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By M. van Swaay, C. E. Birchenall

A. S. lBrling (Johnson, Matthey & Co. Ltd., Laboratories)— Because of its initial emphasis upon the production of membranes by powder metallurgy and by normal casting and rolling techniques, this paper is of considerable interest to those concerned with the design and application of industrial diffusion units. As the subsequent performances of the three grades of palladium were not compared in detail, it can perhaps be concluded that specific permeabilities were very similar. A short table in which the absolute diffusion rates obtained by the Authors with their three grades of palladium were compared with those of other investigators18-25 would, however, have been of particular value in view of the very variable results obtained with this membrane material. The Authors state early in the paper that the permeability of the thoriated samples decreased in much the same way as that of the nonthoriated samples. Later, they emphasize that sintered palladium without thoria was very susceptible to poisoning and did not respond as well as the other materials to the decontamination treatment. These results, which suggest that sintered membranes are less effective than those produced by normal methods, have considerable industrial implications, and amplified experimental details would be very welcome. The results of the Authors differ in one important respect from those of other investigators. Thus, no "bleeding" was required to maintain a constant rate of diffusion, although Davis, Darling, and De Rosset found this to be necessary. Davisz3 found that "bleeding" was necessary even when the hydrogen had already been purified by diffusion through a palladium tube, and it would be of value to know the purity of the gas stream emerging from the purification train shown on Fig. 1 of the Authors' paper. The Authors show that diffusion rates varied according to the square root of the pressure difference providing that the palladium membrane was not contaminated in any way. This finding is in agreement with the results of those workers2,18,19,23,24 who diffused their hydrogen through the membrane into a partly or completely evacuated system.Those workers who did not find this square-root law dependence did not have a partial vacuum on the downstream-side of the membrane.'' The difference between the two experimental con- ditions appears to be significant, as the absolute diffusion rates per sq cm of diffusion area are lower when the square-root law dependence is not observed. While the effect could be attributable to poisoning of the membrane it is conceivable that a positive pressure on the downstream side of the membrane might influence the mechanism of diffusion. In view of the capricious behavior of palladium, factors of this type, which are likely to influence its industrial significance, should be carefully considered. M. van Swaay and C. E. Birchenall (authors' 9-eply) — Our Eq. 191 may be compared with several others for hydrogen diffusion in palladium: D = 5.95 x exp (-5770/1)' D = 3.55 x 10"3 exp (-5550/)' D = 4.3 x 10"3 exp (-5620/1')' Other values are given in the literature, but in many cases surface poisoning may have affected the results. No analysis was performed on the hydrogen gas stream after purification. It should be noted that the presence of liquid nitrogen traps near the heated membranes may have set up convection currents and provided the equivalent of "bleeding." The question of whether a partial vacuum existed on the downstream side of the membrane is not clear. Does it imply that there is something unique about the permeability measured near one atmosphere pressure? We do not believe that there is. When square root pressure dependence is not observed, diffusion rates are not measured. Is "absolute diffusion rate per sq. cm. of diffusion area" equivalent to permeability? The terminology is new to us. In any case we doubt very much that pressures of the order of several atmospheres can affect the mechanism of diffusion.

Jan 1, 1962

By H. I. Najarian

This paper is a companion piece to the description of the electrothermic process that begins on page 141. It will be confined to a brief story of the development. of the Weaton-Najarian vacuum condenserf at this plant, together with up-to-date design and operating data. The Josephtown smelter was designed primarily for production of zinc oxide. However, the development of a method for production of zinc metal had always been under consideration, and accordingly one of the original eight units of the elcctro-thermic furnaces built in 1930 was set up to produce metal. The design of this furnace was identical with that of the oxide furnaces except that in place of oxide tewels opening into oxide manifolds, conventional conical clay condensers—similar to condensers used in horizontal retort smelting—were installed around the periphery of the furnace and in several tiers vertically for condensing the zinc vapors. The early experimental work in trying to condense zinc out of the mixtures of zinc vapor and carbon monoxide gas from the electrothermic furnaces indicated that, while the gases from electrothermic smelting would condense in surface-type condensers, the formation of blue powder was excessive and condenser efficiency low. Furthermore, operating a large unit of electric furnace with several hundred small condensers, with attendant high labor cost and unfavorable operating conditions, did not appeal to us. We also realized that a single unit of surface condenser capable of condensing 12 torg tons of metal per day would be of huge dimensions and possibly difficult of control. So we took as our aim the development of a method whereby a single condenser unit of reasonable dimensions would condense zinc, in one step, from the large volume of gases that the electric furnaces produced. We set about searching for knowledge on zinc metallurgy and design of zinc condensers in particular. Our study of the prior art focused our attention on the oft-repeated statement by earlier experimenters, that the most efficient way to condense metallic vapors, such as zinc vapors, was to bring the vapors into "intimate contact" with molten metal; but the methods offered for securing this "intimate contact" in any practical manner left much to the imagination. We were handicapped by not having some-one on the Josephtown smelter staff who could lay claim to being an expert zinc metallurgist and could give guidance from actual experience on the practicability of various schemes that haunted our imagination. Laboratory Experiments However, we had an expert ex-steam engineer in the person of George I?. Weaton, manager of the Josephtown smelter, who had had long experience with steam-jet condensers and would reiterate his belief at every opportunity that the logical and the most efficient way to condense zinc would be with a jet-type condenser. We became intrigued by the possibilities of a zinc con-

Jan 1, 1944

By Nicholas J. Grant, John Chipman

A full understanding of the behavior of sulphur in the basic open-hearth process has been delayed by lack of dependable data covering a wide range of slag conditions in the absence of other complicating factors that are likely to be present under operating conditions. It has been generally accepted that strongly basic slags will dissolve more sulphur than will those in which the acidic and basic constituents are more nearly balanced. It has been known that both slag and metal would absorb sulphur from the flame when the sulphur content of the fuel is high. It has been generally believed that manganese assists in the transfer of sulphur from metal to slag. Almost nothing has been known of the effect of temperature upon desulphurization;the data have been conflicting and there has been a tendency to depend rather heavily upon analogy with the better understood desulphurizing reaction of the blast furnace. Many attempts have been made to build up from open-hearth data a satisfactory theory of the chemical reactions involved in the process. That this has been an extremely difficult task is owing to two reasons that have been very generally recognized. The first is the parallel and simultaneous reaction of sulphur transfer between flame and bath. The second is the difficulty of distinguishing between the factors that ultimately limit the transfer from metal to slag—i.e., equilibrium conditions—and those whose influence is only upon the rate of transfer. It has been the object of the work here recounted to study the equilibrium distribution of sulphur between slag and metal in the absence of these complicating factors, with the hope that a better understanding of the equilibria involved would lead to a better control of the over-all process in the open-hearth furnace. A review of the literature on steelmaking reveals almost complete agreement with respect to the paramount importance of lime in promoting desulphurization. In expressing this effect in quantitative terms, however, and in formulating the relationships between the concentrations of other slag components and the desulphurizing power, there is little agreement. For instance, the "basicity" or basic strength of the slag is commonly measured by some kind of ratio of concentration of basic to acidic oxides. Of these, the following have been reviewed by Schenck:20 V radio = % CaO/%SiO, Körber and Oelsen's _ % CaO'. 100/% CaO + % SiO2 where (%CaO') = % CaO- 1.18% P2O5. Herty's B ratio = % CaO - (0.93 . % SO2) - (1.18% P205) Among others there appear the following: 20 References are at the end of the paper.

Jan 1, 1947

By M. Prats, D. G. Russell

The performance of a well in a bounded, layered reservoir with interlayer crossflow has been investigated mathematically. The system studied comprises a centrally located well in a bounded cylindrical reservoir composed of two layers of contrasting physical properties. The reservoir contains a single fluid of small and constant compressibility. In the case of a well producing at constant pressure, the production rate of the crossflow system declines exponentially after the early transient behavior dies out. For wells which produce with constant rate, the pressure-time relationship is linear following the transient. For very early production time, the production rate of the two-layer crossflow system behaves as that of the two-layer stratified system (the case in which the layers are in communication at the well only). Except for early time, in most practical cases the performance of a two-layer reservoir with cross-flow can be duplicated by that of a single-layer reservoir. The equivalent single-layer reservoir must have the same pore volume and the same drainage and wellbore radii as in the two-layer case. In addition, the equivalent reservoir must have a "kh" (permeability x thickness) product equal to the sum of the "kh" products of the respective layers in the crossflow system. If the porosity and permeability distributions are known, the production and pressure behavior of a well with and without crossflow can be predicted. From a comparison of the observed pressure or production performance of a well and the theoretical behavior, the occurrence of interlayer crossflow can be detected. INTRODUCTION When flow is possible across the bedding plane from a low-permeability layer into an adjacent layer of moderate or high permeability, the earlier depletion of the more permeable layer will cause such flow to occur. If this situation exists, the oil recovery from tight layers can be appreciable; thus, the economic ramifications of interlayer crossflow are apparent. The possible importance and extent of flow between adjacent and connected layers — whether resulting from capillary, gravitational, or viscous forces — have been the subject of considerable speculation for many years. Jacquard1 presented a rigorous analysis of the crossflow due to single-fluid expansion occurring between two adjacent and connected layers when the well produces at constant rate. His presentation was entirely mathematical, however, and no numerical results from evaluation of the mathematical solutions were presented. Our objectives in the preparation and presentation of the present paper are essentially twofold— (1) to analyze the behavior of a well which produces a single compressible fluid from a bounded, layered reservoir with interlayer crossflow, and (2) to present practical numerical results and simplified formulas to facilitate engineering analysis of reservoirs with crossflow. The constant-terminal-pressure case was analyzed rigorously, whereas the constant-terminal-rate case was treated only for semisteady-state conditions. DESCRIPTION OF THE IDEALIZED TWO-LAYER RESERVOIR The reservoir to be studied is assumed to be bounded and cylindrical in shape, with a completely penetrating well at its center. The reservoir is composed of two adjacent horizontal layers between which fluid is free to flow. Each layer is assumed to be homogeneous, isotropic and completely filled with a fluid of small and constant compressibility. The total thickness of the reservoir is small enough

By B. D. Smith, K. H. Coats

Experiments in which calcium chloride displaced sodium chloride from four cores showed the extent of asymmetry in the resulting effluent concentration profiles. These results provided a check on how validly the mixing process is modeled by a differential (i.e., not finite-stage) capacitance mathematical model. The effluent concentration profile from two consolidated cores exhibited considerable asymmetry, while two unconsolidated cores yielded nearly symmetrical profiles. All runs resulted in breakthrough of the 50 per cent concentration significantly before one pore volume was injected. In addition, velocity appreciably affected the effluent concentration profile from a Torpedo sandstone core. The differential capacitance model matched the data significantly better than a simple diffusion model. The capacitance model allows determination of the amount of dead-end pore space in a porous matrix and the effect of velocity on the rate of diffusion into this space. An experimental program yielding insight into the physical validity of the capacitance effect is described. INTRODUCTION Axial dispersion — the mixing accompanying the flow of miscible fluids through porous media — has been the subject of many relativeiy recent studiesl-13 and a comprehensive review of the topic has been given by Perkins and Johnston.14 This dispersion is of practical interest in studies of the miscible displacement process, fixed-bed chemical reactors, and the adsorption of solutes from a flowing stream onto the surface of a porous medium. In the latter case, the effect of dispersion must be considered when adsorption parameters are determined from the nature of concentration profiles. In general, early studies of dispersion assumed applicability of a simple diffusion equation and were concerned with correlation of the experimentallv determined "effective" diffusion coefficient with system properties over a large range of the latter. Recent have been concerned with the deviations between the asymmetrical effluent concentration profiles observed and the symmetrical ones predicted by the diffusion model. In the present study, effluent concentration profiles were obtained from consolidated and unconsolidated cores. These profiles were compared with those predicted by a differential (i.e., not finite-stage) capacitance model. Solutions to the simple diffusion model, for three sets of boundary conditions, were compared with one another and with the experimental profiles. SUMMARY OF PREVIOUS WORK The reader is referred to Perkins and johnston14 for an extensive review of studies of dispersion in porous media. Many investigators have employed the simple diffusion model characterized by Eq. 1 below: The dispersion coefficient D for unconsolidated systems is correlated by u is interstitial velocity and dp is particle diameter. Since heterogeneity of the sand pack affects the mixing, this equation is also expressed as where a is proportional to the degree of heterogeneity and is about 3.5 for random packs of unconsolidated sand.l4 Eq. 3 holds for 2 For a Do homogeneous (regular) type of packing, should be 1 or less.6 Aris and Amundson6 and Carberry and Bretton consider o to be the number of particle lengths per mixing cell in the finite-stage model. Data from consolidated cores indicate dp to be about 0.36 cm for outcrop rocks, Torpedo sandstone having a reported value of 0.17 cm.15 For v /Do less than about 2, the effect of molecular diffusion must be considered and the total dispersion coeffi-

Jan 1, 1965

By R. C. Earlougher

Based on laboratory tests conducted with the use of fresh core samples as well as a considerable amount of field data obtained from numerous water floods in northeastern Oklahoma, it appears that for any given oil saturation there is a critical maximum velocity above which the oil-recovery efficiency falls off very rapidly. In effect, when a water flood is operated above this critical velocity, the injected water-oil ratio rises extremely fast, thus shortening the economic life of the flood and reducing the ultimate oil recovery. This critical velocity apparently varies considerably with the percentage of oil saturation of the sand, so that in effect the higher the oil saturation at the beginning of a flood the higher the velocity that can be used successfully. In reviewing several of the earlier floods in the Mid-Continent area, it is concluded that most of the failures were due to two things: (I) too low an oil saturation, such as 30 per cent, and (2) too high water-injection rates, Although considerably more field data are necessary to establish definite limits, it would seem that the proper field injection rate for a 330 by 330 or 440 by 440-ft. spacing varies from approximately I bbl. per foot of sand per day where the oil saturation is as low as 30 per cent up to 5 bbl per foot of sand per day when the oil saturation is as high as 45 to 50 per cent, Introduction With secondary recovery by water-flooding receiving more and more attention throughout the industry, a greater working knowledge of multiphase flow under field conditions becomes more and more necessary A great deal of research has been carried on in highly idealized laboratory conditions, from which certain trends have been indicated, but with few exceptions no direct application to field use has been reported. widely varying conclusions have been drawn from the mass of idealized laboratory experiments and often this divergence apparently was due to the neglect of connate or interstitial water. Since interstitial water is such an important factor in water-flooding operations, it then follows that any laboratory flooding experiment must necessarily take it into account; and since it is difficult to set up laboratory models to allow for interstitial water, the next best procedure is to use fresh core samples for such tests. Even this procedure has its difficulties, inasmuch as it is possible to run only one flooding test on each sample, as each sample differs somewhat in character from all other samples. However, this disadvantage can be overcome to a large degree by the use of an extremely large number of samples. The next question that arises is: "IS it possible to get uncontaminated core samples having a true oil and water saturation like that existing in the reservoir?" If the sand under consideration is still in the primary stage of production, with a normal or relatively high amount of gas still in solution in the oil, probably it is not possible to get a nonflushed core. On the other

Jan 1, 1943

By A. S. Yue

Small-angle tilt boundaries have been observed in a lamellar eutectic structure. These boundaries are morphologically similar to a theoretical till boundary originally proposed by Burgers. The production of a small-angle tilt boundary in the lamellar eutectic structure is attributed to the formation of an indentation on a planar solid-liquid interface during growth. Constitutional supercooling due to the accumulation of impurity atoms ahead of the interface is primarily responsible for the generation of an indentation. The distance between two faults of like sign, designated as lamellar fault distance, is calculated by the Burgers equation for small-angle boundaries. It was found that the lamellar fault distance decreases exponentially and the tilt angle increases exponentially with freezing rate. SMALL-ANGLE tilt boundaries have been observed in many crystals in the as-grown states by etching techniques. However, a detailed substantial proof for revealing the presence of dislocations in the form of etch-pits was recently accomplished by Vogel. These boundaries are described as an array of dislocations of like sign. The angle of tilt associated with a boundary is treated theoretically by Burgers3 and is given by 0 = b/D for small tilt-angle where b is the Burgers vector of the dislocations and D is their average spacing. During the course of experimentation on the solidi fication of the lamellar Mg-32 wt pct Al eutectic a microstructure which was strikingly similar to a dislocation tilt boundary was observed. An example of the type of microstructure is given in Fig. 1, which shows a combination of transverse and top sections of the lamellar eutectic structure. The lamellae of the top section on one side of the apparent tilt angle are not parallel with those on the other side. Consequently, some lamellae must be terminated somewhere. Fig. 1 shows that the termination of lamellae is analogous to a dislocation tilt boundary in a crystal lattice originally proposed by Burgers. This work represents a closer look at such structures. The factors governing the production of the small-angle tilt boundary are discussed in terms of the freezing condition and impurity distribution in the melt. The effect of freezing rate on the distance between two faults, designated as lamellar fault distance, and the tilt angle is also described. In addition, the lamellar fault distance is determined by means of the Burgers equation for small-angle tilt boundary. EXPERIMENTAL PROCEDURE The slightly impure Mg-32 wt pct Al eutectic rods, 5/8 in. in diam and 12 in. long, were made from 99.99 wt pct Al and 99.98 wt pct Mg and were cast in a high-purity graphite mold. Some of these rods were purified by zone-refining the eutectic using direct-radiation helical-coil furnaces5 A molten zone about 2 in. long was passed through the cast rods at a speed of 5.3 x 104 cm per sec for ten passes of the molten zone. Before the freezing experiment was begun, 2-1/2 in. of the material from the head and tail ends of the zone-refined eutectic were removed from the rod to eliminate any impurity. The freezing experiments were carried out under controlled conditions,8 using a protective atmosphere of purified argon. At the end of each run, observation of the tilt boundary was made throughout the entire length of the rod with a light microscope on the top, longitudinal, and transverse sections (three mutually perpendicular sections) of the lamellar eutectic solid. The experimental data used for the determination of interlamellar spacing and tilt angle were taken from the middle portion of

Jan 1, 1964

By J. Szekely, G. P. Martins

A formulation is given and a general analytical solution is presented for the problem of spherical phase growth in multicomponent systems. The results are valid for describing the rate of bubble growth in the absence of translational motion and, therefore, should be relevant to heterogeneous nucleation processes. Typical worked examples are given, which include bubble growth due to the simultaneous diffusion of hydrogen and nitrogen in molten steel, and the growth of CO bubbles in steel, due to the reaction: C + 0 = CO. The calculations predict that the presence of additional components would enhance the growth rate and also increase the absolute rate at which the individual components are transferred into the bubble. These findings should be relevant to degassing processes. THE problem of spherical bubble growth in the absence of translational motion is appropriate to the description of the heterogeneous nucleation and subsequent growth of gas bubbles while attached to a solid surface. Such problems are of considerable practical relevance to various vacuum degassing and steelmaking processes where bubble nucleation and subsequent growth play an important part in the overall reaction mechanism. A definitive formulation of spherical phase growth has been given in the now classical paper by Scriven1 and the analogous problem for solid phase growth has been discussed by Horvay,2 furthermore a thorough review of the relevant literature has also become available.3 All this previous work was concerned with one component or binary systems. The purpose of this paper is to show that the technique developed by Scriven may be generalized to alow the consideration of multicomponent systems. The results of this generalization would be particularly relevant, as gas bubble nucleation in the metallurgical systems previously mentioned frequently involves the simultaneous diffusion of several components. In the following a general formulation is given and typical worked examples are presented. FORMULATION Consider the growth of a spherical gas bubble due to diffusion in a quiescent liquid of infinite extent, as sketched in Fig. 1. The formulation of such problems requires the statement of the following conservation equations relating to the liquid phase: Equation of continuity Equation of motion Conservation of the diffusing species—Diffusion Equation. The following assumptions are made: a) The fluid is incompressible, quiescent, and of infinite extent b) The bubble is stationary, i.e., it undergoes no translational motion c) Spherical symmetry is observed throughout d) The mass diffusivity is constant e) Chemical equilibrium exists at the surface of the bubble, and any reactions occurring there are fast compared to the diffusion process f) Inertia and surface tension effects are neglected. Equations derived on the basis of these assumptions by previous investigators were found to provide a reasonable representation of bubble growth while attached to a surface in organic and aqueous systems4,5 For gas bubble growth in molten metal systems assumptions a) to d) chould hold reasonably well. The exclusion of chemical kinetics as a possible rate limiting step may not be universally valid, but should hold for many systems operating at high temperatures. The effect of hydrodynamic inertia may be neglected for moderate growth rates; finally, the assumption neglecting the effect of interfacial tension on the bubble growth was made for the sake of mathematical convenience; its inclusion would have required the use of quite cumbersome numerical techniques. While surface tension effects could be appreciable on the initial values of the overall growth rate, especially at low absolute pressures and in case of small bubbles, they are not thought to modify the relative effects present in multicomponent systems, the study of which is the objective of this paper. Within the framework of the above assumptions

Jan 1, 1970

Experimentation which measures differences in pressure across the interfaces of immiscible fluids in the interstitial spaces of porous media may be termed "capillary pressure experimentation". In the literature of petroleum technology since 1941 there have appeared twelve papers popularizing capillary pressure concepts and developing applications of these concepts for the solution of problems of practical reservoir engineering importance, such as the determination of connate water, fluid distribution. in transition zones, reservoir rock textural properties, and oil recovery from petroleum reservoirs.' Although a review of the literature would be justified at this time in order to reconcile the conflicting viewpoints which are contained in the cited papers, the object of this note will be of more limited scope. It is believed that the recent paper of Muskat alls sufficient attention to many of the uncertainties which arise upon examination of the published literature. such that until satisfactory counter-proposals can be made it will serve our purpose only to mention some other like uncertainties. This will emphasize further the need confronting petroleum technologists to re. consider and reformulate the application possibilities of capillary pressure experimentation. In particular, I sug- gest that we examine the thesis that capillary pressure experimentation as above defined can lead to measurements reflecting the recovery of oil from petroleum reservoirs, as was proposed first" by Amyx and Yuster" and was first reduced to practice by the experimentation of Welge. In fact. I shall deal exclusively with the Welge papers since it is the principle one on this subject which has appeared to date. I shall attempt to show that the possibility of describing oil recovery features in terms of capillary pressure phenomena has not been established entirely. The Welge paper was a pioneering effort to evaluate this recovery application possibility. P. P. Reichertz' comments on the Welge paper state that non-wetting phase discontinuities are developed occasionally in the Welge experiment, and restate Muskat's argument that discontinuous fluid elements (partially saturating the interstices of porous media which are elsewhere saturated with some other immiscible phase or phases) are not subject to the requirements of hydrostatic equilibrium. It is the purpose of my comment to show that it is unnecessary to make Reichertz' postulation regarding non-wetting phase discontinuities (however valid) when it is desired to criticize welge's theoretical treatment of his problem. It can be shown that Welge's method of measuring values for ''capillary pressure" is invalid in many instances of application, such that his reported curves of capillary pressure Versus fluid saturation often have no physical meaning, even throughout the interval of fluid saturation where it might be otherwise suspected that no phase discontinuities occur. By considering established principles of capillary pressure experimentation it can be shown that the pressure difference experimentally observed between wetting and non-wetting fluid Phases which are contained in external reservoirs will reflect on the capillary pressure difference at the interfaces of contact between these phases only when the following conditions are satisfied: (a) There shall be a balance between the opposing forces of gravity and capillarity, as obtains under conditions of hydrostatic equilibrium when the positions of the interfaces of contact become fixed in pore spaces of certain geometry (b) The wetting and non-wetting fluids within the interstitial spaces shall everywhere be continuous with the external wetting phase reservoir and the external non-wetting phase reservoir, respectively. It will become apparent immediately that in any instance when a greater pressure is recorded in the external wetting phase reservoir than in the external non-wetting phase reservoir, one may establish either that static equilibrium has not been attained or that discontinuities in one or more of the fluids have been developed. This is because the pressure otherwiee is always ereatest in the non-wetting phase at each static interstitial interface of contact with the wetting phase. such that the externally measured pressure in the non-wetting phase likewise must be greatest if the above conditions are to be satisfied.

Jan 1, 1949

By R. D. Reiswig, J. M. Dickinson

The 0s-Ir equilibrium diagram was determined. The diagram is of the simple peritectic type, with a peritectic temperature of about 2660°C. The solid miscibility gap is narrower than previously reported, the nearly vertical solvus lines occurring at about 42 and 63 wt pct 0s. Widmanstaetten figures resembling martensite in some of the two-phase alloys account for a previously suspected transformation. In view of the long history of use of such alloys, it is surprising that the 0s-Ir equilibrium diagram has not yet been completely determined. The boundaries of the miscibility gap in this system have been estimated to be between 24 and 39 wt pct 0s and 79 and 100 wt pct OS. It has been predicted3 that alloys of ruthenium, osmium, and rhenium with the fcc platinum metals should solidify peritectically in their two-phase regions. The metallographic examination of natural osmiridium alloys has been said4 to indicate, by the presence of a martensitic structure, the existence of a transformation or a phase separation. On the basis of superconducting transition temperature measurements, a 70 at. pct 0s alloy was found5 to be two-phase prior to annealing. EXPERIMENTAL The elemental components used in this work were obtained from several suppliers as sponge. The purities, stated by each supplier to be in excess of 99.8 pct, were confirmed in each case by a semiquantitative spectrographic analysis. The pure components were premelted in an inert-gas tungsten arc furnace with the evolution of some fume, crushed, and pickled for use as alloy melting stock. Upon arc melting to the final compositions, no fume evolution was observed. Because weight losses of the order of 15 mg or less were observed in preparing alloy buttons weighing 15 g, "synthetic analyses" were used in determining the compositions of the alloys. Alloys used in this investigation contained 15, 20, 33, 40, 42, 43, 45, 50, 55, 60, 63, 64, 66, 70, 79, and 80 wt pct 0s. Heat treatments of the alloy buttons and pieces thereof were performed in a previously described6 tungsten tube furnace under pressures of 105 torr or less. It was found that homogenization treatments on the specimens were essential to remove the severe coring which was present, a 3-hr treatment above 2300°C removing all the metallographi-cally visible evidence of coring. Following the various heat treatments, the specimens were "vacuum-quenched" by melting a tungsten fuse wire and allowing them to drop onto a water-cooled copper plate. In a few instances, specimens were quenched into molten tin for comparison, but no difference was apparent. Vacuum-quenched specimens cooled from 2400°C to below a red heat in less than 60 sec. Typical equilibration times varied from 3 hr above 2300°C to 88 hr near 1100°C. The utilization of successively longer equilibration times and the approach to equilibrium from both directions indicated that the times used were sufficient to give a close approach to true equilibrium. Heat-treatment temperatures were measured with a calibrated Leeds and Northrup optical pyrometer through a 0.120-in. lateral sight hole in the tungsten heater tube. It was known that the assumption of black-body conditions inside the 1-in.-diam by 10-in.-long tube was unwarranted. The empirical results of work with thermocouples and melting

Jan 1, 1964

By C. E. Lesher

Coal has been fighting a rear-guard action since the last World War. The battle against competitive fuels has been largely guerilla warfare with more sniping within the ranks than of organized opposition. Oil and natural gas are the fuels that over these twenty odd years have driven coal backward and out of many profitable markets. Now, somewhat timidly, the coal industry is trying a new weapon; namely, Research, or let us more properly say, Organized Research. Engineers have been designing this weapon for many years, supported by those interested in coal, including some coal producers. A part of this pioneer work has been Fundamental Research, the Ph.D. kind that is over the heads of most of us. Another part has been aimed at immediate objectives and realizable profits, the practical, man-in-the-street sort. That is Industrial Research. Enough has been accomplished to make a fair exhibit, but whether this new weapon will have sufficient fire power to rout the opposition, whether the industry will really go into production and use it, the next few years will tell. Need foR Coal Research To utter "Research" is to use the modern magic word; to conjure up the miraculous—rubber from weeds; radar; magnesium from sea water; yes, even gasoline from coal. Research is a very general term. It means something different to every man. What is the coal industry seeking with its research; or what should it seek? And, specifically, how is it going about the job; and is it taking the best way? There are many who say that Coal has been asleep at the switch, while Oil and Gas have been taking the energy business. In an organized way this is true. Large-scale, privatelyfinanced research is just started in the Pennsylvania anthracite industry, and it is still a dream for bituminous coal. What has been done so far collectively is purely defensive; as, for instance, to improve mechanical devices for burning coal so as to be able to recover markets for house-heating fuel long since abandoned to oil and gas. To appreciate just how seriously bituminous coal has slipped back in the national economy in the past 2 5 years, one has only to recall that, in the last war the Navy required for its operations all the high-grade, low-volatile coal that could be produced, and that anthracite was withdrawn from the middle and northwest markets to keep the eastern seaboard warm. All coal was "rationed" by zones, if not to individuals. Now the Navy, the Armed forces and the Merchant Marine are propelled by oil and gasoline. Gasoline and heating oil are rationed to individuals. Production of all coal in this country in 1918 reached the historic figure of 678,200,-000 tons, and in 1943, after 25 years, it is expected to reach a special wartime total of 660,000,000 tons. Meanwhile, production of crude oil this year may exceed 1 ,500,000,000 bbl., and like that of natural gas, reach four times the amount produced in 1918.

Jan 1, 1944

By G. R. Gray, T. S. Chapman, J. L. Foster

The wall-building properties of salt-water drilling muds can be improved markedly by the addition of: (I) natural gums, such as traga-canth, karaya, and ghatti; (2) seaweeds, such as Irish moss; or (3) gelatinized starch. Results of laboratory tests have been confirmed by field trials. For drilling operations in which the mud becomes contaminated by salt, either through penetrating salt-bearing rocks or by addition of sea water to the mud, the added cost resulting from the use of one of the substances listed above is more than offset by freedom from stuck drill pipe and ease in running casing. Introduction It has been recognized for many years that oil production might be seriously hampered by infiltration of water from the drilling mud.l-4 As knowledge of the mechanism of the wall-building process advanced, methods were developed for evaluating the filtration characteristics of muds.5-ll The wall-building properties of freshwater muds are commonly regulated by the addition of bentonitic clays, or of agents to promote the dispersion of the natural mud solids. When strata bearing soluble salts are encountered in the course of drilling, the salts are incorporated in the mud; the clay solids are flocculated and water loss is increased tremendously. Methods gen-crally used in controlling filtration of freshwater muds are no longer applicable. The problem of reducing water loss from salt-water muds is not confined to any particular area, but is acute in parts of West Texas. Salt beds several hundred feet thick must be penetrated before the oil-bearing formation is reached. Since the formation drilled does not provide mud-making material, it is necessary to use large quantities of commercial clays, and even the best commercial clay does not afford relief from the problem of high filtration. A laboratory study has been made of methods of improving the filtration characteristics of salt-water muds, and some of the methods have been used in field practice. Laboratory Investigations Procedure Inasmuch as the immediate object of the investigation was the development of means of improving the wall-building properties of muds used in West Texas, an attempt was made to employ muds in the laboratory study comparable to those in field use. Samples of muds used in drilling the producing formations in six wells were secured. The properties of these samples are summarized in Table I, which lists the densities, viscosities, filtrations, and analyses of the filtrates for calcium, chloride, and sulphate. Viscosity was measured in the Stormer viscosimeter at 600 r.p.m. Water loss was determined at 80°F. with the Baroid low-pressure wall-building tester8 at a pressure of 100 lb. per sq. in. Filtration rates are considerably higher than those of usual fresh-water muds, which amount to about 20 C.C. in 30 min. Water loss was so rapid in samples 4, 5 and 6 that filtration was complete in less than 10 min. and the values for 30 min. were extrapolated from the rates at shorter

Jan 1, 1942

By A. D. Mutch

IT has long been known that there are wide variations in the thermo-electric potential of pyrite. In the last few years a study of this variation and other properties of pyrite was carried out at the University of Toronto by F. G. Smith on specimens of pyrite from many localities.1-3 As a result of these studies the pyrite geothermometer was developed by Professor Smith. The calibration of the pyrite geothermometer is based on the assumption that "crystals of any one electronically conducting mineral species deposited at a high temperature have a more positive thermo-electric potential than crystals deposited at a low temperature, and the thermo-electric potential varies continuously between any given limits of the temperature of deposition." The cause of the variation was postulated to be crystal discontinuities, such as lineage boundaries. As yet this postulated relationship has not been established as fact. On theoretical grounds it is indicated that the thermo-electric potential of pyrite or any other partial conductor is dependent upon a number of factors as well as the temperature of formation. For this and other reasons there is ground for doubt as to the validity of the relationship postulated above. To date a large number of readings have been made with the pyrite geothermometer which have been recorded in terms of the calibration of the instrument in degrees centigrade. So far most of the pyrite tested by this technique has been in association with gold ore. The values for the temperature of formation obtained in these tests appear to be reasonable and, in relation to geological problems, to vary in the right sense. Determinations on some specimens not in association with gold ore have given readings that appear to be much too high, taking into account the probable maximum temperature of the host rock. To sum up, although many determinations made with the. pyrite geothermometer appear to give reasonable values for the temperature of formation of the pyrite, there are at the same time other readings which seem anomalous. On the basis of an examination of available results of work with the pyrite geothermometer, two problems must be considered: 1-the validity of the calibration of the pyrite geothermometer; and 2-the nature of the distribution of the thermo-electric potentials of pyrite in relation to the specific problems that have been examined. In this paper the academic problem relating to the validity of the calibration of the pyrite geothermometer will not be discussed. Instead, the variations of thermo-electric potential of pyrite in association with gold veins will be discussed with regard to specific examinations. The first of these two examinations deals with the distribution of thermo-electric potentials of pyrite in association with a gold vein and was carried out in the McIntyre Porcupine Mine, Schumacher, Ont., in the summer of 1949 as part of a study with this technique. The second problem deals with variations of thermo-electric potential of pyrite in gold ore specimens from all over the world. The specimens used in this study were part of the private collection of Frank Ebbutt, geologist for Howe Sound Exploration Co. Results of Detailed and Reconnaissance Studies In discussion of the results of determinations made in these two studies the values of thermo-electric potential in millivolts will be used. It will be noted that in some of the diagrams the determinations are recorded in terms of pyrite geothermometer temperatures. Fig. 1 is a calibration chart relating, pyrite geothermometer temperatures and thermo-electric potentials. A full discussion of the technique is given in the original paper by F. G. Smith.' Briefly, the determinations are made by placing two stainless steel probes, one hot and the other cold, against the surface of the pyrite crystal being tested. The thermo-electric potential that is developed is read with a null-point potentiometer that is calibrated in what

Jan 1, 1952

By L. S. Darken

The manufacture and treatment of metals comprises operations whose effectiveness depends in large measure upon diffusion phenomena. The significance of such phenomena has, for a few simple cases, long been understood, but in more complex cases it has not been adequately recognized. This paper presents a mathematical analysis of some of the cases in which diffusion leads to the formation of a new phase within the metal, and this analysis provides a basis for interpreting quantitatively many apparently diverse experimental observations recorded in the literature, some of which are outlined in the following pages. OBservt1ons Recorded in Literature An outstanding instance is the general type of phenomenon in which diffusion of an element into an alloy is followed by a phase change, which most frequently is a reaction (precipitation) of the diffusing element with one or more components of the alloy to form a compound. Thus in certain alloys heated in contact with oxygen not only the usual oxide scale appears but, in addition, beneath the surface, a well-defined zone in which free oxide particles are dispersed with notabIe uniformity. This zone, commonly referred to as the subscale or zone of internal oxidation, is remarkable in that the visible boundary between it and the unaltered metal is usually sharp. Such a subscale, which appears to have been recognized first in oxidized copper alloys, has been described and studied by C. S. Smith,l by Rhines,2 and by Rhines, Johnson and Anderson;3 but it appears also in other alloys when they are exposed to conditions that bring about the precipitation of some compound, not necessarily an oxide. Another clear case of this same kind is the diffusion of carbon into a steel containing an element such as molybdenum, chromium, vanadium or tungsten, whose carbide is less soluble in iron than iron carbide, the result being that some part of that element is precipitated as a dispersed carbide. A similar phenomenon may occur on the welding of two alloys each of which contains one of a pair of elements that react to form a compound or a new phase of any sort. But in addition to the precipitation of a compound formed from the diffusing element, other effects may result merely from the presence of the diffusing element. For instance, if homogeneous austenite, nearly saturated with respect to carbon, is heated in contact with silicon in the absence of oxygen, one would expect to find, behind the several iron-silicon phases analogous to a scale, a zone of austenite containing dispersed carbide, because of the fact that silicon decreases the solubility of carbon in iron. As still another example, oxidation of an alloy may result in diffusion toward the surface of one or more of the constituents; for instance, during oxidation of a steel containing an element such as "copper, which is less prone to oxidation than iron, there is a notable enrichment of copper just beneath the scale-metal interface. AS an example of a yet more

Jan 1, 1942

By Robert S. Dewey

Drilling in West Texas during 1942 was substantially less than in the previous year. In all. 1267 Wells were drilled, as compared with 2325 wells in 1941. Of these 1267 wells, 1052 oil wells, 10 gas wells and 69 dry holes were drilled in proven fields and 36 oil wells, one gas well and 99 dry holes were wildcat operations. Of the 36 wildcat wells completed as oil producers, 16 led to new field discoveries, three found new productive horizons in old fields, and 17 extended the productive limits of established fields. Where semiwildcat drilling took place along established productive trends, there was often no sharp demarcation between wildcat wells that extend field limits and normal development to fulfil lease obligations, other than the arbitrary classification of a well as a wildcat if it was drilled at a distance of 2 miles from a producing oil well. The dry hole drilled on the edge of a field may have proved a more hazardous operation than a semiwildcat drilled several miles from production but favorably located on structure. The percentage of successful wildcatting ranges from 26.5 down to 14 per cent, dependent upon the degree of inclusion of the semiwildcat operations. Irrespective of which figure was used, the West Texas area maintained its better than average exploratory position. No doubt a number of factors may have influenced the extent of the 1942 development. Among those arising from the economic dislocation attendant on the war effort, the following are worthy of note. Owing to inductions into the armed forces and shipyard competition for mechanically trained men, experienced drilling personnel was sharply reduced, thereby increasing drilling costs and well-completion hazards. Replacement labor has not met the same standard of responsibility or workmanship to which the oil industry has grown accustomed. Increased military consumption of aviation gasoline and other crude products, coupled with decreased domestic consumption of lower-octane gasoline, has stimulated the market demand for the types of sweet crude most readily processed with available refinery equipment to meet war requirements, and has depressed the market demand for the sour West Texas crudes. As a majority of the purchasers of West Texas crude normally ship a substantial portion of sour crude to the refineries on the Atlantic seaboard, the loss and diversion of tanker service between Gulf Coast and north Atlantic ports have further curtailed the market demand for this type of crude oil. As some purchasers of crude oil were able to move by pipe line their West Texas trunk-line capacity to Midwestern refining centers, they were not impelled to curtail purchases of West Texas crude. The varying ability of the purchasers of crude oil to market West Texas crude was reflected back to various fields to which they were connected, causing an unequal distribution of production as among fields and operators. The pipe-line runs from the West Texas-New Mexico area decreased from approximately 354,000 bbl. Per day in January to about 265,000 bbl. in December 1942. .Approximately 2,991,000 bbl. of West

Jan 1, 1943

By S. C. Miller, R. D. Carter, H. G. Riley

A merhod based on theoretical considerations is presented for estimating srabilized performance of gas wells from data obtained from short-term flow tests. Calculated results are presented for II gas wells evaluated with four-to five-hour flow tests. For seven wells on which comparison war available, satisfactory agreement between measured and calculated performance was obfained. Although the final results are favorable, diflerences in flow capacity k,h obtained from flow tests conducted at different rates were observed. This inconsistency did not seriously affect the calculated results in the test wells. INTRODUCTION In order to negotiate the sale of gas from newly drilled gas wells and to plan otherwise for the orderly exploitation of gas reserves, it is necessary to predict the long-term withdrawal rates physically possible for each well. Since low permeability gas wells do not stabilize except after a lengthy period of flow, the operator is unable, without wasting large amounts of gas, to measure directly the stabilized performance prior to contracting for sale of the gas and connecting the well to a pipeline. This problem is not new, but is one which has recently received considerable attention because of the rising importance of natural gas in the economy and new emphasis on the development of gas reserves. Thus, a method is needed for estimating stabilized performance from information obtained from short-flow tests in which stabilized flow is not attained. Such short tests would be suitable for wells not connected to a pipeline since the tests require only small amounts of time, labor and production of gas. Other requirements of such a method are short calculation time and use of a model of the gas well and its reservoir drainage area which is as consistent as possible with present theoretical, experimental and field knowledge. The method presented herein was developed in an effort to meet these requirements. It has been named the "two-Row method". In addition to the section on the evelopment and description of the method, a description of field application of the method and a discussion of well test results are in- cluded. Finally, there is a section on an additional consideration prompted by some of the test results. The Appendix contains certain details of the derivation of the two-flow method and a sample calculation for Test Well 1. MATHEMATICAL DEVELOPMENT AND DESCRIPTION OF THE METHOD The method is based upon the following assumptions: (1) The system can be described as a finite cylindrical gas reservoir produced by a single cylindrical well located at the center of the reservoir. Flow is strictly radial. (2) Flow obeys Darcy's law except very near the well where a quadratic flow law is assumed. (3) The system is also characterized by a laminar flow skin factor. The use of a quadratic or turbulent flow term is more fully justified in Refs. 1 and 2. When such a system is opened at the wellbore to constant rate flow from an initial condition of uniform pressure distribution, the radius or drainage quickly passes through the non-Darcy flow and "skin effect" region imrnediately surrounding the well. After the drainage radius or "transient" has passed beyond this region and before it reaches the external boundary, drawdown can be expressed by'." After the drainage radius reaches the external boundary, stabilized flow exists and drawdown is given by'," Eqs. 1 and 2 form the basis for the method. The validity of these equations will now be examined in the light of some well test data previously available. It has been found by actual measurements on gas wells that the relationship between drawdown and flow rate, that is the performance curve, is closely approximated by' Eq. 3 is a straight line on log-log graph paper. Eq. 2 and, for any lixed value of time, Eq. 1 plot as a curve which is slightly concave upward on log-log graph

By B. A. Kulp, R. R. Reeber

Lattice parameters for the wurtzite form of' CdS mere measured by powder X-ray diffraction techniques over the temperature range 26° to 1000 K'. A negative thermal -expansion coefficient was determined parallel and perpendicular to the c axis below 13.5°K. Near 808°K, the curves of the a, parameter, the differential thermal expansion, and the resistivitv vs absolute temperature exhibited a reversible discontinuity. j\. direct determination of the lattice parameters of CdS over an extended temperature range is of particular use in interpretation of the effects of high pressure on the band structure of semiconductor materials. For example, Langer' has studied the effects of pressure on the absorption edge of CdS from 77°K to room temperature. In order to properly interpret his results it is necessary to know the change in lattice constants as a function of temperature for the wurtzite, zincblende, and rocksalt2 modifications of this material. Thermal-expansion measurements for CdS, wurtzite phase, have previously been determined over a limited temperature range.s74'5 The zincblende phases, of other compounds with similar bonding, have been investigated by Novikova et a! .'' Previous thermal-expansion measurements for metals with hexagonal symmetry have for the most part used bulk sample techniques for low-temperature result. Most X-ray measurements at low temperature have been on materials with cubic symmetry.'jQ The use of X-ray powder-diffraction techniques offers a convenient and accurate method of measurement over a wide temperature range. The X-ray method, besides measuring unit cell size, also provides information about change in structure type and the nature of some of the stacking defects present. I) EXPERIMENTAL PROCEDURE The thermal expansion was measured by X-ray powder-diffraction techniques. Lattice parameters for the range 300" to 1000°K were determined in a 19-cm Unicam camera. From 26" to 300°K a 34-cm back-reflection camera with the Van Arkel" film arrangement was used. The sample was bonded to a copper cold finger below a helium, hydrogen, nitrogen, oxygen, dry ice, or ice brine bath in a metal cryistat. che inner bath was surrounded by another one for radiation shielding. Nitrogen was used in this outer bath for the very low-temperature runs while dry ice and acetone was used for the 195°K point. CuKa X-rays, filtered with a nickel foil, entered the cryostat through a 0.001-in.-thick aluminum window. During a typical 9-hr exposure the sample was continuously rotated through a 30-deg arc. Heat losses from the sample holder limited the minimum temperature attained to 26°K with helium in the inner dewar. Temperature calibration between 25" and 125°K was determined with an Allen Bradley 300-ohm carbon resistor. The resistor was attached to the back of the copper finger with a thin layer of silicone grease. Liquid He, HZ, N2, and O2 baths were used to calibrate the resistor. Temperature variation is estimated to be *2"K with a slightly higher uncertainty at room temperature and 264°K. The thermal expansion of high-purity germanium from 373" to 900°K was measured as a calibration for the Unicam camera. This value was compared with the known value1' for the thermal expansion. A discontinuity in the thermal-expansion coefficient of the CdS a, parameter was observed. Similar discontinuities in the resistivity and differential thermal analysis at the same absolute temperature indicate that the temperature error is *5°K in the temperature range above 500°K. Temperature errors in the Unicam camera below 500°K are appreciably higher due to large gradients in the resistance furnace. II) SAMPLE PREPARATION The CdS was Eagle Picher ultrapure grade. The crystallite size range of the as-received powder

Jan 1, 1965

By J. R. Kyte, C. C. Mattax

Previous workers have developed differential equations to describe oil displacement by water imbibition, but have not explicitly defined the relationship between recovery behavior for a single reservoir matrix block and its size. In the present work, imbibition theory is extended to show that the time required to recover a given fraction of the oil from a matrix block is proportional to the square of the distance between fractures. Using this relationship, recovery behavior for a large reservoir matrix block is predicted from an imbibition test on a small reservoir core sample. The prediction is then extended to analyze recovery behavior for fractured- matrix, water- drive reservoirs in which imbibition is the dominant oil-producing mechanism. Experimental data are presented to support the basic imbibition theory relating matrix block size, fluid viscosity level and permeability to recovery behavior. INTRODUCTION Imbibition has long been recognized as an important factor in recovering oil from water-wet, fractured-matrix reservoirs subjected to water flood or water drive. l-3 Recently, two approaches have been published which might be used to predict imbibition oil-recovery behavior for reservoir-sized matrix blocks. Graham and Richardson4 used a synthetic model to scale a single element of a fractured-matrix reservoir. lair,' on the other hand, used numerical techniques to solve the differential equations describing imbibition in linear and radial systems. This latter method requires auxiliary experimental data in the form of capillary pressure and relative permeability functions. These two approaches, i.e., synthetic models and numerical techniques, have been used to study a variety of reservoir fluid-flow problems. One pur- pose of this work is to present, with experimental verification, a third method for predicting imbibition oil recovery for large reservoir matrix blocks. This method uses scaled imbibition tests on small reservoir core samples to predict field performance. The imbibition tests are easier to perform than the capillary pressure and relative permeability tests required to apply the numerical method. Furthermore, when suitably preserved reservoir-rock samples are used, the properties of the laboratory system are the same as those of the field. This offers an important advantage over the use of synthetic models because there is usually some question as to how accurately reservoir-rock properties can be duplicated in such models. Based on the recovery behavior for a unit matrix block, an analysis is presented to predict oil recovery for a fractured, water-drive reservoir made up of many such unit blocks. In the analysis, it is assumed that the flow resistance and the volume of the reservoir fracture system are negligible compared with that of the porous matrix. These assumptions are generally consistent with observed characteristics of many fractured-matrix reservoirs, and have been employed in previous studies.2,3,6-8 further assumed that the effect of gravity on flow in the matrix blocks is negligible. On first thought, the latter assumption might appear to seriously limit application of the method. However, in a fractured reservoir, the effect of gravity on flow in a matrix block will be restricted by the height of the block. Furthermore, matrix permeabilities are often very low (10 md or less) in such reservoirs. This means that capillary or imbibition forces will be large, thus tending to minimize the relative importance of gravity. For these reasons, imbibition should be the dominant oil-recovery mechanism in many fractured-matrix, water-drive reservoirs. The predictive method presented in this report is applicable to such reservoirs. SCALING IMBIBITION THEORY The "scaling laws" applicable to the operation.

By C. R. McEwen

This paper presents a technique for calculating the original amount of hydrocarbon in place in a petroleum reservoir, and for determining the constants characterizing the aquifer performance, based on pressure-production data. A method for doing this based on a least-squares line-fitting computationwus proposed by vanEverdingen,Timmerman andMcMahon in 1953. We found that their method would not work when there is error in the reservoir pressure data — even moderate error. The technique presented here appears to give reasonable answers when pressure data are uncertain to the degree expected in reservoir pressure determinations. The major change introduced in the present analysis is to limit the least-squares line-fitting to yield only one constant— the amount of hydrocarbon in place. The water-influx constant is then taken as proportional to the oil (or gas) in place. The constant of proportionality can be computed from estimates of effective compressibility and reservoir water saturation. It is also pointed out that the commonly used least-squares analysis assumes all of the uncertainty to be in the dependent variable. The material balance should be arranged so that this condition is fulfilled if correct inferences are to be made from statistical calculations. Examples are shown of the application of the new technique to gas reservoirs—both hypothetical and real—and to the oil-reservoir example of van Ever-dingen, Timmerman and McMahon. INTRODUCTION The amount of hydrocarbon originally in place in a petroleum resenroir can be estimated by means of the material-balance calculation. Simultaneous observations of pressure and amounts of produced fluids are required, together with the PVT data applicable to the reservoir fluids. If water encroachment is occurring, it is desirable to try to infer the behavior of the aquifer, as well as the original hydrocarbon in place, from the pressure-production data. This imposes additional demands on the method of calculation, and uncertainty in the data can result in large uncertainty in the answer. In addition, if the size of a gas cap is to be established, the whole problem becomes indeterminate, as pointed out by Woods and Muskat.1 Brownscombe and Collins2 simulated a gas reservoir and its aquifer on a reservoir analyzer and derived quantitative information on the effect of uncertainty in pressure and aquifer permeability on computed gas in place. Among the various techniques of estimating the performance of an aquifer, the method of van Ever-dingen and Hurst? based on compressible flow theory, seems to have been the most generally successful (see Ref. 4, for example). In this paper we shall confine ourselves to their representation of the aquifer. In 1953,' van Everdingen, Timmerman and McMahon5 introduced a statistical technique for deriving the amount of oil originally in place and the parameters which describe the aquifer. (We shall refer to this technique as the "VTM method'', as suggested by Mueller.6) Their example reservoir had no gas cap. It has been our experience that the VTM method gives a reasonable answer when the data are very accurate, but that inaccuracy (particularly in pressure) can cause the method to break down. The effect was first observed in gas reservoirs, but has since been seen in oil reservoirs also. In this paper we present another statistical method which has been successful in achieving a reasonable answer where the VTM method has failed. In the new method, one less parameter is derived from material-balance computations. It is assumed that values can be established for effective compressibility in the aquifer and reservoir water saturation independently of the material-balance calculation. The water-influx constant can then be obtained from these data and the quantity of hydrocarbon in place.

By F. G. Tahmoush, N. J. Grant, E. P. Abrahamson

The effect of grain size on the brittle -ductile transition temperature of pure iron and three dilute Fe-W alloys has been investigated by slow bend tests. The brittle-ductile transition temperature for pure iron increased with increasing grain sizes from 8000 to 500 grains per sq mm where the transition temperature then decreased with further increase in grain size. The dilute additions of tungsten lowered the transition temperature for fine grain sizes, suppressed a reversal of the curve in the coarse grained portion, and raised the transition temperature for this region. The frequency of twin occurrence increased with increasing grain size and decreasing temperature. The object of the present investigation was to re-examine the effect of grain size on the brittle -ductile transition of pure iron and several dilute Fe-W alloys. Current literature normally presents a simple relationship between grain size and the brittle-ductile transition temperature, namely, that the transition temperature increases with increasing grain size. Heslop and etch' have studied the transition temperature of mild steel by V-notch Charpy impact tests for the grain size range between 200 and 6000 grains per sq mm. The result was a linear plot of In 1-1/2 vs brittle-ductile transition temperature, where 1 is the grain diameter. Recent experiments by sipos2 revealed the possibility of a reversal in the slope of the grain size vs transition temperature plot for pure iron; however, his investigation was limited in scope, and the data obtained were insufficient to permit a definitive curve. The present investigation was undertaken in an effort to confirm or extend the grain size effect observed in iron by Sipos. PROCEDURE All alloys were vacuum induction melted, using 99.95 pct Fe containing 0.03 pct 0 and 0.004 pct C. Four ingots were made, ranging from pure iron to iron with 0.035 pct W. The chemical composition of each alloy, after processing, is given in Table I. The four alloys were prepared as 45 lb heats and cast into 4 in. diam by 16 in. molds. They were then extruded into 3/4 in. rods at 1800oF. Specimens for chemical analysis, taken from various positions along the rods, revealed no variation in tungsten content along the length. The extruded rods were reduced to 0.156 in. diam stock by a series of cold swaging operations involving intermediate vacuum annealing treatments. This procedure yielded a final cold reduction in area ranging from 10 to 90 pct. The swaged rods were chemically cleaned, cold pressed to a cross section of 0.10 by 0.18 by 1.0 in. long (2.54 by 4.73 by 25 mm). The specimens were wrapped in iron foil and vacuum sealed (10-4 mm Hg) in quartz. Various heat treatments at temperatures from 700" to 1300oC were utilized to produce grain sizes from 8000 to 1 grain per sq mm. Grain sizes were determined by measuring the average area of grains in a polished section. In specimens with grain size greater than 20 grains per sq mm, the total number of grains in the cross section was counted and then divided by the area to yield grains per sq mm. Grain size was measured both for longitudinal and transverse cross sections. The average of the two measurements was plotted vs transition temperature. An Instron Table Model testing machine was used to determine the transition temperature of specimens tested in three point horizontal bending. The specimen was supported by two 1/4 in. dowels one in. apart. Bending was accomplished with a push rod, the end of which had an 1/8 in. radius. The head speed was 50 in. per min. Temperatures were established through the use

Jan 1, 1963