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By E. L. Claridge, K. S. Lee

Areal sweep efficiency of oil displacement by enhanced-viscosity water exhibiting pseudoplastic behavior was measured in a Hele-Shaw model representing one-quarter of a five-spot pattern. The pseudoplasticity of polymer solutions and the velocity distribution in the five-spot pattern produced a condition under which the mobility ratio between the displacing and the displaced fluid could not be assigned a single value. Instead, the movement of the displacement front is governed by local mobility ratios which are also time dependent. The areal sweep at breakthrough with polymer solutions was poorer than the sweep obtained with Newtonian fluids of comparable viscosity. However, the areal sweep at 1 PV throughput was greatly improved as compared to flood water without polymer. It was also demonstrated that, even after the oil-cut had declined to a low value during a regular waterflood, switching to polymer flood efficiently swept out the oil remaining in the model. INTRODUCTION The behavior of fluid displacements in isotropic porous media for various patterns of injection and production wells has been extensively investigated.1-7 These investigations all concerned Newtonian fluids, i.e., the viscosity of each fluid was constant regardless of flow rate. The generally unfavorable influence on areal sweep efficiency of higher mobility of the displacing fluid as compared to the mobility of the displaced fluid has been established for both miscible and immiscible fluids. The principle was also established that a close correspondence exists between miscible and immiscible flood front behavior,2, 3 although oil recovery in a waterflood at unfavorable mobility ratio may be less than that observed in a miscible displacement at the same mobility ratio. This is true even when oil recovery is expressed on the basis of movable oil. The reason is that oil saturation only slowly achieves its final value behind the water-flood front in accordance with the Buckley-Leverett8 simultaneous flow relations. It is convenient to use miscible displacements for laboratory simulation of waterflood frontal advance since the interfacial tension forces which are negligible in proportion to viscous forces on a reservoir scale9 are thus made nonoperative in the laboratory model. For miscible displacements, the Hele-Shaw type of model adequately represents a porous medium so long as the appropriate scaling rules5-10 are observed in its design and operation. During simulation of waterflood front behavior in the laboratory by using miscible displacements, the behavior of connate water may ordinarily be disregarded since it is usually indistinguishable from flood water in this process. However, when the flood water is deliberately thickened to improve the mobility ratio between water and oil. the effect on the sweep efficiency due to generation of a connate water bank during the process must be considered. In a uniform porous medium, such a bank is generated11 and efficiently displaced by injection of thickened water.l2 The oil originally in-place at the start of the waterflood is then displaced by connate water followed by thickened water. If the flood water must be thickened to obtain a favorable mobility ratio, the mobility of the oil phase is appreciably less than that of the connate water. Hence, the oil phase is inefficiently displaced by the connate water bank, and a considerable proportion of the oil comes in contact with and is displaced by the thickened waterflood front' A recent study 12 of five-spot displacements using miscible Newtonian fluids in which connate water banks of various sizes were simulated shows that, for connate water banks as large as 40 percent of 1 PV, major improvements in sweep efficiency resulted from use of a thickened

Jan 1, 1969

By R. E. Cook

This paper presents results of a study to determine to what extent errors in estimated free gas saturation affect the results of static pressure calculations from build-up curves in two-phase systems. Use is made of the method of pressure build-up curve analysis developed by Miller, Dyes and Hutchinson1 , with modifications for two-phase flow advanced by Perrine2. Cornhined fluid compressibility of gas-oil mixtures is included, with special attention given to the discontinuity that occurs in fluid compressibility at the saturation pressure and its effect on static pressure calculations from build-up curves. The sensitivity of static pressure calculations to errors in gas saturation is considered over wide ranges of formation and fluid properties and reservoir pressure conditions. It is concluded from this study that for analyses of two-phase pressure build-up curves (I) the use of under-saturated crude compressibility data, even when producing GOR's are at or near solution values, will result in very significant negative errors in calculated static pressrrre, and (2) except for large values of buildup curve .slope and/or very low crude gravities, rather large errors in calculated gas saturation can he tolerated without .significant effect on calculated static pressures. The conc1usions arc qualified as referring only to the effects of gas saturation and excludc possible errors in the nuumerous other factors that enter into the ancllysis of pressure build-up curves. INTRODUCTION As part of the analysis of basic data for several major Eocene reservoirs in the Bolivar Coastal field (Western Venezuela), it was necessary to analyze a large number of pressure build-up curves for oil permeability and static reservoir pressure. From performance data it became apparent that gravity segregation is very active in these reservoirs. As a result of this performance it was recognized that the free gas saturation within the oil leg of the reservoirs would be small but would be subject to certain errors in calculation due to the inaccuracy of relative permeability data in the low gas saturation region. Since all of the various methods of build-up curve analysis were originally derived for sin- gle-phase, constant compressibility systems, and since the presence of a small but rather indeterminate gas saturation would greatly affect the reservoir fluid compressibility, a study was undertaken to investigate the effect of gas saturation on the results of two-phase pressure build-up analyses. TWO-PHASE BUILD-UP CURVE ANALYSIS The method of analysis used in this investigation is basically that originally developed by Miller, Dyes and Hutchinson1, with modifications for two-phase flow advanced by Perrine2. Miller, et al, showed that the original equation for single-phase permeability away from the well bore, held for two-phase flow except that the calculated permeability is the effective permeability to oil away from the wellbore. This finding was acknowledged by Per-rine, who also presented the equation for effective gas permeability* as Since Eqs. 1 and 2 contain no terms influenced by fluid compressibility, no distinct problem should develop in calculating permeability from two-phase build-up curves. In regard to the calculation of static reservoir pressure from build-up curves in single-phase systems, the modified Miller, et al, method as presented by Perrine is briefly as follows. 1. From build-up curve data, PVT data for the reservoir fluid and the well spacing and sand thickness, calculate the climensionless shut-in time corresponding to the highest value of actual shut-in time (t, hrs) on the straight-line portion of a semi-log build-up curve. Dimenrsionless shut-in time is related to actual shut-in time by the relation, t- 0.000264 kt 2. From a graph of dimension less shut-in time vs dimensionless pressure difference (Fig. 1 1 ) find the value of dimensionless pressure difference corresponding to the value of 7 calculated under (1) above. Dimen-

By J. Szekely, V. Stanek

Steady state heat transfer and fluid flow rates are predicted for the counter-current contacting of gas and solid streams. For a .fixed pressure drop across the bed the convective heat transfer rate is affected by the gas flow rate, which in turn is affected by the temperature distribution in the system. Variations in bed voidage and in particle size were found to change the predicted temperature profiles quite markedly, in particular when the thermal capacities of the gas and solid streams were equal. IN Part I we examined the effect of step and pulse changes in the inlet gas temperature on transients in the flow of gases through fixed packed beds. Here we shall discuss heat flow and fluid flow interactions in the counter-current heat exchange between packed solids and a gas stream. Counter-current heat exchange in packed beds has been extensively studied. In his now classical paper, Furnas' assumed constant property values and developed a simple analytical. expression for the temperature profiles in the gas and in the solid stream. A highly sophisticated analysis of counterflow systems, allowing for transients and interparticle conduction was developed by Amundsen. In preparing a very readable review of this topic Elliott' also presented a number of elegant solutions, including the case involving heat generation. A great deal of work has been done on the application of these concepts to the modelling of the blast furnace. However, in all this previous work the mass flow of the gas was regarded as a quantity independent of the gas-solid heat exchange process. In the following we shall consider counter-current heat exchange between a gas stream and a packed bed of solids, under conditions where the pressure drop across the bed is specified, rather than the mass flow of the gas. FORMULATION Consider a packed bed, extending from y' = 0 to y' = L, in which moving solids and a moving gas are contacted in a counterflow arrangement. Let cold solids, with an initial temperature Tsi and mass flow GA, enter at y' = L, and hot gas with an initial temperature of Tgi and mass flow Gg enter at y' = 0. In contrast to the problems considered in Part I this system has a nontrivial steady state and we shall restrict our attention to the study of the pressure drop flow relationships and the resultant temperature distributions for steady state conditions. Under these conditions the formulation of the problem requires the statement of the following: 1) heat balance on the gas 2) heat balance on the solids 3) the mechanical energy balance equation and in addition the knowledge of the equation of state, and a functional relationship between viscosity and temperature and an expression for the heat transfer coefficient in terms of the other parameters. On neglecting temperature gradients within the solids and for a constant mass flow of the gas, the solution to this problem is well known.'" The expressions for the temperature profiles of the gas and solid streams may be put in the following form: where Tg and T, denote the dimensionless gas and solid temperatures respectively, y is a dimensionless distance, and R is the ratio of the thermal masses. These quantities are defined as follows: For the particular case of equal thermal mass capacities by the gas and the solid, that is R = 1, the Eqs. [1]and[2] simplify to Eqs. (71 and[8], respectively: i.e., the resultant profiles are linear. As for most practical cases , solutions given by Eqs. [7] and [8] will contain only the inlet temperatures as parameters. For a fixed, predetermined value of C;b the above

Jan 1, 1970

By M. E. Nicholson

The effect of boron on the austenitic transformation rate of iron is smaller than on low carbon steels. The influence of austenitizing temperature on B-Fe is the reverse of its influence on steels. THERE have been many studies made of the influence of boron on the hardenability of steel, but apparently none has been made of its influence on the y-a transformation of pure iron. There are several facts suggesting that boron should have a pronounced effect on the transformation rate of iron. First, Simcoe et a1.l indicated that boron reduces the nucleation rate of ferrite and bainite. Second, they showed, along with others,', " that the lower the carbon content of steel the greater the influence of boron on hardenability. If this trend extends to pure iron, the influence on rate of ferrite formation should be considerably greater for iron than for medium carbon steels. According to Rahrer and Armstrong," the multiplying factor for boron in pure iron should be about 2.40, compared with 1.50 in a 0.35 pet C steel. According to an extrapolation made by Grange and Mitchell,' the effect should be even greater, and the multiplying factor should be about 3.5 in iron. Many investigations of the boron influence'.7, 2, 5 indicated that boron is effective only when in solid solution. On the other hand, Chandler and Bredig" suggested that boron increases hardenability by combining with nitrogen, thereby preventing formation of AlN, which catalyzes the decomposition of austenite. If their hypothesis is valid, boron should have no effect on an alloy free from nitrogen. Digges et al." showed that so far as low nitrogen high purity Fe-C alloys are concerned this is not the case. No experiments, however, have been made on low nitrogen iron. To determine whether or not boron has an effect on low nitrogen iron and, if an effect exists, to determine whether it is as large as predicted from the investigations of boron treated steels, the following work was performed. Because of the rapidity with which iron transforms from austenite to ferrite at even a moderate degree of supercooling, it was decided to study the influence of boron on the transformation rate of iron by determining the effect of quenching rate on the temperature of the beginning of transformation. The technique, essentially that used by Greninger' and Duwez,H consisted of heating small specimens, 0.1 in. sq and 0.010 in. thick, in an atmosphere of purified helium with a resistance heater coil, and then quenching the sample in a jet of helium gas. At the time the jet was applied, the heating coil was removed from around the sample. The sample was suspended in the furnace on 30 gage chrome1 and alumel wires, one welded to each side of the specimen, which also served as a thermocouple for measuring the specimen temperature. Specimens were prepared from vacuum-melted iron obtained from the National Research Corp. which was rolled to a thickness of 0.060 in. and then decarburized in wet hydrogen for 51/2 hr at 700°C. This treatment also removed any boron present in the iron. The resulting iron contained 0.001 pet C. 0.0002 pet N, and 0.005 pet 0. One half of the piece was then boronized by surrounding it with 325 mesh boron powder and heating it for about 2 hr at 900°C in H,. The boronized iron was then homogenized at 1100°C for 24 hr. The iron boride case formed by boronizing was removed by grinding 0.010 in. from each side of the plate, and the piece was finally rolled to a thickness of 0.010 in. The resulting alloy contained

Jan 1, 1957

By J. C. Wilhoit, E. M. Galle

A three-dimensional photoelastic study was made to determine the stress state around the wall and bottom of a wellbore due to fluid pressure within the wellbore and unequal principal geostatic stresses. Models simulating the wellbore were made from a phthalic anhydride-cured epoxy resin. The frozen stress technique of three-dimensional photoelastic-ity was used to determine the stresses within the model. Two separate problems were solved: (1) hydrostatic pressure on all sides of the model with the exception of the inside of the hole, and (2) uniaxial compression perpendicular to the center line of the hole. The results are presented in the form of contour curves for each stress component. The curves cover a region which extends several hole radii from the bottom and wall of the hole. By proper use of these results, the state of stress may be calculated for any point on the wall or bottom of the hole, as well as for any point within the material that surrounds the hole. A systematic method is given for calculating these stress components for any combination of fluid pressure within the wellbore and system of unequal principal geostatic stresses, provided one of the principal geostatic stresses is parallel with the wellbore. The results show that stresses around the wall and bottom of a wellbore, induced by an uneyual system of principal geostatic stresses, are appreciably different from those induced by geostatic stresses that are hydrostatic. For uneyual principal geostatic stresses, the experimentally determined stresses on the wall of the hole several radii from the bottom are in good agreement with the stresses calculated by elastic theory. INTRODUCTION Interest in the problem of determining the stresses around and near the bottom of a wellbore, due to geostatic loading and fluid pressure within the wellbore, originated in the petroleum industry. The stresses on the wall of the wellbore are of interest due to their relation to lost circulation during drilling, the fracturing of formations during squeeze cementing and hydraulic fracturing of producing formations. The stresses on the bottom of the hole are of interest to the drilling segment of the industry because to produce a hole in the earth it is necessary to remove material from the bottom of the hole. This removal of material is produced by structural failure of the rock, whatever the criterion for failure may be. Cunningham and Eeninkl have shown that for certain conditions the effect on drilling rate of the bottom-hole stresses caused by a hydrostatic overburden pressure is small compared to other effects. This question, however, needs further experimental and analytical investigation. Much information concerning the stresses on the walls of wellbores has been published considering both equal and unequal principal geostatic stresses. The problem of determining the stresses around the bottom of the wellbore is considerably more complicated. However, previous investigators have obtained numerical and experimental solutions to the problem for equal principal geostatic stresses. whitworth2 and woods3 have obtained numerical solutions. word415 obtained a three-dimensional photoelastic solution, Durelli and Deily 6 obtained surface stresses only by photoelastic means, and Cheatham and Wilhoit7 determined the stresses around the bottom of a short cylindrical cavity. While Miles and McGuire, Harrison and Kieschnick and Hubbert and Willis 10 obtained the stresses on the wall of a wellbore for unequal principal geostatic stresses, they did not concern themselves with the stresses near the bottom of the hole. The estimates made by Hubbert and Willis of the differences between the principal geostatic stresses indicate that, to obtain a satisfactory solution for the stresses around the bottom of a wellbore, unequal principal geostatic stresses should be considered. This work is directed toward obtaining such a solution. The materials in the earth's crust are nonhomo-geneous, permeable and anisotropic. Previous

By G. Sandoz, D. A. Meyn

The fracture surfaces of specimens of titanium a1loys which exhibited susceptibility to subcritical crack growth in a wide variety of environments, including aqueous solutions, alcohols, hydrocarbon gases, carbm tetrachloride, and dry air, were examined. The dominant and characteristic fracture mode was cleavage. which became mixed with an increasing porportion of ductile fracture modes (dimples. and so forth) as the applied KI was increased. The cleavage plane in all the alloys was oriented at 15 deg from (0001) of the a phase. No indices could be assigned to the 15 deg cleavage Plane because of uncertainty as to which zone it belonged to. SLOW crack growth and delayed fracture take place in certain titanium alloys at stress intensity (KI) lower than the critical values for complete fracture (KIc) found in short-time tests for plane strain fracture toughness.' Such crack growth may take place in very dry air on sustained loading if the alloy contains a sufficient amount of hydrogen and if the stress intensity factor is higher than a threshold value designated KIH.2 Similarly, a number of environments such as water, alcohols, and hydrocarbons may cause slow crack growth provided the stress intensity factor exceeds the threshold value KISCC. In this paper it is intended to examine some fracto-graphic and crystallographic details of this subcritical crack propagation process as related to alloy composition, environment, and stress intensity. It has been previously reported that subcritical crack growth takes place in titanium alloys in aqueous environments by cleavage.2"6 The observations to be described here indicate that in the alloys investigated the mode of subcritical crack propagation is more dependent on the stress intensity during cracking than on the environment. The fracture mode is illustrated with photographs of the fracture surfaces at a wide range of magnifications. The crystallographic character of the cleavage mode is also presented and the results discussed. EXPERIMENTAL APPROACH The studies were made on four titanium alloys— Ti-8A1-1Mo-lV, Ti-5A1-2.5Sn, Ti-7Al-1Mo-lV, and Ti-0.350. Of these four alloys the first two were mill annealed and fine grained. The latter two were noncommercial and coarse grained, having been prepared for other experimental purposes. The crystallographic studies required a large-grain size. Consequently the fine-grained alloys were an- nealed in a vacuum at 1950°F and furnace cooled to produce samples for these studies. This treatment did not alter the microstructure significantly except for grain size. All the aluminum-containing alloys showed primary a with a network of ß-phase particles within the a grains; Figs. 1 and 2 show this microstructure for the specific case of fine-grained Ti-8A1-1Mo-1V. The cracks in the figures will be discussed later. Fractographic studies were made on all the alloys, but the electron fractographs displayed herein are from the Ti-8A1-1Mo-1V alloy in the fine-grained condition. Emphasis was placed on this commercial alloy because considerable information was available on the stress-corrosion cracking characteristics in a variety of environments. Sufficient supplementary studies of the alloy after the anneal to produce large grains were conducted to establish that the stress-corrosion cracking susceptibility and fractographic characteristics were not changed significantly. Thus it could be inferred that the crystallographic data obtained exclusively on large-grained specimens would apply also to fine-grained specimens. Fracture surfaces for study were obtained using precracked cantilever beam specimens loaded as described by Brown. The precracked section of a specimen was immersed in the environment of interest. Values of initial stress intensity factor Kli were chosen slightly higher than KISCC in order to obtain a fairly extensive region of slow crack growth. Fracture surfaces representative of a variety of stress intensity levels could then be examined because in the cantilever beam test KI increases as the crack propagates.

Jan 1, 1970

By G. C. Bernard, L. W. Bernard, L. W. Holm, W. L. Jacobs

The effect of loam on the permeability of porous media to water was studied as a {unction of foaming agent concentration, specific permeability, pressure gradient, length of a porous medium and its oil saturation. At a given fluid saturation in a porous medium, the permeability to water was found to be the same whether loam was present or not. Foam decreases the permeability to water by developing a higher trapped gas saturation than that obtained by water flooding without loam present, increasing the concentration of foaming agent increased the trapped gas saturation and thereby decreased the permeability to water. The presence of oil reduced the capability of most foaming agents to decrease the permeability of a porous medium to water. A few surfactants were found to be effective loaming agents even in the presence of oil. These results are similar to those reported in a previous paper on the effect of loam on the permeability of porous media to gas. The effect of loam was found to persist in long porous media at moderately high reservoir temperatures and during the passage of many pore volumes of surfactant-free water. INTRODUCTION This paper describes part of a study on a novel approach in the use of surfactants for oil recovery; the use of foam rather than water to displace oil. Previously it was found that foam can displace oil which normally is not displaced by water.4 The foam is formed by successively injecting a suitable surfactant solution and gas into a porous medium. Foam appears to have at least two uses in the field: (1) it shows promise as a superior oil recovery agent, and (2) it shows promise as a selective permeability reducing agent. Foam may be very useful in water floods, or in other oil recovery processes, where highly permeable streaks or unfavorable mobility ratios are a problem. A previous paper reported the effect of foam on the permeability of porous media to gas.1 In the present study the effect of foam on the permeability of porous media to water is reported. The specific objectives of the study were to determine: (1) the effect of foam on the permeability to water in porous media of various specific permeabilities, (2) the effect of foam on the permeability to water in the presence of oil, (3) the effect of foam and crude oil on the trapped gas saturation, (4) the effect of foam on permeability to water at trapped gas saturation, (5) the effect of pressure gradient on the permeability to water under foaming conditions, (6) the persistence of foam during the passage of surfactant-free water through the porous medium, and (7) the effect of various foaming agents, length of the porous medium and temperature on the permeability reduction caused by foam. EXPERIMENTAL PROCEDURES EQUIPMENT AND MATERIALS The experimental apparatus consisted of consolidated and unco n soli dated porous media, wet test meters and constant delivery pumps. The porous media consisted of consolidated sandstone cores (6 to 36 in. long), and unconsolidated sand packs (3 to 30 ft long). The consolidated cores had permeabilities of 32 and 1,000 md and porosities of about 20 per cent. The sand packs had permeabilities of 3,500 to 211,000 md and porosities of about 40 per cent. (Throughout this report a term such as 100 md sand" is used. This term means that the porous medium had a dry, nitrogen permeability of 100 md.) Fluids used in the experiments were distilled water, 1 per cent NaCl solution, aqueous solutions of foaming agents, nitrogen gas, air and crude oil.

Jan 1, 1966

By I. R. Kramer, H. Shen, S. E. Podlaseck

The tensile and creep properties of aluminum in vacuum have been investigated. It was found that the general effect of a vacuum environment was to reduce the rate of work hardening. Results obtained from creep tests showed that lowering the test pressure from 2 x 10-4 to 10-7 torr produced a decrease in the activation energy as much as 500 cal per mole. An attempt is made to explain these effects in terms of how the surface-stress field of a specimen may be affected by a vacuum environment during plastic deformation. In a previous paper,' the results were reported of some of our early work on the effect of vacuum environment on the stress-strain curve of aluminum single crystals. This effort has been extended to the studies of the tensile and creep properties in vacuum as a function of various metallurgical parameters. Some of the recent surface-effect studies2'3 have revealed that a region of high dislocation density, the so-called "debris" layer, is formed near the surface of the specimen as a result of plastic deformation. This layer acts as a surface barrier to oppose dislocation movement. The strength of this barrier depends on the surface condition such as oxidation or surface removal. Experimental results obtained from surface-removal work2, 3 indicate that such a surface barrier, which may be characterized by a stress field, affects the applied stress and the rate of work hardening. In the case of aluminum, this stress field was found to be directly proportional to the strain and the strain rate; however, the slope of this curve is independent of orientation of the crystal and may be altered by using different surface treatment. Since the escape of dislocations may be retarded by the presence of an oxide on the surface of a specimen, it is expected that a change in the rate of oxidation in vacuum will affect the process of dislocation accumulation in the debris layer. Consequently, it also affects the plastic behavior of a metal. This paper reports the changes in some of the creep and tensile properties of aluminum in vacuum and discussions of the observed effects in terms of the concept of the "debris" layer. EXPERIMENTAL PROCEDURE Tensile Tests. A sketch of the tensile apparatus is given in Fig. 1. This apparatus was contained in a bell jar (14 in. diam by 24 in. high) connected to a 10-in. vacuum system. The load was applied to the specimen by means of a gear train which was driven by a magnetic clutch located outside the vacuum chamber. The specimen, held by a pair of square shoulder grips, was attached to the load cell at the top and the drive gear at the bottom. A displacement transducer was placed between the two grips as shown in the figure to measure the elongation. Signals of elongation and load were amplified and recorded on an X-Y recorder. The system was capable of detecting loads as small as 0.025 lb and displacements of 0.0002 in. Shoulder-grip specimens of aluminum single crystals, having a nominal square cross section of 1/8 by 1/8 in. and a 3-1/2-in, gage length, were grown by the Bridgeman techniques. The original purity was 99.997 pet. The orientations of the crystals investigated are shown in Fig. 4(a). The crystals were annealed at 600°C for 2-1/2 hr, electropolished, and placed in the vacuum test chamber without any delay. All the crystals were deformed at a strain rate of 4 x 10-5 sec-1 at 24o ± 3°C. A study was made to find whether a chemically passive surface film would give the same effect as a vacuum environment. Specimens of aluminum 1100 (0.187 in. diam with a grain size of 0.1 mm)

Jan 1, 1965

By Hans Allenius, R. T. Hukki

This paper describes in quantitative terms the effect of sharpness of classification on the performance of the closed grinding circuit. The analysis is based on a large number of laboratory experiments designed to simulate the two most common industrial closed grinding systems. The experimental results show quantitatively the degree of improvement achievable by more efficient classification. In an earlier paper1 the senior author has presented a trend showing qualitative analysis of mill and classifier performance in tile closed grinding circuit. According to this analysis, the master key to a major improvement appeared to be effective removal of finished fine material from the classifier sands, or in other words, improved sharpness of classification, leading simultaneously to a substantial reduction of the circulating load. One purpose of this paper is to present the results of a quantitative investigation of the closed grinding circuit. Another is to set forth the essential pertinent variables revealed by the quantitative experiments carried out by the junior author. In the two most common systems of closed-circuit grinding, (1) feed to the circuit is introduced into the grinding unit, normally the ball mill, operating in closed circuit with the classifier; or (2) feed to the grinding circuit is introduced into the primary grinding unit, normally the rod mill, discharging into the classifier in closed circuit with the secondary grinding unit, normally the ball mill. In the following discussion, these two systems are analyzed separately in the indicated order. BALL MILL - CLASSIFIER CIRCUIT The Test Apparatus and Procedure: The test appara- tus included: (1) a F 195 mm x 220 mm laboratory ball mill rotated at a speed 77% of the theoretical critical speed, and a 7-kg batch of F 20 mm-F 50 mm steel balls; (2) a conventional 65-mesh test sieve and a Ro-Tap sieve shaker serving as a classifier; and (3) a Permaran instrument manufactured by Outo-kumpu Co. for surface area determinations by the permeability method. As no continuous closed-circuit experiments could be brought about on a laboratory scale, the process was broken down into alternating grinding and sizing steps in such a way that the new feed plus the returning sands always formed a batch of 1000 gm. For each selected grinding period and for each selected sharpness of classification the basic steps were repeated six times. Steady-state conditions were then reached. Crystalline vein quartz was used as a test material. Feed to the process consisted of -10-mesh fraction of this quartz crushed in rolls. This fraction included 15% of-65-mesh material. Experimental Results: The general flowsheet is shown in Fig. 1. Table I gives the essential data obtained representing steady-state conditions under the indicated set of variables. The table is based on 110 grinding experiments, 440 screen analyses and an equal number of specific surface area determinations. Fig. 2 shows the relationship between the cumulative net energy consumption and the cumulative number of mill rotations as evaluated by separate experiments. Note that this relationship is not linear but is instead represented by a slight curve. The data given in Table I are presented in graphical form as follows: Fig. 3 shows the produced -65-mesh material in grams per minute vs. time of grinding in minutes; the sharpnesses of classification at 65 mesh were 100%, 75% and 50%. It is clearly indicated that the highest-capacity figures call for relatively short grinding times and for the sharpest possible classification. Fig. 4 presents the specific surface area on the final -65-mesh product in square centimeters per gm vs. time of grinding in minutes. In conventional mineral dressing processes, a final product characterized

Jan 1, 1969

By Gilbert L. Eggert

The effects of reactor irradiation on age hardening in a Cu-2 wt pct Be alloy have been investigated in two neutron-energy ranges. During some of the irradiations, specimens were exposed to high-energy fission neutrons which passed through a boron-10 shield; during other bombardments, the boron-10 was omitted and specimens were irradiated in a reactor thermal column, or the fuel configuration was modified to increase the thermal-neutron flux at a location in the core. Differences in length, X-ray diffraction angle, and hardness indicated that low-energy neutron irradiation made a small contribution to changes in the measured properties. The influence of defects generated by knock-om with less than the Brinkman critical energy or by prompt (n,y) recoil is suggested as the cause of this effect. EXPERIMENTS designed to test the effects of reactor irradiation on the properties of age-hardening alloys have to the present time employed fluxes un-differentiated according to neutron energy. Billing-ton and Siegell in 1950 were the first to perform such an experiment and to compare the results with those obtained by thermal aging. These authors concluded that precipitation in a Cu-2 wt pct Be alloy was not enhanced by the radiation. However, 4 years later, Murray and Taylor,2 working with specimens of the same Cu-2 wt pct Be alloy, reported that an increase in density, hardness, and resistivity which followed reactor irradiation resembled changes associated with thermal aging at about 100°C. (It should be noted that these authors reported that higher aging temperatures caused a decrease in resistivity.) cupp3 reported hardness results similar to those of Murray and Taylor. Koppenaal4 showed that irradiation-enhanced precipitation and irradiation defect hardening were not simply additive but that they acted separately in an irradiated alloy. Kernohan et a1.,5 working with Ni-Be, offered evidence that beryllium was removed from solid solution by reactor irradiation and suggested that the mechanism was one of increased diffusion through the use of vacancies in the structure. piercy6 also found that more precipitate particles were formed by fission-neutron irradiation of a Cu-Co alloy which contained a small amount of particles before irradiation. He proposed that the additional particles were caused by an appreciable amount of diffusion during the final cooling of displacement spikes. The retrogression of extant precipitate particles found by Murray and Taylor2 and Boltax7 as well as piercy6 indicated that nuclei were dissolved within a high-energy spike region and, upon resolidification of the perturbed volume, new nuclei precipitate and grow by enhanced diffusion. Bleiberg et al.' and Konobeevski et al.' explained phase changes obtained by irradiating fissionable alloys in terms of retrogression and re-precipitation in regions of high-energy spikes. Parsons and Balluffi10 used electron microscopy to verify that crystallization did indeed occur in displacement spikes which were formed in amorphous germanium by fast-neutron irradiation. The concept that low-energy neutron irradiation might cause structure-sensitive property changes in semiconductors by atomic recoil associated with the (n, y) reaction was first proposed by Schweinler" and walker." This thesis was tested by Cleland and crawford" and found to be valid. Coltman et al.14 exposed a variety of pure metals to thermal-neutron irradiation at cryogenic temperatures and attributed the resulting resistivity changes to the action of defects created by (n, y) recoil. The present work was undertaken to extend the concepts of Schweinler," walker," and Coltman et al.I4 to the case of an age-hardening alloy and to determine whether or not the action of defects produced by thermal-neutron irradiation would en-hance age hardening. EXPERIMENTAL PROCEDURE Omeea West Reactor Irradiations.* Thermal-

Jan 1, 1965

By A. M. Gaudin

Activation of sphalerite with silver ions results from the exchange of two Ag ions for one Zn ion in the sphalerite lattice. The exchange is proportional to the logarithm of time and proceeds until either of the reactants is consumed. Sodium cyanide prevents the activation of sphalerite by controlling the ratio [Zn++]/[Ag+]' in solution. If sphalerite has already been activated with excess silver, cyanide ions can deactivate sphalerite provided oxygen is present. SOLUBLE: silver salts are effective activators for flotation of sphalerite with potassium ethyl xan-thate as collector.* Since sphalerite takes up large quantities of silver ions rapidly,2-4 investigation of this system appeared fruitful for studying the mechanism of sphalerite activation and deactivation. Experimental data presented here comprise studies of the mechanism and rates of activation and deactivation of sphalerite with silver and cyanide ions. A 20-lb sample of sphalerite from Ottawa County, Oklahoma, was handpicked, crushed, screened, hy-drosized to produce a 65/100-mesh fraction, and purified by electrostatic separation. The sphalerite was then leached with benzene and absolute ethyl alcohol to remove possible organic contaminants and with 0.1 M NaCN to remove any copper that might have been picked up during screening. The benzene had been specially purified by grinding with fine sphalerite for 12 hr to remove trace impurities that might have had a specific affinity for sphalerite. Ii'inally, the mineral was washed, dried in flowing nitrogen, and stored in large ground-glass stoppered weighing bottles under a small nitrogen pressure. The specific surface of two samples from the 65/100-mesh sphalerite stock, measured by krypton gas adsorption," was 420 cm2 per g. Compared with spheres of the same size and specific gravity, the prepared mineral had five times as much surface. Results of a wet chemical analysis and of a spectro-graphic study are given in Table I. Manganese, nickel, tin, indium, thallium, cobalt, and magnesium were not detected spectrographically. All solutions were preparid by -adding reagent-grade chemicals to conductivitv water. which had been previously saturated with the desired gases. Nitrogen and oxygen were purified, but no attempt was made to purify the laboratory air. Radioanalysis was carried out with prepurified Ag110 tracer obtained from the Oak Ridge National Laboratory. The complete decay scheme for Ae is complex. Its primary emissions are 0.09 and 0.55 mev ß rays and 1.48 mev y raysB and its half-life is believed to be 270 days. In preparation of solutions of AgNO3, the amount of Ag110 added was negligible compared to that of the inert silver. Abstraction of silver from solution by sphalerite was measured after agitation of 1.5 g sphalerite with 20 ml of solution in 50-ml pyrex flasks. All sample preparations were carried out in a dry box so that the proper atmosphere could be maintained. After the mineral had been agitated in the silver nitrate solution, an aliquot of the solution and a sample of the wet mineral were transferred to separate counting vials and weighed. The solid sample was dried and re-weighed and the activity in both vials measured by means of a scintillation counter. With scintillation counting it is possible to count y radiation from the solid and liquid, a distinct advantage over the older ß-ray counting techdiques.4 All measurements of silver activity were made using a sodium-iodide well-type scintillation counter. The amount of zinc in solution was measured colorimet-rically by the monocolor method of Sandell.7 Activation Studies Exchange Between Zinc Ions and Silver Ions During Activation: The increase of Zn++ in solution during activation with Ag+ is shown in Table 11. These data indicate a replacement of one Zn++ by two Ag+. Analysis of a separate two-month agitation test indicated that the replacement of Zn++ by Ag+ was, as expected, in the molar ratio of 2.0.

Jan 1, 1958

By D. R. Uhlmann, T. P. Seward, K. A. Jackson, J. D. Hunt

microscopic ohservations on alloys of organic trzaterials show that dendrite arms can melt off under normal conditiorzs of growth. This occurs because of the interactiorz of' heat and matter fluxes during dendritic growth. The re melting occurs where the den-drite arms are joined onto the main deizclrite sterrz. Many detached crystals can be produced in this fashion. It is postulated that this remelting phenornenon occurs in metal alloys, giving rise to the equi-axed region in castings. Experiments peyformed orr castings of transparent materials support remelting as a primary source of detached crystals. Ob~ervations an equiaxed tones in metal castings are discussed in terms of this and other mechanisms. It is concluded that the partial remelting of dendrites is on important mechanisnl for producing the equiaxed regions in castings. THE freezing of a casting can be divided into three regions: a chill zone formed near the mold wall, a columnar region, and a third region, at the center of the casting, which is called the equiaxed zone. The origin of the grains that comprise the equiaxed region is the subject of this paper. We will first outline the mechanisms which have been proposed to account for the origin of the equiaxed region and discuss some recent experiments which cannot be explained by these theories. We will then present some microscopic observations of dendritic growth which have led us to conclude that the equiaxed zone in castings can arise from partial remelting of dendrites. This proposal is supported by observations on transparent castings. Finally, we will discuss several observations on metal castings which could not be explained previously, and which can be accounted for by the present proposal. Previous Mechanisms. Winegard and Chalmers3 pointed out that the molten central region of an ingot could be constitutionally supercooled, because of the solute layer at the growing interface. In this supercooled region, nucleation on particles could occur, giving rise to the equiaxed crystals. Another mechanism has also been suggested,4y5 that the nuclei originate in the chill zone then float or are carried by convection to the center of the casting, where they grow to produce equiaxed crystals. In this case, all the crystals nucleate immediately on casting, so this mechanism will be termed "big-bang" nucleation. Walker's Experiments. J. L. Walker has made observations on the solidification of nickel and Ni-Cu alloys which cannot be accounted for by either of the above mechanisms. In studying the grain size resulting from freezing of nickel at various undercoolings, walker6 found that at large undercoolings the grain size was small, due to mechanical nucleation, as discussed by walker7 and Horvay.' At small undercoolings, the grain size was large, and the growth dendritic. In Ni-Cu alloys, however, for initial undercoolings starting from just below the melting point and extending for a hundred or so degrees of undercooling, fine grains were also observed. Samples were undercooled 200 Centigrade degrees without nucleating, and were then heated 130 Centigrade degrees so that the undercooling was 70 Centigrade degrees, and nucleated. The samples had a small grain size, indicating multiple nucleation. There were no heterogeneous nuclei in the liquid which could operate at the temperature of growth. Constitutional supercooling could not have been greater than the supercooling of the initial melt, since the temperature rose as the freezing continued. walker -as also shown that a Ni-Cu alloy which can be undercooled to below its solidus will produce typical columnar and equiaxed regions when cast into a cold mold. This alloy could not reach a temperature below its solidus by constitutional supercooling. It could not, therefore, have nucleated heterogeneously. Neither the big-bang mechanism nor the Winegard-Chalmers mechanism can account for the fine grain

Jan 1, 1967

By D. C. Hilty, W. Crafts

A qualitative pseudoternary solidification diagram for the Fe-S-O system modified by manganese is proposed and supported by experimental derivation of an isothermal section at 1475°C and substantially 1 pct Mn in the solid-metal phase. The solubility of oxygen in liquid iron containing 1 pct Mn and sulphur contents up to 0.9 pct has been measured at 1600°C and found to increase as the sulphur content exceeds 0.15 pct. AS has been pointed out previously,' all oxide and sulphide inclusions in steel, excluding mechanically entrained matter, result from modifications of the basic Fe-S-O system. Therefore, one method of attack on the problem of the mechanism of deoxida-tion and inclusion formation is to examine the influence of deoxidizers on the Fe-S-O liquidus diagram. This approach has been adopted in work on the subject being carried out at the Metals Research Laboratories of the Electro Metallurgical Co. and has resulted in the postulation of types of solidification diagrams for the Fe-S-O system modified with common deoxidizers. This method has been of considerable assistance in interpretation of the factors affecting the formation of inclusions.' For the most part, however, these diagrams have been highly speculative. They were constructed primarily by inference from the pertinent binary and ternary systems and from the appearance of inclusions produced by specific deoxidizers. Moreover, since the systems contain four or more components, simplifying assumptions and qualifications were necessary in order to permit their representation as modifications of the Fe-S-O diagram. Consequently, experimental confirmation of the type of construction employed for these diagrams is desirable, and the present paper is concerned with such evidence. The addition of manganese to the Fe-S-O system was selected for initial investigation. Manganese is an important component of practically all steel and is, therefore, of fundamental interest. Because of its great affinity for sulphur, manganese has a more profound effect on the sulphide side of the Fe-S-O diagram than any of the other common deoxidizing eletments. In addition, more quantitative information pertaining to the contiguous binary and ternary systems involving iron, manganese, sulphur, and oxygen is available than for the other deoxidizers. Fe(Mn)-S-O Solidification Diagram Many of the side diagrams of interest in connection with this system are known. The Fe-Mn binary has been well established by several investigators;% the Fe-O system has been clarified by Darken and Gurry;' and FeO-MnO diagrams have been published by Herty,5 Andrew, Maddocks, and Howat,6 and by Hay, Howat, and White.7 The Mn-O diagram does not appear to have been derived experimentally, but the portion of 'it that is of interest can be visualized easily from a consideration of the melting points of Mn and MnO and the fact that a broad miscibility gap must exist between them. The ternary Fe-Mn-O diagram has been discussed by Benedicks and Löfquist,8 Wentrup,9 and by Körber and Oelsen.10 Experimental study of the Fe-Mn-O system has been carried out by Körber and Oelsen and to a lesser degree by Chipman, Gero, and Winkler,11 Hilty and Crafts," and others. On the basis of published information, then, an outline of the Fe-Mn-O liquidus diagram can be constructed as illustrated by Fig. 1. In this, as in all succeeding diagrams, transformations such as the ?-? reaction in iron have been ignored for purposes of simplification. The arrows denote falling temperature. The distinguishing feature of this diagram is the broad region of liquid immiscibility extending

Jan 1, 1955

By G. R. Speich, D. J. Mack

The transformation of was studied by isothermal methods. At all temperatures, the ß transforms quickly to fine grained ß" which develops silver-rich striations. At higher temperatures the striations disappear, the final structure being Widmanstatten a in ß'. At lower temperatures, the striated ß" is consumed by pearlite nodules of a + ß' which in turn form the Widmanstatten a in ß'. The transformation is unlike any previously reported for a eutectoid. AS part of a general program of study on the eutectoid reaction, the Ag-Cd eutectoid seemed particularly attractive because the ß phase which undergoes the reaction is another of the typical "electron compounds," AgCd, having the disordered body-centered cubic structure. This work deals with the eutectoid which occurs at 50.5 wt pct Ag, and not with the eutectoid which has been reported at 42.9 pct Ag.' There has been no work reported specifically on the Ag-Cd eutectoid which was studied. The only information available on this eutectoid is that work done in the determination of the phase diagram. For the most part, the terminal portions of the diagram, Fig. 1, are well established; however, the region from 40 to 60 pct Cd is still somewhat in doubt. The X-ray evidence'..' in this region is in conflict with the results of thermal analysis. X-ray analysis3 does not show a polymorphic transformation at about 240°C as indicated by thermal analysis.1,5 Even the X-ray evidence, within itself, is confusing in this region of the diagram. One investigator2 reports the ß phase as hexagonal close-packed and has found three phases in the one-phase ß field. Other X-ray investigators"' ' report the ß phase as body-centered cubic. The authors believe that much of the confusion resulted from incomplete homogenization of the alloys. It was found that it takes almost a week to produce a completely homogeneous two-phase structure at 370°C. Another possible source of error is the volatilization of cadmium from the surface and cracks of the specimen during annealing with the possible formation of a cadmium-poor phase. The only metallographic data available on this eutectoid alloy are those of Durrant1 and Fraenkel and Wolff.5 his information is very limited. The phase diagram chosen as most nearly correct is that in the Metals Handbook," which is almost identical with the phase diagram suggested by Durrant.1 Materials and Procedure The alloy was prepared from high purity silver (999.5 plus fine) and high purity cadmium (0.02 Pb, 0.005 Cu, trace Fe). The metals were melted in carbon under a nitrogen atmosphere. Some cadmium was lost by volatilization but by remelting several times and adding cadmium a 200 g ingot of approximately eutectoid composition was obtained. Because the CdO fumes are quite toxic, the exit gas from the furnace was led through a water trap to condense the CdO. The ingot was homogenized at 650°C for 24 hr, no attempt was made to prevent decadmiumization. This resulted in a narrow decadmiumized rim on the ingot which was removed. Filings for analysis were obtained from cross sections of the ingot. Silver was determined by the Volhard thiocyanate method,? cadmium by difference. The ingot analyzed 50.8 pct Ag at the top of the ingot and 50.7 pct at the middle and at the bottom of the ingot. This alloy was only slightly hypo-eutectoid compared to the accepted value of 50.5 pct Ag and was used for the isothermal studies. It was felt that further attempts to adjust the composition might be futile because of the volatility of the cadmium. The ingot was sectioned to specimens approximately 3/4 x 3/4 x 1/8 in. These specimens were "austeni-tized" for 3 hr in air at 650°C to yield homogeneous ß and then quenched into a salt bath held at constant subeutectoid temperatures where the transformation

Jan 1, 1954

By C. H. Li, R. J. Stokes, T. L. Johnston

The phenomenon of solid-solution strengthening has previously been studied in a number of binary alloy systems.1-8 There has been, however, very little information published concerning the strengthening effects of specific solutes in magnesium alloys. Schmid and his coworkers9,10 investigated the behavior of aluminum and zinc in binary and ternary magnesium-alloy single crystals, but this work was done before high-purity materials were readily available. Workers at the Dow Chemical companyH reported increases in the critical resolved shear stress upon alloying magnesium single crystals with zinc and indium. Recently, Hardie and parkins* investigated the extent of hardening produced by the addition of various solutes to poly crystalline magnesium. The present work was undertaken to provide data on the strengthening effects of a number of solutes in high-purity magnesium, for the purpose of supplying further experimental information which might be useful in describing a general mechanism for solid-solution strengthening. To simplify interpretation of the results, the mode of deformation was limited to basal slip, through the use of single crystals. EXPERIMENTAL PROCEDURE Magnesium and magnesium binary-alloy single crystals containing indium, cadmium, thallium, aluminum, and zinc were prepared in the form of l/2-in.-diam rods, approximately 8 in. long, using a modified Bridgman technique in which the crystals were slowly cooled from the melt in a steep temperature gradient, in an atmosphere of helium. It was found that a solid-liquid interface travel speed of about 0.7 in. per hr consistently produced single crystals. The poly crystalline starting materials for the preparation of single crystals consisted of 1/2-in.-diam extruded rods, prealloyed to the desired composition. The unalloyed magnesium and magnesium-indium extrusions were furnished by the Dow Chemical Co. The other alloys were prepared at the Rensselaer Polytechnic Institute Metallurgical Laboratories. Some preliminary studies of the strengthening effect of indium were conducted at room temperature using a constant rate of tensile loading of 1040 g per min. Stress was applied to the crystals by means of a simple 5:l lever arm. The lever was loaded by a constant rate of flow of shot into a receptacle suspended from the long arm of the lever. Plastic flow was detected by an electrical resistance strain gage cemented to the surface of the crystal normal to the minor axis of the predicted glide ellipse. The crystals were acid machined to produce tensile specimens with a reduced section between the grip ends, with an additional step in the center of the reduced section to compensate approximately for the slip-retarding effect of the strain gage. The balance of the single crystals were extended in an Instron tensile tester. This machine employs a synchronously driven screw and automatically records applied load as a function of cross-head separation. It became unnecessary therefore, to employ a strain gage to detect deformation or to acid machine a reduced section. Preparation for testing reduced merely to chemical cleaning of the surface, thus minimizing the amount of handling and probability of accidental damage to the crystals. The rate of elongation employed in all the tests was 0.002 in. per min, corresponding to a strain rate of approximately 0.0004 per min. EXPERIMENTAL RESULTS The investigation confirmed the finding of many workers that the yield strength of hexagonal metal crystals is strongly orientation-dependent. This is illustrated in Fig. 1, in which o, the tensile stress required to produce gross plastic flow in eleven unalloyed magnesium crystals stressed at a constant rate of loading is plotted as a function of sin X, cos Ao where X, is the angle between the

Jan 1, 1960

By A. R. Gregory

A shear wave velocity laboratory apparatus and techniques for testing rock samples under simulated subsurface conditions have been developed. In the apparatus, two electromechanical transducers operating in the frequency range 0.5 to 5.0 megahertz (MHz: megacycles per second) are mounted in contact with each end of the sample. Liquid-solid interfaces of Drakeol-aluminum are used as mode converters. In the generator transducer, there is total mode conversion from P-wave energy to plain S-wave energy. S-wave energy is converted back to P-wave energy in the motor transducer. Similar transducers without mode converters are used to measure P-wave velocities. The apparatus is designed for testing rock samples under axial or uniform loading in the pressure range 0 to 12,000 psi. The transducers have certain advantages over those used by King, 1 and the measurement techniques are influenced less by subjective elements than other methods previously reported. An electronic counter-timer having a resolution of 10 nanoseconds measures the transit time of ultrasonic pulses through the sample; elastic wave velocities of most homogeneous materials can be measured with errors of less than 1 percent. 5- and P-wave velocity measurements on Bandera sandstone and Solenholen limestone are reported for the axial pressure range 0 to 6,000 psi and for the uniform pressure range 0 to 10,000 psi. The influence of liquid pore saturants on P- and S-wave velocity is investigated and found to be in broad agreement with Biot's theory. In specific areas, the measurements do not conform to theory. Velocities of samples measured under axial and uniform loading are compared and, in general, velocities measured under uniform stress are higher than those measured under axial stress. Liquid pore fluids cause increases in Poisson's ratio and the bulk modulus but reduce the rigidity modulus, Young's modulus and the bulk compressibility. INTRODUCTION Ultrasonic pulse methods for measuring the shear wave velocity of rock samples in the laboratory have been gradually improved during the last few years. Early experimental pulse techniques reported by Hughes et al.2 and by Gregory 3 were beset by uncertainties in determining the first arrival of the shear wave (S-wave) energy. Much of this ambiguity was caused by the multiple modes propagated by piezoelectric crystals and by boundary conversions in the rock specimens. Shear wave velocity data obtained from the critical angle method, described by Schneider and Burton4 and used later by King and Fate sand by Gregory, 3,6 are of limited accuracy, and interpreting results is too complicated for routine laboratory work. The mode conversion method described by Jamieson and Hoskins7 was recently used by King 1 for measuring the S-wave velocities of dry and liquid-saturated rock samples. Glass-air interfaces acted as mode converters in the apparatus, and much of the compressional (P-wave) energy apparently was eliminated from the desired pure shear mode. A more detailed discussion of the current status of laboratory pulse methods applied to geological specimens is given in a review by Simmons.8 A new shear wave velocity laboratory apparatus has been developed for testing rock samples under elevated pressures. This apparatus employs liquid-solid interfaces as mode converters. The technique for generating pure shear waves at liquid-solid interfaces was developed from studies of critical angle methods.6 Two identical transducers are placed in contact with opposite ends of the rock sample, one transducer acting as an ultrasonic energy emitter or generator and the other acting as an ultrasonic energy receiver or motor. The P-wave energy emitted from the piezoelectric crystal in the generator transducer is converted into pure S-wave energy at the Drakeol-aluminum

By M. R. J. Wyllie, Walter D. Rose

The use of electrical well logs for the quantitative determination of such reservoir parameters as connate water saturation, formation permeability and connate water salinity has recently been attracting the attention of a number of workers1,2,3,4,5. While the theory of the determination of connate water salinity from the self potential S.P. log has received rather detailed treatment, relatively little attention has been paid to the theoretical aspects involved in the quantitative interpretation of resistivity data. It is clear that if electrical well logs can be used for the quantitative evaluation of physical characteristics of reservoir rock, they will provide a valuable tool to supplement cheaply information obtained by more laborious core analysis. In certain cases it is conceivable that the coring program could be considerably curtailed if the electric log could be relied upon to give reasonably accurate quantitative information. It is our object in this paper to examine the theoretical basis of quantitative log interpretation as expressed in such well-established logging concepts as formation factor and cementation factor. It is also our object to investigate the physical aspects of the rela- tionship which is presumed to exist between resistivity index and brine saturation in reservoir rock. In particular, we will endeavor to draw attention to the fact that it is possible to express these logging concepts in terms of capillary pressure-saturation relationships, permeability and tortuosity, parameters which we will consider in this paper to be fundamentally indicative of rock texture. The probability of being able to obtain from log recordings alone the data theoretically essential to permit quantitative log interpretatiou will be examined, and consideration will also be given to the problem of formulating simple semi-empirical relationships for use in the field. THEORETICAL CONSIDERATIONS The concept of formation resistivity factor, or as it is now commonly called, formation factor, appears to have been introduced by G. E. Archie",". Formation resistivity factor as defined by Archie is the resistivity of a rock 100 per cent brine-saturated divided by the resistivity of the brine. This relationship had previously been used by physical chemists and the concept is, for example, implicit in an early treatment by Fricke7 of the conductivity of aqueous slurries. Archie was able to establish the fact that although the relationship between formation factor and porosity did not change too greatly for different rock textures, the relationship between formation factor and permeability was markedly dependent on rock texture. The relationship found by Archie between formation factor and porosity was expanded by H. Guyod8. Archie had suggested that the formation factor, F, could be expressed in terms of the porosity, F, as follows: F =F-m .... (11 where, F = effective porosity fraction of the sand, and, m = an exponent greater than about 1.3. Guyod introduced the term cementation factor for the exponent, m, since it may be qualitatively shown that formation factor for any given porosity tends to increase as the sand becomes more cemented. It would appear that the concept of m as an exponent representing the cementation in a sand is strictly only of qualitative value, since the quantitative estimation of m by means other than the determination of F and F has not been possible. Guyod suggests that m can be estimated from a visual examination of a sample of rock, but this method appears to be both arbitrary and unreliable. It can be said, however, that in intergranular reservoirs of practical interest, the range of m is from about 1.4 to 3.0. A possible explanation for the fact that m is found to lie between these limits will be offered below. The determination of formation factor is an essential preliminary to the

Jan 1, 1950

By D. C. Jillson

WORK in recent years1-' has indicated a complexity of the processes of deformation of metal crystals not previously appreciated and not fully accounted for by any hypothesis so far advanced. Furthermore, the nature and mechanism of formation of nuclei of recrystallization have not been determined precisely. The deformation of single crystals of zinc has been studied frequently, but the purity of the zinc and the perfection of the specimens sometimes have been given little consideration. Methods have been developed recently that readily yield zinc single-crystal specimens of high quality.5 In the present work, such specimens were deformed in various ways under various conditions, and deformed specimens were annealed to obtain information regarding recovery, recrystallization, and grain growth. The paper attempts to correlate and evaluate previous data, as well as to present new data, in order to determine areas in which more detailed work might be done most profitably. Tests at temperatures from the freezing point (419.46°C) to room temperature revealed glide only on basal planes in a close-packed direction (100)*, as reported by Mark, Polanyi, and Schmid6 and others. Markings probably similar to those observed by Kolesnikov7 and Boas and Schmid8 were noted in specimens stretched at elevated temperatures, but it seemed clear that these were not caused by prismatic or pyramidal slip (see second paragraph of section on Phenomena Involving Bending of the Basal Plane). Twinning Twinning on the octahedral plane of a face-centered cubic metal has been pictured as a process of simple homogeneous shearing along that plane in a [112] direction. It was recognized by Mathewson and Phillipsv and others""" that the (102) twinning of zinc required a somewhat more complex mechanism and might be considered as a homogeneous shearing of (102) planes in a [211] direction plus slight adjustments of atoms to positions of greater stability or lower energy, or as a single movement of each of the atoms in the same sense into the final positions. Gough and Cox" modified Mathewson's mechanism to obtain a more stable lattice configuration, but it is not clear that they succeeded, and their mechanism requires movement of some of the atoms in a sense opposite to that of the overall twinning movement. They also suggested that twinning may occur as a result of previous basal slip. This conclusion was based on the observation that twinning caused by alternating torsion was clearest and most profuse at positions for maximum basal slip rather than for maximum stress on (102) planes in the close-packed direction (not the twinning direction), and no mechanism was described. It might be wondered whether resolution of stresses on the twinning plane in the twinning direction would have afforded a simpler explanation. If twinning is essentially a simple homogeneous shearing along the twinning plane, it would seem that twins should grow by a smooth, continuous mechanism, and, indeed, that a simple reversal of stresses should reverse the shearing and de-twin the crystal. Cylindrical tablets 1/8 to 1/4 in. thick were cleaved from singlle-crystal specimens and were squeezed, perpendicular to a second-order prism plane, to give a tensile stress perpendicular to a first-order prism plane. A "click" was heard and a thin, needle-like twin appeared on the basal cleavage face. If squeezing was continued smoothly, the twin, viewed at magnifications up to X500, grew smoothly and quietly (fig. 1). X-ray examination verified that the twinning was of the (102) type. Rotating the compression axis 90" to reverse the stress then caused a smooth, continuous shrinkage and ultimate disappearance of the twin (fig. 2). The squeezing also caused a rumpling of the basal

Jan 1, 1951

By R. V. Smith

The theory for unsteady radial flow of gas, as simplified by Aronofsky and Jenkins, has been reviewed and compared with actual well performance. This study indicated that the theory should be modified by the introduction of an empirical "rate of flow" function "Y(q)". The expansion of the theory on the flow of gas to include a Y(q) term bridges the gap between the theory of unsteady-state flow of gas and actual gas-well behavior. Apparently, the Y(q) term is a function only of the rate of flow for a given well. The completion factor or skin effect is associated with the Y(q) function in such a manner that at least two or more sets of drawdown or pressure build-up tests are needed to separate the Y(q) function and the completion factor. Since the Y(q) function used in this report represents an energy loss dependent on rate of flow near the well-bore of a gas well which is in addition to the loss required by Darcy's law, the Y(q) function is related to the exponent of the back-pressure curve for a gas well. Techniques and equations are presented which permit the estimation of stabilized and "short-time" deliver-abilities. INTRODUCTION The published theory of radial unsteady-state flow of gas through porous media may be divided into papers1-" which use Darcy's law as a premise and other papers4-7,16-10 which recognize that Darcy's law may not hold for flow into gas wells. Miller8 compared theory based on Darcy's law with actual gas-well behavior and concluded that flow into gas wells deviates from Darcy's law. Houpeurt4,5 in a thorough investigation of flow into gas wells concluded that the flow rate into a gas well is proportional to the difference between the squares of upstream and downstream pressures elevated to a power between 1.0 and 0.5. Houpeurt also concluded that the deviation from Darcy's law is caused by irreversible, kinetic energy exchange between the flowing gas and the porous media. Tek9 presented a complete evaluation of the flow problem in gas wells. Several investigators state that the inclusion of gas compressibility into flow equations based on Darcy's law does not begin to explain the flow problems suggested by gas-well behavior. For many years, natural-gas engineers have realized that gas wells by actual test exhibit behavior which cannot be explained entirely by Darcy's law. Many tests on gas wells have indicated that a value of 0.85 for the exponent in the back-pressure equation is a fair average for many wells. However, Darcy's law either for steady or unsteady-state conditions indicates that the exponent should be 1.0. The purpose of this paper has been to examine this deviation from Darcy's law and to present a reasonable mathematical means of evaluating the deviation. The method presented in this paper combines previous theory with an empirical function to provide a description of gas-well behavior. All equations in this report are for constant terminal-rate-of-flow conditions. While present methods of testing wells usually are not based on this concept, they are believed to approach the constant terminal-rate conditions closely in many tests. However, several gas wells were tested by holding the rates of flow constant in order to approach more closely the constant terminal rate of flow; the results confirm the concepts presented in this paper. REVIEW OF THEORY FOR UNSTEADY-STATE FLOW OF GAS The basic partial differential equation for the flow of natural gas has been given in technical literature; the equation for a cylindrical reservoir with the well in the center is

By K. E. Brown, G. H. Fancher

An 8,000-ft experimental field well was utilized to conduct flowing pressure gradient tests under conditions of continuous, multiphase flow through 2 3/8-in. OD tubing. The well was equipped with 10 gas-lift valves and 10 Maihak electronic pressure recorders, as well as instruments to accurately measure the surface pressure, temperature, volume of injected gas and fluid production. These tests were conducted for flow rates ranging from 75 to 936 B/D at various gas-liquid ratios from 105 to 9,433 scf/bbl. An expanding-orifice gas-lift valve allowed each flow rate to be produced with a range of controlled gas-liquid ratios. From these data an accurate pressure traverse has been constructed for various flow rates and for various gas-liquid ratios. A comparison of these tests to Poettmann and Carpenter's correlation indicates that deviations occur for certain ranges of flow rates and gas-liquid ratios. Numerous curves are presented illustrating the comparison of this correlation with the field data. Poettmann and Carpenter's correlation deviates some for low flow rates and, in particular, for gas-liquid ratios in excess of 3,000 scf/bbl. These deviations me believed to be mainly due to the friction-factor correlation. However, Poettmann and Carpenter's correlation gives excellent agreement in those ranges of higher density. This was as expected and predicted by Poettmann. He pointed out that their method was not intended to be extended to those ranges of low densities whereby an extreme reversal in curvature occurs.l As a result of these experimental tests, correlations using Poettmann and Carpenter's method were established between the friction factors and mass flow rates which are applicable for all gas-liquid ratios and flow rates. Definite changing flow patterns do not allow any one correlation to be accurate for all ranges of flow. INTRODUCTION The ability to analytically predict the pressure at any point in a flow string is essential in determining optimum production string dimensions and in the design of gas-lift installations. This information is also invaluable in predicting bottom-hole pressures in flowing wells. Although this problem is not new to industry, it has by no means been solved completely for all types of flow conditions. Versluys,2 Uren, et al, 3 Gosline,4 May,5 and Moore, et al,6,7 were all early investigators of multiphase flow through vertical conduits. However, all of these investigations and proposed methods were very limited as to their range of application. Likewise, many are extremely complicated and therefore not very useful in the field. Only in the last decade have any significant methods been proposed which are generally applicable. The most widely accepted procedure in industry at the present time is a semi-empirical method developed from an energy balance, proposed by Poettmann and Carpenter8 in 1952. Their correlation is based on actual pressure measurements from field wells. Accurate predictions from this correlation are limited to high flow rates and low gas-liquid ratios. Although this method will be discussed in detail later, it should be pointed out that two important parameters, namely the gas-liquid ratio and the viscosity, were omitted in their correlation. The viscosity was justifiably omitted since their data was in the highly turbulent flow region for both phases, and most wells fall in this category. The gas-liquid ratio was incorporated to some extent in the gas-density term. In 1954, Gilbert9 presented numerous pressure gradient curves obtained from field data for various flow rates and gas-liquid ratios for the determination of optimum flow strings. However, no method is presented for predicting pressure gradients except by comparison to these curves. Baxendell, et al,10 proposed a method based on Poettmann and Carpenter's procedure