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By B. C. Allen

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

Jan 1, 1967

By J. G. Early, F. V. Lenel, G. S. Ansell

The isothermal shrinkage rates of copper-powder compacts were determined in the temperature range from 760o to 1060oC. The rates for compacts fabricated from a pure spherical copper powder were compared, on the one hand, with those fabricated from a spherical powder containing a dispersion of aluminum oxide in the copper matrix and, on the other hand, with those fabricated from a pure copper powder having irregularly shaped particles. The irregular copper-powder compacts shrank much faster than the spherical copper-powder compacts and these, in turn, shrank faster than dispersion -strengthened copper -powder compacts. The experiments were run under a small external load. By varying this load, the stress dependence of the isothermal shrinkage rate could be measured for compacts from spherical-copper powders. This stress dependence was found to be approximately proportional to the 4th (dispersion-strengthened alloys) or 4.5th (pure metals) power of the stress. It is concluded that the material-trans port mechanism is due to dislocation climb rather than to Herring-Naharro creep. In this investigation the isothermal shrinkage rates of compacts made of copper powder with an average particle size of 70 g in the temperature range from 780o to 1060°C were studied. The aim of the investigation was to determine the mechanism of material transport responsible for the shrinkage of these compacts. Since the phenomenon observed in this investigation was shrinkage of compacts at high temperatures, it will be necessary to consider all the material-transport mechanisms possible in sintering. It is unlikely that evaporation and condensation, surface diffusion, or even volume diffusion of vacancies, in which surfaces of small radius of curvature are vacancy sources and those of larger radius of curvature vacancy sinks, will materially contribute to a sintering process involving shrinkage, i.e., one in which the centers of adjacent particles move towards each other. The two principal mechanisms which were considered were the so-called Nabarro-Herring mechanism and a plastic deformation mechanism by dislocation movement. Both of these mechanisms were originally conceived to explain creep, i.e., the plastic deformation of metals at elevated temperatures under a constant applied stress. The shrinking of metal-powder compacts which was studied in this investigation can be readily treated as a creep process. This means that the shrinkage rates observed are considered as creep rates under the influence of an applied stress. It is true that the stresses in sintering experiments are generally not constant but decrease continually with time, but, by considering creep rates or shrinkage rates over a relatively short time interval, the small changes in stress during this time interval can generally be neglected. Nabarro-Herring microcreep is a high-temperature deformation mechanism which is caused by a diffusional flow of vacancies from boundaries under a tensile stress towards those under a compres-sive stress. Herring1 has shown that in this type of microcreep the strain rate e is proportional to the applied stress and follows an equation of the form ma, aexp(-Q/RT) [l| where <j is applied stress, Q is the activation energy for self-diffusion, R is the gas constant, and T is the absolute temperature This type of creep can explain the shrinkage of a porous compact. The surface of the pores are subjected to the tensile stress of surface tension, while the grain boundaries are under a compressive stress also due to surface tension. Vacancies diffuse from the pore surface through the lattice to the grain boundaries, where they are eliminated. In order to maintain vacancy equilibrium at the pore surface the vacancies leaving the region of the pore surface are replenished from the volume of the pore, which means that the pores shrink.

Jan 1, 1964

By Fred H. Poettmann

An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of the compressibility factor of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. Comparison of calculated results with field measured results were made on 20 dry gas wells from a given field and 11 distillate wells from different fields. The agreement between calculated and observed results is good. In addition to their use in the calculation of sandface pressures of flowing wells, the factors can be used in the direct calculation of the static bottom hole pressure of gas wells, the capacity of gas transmission lines, and in the calculation of the theoretical isothermal horsepower necessary to compress a natural gas. Examples demonstrating the use of various equations are given. INTRODUCTION Many of the equations used to calculate the sandface pressures of flowing gas wells from well head data do not take into consideration rigorously the deviation of the natural gas from ideal gas behavior. For low pressure wells this error is not serious. For high pressure wells flowing at high rates this error call be serious. Sandface pressures are used to determine the producing capacity of gas wells as shown in the U. S. Bureau of Mines&apos; Monograph 7.&apos; An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of compressibility of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. In addition to their use in the calculation of sandface pressures, these "factors" can also be used to give a direct solution in the calculation of the static bottom hole pressure of gas wells, the calculation of the capacity of gas transmission lines, and the calculation of the isothermal horsepower necessary to compress a gas. CALCULATION OF SANDFACE PRESSURE OF FLOWING GAS WELLS The starting point in the derivation of any specific flow equation is an energy balance on the fluid flowing between any two points in the system. This energy balance based on one pound of flowing fluid is expressed by the well known general flow equation: jp~- vdP+ Ah + -— + wt + r. = o . . (i) P, 2 g. where V = specific volume of flowing fluid in cu ft/lb P = pressure in Ib per sq ft ah = difference in height above datum plane in, ft ------ = kinetic energy change of one lb of flowing fluid, v equals velocity in ft/sec and g. = 32.174 Ws = Work done by fluid while in flow (similar to shaft work in driving a turbine) W, = Znergy losses due to the irreversibilities of the flowing fluid This equation contains no limiting assumptions and can be made the basis of any fluid flow relationship by limitations or substitutions. The energy units are usually expressed in term* of foot-pounds of energy per pound of mass. Considering the vertical flow of gas through tubing or annu-lus, the external work W, done by the gas is zero. Let us also assume that the value of the kinetic energy function is small and can be neglected. Equation (1) is reduced to: /P: VdP + Ah+Wt = 0 .......(2) Pi The energy loszes PI can be expressed in terms of the well known Fanning equatinn: 4/Lf: rf = —— ............(3) 2g,D where L = the integrated average velocity in ft/sec of vertical flow in a uniform flow string -~h = L v = the integrated average velocity in ft/sec / = dimensionless correlating function

Jan 1, 1951

By Fred H. Poettmann

An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of the compressibility factor of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. Comparison of calculated results with field measured results were made on 20 dry gas wells from a given field and 11 distillate wells from different fields. The agreement between calculated and observed results is good. In addition to their use in the calculation of sandface pressures of flowing wells, the factors can be used in the direct calculation of the static bottom hole pressure of gas wells, the capacity of gas transmission lines, and in the calculation of the theoretical isothermal horsepower necessary to compress a natural gas. Examples demonstrating the use of various equations are given. INTRODUCTION Many of the equations used to calculate the sandface pressures of flowing gas wells from well head data do not take into consideration rigorously the deviation of the natural gas from ideal gas behavior. For low pressure wells this error is not serious. For high pressure wells flowing at high rates this error call be serious. Sandface pressures are used to determine the producing capacity of gas wells as shown in the U. S. Bureau of Mines&apos; Monograph 7.&apos; An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of compressibility of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. In addition to their use in the calculation of sandface pressures, these "factors" can also be used to give a direct solution in the calculation of the static bottom hole pressure of gas wells, the calculation of the capacity of gas transmission lines, and the calculation of the isothermal horsepower necessary to compress a gas. CALCULATION OF SANDFACE PRESSURE OF FLOWING GAS WELLS The starting point in the derivation of any specific flow equation is an energy balance on the fluid flowing between any two points in the system. This energy balance based on one pound of flowing fluid is expressed by the well known general flow equation: jp~- vdP+ Ah + -— + wt + r. = o . . (i) P, 2 g. where V = specific volume of flowing fluid in cu ft/lb P = pressure in Ib per sq ft ah = difference in height above datum plane in, ft ------ = kinetic energy change of one lb of flowing fluid, v equals velocity in ft/sec and g. = 32.174 Ws = Work done by fluid while in flow (similar to shaft work in driving a turbine) W, = Znergy losses due to the irreversibilities of the flowing fluid This equation contains no limiting assumptions and can be made the basis of any fluid flow relationship by limitations or substitutions. The energy units are usually expressed in term* of foot-pounds of energy per pound of mass. Considering the vertical flow of gas through tubing or annu-lus, the external work W, done by the gas is zero. Let us also assume that the value of the kinetic energy function is small and can be neglected. Equation (1) is reduced to: /P: VdP + Ah+Wt = 0 .......(2) Pi The energy loszes PI can be expressed in terms of the well known Fanning equatinn: 4/Lf: rf = —— ............(3) 2g,D where L = the integrated average velocity in ft/sec of vertical flow in a uniform flow string -~h = L v = the integrated average velocity in ft/sec / = dimensionless correlating function

Jan 1, 1951

By N. M. Levine, W. M. Fassell

In this laboratory study the problem of aerative conditioning to separate chalcopyrite and pyrite from cobaltite was simply effected with a sulfy-drate collector and pH by proper choice of mixing variables. It was shown that for a given impeller type and geometry, selectivity is governed by a relation between the Froude number and a modified power number multiplied by impeller tank-diameter ratio wherein the power factor is expressed as power intensity or horsepower per unit volume of contained pulp. In applying this approach to other systems, other criteria would be used in place of selectivity. The purpose of this paper is to show how solutions to problems of aerative conditioning of pulps may be enhanced by development of mixing parameters in a given system through application of a fundamental approach to agitation. The term aerative conditioning refers to a combination of processes which include mechanical gas dispersion, gas solution in the liquid phase, transport of dissolved gases and other reactants to the reaction zone, physico-chemico interaction within the liquid phase and/or at the solid surface, and, finally transport of products away from the reaction zone. Important elements of these processes are: 1) Air-Liquid Contact Area: This area limits the rate at which a given gas may dissolve in a given liquid. Thus, an aerative conditioning system should be designed for optimum gas dispersion. 2) Diffusional Factors: Such factors as concentration gradient, diffusion film thickness, and diffusivity may govern the rate at which dissolved constituents are transferred to the zone of interaction at a particle surface and the rate at which reaction products are transported therefrom. Thus, such systems would be designed for maximum turbulence to effect good mixing and to minimize diffusion film thickness. 3) Solids-Turbulent Liquid Contact Time: Sufficient time should be provided for interactions to take place at solid-liquid interfaces. The region of maximum turbulence for mechanical systems being in the impeller zone, it is important that the number of passes through this zone be optimized. This means that a proper balance should be struck be- tween flow and turbulent power to achieve optimum conditioning time. Too high a flow rate and insufficient turbulence may be improper if the reactions are diffusion limited. On the other hand, too much turbulent power and too little time in the reaction zone due to insufficient flow power may also be limiting. 4) Geometry and Impeller Design: The design of the conditioning vessel and the type of impeller employed are important factors in determining the relative distribution between flow and turbulent power and the degree of gas dispersion. Maximization of power input would be to no avail if the distribution between flow and turbulent power were improper or gas dispersion insufficient. 5. Physical Chemistry: The reactions between dissolved gases and solid surfaces may be limiting if gas solubility, activation energies and/or free energies are not favorable. J. H. Rushton, E. W. Costich, and H. J. Everett&apos; have summarized the mechanical elements of the combination of processes listed in a fundamental mixing equation. This equation was derived by dimensional analysis and relates the physical variables for a single impeller, centered in a cylindrical, vertical axis, flat-bottomed tank. It is, where T is tank diameter in feet; H is liquid depth in feet; C is height of impeller off tank bottom in feet; S is pitch of impeller; L is length of impeller blades; W is width of impeller blades; R is number of baffles; D is impeller diameter in feet; Np is the power number, pg/dN3D5; P is power in foot-pounds per second; g is the gravitational constant, feet per second; J is width of baffles; B is number of im-

Jan 1, 1961

R. Culver, Colorado School of Mines I appreciated Professor Starfield&apos;s presentation, because his approach to blasting research reflects my feelings that a lot of practical work can be done toward making short-term advances that can be used by the blasting industry. We should not forget this in our attempt to obtain solutions to such idealized problems as a mathematical theory of cratering. The blasting industry would like very much to have the efficiency of the basic blasting processes improved from the range of 20 percent up into the range of 50 percent. And many of these problems should be approached and attacked in the laboratories. Blasting research at the Colorado School of Mines for the past two or three years has been aimed at improving the pre-splitting process, because we feel it will become increasingly important to the construction industry. We have attempted to develop a unified theory of how pre-splitting works; and the more we investigate, the more variables we find. We may never obtain an entirely satisfactory theory of pre-splitting, but we have developed a tentative explanation. One of our first conclusions was that we are making very poor use of the explosive in current pre-splitting practice. But to appreciate this we must first consider how pre-splitting works. A series of parallel boreholes are loaded with low density charges which are detonated simultaneously. (Delayed detonation has been tried, but most people agree that simultaneous detonation is best, and this is what we found.) Stress waves traveling out from each borehole interact with the stress waves from the two adjacent boreholes influencing the direction of the fractures that occur and propagate from each borehole. It has been suggested in private communication with Mr. Wilbur Duvall of the U. S. Bureau of Mines, that the fracture between the adjacent boreholes is a result of the net particle velocities above and below the pre-split plane which tend to set up a net tension along the pre-split plane. Regardless of what the exact mechanism is that causes the fracture to propagate from one borehole to the next, we know that it, in general, relies upon an interaction of the stress waves. However, if there is a large compressive stress normal to the pre-split place, it can practically eliminate any possibility of obtaining the desired pre-split by preventing the desired fractures from getting started. Aside from obtaining a fracture along the pre-split plane, the other major aim of pre-splitting is to minimize the fracturing that occurs around the borehole. We do this by drilling a large hole and putting a small charge in the middle of it. This results in a badly decoupled charge which is very inefficient; most of the energy is used in compressing the air in the borehole. Out of discussions about how pre-splitting works, we decided that perhaps there was some other explosive geometry which would make more efficient use of the explosive, and result in optimizing the pre-splitting process. Starting in the laboratory with small plexiglas blocks, we found that a fully-coupled explosive charge of 5 grains/in. of PETN gave random fractures extending about I in. from the borehole. A 1/4 in. plexiglas plug fit into a 1/4 in. hole in a similar block with the same fully coupled charge gave random fractures extending out only about 1/2 in. due to the energy absorbed in fracturing the plug. If the plug was split longitudinally but otherwise using the same geometry, it was possible to drive a fracture about 2 in. in either direction from the borehole, with an even smaller amount of fracturing around the borehole.

Jan 1, 1967

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.&apos; Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George&apos; showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille&apos;s Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell&apos;s equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille&apos;s Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy&apos;s Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy&apos;s Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI&apos; By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By S. T. Yuster

An analysis has been made of the factors responsible for tilted fluid contacts in petroleum reservoirs. The factors are static and dynamic with the former being controlled by those variables responsible for the capillary rise of fluids, and the latter include rate of formation tilt and hydraulic circulation. The explanation that rate of formation tilt may be responsible for tilted contacts appears untenable. The role of some of these factors in the migration, fractionation. accumulation and possibly the prospecting for oil is indicated. INTRODUCTION While it is generally considered that the segregation of gas, oil, and water in a petroleum reservoir results in approximately horizontal planes separating these phases. there are factor; which modify this simplified picture to a very great extent. Some of these factors are static. and the departure of the fluid interfaces from horizontal may represent a static equlibriun. Some of these factors may be dynamic and the interface positions may be non-equilibrium and represent a steady .state condition. Of course combinations of these two situations may also exist. The reasons most commonly given for this behavior are hydraulic circulation of fluids, change in character of the formation, and a rate of tilt of the formations more rapid than the rate at which the fluids may re-establish an equilibrium. Russell&apos;s Principles of Petroleum Geology&apos; contains an extensive discussion of tilted fluid interfaces and their importance in the migration and accumulation of petroleum. Russell cites examples of tilted water tables at Lance Creek, Wyo.; Rock River, Wyo.: Cut Bank. Mont.; Cushing, Okla.: and Graham; Okla. Also given was the Wasson Field of West Texas which has saucer shaped oil-water and gas-oil interfaces with the saucer being deeper in the case of the oil-water contact. The Bradford Field in Pennsylvania has a tilted water table. San Ardo. Coalinga None and some other California field.; have tilled contacts. A recent paper by King Hubbert discuses the effect of hydraulic circulation of the water underlying the oil in a given stratun and it- implications in the accumulation of and drilling for the oil. The foregoing would indicate that tilted fluid interfaces are not uncommon and that it would be of importance to underbtand the forces which are responsible. Further. it would be of interest to examine certain idealized models of situations which may cause tilting with the thought in mind of deriving relatinnships between the important variables. These relationships may only hold exactly for the model* assumed but the results may apply semi-quantitatively to actual formations and at least indicate trends. The discussion will be divided into the effect of static factors and the effect of dynamic factors. STATIC FACTORS It has already been mentioned that one reason given for tilted contacts is a variation in formation properties. Specifically this is a change in the pore size of the formation capilaries. If the internal surface of the reservoir is preferetially wet by water, capillarity will cause the water 10 rise to a greater extent above the free water table in a small capillary than in a large one. Consequently the water-oil contact will be higher in the lower permeability sands than in the higher permeability sand.;. The free water table may be defined as the position the oil-water interface would take if capillarity were absent. Since the phenomenon is the capillary rise of water in an oil environment, a derivation of this shold give a relationship between the variables. Fig. 1 is an idealized model of the situation with a uniform bore circular capillary ubstitttting for the tortuous non.circular formation pore. The upward force.; on the column of water will be equated to the forces downward to give the equilibrium situation. forces upward = force downward where r is the radius of the capillary in ceritimetera. a is the interfacial ten4on oil-water in dynes per centimeter, 0 is the

Jan 1, 1953

By C. R. Masson, M. L. Pearce

The nitrogen contents of seven specimens of iron and steel were determined by the three methods. Good agreement won generally observed between the results of the isotope -dilution and Kjeldahl determinations, tltzts establishing the reliability of the isotope -dilutzon technique. For some specimens, the vacuum-fusion values at 1650 °C were lower than the corresponding Kjeldahl values by up to 0.0015 pct absolute. These differences were eliminated for a specimen of "pure" iron by performing the vacuum-fusion analyses at 2100 ° to 2240 °C. The reason for this relatively high temperature required m the vaczium-fusion analyses is discussed. ThE determination of nitrogen in iron and steel has been the subject of numerous investigations and a concise review of the extensive literature in this field has recently appeared.&apos; Two methods of analysis are most commonly employed, the vacuum -fusion and the chemical or Kjeldahl method. Except in special cases where the presence of certain alloying elements may present difficulties, both methods are generally regarded as applicable, although the vacuum-fusion method is more sensitive and is often preferred for samples of very low-nitrogen content. The method of isotope dilution, first employed for the determination of gases in metals by Kirshenbaum and Grosse,2 has recently been applied to the determination of nitrogen in iron and steel.3,4 The method is attractive in that it does not require the quantitative extraction of gas from the metal specimen. Staley and Svec3 modified the standard Kjeldahlpro-cedure by introducing, along with the steel sample, a measured amount of ammonium sulfate enriched in the isotope 15N. The nitrogen content was obtained by measuring the isotopic ratio 15N/14N in the resultant solution. The technique involved the distillation of nitrogen as ammonia from alkaline solution and subsequent oxidation of NH4+ in the distillate to gaseous nitrogen. The results for iron and steel samples of commercial origin were often in reasonable agreement with values quoted by the suppliers, although occasional marked discrepancies were observed, particularly with the results of vacuum-fusion analyses. Preliminary work in this laboratory4 on the determination of nitrogen by isotope-dilution in the gas phase yielded results for three samples which were significantly higher than the values obtained by vacuum-fusion. The present paper describes an extension of this work to a wider variety of samples. Analytical results by the Kjeldahl method are also reported. EXPERIMENTAL The technique employed for the isotope-dilution determinations was similar to that described elsewhere.4 Several minor modifications were made to the apparatus. These included the use of molybdenum instead of platinum-rhodium suspending wires when crucibles were degassed at temperatures above 1600°C. The circulatory system used previously for converting CO to CO2 was replaced by a single chamber, the walls of which were cooled directly in liquid nitrogen. Temperatures were measured with an optical pyrometer which had been recently calibrated and, as in the previous study, were minimum values obtained by sighting on the center bottom of the crucible. Temperatures obtained by sighting on the interior walls were always higher by 100&apos; to 130°C with the design of crucible employed. Flat-bottomed crucibles exhibited an even larger temperature difference. To check the efficiency with which crucibles were degassed in the isotope-dilution apparatus, several experiments were done in the vacuum-fusion apparatus, suitably modified4 for isotope-dilution studies. Faster pumping speeds and higher degassing temperatures were possible, the latter due to the use of a generator with a higher power output (10 Kva at 398 kc per sec). In these experiments the combustion of CO was omitted and a correction4 was made for the contribution of CO to the ion current at m/e 28, used in determining the isotopic ratio R = l5NP4N. This correction did not seriously influence the re-

Jan 1, 1962

By Irving Fatt, Herman Dykstra

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.&apos; Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George&apos; showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille&apos;s Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell&apos;s equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille&apos;s Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy&apos;s Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy&apos;s Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI&apos; By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By H. J. McQueen, G. C. Kuczynski

ThE useful properties of k6-Alfenol and the thermenol alloys (summarized by J. E. Nachman and W. J. Buehler&apos;) have encouraged research into those alloys which, having compositions near 25 at. pct Al, 75 at. pct Fe, undergo an ordering transformation between 500° and 550°C. The equilibrium diagram of the iron-rich iron-aluminum alloys was first determined by Bradley and Jay.2,3 They distinguished three structures: the disordered, which is bcc; FeAl, which is simple cubic with one Fe atom and one Al atom per lattice site; and Fe3Al, which is fcc with three Fe atoms and one Al atom per lattice site. This last structure may be conceived as eight body-centered cubes with Al atoms at the centers of alternate ones, so that Al atoms have only Fe as first and second nearest neighbors. Later, Osawa and Murata4 determined the boundaries of the different superlattice regions in the iron-rich Fe-Al solid solution by dilatometric and X-ray methods. Two of the six phases, which they found between 0 and 50 at. pct Al, were never identified by other workers. A. Taylor and R. M. ones,&apos; concurrently with and independently of this research, redetermined this diagram by measuring lattice parameters at temperature. Further reference will be made to their results. EQUILIBRIUM DIAGRAM A) Experimental Procedure—The alloys were prepared from NRC gas-free iron (99.9 pct Fe) and 99.99 pct Al. They were melted in alumina&apos; crucubles under vacuum in an induction furnace. If the ingots were unsound or showed more than a 3 pct weight loss, they were rejected. The ingots were homogenized at 1100°C for 24 hr before hot-rolling at 700" to 900°C from 1 in. to 0.25 in. thick. It is interesting to note that alloys containing more than 28 at. pct Al were able to take an 80 pct reduction of area in the ordered FeAl region. The dilatometer specimens and specimens for chemical analysis were cut from these plates. A Leitz dilatometer was used to measure the coefficient of linear expansion as a function of temperature. The specimens were slowly cooled from 900" to 300°C where they were annealed for 10 hr before slowly cooling to room temperature. The expansion was recorded photographically as the alloys were heated and cooled at 1.5oC per min between 100" and 1000°C. The magnetic measurements determining the Curie points were performed on the dilatometer specimens in the dilatometer, by using direct current in the furnace windings both to heat the specimen at 1.5°C per min and to serve as the primary coil. The regular specimen holder was replaced by a thin alundum tube on which was wound, as a secondary, a closely spaced coil of fine copper wire. A reversal of current in the furnace windings produced, in the secondary, an emf which was proportional to the induction in the specimen, and which could be detected on a galvanometer. In this way, it was possible to determine the Curie points of alloys to within * 5°C. B) Results and Discussion—The coefficients of linear expansion, as obtained from the dilatometer curves, are plotted as a function of temperature and composition in Fig. 1. Since in many cases the heating and cooling curves were superimposed, it was decided to measure slopes of heating curves only. Definite high peaks, due to the transformations, were observed on each curve between 400" and 520°C, and, for alloys containing more than 23 at. pct Al, a second set of smaller peaks at temperatures above 660°C. The sharpness of the peaks indicates that ordering to Fe3Al is a first-order reaction. The compositions and the temperatures of these peaks are listed in Table I. When these temperatures are plotted as a function of the composition, the result is the constitution diagram presented in

Jan 1, 1960

By I. R. Dunlap, R. F. Burdyn, F. D. Patchen

The composition and properties of a new type of cementing mixture are discussed. In these compositions, API Class A or C cements are added to n stable water-in-oil emulsion instead of the crsual water. The cement disperses in the oil phase and remains out of contact with the water under normal conditions of mixing and storage. At higher temperatcrres, such as those encountered down-hole during placement, the emulsion breaks and cement hydration can then proceed. An extremely low filtration rate is obtained; the major part of the filtrate is oil. Thickening times of the mixture may be increased to meet the 18,000-ft casing cementing schedule by varying the amount of emzilsifier. As in conventional Portland cement mixtures, high-temperature strength retrogression can be overcome by addition of silica flour. Results of several field app1ication.r show that mixing presents no diffculty if emulsion blenders are used and the emulsion is prepared beforehand. INTRODUCTION Water-in-oil emulsions., in which oil is the continuous or external phase and in which water exists as discrete droplets, have for some time been used successfully in drilling muds to reduce filtration loss.1,2 Applied to cement slurries, the same results are obtained; i. e., the fluid-loss is greatly reduced. In addition, thickening times may be extended, lower densities and strengths obtained, and water-base borehole fluids more easily displaced without contamination of the cement. A low filtration rate is often a desirable property in oil well cements since loss of fluid increases placement difficulties and may also cause damage to water-sensitive producing formations.&apos; In the casing cementing operation where the cement slurry is pumped into the narrow annulus between open hole and casing, rapid loss of fluid to a porous formation can cause the slurry to thicken and plug the annulus before the desired fill is obtained. Where a casing or a liner is cemented against a productive formation and the well completed through perforations, the fluid lost between the time the cement first contacts the formation and the time a set is obtained may invade the zone past the depth of the perforations. If the sand contains a material which will swell upon contact with cement filtrate, permanent damage may result. Previous methods for reducing the fluid-loss of cements have employed bentonite4 as an additive, usually with a lignosulfonate as a dispersant, or a derivative of some naturally occurring polymeric material such as cellulose ether." Oil emulsion cements have also been proposedv or fluid-loss reduction, but these have been of the oil-in-water type. Bentonite cements have been used most widely and have been successful in reducing incidence of premature setting of cement attributable to loss of water by filtration. It is the purpose of this paper to describe preparation and properties of a water-in-oil emulsion cement and to relate procedures followed and results obtained in several field applications. DESCRIPTION OF SYSTEM AND MECHANISMS A water-in-oil emulsion cement is prepared by adding an API Class A or C cement to a stable water-in-oil emulsion. Fig. 1 is a photomicrograph of this emulsion before addition of cement. Here the droplets are water and the surrounding medium is diesel oil. High emulsion stability is indicated by the small droplet size [1-5 microns], and by their uniformity.&apos; To form a stable water-in-oil emulsion as illustrated, several conditions must be met. A predominantly hydrophobic emulsifier must be present in sufficient concentration to produce a strong interfacial film; initially, the phase volume ratio (the water-to-oil ratio) must be low;

By Elmars Ence, Harold Margolin

The titanium-aluminum system has been investigated in the composition region 0 to 34 pct Al in the temperature range 800" to 1450°C. The phases encountered in this region were: a,ß, TiAl3, The reactions observed are as follows: 13 ; L - 6T. A1, 0 (15 pct Al) + 6 (18 pct Al) - yTi Al (16.5 pct Al) at -1170°C andP (7 pctpct Al) + y (9.2 pet Al) - ah(9 pct Al) at - 1060°C. A eutectoid reaction: y — a +d belm 700°C is postulated. THE Ti-A1 system has been the sub.ect of a number of investigations. Several of these1-3 have indicated extensive solubility of A1 in both a and ß titanium. Ence and Margolin, as a result of work on the Ti-A1-0 system:&apos;5 have shown that the a solubility ofalumi-num is considerably restricted, and found that a compound, Ti2A1 existed in the region formerly designated as Q a This structure was identified as hexagonal with c/a = 0.803. Pietrokowsky confirmed the existence of this phase7 and pointed out that the structure was isomorphous with Ti3Sn.8 Although the existence of Ti,A1 has been confirmed by others,9-12 there has been considerable disagreement regarding the composition and mode of formation. A detailed reinvestigation of the Ti-A1 system has been published by Sagel et al.13 The tentative diagram indicated two phases, a, and e, occurring in the former all a region. The a, phase has the same structure as Ti2A1 and was indicated as having a broad region of solubility. Epsilon, a tetragonal phase, was shown to form within the a, solubility region. AS a result of unpublished work,14 Ence and Mugy3 olin disagreed with the interpretation of Sage1 et al., although some common features existed. The present study was conducted in an attempt to clarify prevailing uncertainties. EXPERIMENTAL PROCEDURE Alloy Preparation—Alloys were prepared from iodide titanium (99.9 pct Ti with less than 0.01 pct Zr) or Bureau of Mines electrolytic titanium (BHN-73) and high purity aluminum (99.99 pct). Alloys were arc-melted in argon or helium atmosphere as 15-g buttons in the composition range up to 34 pct Al. Depending on need, alloys were made in increments varying from 0.25 to 2 pct Al. Up to five 15-g buttons of some compositions were made. Weight losses during melting did not exceed about 1 pct of the charge and chemical analysis revealed that both titanium and aluminum were evaporated. In general, nominal and analyzed compositions agreed within 0.5 pct and therefore nominal compositions were used in plotting the data. Unavoidably, some overlap of composition occurred, particularly where small increments of A1 were used. The small increments were primarily used to obtain alloys which would fall into the narrow a -, r region and this purpose was achieved. In general, the data obtained from Bureau of Mines base titanium and iodide titanium alloys were in agreement. Forging—Both as-cast and forged samples were employed. Samples were heated for hand forging by an oxygen-hydrogen torch to the region 1200" to 1300°C. A titanium anvil and cover plate were used to prevent any iron pick-up and consequent formation of a low melting point compound. Frequent reheating kept the temperature in the desired range. Under these conditions, alloys containing up to 15.5 pct could be successfully forged. To check on the depth of contamination, forged alloys were heated slightlybelow the ß transformation temperature. Metal was removed to a depth below the contaminated surface so revealed, and the subsequent results obtained from these samples agreed closely with those secured from as-cast material. Heat Treatment—Prior to heat treatment, all alloys were vacuum annealed to remove hydrogen. Samples

Jan 1, 1962

By C. G. Dunn

The measurement of interfacial teusions or grain boundary energies in metals is an important metallurgical problem, especially since it bears on growth and nucleation processes. Statistical methods of measuring equilibrium grain boundary angles, which relate interfacial tensions, have been used by some investigators1&apos;2 but more direct methods would be preferred. A direct way, based on a simple extension of a successful method of growing single crystals of silicon ferrite to predetermined orientations in flat specimens,3 is to produce three-grain specimens in such a way that the equilibrium common grain boundary will be perpendicular to the surface of the specimen. The angles to be measured then appear as the grain boundary angles in the surface of the specimen. The method of producing a single crystal specimen with a predetermined orientation is basically the same as that employed by Yoshida and Fuji-wara4 in their work on aluminum wires. The specimen, prior to any single crystal transformation, must have a matrix which will support the growth of a crystal of the desired orientation. Growth may occur through exaggerated grain growth or, if the matrix is strained a critical amount. by normal recrystallization. In either case the matrix must have stability at the temperature used to effect the transformation, this stability appearing as a long induction period for exaggerated grain growth or for the formation of recrystallization nuclei. Additional control is gained by using a high temperature gradient through which the specimen is moved at a suitable rate. To obtain the desired orientation, the specimen is fed a short way into the furnace producing one or more crystals in the hot end. After the specimen is removed from the furnace, the orientation of a crystal is determined, so that this crystal may be reoriented by properly deforming a narrow piece of the matrix between the end crystal and the rest of the specimen. This part of the specimen in the case of silicon ferrite is preferably held at red heat during the reorienting process. Fig 1 shows a specimen which is ready to be transformed into a single crystal through growth of a reoriented "seed" crystal. When the method just described is applied to the production of a three-grain specimen two crystals are grown first side by side in one end, the specimen is then reversed and the third grain grown from the opposite end. A suitable group of grains each of different orientation is one where all three grains have the same crystallo-graphic plane in the plane of the specimen. Fig 2 shows a photograph of a three-grain group prepared as described. The notches are introduced in the open ends of the grain boundaries to anchor them during the final annealing operations which ultimately should bring the grain boundaries to the lowest energy configuration. Two-grain groups with different crystallographic planes in the plane of the specimen can be similarly prepared and treated. If the two grains have different surface (gas to metal) energies per unit area, the equilibrium condition leads to a curved grain boundary.* * This feature of the problem was pointed out by J. c. Fisher. References 1. Cyril Stanley Smith: Grains. Phases and Interfaces: An Interpretation of Microstructure. Trans. AIME 175, 15. Met. Tech. TP 2387, June 1948. 2. D. Harker and E. Parker: Grain Shape and Grain Growth. Trans. A.S.M. (194,5) 34, 156-195. 3. C. G. Dunn, A. Seddon, and R. Wylie: Unpublished Work, 1946-1947. 4. Takeo Fujiwara: A Method of Producing A Long Single-Crystal Wire of Aluminum with any Desired Crystallographic Axis. Jnl. of Sci. Horoshima Univ. A, (1939) 9, No. 3, 227.

Jan 1, 1950

By T. S. Lundy, R. A. Padgett

The fact that cobalt diffuses in silver at a much slower rate in a region near a free surface than in bulk material has been demonstrated in a variety of experiments. Various possible mechanisms of this near-surface effect (NSE) are examined in light of experimental evidences. The tendency for surface segregation of some solute atoms appears to be a likely mechanism to explain the effect. UNIDIRECTIONAL and isothermal diffusion from a plane source of radioactive tracer into an isotropic, homogeneous medium follows the Gaussian solution to Fick&apos;s second law, or: where A(x,t) is the position and time-dependent concentration of the diffusing species, M is the quantity of diffusant per unit area initially at x = 0, and D is the diffusion coefficient. For a given time, say t = tl, one can easily see that: d In Aixji)_____1_ r2] d(x2) 4Dti Thus, if diffusion data obtained by serial sectioning are plotted as In A(x,tl) vs x2, the diffusion coefficient is obtained from Eq. [2]. The ideal behavior seldom is observed in real systems. Deviations from ideality generally occur either at small or large values of penetration distance. The overall picture is shown schematically in Fig. 1 where Regions I, 11, and 111 are due, respectively, to some near-surface effect or effects (NSE), volume diffusion, and short-circuiting effects. For different systems and conditions of specimen preparation and analysis, the relative importance of Regions I, 11, and I11 may be drastically different. Region I is completely absent in many systems and there is no NSE. In others, however, there may be considerable difficulty in determination of volume diffusion coefficients due to the overshadowing influences of Region I. Such is particularly true when indirect techniques such as the surface concentration decrease or the Gruzin method&apos; are used to find D. In this paper several experiments which had as their goal a better understanding of near-surface effects are reported. Specifically, it is well-known that unusual penetration behavior results for the diffusion of several impurities in ilver- and that considerable controversy exists with regard to interpretation of the published diffusion data. We chose to examine those unusual results which occur for cobalt diffusion in monocrystalline silver395 primarily because knowledge of experimental procedures and materials were readily available. Both radioactive co60 and co5&apos; could be utilized to offer a wide range of available concentration of the diffusing species. Experiments were also performed on the diffusion of AgnO in silver. They gave base-line data for the system—both for technique evaluation and for examination of the vacancy distribution near the surface. I) PROCEDURES Cylindrical-shaped specimens 1.25 cm diam and 1 to 1.25 cm long were cut from 99.999 pct Ag single crystals obtained from Monocrystals Co., Cleveland. One end surface of each specimen was polished flat and etched with a mixture of 20 ml saturated Cr03 solu-tion-20 ml H20-3 ml concentrated HC1. Radioactive tracer (co60 or co5&apos; or Ag&apos;lO, each having a radio-chemical purity of greater than 99 pct) was deposited onto the prepared surface either dropwise with evaporation to dryness of the solution containing the tracer (0.5 N HC1 solution for the co60 and co5&apos; and 0.6 N HNO3 solution for the A"&apos;), by electroplating, or by evaporation from a tantalum or tungsten filament in an evacuated bell jar. The amount of deposited cobalt was varied from many atomic layers of cobalt containing the co60 to approximately one co5&apos; atom per lo6 surface atoms of silver. This large variation in amount of deposited cobalt yielded information about both the influence of a thick-source layer of tracer and solubility effects on the NSE. Such variations were possible because of the large differences in half-lives,

Jan 1, 1969

By P. S. Kotval, H. Hahell

PRECIPITATION of M23C6 carbides at grain boundaries in austenitic steels and nickel base superalloys has received considerable attention. Hatwell and Berghezan,1 in a study using carbon extraction replicas, observed that dendritic growth of the M23C6 carbide phase occurred at grain boundaries in austenitic steels. Merrick and Nicholson2 have observed that in thin foils of "Nimonic 75" alloy the precipitation of M23C6 carbide was discontinuous at grain boundaries. Lewis and Hattersley3 have suggested that the type of M23C6 precipitation observed in Ni-Cr austenites represented the early stages of discontinuous precipitation. In a more recent study, Singhal and Martin4 have concluded that grain boundary M23C6 precipitation involves the migration of an austenite grain boundary by a mechanism very similar to that proposed by Tu and Turnbull.5 Tu and Turnbull&apos;s suggestion essentially involves grain boundary migration under the driving force arising from the difference between the surface free energies of the opposite sides of the plate. Thus, Singhal and Martin&apos;s observation4 implies that the first stage of discontinuous precipitation has taken place and that the grain boundary has provided a diffusion short circuit for the sub-stitutional solute atoms (principally chromium) which assist the preferential growth of the M23C6 plate in contact with the grain boundary. However, no evidence of the characteristic cellular morphology typical of discontinuous precipitation was found in Singhal and Martin&apos;s studies. Presumably, this is due to the low volume fraction (i.e., low supersaturation of solute) of the precipitating carbide reported by Singhal and Martin.4 Recently, Raymond6 has studied precipitation of the M23C6 carbide in Incoloy alloy 825 and shown that the growth of this phase is perpendicular to grain boundaries at 1400°F and in the plane of the grain boundary at 1700°F. The former aging condition resulting in discontinuous or "cellular" precipitation. Raymond has suggested an explanation for this behavior based on the relative rates of chromium diffusion by volume and grain boundary diffusion at the two different aging temperatures. In the course of a recent investigation on precipitation behavior in several &apos; strengthened superalloys, precipitation of M23C6 carbide at grain boundaries was studied. Under conditions of a high degree of supersaturation, the M23C6 carbide precipitates in the discontinuous or cellular morphology in Waspalloy (Ni-18.51 Cr-2.0 Fe-3.53 Mo-1.16 Al-2.78 Ti-0.09 C). This note presents electron microscopy observations of this mode of precipitation and its effect on mechanical properties. Specimens of Waspalloy after "solution" heat treatment at 1950°F show essentially single phase matrix with a few residual particles of "primary" MC carbide. In normal commercial heat treatments, precipitation of Ni3(Al,Ti) ordered fcc r&apos; phase occurs throughout the matrix and M23C6 precipitates as globular particles at the grain boundaries. In these commercial heat treatments the degree of supersaturation during precipitation is low. However, if specimens of Waspalloy are quenched from the solution heat treatment temperature of 1950°F and then aged at an aging temperature where the degree of supersaturation is high, discontinuous precipitation of M23C6 occurs. Figs. 1 and 2 show thin foil micrographs of Waspalloy, solution heat treated at 1950°F, water quenched, and aged at 1292° and 1598°F, respectively, for 500 Fig. 1—Thin foil of Waspalloy, solution heat treated at 1950°F for 1 hr, water quenched, and aged for 500 hr at 1292°F. Magnification 15,500 times. Fig. 2—Thin foil of Waspalloy, solution heat treated at 1950°F for 1 hr, water quenched, and aged for 114 hr at 1598° F. Magnification 13,000 times.

Jan 1, 1970

By J. Husson, R. Iffly, M. Gondouin

A systematic variation of well deliverability, as reflected from isochronal back-pressure tests performed at regular intervals, has been observed in some gas condensate wells producing at high rates. The same effects have been obtained using a numerical model of gas and condensate flow which takes into account secondary gasoline deposited in the pore space as a result of pressure reduction, and non - Darcy flow of gas in the vicinity of the wells. Matching calculated values with previous test results has been possible, and future predictions have been obtained. An application of this method to the Hassi Er R&apos;Mel gas-condensate field in Algeria is tentatively shown. INTRODUCTION Flow capacity of gas wells is generally derived from an analysis of back-pressure tests. The empirical equation q = C (?p2)n used by Rawlins and Schellhardtl can be derived rigorously assuming that steady-state radial flow of a dry gas of constant viscosity and compressibility is established during each flow period of the well tests. Furthermore, when Darcy&apos;s law applies in the entire flow region, the theory predicts that the exponent n is equal to 1. In low-permeability reservoirs, it was soon discovered that the time required to reach a stabilized flow often exceeded the duration of the flow periods normally available for testing wells. Consequently, transient gas flow had to be considered instead of the steady-state assumption previously used. This led to the isochronal testing procedure established by Cullender2 which has largely replaced conventional back-pressure testing. For dry gas fields, this method yields definite values of C and n equivalent to those of the empirical equation. These values should remain constant for each well as long as the permeability of the formation and the characteristics of the gas (viscosity and compressibility) do not change appreciably. This is the case when reservoir pressure remains -close to the original value and when the formation near the wellbore remains free of plugging. Under those conditions, stabilized flow potential curves of gas wells can be established from a single sequence of isochronal flow and shut-in periods. An analysis of a pressure build-up following a longer production period provides additional data on the transmissivity (k h/ u) of the reservoir, and eventually on the &apos;drainage radius rd of the well, which can be related to the value of C so that future performance of the well can be predicted using the concepts developed by A. Houpeurt.3 At high flow rates, Darcy&apos;s law no longer applies in the vicinity of the wellbore, and inertial effects in the high velocity gas flow introduce additional pressure drops. As a consequence, exponent n of the backpressure tests becomes smaller than 1, and a slight curvature of the log-log plot of ?p2 vs q can be predicted when going from very low to high rates of flow (Elenbaas and Katz).5 The effects of variations of viscosity and compressibility with pressure on the radial flow of dry gas in an infinite reservoir were taken into account by Jenkins and Aronofsky.7 Numerical solutions of the transient flow of an ideal gas in finite radial reservoirs were presented by Bruce, Peaceman, Rachford and Rice.8 In the case of gas condensate wells, however, the presence of gasoline in the pore space as soon as reservoir pressure is reduced below the dewpoint pressure further complicates the interpretation of flow tests so that the prediction of stabilized well performance becomes very difficult. Field observation shows that both C and n derived from isochronal tests vary in time, even when reservoir pressure has not changed appreciably. Such a variation cannot be attributed to any change of the gas characteristics, and must result from the effect of a gasoline saturation on the gas flow.

By D. E. Baldwin

A method has been devetoped for predicting the produced concentration profile for a miscible slug in a five-spot pattern. The technique consists of dividing the five-spot into radial etements and applying an approximate radial solution of the dispersion equation to each element. To test the method, laboratory experiments were conducted in five-spot models. The models were 2-ft X 2-ft X 2-in. Berea sandstone slabs simulating one quarter of a five-spot. An aqueous system was used with tritiated water as the tracer fluid. Effiuent concentration profiles were obtained for slug sizes ranging from 0.7 to 10.2 per cent of the pore volume. Agreement between predicted and experimental profiles was excellent. A prediction was also made for a field tracer test. For this case the predictive technique was modified to account for stratification by use of a layer cake model. INTRODUCTION Dispersion in porous media is of growing interest to the petroleum industry because of the increasing importance of secondary recovery operations. One of the controlling factors in the recovery of oil by miscible displacement or by the use of waterflood additives is the degree of mixing between the fluids of interest. Consequently, one of the prerequisites of any recovery prediction is an adequate method of predicting dispersion. Also, any quantitative interpretation of waterflood tracer tests is dependent upon the ability to determine the dispersion of the tracer as it flows through the reservoir. During the past few years there have been reported in the literature the results of a large number of investigations, both theoretical and experimental, concerning dispersion in porous media. (An excellent review of these results has been presented by Perkins and Johnston." Only a few of these investigations, however, deal with non-lin-ear flow systems. Raimondi et al.9 have presented an approximate solution of the dispersion equation for radial, diverging flow. Lau et al. 7 and Bentsen 1 have presented laboratory data for radial systems and have shown that the dispersion can be adequately predicted by Raimondi&apos;s solution. Bentsen has also presented a small amount of data for a radial, converging system. Brigham and Smith&apos; have applied Raimondi&apos;s solution, with approximating assumptions, to a five-spot pattern to predict the behavior of a field tracer test. The afore-mentioned investigations have been concerned almost entirely with radial diverging flow and have neglected the effect of converging flow. For this reason the present investigation was undertaken to develop a method of predicting dispersion in a five-spot pattern including the effects of both diverging and converging flow. The method which was developed consisted of dividing the five-spot into diverging-converging radial elements and applying an approximate solution of the disperson equation to each element. DEVELOPMENT OF PREDICTION METHOD The development of the prediction method consisted of two phases: construction of a radial model of a five-spot pattern and derivation of equations to describe the dispersion in the radial model. FIVE-SPOT MODEL A radial model which simulated the flow characteristics of a five-spot pattern was constructed by dividing the five-spot into diverging-converging radial elements (Fig. 1). Because of symmetry the model represented only an octant of a complete five-spot. Each element had an included angle of l° (making a total of 45 elements) and a radius r, such that the sum of the individual element areas was equal to the area of the five-spot octant. The normal five-spot fractional flow behavior was determined by averaging the experimental five-spot data of Caudle and Witte,&apos; Dyes, Caudle and Erickson 5 and Fay and Prats. 4 The resulting curve is shown as a solid line in Fig. 2. To match this curve with the radial model it was

Jan 1, 1967

By E. V. Kleber, V. F. Novy, R. C. Vickery

The constitutional diagram has been determined for the system gadolinium-nickel. Nine intermetallic compounds have been found at compositions corresponding to the following gadolinium-nickel ratios: 3:1, 3:2, 1:1, 1:2, 1:3, 2:7, 1:4, 1:5, 2:17. The GdNi and GdNi5 compounds have congruent melting points of 1300&apos; and 1500°C, respectively while the remaining compounds melt in-congruently. Eutectics exist at 15 wt pct Ni, 31 1/2 wt pct Ni and 87 wt pct Ni with melting points of 6703 8803 and 1220°C, respectively. IN a continuing investigation of the properties of rare earth alloys, a study has been made of the gadolinium-nickel system. Previous work encompassed the iron containing alloys and a subsequent paper will deal with the constitution of the gadolinium-cobalt system. Vogel,1 examined alloys of nickel with lanthanum and cerium. R3Ni, RNi, RNi2, RNi3, RNi4, and RNi5 compounds were found. Endter and Klemm,2 Fulling et al.3 Heumann,4 and Nowotny5 found the 1:2 compositions of this series to exist in a C-15 (face-centered cubic) structure, and the 1:5 compositions in a hexagonal system. Jepson and Duwez6 more recently examined these 1:2 and 1:5 compositions and generally confirmed earlier data while Wernick and Geller7 most recently have given additional data on the GdNi5 compound. Comparisons with our results will be made in the appropriate section of this report. EXPERIMENTAL Methods of alloy preparation, annealing procedures, and experimental techniques have been given in our earlier paper.8 Chemical analyses of the alloy samples were made by dissolving the specimen in nitric acid, precipitating the gadolinium as hydroxide and the nickel with dimethylglyoxime. Both precipitates were ignited to oxide and weighed. RESULTS Microstructure— Metallography of alloy specimens in this series has been conducted on both arc-melted and annealed materials. Etchants used have been 5 pct nital with approximately 10 pct distilled water added, for high gadolinium samples; Carapella&apos;s ferric chloride solution for intermediate compositions; and Marble&apos;s (copper sulfate) reagent for high nickel content alloys. Because of difficulties encountered in the grinding and polishing of specimens containing 40 to 75 wt pct Ni, no photomicrographs were made of such specimens. The microstructure of an arc-melted 5.3 wt pct Ni alloy is shown in Fig. 1. Light etching primary grains of gadolinium are embedded in an eutectic matrix. The microstructure of an alloy of 9.55 wt pct Ni alloy, Fig. 2, annealed 50 hr at 700°C, consists almost entirely of the intermetallic compound Gd3Ni. The structure of an arc metal alloy of approximately 19 pct Ni, Fig. 3, consists of grains of the compound GdNi embedded in the Gd3Ni2-Gd3Ni eutectic. The arc-cast structure of the 38.7 wt pct Ni alloy is shown in Fig. 4. Large primary grains of a compound rest in a matrix structure of coarse GdNi-GdNiz eutectic. Because of the occurrence of several peritectic compounds in the central region of the diagram, identification of the primary structure in this alloy is not certain. As has been indicated above, microstructures of alloy specimens containing between ca 40 and 75 wt pct Ni have not been photographed. These specimens were highly brittle, and macro- and micro-cracking were impossible to control in the grinding and polishing procedures. Prolonged annealing did not alleviate this condition. Visual observations in small specimens did, however, provide evidence for a multiplicity of phases and peritectic dissociations of compounds although rationalization of structures was not possible.

Jan 1, 1962

By Morris Cohen, Robert C. Ruhl

Fe-Ni-B alloys were inresligated by X-ray diffraclion after splat quenching. Although this rapid cooling did not produce a measurable supersaturation of dissol1ed boron in either binary Fe-B or Ni-B alloys, a marked increase in dissolved boron was achieved by the splal quenching of lernary Fe-Ni-B alloys. Boron additions up to 2.0 wl pcl to Fe-13Ni and Fe-24Ni alloys cause an increase in retained austenite from 0 to 59 pet and to 92 pet, respectively. The martensitic phase in the Fe-13Ni-9 at. pct B alloy is .found to conlain about 0.6 at. pet interstitial boron, as evidenced by the tetragonality of this phase, and about 3.6 at. pct substilutional boron, us deduced from the lattice paratrieler decrease, the balance of the boron being precipitated as (Fe,Ni)aR. The austenitic Fe-Ni-B plznses also contain both interstitial and substitutional boron. Iron-Boron System. The phase diagram and related information about the solid solutions and intermediate phases in the Fe-B system are given by ansen,&apos; Elliott.2 and Pearson.1 The equilibrium solid solubility of boron in both ferrite and austenite is quite small: the maximum solid solubility of 0.02 wt pct B (0.11 at. pct B) occurs in iron at the eutectic temperature of 1150°C. while the maximum solubility in a iron is less than 0.01 wt pct.l There is disagreement in the literature as to whether these solid solutions are substitutional or interstitial. Based on the measured activation energy of boron diffusion in iron, it appears likely that boron moves interstitially in austenite. 4 However, this observation does not rule out the possibility that some of the dissolved boron may also occupy substitutional sites in this phase. Investigations of internal friction of boron in iron have suggested that boron is interstitial there.&apos; Shevelev, 5 on the other hand, reports a decrease in the ferrite lattice parameter with dissolved boron content, thus indicating a substitutional solution. Unfortunately. Shevelev&apos;s methods and analysis are unclear. Goldhoff and spretnak6 have measured the lattice parameters of pure iron and an Fe-0.005 wt pct B (0.027 at. pct) alloy at both room temperature (ferrite) and from 920° to 1200°C (austenite). They reporte: a lattice contraction in the ferrite of 0.0003 ± 0.0002 due to boron, thus indicating a predominately substitutional solution. Appreciable (0.0010 to 0.0060) lattice contractions were found in boron-containing austenites, but these effects were much larger than could be accounted for by the substitutional solution of all the boron present. Nickel-Boron System. Elliott 2 gives a summary of thephase diagram and recent work on this system. The solubility of boron in nickel reaches a maximum of 0.03 wt pct at the eutectic temperature of 1080°C. Iron-Nickel System. ansen&apos; presents the equilibrium diagram for this system and also discusses the metastable austenitic and martensitic phases along with the a=? transformations. The lattice parameters of Fe-Ni ferrites have been recently redetermined by Abrahamson and Lopata.7 Their data, Fig. 1, show an unusual change in slope at about 1.7 at. pct Ni. Very few measurements of the lattice parameters of Fe-Ni martensites are available in the literature. The values of Roberts and Owen8 are considerably higher than those measured in the course of the present work: they find that a, is constant at 2.874? from 8 to 30 at. pct Ni. Both the slope change in the ferrite parameters and the occurrence of a maximum plateau in the marten-sitic lattice parameters vs composition denote the

Jan 1, 1970