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By T. P. Meloy

Recently, Gilvarry1 has criticized the Gaudin-Meloy2 derivation of the size distribution equation for impact grinding. The criticism states that as the derivation stands it is good for only a long, thin wire being fractured. This paper contains a second derivation in reply to the criticism. Consider a homogeneous solid particle. This particle is broken into fragments by impact. It is assumed that the material resembles galena and that the particles were broken into chunky parallelepipedes which may be treated as cubes. The fragments are now reassembled — as seen in Fig. 1 — and a line is passed through the fractured solid perpendicular to one of its faces. For simplicity, the length of the line segment in the cube is considered to be 1. Fig. 2 represents the line segment in the cube showing the locations of the crack surfaces cutting the line and one point, P, chosen at random on it. The question arises as to what is the probability of the point, P,

Jan 1, 1963

By Strathmore R. B. Cooke, Iwao Iwasaki

RECENTLY spectrophotometry has been reported to provide a convenient technique for the rapid and reproducible determination of xanthate concentration in pulp solutions,12 and for a kinetic study of xanthate decomposition in acid solutions." Since the application of this analytical technique is feasible for those compounds showing pronounced light absorption maxima in the near ultraviolet region, it was deemed advisable to investigate the absorption spectra of some of the organic compounds that are used in flotation. It is known empirically that certain groups of atoms in an organic compound cause characteristic light absorption in the ultraviolet and near ultraviolet range, and the wavelengths and intensities of the corresponding absorption maxima are relatively independent of the nature of the remainder of the compound. The characteristic values of such groups, which are known as chromophores, are given in the literature.4,5 According to this information, many of the sulphydryl compounds are expected to show absorption maxima in the near or long wavelength ultraviolet region, whereas the saturated fatty acids and the saturated alkylamines do not. This article reports the absorption spectra of the six following types of sulphydryl compounds; mono-, di-(xanthate), and trithiocarbonates, dithiocarba-mate, dithiophosphate (aerofloat), and mercaptan. A Beckman DU quartz spectrophotometer was used to investigate the spectra in the wavelength region of 215 to 350mp. Materials: All the mono-, di-, and trithiocarbonates used in this investigation were prepared in the usual manner" from appropriate compounds obtained from Eastman Distillation Product Industries. The dithiocarbonates included the normal alkyl compounds from methyl to octyl inclusive, as well as the isopropyl, isobutyl, and isoamyl xanthates. Iodo-metric titration gave 99.7 and 99.5 pct purity for

Jan 1, 1958

By Frederick C. Langenberg

IT has been shown1 that copper can be removed from iron-base alloys by solvent extraction with molten lead and sodium sulfide slags. In these processes copper removal is favored by a positive deviation of copper in iron from ideal behavior. Chou' determined the distribution of copper between liquid silver and iron and obtained a value for the activity coefficient of copper in iron at 1600°C, y°, of 9.12. Chipman" calculated the activity coefficient from the Fe-Cu phase diagram to be 12 at 1600°C. More recent work by Koros and Chipman" yields a value at 1600°C for y V equal to 8.0. In this latter work, the distribution of copper between silver and iron was measured at 1600°C, while the activity of copper in the silver phase was determined from calculations based on the Ag-Cu phase diagram. The present work presents another value of based on calculations from the Cu-Pb phase diagram, on the heat of mixing data for the Cu-Pb system, and on an experimental study of the distribution of copper between iron and lead at 1600°C. These experiments were part of a larger research on the removal of copper from iron-base alloys conducted at The Pennsylvania State University. Experimental Procedure—The distribution of copper between pure iron and lead at 1600°C was made in the furnace assembly shown in Fig. 1. The melts were made in high purity alumina crucibles under an atmosphere of prepurified argon. Temperatures were read with an optical pyrometer sighted into a %-in. hole drilled in the inductor. Extensive calibration of the optical readings with immersion readings had been carried out previously. The initial charges consisted of 100 g of electrolytic iron and varying weights of copper. The melts were brought rapidly to 1600°C and 75 g of lead added. The temperature was quickly readjusted to 1600°C, and the melts were held for 10 min at this temperature. A sample was then drawn from the iron layer in a fused silica tube. This sample was analyzed to determine the copper content of the iron layer at equilibrium, while the copper content of the lead layer was determined from a material balance. The validity of the material balance was confirmed by a chemical analysis of the entire lead layer for one heat in which the crucible was removed and quenched after the iron sample was taken. The calculated copper content of the lead-rich phase was 1.18 pct; while the entire lead layer analyzed 1.20 pct Cu. The distribution results are shown in Fig. 2. The distribution constant, N,.'r'"/N, is equal to 3.95. Discussion—From the Cu-Pb phase diagram' it can be seen that lead-rich liquid Pb-Cu solutions

Jan 1, 1957

By C. E. Birchenall, H. M. Schadel, G. Derge

EXISTING distribution data' for silicon between liquid iron and silver at steelmaking temperatures, 1500" to 1600°C, has made activity relationships in liquid silver-silicon alloys desirable as a method of determining the silicon activity in molten iron. To this end, through the use of radioactive Ag110 and the molecular beam technique described in a previous paper,' the vapor pressure of silver as a function of temperature has been measured over three silver-silicon alloys containing 3.9, 9.3, and 15.4 atomic pct (eutectic composition) silicon. The technique was that described for pure silver with the exception that a porcelain liner was used inside

Jan 1, 1951

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 P. A. Toynbee

An experimental air-slide classifier1 has been applied to the de-dusting of ground dolomite in an attempt to produce a grade of -30 +150 mesh (B. S. Sieves) material from a raw material containing 30-35% of the -150 mesh fraction. Air flows varying between 1.5 and 2.5 cu ft/sec sq ft of screen area were used. The throughput of dolomite was between 80 and 100 lbs/h. inch of screen width. The size analyses of the de-dusted material and of the original dolomite are shown in table at right. The proportions of the +100 mesh material in the feed and in the de-dusted products have been used to calculate materials balances, on the assumption that there is no loss, as dust, of this +100 mesh fraction. By interpolation, it can be shown that a de-dusted product recovery of 68.5% will be obtained at an air flow of 2.13 cu ft/sec sq ft of screen area. The feed material contains 68.5% of +150 mesh material, so that if the de-dusting gave a perfectly sharp cut, the product would contain no material less than 150 mesh. Further calculations based on the size analyses, show that, at an air flow of 2.13 cu ft/sec sq ft of screen air, the -150 mesh fraction in the de-dusted product will fall just below the specified maximum limit of 5%.

Jan 1, 1964

By A. G. Metcalfe

THE failure to detect any change in the thermal properties of cobalt at the Curie point would appear to indicate that the apparatus may have a limited sensitivity. The Curie temperature has been determined by direct methods to be 1121+3°CP and 1131°C.3 The specific heat has been determined many times'.' and weighted values are given in Table I. The allotropic transformations in iron and titanium, used by the authors to test the experiment method, involved a volume change of the order of 3 pct on going from the close-packed to the body-centered-cubic lattice. These energy changes are likely to be much larger than those involved in a diffusionless transformation from a hexagonal to a cubic-close-packed lattice. However, it has been pointed out that thermal observations are unreliable in the detection of phase changes when these are near a Curie point.' James 0. McCaldin and Pol Duwez (authors' reply)—The sensitivity of the present technique is limited to first-order transformations, so that gradual changes in specific heat, e.g., in the vicinity of Curie points, are not detected. Furthermore, the existence of first-order transformations with latent heats much smaller than those occurring in the known allotropic transformations of iron and titanium is, we agree, still pending.

Jan 1, 1956

By J. O. McCaldin, P. Duwez

ALLOTROPIC transformations between 1000° and 1900°C have recently been reported for several metallic elements. Since the proposed transformations are based on limited evidence, it was decided to examine the elements in question as well as some refractory metals by thermal analysis with a photoelectric technique similar to that described by Hug-gins, Roll, and Udin.1 In this method, a lead sulphide cell was used to detect thermal radiation from an electric-resistance heated strip specimen. A thermocouple spot welded to the specimen was used to calibrate the temperature of the system under steady temperature conditions, and recording was accomplished with a cathode ray oscilloscope. In the method used by the present authors, the temperature calibration was omitted and the cathode ray oscilloscope was replaced by a recording galvanometer. This technique, in which electric current passing through the specimen heats it, will be referred to henceforth as Method 1. Another arrangement was required for those cases where the specimen could not be formed into a wire or strip suitable for resistance heating. In such cases the specimen was a sintered compact heated by thermal radiation from a hot tungsten strip, Fig. 1. The specimen was insulated from the heating strip with a thin layer of thoria powder or suspended on 0.004 in. tungsten wires. The take-up spring had just sufficient tension to prevent buckling of the heating strip due to thermal expansion. This technique will be called Method 2. Both methods were tested with specimens of iron and titanium and the well known allotropic transformations, a toy and ? to 8 in iron and a to in titanium, were very clearly detected. Fig. 2 shows one of the records obtained for titanium. For this particular experiment, the iodide titanium specimen was a square rod 0.080 in. on an edge and 3 in. long.

Jan 1, 1955

By Austin E. Dwight

IT has been shown by Oelsen and Wever' that the effect of a solute element on the allotropic transformation in iron is dependent upon the quantity

Jan 1, 1957

By W. Rostoker

IN the course of the development of the phase equilibrium diagram for the system Zr-Cr,' the structure of an as-cast allov having the composition ZrCr2 was analyzed and established to be isomorphous with MgZn2 (C14, hexagonal lattice, 12 atoms per unit cell). In a recent paper on the same system, Hayes, Roberson, and Davies' report for the ZrCr2 phase an isomorphy with MgCu2 (C15, cubic lattice, 24 atoms per unit cell). It appeared that this conflict might be resolved by assuming a high and low temperature modification for ZrCr2. That this was the case with the phase TiCr2 has recently been demonstrated by Levinger." Specimens of ZrCr2 annealed at 1200°, 1100°, 994", 900°, 834", 800°, and 700°C, respectively, and subsequently quenched were examined by X-ray diffraction analysis. It was successfully demonstrated that a transition from the MgZn, structure at lower temperatures to the MgCu, structure did occur at some temperature between 900" and 994°C. Table I lists the observed structures at the various annealing temperatures. In Table II, a summary of line spacings and intensities is given for each of the allotropic modifications. The first six lines of the MgCu2 structures have been located in the table to illustrate the close similarity between the patterns. Lattice parameters of the two modifications were calculated by a least squares solution of equations for interplanar spacings for a series of high angle lines. The results are as follows: MgZn2 type - c = 8.262 kX, A = 5.079 kX. MgCu2 type — a = 7.195 kX. It is interesting to note that TiCr2 behaves in reverse fashion yn that the MgCu, structure is the low temperature modification and the MgZn2 structure is the high temperature modification. References lR. F. Domagala, D. J. McPherson, and M. Hansen: This issue p. 279. 'E. T. Hayes, A. H. Roberson, M. H. Davies: Trans. AIME (1952) 194, p. 304; Journal of Metals (March 1952). 3B. W. Levinger: Trans. AIME (1953) 197, pp. 195-196; Journal of Metals (February 1953).

Jan 1, 1954

By J. B. Clark, F. N. Rhines

THE A1-Mg phase diagram in the composition range from 30 to 60 pct Mg remains uncertain. Four intermetallic compounds are reported in this composition range. All of the published diagrams are in agreement as to the existence of intermediate phases near 37 and 52 pct Mg (Mgl,A1,). Confusion exists, however, as to the number and identity of the intermetallic phases present in the intervening composition range from 37 to 52 pct Mg. Mikheeva and Kurnakovl denote the existence of a phase e near 42 pct Mg. Kawakami," Reiderer? and Laves report a phase near 48 pct Mg. Eickhoff and Vosskuhler, from a critical survey of the literature, composed the diagram shown in Fig. 1, with the exception of the eutectoid horizontal of the e-phase shown at 210°C. RaynorV n a similar survey discounts the existence of the phase proposed by Ka-wakami et al.' at 48 pct Mg and reports a composite diagram similar to that of Eickhoff and Vosskuhler." This uncertainty as to the number of intermetallic phases in the A1-Mg system may be eliminated by annealing a diffusion couple of pure aluminum and

Jan 1, 1958

By A. G. Allten

EXAMINATION by metallographic and X-ray diffraction means of an austenitic steel containing 0.06 pct C, 1.26 pct Mn, 0.38 pct Si, 21.15 pct Ni, 18.72 pct Cr, 3.07 pet W, and 9.14 pet Mo indicated that a - phase, which had not been reported in the literature, existed in this steel. Both the s and car-bides of the M6 C type were present in the as-forged steel. The carbides dissolved completely in the aus-tenite at approximately 2200°F (1205°C). The s, however, was present at all temperatures up to the solidus temperature of the steel at approximately 2375°F (1300°C). Ferrite was not found in any condition of the steel. The faintness of some of the s lines in X-ray patterns obtained from samples of the steel made it desirable to isolate the s prior to verification of its entire pattern. It was found that the s phase could be separated from samples of the steel which had been water quenched from 2250°F (1230°C) by dis-

Jan 1, 1955

By Jr. F. M. Perkins.

Capillary forces play a controlling role in water-drive displacement processes both in laboratory experiments and in actual reservoirs, but their quantitative importance may be quite different in the two cases. Because of the importance of conducting laboratory experiments which are representative of field conditions, it is necessary to understand exactly the role of capillary forces in the displacement process. Though a number of experimental investigations related to this subject are contained in the literature, there appears to be a lack of information pertaining to unsteady-state experiments in water-wet media. This experimental study was conducted to obtain additional laboratory data to clarify further the role of capillary forces in both the macroscopic and microscopic flow of oil and water in porous materials. THEORETICAL CONSlDERATlONS The capillary pressure is defined as the difference in pressure between a continuous oil phase and a continuous water phase in a porous material.' The magnitude of this pressure difference depends on the interfacial curvature and the interfacial tension. The interfacial curvature is determined by the geometry of the pore spaces, the wettability of the rock surfaces, and the quantity of cach phase present. Capillary forces are involved in a water-drive displacement process in that they exert a controlling influence on the microscopic fluid distribution which in turn is reflected in the saturation or macroscopic flow behavior. Microscopic Fluid Distribution Because of the microscopic nature of the displacement of oil by water, it is necessary to consider the flow and the fluid distribution in individual pores. On this microscopic scale the capillary Forces, which act over a distance of one or two sand grain diameters, control the distribution of oil and water under static equilibrium conditions. When an external force is applied to the fluids, such as in a water-injection experiment, the applied forces tend to distort the oil-water interfaces. However, in most fine-grained, water-wet sands, the applied pressure difference across one or two grain diameters is usually several orders of magnitude less than the capillary pressure difference. These con-siderations lead to the theory' that even during flow the capillary forces continue to control the microscopic distribution of oil and water within the pores of a porous material for all practical reservoir and laboratory flow rates. This concept of capillary forces controlling the microscopic distribution of fluids has been substantially verified by other investigators3-7 who have found a lack of dependence of relative permeability and residual oil saturation on rate of fluid injection. Macroscopic Distribution The microscopic influence of capillary forces cannot be observed easily and only the effect on the macroscopic or average saturation can be detected. The saturation, of course, is really the point of interest. During a water flood, large differences in saturation at the flood front cause large capillary pressure gradients. This, in turn, causes water to advance ahead of the flood front thereby reducing the capillary pressure gradient in this region. The result is that in homogeneous porous media capillary pressure gradients tend to cause a diffuse displacement front. At low rates in laboratory columns, the front may extend over the entire column length. When the advancing water first reaches the outflow face of a core, the water, which is the wetting phase, cannot be produced because the pressure in the water just inside the core is lower than the pressure in the oil-filled space around the outflow face. This difference in pressure is equal to the capillary pressure for the water saturation existing at the outflow face. Water, therefore, accumulates at the outflow end of the core which causes a reduction in the capillary pressure. Because the capillary pressure does not vanish except at the residual oil saturation,7,8,9 water will not be produced until the residual oil saturation exists at the outflow face. This entire effect,"' which is called the "boundary effect", results in a region of relatively high water saturation near the outflow face. At low rates of injection in a short column, this region of high water saturation may extend over a considerable portion of the column. The influence of capillary forces on the macroscopic flow of oil and water have been described by Leverett.10 For unidirectional, viscous flow in the absence of gravity segregation, the expression in dimensionless form for the fraction of water in the flowing stream, f, is

Jan 1, 1958

By F. W. Jessen, John C. Miller

In many areas where carbonate rocks form important parts of the stratigraphic sequence, stratigraphers have experienced varying degrees of difficulty in differentiating and correlating limestone and dolomite units in both surface and subsurface work. With early Paleozoic rocks of the Mid-Continent, insoluble residues yield a remarkable amount of strati-graphic data and relatively good correlations may be carried over broad distances.' Unfortunately, neither such information nor electric logs and radioactive logs have been particularly helpful in interpreting the limestone sections of the Permian Basin of West Texas. This is because: (1) the variations in the sections may be very slight; (2) no completely satisfactory method of interpretation has been developed; and (3) the measurements themselves are not sensitive enough for small variations. Also, such logs are influenced by the fluid content. Paleontology and micro-paleontology remain the ultimate arbiters. As a routine tool, however, paleontol-ogical examination is slow and tedious. Chemical analysis may be used, but this, too, is extremely slow. Although rocks are not classified according to chemical composition, there is considerable variation with rock types. Correlation by chemical composition has two advantages, first, the characteristics determined are subject to minimum human error and interpretation, and secondly, the lithologic changes are not masked by fluid content as in the case of electric and radioactive logs. Some fossils concentrate certain elements which tentatively might be used to date rock units.' Rapid chemical analysis by spec-trographic means could be used as an adjunct to other means employed in correlation work, or might, in itself, present a suitable method. PURPOSE OF THIS INVESTIGATION Sloss and Cooke' have published data concerning spectrographic analysis of limestone rocks specifically for purposes of direct correlation of a single formation. These authors found satisfactory evidence that differences in percentage of four elements (Mg, Fe, Al, and Sr) in the Mississippian limestones of northern Montana were useful in carrying out correlation of this formation over a distance of approximately 50 miles. It was concluded from the preliminary work that the spectrochemical method offered possibilities of solution of some problems of correlation heretofore not possible. Since the work of Sloss and Cooke' was confined to one particular limestone zone, extension of the use of the method to examine two or more geologic formations would aid materially in the over-all problem of correlation of such rocks. Equipment is now available commercially with which very rapid spectrographic analyses may be made, and hence the problem was to determine whether the variations existing in the minor constituents of limestones were sufficient for use in possible correlation. Qualitative and semi-quantitative investigations were made to determine whether significant changes in the chemical condition occurred. It was a further purpose to investigate the geologic time-boundaries to see whether significant chemical variation could be found corresponding to the paleontological breaks. It was desirable to attempt correlation of a thick section of limestone or dolomite rock and to have as much information as possible on the section. Furthermore, it was felt that examination of formations more difficult to correlate by other means would enhance the value of the method should definite points of correlation be found. Samples were chosen from the Chapman-McFarlin Cogdell No. 25 well in the Cogdell field, Kent County, Tex., and from the General Crude Oil Co., Coleman No. 193-2 well in the Salt Creek field, Kent County, Tex. These fields belong to the famous series of "Canyon" reef fields of West Texas. Cores from the above wells were available from the United States Geological Survey, Austin, Tex. THE SPECTROGRAPHIC METHOD The choice of procedure to be followed in this investigation was based on the anticipated requirements peculiar to the problem. Since the problem was primarily to investigate the possibilities of applying the spec-trograph to problems of correlation in thick carbonate sections, a precise quantitative analysis did not appear necessary. A qualitative analysis to show the possible absence of presence of any element, or a semi-quantitative analysis of the elements present to show the relative changes in magnitude of selected elements was required. Both types of analysis were employed. The two most widely applied methods of semi-quantitative estimates are those of Harvey and of Slavin4,5 though various other procedures have been described.6 while the Harvey method has been modified by Addink,7 this refinement did not seem necessary to the present problem. Essentially, the procedure employed is a variation of the total energy method of Slavin with two exceptions: (1) stressing matrix effect, and (2) using densitometer measurements. As measured by a densito-

Jan 1, 1956

By Robert Maddin

crystal prior to, polishing in order to eliminate coring. This treatment may be accomplished by wrapping the single crystal tightly in very thin, dead soft, brass foil and annealing in the presence of air for 20 hr at 800°C. Since the wrapping encircles the sptcimen three to four times, only a very slight amount of oxidation occurs on the specimen surface. On unwrapping one of these cylindrical single crystals. in. in diam by ro in. long (72.75 pct cu, 27.23 pct Zn, 0.01 pct P11, 0.01 pct re), mall light-gray depnrrits in the form of circular arcs werenoted on the part nf the foil which had been in contact with the single crystal, Fig r. (By superim- approximatetl). These deposits, which, from their color, suggest the appearance of sublimated zinc, were found to coincide roughly with a set of octahedral planes nearly perpendicular to the rod axis. The pattern shorn in the figure held no relation to the profle of the sample since the markin~s on the crystal More annealing werc attributed to traces of cube planes. It seems very likely that the deposits were formed by sutllimation of zinc diffusing from octahrdral planes since diffusian would Eogically take place along planes of maximum atomic spacing. However, it is difficult to understand why a continuous sublimation of zinc should occur from a single crystat in contact with a wrapping roil OF the same composition, and why diffusion would take place along specific octahedral planes and in a regular pattern.

Jan 1, 1949

By H. I. Meyer, D. F. Searcy

INTRODUCTION The analysls of our previous paper' on the behavior at two immiscible fluids separated by gravity into two dlstinct saturated zones in the porous medium was shown to be theoretically valid only if one of the two fluids was immobile. The practical problems associated with flow of both phases have so far been impossible of solution by these analytic methods. We, therefore, decided to resort to a simulator study to answer the following pertinent questions: 1. If the lighter fluid is produced from a point above the fluid-fluid interface, how long will it take for the heavier fluid to come up to the point where production of both fluids is taking place? 2. After steady-state two-phase production is established, what is the relative production rate of each phase, on what physical variables does this depend, and what are the boundary conditions at the outflow face? 3. A third question was at least partially answered in the course of this investigation: that of the shape of the interface under flow conditions. These questions are of fundamental importance in the fields of hydrology and the reservoir mechanics of oil and gas production. In order to simplify equipment used and still retain a fair physical representation of these phenomena, it was decided to use a Hele-Shaw type of analogy in which the flow took place between two vertically mounted pieces of plate glass. The advantage of this system is that it eliminates any surface effects between the matrix of the porous medium (e.g. packed sand) and also allows equilibrium conditions to be established more quickly. The principle disadvantage (apart from the obvious one of being one more step removed from the prototype) is that our equipment limited us to two dimensional flow studies. In spite of these limitations answers to the questions were obtained which seem adequate for our purposes. We would like to see more work of this nature done to verify and to improve our conclusions. DESCRIPTION OF EQUIPMENT AND PROCEDURE A drawing of the equipment used in this study is shown in Fig. 1. Fluid flow takes place between the two 36 in. x 12 in. pieces of plate glass held apart at the long edges by two spacers of cellulose acetate sheet (Kodapac IV) which is available in several thicknesses. This sandwich was clamped together by small c-clamps whose stress was distributed by long pieces of 3/8-in. keystock. Accurate spacing was obtained by tightening these clamps as indicated by micrometer measurements on the outside of the glass. At the upstream end of the plates a piece of 6-in. diameter pipe simulated an infinite reservoir, while at the downstream end a 2-in. Lucite cylinder with a small hole near the top of the flow region served to drain the fluid. Sealing was achieved by O-rings, the whole system being tightened by pressure on the Lucite tube provided by set screws (not shown in the drawing). The total head

Jan 1, 1957

By Bernard Greifer, Walter Rose

The purpose of this note is to call attention to a source of difficulty which can be responsible for inaccurate estimates of wetting liquid pressure gradients in mixture flow experiments of the Hassler1 type. It has been our experience occasionally to observe what were indicated to be negative pressure gradients, and these were regarded as anomalous in the sense that physically they seemed to contradict the requirement that the flux be in the direction of the potential field. At first it was thought that our scheme of assembling barriers and core sample led to such asymmetry in the distribution of isobars that the manometric leads at each end of the core were responding to internal pressures (within the core sample) which could be either positive or negative with respect to each other, and which in fact might tend to reflect on different effective core lengths in an unpredictable fashion as the wetting liquid saturation was changed. However, no compelling evidence of this possibility has been established. In addition, we were cognizant of the requirements to be satisfied in selecting manometric instrumentation to minimize the delay in response of the manometer to the differential pressures being measured, and were thus assured that our observations of anomalous pressure gradients could not be explained by faulty instrumentation. What we suggest is that if a leak sink occurs in the fluid lines connecting the core to either side of the differential manometer, errors exceeding 100 per cent may result in the estimation of wetting liquid pressure gradient, even though the leak is of such small magnitude that its existence would tend to be obscured by evaporation effects. This is because in a system with leaks at the specified places, the manometer rec- ords at steady state the pressure drop across the manometer barrier elements in addition to the pressure drop across the core sample. This possibility will be illustrated below analytically and by numerical example for the special case where the leak occurs on the high presure side of the core, since we are especially desirous to explain the significance of our observations of the so-called negative pressure gradients. It will be indicated, however, that leak sinks on the low pressure side of the core can account for observations of anomalously high values of pressure gradient, and that multiple leaks on both sides of the core can provide for some compensation so that the errors in pressure estimation are reduced. However, the major point to be emphasized is the fact that the impractical-ity of detecting the small leak sinks which give rise to the difficulties makes it a complicated task for the experimenter in a particular case to know with certainty that his estimation of pressure gradient lies within the limits of error which can be tolerated. Fig. 1 shows the electrical analog of the flow system we have employed in our studies. The inflow and outflow barriers. Rbl and Rb2, the manometer barriers, Rm1, and Rm2, and the core sample, Rc— for a particular fluid saturation and distribution— are all designated as resistance elements; the flowmeter is designated by an ammeter, A; the pressure source is designated by E; and the manometric device is designated by the voltmeter, V. Included in the circuit are the variable resistances, Rx and Ry, which may be regarded as the leak sinks, and which, in general, can vary in magnitude from zero (i.e., a large hole or shunt in the system) to infinity (i.e., no

Jan 1, 1950

By S. C. Sun

Most previous work on sedimentation of coal 1 and mineral 2-3 suspensions has been conducted in graduated 1-liter glass cylinders of 6-cm diam. With this type of large container it is often difficult to see through the suspension and tedious to perform a large number of tests. Furthermore, the heavy glass walls and the graduation lines of glass cylinders cause internal and stray reflections, respectively. To obviate these difficulties, an Atlab Emulsion Viewer from Arthur H. Thomas Co. was adopted as an alternative apparatus. Equipment: The viewer," shown in Fig. 1, consists of: 1) a stainless steel frame rack holding 21 flat-bottom Nessler tubes or an ungraduated replica 1.64 cm ID and 1.80 cm OD, 2) a movable masked 150-w lumaline lamp behind the tubes, and 3) a scaled glass panel with 100 vertical divisions in front of the tubes. The tubes are snugly held by springs in slots formed by spacer bars, which also serve as shields to eliminate stray light. The lumaline lamp is mounted behind a slit in a movable housing so that it can be positioned behind the suspension to be examined. The lowest or 100-divi-sion line on the front glass plate is leveled with the upper side of the bottom of all tubes. The scaled portion of each tube, roughly 19 cm high and 40 ml in volume, is used to study coal and mineral suspensions. Procedure: The following procedure was used in many tests. A 1.6-gm sample of dry coal was mixed with 16 ml of distilled water in an ordinary test tube and allowed to stand for three days, with occasional shaking to insure thorough wetting of all particles. The slurry was transferred to a Nessler tube and diluted to 32 ml. The pH regulator and flocculating reagent were added, and the slurry was diluted to reach the uppermost or zero-division line. The tube was immediately stoppered and inverted downward and up again ten times during a period of 35 to 40 sec. The lumaline lamp was turned on during the inversion period. After inversion the tube was quickly returned to the viewer rack. The time elapsed for each 10-division drop of the demarcation line between solid and liquid was recorded by stopwatch until the 80-division line was reached in the zone of compression. Additional readings were taken at 15, 30, and 60 min after settling began. The clarity of the supernatent liquid was observed also. As the settling rate became considerably slower at the 75-division line, it was convenient at this time to start the next test in a separate Nessler tube. This was continued until the suspensions in any number of the 21 tubes were tested. An attempt was made to correlate the experimental results between the Nessler tube and a 1-liter glass cylinder. Table I shows that coal particles settle much faster in the cylinder than in the tube, which has a large wall effect.' The correction factor for the tube impedance is 1.662 2 0.145 at the 40-division line in the hindered settling zone, and 1.614 & 0.139 at the 75-division line in the compression zone. This rough correlation was established by dividing the pulp height of each container into 100 divisions and comparing the settling rates of the two containers at the same divisions. Tests were also performed to determine the accuracy of the viewer. The results, not presented, showed that error was within 10 pct.

Jan 1, 1960

By Paul B. Crawford, Melvin B. Burton

A procedure is given which describes how the gelatin model may be-used to study the effect of mobility ratio on areas swept before and after breakthrough in fluid injection programs. Differences in mobility ratio are achieved through the proper selection of electrolytes for the invading and displaced fluids. The progress of the front is followed visually and photographed or traced onto plates (it desirrd positions before and after breakthrough. Example applications to standard flooding pattrrrls, vertically and horizontally fractured reservoirs and the in-situ combustion recovery process ore presentrtl. INTRODUCTION In water flooding, gas cycling and other fluid injection programs, the sweep efficiencies and swept areas after breakthrough are known to depend on the mobility ratio. Previous investigators have described the application of the X-ray technique, stepwise use of the poten-tiometric model and numerical procedures for studying these problems.1,3,4,6 Others have described the application of the electrolytic and gelatin models for studying sweep efficiencies at a mobility ratio near one.2,5,7,8,9 It is a purpose of this paper to describe a procedure for using the gelatin model to study swept areas at mobility ratios other than one. PROCEDURE The technique developed for gelatin model studies is composed of four phases: the construction of the model, the selection and preparation of electrolytes, the running procedure, and the recording of the swept areas. Each phase is discussed independently in order that the over-all procedure will not be confused. Construction of the Model Since some of the advantages of the gelatin model are its economy, and speed, it is desirable to have as small a model as is possihle without creating error through the inability to follow visually the progress of the colored front. For this work, it was found that a distance of 4 to 6 cm between salt bridges is convenient to use. Since the size is relatively small, it follows that the gelatin layer must be thin. For this study, 1/8 in. was used as the gelatin thickness in each case. The model was constructed on a flat 1/2-in. plastic (Lucite) base with boundaries constructed from 1/8-in. plastic strips. The well pattern to be studied was outlined with the 1/8-in. plastic strips on the base with narrow apertures (- - 2 mm) in the boundary to represent the wells. Behind each well opening, a rectangular area of some 8 to 12 sq cm was outlined by additional plastic strips. The plastic strips were fastened to the base by any suitable non-conducting cement so that the boundary system was liquid tight. The electrodes were constructed from sheet copper in a fashion that would allow easy removal. In this work, it was found that by simply forming a large U-shaped clip from a strip of the copper that would slip over the boundary was satisfactory and easily removed. The electrodes should be as wide as one of the sides of the rectangular area behind the well opening. If a fractured pattern is studied, fractures inside the well pattern may be represented by strips of copper of the desired shape mounted in some easily removable fashion. The reason that apertures (or salt bridges) were used for wells instead of metallic electrodes is that the plating of the electroactive ion at the cathode and the introduction of an electroactive ion at the anode has a detrimental effect on the swept area outline if these operations \rere permitted to be carried on within the well pattern itself. The anode may be used within the well pattern

Jan 1, 1957

By A. K. Schellinger, R. D. Lalkaka

IF the ball mill is considered only from an energy standpoint, it can be thought of as a converter of kinetic energy into heat energy and surface energy. The law of the conservation of energy must apply to the ball mill as it does to any machine or process in nature. The heat energy output of the ball mill is apparent to any casual observer of the operating mill since the outflow pulp will be appreciably warmer than the inflow water and rock. The rock in the ball mill is crushed by shearing of its ionic bonding caused by some impact-induced stresses beyond the elastic limit. As the bonds holding the mineral crystal lattices together are ruptured, new surface area is created on each unit of which a definite number of unsaturated bonds exist. Such unsaturated energy of bonding may be termed the "surface energy," and is a potential energy figure. This created energy was withdrawn from the ball mill system and represents an absorption, or disappearance of heat. To reduce the size of the rock, surface area must be created and with it the at- tendant characteristic surface energies of the minerals concerned. Thus the creation of surface energy, from an energy viewpoint, is the creation of useful work by the ball mill. Because of the controversial nature of the energy efficiency figures for modern operating ball mills, it seemed worthwhile to approximate the ordinary magnitude of such efficiencies from the above viewpoint. This was done by an energy balance of the three aforementioned forms of energy, kinetic, heat, and surface energy, for two 9Y2x10-ft grate-type ball mills grinding cement raw materials. Kinetic energy input to the balls was approximated as closely as possible while the heat energy output was measured by means of a thermometer and water and rock flow rates. The assumption was made

Jan 1, 1952