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By Robert G. Nisle

In conducting a pressure build-up test on an oil well, it is often necessary to shut-in the well for a short time prior to initiation of the test. The effect of such a short tern shut-in on the resulting pressure build-up curve is derived. The derivation is based on the Kelvin point-source solution and is a straight forward extension of the fundarnental theory. The magnitude of the effect is evaluatecl and illustrated by an example. It is shown that if the production subsequent to the short term shut-in is at least 10 times the duration of the shrct-in, the effect will he less than 10 per cent. INTRODUCTION It often happens that before a pressure build-up test can be made an additional valve must be mounted on the wellhead, or on arrival at the well, it might be learned that the well had been shut-in several hours the previous day because of a shortage of tankage. In such cases the question is How will such an interruption of production affect the results of a pressure buildup test This work explains how to take account of such a short term shut-in in order that the test can proceed without further delay. The solution presented here makes use of the Kelvin point-source solution used by Horne1 in his treatment of the pressure build-up in wells. Use is also made of the super-position theorem. MATHEMATICAL DERIVATION The well is assumed to have been in production at a constant rate for a relatively long time (several days or more). It is then shut-in for a short time, after which it is again placed in production at the previous constant rate. It continues to produce at this rate until shut-in for a pressure build-up test. The Kelvin point-source solution is expressed by Eq. 1. The sequence of production rates is listed in Table I. TABLE 1 — SEQUENCE OF PRODUCTION RATES Time interval Production Rate At time AT the pressure will be the resultant of the sequence of production rates shown in Table 1. An expression for the super-posed effects may be derived from this table. (Effect of + q for T + ? T) + (Effect of - q for T + ?T-t,) + (Effect of + q for T + ? T - t,) + (Effect of - q for ? T) = Resultant........(2) The desired result is obtained by substituting the effect defined by Eq. 1 for the terms in Eq. 2. The result is Eq. 3. When the logarithmic approximation is made for the exponential integrals and the terms collected the result is Eq. 4. Let T — t2 = T = flowing time following short term shut-in t2 — t1 = 6 = duration of short term shut-in Then T - t1 = r + 6 Substitution of these quantities in Eq. 4 gives p(rw ?T) = P,, -When d<<t - AT then d—&apos;-, T— approaches 1. r + AT In this case the effect of the short term shut-in may be ignored. In order to get some idea of the numerical magnitudes involved take the worst possible case, when AT = 0, that is at shut-in. If the error is made less than some maximum acceptable value at this time, it will be less than the maximum for all subsequent times. d + r Let the difference between the value of y-— and 1 be less than 0.1. Then —6+r — 1 < 0.1 S < O.l T Therefore, if the flowing time following a short term shut-in is at least 10 times the duration of the short term shut-in, the error introduced by ignoring the short term shut-in will not exceed 10 per cent of T+AT A T

Jan 1, 1957

By A. R. Troiano, W. J. Barnett

The existence of a grain size stabilization effect on martensitic type reactions as shown by Scheill in an iron-29 pct nickel alloy and by Troiano and Tokich2 in cobalt prompted a review of other martensitic reactions to determine if this stabilization effect is characteristic of all martensite type reactions. Preliminary work has shown this effect to be present both in the gamma —+ epsilon transformation in an iron-20 pct manganese alloy and the martensite transformation of SAE 4140 and 3 pct Cr-O.40 pct steels. No appreciable effect was found in an SAE 2340 steel. The M, temperature for the gamma —+ epsilon transformation was lowered from 380°F to about room temperature by varying the annealing treatment following cold work as shown in Table I. The effect of austenitic grain size on the M, of three steels is shown in Table 2. M, was deter- mined by the conventional quench-temper method of Greninger and Troiano. In a single crystal the change in external shape concomitant with the homogeneous shear mechanism of the martensite transformation can take place unhindered. In a polycrystalline specimen a restraint of these changes must occur at the grain boundaries. Therefore, the smaller the grain size the greater the shear strain energy necessary for the formation of a martensite crystal. The degree of lowering of M, due to the reduction of grain size is much greater when the change in crystal structure involves only a small energy change, such as face-centered cubic —+ close packed hexagonal (that is, CO and Fe-20 pct manganese alloy). The maximum lowering of M, observed in the steels investigated was 50°F with a change in the ASTM austenitic grain size of 1-2 to 8-9. In comparison, the crystal structure change face-centered cubic —+ body-centered tetragonal involves a considerable energy change. There is little doubt that with much finer grain sizes the increased grain boundary restraint would greatly enhance this stabilization effect. The implications of this phenomenon are multifold. Undoubtedly. under certain conditions it offers a method of stabilizing high temperature phases for room temperature

Jan 1, 1949

By I. Fatt

Laboratory relative permeability data on reservoir rock are obtained on samples which are not subjected to overburden pressure during the permeability measurements. These data are then used for calculating the performance characteristics of reservoirs in which the rock is under the pressure of the overburden. Recent observations have shown that the permeability and porosity of reservoir sandstones are decreased by application of overburden pressure. These observations led us to a study of the effect of overburden pressure on the relative permeability characteristics of sandstones. A previous note from this laboratory1 showed that overburden pressure, simulated by applying hydraulic pressure to the outside of a plastic mounted core. caused a reduction in permeability of the core by as much as 50 per cent at 10,000 psig. In a multiphase fluid flow system, the relative permeability at a given saturation will change if the permeability or the effective permeability changes but not if both permeability and effective permeability change by the same ratio. The tests described in this note were made to determine the effect of overburden pressure on permeability and effective gas permeability in the gas-oil system. The gas-oil system was chosen because the available equipment was best suited for studying this system. The resultant data can be applied to other systems of interest because the gas permeability in the gas-oil system is the permeability of the nonwetting phase and, as such, is equivalent to the gas permeability in the gas-oil-water system and to the oil permeability in the oil-water system. EXPERIMENTAL METHOD Cylindrical test plugs, one in. in diameter and one in. long, were cut from sandstone core samples from three different reservoirs. After extraction in toluene, the plugs were mounted in Lucite by conventional core mounting methods.3 The core properties are given in the legend in Fig. 1. The mounted cores were machined to fit the apparatus shown in Fig 4. Air permeabilities as a function of overburden pressure were measured by connecting lines (1) and (2) to a conventional air permeameter. To measure porosity changes as a function of overburden pressure, the lines leading to (1) and (2) and the core were saturated with kerosene; line (1) was capped and a small bore precision calibrated pipet was connected to (2). Changes in pore volume of the core as overburden pressure was applied were noted by reading the amount of kerosene produced into the pipet. To correct for the change in volume of the lines inside the hydraulic cell as a function of pressure, a pressure-vs-volume run was made with a solid Lucite cylinder substituted for the core. The change in volume of the lines was about 10 per cent of the change in pore volume of the core. No correction was needed for the permeability measurements because there was no measurable pressure drop in the lines at the maximum overburden pressure. Relative gas permeabilities were measured by the stationary liquid method described by Osoba, et al.&apos; Gas saturations were obtained by allowing the kerosene from a kerosene saturated core to evaporate out. This procedure was followed

Jan 1, 1953

By J. A. Solomon, H. E. Shafer

As a result of the great demand for metallic aluminum and the scarcity of domestic bauxite, numerous processes have been proposed and developed to extract the oxide of this metal (Al2o3) from clays, shales, and other low-grade raw materials.1-4 An exploratory study was made to extract alumina with sulfuric acid from relatively impure coal-associated draw-slate and to establish an optimum calcination temperature for maximum recovery. Draw-slate is the term used to describe the hard, slaty material directly overlying many coal seams and may range from a few inches to a few feet in thickness. Alumina content of these draw-slates may range from as low as 15% to over 35%. Although the following results are limited in scope, some of the data should prove beneficial for further work. Coal-associated clay, shale, and gob heretofore have been considered nuisance products; any successful alumina extraction process would greatly enhance the worth of these almost limitless resources. This research demonstrated that an optimum calcination temperature for alumina extraction could be established for a coal-associated draw-slate and that this temperature was lower than those suggested in previous work with unspecified clay types. It should be noted that slightly higher acid concentrations and somewhat finer particle sizes were used in this series of tests as compared to previous work. EXPERIMENTAL WORK Essentially, alumina extraction proceeded in four steps: 1) grinding, 2) calcining, 3) acid leaching, and 4) precipitating of aluminum sulfate. An initial series of reference tests to determine the optimum temperature of solubility for alumina was run using relatively pure kaolin. Kaolin forming clays are hydrous aluminum silicates of the approximate composition 2H2O A12O3 2SiO and kaolinite is the mineral that predominates in most kaolins. 5 The kaolin was ground to -30 mesh and subsequently calcined at temperatures ranging from 100°C to 700°C. Each sample was calcined for 1 hr in a muffle furnace and in turn subjected to sulfuric-acid leaching (H2SO4, 9 molar) for a 2-hr period. The filtrates were analyzed for the amount of dissolved alumina recovered.637 Also, each sample of leached or barren residue was

Jan 1, 1968

By J. J. Arps

This paper is a study of the effect of temperature on the electrical resistivity of sodium chloride solutions based on the published resistivity and density data in the International Critical Tables. This temperature effect is of considerable importance in quantitative interpretation of electric logs, where it is frequently necessary to correct mud resistivities measured under surface conditions to temperatures existing at the bottom of the bore hole. An empirical approximation formula was developed for this conversion which has proved to be very useful and seems to provide results well within the range of accuracy of the data involved. This approximation formula states: sistivities of sodium chloride solutions at temperatures of t and t degrees Fahrenheit, respectively. INTRODUCTION Research by various investigators during the past 20 years has clarified the physical principles of the phenomena which cause the natural or spontaneous electric potential in rotary drilled bore holes. The basic relationship which is most commonly used reads: in which the SP deflection, as measured from the shale base line, is expressed in millivolts. K is a constant, which appears to vary between 50 and 110; the low value applying to shaly sands, whereas the higher values are more common in carbonate rocks. A good average value for K = 70. for which value there is considerable theoretical justification." In order to calculate the resistivity of the connate water R and to estimate its "equivalent salinity" (as NaCl) from an electric log by means of this SP relationship from a knowledge of the static self potential and of the resistiv- ity of the mud filtrate R it is necessary to first correct the resistivity of the mud filtrate measured under surface conditions to the resistivity of this same mud filtrate in the well bore at a different temperature. In order to make this temperature conversion for the mud filtrate the variation of the electrical resistivity of sodium chloride solutions with temperature is commonly used. Since some discrepancies were found in the charts ordinarily used for this purpose, it was felt desirable to make a new study of this relationship based on the published measurement data. Because of the fundamental nature of these relationships and as an aid to other workers in this field, an attempt has been made in this study to show every step in the calculations. CONDUCTIVITY VS MOL CONCENTRATION The most complete published reference on the temperature relationship of sodium chloride solutions of different concentrations is provided in the International Critical Tables.&apos; The basic measurement data on the electrical conductivity of aqueous sodium chloride solutions, at different temperatures, as given in these tables, are reproduced in Table 1. The electrical conductivity values in this Table 1 are expressed as 10&apos; times the specific conductivity k in ohm-&apos;cm&apos;l per unit of concentration in milligram mols per liter of solution C, or: RESISTIVITY VS MOL CONCENTRATION These conductivity values from Table 1 were first converted to the corresponding electrical resistivity values (R) , expressed in ohm-meters, as is conven-

Jan 1, 1953

By J. S. Brown, A. G. Guy

With the exception of the work of Tammann and Hartmann,1 no published information has been found on the structural changes produced in eutectic structures as the result of heating following plastic deformation. In part this lack of information may be due to the fact that many eutectic structures contain an intermetallic compound as a prominent phase, and as a consequence have been considered to be unworkable. For example, Tammann and Hartmann were able to obtain useful data only on those alloys that they could greatly reduce in thickness by cold rolling. This restriction placed on the investigation of alloys containing intermetallic compounds has been largely removed by the work of Savitskii2 which showed that large deformations of such alloys can be produced by relatively slow compression at temperatures near the melting range. It was possible, therefore, to carry out the present work on a range of binary eutectics including one composed of two intermetallic compounds. The essential results obtained on the alloy systems studied are illustrated by the Pb-Mg eutectic containing 33.2 pct Mg, Fig 1. The cast structure, Fig la, was obtained by melting together magnesium of 99.8 pct purity and chemically pure test lead, casting into a heated, small steel mold, and furnace cooling in the mold from about the eutectic temperature. The fairly coarse eutectic structure thus obtained was too brittle to work at room temperature without cracking. Fig 16 shows the worked structure obtained by compressing a 1/2-in. cube 70 pct in about 15 sec at 550°F and then water quenching. The pronounced changes in the distribution of the two phases produced by heating the worked alloy at 850°F for 1 hr are shown in Fig lc. Recrystallization of both phases appears to have taken place, and the mechanical properties of the cast alloy must have been significantly changed by the working and heat treatment. Similar results were obtained with the Mg-59.5 pet Bi, Mg-36.4 pet Sn, Mg-65.4 pet Cu, and Bi-40 pet Cd eutectics, only the last of which could be worked at room temperature. Tammann and Hartmann reported a thickening and shortening of the needles of the eutectics which they heated about 10°C below the melting range for 1 hr after drastic cold rolling. They found the following eutectics, given the indicated amounts of reduc- tion, to have a granular structure after heat treatment: Sn-9 pet Zn (98 pet); Cd-82.5 pet Pb (60 pet); and Bi-43.5 pet Pb (90 pet). On the other hand the alloy Al-11.7 pet Si (60 pet) showed no change after heating. Tammann and Hartmann observed a distinct shrinking of the needles in unworked eutectics subjected to heat-treatment. In the present work inappreciable change in the eutectic structure was found on heating undeformed alloys. In summary, it appears that eutectic structures can be recrystallized into a "spheroidized" condition by heating near the eutectic temperature after severe deformation. If the eutectic contains one or more brittle phases the necessary deformation can be accomplished by pressing at high temperatures. It is reasonable to expect that this tendency towards equiaxed grains from the plate- or needle-like eutectic structure should be general since the energy relations and mode of growth in recrystallization are so different from those that hold for eutectic crystallization. References 1. G. Tammann and H. Hartmann: Ztsch. Melallkunde (1937) 29, 141-144. 2. E. M. Savitskii: Doklady Akad. Nauk S.S.S.R. (1940) 62, 349-351. Abstr. in Melal Prog. (July, 1949) 56, 126, 128.

Jan 1, 1950

By B. Welber, R. Webeler

A CCORDING to accepted theory, fatigue in A] metals is connected with the occurrence of local strain hardening even at applied stresses below the yield point as a consequence of stress concentrations created by the presence of structural inhomogeneities.1 It seemed possible, therefore, that

Jan 1, 1954

By P. A. Albert

THE to a transformation has been investigated by Newkirk1 in sponge titanium alloys which had been relatively slow-cooled so that several grains formed in a former grain. For a nucleated from , Newkirk assumed the following relationships and found them consistent with his experimental results: (00.1)a (110)Pll.01. II [111] Liu and Margolin,&apos; in their investigation, found that the habit planes of martensitic in titanium consisted of planes of the families (3341, and (3441,. Using Newkirk&apos;s orientation relationship, the (3341 habit plane is found to correspond to the (1450) plane of a.

Jan 1, 1954

By W. R. Aufricht, E. H. Koepf

The theory, measurement, and application of capillary forces in reservoir rock have been treated ex-tensively in the various petroleum publications.1,2,3,4 These forces are of prime importance in oil production, and data on capillary properties are among the most important tools used in the study of reservoir mechanics. The principal application of measured capillary pressure data by the production and reservoir engineer is in the determination of the initial distribution and mobility of fluids in the reservoir. The distribution refers to the magnitude of the oil and interstitial water saturations under capillary equilibrium conditions and to their variation throughout the reservoir as a result of changes in rock properties and nearness to free water. The magnitude of the water (or oil) saturation, as well as the porosity, is required in volumetric calculations of oil in place. In low permeability reservoirs, where long transition zones are common, the magnitude of the oil content, even below the depth interval where commercial rates of flow of oil can be obtained, must be evaluated since this oil contains energy available to the production of the remainder of the reservoir. The mobility of the water phase is of particular importance in water-flood calculations since mobile water may condemn what would otherwise be a successful water flood. In reservoirs with predominantly small pores, high immobile water contents are possible. Conversely, reservoirs with predominantly large pores may contain mobile water even though the interstitial water contents are relatively low. This presentation reviews the distribution and mobility of interstitial water contents as determined from capillary pressure data and shows typical data for various types of carbonate reservoirs. A discussion of the variations found in different types of carbonate reservoirs is given. DISCUSSION Interpretation of Laboratory Data Fig. 1 is a typical laboratory capillary Pressure curve where water saturation as Per cent of Pore space is plotted vs capillary Pressure (psig) for an air-water system. This par- ticular curve was obtained by measurement on a sample of San Andres dolomite with intergranular-type porosity. The sample studied had a permeability of 10.0 md and a porosity of 18.8 per cent. The capillary pressure-saturation relationship illustrated is an inherent property of the rock (a function of the size and distribution of the pores) and represents the ability of this water-wet rock to retain water against the pressure differential exerted by a non-wetting fluid (oil or gas) to remove it. In the laboratory a known pressure differential is exerted from a pressure source; in the reservoir the pressure differential is controlled by the density difference between the hvdrocarbons and the water. The laboratory capillary pressure values may be converted into terms of equivalent height of water column using known values of reservoir oil and water density and measured or average values of interfacial tension

Jan 1, 1958

By Henry A. Stiff

The classification and correlation of water analysis data presents many problems which can be solved by graphic methocis. The pattern system, a new type of graphic procedure described in this communication, is believed to have several advantages over older methods. Examples of the application, of the pattern system to the solution of problems encountered in petroleum production are given. INTRODUCTION Several graphic methods for presenting analytical water data have been developed and are now in use.1,2,3,4 It is believed, however, that a recently developed type of graph called the "pattern" offers several advantages over other methods. This system presents a better picture of the total salt concentration than is usual in such graphs. The effect of dilution or concentration has been reduced to a minimum, and at the same time distinction between various types of water has been improved. The system is extremely versatile, yet so simple it can be plotted on ordinary graph paper and adapted to almost any type of filing system. DISCUSSION The essential feature of the pattern system is the graph shown in Fig. 1. Horizontal lines extending right and left from a vertical line at zero form the graph. Positive ions are plotted to the left while negative ions are plotted to the right. The figure immediately beneath each ion gives the scale. Most oil field waters can be plotted on a scale where 100 milli-equivalents of sodium and chloride and 10 milliequivalents of each of the other ions are represented by one scale unit. For highly concentrated brines, 1,000 milliequivalents of sodium and chloride and 100 milliequivalents of each of the

Jan 1, 1951

By Henry A. Stiff

The classification and correlation of water analysis data presents many problems which can be solved by graphic methocis. The pattern system, a new type of graphic procedure described in this communication, is believed to have several advantages over older methods. Examples of the application, of the pattern system to the solution of problems encountered in petroleum production are given. INTRODUCTION Several graphic methods for presenting analytical water data have been developed and are now in use.1,2,3,4 It is believed, however, that a recently developed type of graph called the "pattern" offers several advantages over other methods. This system presents a better picture of the total salt concentration than is usual in such graphs. The effect of dilution or concentration has been reduced to a minimum, and at the same time distinction between various types of water has been improved. The system is extremely versatile, yet so simple it can be plotted on ordinary graph paper and adapted to almost any type of filing system. DISCUSSION The essential feature of the pattern system is the graph shown in Fig. 1. Horizontal lines extending right and left from a vertical line at zero form the graph. Positive ions are plotted to the left while negative ions are plotted to the right. The figure immediately beneath each ion gives the scale. Most oil field waters can be plotted on a scale where 100 milli-equivalents of sodium and chloride and 10 milliequivalents of each of the other ions are represented by one scale unit. For highly concentrated brines, 1,000 milliequivalents of sodium and chloride and 100 milliequivalents of each of the

Jan 1, 1951

By J. H. Palm

Experiments have shown12 that the formula -S = St - (St - Se&apos;)e ne [1] expresses very well the relation between the true stress S and the true form monotonic deformation of plastic metals in single tension and compression (Fig 1). St (asymptotic or final stress), Se&apos; (threshold stress) and ne (characteristic or specific strain) are constants, the significance of which immediately follows from Fig 1. Only at the initial stages of deformation the experimental curve runs below the theoretical curve. This may be due, at least partly, to the uneven stress distribution caused by the anisotropy of the crystals. It is now obvious that a similar formula H = Ht- (Ht- He)e ne&apos; [2] might be valid for the relation between the hardness and the strain. The hardness can be only a function of the strain and must therefore be independent on the hydrostatic tension present in the neck during straining. Hence, if Eq 2 is correct it will also represent the relation between hardness and strain in the middle section of the neck, the strain of which is generally assumed to be almost or fully homogeneous. For aluminum, copper, and several copper alloys it is indeed observed that Eq 2 agrees very well with the experimental Vickers hardness-strain relation from zero strain on up to the strain at fracture. Moreover nc&apos; is, for several metals fairly equal to nc- Hence H = C1 + C2S [3] C1 and C2 are constants during uniform uniaxial tension. Eq 3 was also obtained for copper by Voce.3 According to Hencky&apos;s theory4 the ratio of the Brinell or Vickers hardness and the yieldstress (expressed in kg per mm2) of a non-strainhardening metal is approximately equal to 2.8. If Eq 1, 2 and 3 are correct the ratio Ht/S, must accordingly be the same for all plastic metals and be equal to 2.8. It is now experimentally established that this ratio varies between 2.7 and 3.1 with a mean value of 2.9. Taking into account that Ht and especially St can be obtained only by extrapolation from the range of rather low strains, the agreement with the theory is very satisfactory. References 1. J. H. Palm: Appl. Sci. Res. Al (1948) 198. 2. E. Voce: Jnl. Inst. of Met. (1948) 74, II, 537. 3. E. Voce: Metal Treatment (1948) 15, 53. 4. H. Hencky: Zlsch. f. angew. Math. and Mech. (1923) 3, 241.

Jan 1, 1950

By P. A. Beck, W. D. Manly

In a recent note Sully and Head1 showed that the Cr-Fe sigma phase is isomorplious with the Cr-Co gamma phase, and that the lattice constants are also nearly identical. In a preliminary investigation of the ternary Cr-Co-Fe system at 800°C at this laboratory the above findings were confirmed, and it was found by microscopic techniques, using various etching reagents, that the two binary phases form an urinterrupted series of solid solutions with each other. These solid solutions occupy a straight narrow band which cuts across the 800°C isothermal section of the ternary system, connecting the two binary phases. A detailed investigation of the Cr-Co-Ni ternary system at 1200°C disclosed that here, too, the Cr-Co gamma phase extends deep into the ternary system in the form of a long narrow lip. The fact that this sigma type lattice is sustained even when well over half of the Co atoms in it are replaced by Ni atoms, with relatively little change in the Cr content, clearly indicates that Ni itself has a certain tendency to form the sigma phase with chromium. This tendency is hidden in the binary Cr-Ni alloys, where the sigma phase is not known to occur, but it becomes operative in the presence of a suficient amount of Co. The interpretation of these facts in terms of electron concentrations is rendered difficult by the uncertainty of our present knowledge of the valency electron structure of the transition elements in their alloys. However, Sully and Heal&apos;s results and the present work suggest that intermetallic phases with signla type lattice may occur more frequently in these little investigated alloys than heretofore suspected. In particular, it is expected that a similar phase may exist in the V-Co and perhaps in the V-Ni system, in analogy to the known sigma type phase in the V-Fe system, and that all these sigma type phases may form extensive solid solutions with one another.

Jan 1, 1950

By M. Amsterdam, F. Rothwarf, L. Muldawer

SILVER-cadmium near the composition AgCd shows three equilibrium phases. As with 13 brass, the high temperature phase is disordered body-centered cubic (8) and the low temperature phase has the ordered CsCl structure . However, there is an intermediate temperature phase which is hexagonal close-packed ((). In a recent paper, Speich and Mack&apos; report on a study of the Ag-Cd eutectoid near the AgCd composition. Unfortunately, the phase diagram upon which they base some of their conclusions is incorrect. That diagram is taken from the Metals Handbook&apos; and the error is that the 0 and ( phases have been interchanged. The Handbook gives the low temperature phase as hexagonal (designated 5) and the intermediate temperature phase as cubic ordered (designated . The error may be typographical or it may be one of confusion resulting from the use of 5, ,, and 0 for the intermediate phase in various papers. A careful search of the literature reveals that a number of authors have indicated the correct relative positions of the 13, 5, and 0 phases. The comprehensive work of Fraenkel and Wolf clearly stated that the high and the low temperature phases are either identical or are very similar. olander,&apos; on the basis of electrochemical measurements, showed that the 13 phase is disordered and the 1 phase (designated 8" in his paper and in refs. 3 and 5) is ordered. Further work by Durrant5 using thermal and metallographic analyses provided a more precise phase diagram. A summary of these works was given by Hansen6 and shows the correct relative positions of the phases. Owen, Rogers, and Guthrie7 located correctly the upper two phases by X-ray diffraction. Their failure to find the low tem-

Jan 1, 1954

By R. F. Mehl, J. T. Ransom

For many years the Metals Research Laboratory of Carnegie Institute of Technology has been concerned with the statistical nature of the engineering properties of steel from an experimental viewpoint, particularly those properties representing ductility.&apos; In the past three years new work has been directed toward evaluating the statistical nature of the endurance properties. It has been shown that both the fracture curve and the endurance limit in fatigue are markedly statistical in nature. The S-N curve (and the endurance limit) of ferrous materials is often determined with specimens which number as few as ten. The common procedure is to test the first specimen at a stress well above the expected endurance hmit. Each succeeding specimen is then tested at a progressively lower stress, until, after five or six tests, a specimen runs ten million or so cycles without failing. Two or three more specimens are then used to find the highest stress at which failure will not occur; the limiting stress determined in this way is called the endurance limit. It has now been found, however, that the variability in the fracture curve and in the endurance limit in heat-treated alloy forging steels is so great that S-N curves must be drawn on the basis of distribution curves which can be appraised only by statistical methods. Two methods have been adopted in this study: (1) straightforward statistical studies of cycles to fracture of a number of specimens at each of a series of stress levels, and (2) a new abbreviated statistical method, known as "staircase testing."2 The latter corisists in testing a series of specimens, one by one, with the test stress for any given specimen automatically

Jan 1, 1950

By Gearge C. Wallick

This paper describes experimental procedures for the calibration of capillary tubes to be employed as comparison standards in gas flow-rate measurements and considers several types of flow which were observed in the calibration of seven capillaries of varying diameter. It is shown that under certain experimental conditions deviations from Poiseuille flow are observed which may not be attributed to turbulence, and that this flow behavior may be described empirically by introducing the classical kinetic energy correction into the Poiseuille equation. INTRODUCTION Techniques have been developed for the measurement of the volume rate of flow of nitrogen through glass capillary tubes as a function both of the differential pressure applied and of the absolute gas pressure. Capillary tubes thus calibrated are frequently used to determine the rate of gas flow through a porous sample in the measurement of slip-corrected permeability. The purpose of this note is to describe the calibration procedure and to discuss some observed deviations from the ideal flow behavior predicted by the Poiseuille equation. EXPERIMENTAL PROCEDURE The volume flow rate of nitrogen as a function of the differential pressure was determined experimentally for a series of seven glass capillary tubes of varying diameter. As is shown in Table 1, the capillary radii in the series ranged from 0.004 cm for K1 to 0.07 cm for K7. The capillary tubes were cut from capillary tubing purchased on special order from several manufacturers and the bore radii were determined by microscopic measurement. The gas volume flow rate was measured for each capillary tube at a series of differential pressures in the range from 0 to 3 cm of mercury and at average absolute pressures of 1.0, 2.5, 4.0, and 6.0 atm. Experimental Procedure for Small Capillaries A schematic diagram of the apparatus used to calibrate the three smallest capillaries, Kl, K2, and K3, is shown in Fig. 1. By means of a standard Ruska Instrument Corp. volumetric pump (equipped with a synchronous motor drive, two stages of gear reduction, and a quick-change lathe gear box), nitrogen was displaced by mercury from a metal cell immersed in a constant-temperature bath. The pump, the line to the cell, and a part of the cell were filled with mercury. As mercury was forced into the cell, it displaced nitrogen which passed through the capillary tube being calibrated and into a large container with a volume of approximately 30 liters. Since the volume of this container was very large compared to the total volume change of the gas resulting from the action of the displacement pump, the absolute pressure of the system was essentially constant throughout any one run. Prior to any determination this pressure could be set at any desired level by means of an auxiliary nitrogen cylinder. The differential pressure across the capillary was measured with a Meriam Red Oil manometer and recorded together with the corresponding pump displacement rate which was equal to the gas flow rate. By repeating this process for a series of different displacement rates at each of the absolute pressures of interest, the data necessary for plotting the calibration curves for capillaries K1, K2, and K3 were obtained. All calibration measurements were made in a constant temperature room to minimize errors due to temperature fluctuations. In each run. the flow was maintained until equilibrium was established. Experimental Procedures for Large Capillaries The flow rates through Capillaries K4, K5, K6, and K7 required to obtain the pressure drops desired were larger than could be obtained from available constant displacement pumps, and it was thus necessary to employ an alternative calibration procedure. The arrangement of apparatus used in calibrating these capillaries at an average pressure of one atmosphere is shown in Fig. 2. Each capillary was calibrated by flowing nitrogen through the capillary and recording the differential pressure as a function of the flow rate. &apos;The differential pressure was measured with a Meriam Red Oil manometer and the flow rate was determined by collecting the effluent gas over water at constant pressure and recording the increase in volume per unit time after an equilibrium had been established. Appropriate corrections were made for the

Jan 1, 1953

By L. Guttman

LESTER GUTTMAN* The question of whether classical thermodynamics alone imposes any lower limit to solid solubilities was raised during a discussion among various members of the Institute for the Study of Metals. Although our conclusions are not new,1 they may be worth reiterating, since confusion on this subject seems to persist. In a binary system (A,B), the conditions for equilibrium, at constant pressure and temperature, between a solid solution and a liquid solution are µAs = µAl [la] µBs = µbl [lb] Here µ denotes the chemical potential either of component A or B, as shown by the subscripts, and the superscripts s and l refer to the solid and liquid solutions, respectively. These two conditions are just sufficient to determine the compositions of both phases. Suppose, however, that the solid phase is found experimentally not to contain any of component B; then we cannot evaluate µbs, which is defined by Here nAs and nBs are the number of mols of A and B, respectively, in the solid, whose free energy is Fs. Eq lb cannot be used, but it is no longer needed: we stated at the outset that the solid has the composition "pure A," and only the liquid composition need now be determined, from Eq la. All the equilibrium properties of the system can be derived from Eq la rigorously and simply. Hence there is no purely thermodynamic reason to exclude phase diagrams which show precisely zero solid solubility. Marsh2 has objected to such diagrams as implying that even the transformation of pure A begins at the eutectic temperature. In any case, the user of the diagram must have a certain minimum knowledge of how to interpret it, and it would seem simpler to remember the general rule that eutectic temperatures have no significance for pure components, rather than to show, say, by broken lines, on a scale which will often be exaggerated, a hypothetical solid-solubility about which we know only that it is less than a certain amount. The case of an intermetallic compound in equilibrium with a binary liquid solution does not require a separate treatment since nothing in the foregoing was dependent on the nature of the components. Therefore, thermodynamics alone does not exclude the possibility that (intermetallic) compounds may exist with compositions always precisely those given by their chemical formulas. With the aid of extra-thermodynamic methods, one may conclude that the solubility of one solid in another is never exactly zero. On the other hand, one would generally expect that the solubility will be small unless the components resemble one another (as do the metals), or form weakly-bound crystals. Therefore, it is useful to know that when there is no direct evidence for solid-solubility, one may neglect it without violating thermodynamic principles.

Jan 1, 1950

By Leonard B. Lipson

Boyer, Morgan and Muskat,&apos; with improvements by Morgan, McDowell, and Doty,l and Laird and Putnam,&apos; have described a scheme for the determination of fluid saturatic in porous media by measuring the x-ray linear absorbing power of particular fluids in the media. This method is one of several which depend on the linear absorbing power of the fluids in the porous medium. Other examples of linear absorption methods involve measurement of dielectric constant, gamma ray absorption, and ultrasonic attenuation. It is the purpose of this note to demonstrate by theortical considerations that the absorption versus saturation curve for a linear absorption method is not necessarily a single valued function of the saturation. Such non-unique behavior must be considered and evaluated before suitable saturation determinations can be made by a linear absorption method. To illustrate the discussion, examples will be given only for the simplest cases of combinations of two different dielectrics. The dielectric constant method was chosen for illustration because it was thought to demonstrate most graphically the point in question. According to Argue and Maass,4 the resultant dielectric constant of a combination of two different dielectrics depends on the orientation of the dielectrics in the electric field of the test condenser used to measure the dielectric constant. One ease involves alternate slabs of dielectrics E1 and E2 perpendicular to the electric field of the test condenser, as shown in Fig. 1A. For this case: l/&apos;E, = A/E, + B/E,.......(1) where E,,, is the dielectric constant of the combination, A is the ratio of the path length through dielectric E, to the distance between the plates of the condenser (assuming the dielectrics have the same cross sectional area as the condenser), and B is the ratio of the path length through dielectric E2 to the distance between the plates of the condenser. It will be noted that the constants A and B are numerically equal to the fractional "saturation" of the region between the test plates of the condenser by the two dielectrics E1 and E2, respectively. Another case involves alternate columns of the two dielectrics parallel to the electric field and forming a continuous path between the condenser plates, as shown in Fig. 1B. For this case: E., = AE1 + BE2.........(2) where E., is the dielectric constant of the combination, A is the ratio of the cross sectional area of dielectric E, to the cross sectional area of the condenser plates (assuming the lengths of the dielectrics equal the distance between the condenser plates) and B is the ratio of the cross sectional area of dielectric E2 to the cross sectional area of the condenser plates. As before the constants A and B are the effective "saturation" of the condenser by the two dielectrics. Still another case is described by Lichtenecker5 where dielectric E2 is shown in the form of small particles distributed at random in dielectric E1. This is shown in Fig. 1C. For this case: log Em = A log E1 + B log E2.....(3) where Em is the dielectric constant of the combination. A is the ratio of the volume of dielectric E1 to the volume of the condenser, i.e., the effective "saturation" of the condenser by dielectric E,. B is the ratio of the volume of dielectric E2 to the volume of the condenser, i.e., "saturation" of dielectric El. Equations (l), (2) and (3) are plotted in Fig. 2 for E1 = 2.5 (oil) and E2 = 80 (water). Equations (1) and (2) may he thought of as representing the limiting cases of the configuration of two fluids which might be expected to exist in a porous medium. Equation (3),

Jan 1, 1951

By Leonard B. Lipson

Boyer, Morgan and Muskat,&apos; with improvements by Morgan, McDowell, and Doty,l and Laird and Putnam,&apos; have described a scheme for the determination of fluid saturatic in porous media by measuring the x-ray linear absorbing power of particular fluids in the media. This method is one of several which depend on the linear absorbing power of the fluids in the porous medium. Other examples of linear absorption methods involve measurement of dielectric constant, gamma ray absorption, and ultrasonic attenuation. It is the purpose of this note to demonstrate by theortical considerations that the absorption versus saturation curve for a linear absorption method is not necessarily a single valued function of the saturation. Such non-unique behavior must be considered and evaluated before suitable saturation determinations can be made by a linear absorption method. To illustrate the discussion, examples will be given only for the simplest cases of combinations of two different dielectrics. The dielectric constant method was chosen for illustration because it was thought to demonstrate most graphically the point in question. According to Argue and Maass,4 the resultant dielectric constant of a combination of two different dielectrics depends on the orientation of the dielectrics in the electric field of the test condenser used to measure the dielectric constant. One ease involves alternate slabs of dielectrics E1 and E2 perpendicular to the electric field of the test condenser, as shown in Fig. 1A. For this case: l/&apos;E, = A/E, + B/E,.......(1) where E,,, is the dielectric constant of the combination, A is the ratio of the path length through dielectric E, to the distance between the plates of the condenser (assuming the dielectrics have the same cross sectional area as the condenser), and B is the ratio of the path length through dielectric E2 to the distance between the plates of the condenser. It will be noted that the constants A and B are numerically equal to the fractional "saturation" of the region between the test plates of the condenser by the two dielectrics E1 and E2, respectively. Another case involves alternate columns of the two dielectrics parallel to the electric field and forming a continuous path between the condenser plates, as shown in Fig. 1B. For this case: E., = AE1 + BE2.........(2) where E., is the dielectric constant of the combination, A is the ratio of the cross sectional area of dielectric E, to the cross sectional area of the condenser plates (assuming the lengths of the dielectrics equal the distance between the condenser plates) and B is the ratio of the cross sectional area of dielectric E2 to the cross sectional area of the condenser plates. As before the constants A and B are the effective "saturation" of the condenser by the two dielectrics. Still another case is described by Lichtenecker5 where dielectric E2 is shown in the form of small particles distributed at random in dielectric E1. This is shown in Fig. 1C. For this case: log Em = A log E1 + B log E2.....(3) where Em is the dielectric constant of the combination. A is the ratio of the volume of dielectric E1 to the volume of the condenser, i.e., the effective "saturation" of the condenser by dielectric E,. B is the ratio of the volume of dielectric E2 to the volume of the condenser, i.e., "saturation" of dielectric El. Equations (l), (2) and (3) are plotted in Fig. 2 for E1 = 2.5 (oil) and E2 = 80 (water). Equations (1) and (2) may he thought of as representing the limiting cases of the configuration of two fluids which might be expected to exist in a porous medium. Equation (3),

Jan 1, 1951

By William H. Hartwig

A paper by Rose1 has called attention to some of the problems of wetting-liquid relative permeability measurement. The premises and conclusions set forth by Rose, namely the applicability of the Hassler scheme of measurement, will be accepted. In addition, it will be concluded that certain electrical analog circuits can be used as a pattern for consideration of possible hydraulic systems of measurements. NEW SCHEME OF MEASUREMENT The object of this note is to propose a new scheme of wetting liquid relative permeability measurement. It is significantly different from those heretofore described, nonetheless it is based on Hassler concepts. The scheme is illustrated in Fig. 1 in terms of the corresponding electric circuit analog. It may be designated descriptively as the "comparison" method of wetting-liquid relative permeability measurement. In this circuit, R, represents the resistance of the core sample which is being studied for relative permeability characteristics, R represents a "standard" resistance, R represents the combined series resistance of the barrier pads, R R2 represent the combined series resistance of barrier pads in the manometer circuit, C, C represent the capacitance of the manometers, E is a constant voltage source, S is the switch or stopcock. The following conditions are imposed upon .the network: Rb » R, and R, R,» R, R, » R., and the condensers C, and C,

Jan 1, 1953