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By W. R. Hibbard

Evidence is presented which confirms previous findings that models of solution strengthening depending solely on lattice parameter changes are incomplete. Direct evidence for the Suzuki interaction of chemical effects was obtained from alloys with constant lattice parameter, for which solution strengthening was nearly independent of temperature from 300° to 20°K. SOLUTION hardening principles have been reviewed recently by Parker and Hazlett.' In addition, the interactions of dislocations and solute atoms were reviewed by Cottrell.' It is not proposed to review this information again here, but to refer only to those details which are pertinent to the developments which have occurred since these papers were published. Literature Survey To set the stage, it has been known for some time that solid solutions are stronger than the pure parent metals, and that the strength increases with increasing amounts of alloying element. One of the most extensive earlier investigations was that of Lacy and Gensamer,3 who reported that the solid solution strengthening of iron is a power function of the composition, that the relative strengthening is a function of the solubility limit, and that the rate of strain hardening is a function of the amount of solution hardening. Thus, the slope of the plastic portion of the stress-strain curve increases with increasing yield strength. An approach to the development of principles resulted from work by Gulyeav,4 who reported that the strengthening effect of solid solution alloys is periodic in character when plotted as a function of the atomic number of the solute. A more quantitative approach was to relate the amount of solution hardening to the lattice parameter of a solid solution. This was done quite early by Norbury,5 and later by Brick, Martin, and Angier,6 Frye and Hume-Rothery,7 and French and Hibbard. This relationship is only approximate in character. The next development was to relate the amount of solution hardening to lattice stress, as proposed by Frye and co-workers.9 They calculated what they called ionic overlap from the lattice parameter changes represented as a change in volume, using Bridgman's hydrostatic compression equation. The resulting correlation was somewhat improved as compared to the simple correlation with lattice parameter. The next step was carried out by Dorn, Pietrow-sky, and Tietz,10 who suggested an effect of valence differences in addition to the effect of lattice parameter. Their proposed parameter shows flow stress as a single valued function of the concentration and a relationship involving these two atomic variables. In addition, they contributed new data on the temperature dependence of solution hardening which indicated that it was a strong function of temperature for aluminum alloys. Allen, Schofield, and Tate11 carried the valency effect even further by reporting data indicating that with a given solvent element the stress-strain curve is a function of electron density, entirely neglecting the size factor, which varied by a factor of two. This evidence led to a quantum mechanical calculation by Cottrell, Hunter, and Nabarro,12 based on the formation of a dipole around an edge disloca-

Jan 1, 1959

By S. M. M. Safvi, A. Jowett

Small-scale continuous flotation tests are described in which the influence of 1) pulp density and 2) feed rate on the rate of flotation are investigated. The results provide further evidence of first-order kinetics for flotation and indicate that tests at different feed rates provide a particularly simple method of determining rate constants. Flotation kinetics are discussed in general terms. Over a period of many years numerous research workers have studied the rate of recovery of valuable materials from flotation pulps with a view to deter-mining the mechanism of the froth flotation process. Froth flo ation is fundamentally a collision process involviug at some stage collision and then mutual attachment between air bubbles and mineral particles. It is possible to draw analogies therefore between the flotation process involving mainly macroscopic particles and the ordinary processes of chemical reaction kinetics involving collisions between atoms, molecules and ions. By adopting this analogy we may postulate a general equation representing the kinetics of the flotation process: -dC/dt =K.CC ,Aa (1) The rate constant, K, will be a complex function involving reagent concentrations, particle and bubble sizes, induction times and no doubt flotation cell design. However, these are factors which can be kept constant in any series of experiments, permitting investigation of the exponents a and c, which determine the order of the reaction occurring in flotation. The various research investigations carried out so far have all aimed at evaluating a and c and in the majority of cases only since the concentration of air has usually been kept constant in a series of tests, so that a relationship of the following type has been investigated: -dC/dt = K1 Cc (2) The techniques of both batch testing and continuous testing have been used to investigate this relationship. The technique of continuous testing, in which steady-state conditions are established, permits direct investigation of the above equation. In the case of batch testing, C is decreasing continuously

Jan 1, 1961

By W. C. Peters, M. W. Pullen, C. A. Bays

During the past three and a half years considerable improvement in the techniques of solution extraction of salt has been made by the use of wells which are cross-connected by hydraulic fracture at the base of the salt. Fracture is initiated by the application of hydraulic pressure. Underreaming and perforating techniques are used to control initiation. The fracture is then extended by continuous pumping until a pressure communication is obtained. Pressure communication is followed by washing-through to obtain a low-pressure connection. Well construction using non-shrinking cements that will bond with the salt and with associated strata is essential to the process. The connecting procedure described permits solution to attack the salt deposit from its base upward, thereby permitting greater recovery, fewer well repairs, better saturation of brine, and overall economy of development and operation. The fracture method of cross-connection requires special pumping of the fluid and is limited by present experience to initial well spacings up to about 1200 feet. The method has been used in bedded salts and is applicable for wells in salt domes. Since spring of 1956, new developnents in salt extraction wells have followed procedures substantially different from those in prior use. Although multiple well systems, connected either by the natural consequence of the solution process or by undercutting under protective pads, have been used previously, the past three and a half years have brought about new designs and new operation procedures based on cross-connection of the wells using hydraulic fracture. To date these techniques have been applied largely in the bedded salt deposits of Michigan, Ontario, Ohio, West Virginia, and New York. To the writers' knowledge they have not been used in salt dome wells. The methods have not yet been in use for a sufficient period to permit any statistical comparison with the older methods. It is evident from experience to date that the methods result in higher recoveries, lower capital and operating costs, better saturation of produced brine, reduced well maintenance and repair, and in considerably fewer production units to insure

Jan 1, 1961

By W. A. Tiller, J. D. Harrison

HOT pressing of powder particles has gained importance recently, since it affords a method in which high densities are rapidly attained. In a recent study on hot pressing of alumina powders, Mangsen, Lam-bertson, and Best1 have shown within the limits of their experiment, the validity the rate equation for densification in hot pressing, originally proposed by Murray, Livey, and Williams.2 i.e., where D = fraction of theoretical density, t = time, P = pressure and 77 is the viscosity, all in appropriate units. This equation was derived from earlier work of Shuttleworth and Mackenzie3 which is based on the closing of spherical pores under the action of surface tension. The integrated form of this equation yields a straight-line relation between log (1 - D) and t. Such conditions were found by Felten4 to be true only after extended periods of pressing. In an endeavor to quantitatively evaluate the exactitude of this equation in the initial sintering stage, i.e., prior to sealing of the pores, spherical anti-

Jan 1, 1962

By D. W. Smith, Robert F. Mehl

It has been shown by numerous studies that the orientations of new metal crystals are determined by the orientations of the crystals in the original matrix, whether these new crystals are formed by recrystalliza-tion, by precipitation from solid solutions, or by transitions in the solid state. The orientations of crystals formed by recrystallization of cold-worked metals that bear preferred orientations are occasionally simply related to the initial preferred orientation; often, however, the relationship is not simple, but complicated and obscure in origin.1 The orientations of crystals formed by precipitation from solid solutions have been shown by many studies in this and other countries to be determined by the orientation of the crystals of the solid solution stable at the higher temperatures, though here again complicated cases have been found and no general theory is available.2 Related to this latter class are the relationships found in crystals formed by suppressed transforma-

Jan 1, 1935

By D. W. Smith, Robert F. Mehl

It has been shown by numerous studies that the orientations of new metal crystals are determined by the orientations of the crystals in the original matrix, whether these new crystals are formed by recrystalliza-tion, by precipitation from solid solutions, or by transitions in the solid state. The orientations of crystals formed by recrystallization of cold-worked metals that bear preferred orientations are occasionally simply related to the initial preferred orientation; often, however, the relationship is not simple, but complicated and obscure in origin.1 The orientations of crystals formed by precipitation from solid solutions have been shown by many studies in this and other countries to be determined by the orientation of the crystals of the solid solution stable at the higher temperatures, though here again complicated cases have been found and no general theory is available.2 Related to this latter class are the relationships found in crystals formed by suppressed transforma-

Jan 1, 1935

By C. David Mann

Metal prices continued to improve in 1964, resulting in the opening of new mines and re- activation of old ones. Larger and deeper shafts are being bored. At the AEC's Nevada Test Site, a 72-in. diam shaft is being bored to 3200 ft. In New Mexico a 1650-ft shaft was bored with a 48-in. bit, then reamed to 124 in. to 935 ft, and 102 in. to 1650 ft. Deviation was only 26 in. In California a shaft sinking machine has been developed which combines drilling and mucking equipment into one mobile, integral unit.

Jan 2, 1965

Jan 1, 1970

By W. D. Johnston, T. P. Thayer

THE minerals that collectively are known as chromite form an isomorphous series of the general formula (Mg,Fe) 0. (Cr,Al,Fe) 203. So wide is the range in chemical composition in this group that chrome ore consisting entirely of the mineral chromite may range from less than 30 pct to more than 60 pct Cr203. The most comprehensive published data on the chemical com- position of chromite are by Stevens,62 who made complete analyses of 52 samples of chromite concentrate from many localities in North, Cen- [ ] tral, and South America. These samples were mechanically purified to remove associated silicates and might be regarded as the cleanest chromite that could be obtained by any mechanical milling process. Fig 1 shows the predominant zone of isomorphism, within the triangular prism of composition defined by the mineralogical end members of the series, wherein his analyzed samples fell.

Jan 1, 1949

By N. A. D. Parlee, I. D. Shah, W. C. Phelps

THIS note reports on a continuation of a program on the thermodynamics of Fe-S-X systems in the "steel-burning" temperature range begun by Bock, Barloga, and parlee.' Small coils of 0.039-in.-diameter pure iron (Ferrovac-E) wire were equilibrated with Fe-S-0 melts in ingot iron crucibles under argon at 1324°C in the assembly shown in Fig. 1, the lower part of which was heated in a large Globar furnace. Fig. 1 shows (R) the coiled iron wire sample, (M) the Fe-S-0 melt prepared from desired proportions of ferrous sulfide and ferric oxide, (K) the iron crucible, (I) a mullite guide tube, (J) an alumina crucible, (L) alundum sand, (N) crushed mullite, (Q) hollow cylinders of K30 brick, (C) a steel rod, (B), (El, (F), (G), (P), and (O), details of brass water-cooled head, and (H) a mullite tube 2-3/4 in. ID and 26 in. long. The rod (C) bearing the sample could be removed at will and be replaced by a tube for sampling the melt, or by a thermocouple for comparing the melt temperature with a control thermocouple not far from the 2-3/4-in. mullite tube. After equilibration the iron coils were treated with acid to remove the outer layer of metal and then they were analyzed for sulfur by a standard combustion method. The melt samples were analyzed for oxygen by a variation of Lander's2 hydrogen-reduction method for mattes, and for sulfur by the ASTM combustion-iodometric method NO. E 30-47. When the results of some forty-two runs were examined it was found that the sulfur and oxygen contents of the equilibrated melts showed good consistency, in that the plotted compositions fell along the smooth curve shown in Fig. 2. The points on this curve represent the experimental compositions of melts in equilibrium with ?-iron (Fe-S-0) solid solutions. These solid solutions are saturated with sulfur and oxygen with respect to the melt and therefore have the same sulfur and oxygen activities as the melt. The curve drawn through the points therefore delineates the ? liquidus. It falls in such a position as to roughly confirm the liquidus curves of Hilty and crafts3 at 1200" and 1300°C which are

Jan 1, 1965

By R. W. Stahl

Employees and dollars are necessary to all enterprises and any force, such as fire, which destroys either, can bring very serious consequences, including business failure. Since everyone acknowledges the necessity of conserving human life, we will devote most of our paper to the economic factors involved. A coal-mine fire is considerably more difficult to combat than a fire in a surface building because of the combustible surroundings in the mine, the explosive gases emitted from the coal, the suspension of explosive dust when mine timbers burn and the unsupported roof falls, the limited space in which approach to the fire can be made, and the limited avenues of escape. A survey of coal-mine-fire protection indicated that a rather low value was being placed on property and equipment. This prompted comparison with other industries. The comments made in this comparison are not intended as an indictment of the coal industry, since we do have mines that are well protected against fire, but the comments on conditions at the mines visited are factual and may help others to improve similar conditions. SURVEY PROCEDURES Plants of the steel, aluminum, rubber, chemical, and petroleum industries were surveyed, and all facets of the fire-protection scheme were covered. The industrial plant invariably had four times as much water readily available for instant use than the mine. In many mines where water is available, no equipment for applying it is provided, such as hose, nozzles, and adapters, so that time is lost in collecting this equipment. (See Table I.) EXTINGUISHERS Many more and generally larger portable extinpishers are available at the plant as compared to the mine. The extinguishers are generally placed nearer to sources of danger. In addition, respiratory protective equipment is always available at strategic points in plants but only in a few mines. (See Figs. 1 and Table 11) INSPECTING AND TESTING EQUIPMENT Plant water facilities are checked weekly and flushed at 6-month intervals, and hose is pressure-tested at least yearly; some mines check water yearly, but hose is not tested unless used. Fire extinguishers are inspected weekly in plants and completely overhauled yearly; one mine had monthly checks and overhauls only after use. FIRE BRIGADES AND TRAINING Every plant had designated fire-fighters and some complete full-time brigades; at one mine a chief mechanic was designated as being in charge of fires, and other depended entirely upon officials who might not be familiar with the equipment. COST OF FIRES AND PERCENTAGE OF CAPITAL INVESTMENT IN FIRE PROTECTION The direct cost of recent mine fires ranged from $128,000 to $240,000; indirect costs, such as lost tonnage, idled equipment, lost orders, and the like might run the cost to over $500,000. (See Figs. 2 and 3).

Jan 1, 1961

By B. D. Lichter

In a previous paper, Oelsen, Schuermann, and Hey-nertl pointed out the possibility of obtaining complete thermodynamic functions for alloy systems from calorimetric measurements alone. Specifically, if the heat content of a heterogeneous, multicomponent system is known as a function of temperature and composition, then it is possible to derive the heats, entropies, and free energies of formation of liquid phases and of solid intermediate phases of fixed composition. The authors present equations and graphical techniques applicable to eutectic systems and systems with intermediate phases without solid solubility at lower temperatures. eijering has considered possible extension of the treatment to systems with complete solid-state miscibility at lower temperatures; however, experimental difficulties practically restrict the method to systems with very limited miscibility in the solid state. The purpose of this note is to present an alternative derivation of the heats and entropies of formation of liquid phases and of solid intermediate phases from heat-content measurements alone. Fig. 1 shows three types of phase diagram to which the analysis may be applied. If the heat content is determined as a function of composition x, at temperature T, we have quite generally and the heat of mixing of the liquid is obtained directly from heat-content measurements. If the temperature T lies in a two-phase region (solid-liquid) then

Jan 1, 1967

By Jack L. Taylor

As expected from similar crystal structures and favorable atomic size factors, titanium, vanadium, and molybdenum are completely soluble in one another above the transformation temperature of titanium. The fl phase parameters of the continuous solid solution are shown graphically. Limiting compositions for retained fl phase have been determined. VANADIUM and molybdenum both have body-centered-cubic structures at all temperatures and, from the atomic diameter comparison factor, 3.9 pct, would be expected to form a complete series of solid solutions. The existence of complete solubility has been confirmed by work' at the Jet Propulsion Laboratory. Furthermore, vanadium and molybdenum have favorable atomic size factors to form complete binary solid solutions with the B phase, high temperature form of titanium, which also has body-centered-cubic structure. Pietro-kowsky and Duwez' and Hansen et al." have established the existence of the complete series of solutions in these binary systems. It would be logical, therefore, to expect that p-titanium, vanadium, and molybdenum would be completely soluble in one

Jan 1, 1957

By William B. Hughes

The rubber-sleeve core barrel was developed to improve core recovery from unconsolidated sands, where it is most difficult to obtain cores with conventional barrels. The use of a rubber-sleeve core retainer, together with other departures from clsual design, has required a considerable amount of testing to prove its op-erability. Tests run in shallow experimental holes and in drilling wells in the U. S. and Vemzuela have, to a large extent, proved the operation of the barrel. Internal mechanism troubles, such as sandbinding of the sleeve, have been largely overcome. Cores have been recovered from completely unconsolidated sands where conventional coring has almost been abandoned because of poor recovery. In addition to retaining the core until brought to the surface, the barrel gives a "packaged-ar-cut" core, which is coilverzient for handling and transportatiorz. In the initial work, drag blade cutters, roller cutters, and tungsten carbide insert cutters were usrd for cutting unconsolidated sands. Further bit head development is presently being conducted using diamond heads in unconsolidated sands where shaler, hard sands, and limestones are encountered in adjacent formations. Thir work should render the barrel capable of cratting and recovering most types of formations, possibly including broken and frac- tured fornlations. This development is being carried on in cooperation with a diamond bit manufacturer. INTRODUCTIO N For many years the oil industry has needed greater recovery of cores from unconsolidated formations. Conventional equipment has been used to core unconsolidated sands with little success. Specifically, a core barrel was needed which would recover unconsolidated sands in a condition that would give useful reservoir information. DEVELOPMENT OF 'THE RUBBER-SLEEVE CORE BARREL Basic Requirements of Unconsolidated Sand Corino The basic need was defined as a core barrel that would obtain a continuous unconsolidated core with sand grains in place as deposited in the formation. A preliminary survey of coring equipment and search of the literature pointed out the weaknesses of conventional core barrels. Laboratory tests using unconsolidated sand in a metal tube simulated actual sand movement into the core barrel during conventional coring. In conventional barrels the core sometimes crumbles and bridges, or fails under compressive column action, becomes oversize, and wedges against the walls of the inner barrel. The core barrel requirements established by the surveys and preliminary tests are as follows. 1. The core should be held to- gether as it is cut so it cannot crumble and bridge against the walls of the coring tool, care being taken not to permit damage from fluid circulation. 2. The core should be continuously supported as it is cut so it will not have to support itself in compression. 3. The core should be packaged in the barrel to retain an undisturbed condition during the trip out of the well. The packaging should be such that the core can be removed from the barrel and shipped to the core analysis laboratory without physical disturbance or alteration of fluid content by exposure to the atmosphere. Operation of the Rubber-Sleeve Core Barrel The rubber-sleeve core barrel (Fig. 1) meets the basic requirements for the recovery of unconsolidated sands.

By Albert Sauveur

It is delightful to read a technical paper like that of J. E. Johnson, The Effect of High Carbon on the Quality of Charcoal-Iron, presented in October, 1912, at the Cleveland meeting of the American Institute of Mining Engineers.' The clear, simple, and straightforward manner in which he describes his experiments and results makes you feel as if you had been, so to speak, at his elbow during the course of his investigations, while his method of procedure is so rational that you can fairly anticipate each step in the logical sequence of the tests performed. The following notes suggested by Mr. Johnson's paper are presented here in the hope that they may help, if only a mite, towards the final solution of a problem of considerable scientific and industrial importance. Physical Properties of Cast-Iron us. Its Ultimate Composition. Mr. Johnson writes that " an investigation along the lines of consumption showed that different irons have different characters totally independent of their analyses," and he declares that " the presence or absence of these elements [meaning carbon, phosphorus, silicon, and manganese] alone will not account for all, scarcely for a half, of the facts which have long been known." He further tells us that some foundries have " proved, by the most irrefutable tests, that they could take a certain iron of a given analysis and produce certain results," while with " another iron of the same analysis they could not produce these results at all." I feel confident that every experienced and thinking metallurgist will readily believe Mr. Johnson's statements and will share his views in regard to the hopelessness of inferring the

Jan 1, 1914

By Charles S. Barrett

NUMEROUS determinations1-7 of the tex-ture of cold-rolled polycrystalline iron, steel, and ferritic alloys have been made with good agreement among the various observers as to the principal features of the texture common to all, but there has been no adequate explanation of the texture in terms of the behavior of individual grains. This study presents an explanation of the texture based on the observed rotation of single crystals when deformed in a manner similar to a grain in the aggregate, a method we have found useful in leading to a better understanding of compression and tension textures;8,9,10 in particular, the aim has been to determine experimentally the end orientations of rolled single crystals of iron. These are discussed in connection with the point of view of Wever1 and of Boas and Schmid2 that the rolling texture is a simple compression texture (compression normal to the rolling plane) superimposed on a simple tension texture (tension in the roll-ing direction), and the point of view of Kurdjumow and Sachs3 that three ideal end orientations exist.

Jan 1, 1940

By D. R. Parrish, F. F. Craig

In some respects, forward combustion (alias: fie-flooding, underground combustion, in-situ combustion, dry combustion) is an efficient oil recovery method. For example, its displacement efficiency (as much as 95 percent in reservoirs with high porosity and high oil saturation) is good. In its use of heat, however, forward combustion is grossly inefficient. Most of the heat generated during forward combustion is wasted. About one-fifth of the heat is picked up by the incoming air and re-used (regenerated); the remainder is left behind the combustion zone and ultimately is lost. Compressed air is expensive, and heat generated from compressed air via underground combustion is too valuable to be thrown away. Improvement is needed. Since the early 1950's, improvements in forward combustion by addition of water injection have been discussed, particularly in the patent literature, with increasing frequency.'-'' These concepts are based on the fact that relatively inexpensive water can be used to pick up much of the heat that is ordinarily wasted during forward combustion, and transport it forward to a more useful place, thereby reducing the amount of air required to move a heat front through the reservoir. Several approaches have been proposed. Merriam and Squires1 taught that a combustible (fuel) gas should be injected along with the air and water. This, however, would give at least a tendency toward reverse combustion instead of forward combustion, and would reduce the velocity of the heat bank, defeating the primary purpose of the water injection. Pelzer2 described primarily a batchwise method of forward combustion and water flooding. He advocated burning part way through a reservoir with forward combustion, then switching from air to water injection alone to push the heat toward the producing wells. Though possible, this method has serious disadvantages, the major one being that, by the time water injection is started, much of the heat has been irretrievably lost to the overlying and underlying formations. We have described what is considered a practical Combination Of Forward Combustion And Water-flooding (COFCAW).3,4 Air and water are injected simultaneously (or alternately) after a small heat bank has been formed by forward combustion. Some of the injected fluid fills up the region behind the heat bank; the rest enters the heat bank. Upon encountering heated rock, the water is converted into steam, which then flows ahead of the combustion zone and displaces much of the oil in place. Only enough air is injected to provide heat for vaporization of the water and to compensate for reservoir heat losses. Since the size of the heat bank is minimized, heat losses also are minimized. Because of more efficient oil displacement ahead of the combustion zone, fuel consumption is reduced. Too, unlike a forward combustion zone that cannot move until all fuel at a point has been consumed, COFCAW leaves some

Jan 1, 1970

By L. H. Simons, H. H. Spain

I NT RODUCTION Theory indicates that linear water-floods should exhibit scaling and stabilization properties in both oil-wet and water-wet porous media'. Experimental verification of these proper-ties in oil-wet media was obtained some time ago', and more recently, Perkins', employing a high permeability unconsoli dated sand and a low oil-to-water viscosity ratio, has obtained flooding data in a water-wet medium which follow the pattern of scaling and stabilization. Also, Root and Calhoun3 have found similar trends in the displacement of gas by liquids from unconsolidated sands. In general, however, the experimen-tal evidence appears still somewhat conflicting since scaling and stabilization of water floods in water-wet media has not been observed in most of the studies to date'.".'. The purpose of this paper is to provide a more comprehensive picture of waterflood behavior in water-wet media and to corroborate the validity of the scaling and stabiliza-tion concepts. The need for differentiating between the intrinsic nature of water-oil displacements inside a porous medium and perturbating secondary end effects is discussed, pertinent experimental procedures are outlined and the results of flooding tests conducted at low and at high oil-to-water viscosity ratios on con- solidated, water-wet Alundum cores are analyzed. END EFFECTS IN WATER-WET MEDIA Outlet End Effects The peculiar feature of the outlet end effect in water-wet cores is that it not only results in an excessive wetting phase saturation at the outflow face,'.' but that it also retards the moment of water breakthrough: i.e., causes an undue delay in the appearance of water in the produced effluent. Conditions existing in a water-wet core when water first arrives at the outflow face are schematically shown in Fig. 1. At this flooding stage the saturation distribution, Fig. la, has not yet been distorted by the outlet end effect. A water-invaded pore at the outlet core face, opening into the oil-filled void space between the end of the core and the end plate of the flooding cell, is illustrated in Fig. lb. The curvature of the water-oil interface is concave toward the outlet, and the pressure on the water side of the interface is lower than on the oil side by an amount equal to a certain capillary pressure (Fig. lc). Before the water (of this particular pore) can be produced from the core, it is apparent that the pressure in the water phase must exceed that in the oil outside the core. Accordingly. when water first reaches the outlet face, it will not leave the core but will accumulate inside, and only oil will be produced. Eventually, as the water injection is continued. sufficient pressure is built up in the water to reverse the curvature of the interfaces in the outlet pores, and only then will water be produced from the core. This stage, illustrated in Fig. 2. corresponds to the conventional "water breakthrough" observed in flooding experiments. For purposes of discussion, it is convenient to distinguish between the flooding stage at which water first arrives at the outlet face of a core (Fig. 1) and the stage at which water is first produced from the core ( Fig. 2). The former will be referred to as "water arrival" and the latter water breakthrough. In oil-wet media

By P. K. Leung, S. R. Allada, P. M. Dranchuk, D. Quon

The alternating direction explicit procedure (ADEP) makes use of the boundary conditions to reduce multi-dimensional problems to a series of one-dimensional problems. The method, previously applied to reservoirs containing only an under-saturated oil, has now been extended to cover the case of natural gas reservoirs. l his involves solving a non-linear partial differential equation, application of the procedure is straightforward and no calcuIational problems were encountered. INTRODUCTION There has been a growing interest in formulating mathematical models of petroleum and natural gas reservoirs — models which permit the engineer to examine and evaluate the physical and economic consequences of various alternative production policies. The tremendous reduction in the cost of solving such models in recent years has made possible their use as an almost routine management tool. This reduction is the result not only of improved computer hardware but also of the development of more efficient mathematical techniques. The present paper is concerned with the application of a recently proposed numerical method (ADEP) to two-dimensional gas reservoirs. STATEMENT OF THE PROBLEM Given a two-dimensional Region R, bounded by a closed Curve C (Fig. 1) such that the behavior on Curve C is known, the differential mass balance for each fluid phase in R, neglecting gravitational effects and assuming Darcy's law for fluid transport, can be written as:

Jan 1, 1967

By Robert Bakish, William D. Robertson

AFTER more than fifty years of investigation and continuing failure in service, a satisfactory mechanism to explain stress corrosion cracking in homogeneous alloys is still lacking. The relative chemical activity of grain boundaries and adjacent grains, inferred from the boundary structure, has been used to explain intergranular cracking in a brass.' This concept is probably correct as a general hypothesis, but it requires much more extensive development in order to explain satisfactorily the observed phenomena. For example, the specific function of the solute in an alloy must be considered, because intergranular failure does not occur in pure metals,' which are structurally similar to homogeneous alloys. Also, in this connection, an inter crystalline fracture path in binary copper alloys can be changed to a transcrystalline path by relatively small ternary additions.' The fracture path in ß brass is predominantly transcrystalline,' in contrast with an inter crystalline path in a brass. Whether the two different fracture paths are the result of a difference in composition, crystal structure, or the state of long range order is unknown and cannot be determined with ß brass, because only the ordered state can be obtained at room temperature. The study of chemical activity at structural sites in the Cu-Zn system is restricted by the formation of opaque films in an ammonia environment in which stress corrosion cracking is generally observed. Furthermore, both components of the alloy are chemically active and the interpretation of observations is therefore relatively complicated. The Cu-Au system is a better choice for the purpose of studying structural factors. In particular, CuAu is very susceptible to cracking in ferric chloride and opaque films are not formed in this solution; it may be obtained in different states of long and short range order; and, finally, only copper is oxidized in dilute ferric chloride, which considerably simplifies the chemical problem. To provide information necessary for a more general explanation of stress corrosion cracking in homogeneous solid solutions, the following structural factors have been investigated in a Cu-Au alloy having a composition corresponding to Cu,Au: 1) the effect of long and short range order; 2) the structural sites from which copper is removed from the annealed and cold worked polycrystalline alloy; and 3) the effect of annealing time and temperature on structural reactions in the cold worked alloy. Experimental Procedure A Cu-Au alloy of nominal Cu3Au composition was cast from cathode copper and high purity gold and fabricated into sheet and wire. Chemical analysis for copper and gold indicated 48.92 wt pct Cu and 51.01 pct Au. Quantitative spectrographic analysis indicated 0.01 pct Ag, 0.002 pct Pd, 0.001 pct Pb, and 0.002 pct Fe, with traces of magnesium, silicon, and zinc. Presumably most of the remaining 0.055 pct corresponds to the limits of analytical precision. Heat treatments of wire and sheet were conducted in argon or vacuum. Wire specimens, 0.064 in. diam, were heated for 1 hr at 850 °C to establish a definite

Jan 1, 1957