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By G. R. Wilms

A study has been made of the structural changes in polycrystalline high purity aluminum during the tertiary stage of creep under conditions of constant tensile load. It appears that there is no basic modification in the particular mechanism of deformation that characterized the preceding secondary stage of creep, but that the changes in crystalline structure produced during the tertiary stage are only a consequence and not a cause of the accelerated strain. Intercrystalline fissures were observed on entry into the tertiary stage, and these might supplement the accelerated rate of strain owing to local stress concentrations. There is evidence that the formation of these fissures may be associated with the presence of surface imperfections, and it is suggested that a more generalized treatment of the results may explain certain creep characteristics of commercial alloys. IN previous work'-4 a study was made of the changes produced when specimens of annealed aluminum were deformed at various temperatures and rates of strain, especially under conditions leading to creep under constant tensile load. It was shown that, as the temperature was increased or as the rate of strain was decreased, elements of the substructure produced within the grains became coarser, and with the strain rate constant at a given temperature, their size tended to an equilibrium value. The preliminary process of the breaking down of the grains into a substructure was identified with primary creep.' The subsequent equilibrium, condition was associated with secondary creep. The question then arose whether the tertiary stage corresponded to any further significant change in the substructure. The question is also of interest in view of the opinion, expressed for instance by Andrade,5 that the tertiary stage is merely an accelerated rate of strain due to the reduced area of section of a specimen under continuous tensile load, and the other opinion, as suggested by the observation by Sully, Cale, and Willoughby6 of a tertiary stage in com-pressive loading, that this third stage is a real effect in its own right. The object of this paper is to record some observations on the tertiary stage of high purity aluminum. Experimental Procedure The material was aluminum of 99.98 pct purity as previously used. The specimens had a rectangular section of l/8 x l/2 in., and extensions were measured over a 1 in. gage length. After machining to shape, the specimens were annealed to give a standard grain size of 0.2 mm and then electropolished. The general procedure involved metallographic and X-ray diffraction examination at progressive stages of elongation (marked by arrows on the curves shown in Figs. 1 and 2), the specimen being extended to fracture under constant load at a given temperature. The X-ray tests were made by the back-reflection method from a stationary specimen, using CoK radiation. The longer edge of the micrographs in the paper corresponds to the direction of applied stress. Results The previous work showed that, in the secondary stage of creep in aluminum, three basic types of structure could be developed according to the temperature and rate of strain. These were: 1—slip, which predominated at the lower temperatures and higher rates of strain and produced the finest and least perfect substructure; 2—cell structure, which superseded slip as the temperature was raised and the rate of strain decreased and which was characterized by a coarser and more perfect structure and an absence of slip lines; and 3—a stage termed "boundary microflow," which predominated at still higher temperatures and lower rates of strain when the cell size had increased and become comparable

Jan 1, 1955

By J. C. Griffiths, D. W. Bennion

A mathematical model, which does not assume a priori that stratification exists, but was designed to test for the stratification was developed. The model segmented the reservoir horizontally into areas of common variance, then divided it vertically into strata (if strata were present). Next, trend surface techniques were used to determine the lateral extent and variation of each stratum. The model was tested on two reservoirs (sandstone and limestone) using porosity as the reservoir rock property. The sandstone reservoir contained approximately 60,000 samples from 2,000 cored wells, while the limestone reservoir had approximately 24,000 samples from 430 cored wells. Within the areas of common variance tested, the model was able to distinguish four separate lithological units or zones in the sandstone reservoir, four in the Marly section and seven in the Vuggy section of the limestone reservoir. INTRODUCTION To accurately predict the movement and production of fluids from a reservoir rock, it is necessary that the reservoir engineer have a knowledge of the rock properties and their distribution throughout the reservoir. For this study, a reservoir rock is defined as a solid containing interconnecting holes or voids which occur relatively frequently and are dispersed within the rock in a regular or random manner. The fraction of bulk volume that these interconnecting voids occupy is called porosity. The rock must also possess sufficient permeability to allow fluids to move through it and it may be composed of one or more strata or lithological units. A stratum or lithological unit as defined in this study is a body or volume of reservoir rock whose properties are so distributed that its lateral and vertical extent can be traced throughout or through a portion of the reservoir. Operationally, the existence of strata are question- able unless the variance within strata is less than among strata. Within the past few years computers have been widely used as a tool for calculating movement and production of fluids from reservoirs. Most prediction models require some type of a mathematical description of certain reservoir rock properties. In the past, most of these models have been relatively simple. Some have assumed vertical variation but no lateral variation, while others have assumed lateral variation but no vertical variation. In general, most of these models have not used functional relationships to predict reservoir rock properties as functions of position. The object of this study was to develop a model which would predict lateral and vertical variations of reservoir rock properties. Since samples are usually available from only a small portion of the total reservoir rock, it seemed logical that if measurements from these samples were to be used to infer the properties of the actual reservoir, the data should be treated statistically as a sample from the total population (reservoir). Therefore, the model developed in this study to predict reservoir rock properties was a stochastic model. The model was tested using porosity (a macroscopic reservoir rock property) measurements from two reservoirs — the first, a sandstone reservoir from which 60,000 samples were obtained; and the second, a limestone reservoir with 24,000 samples. Several investigators have proposed methods to determine the vertical and areal variation of a reservoir rock property. Stiles: Dykstra and Parsons 2 and Suder and Calhoun3 have all developed waterflooding prediction techniques which assume vertical variation but no lateral variation. Stiles developed a method to segment a reservoir arbitrarily using frequency distribution. Law4 suggested that porosity has a normal frequency distribution and that permeability has a log-normal frequency distribution. Elkins and Skov 5 proposed that when a reservoir is segmented vertically, the

Jan 1, 1967

By W. C. Knopf, G. Samsel

For several years International Minerals & Chem-ical Corp. has used a radiation method to assay potassium content of products from potash and feldspar beneficiation. The procedure is rapid, accurate, and inexpensive and is easily handled, if necessary, by nontechnical personnel. Data are presented to show the accuracies that may be expected if the technique is used for control of pilot plants or large-scale plants. Natural potassium is composed of three isotopes —K, K and K. Five other isotopes, artificially produced, have been detected. In natural potassium only the K isotope, with a half life of 1.4x10 years, is radioactive. Its modes of decay are beta and gamma rays, positrons, and x-rays. Only the more abundant beta rays, however, are important in radiation measurements using geiger tubes. Barnes and Salley' measured radiation of potassium salts in solution in 1943. Gaudin and Parnell2 first reported the use of solid salts arranged in a vessel surrounding the ß counter in 1948. Later, Scheel used the method to assay potassium content of various crude and finished potash salts. Experimental: Dip-type Geiger-Muller tubes (TGC-5) supplied by Tracerlab Co. were used in all radiation counting measurements. The tube was encompassed by a glass container about M in. larger in diameter than the tube. This container, which served as a sample holder, was closed at the bottom with a rubber stopper to facilitate removing the samples. Samples were not weighed, but about 40 g of sample were needed for each test. Electrical impulses from the tube were counted on either a Tracerlab scaler or a rate meter. To obviate the need for constant attendance, preset features were incorporated into the scalers, so that at a predetermined time or count the units were automatically deactivated. When rate meters were used, counting rates were read directly from instrument or from a recorder used in conjunction with the rate meter. Each tube was calibrated, according to the manufacturer's instructions, to determine the correct operating voltage to insure reproducible results. A linear calibration plot of percent K2O vs counting rate was also obtained for each tube by recording the counting rate plus background count of several standards of different K2O content chemically analyzed by the chloroplatinate method.' These standards were of approximately the same particle size distribution as samples to be assayed. Specific background count caused by cosmic rays and other surrounding radiation was checked periodically by counting a sample of pure NaCl. Fig. 1 is a representative calibration plot. Assays were determined directly from the standard plot or calculated by subtracting the background count from the counting rate, then multiplying by the slope of the line. Chemical assays of the test samples were made by the Sherril method," a flame photometric technique, or the chloroplatinate method. Data: The radiation assay method has been used for three years by International Minerals & Chemical Corp. in the laboratory and in pilot plants processing ores containing potassium. These dry concentration plants process sylvinite and langbeinite ores at Carlsbad, N. M., and feldspar ores at Top-sham, Maine. Sylvinite ore is predominantly a mixture of syl-vite (impure KCl) and halite (impure NaCl). Contaminants include sulfates, such as langbeinite (2MgSO - K2SO4), kieserite (MgSO H2O), poly-halite (MgSO4.K2SO, 2CaSO, . 2H2O), and slimes. Langbeinite ore is predominantly langbeinite and halite with small amounts of sylvite, sulfates other than langbeinite, and slimes. Several variables, in addition to correct calibration and standardization of tubes, were found to be important in obtaining reproducible results. Particle size distribution of standard samples should be

Jan 1, 1959

By Henry A. Wriedt, John Chipman

Equilibrium in the reaction of hydrogen gas with oxygen in liquid nickel, iron, and their alloys has been studied at temperatures of 1500° to 1700°C. The equilibrium con^stant, 0/p, [% O], is greater in nickel then in iron by a factor of 45 at 1594 C. In the alloy steel range, the activity coefficient of oxygen is slightly increased by the presence of nickel. NICKEL is more resistant to oxidation than is iron, in both the solid and the liquid state. The solubility of oxygen,' however, is greater in nickel than in iron. The two metals and their liquid alloys constitute an interesting series of solvents in which the chemical behavior of oxygen can be studied by methods similar to those used for liquid iron.' Experimental Method The furnace assembly, including the tube for preheating the entrant gas, was the same as that described by Gokcen and Chipman. " controlled mixture of water vapor, hydrogen, and argon preheated to approximately the melt temperature impinged upon the surface of the liquid metal. The charge, weighing about 35 g, was held in an alumina crucible at constant temperature in the gas stream for a prolonged period, then quenched in a stream of cold helium, sampled, and analyzed for oxygen by the vacuum fusion method. The temperature of the liquid metal was measured by a Leeds and Northrup optical pyrometer which had been checked against a similar instrument certified by the National Bureau of Standards. The freezing point of electrolytic iron in hydrogen, taken as 153j°C, was used for frequent checks. This point and the emissivity determined by Dastur and Gokcen" established the transmissivity of the optical system. The emissivities of Fe-Ni alloys at 1535" are known from the experiments of Smith and Chipman,h nd it was assumed that the variation with temperature is parallel with that of iron. Recorded temperatures are probably accurate within k5"C. Preparation of Gas Mixtures—Since the ratio H,O:H, had to be much higher for nickel than for iron, it was found convenient to construct two separate systems for gas preparation. In both cases, the ratio of argon to the sum of the other two gases was at least 4, the proportion of hydrogen and water vapor being varied to produce H,O:H, ratios from 0.2 to 70. The primary purpose of the argon was to diminish the errors caused by thermal separation' in the gas phase. In addition, its presence lowered the saturation temperature required for a given H,O:H, ratio and minimized the difficulty of preventing condensation. Both systems were modifications of the one used by Dastur and Chipman.' For H,O:HI ratios greater than 2, welding-grade argon purified by passage over magnesium chips at 620°C was mixed with hydrogen produced in the electrolytic cell shown in Fig. 1. The design was based on a cell used by Bodenstein and Pohl," the important features of which area nickel wire cathode and sodium hydroxide solution as the electrolyte. The rate of hydrogen evolution was controlled by a calibrated ammeter and a rheostat in the circuit, the current efficiency being taken as 100 pct. Precise control of the argon flow rate at about 300 ml per min was achieved by means of a capillary flowmeter having a controlled pressure drop. The molar flow rate was measured volumetrically before each run, and a constant flowmeter setting was maintained thereafter. The A-H, mixture passed through a water saturator of the type previously described," the saturation temperature being maintained automatically with a fluctuation of k0.04"C. The tube between saturator and furnace was heated by a resistance winding. The system was of all Pyrex construction with the exception of the stainless steel tube containing magnesium chips. This was connected with the glass tubing at the upstream end by

Jan 1, 1957

By C. Wachmann

The theory presented ill this paper makes possible examination of the phenomenological aspect of secondary oil recovery by alcohol flooding. Limitutions of the theory are contingent on three primary assumptions: (1) chemical equilibrium, (2) no fingering, and (5) no dispersion. The second assumption implies one-dimensional flow. In a geometric sense the theory extends the Buckley-Leverett construction to systems of two slightly miscible fluids and to systems of three components. This is made possible by considering single-phase fluids to be made up two phases, namely of an excess of one phase and a negative amount of the other phase. The procedure is discussed in the paper. The theory also permits direct determination of the relationship between the aqueous phase saturation and the concentration of water in the aqueous phase in a zone of variable composition. The velocity of planes of constant water concentration and of constant saturation can be computted likewise and the existence of saturation discontinuities inferred. Consequently the behavior of such a Zone, which may exist at some time between a displaced and a displacing fluid, May be determined. mathematical details are given in Appendices. Problems of experimental verification are pointed out on the basis of a supporting experiment. Implications of the theory and effects of violations of primary assumptions are discussed briefly. The major conclusion is that, if the primary assumptions are met, with pure alcohol and alcohol-rich .slugs piston-like displacement of oil and water is possible. INTRODUCTION The recovery of oil from porous media by alcohol displacement has been studied for several years. Extensive experimental investigations into alcohol flooding have been carried out in the laboratory although little has been done in the field. A large amount of practical information is available, the extent being indicated by the first three papers cited 1-3 and their respecrive bibliographies. This has permitted the Formulation of inferential theories. A more analytical approach in which theories are developed primarily by reasoning from known physical principles and relationships has, however, lagged behind. In fact, an analytically derived theory of alcohol displacement has not been available. The theory presented in this paper on oil and water displacement by alcohol from a porous medium is a result of the analytical approach. The theory is idealized, as certain assumptions had to be made to make the mathematics tractable and reduce complexity of argument. In particular, major assuptions concerning conditions of equilibrium, interfacial stability, longitudinal mixing, etc., led to the exclusion of fingering, for example, from all considerations. In many laboratory experiments reported in the literature fingering could not be avoided. There is, therefore, disagreement between theories based on experimental evidence available and the analytically derived theory presented here. This theory presented is based on known physical data and makes use of the Buckley-Leverett construction and its suggested extension. The mathematical derivation of the theory is given in Appendices. Three examples relevant to alcohol displacement are discussed to explain the use of this theory: (1) system of two immiscible fluids (the Buckley-Leverett case); (2) system of two slightly miscible fluids involving an extension of the Buckley-Leverett construction; and (3) system of three components, including injection of pure alcohol or alcohol-rich fluid as a special case, which involves a more general extension of the Buckley-Leverett construction. In these discussions strict assumptions were made to impose equilibrium conditions and exclude mixing and fingering. Effects of relaxing these assumptions and consequent extensions of the theory are indicated. The complexity of the alcohol displacement process makes experimental verification of the theory essential. Some relevant evidence is offered in this paper.

Jan 1, 1965

By P. A. Beck, Hsun Hu

It has been known for many years that in cold drawn polycrystalline aluminum the recrystallization texture is practically identical with the deformation texture.l,2,3 V. Goeler and Sachs4 stated that in cold rolled polycrystalline aluminum, too, the deformation texture is retained upon recrystallization. This behavior was interpreted by Dehlinger9 as an indication that each recrystallized grain inherits the orientation of the matrix in which it grew. However, Burgers and Basart showed6 that in deformed aluminum single crystals the orientation of the recrystallized grains strongly deviates from that of the matrix. Barrett demonstrated8 that even in deformed polycrystalline aggregates the local orientation within each deformed grain changes on recrystallization. No explanation has as yet been offered of how the aggregate texture can be retained, while the local texture is everywhere changing. According to Burgers and Louwerse6 the orientation change on recrystallization in compressed and rolled aluminum single crystals corresponds to a rotation around [112] axes lying in the active slip planes and perpendicular to active slip directions. This orientation change was rationalized by them on the assumption that the orientation of the recrystallized grains is determined by the orientation of the available nuclei, and that these nuclei are small fragments of the deformed crystal, rotated in the deformation process. Barrett pointed out,? however, that these assumptions were by no means proven, and that the total volume of material necessary for the nuclei is so small, that it must be available in any orien- tation whatever. It is, therefore, unlikely that an "oriented nucleation" theory could satisfactorily explain the orientation changes in recrystallization of a deformed crystal. Furthermore, in contradiction to Burgers and LOU-werse's conclusions, Barrett's results for the orientation change could be best expressed in terms of rotations around. [Ill] axes. Thus agreement is lacking not only in the interpretations but apparently even in the experimental results contributed by the various investigators. The orientation relationships on coarsening* in a highly oriented polycrystalline matrix were first investigated by Burgers and Basart.5 They produced a fine grained highly oriented matrix by the recrystallization of a compressed or rolled single crystal of aluminum, and studied the orientation relationships in three successive generations of crystals: the "deformation texture" in the single crystal, the recrystallization texture, and the coarsening texture. Burgers24 showed that the preferred orientation of each successive generation was almost always widely different from that of the preceding one, but that the coarse grains often approximately reverted to the orientation of their grandparent, the deformed single crystal. This observation, and the idea that the orientation of the coarse grains is determined by that of the available "nuclei," led to the concept that the coarse grains are nucleated by the remnants of the deformation texture.12,15 On the other hand, Bowles and Boas16 found, in a carefully conducted experiment, that in recrystallized fine grained copper of cube texture coarse grains grow in orientations which can be derived from the orientation of the recrystallized matrix by rotation around a [lll].] direction: the coarsening texture here does not appear to be related in any simple manner to the original rolling texture from which the cube texture had been obtained by recrystallization. It may be assumed that in a recrystallized material, even with a strong texture, there always are present some grains of practically any orientation. These may serve as "nuclei" for the coarse grains, provided that the conditions are favorable for their growth. The existence of a coarsening texture may be considered as an indication that grains with certain relative orientations with respect to the preferred orientation of their neighbors can grow much faster than others. This "oriented growth" theory was briefly suggested by van Arkel, as early as 1936,13 and it was mentioned by Burgers." Recently, C. G. Dunn produced direct

Jan 1, 1950

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas'-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller's results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

By J. T. Norton, N. J. Grant, A. M. Gervais

An investigation of the creep deformation of coarse grained specimens of high purity aluminum in the temperature range 800' to 1150°F, permitted the formulation of a theory explaining the formation of kink bands. The X-ray Laue back-reflection technique was used in conjunction with metallographic studies to determine the crystallographic elements involved in kinking and to measure the rotations of the bands. THAT metals deform by the formation of kink bands was first shown by Orowan1 in 1942. He manually compressed cadmium single-crystal wires, the basal planes of which were parallel to the wire axis and to the direction of compression. He found that kink bands formed quite suddenly. Similar experiments were performed by Hess and Barrett2 on zinc with a hydraulic testing machine to permit slower more careful compression. They observed that kink bands formed progressively with increasing compression. Recently Washburn and Parker3 observed the formation of kink bands in zinc single-crystal specimens during tension creep experiments. Each of these authors observed the formation of kink bands but did not make a complete analyses of the crystallographic relationships. In addition to these studies on hexagonal metals, extensive investigations of kink bands formed during deformation of aluminum in tension at room temperature have been reported. Two types of deformation bands have been observed during the deformation of aluminum at room temperature. These are: 1—kink bands: these exhibit a sharp curvature of the lattice along certain surfaces, and 2—bands formed by secondary slip along certain regions. As has already been shown by Honeycombe,4 it is important to point out the difference characterizing the two types of deformation bands. In the first case. for moderate deformation, only one system of slip planes normally is active; in the second case, however, two slip systems are active in the deformation bands. The latter have a rumpled surface because of the action of the two slip systems. In the present work only the first type of band was studied and to avoid any confusion the term kink band will be used exclusively in the discussion which follows. Honeycombe' observed that very narrow kink bands (width, 0.01 mm) formed along the (110) planes during the deformation of high purity aluminum at room temperature. He observed narrower ones in commercially pure aluminum and found also that their width decreased with decreasing temperatures. Chen and Mathewson5 reported the formation of kink bands during tensile testing of single crystals of high purity aluminum at room temperature and pointed out that some rotation occurred about a [211] direction. The influence of the bending moment on the formation of kink bands was illustrated by the experiments of Rohm and Kochendorferl0 who used a Polanyi apparatus to obtain pure shear during tensile testing of high purity aluminum single crystals. Under such conditions only one slip system was active and no kink bands were observed; consequently, no noticeable asterism was detected after deformation. The influence of the bending moment will be discussed later. Calnan8 gave a detailed account of the work performed on kink bands obtained during deformation of aluminum at room temperature. Because no explanation of the process of kink band formation in creep was given in the previous investigations and because some of the above observations are vital to the following discussion the brief review of the literature has been given. It is proposed in the present work to provide an explanation of kink band formation during creep deformation at elevated temperatures. Results and Discussion Kink bands were observed to form during tensile creep testing of high purity (99.995 pct) aluminum specimens, having a very large grain size, in the temperature range 800" to 1150°F. These observations were made in grains which occupied the whole cross section of the specimen. The specimens were originally round (diameter, 0.187 in.; gage length, 1 in.) and had parallel flats milled to permit easier metallographic and X-ray observations. The final

Jan 1, 1954

By E. Topanelian

In recent years considerable progress has been made in the development and application of mathematical techniques for the solution of certain problems involving economic "strategies". Such a problem might involve, for example, the scheduling of shipments of a commodity from a number of sources to a number of destinations. The object would be to schedule the shipments in a manner so as to satisfy the destination requirements and at the same time minimize the transportation costs. The solution to such a problem is not necessarily intuitively obvious. The "obvious" solution is frequently far from optimum. If the shipments are to be made from, for example, only two sources to four destinations, the optimum schedule is readily found. However, if shipments are to be made from, say, 10 sources to several hundred destinations, even a competent and experienced scheduler may spend considerable time in finding a reasonable answer. Even then he is not sure that he has the optimum solution. Furthermore, he has no way of knowing how far from optimum the answer is. Consequently, he does not know whether he should accept this solution or seek a better one. Prior to the advent of large high-speed digital computers, little more could be done with such problems because of their great size and multiplicity of possible solutions. A problem involving 20 sources and 50 destinations would require choosing, from a very large number of possible combinations, the optimum combination of 1,000 variables. The best one could do was to utilize intuition, extrapolation from past experience, and other non-exact approaches. With a high-speed computer, however, such problems can be solved providing a reasonable computational procedure (or algorithm) can be utilized. The purpose of this paper is to describe such a procedure (linear programming) and to apply this procedure to a production scheduling problem. THE RESERVOIR PROBLEM A simple reservoir model is used throughout this analysis to illustrate the use of linear programming. Even the simplest reservoir behavior problem is nonlinear in both space and time, but if the geometry is fixed for a particular study and the time variable is quantized, the resultant system may be described by linear constraints on the variable production rates. Crude oil is available from five separate sources and is delivered to a pipeline. Sources 1, 2, 3 and 4 are ideal reservoirs and therefore are subjected to reservoir flow restrictions. Source 5 is labeled "Outside Source" and crude oil from this source is assumed to be available in unlimited quantities without considering reservoir conditions. The general problem is to determine the schedule of crude oil production from five sources which, over an eight-year period and subject to certain restrictions, will result in maximum profit. "Profit" is defined to encompass all economic factors and expenses involved in producing and selling crude oil to a pipeline facility. Such economic factors are lumped to the extent that the term represents the dollars profit from one barrel of crude oil from any of the five sources entering the pipeline system. Table 1 presents the assumed profit per barrel for oil from any of the five sources over each of the four time periods. In this chart the eight years is broken into four equal intervals of two years. The selection of four time periods of two years each and the values representing the potential profit are completely arbitrary selections for the purpose of illustrating this idealized reservoir problem. In any practical application of this work a careful economic study would have to be made in order to estimate potential unit profits for time periods as far in the future as eight years. In this particular study it is assumed that all of the potential unit profits (C) are known and fixed before the production schedule is attempted. For each reservoir arbitrary values are assigned for

By W. B. Nelligam, J. Tittman

Refinements in radiation logging techniques during recent years have involved increasing usage of scintillation ditectors. These detectors produce voltage pulses whose heights are related to the energies of the gamma rays which initiate them. Analysis of the gamma-ray spectrum, as indicated by the pulse heights, yields information about the chemical elements composing the formations surveyed. Refined scintillation counter techniques can furnish chemical information concerning earth formations in situ, from a study of the gamma-ray spectra emitted by the formation either naturally or as a result of neutron bombardment."' Accompanying the rising interest in gamma-ray scintillation spectroscopy, there has been increased activity in the development of accelerator-type neutron sources (in contrast to encapsulated chemical-mixture sources). Such neutron generators are attractive for several reasons: (1) they greatly reduce radiation hazards to personnel; (2) there is a great reduction in contamination danger if they are lost in the hole; (3) they can produce larger neutron intensities than can conveniently available encapsulated sources; and (4) they are capable of being pulsed, thus permitting new techniques in logging. In the past, both accelerator and encapsulated neutron sources have been used by others in conjunction with scintillation-detector pulse-height analysis. The results have not been too encouraging, due to the interference among different gamma-ray spectral lines and to the fact that the gamma-ray peaks were not too clearly distinguishable above the large and ill-defined background "noise".'.' This paper is a status report on laboratory studies of a technique using a borehole accelerator as a neutron source, which gives an improved scintillation spectrum, thus permitting more accurate chemical analyses of the formations penetrated. The Schlumberger-accelerator neutron source' is presented; the origins of inelastic and of thermal-neutron, capture gamma rays are dis- cussed, and results are given for some laboratory measurements performed in borehole geometry. THE NEUTRON GENERATOR-TUBE ACCELERATOR In the attempt to develop an accelerator neutron source which would have the desirable properties outlined in the "Introduction" and which would operate satisfactorily under borehole logging conditions, a small-diameter, cylindrical, neutron generator tube has been developed. This tube utilizes the principle of accelerating deuterons (heavy hydrogen nuclei) by a high voltage so that they bombard a tritium (heavy, heavy hydrogen) target. The resulting reactions produce large numbers of neutrons of 14 Mev energy. Furthermore, the tube is permanently sealed and, thus, the use of pumping techniques in the sonde is avoided. The tube consists of a pressure control, an ion source in which the deuterons are stripped of their electrons, an accelerating gap down which the deuterons are sped by the high voltage, a secondary electron suppressor and a tritium-loaded target. Obviously, the tube requires auxiliary circuitry in a sonde for the control of the ion source, tube pressure, high voltage and other operating variables. Neutron yields, both continuous and pulsed, have been produced under simulated field conditions in the range between 1 and 10 times those conventionally used in neutron logging applications. For the experiments discussed in this paper, neutron-pulse repetition rates in the range between 500 and 5,000 pulses/sec are adequate. Furthermore, by making suitable adjustments in operating conditions, one can vary the pulse width from a minimum of several microseconds up to dc. As will be seen later, the present application to well logging does not require that one have available pulses of neutrons which are appreciably shorter than the time it takes for fast neutrons to slow down to thermal energy in water. As a consequence, much of our interest has been directed towards the operating characteristics of the tube with pulses longer than about 10 microseconds in duration. Our experience to date shows that tubes can be operated in this manner with reasonably constant, average neutron outputs.

By Ken-ichi Hirano, B. L. Averbach, Morris Cohen, N. Ujiiye

The influence of plastic deformation in compression on the self-diffisivity of a iron has been measured in the temperature range of 742º to 885°C. The diffusivity is enhanced in proportion to the strain rate, but this dependence decreases with increasing temperature. The magnitude of the strain is relatively unimportant in this connection. Strain rates from 0 to -2 x 10-3 sec-1 were investigated, with a corresponding increase in diffusivity up to 3 x 103 times. The results are analyzed in terms of vacancy diffusion and the excess vacancies introduced during dejornzntion. It is concluded that grain boundaries are the main vacancy sinks in polycrystalline iron and that the vacancy lifetime is therefore dependent on the grain size. A typical vacancy lifetime at 800°C with a nzean grain-boundary intercept of 0.3 cm is of the order of 1 sec. LATTICE imperfections are considered to be the dominant mechanism of diffusion in close-packed crystals. Vacant lattice sites are usually the most important defect, but the enhancement of diffusion along grain boundaries and other short-circuiting paths has been well documented. Inasmuch as plastic straining produces a variety of defects, it would be expected that the application of stresses sufficient to cause plastic flow during a diffusion run might result in an increase in the self-diffusivity. Enhanced self-diffusion in a iron under compressive creep has been observed by Buffington and Cohen' and subsequent coworkers.2 Lee and Maddin3,4 have also found an enhancement in the self-diffusivity of silver single crystals undergoing torsional deformation. On the other hand, Darby, Tomizuka, and Balluffi5 have not observed any significant diffusion increase in single crystals of silver deformed either in tension or in compression, although the results in this case may have been affected by the occurrence of recrystallization. With poly crystalline silver, however, Forestieri and Girifalco6 have found en- hanced diffusion during compressive creep. A small decrease in the self-diffusivity of zinc single crystals under compressive loading has been reported,7 but the applied stresses in these experiments were too low to cause appreciable plastic deformation. For the cases in which enhanced diffusion has been found, a number of common effects have been noted. Usually, the ratio of the diffusivity during straining, Ds, to the diffusivity in the unstrained condition, D,, varies linearly with the strain rate, and does not seem to be a function of the plastic strain, at least up to ? = 0.2. Values of Ds/Du of the order of 100 have been reported'-4 but the enhancement decreases with increasing diffusion temperature. The activation energy for diffusion decreases markedly with increasing strain rate and approaches a level of roughly one-half the unstrained value. Most of the current explanations of these observations assume that excess vacancies are generated by the deformation, but rather large concentrations of excess vacancies and/or long lifetimes are required by these theories.',',',' Since the original work on iron, there has been an important improvement in the compressive-loading technique.2 The early data were also analyzed without taking into account the motion of the coordinate system in the specimens undergoing plastic deformation. This problem has now been solved by a number of investigators (see Refs. 11, 12, and the appendix of the present paper). Consequently, the strain-diffusion runs on iron for the Ds measurements were repeated and extended over wider ranges of temperature and strain rate. In addition, the original diffusivity data9 on the unstrained iron have been corrected for the divergence of the beam in the counting system and new data points have been added, resulting in somewhat different values for the self-diffusi-vities in a iron.10 The new values for Du are used in this paper. A comparison of Ds and Du confirms the large enhancement in the self-diffusivity of iron during compressive creep, as previously reported.',2

Jan 1, 1963

By David E. Nicholas

INTRODUCTION In this paper, a numerical process for selecting a mining method, with the emphasis on underground mass mining techniques, such as caving, induced caving, and stoping, is proposed. In the past, selection of a mining method for a new property was based primarily on operating experience at similar type deposits and on methods already in use in the district of the deposit. Then, the chosen method was modified during the early years of mining as ground conditions and ore character were bet- ter understood. Today, however, the large capital investment required to open a new mine or change an existing mining system make it imperative that the mining methods examined during the feasibility studies and the method actually selected have a high probability of attaining the projected production rates. Although experience and engineering judgment still provide major input into the selection of a mining method, subtle differences in the characteristics of each deposit, which may affect the method chosen or the mine design, can usually be perceived only through analysis of measured characteristics. The parameters that must be examined when choosing a mining method include: 1) geometry and grade distribution of the deposit; 2) rock mass strength for the ore zone, the hanging wall, and the footwall; 3) mining costs and capitalization requirements; 4) mining rate; 5) type and availability of labor; 6) environmental concerns; and 7) other site-specific considerations. This paper encompasses a detailed look at the first two parameters since they, plus mining costs, have the greatest impact on the selection of a mining method. The proposed method selection process is for a project where drilling has defined sufficient geologic reserves, but little or no underground development has been done. Since each deposit has its own characteristic geanetry/grade distribution, and rock mechanics properties, mining method selection should be at least a two-stage process. In Stage 1, the deposit is described in terms of geometry, grade distribution, and rock mechanics properties. Using these parameters, the mining methods can be ranked to determine which are most applicable; they can then be considered in general terms of mining and capitalization cost, mining rate, type and availability of personnel, environmental concerns, and other site-specific considerations. In Stage 2, the most likely mining methods are costed out, based on a general mine plan. Mining and capitalization costs are used to determine a cut-off grade fran which a minable reserve can be calculated; economic comparisons can then be made to determine the optimum mining method and economic feasibility. During the mine planning phase of Stage 2, rock mechanics information would be used to provide realistic estimates of underground opening size, amount of support, orientation of openings, and caving characteristics, and open pit slope angles. If ground control or operational problems should be encountered with the methods being considered, modifications could be made. Although planning on paper extends start-up time, it is cheaper to err on paper than to find the error after mining has begun. METHOD SELECTION - STAGE 1 The main purpose of Stage 1 is to select those mining methods which should be considered in greater detail. The simplest way to do this is by defining those characteristics required for each mining method and then determining whether the characteristics of the deposit are suitable. However, no one mining method is so restrictive that it can be used for only one set of characteristics, as indicated by the classification system proposed by Boshkov and Wright (1973). In the mining method selection proposed, geometry, grade distribution, and rock mechanics characteristics are ranked according to their acceptability for ten general mining methods.

Jan 1, 1981

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson's ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

By T. G. R. Rawlins, L. E. Brosselard

Direct platinum carbon replicas have been used to study substrates prior to growth and after initial nu-cleation of the layer. Replicas have been directly stripped and correlations have been made with other replica techniques. Mechanically polished substrates are very flat with occasional areas of "dirt", which is apparently silicon. When such substrates are etched in hydrochloric acid gas, scratches and hexagonal defects (thought to be polishing compound) are revealed, together with areas of apparent redeposition. Chemically polished substrates are much less flat although much more homogeneous in appearance. Heat treat)nents have no effect. Nuclei deposited on these surfaces, using a normal silicon tetrachloride system, have been examined. Nuclei on mechanically polished subsrates occur in random areas only, whereas on chemically polished surfaces they are more uniformly distributed. THE interest in the study of thin films and now their rapidly expanding use in many fields has increased over a period of years. Much of this current interest, particularly in the field of single-crystal or epitaxial thin films, has derived its stimulus not only from possibilities for application but also from fundamental electron-microscope studies which have indicated the manner of growth of such layers from the initial nuclei.1-5 Previous work involving study of growth processes may be divided into three categories. First, vacuum deposition, primarily of metals, on a variety of substrates has been studied by electron microscopy and electron-diffraction techniques. These have shown the three-dimensional aspect of nucleation and the remarkable liquidlike behavior of the growing nuclei which coalesce to form a complete layer. More recently this work has been expanded in two ways: by growth inside the electron microscope this has obvious advantages for kinetic studies; and by growth in ultrahigh vacuum—much of this work has been done on semiconductors.8-11 It is of interest to note that metals, specifically gold deposited on rock salt, will form only polycrystalline layers in ultrahigh vacuum unless the substrate surface is contaminated.12 In general the mode of growth for vacuum-deposited semiconductor films is the same as that for metal films. The second method of growth that has been studied is that of electrodeposition.13,14 The little that has been published suggests that the mode of growth is similar to the vacuum case, except that irregularities may perturb the electric field and disturb the growth process. The third and last primary method of growing epitaxial layers is by use of chemical methods. These techniques have generated much interest and much has been published on them. Considerable electron-microscope work has been done on the defects in the layers; however comparatively little work has been undertaken on the initial nucleation and early stages of growth. Confining ourselves now exclusively to the case of silicon, Charig et a1.15 have considered the growth of silicon on silicon substrates by hydrogen reduction of trichlorosilane, and studied the films by means of replica and transmission techniques. Subsequently they have studied the same system for growth on quartz,16 and with the addition of pyrolysis of silane on quartz and alumina.17 Also Manasevit el al. have studied deposits using silane and silicon tetrachloride on sapphire.18-14 Finally, in this volume studies of deposition on beryllia and sapphire are reported. Although Revesz and Evans20 have examined complete layers, grown by means of the widely used silicon tetrachloride reaction, no detailed examination similar to that published by Charig and Joyce21 for the trichlorosilane system has been given. Therefore this investigation has examined substrate surfaces prior to growth and then nucleation on these surfaces for the silicon tetrachloride system. EXPERIMENTAL In this work the surfaces have been studied by means of standard replica techniques. Because of the very real problems associated with artifacts introduced,22 different replicas and different cleaning

Jan 1, 1967

By H. Kurushima, S. Tsunoda

An investigation of the hydrometallurgy of Cu-Zn concentrates by The Dowa Mining Co. of Japan is described and a detailed flowsheet of the Kosaka hydro-metallurgical plant is given. Sufficient operating experience has shown that the Dorrco FluoSolids system has proven successful for recovery of both zinc and copper by roasting in a fluidized bed. At present, 2400 metric tons of concentrates per month are being treated and recoveries of 93 pct Cu and 65 pct Zn are being effected. A SURVEY of the Japanese chemical industry in 1949 revealed, among other things, that sulphur-bearing blast furnace gas from the Kosaka smelter of The Dowa Mining Co. Ltd., Kosaka, Japan, was being exhausted to the atmosphere as waste. In addition, it was costing that company an average of ten million yen ($28,000) annually for damages to the surrounding property caused by the sulphur dioxide in the gas. It was recommended by this survey that the gas be utilized for the production of sulphuric acid by the contact process. Mr. Kurushima visited the United States in May 1950 to investigate the engineering, construction, and operation of a contact acid plant. Any acid produced at Kosaka would necessarily have to be 98 pct H,SO, to prevent corrosion in railroad tank cars transporting it to the point of use. However, the production of 98 pct acid requires constant volume and SO, content of the gas. As the converter gas at Kosaka fluctuates in both volume and quality, it was decided to evaluate the smelting process with relation to other methods of recovery. This evaluation revealed a relatively new type of roaster, the Dorrco FluoSolids reactor, which was reported to be capable of roasting the copper sulphide concentrate in an excess of air with the production of an SO1 gas strong enough for acid production and a water-soluble copper sulphate calcine. The copper sulphate then could be leached from the roasted ore and electrolytic copper recovered from the leach solution in much the same manner as practiced by the Chile Exploration CO. for treating naturally occuring copper sulphate ores. Use of a reactor of this type would eliminate the need for a blast furnace and converter and, in addition, would effect savings in labor and fuel. The Kosaka ore is a microscopically fine mixture of copper, zinc, and lead sulphides. The lead and a small amount of the barite present can be separated by flotation, but any separation of copper and zinc proved extremely difficult. In blast furnace operation at Kosaka, zinc had been slagged off until a stockpile of about 12,000,000 tons containing 5 pct Zn had been accumulated. Mr. Kurushima felt that if any of the zinc in the concentrate was sulphat-ized and leached with the copper, it also could be recovered electrolytically. The Dorr Co., sponsors of fluidization technique in the metallurgical field, suggested that sulphate roasting be tested out on a laboratory scale and that, if successful, a commercial Dorrco FluoSolids system be constructed. They indicated that the results from such laboratory tests could be transposed to a commercial scale without pilot planting the roasting operation. It was therefore decided to send samples of flotation concentrate to the West-port Mill, laboratories of The Dorr Co., for testing. The objective of Mr. Kurushima's visit to the United States thus had changed from investigation of sulphuric acid plants to a fundamental examination of the hydrometallurgy of copper and zinc. Testing Program In February 1951, Mr. Tsunoda went to the United States to witness the application of the FluoSolids system to sulphate roasting at The Dorr

Jan 1, 1956

By M. R. J. Wyllie, H. W. Patnode

In the quantitative interpretation of electric log data it is essential to know the formation factor, defined as the ratio of the resistivity of the formation 100 per cent saturated with brine to the resistivity of the brine.' This concept implies that the formation factor for any given rock is constant irrespective of the resistivity of the brine or solution with which it is saturated. It is apparent that this can be true only when the rock matrix is wholly non-conductive. As reservoir rocks may contain clay or shale having an appreciable conductance one may expect these constituents to influence the determination of true formation factor. The formation factor may be theoretically derived from log data by dividing the resistivity of the mud filtrate invaded formation by the resistivity of the mud filtrate. Such a method of calculntion has implicit in it the assumption that the fluids in the invaded formation are wholly replaced by mud filtrate. that the solid matrix is non-conducting, and that the formation factor of the invaded zone is identical with the formation factor of the uninvaded zone. Since the validity of the first two basic assumptions regarding the insulating character of porous matrices and the displacement of the interstitial fluids in porous media do not appear to be fully established, the formation factors of a number of cores and clay slurries have been measured under conditions suitable for verifying the assumptions and the extent of any errors inherent in them. CORE STUDIES Apparatus and Procedure Resistivity measurements were made on short cylindrical permeable cores which had been previously mounted in lucite.2 The cores were clamped by means of insulated bolts between brass plates about 5 cm square and 1 cm in thickness. The plates were provided with a ring seal to prevent leakage between them and the core mount, and had a centrally located orifice so that fluids could be flowed through the mounted core. The brass mounting plates were used as electrodes and any current flow between them necessarily passed only through the constituents of the intervening core. Fluid saturation of the core, and fluid flow through the core, were effected by a centrifugal pump connected to the outflow end of the core, thus providing a differential pressure across the core of approximately one atmosphere. The procedure used was first to evacuate each core by means of the pump and then to saturate the core with an aqueous sodium chloride solution of known resistivity. The resistance of the core was measured and flow of the solution through the core continued for sufficient time to establish a constant resistance reading. After equilibrium had been reached with one solution, another sodium chloride solution of a different resistivity was flowed through the core and the flow continued until a constant resistance reading was again obtained. This procedure was continued until resistance measurements of the core had been made with a series of solutions within a salinity range from 1.0N NaCl to distilled water. The data obtained enabled the apparent formation factor of given porous rocks when saturated with fluids of different resistivity to be computed and also provided information regarding the ability of an invading fluid to displace interstitial water from a core. Results Berea Sandstone — The first core examined was a specimen of Berea sandstone." This core had been cut essentially parallel to the bedding for permeability studies. The core was clamped in the core holder and saturated with 1.0N NaCl solution and the resistance determined. It was subsequently flushed and the resistance measured when saturated in turn with 0.1N, 0.025N, 0.01N, .005N sodium chloride solutions and finally with distilled water. In flushing the core with each

Jan 1, 1950

By J. L. Lytton, T. E. Tietz

The recovery of flour stress of recrylstallized are-cast molyhdenum after 10 pet prestrain at 150°C was studied for recovery temperatures of 725o 801o and 901oC. The yield phenomenon observed after recovery was such that the yield drop diminished and disappeared as recovery proceeded. A fractional flow-stress recovery parameter fr, was developed and it was shown that, independent of recovery ternperatzwe, equal f, values of about 0.16 produced superposition of stress-strain curves except for the initial yield phenomenon. The activation energy for low degrees oj recovery was found to he 32,600 cal per mole, in close agreement with a reported valzie for difjzdsion of carbon in molybdenum. For values of fr greater than about 0.15 where recovery was thought to predominate over strain aging, the activation energy varied from 43,600 to 82,500 cal per mole and increased with increasing recovery and recovery temperature. A 10 pet pre-strain shifted the ductile-brittle transition temperature, as indicated by tensile elongation, from 10°C. to about -22"C. A 100-hr recovery anneal at 801oC was shown to shift the transition temperature to about —5oC, the major shift occurring during the first hour of recovery. ThE recovery of cold-worked metals is accompanied by changes in the arrangement of the dislocations generated during cold work. In recent years, the use of transmission electron microscopy has allowed direct observation of some of the dislocation configurations formed, such as "tangles", networks, cells, subboundaries, and loops. These observations have recently been reviewed by Keh and Weissmann.' Accordingly, some understanding has been gained concerning the nature of the dislocation rearrangements involved. The relationship between recovery and the decrease of mechanical strength, however, has only recently been explored. Previous efforts of the authors were directed toward investigating the decrease of tensile flow stress of aluminum and Al-1 pet Mg during recovery2 and the effects of concurrent elastic and plastic strain on the flow-stress recovery of aluminum.3 In addition, an investigation of the effect of four different solute additions on the tensile flow-stress recovery of aluminum has been made.4 Many important metals, however, have the bee crystal structure, e.g., iron, molybdenum, tungsten, vanadium, columbium, tantalum, and chromium. These metals might be expected to behave differently during recovery from those with other crystal structures for two reasons. First, the previous and present investigations of aluminum and its alloys have shown that tensile flow-stress recovery is strongly affected by foreign atoms in the lattice. In the bee metals, interstitial impurities are usually present and might be expected to have various effects upon both flow behavior and recovery. For example, heterogeneous yielding might occur during prestraining. The diffusion of these interstitials can also relock dislocations during recovery so that a yield point might be obtained upon restraining (strain aging). Second, some of the bee metals (e.g., iron, molybdenum, and tungsten) undergo the familiar structure-sensitive ductility transition and exhibit brittle fracture at suitably low temperatures. It is of considerable interest to determine the effects of recovery on the transition temperature of such metals. The purpose of the present investigation was to extend our knowledge of flow-stress recovery to the bee metals and to study the effects of recovery on the ductile-brittle transition temperature. Unalloyed recrystallized are-cast molybdenum was chosen as a test material, since it exhibits a well-defined ductility transition near room temperature. As in the previous studies, the degree of recovery was measured in terms of the decrease of tensile flow stress. Prestraining and restraining were carried out at 150°C to avoid the possibility of brittle fracture. EXPERIMENTAL PROCEDURE The are-cast molybdenum sheet used in this investigation was obtained from the Climax Molybdenum Co. of Michigan. It was 0.060 in. thick by 10

Jan 1, 1964

By M. M. Singh, H. L. Hartman

This paper reports on the results of a fundamental investigation of the behavior of rock under impact of a chisel-shaped bit. Drop-tester studies were conducted with strain gauges attached to the rock and striking bit-edge. It was established that rock behaves viscoelastically. Little correlation was found to exist between the strain waveforms detected on the rock surface and in the bit; thus, strain-time curves obtained with transducers mounted on the bit cannot be used to explain the sequence of events in rock breakage. It is estimated that nearly 1 per cent of the total energy of the blow is expended in permanent deformation of the rock. The strain- energy distribution on a rock surface as a result of chisel impact, which follows a simple law, is presented graphically. Experiments also were conducted with gauges embedded in the rock vertically below the line of impact and at an angle of approximately 45' to the vertical. No essential difference was observed in the type of wave obtained with embedded gauges and with gauges on the surface, as may have been anticipated from theory. INTRODUCTION Through the ages great strides have been taken towards improvement of the various techniques applied in the breakage of rock. Indeed, numerous applications of the rock-failure process are an integral part of present-day industry, including oil well drilling. Yet, astonishingly, little is known regarding the behavior of rock under dynamic loading or the mechanism of rock failure. The value of impact loading studies from the point of view of drilling is evident, however, and requires little elaboration because impact of a chisel edge on rock forms the basic action constituting most common methods of drilling. RELATED STUDIES Impact studies of communition and fragmentation conducted by Fahrenwald, et a1,8 Poncelet,l7 Axelson, et a1,2 Piret,16 Hartman and pfleider,ll Charles and deBruyn,5 and others have been of considerable help in understanding rock-breakage phenomena. Further insight into the basic action of drilling and penetration has been obtained by the work of Irving,13 Cherkasov and Shlyapin,6 BOrcherdt,3 Shepherd,19 Shreiner and Pavlova,20 Drilling Research Inc.7 Hartman,10 Appl and Gatley1 and several other investigators. However, knowledge concerning the stresses and strains induced in the rock and bit during impact remains scant. Recent photoelastic studies by Tandanand and Hartman (1961. 1962)22, 23 have shed light on stress distributions and Fracturing produced in plastics by chisel-shaped bits. In the field of transient strain Pulses and their role in rock drilling, the only extensive work has been performed by Drilling Research Inc. (DRI). They attached strain gauges to the shank of a bit and conducted drop-tester studies, using a die-shaped bit to obtain force-time diagrams. Their work led to the conclusion that, for a given rock type, the first peak of force occurs at a fixed level regardless of the total energy in the system, provided it exceeds a certain minimum threshold level. Further, on this basis an explanation was offered for the sequence of events in crater formation as the result of a single blow on rock. PURPOSE OF PRESENT STUDY The investigations reported in this paper were conducted in a manner similar to the DRI approach, but with the objective of determining the strain distribution in the rock around the area of bit impact and, to a limited extent, the strain in the chisel-shaped bit itself. It was expected that a knowledge of the disposition of these strains, along with the rate of attenuation of strain energy in the rock

By G. C. Bernard, L. W. Bernard, L. W. Holm, W. L. Jacobs

The effect of loam on the permeability of porous media to water was studied as a {unction of foaming agent concentration, specific permeability, pressure gradient, length of a porous medium and its oil saturation. At a given fluid saturation in a porous medium, the permeability to water was found to be the same whether loam was present or not. Foam decreases the permeability to water by developing a higher trapped gas saturation than that obtained by water flooding without loam present, increasing the concentration of foaming agent increased the trapped gas saturation and thereby decreased the permeability to water. The presence of oil reduced the capability of most foaming agents to decrease the permeability of a porous medium to water. A few surfactants were found to be effective loaming agents even in the presence of oil. These results are similar to those reported in a previous paper on the effect of loam on the permeability of porous media to gas. The effect of loam was found to persist in long porous media at moderately high reservoir temperatures and during the passage of many pore volumes of surfactant-free water. INTRODUCTION This paper describes part of a study on a novel approach in the use of surfactants for oil recovery; the use of foam rather than water to displace oil. Previously it was found that foam can displace oil which normally is not displaced by water.4 The foam is formed by successively injecting a suitable surfactant solution and gas into a porous medium. Foam appears to have at least two uses in the field: (1) it shows promise as a superior oil recovery agent, and (2) it shows promise as a selective permeability reducing agent. Foam may be very useful in water floods, or in other oil recovery processes, where highly permeable streaks or unfavorable mobility ratios are a problem. A previous paper reported the effect of foam on the permeability of porous media to gas.1 In the present study the effect of foam on the permeability of porous media to water is reported. The specific objectives of the study were to determine: (1) the effect of foam on the permeability to water in porous media of various specific permeabilities, (2) the effect of foam on the permeability to water in the presence of oil, (3) the effect of foam and crude oil on the trapped gas saturation, (4) the effect of foam on permeability to water at trapped gas saturation, (5) the effect of pressure gradient on the permeability to water under foaming conditions, (6) the persistence of foam during the passage of surfactant-free water through the porous medium, and (7) the effect of various foaming agents, length of the porous medium and temperature on the permeability reduction caused by foam. EXPERIMENTAL PROCEDURES EQUIPMENT AND MATERIALS The experimental apparatus consisted of consolidated and unco n soli dated porous media, wet test meters and constant delivery pumps. The porous media consisted of consolidated sandstone cores (6 to 36 in. long), and unconsolidated sand packs (3 to 30 ft long). The consolidated cores had permeabilities of 32 and 1,000 md and porosities of about 20 per cent. The sand packs had permeabilities of 3,500 to 211,000 md and porosities of about 40 per cent. (Throughout this report a term such as 100 md sand" is used. This term means that the porous medium had a dry, nitrogen permeability of 100 md.) Fluids used in the experiments were distilled water, 1 per cent NaCl solution, aqueous solutions of foaming agents, nitrogen gas, air and crude oil.

Jan 1, 1966

By T. K. Perkins, O. C. Johnston

Because of the influence of dispersion on miscible-displacement processes, diffusion and dispersion phenomena in parous rocks are of current interest in the oil industry. This paper reviews and summarizes a great deal of pertinent information from the literature. Porous media (both unconsolidated packs and consolidated rocks) can be visualized as a network of flow chambers, having random size and flow conductivity, connected together by openings of smaller size. In such a porous medium, the apparent diffusion coefficient D is less than the molecular diffusion coefficient Do, as measured in the absence of a porous medium. For packs of unconsolidated granular material the ratio D/D, is about 0.6 to 0.7. For all porous rocks, both cemented and unconsolidated, the ratio of diffusion coefficients can also be represented as D/Do = 1/FF where F is the for- mation electrical resistivity' factor and 4 is the porosity. If fluids are flowing through the porous medium, dispersion may be greater than that due to diffusion alone. At moderate flow rates the porous medium will create a slightly asymmetrical mix zone (trailing edge stretched out), with the longitudinal dispersion coefficient approximately proportional to the first power of average fluid velocity (if composition is nearly equalized in pore spaces by diffusion). If the velocity in interstices is large enough, there will be insufficient time for diffusion to equalize concentration within pore spaces. In this region, longitudinal dispersion increases more rapidly than fluid velocity. At low velocities in interstices, transverse dispersion is characterized by a region in which transverse diffusion dominates. If the fluid velocity gets high enough, there will be a transition into a region where there is stream splitting with mass transfer but with insufficient residence time to completely damp-out concentration variations within pore spaces. There are several variables that must be con- trolled to get consistent longitudinal and transverse dispersion results, viz., (1) edge effect in packed tubes, (2) particle size distribution, (3) particle shape, (4) packing or permeability heterogeneities, (5) viscosity ratios, (6) gravity forces, (7) amount of turbulence, and (8) effect of an immobile phase. INTRODUCTION Diffusion and dispersion in porous rocks are of current interest to the oil industry. This interest arises because of the influence of dispersion on miscible-displacement processes. In a recovery process utilizing a zone of miscible fluid, there is the possibility of losing miscibility by dissipating the miscible fluid or by channeling or "fingering" through the miscible zone. Diffusion and dispersion are two of the mechanisms that may lead to mixing and dissipation of the slug. On the other hand, dispersion may tend to damp-out viscous fingers which may be channeling through the miscible slug. 58 Hence, dispersion may be detrimental or beneficial (if it prevents fingering through the miscible zone). Therefore, it is doubly important that we understand these processes. In this paper we review, summarize and interpret a great deal of information from the literature. In particular, we will briefly discuss molecular diffusion in miscible fluids. Then we will discuss what differences to expect for diffusion in a porous rock. If there is movement of the fluid through the rock, then there may be an additional mixing or "dispersion". Furthermore, the dispersion longitudinally (in the direction of gross fluid movement) and transverse to the direction of fluid movement will not be equal. We will discuss both types of dispersion as well as several variables which can affect dispersion (viscosity differences, density differences, turbulence, heterogeneity of media, etc.). This group of variables has sometimes led to difficulty when comparing literature data. DIFFUSION OF MISCIBLE FLUIDS If two miscible fluids are in contact, with an initially sharp interface, they will slowly diffuse into one another. As time passes, the sharp interface between the two fluids will become a diffuse