect of a crystal&apos;s shape on its plastic deformation, and (b) the effect of metallic surface films on plastic deformation. For the work pertaining to (a), crystals of zinc, tin, and lead were grown which had various shapes. These were tested in simple tension. Macroscopic rotations about the tension axis which are unpredicted by the classical theory of slip were observed, and serrated edges were observed in tin crystals. For the work pertaining to (b), the effects of evaporated and electrodeposited films of copper, nickel, gold, and zinc on the mechanical properties of zinc, tin, and lead crystals were determined. The films influenced both slip and twinning of the crystals in creep and tensile tests. Experimental Details Chemically pure zinc, tin, and lead were used in this investigation. The zinc was 99.999t pct pure;

Jan 1, 1953

By P. Somasundaran, D. W. Fuerstenau

The length of the collector is found to influence the flotation of the mineral even at incipient conditions, which are below the concentration at which interaction at the solid-liquid interface begins to take place to form hemi-micelles. To study this dependence, concentration for incipient flotation of quartz was determined as a function of pH with collectors of various chain lengths. The observed effect of chain length on flotation is ascribed to that of collector adsorbed on the bubble surface. In previous studies, it was shown that at low concentrations the alkyl collector ions adsorb at the solid-liquid interface as individuals.&apos;&apos;2 At higher concentrations, the collector ions adsorbed at the solid-liquid interface associate with each other to form two-dimensional aggregates called hemi-micelles. Above the hemi-micelle concentration, the length of the hydrocarbon chain is extremely important since the hydrocarbons are in effect removed from water during the association, making the energetic conditions more favorable for adsorption at the interface. Because of this enhanced adsorption, one observes a very rapid increase in flotation associated with the hemi-micelle formation at the solid-liquid interface. However, a dependence of flotation on the chain length at concentrations below that required for hemi-micelle association was also observed,&apos; and this cannot be explained by the above mechanism which postulated hydrocarbon chain interactions only at the solid-liquid interface. This prompted an investigation into other possible reactions of the hydrocarbon chains and an examination of the conditions at the bubble surface involved in the flotation system and how these observations might explain the reactions at the solid-gas interface which cause the particle-bubble attachment required for flotation. To obtain more information on chain length effects, flotation, under incipient conditions, was tested by vacuum flotation techniques. The collector-concen-tration-pH relationships for flotation of quartz with alkyl ammonium acetate collectors was delineated by observing the pH at which quartz particles begin to float to the liquid surface. By investigating flotation as a function of pH, it was also possible to study the effect of neutral molecules on incipient flotation conditions, since the aminium ions hydrolyze to amine molecules at higher pH values. EXPERIMENTAL WORK Brazilian quartz specimens were crushed and sized, and the 270 x 400 mesh fraction was used for flotation studies. The samples were leached with concentrated hydrochloric acid until no coloration of the acid occurred. The leached material was washed free of chloride ions and stored in distilled water. The vacuum flotation technique developed by Schuhmann and prakash3 was used to determine the critical pH-concentration curves. This method, which can be used to delineate conditions for incipient flotation, is fairly simple and rapid. About 0.5 gm of 270 x 400 mesh quartz was placed in a 100 ml graduated cylinder which was then filled to the 100 ml mark with the collector solution made from high-purity alkyl ammonium acetate salts. The water used for the test was conductivity water saturated with air that had been passed through a cleansing train consisting of Drierite, Ascarite, a water wash bottle, and a trap. After the pH was adjusted, the cylinder was then conditioned for thirty minutes. In the tests where an acid pH was desired, sufficient acid was added before the collector solution to avoid any effect due to slow desorption of collector from the quartz surface. After conditioning, vacuum was applied to the system and the flotation or nonflotation of the quartz was noted. The pH at which the quartz particles began to float to the liquid-gas interface was taken as the critical PH. Critical pH curves were thus determined for different concentrations of the various collectors. Hallimond tube flotation data were taken from the authors&apos; previous publication1 for correlation with that from the vacuum flotation. RESULTS AND DISCUSSION The results of vacuum flotation studies for determining critical pH-concentration curves, i.e., curves which delineate conditions for incipient flotation, are shown in Fig. I. In generaI, all the curves exhibit an upper and lower pH limit between which flotation will

Jan 1, 1969

By Leendert de Witte

Conventional resistivity logs consisting of a short normal, a long normal, and one or more long lateral curves do not give data that allow a complete quantitative interpretation in beds thinner than 20 ft. Reservoir rocks usually exhibit zones of continuous homogeneity of quite limited thickness where the long lateral curves become useless because of adjacent bed effects and boundary phenomena. If the beds are 12 ft or thicker, the short and long normals may be used for qualitative interpretation, which can be streamlined by the application of simplified departure curves. For beds of a thickness less than twice the long normal spacing, this procedure breaks down. The combination of the limestone curve, the later-olog or guard electrode log, and the microlaterolog permit quantitative interpretation for beds that are at least 10 ft thick, provided the mud resistivity and the hole diameter are known with sufficient accuracy. For beds thinner than 10 ft, combinations of the microlaterolog with short spaced laterologs and pseudo laterologs appear to be promising. Interpretation of these curves again requires the application of simplified departure curves. Resolution of various possible combinations was analyzed using departure curve data calculated on the Whirlwind I computer at the Massachusetts Institute of Technology. A field example is shown using the microlaterolog-microlog combination, and the combination of a 6-in. modified laterolog plus a 6-in. pseudo laterolog. INTRODUCTION For the purpose of quantitative interpretation of resistivity logs in porous formations, we want to obtain two essential quantities from the logs, namely, the true resistivity of the undisturbed formation, Rt, and the resistivity of the part of the formation invaded by mud filtrate, Rt. The apparent resistivities of all conventional logging devices are functions of these two parameters and are also influenced by a third unknown parameter, the diameter of the invaded zone, d. It has been shown&apos; that from the normal curves alone it is impossible to arrive at a unique solution for the three unknowns, Rt, R1, and d1. In very thick homogeneous beds, if invasion is not too deep, we can obtain a fair approximation to Rt from the long lateral curves and then use the two normal curves to find Rt and d1 Even under the most favorable conditions, the resolution of this system is not very good. The short normal does not give a reasonable approximation to R1 unless invasion is very deep (dl>16 hole diameters). For very deep invasion, however, the long laterals no longer approximate Rt. For bed thickness between 20 and 40 ft, the long laterals are affected appreciably by the adjacent beds; and the curves are distorted by boundary anomalies to the extent that they lose their quantitative usefulness in most cases. For the same bed thicknesses, the normal curves still function reasonably well. Although it is impossible to find unique solutions Lor R1 and Rt using the normal curves alone, we can obtain a reasonable approximation for the ratio R1/Rt through the use of simplified departure curves. This fact was brought to our attention by A. J. de Witte, geologist with Continental Oil Co. As the magnitude of Rl/Rt is a major clue to the presence of oil in formations, this method can be used to good advantage for qualitative analysis and will be discussed in somewhat greater detail. With the aid of suitable bed thickness corrections, the analysis of the normal curves may be used for bed thicknesses larger than 12 ft. For thinner beds, the method rapidly loses its resolution; and we have to resort to different types of resistivity logs if we want to attempt to analyze the curves quantitatively. The inadequacy of conventional resistivity curves in thin beds is far more serious than generally realized. Fig. 1 shows a conventional E. S. with a 16-in. and 64-in. normal and a 16-ft lateral through a section of Lansing-Kansas City lime, in comparison to a guard electrode survey through the same section in a neighboring well. The porous zones, which show up as low resistivity breaks on the guard electrode log, are completely masked by adjacent bed effects and boundary anomalies on the conventional curves. Even the short normal shows most of the porous Zones only as Vague deflections and in many cases fails to register Their

Jan 1, 1955