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By J. M. Oblak, R. F. Hehemann, R. H. Goodenow

STUDIES of surface relief and growth kinetics have lead to the concept that widmanstatten ferrite along with upper and lower bainite constitute a continuous series of decomposition products.1-4 Current models4 propose that these products form as plates with a coherent or semicoherent leading edge which propagates at a rate controlled by diffusion of carbon into the surrounding austenite. There are, however, important crystallographic and morphological differences between these products—particularly between upper and lower bainite. For example, upper bainite appears to exhibit a (11lIy orientation habit, whereas lower bainite develops with a more irrational habit near {2251y.5-7 Many of the morphological features of these decomposition products are not yet well-documented. Recent studiess have demonstrated that low-carbon martensites form as sheets of closely spaced needles on {lllly planes while higher-carbon martensites form as plates with {225}? or other orientation habits. The similarity in the crystallography of these two modifications of martensite with upper and lower bainite is striking. Therefore, a study of the morphology of bainite in a series of hypoeutec-toid alloy steels has been initiated to explore these relationships further. The question of immediate interest is whether upper and lower bainite form as plates or needles. A two-surface (approximately perpendicular) metallographic method was employed to study the morphology of bainite in a variety of low and medium alloy steels. Compositions of these steels have been reported elewhere. The behavior of 4340 and 4370 was typical and will be described here. Austenitizing treatments involved 20 min at 2350°F for 4340 and at 2000°F for 4370. Isothermal transformation was conducted in molten-salt baths. Upper bainite was produced at 925°F in the 4340 steel and lower bainite at 575°F in 4370 with transformation times adjusted to produce 10 to 15 pct of the decomposition product. Many of the morphological features of upper bainite have been catalogued in the recent literature.'' The two principal variants observed in the present investigation are illustrated in Fig. l(a). One form appears as long, thin plates or needles and the other as small, frequently irregularly shaped particles. Both variants may occur as isolated forms but more frequently appear in groups as demonstrated in Fig. l(a). Two-surface analysis reveals that these two variants constitute different sections through a single morphological form. To demonstrate this, a number of sections perpendicular to the plane of Fig. l(a) were prepared at various positions along the length of the elongated particles. A section taken at position 1 in Fig. l(a) is presented in Fig. l(b). Here, the dark line represents the edge of the sample and the left-hand portion of this photomicrograph is that from the surface perpendicular to the original plane of polish. Since it was necessary to repolish the original surface after each sectioning, the shape of the bainite particles on this surface, right hand side of Fig. l(b), changes with each sectioning. The disappearance of plate A, Fig. l(a), in Fig. l(b) emphasizes the small cross section of these structures. The group of particles in the lower left-hand

Jan 1, 1964

By D. E. Trout, W. R. Hibbard

Previous investigations have shown that the cold rolling textures1n2 and the drawn wire textures3 of copper change their secondary components after the addition of about 1 pct aluminum and 5 pct zinc, but do not change after the addition of as much as 30 pct nickel. However, few data are available on compression textures. Barrett4 reports from unpublished work with E. L. Layland that compression rolled copper develops a texture which is predominately (110) in the compression plane with a secondary spread to (113) and weaker spread to (100) as shown in Fig 1. However, 70-30 alpha brass similarly treated develops a texture again predominately (110) in the compression plane and with a weak secondary spread to {113} but with moderate (111) secondary intensities illustrated in Fig 2. Experimental Procedure Specimens of the compositions shown in Table 1 remaining from a previous investigation3 were annealed to a grain size of 0.090 mm average diam and machined to cylinders 0.20 in. diam and 0.20 in. high. Cylinders were compressed 90 pct reduction in height between lubricated steel blocks in a tensile machine. Glancing X ray photo-grams using copper K-alpha radiation were taken at an angle of 0 degrees to the compression surface. (111), (002) and (220) rings were analyzed to define the textures shown in Table 1. The results are in agreement with Barrett4 as to types of textures and are essentially in agreement with previous work1,2,3 as to the effects of composition. In the wire study3 it was reported that the 4.99 pct zinc alloy had a brass-type texture, while the data in Table 1 indicate a copper-type texture for compression. The wire specimen of the 4.99 pct zinc alloy was re-examined by X rays and it was established that the [loo] component still exists in the wire axis. Therefore, Table 2 of Ref. 3 is in error and should indicate a double [ill], [loo] copper-type texture for this alloy. This correction results in complete consistency with regard to compositional effects, namely that copper and its alloys containing up to approximately 1 pet aluminum, 5 pct zinc and at least 30 pct nickels develop a copper-type texture and more concentrated copper-aluminum and copper-zinc solid solution alloys will form a brass-type texture. Summary Compression textures developed in copper and its alpha solid solution alloys of aluminum, nickel and zinc are essentially the same types as those re- ported by Barrett4 with compositional effects occurring at approximately the same percent additions as previously reported for rolled sheet182 and drawn wire.3 The Scovill Manufacturing Co., Waterbury, Conn., furnished the copper and brass alloys, performed certain chemical analyses and supplied laboratory facilities where needed. References 1. Brick, Martin and Angier: Tram. A.S.M. (1943) 31, 675. 2. Dahl and Pawlek: Zlsch. Melall. (1936) 28, 266. 3. Hibbard and Yen: Trans. AIME 175, 126. Melals Tech.. Feb. 1948, TP 2334. 4. Barrett: Structure of Metals, mc- Graw-Hill (19421, 386.

Jan 1, 1950

By Cecil Desch

THIS annual lecture, under the auspices of the Institute of Metals Division, and which was illus- trated by lantern slides, has been printed in full and a limited number are available for distribution on request. Some excerpts from the lecture are given below: Ever since the simple geometrical relations of crystals were discovered, it has been recognized that their proper-ties are best explained by assuming that their ultimate particles are arranged on a space lattice, and that the char-acteristics of that lattice determine the shape of the crystal and its physical and mechanical properties. Modern ex-amination by means of X-rays has widened that concep-tion and given it greater; definiteness, and the atoms are now regarded as the particles forming the space lattice. The splendid achievements of investigators in this field have made it possible to state, for a large number of sub-stances, the form and dimensions of the lattice. The char-acteristic of a lattice is that a unit of simple geometrical form is repeated at regular intervals in three dimensions so as to fill the entire crystal. It follows that there must be certain planes in which the atoms are more closely packed than in planes drawn at any angle to them, and it is these planes of closest packing which play the greatest part in determining the growth and other properties of the crystal. There are actually two stages in crystallization, what-ever be the medium in which it occurs. The first is the ap-pearance of crystal nuclei; the second the growth of those nuclei to form crystals of appreciable .size. The first is clearly a kinetic phenomenon. In the molten mass, solu-tion, or vapor, the molecules are in a state of rapid motion and frequent collision. When the temperature has fallen so far. that it is possible for a crystal to exist, a few col-liding molecules may fail to rebound, and so become at-tached to one another, the balance between the attracting and repelling forces-between them causing them to arrange themselves on a space lattice, to which other molecules sub-sequently attach themselves. It was once maintained that the X-ray evidence demanded that the molecule should dis-appear in the solid crystal, but this was a wrong inference, and in many crystals, but not in all, the chemical molecule retains its identity in the solid state. In pure metals the atom and the molecule are identical, so that the conditions are unusually simple. How many. nuclei will be formed in a given mass is evi-dently a problem in probability. Experiments to deter-mine the relation between the temperature and the number of nuclei formed in a given time have been made with some success by using viscous organic substances, but metals offer much greater difficulties, and the few determinations which have been published are vitiated by serious errors. However, the examination of sections of ingots of the same composition and cast at 'the same temperature in similar molds will show, that the number of crystals does not vary widely.

Jan 3, 1927

By E. Maxwell, C. J. Bechtoldt, H. C. Vacher

IN the course of an investigation of the properties of metals at low temperature there was occasion to determine the constitution of four iridium-osmium alloys. There is very little information in the literature1 on the constitution of synthetic Ir-0s alloys. Zvyagintzev' s has made a comprehensive study of different natural Ir-0s alloys and concludes that alloys containing more than 32 pct 0s have the close-packed hexagonal structure of osmium, whereas those containing less than 32 pct 0s have the face-centered cubic structure of iridium. The alloys studied in this work were prepared by the American Platinum Works, Newark, N. J., and were received in the form of fragments approximately 1.5 mm average diameter. The fragments had been obtained by crushing ingots made by fusing charges of iridium and osmium under an arc and air cooling. The ingots were not given a homogenizing heat treatment. Sample fragments Table I. Results of X-Roy Diffraction and Microscopic Examinations Phases Present as Determined by X-ray Diffraction Osmium Alloy Close- Iridium Face- Packed Centered Osmium, Iridium, Hexagonal Cubic Mlcro- WtPot Wt Pct Structure Structure scope 0 99.9 None Present 1 23.6 76.4 None Present 1 38.7 61.3 Present Present 2 59.4 40.6 Present Present 2 79.0 21.0 Present Not detected 2 99.9 0 Present None 1 Note: Chemical analyses of the iridium, osmium, and alloys were furnished by the American Platinum Works. of the iridium and osmium used in making the alloys also were included. Several fragments of each metal and alloy were examined microscopically and by X-ray diffraction. For the X-ray method the fragments were crushed further to pass a 270-mesh screen, then sealed in evacuated fused-silica tubes, heated to 1100°C for 18 hr, and allowed to cool in the furnace. Powder X-ray diffraction patterns were obtained from the annealed fragments by means of a Norelco camera having a diameter of 114 mm, and unfiltered cobaIt radiation. For the microscopic examination several fragments in the as-received condition were mounted in Melmac, (American Cyanamid Co.) and ground using the conventional series of abrasive papers. The polishing was done with 0-2 diamond abrasive on a Microcloth (Buehler Ltd.) lap, wet with xylene. After polishing, the surface was etched electrolytically in a 10 pct solution of chromic acid or in a 10 pct solution of potassium cyanide. Both reagents attacked the osmium-rich constituent, whereas the iridium constituent was attacked slightly by the chromic acid reagent and not noticeably by the potassium cyanide reagent. The results of the X-ray diffraction and microscopic examinations are summarized in Table I. Fig. 1 shows the microstructure of a 21 pct Ir-79 pct 0s alloy. The results indicate an appreciable solid-solu-bility range of osmium in iridium as was reported by Zvyagintzev.' The solid-solubility range of iridium in osmium is more restricted, apparently less than 21 pct Ir. This implies a large range of composition in which two phases can coexist that was not reported by Zvyagintzev.

Jan 1, 1955

By D. C. Hilty

C. E. SIMS*—This is a most interesting and important paper. It is important from two standpoints. First, it has as-spects of being highly accurate and therefore extremely useful to the operating man in showing how far he can go in oxidizing carbon from a steel bath while retaining chromium and the effect of temperature on this limit. Fig 5 is undoubtedly the highlight of the paper, and in checking it against available data, it seems capable of predicting actual results. The other important aspect is the apparently significant fact that reactions within a steel bath, such as between carbon and an oxide, are homogeneous reactions which do not require equilibrium with an external phase. In this case, it seems obvious that the reaction and the equilibrium established were between dissolved carbon (or carbide) and dissolved CrO. The classic reaction which requires equilibrium with solid Cr2O3, did not fit the data. It was recognition of this principle that made Fig 5 possible. G. R. FITTERER*—It might be in assuming the CrO is dissolved in the metal that you are actually approaching the correct factor for activity. If that is true and if the percentages that were used represent an equilibrium constant, this would mean, in effect, that the minimum temperature at which chromium would be reduced by an equivalent percentage of carbon would be about 2400°F from your equation. I believe that is in line with my experience particularly if you deal only with low percentages. J. CHIPMAN†—The author in discussing the equilibrium of the reaction offers two choices of explanation. One postulates an effect of chromium on the activity coefficient of carbon; it would require perhaps more data than are available to us at the present time to test this thoroughly. The other postulate which he offers is a reaction with CrO. This explanation is consistent with physical and chemical principles provided that a solid phase CrO is present, and that is essentially what he is postulating. If that oxide were present one would expect and, I think, almost require the kind of results that he obtained. The weakness of that postulate lies in the lack of confirmatory evidence regarding the presence of solid CrO as such. This should offer an interesting subject for further study. It seems a pity that the theoretical arguments revolving around CrO should have obscured for a moment the very real excellence of this paper. E. CARTER*—I think there is a problem that presents itself in practical application where the metal temperature is from 3200 to 3300 and the temperature desired in pouring is considerably less. B. M. LARSEN†—I get the impression from some of the work that was done earlier that there is probably a localized zone of high temperature at the slag metal interface which effects the removal of the carbon. Without that I wonder if the effect is possible to have a localized superheat and an equilibrium there favorable to low carbon content and

Jan 1, 1950

This issue presents the first of several articles making up the Bump Symposium, which was held at the 1958 Annual Meeting of AIME. Other Symposium papers will appear in the September issue of Mining Engineering. THE term mountain bump describes the sudden rupture of one or more coal pillars under excessive stress. These bursts occur with varying degrees of violence and sometimes include adjacent strata, especially the bottom rock. Many failures do not develop enough violence to be dangerous and are regarded as an aid to coal production, but severe occurrences are accompanied by tons of flying coal, dense clouds of dust, and excessive gas emission. Such bursts sometimes throw heavy machinery several feet. Major factors to be considered in the problem are the nature of the strata above and below the seam and the depth of cover. Bumps are classified as to their nature, extent of damage, and point of occurrence, e. g., face bump, coal bump, high side bump, low side pavement bump, and district bump. The problem is extremely complex, and it cannot be over-emphasized that preventive measures, if they are to be successful, must be based on a thorough study of conditions in the individual mine. In western Canada, for example, the McGillivray mine, operating in a 9-ft seam at 2000 ft, has experienced severe bumps, but there have been no occurrences in the International mine, which operates in the same coal seam at 2400 ft, where the coal averages 17 ft thick. Differences in conditions governing the operation of these two mines are described in one of the following articles (see page 883). Again, most bumps in coal mines take place along pillar extraction lines, but at the Sunnyside mine in Utah they also occur a long way from active workings and sometimes in virgin territory. It is usual, too, for such failures to occur under fairly deep cover. But at Sunnyside, to cite only one instance, there have been disturbances along the main fault zone under less than 500 ft of cover. All too often conditions favorable to bumps are revealed only by actual mining—at Springhill No. 2 mine, drilling in roof and pavement strata disclosed a 60-ft sandstone bed after operations had started— and where extraction has advanced too far for preventive measures to be incorporated in the mining plan, districts have had to be abandoned. But in an era when premium ores are being rapidly depleted in the face of rising demands, abandonment is not easily justified. There must be systematic planning to eliminate coal mine bumps, insofar as this is possible. As in the Gary district of West Virginia (see page 888) much has been accomplished by planned operations based on known factors in bump control. But even this is not enough. Precise instrumentation is needed to indicate where bumps are likely to occur, and in both the U. S. and Canada stress analysis studies are being carried out with this object in view. These pages reveal the progress being made.

Jan 1, 1959

By Roger A. Gregg, Barry J. Piearcey

MANY of the nickel-base superalloys developed recently for use in the as-cast condition exhibit a massive "white-etching" constituent1 in the inter-dendritic regions. Commercial alloys in this category are SM 200,* IN 100, INCO 713, and Nicrotung. The appearance of a similar microconstituent in nickel-rich Ni-A1-B alloys has been reported by Schijbel and Stadelmaier. Their investigation revealed that this constituent was the binary eutectic of the terminal nickel-base solid solution and the inter metallic based on Ni3A1. This binary eutectic is degenerate and NhA1 is the major phase. At lower temperatures the eutectic composition lies within the NkA1 phase field and under equilibrium conditions is single-phase NisAl. Taylor and F&apos;loyd3 have shown that in Ni-Al-Cr alloys containing at least 8 at. pct Cr, liquid compositions which solidify by the eutectic reaction in the nickel-rich portion, precipitate nickel-base solid solution and NiAl rather than nickel-base solid solution and NkA1 in the binary Ni-A1 system. Since the nickel-base alloys contain chromium in excess of 8 at. pct and are further alloyed with one or more of the elements titanium, cobalt, molybdenum, or tungsten, it is possible that the eutectic could contain NiAl rather than NisAl. In addition, Benson4 has reported that in low-nickel austenitic high-temperature alloys, which possess Ni/(Al + Ti) atomic-weight ratios <18.0, the Ni (Al, Ti) phase may precipitate from the melt during solidification. Since SM 200 and similar high-temperature materials were developed from alloys which were designed for solution treatment, the appearance of a eutectic would indicate that the limit of solid solubility has been exceeded. The purpose of this note is to confirm that the massive white constituent in the complex nickel-base alloys investigated is based on the binary eutectic Ni + NbAl and that the limit of solid solubility need not be exceeded to produce it, in common with other observations of cast alloys. Successive polishing of a sample of SM 200 showed that, in agreement with Schobel and Stadelmaier, particles of the constituent were spherulitic and in particular were a) situated between cored dendrite arms, Fig. 1, and b) nucleated at the surface of dendrites, Fig. 2. The Ni/(Al + Ti) atomic-weight ratios for the nickel-base alloys which were observed to contain the massive eutectic constituent in the interdendritic regions are 12.1 (Nicrotung), 9.2 (IN loo), 19.5 (INCO 713), and 14.5 (SM 200). However, the results of X-ray analysis of these alloys in the as-cast condition failed to reveal the presence of the Ni (Al, Ti) phase. An electron microanalyzer was therefore employed to analyze the composition of this constituent in SM 200. The results of analyses of representative particles are as follows5: 8.4 at. pct Ti, 8.8 at. pct Co, 5.5 at. pct Cr, 0.9 at. pct W, 12.8 at. pct Al, and 63.6 at. pct Ni. Assuming that

Jan 1, 1964

By S. K. Sarkar, B. Dr. Singh

INTRODUCTION India like USA has traditionally relied on bord and pillars as dominant underground method. Coal has generally been mined at shallow depth from relatively thick and horizontally bedded coal seams. These&apos; factors contributed towards large scale adoption of bard and pillar. After nationalisation of coal industry in two stages in 1971 and 1973, large scale mechanisation and modernisation programmes were undertaken. Longwall mining was identified as one of the major that area for increasing underground coal production. The idea to introduce longwall mining was mooted to increase productivity and to promote conservation and safety. The nationalised coal industry has already worked about twenty longwall faces with different types of support. The tempo of introducing longwall is catching up and a number of longwall programmes with, Self advancing supports of different types and Capacity are in active stage of implementation. The country has not yet started producing mechanised Supports and therefore supports and machineries are being imported from U.K. and other countries of the continent. The of the major problem faced in the longwall projects is to choose suitable type and capacity of supports. The suppliers and manufacturers of these supports are not competent enough to choose and offer the right type and capacity of supports as their knowledge and information about Indian strata conditions are extremely limited. The Central Wining Research Station (Q.!RS), has undertaken a research programme for evaluating the rock mechanical conditions obtaining in the proposed longwall locales and has worked out a method for selection of proper type and capacity of supports on the basis of projected strata behaviour at the proposed locale. STRATA CCNTROL FAILURES Indian coal industry had made some attempts to introduce longwall caving in the early fifties after a working group set up by the Government of India had recommended its adoption to increase productivity and to modernise mines. Approximately 20 longwall faces were tried in the major Indian coalfields of Jharia, Ranigunj and Karanpurr between 1951 and 1968. The supports used consisted of 20T hydraulic props or 35140~ friction props. A number of these faces had suffered total strata control failures and a large number of support elements were lost. The Central Mining Research Station initiated a research programme to analyse these failures in the general background of behaviour of Indian coal measure strata at longwall faces. All the available data regarding the cases of failures were collected and physico-mechanical properties of overlying roof rocks were determined in the laboratory. Simultaneously, observations were continued to establish the behviour pattern of Indian coal measure strata at longwall faces. These studies were helpful in analysing the occurrences of collapse. BEHAVIOUR OF INDIAN COAL MEASURE STRATA The coal measure strata encountered in the principal Indian coalfields of Jharia, Ranigunj and Karanpura are in general strong in nature however, the immediate roof (mostly up to 1.5 to 2 m) in most of the cases is weak and false bedded shale. MI idea about the strength properties of immediate and overlying roofs may be obtained from the following table.

Jan 1, 1982

By Oscar Weiss

An aerial magnetometer survey was carried out by the author&apos;s geophysical organization over the Vrede-fort dome, where Witwatersrand beds are wrapped around a granite plug 25 to 30 miles in diameter. The well-known magnetic shales of the Lower Witwatersrand system (to be referred to as LWW) give strong negative anomalies over the out-cropping portion of the dome. This is unusual as these same shales cause positive anomalies over large areas near Johannesburg and along a strike of 130 miles between the East Rand and Klerksdorp. It is suggested that the negative polarization is caused by heat and stresses connected with the doming. This negative polarization of sedimentary beds, which usually cause positive anomalies, is a good example of how "magnetic lows" can be caused by "structural highs." Significant magnetic anomalies should be tested by gravity and seismic methods irrespective of the sign of the anomalies. South of the line X — Y (see Fig 2 and 5) the gravity anomalies are smaller over the LWW beds and magnetic anomalies suddenly become weaker and even change signs by becoming positive. This peculiar phe- nomenon is explained by faulting which truncated the nearly vertical LWW shales at depth. In this manner the mass of the LWW beds has been reduced together with the weakening of the negative magnetic anomalies by positive poles which occupy the truncated end. Furthermore, by uplifting the beds between f1 and f2 (Fig 2) positive polarization becomes predominant, thus causing positive magnetic anomalies. General The Vredefort dome is one of the internationally known geological structures, which, among others, has attracted the attention of numerous American geologists. It was for this latter reason that our aerial magnetic results over this structure were selected by us for publication in the United States of America. A full description of the exposed geology has been published by Nell and readers are referred to this paper, which is subject to only slight modifications inasmuch as the subdivision of the Witwatersrand system (to be referred to as WW system) is concerned. The Vredefort dome is about 60 miles southwest of Johannesburg. The WW system, after being exposed in the vicinity of Johannesburg, plunges with southerly dips beneath the Vent-ersdorp and Transvaal systems. Along a section southwest from Johannesburg, as shown diagrammatically in Fig 4, we see no outcrops of the WW system until the Vredefort dome, where the Upper and Lower WW system are wrapped around an almost circular arc of a granite mass. Here the whole WW system is overturned around the perimeter of a huge granite plug 25 to 30 miles in diameter. Less than half of the circumference of this dome is exposed; the rest is covered by Karroo dolerites and sediments. The determination of the exact shape of the concealed part of the dome has been a matter of considerable interest and obviously geophysical methods were eminently suited for obtaining this information. A good start was made with a gravimeter survey carried out by the Geological Survey of the Union of South Africa.2 Our own

Jan 1, 1950

By R. L. Perrine

The rise of drain holes drilled from a well to improve productivity is becoming increasingly common. This paper presents data on the productivity increase that may he expected. The data were obtained by use of an electrolytic tank mode1 of a reservoir. Parameter varied in the study to show their effect on productivity include the length, number, and arrangement of drain holes, formation thickness, and damage near the well-hore. The most important results are that very large increases in productivity can be expected only ill damaged wells. The distance, to which drain holes penetrate is of primary importance. Additional length is more effective than increasing the number of drain holes. INTRODUCTI O N In planning the use of drain holes to improve productivity, it is important to he able to estimate the increase in production that can be obtained for a given expenditure. It is also important to know what combination of parameters related to the use of drain holes can he chosen to give the largest production increase. This paper presents data on the productivity increase that may be expected, as obtained by use of an electrolytic tank model of the reservoir. In this study, :! number of parameters were varied to show their effect on productivity. These included the length, number, and arrangement of the drain holes. The presence or absence of a damaged zone of low permeability around the well-bore and the thickness of the producing formation were also considered. The productivity increase that might be expected due to drain holes is presented as the ratio: productivity of a well after drain holes are drilled and completed to the productivity of the same well in an undamaged state without drain holes. The symbol Q/Qo is used to represent this productivity ratio. Thus, the comparison in each case is with a formation of uniform and undamaged permeability. Additional notation includes I;, for the radial extent of the damaged zone, which is assumed to be cylindrical and concentric with the wellbore. Thus the effect of an actual block is approximated by a discontinuous varia-tion in permeability. For purposes of this paper, the permeability within the damaged zone, denoted by kb, is assumed to be 1/25 that in the remainder of the formation, or k. A necessary assumption in making comparative tests using an electrolytic model is that reservoir flow behavior can be approximated by single-phase, steady-\tate flow according to Darey&apos;s Law. In addition, the formation must be assumed to be homogeneous with equal horizontal and vertical permeability. The well-hore diameter in this study is assumed to be 11¾ in. and the drainage radius of the well equal to 500 ft. The drain holes are considered to have been completed without damage. THE ELECTROLYTlC MODEL &apos;She producing formation was modeled by forming a sheet of phosphor-bronze into a cylinder 40% in, in diameter to represent the boundary of the drainage area. This was enclosed in a waterproofed plywood box, and the box filled to an appropriate level with a dilute sodium chloride solution. Solution concentration was adjusted to give a total resistance from

Jan 1, 1956

By A. Vignes, J. P. Sabatier

A study of ternary diffusion at 1315°C in the Fe-Co-Ni system covering the entire ternary phase diagram has been carried out. Experimental values of the four interdiffusion coefficients DFeNico,DFeCoCo, DFeCoNi were computed at 33 points of the ternary diagram. The limiting values of these coefficients on the three sides of the ternary diizgram have also been determined. This set of data is presented as a contour map on the ternary isotherm for each of the four coefficients. Assuming that the Fe-Co-Ni system can be considered as ideal, the phenomenological coefficients Lk ij (with k = Fe) have been computed and the Onsager reciprocal relutions verified. It is shown that, in the Fe-Co-Ni system, the diffusion process can also be described by only two interdiffusion coefficients DFeFe and DCoNiFe, the second cross diffusion coefficient DCoFeNi being equal to zero and the second direct difusion coefficient being given by The values of the cross interdiffusion coefficients and of the Onsager coefficients are explained in terms of atomic mobilities of the three components with the help of a kinetic calculation due to Lane and Kirkaldy.8 It is shown that all the results are explained if the tracer difusion coefficients of the three components are such that DFe > DNi ~ DCo in complete agreement with experimental data on the three binary systems. DIFFUSION in a ternary alloy system is basically and significantly different from diffusion in binary alloys. In binary diffusion, there is just one independent composition variable and only one coefficient Dij is needed to describe the interdiffusion process. In ternary diffusion, we must allow for cross interaction between two independent species, and four interdiffusion coefficients are necessary to describe the transport process. Kirkaldy et al.1,2 have determined interdiffusion coefficients in the systems, Cu-Mn-A1 and Zn-Cu-Al. Guy and Leroy4 have reported intrinsic diffusion coefficients for the r phase at 1300°C of Co-Ni-Cr alloys as a function of composition using the analysis of Philibert and Guy.3 Interdiffusion coefficients were measured at three different compositions at 850°C in the single phase copper-rich corner of the Cu-Zn-Mn system by Dayananda and race.5 Zie-bold and Ogilvie6 have determined interdiffusion coefficients in the single-phase field of the Cu-Ag-Au system at 725°C. Preliminary results on diffusion at 1136°C in the system Fe-Co-Ni have been reported.7 In this study, data are reported on a more complete determination of interdiffusion coefficients in the Fe-Co-Ni system in the entire ternary at 1315°C. There is complete solid solubility with the fcc structures at 1315ºC, and this system can be considered as nearly ideal. This approximation allows the computation of the Onsager phenomenological coefficients. These values can then be used to test a kinetic calculation of the Onsager L coefficients in ternary substitutional solid solutions due to Lane and Kirkaldy.8

Jan 1, 1970

By L. A. Rapport, J. R. McCord, W. P. Drews, K. H. Coats

Water movement about an oil or gas reservoir can be predicted provided an aquifer influence function is known. This function is generally determined from an electric analyzer study or by fitting an idealized mathematical model to field data. A prohlem arises in determining that influence function which best reproduces field data and satisfies certain smoothness requirements, without making any idealizations concerning aquifer geometry and heterogeneity. This study shows the problem to be solvable through the linear programming technique and presents applications to one oil reservoir and two gas storage reservoirs. In addition, a theorem is stated and proven which confirms influence junction smoothness requirements heretofore accepted on physical intuition and establishes additiotzal smoothness constraints formerly not recognized. INTRODUCTION The pressure decline accompanying production results in water encroachment into oil and gas reservoirs situated adjacent to aquifers. The importance of this water movement derives from the significant dependence of production rate upon reservoir pressure and of pressure, in turn, upon water encroachment. Pressure and rate of water movement are uniquely related through an "influence" function which may be in the form of reservoir pressure response to a unit water encroachment rate or of water movement caused by a unit reservoir pressure drop. This influence function reflects the heterogeneity and geometry of the aquifer and is therefore particular to each reservoir. If the influence function is known, then reservoir pressure may be predicted from a production rate schedule, or vice-versa, with the aid of the material balance equation which relates water influx to reservoir production and pressure. The problem of determining this influence function for a given reservoir has been approached in three different ways. Van Everdingen and Hurst calculated and tabulated certain influence functions pertinent to idealized mathematical models which satisfy simplifying assumptions such as aquifer homogeneity and elementary reservoir-aquifer geometries.&apos; Other studies developed additional tables for a variety of elementary reservoir-aquifer geometrical con- figurations and demonstrated their validity and utility.:&apos; Hicks, et al. described the use of an electrical network to determine an influence function giving "best" match of field history and allowing prediction of future performance.&apos; Finally, Hutchinson and Sikora5 and Katz, Tek and Jones attempted to develop a calculation method for deriving the influence function directly from field data with no idealizing assumptions concerning aquifer geometry and homogeneity. They encountered difficulties with inaccuracies in field data and with satisfaction of well-known smoothness requirements of the influence function. This study is concerned with the determination of influence functions from field data and, more specifically, treats the following problem: given field pressure-production data of arbitrary accuracy, how does one determine the influence function which, subject to satisfaction of known smoothness requirements, gives best agreement with field history? A rigorous solution to this problem is ohtained through linear programming as described below. Example applications to one oil and two gas storage reservoirs are presented. In addition, a theorem is proved which confirms influence function smoothness requirements heretofore accepted on physical intuition and establishes additional smoothness requirements formerly not recognized.

Jan 1, 1965

By B. D. Cullity, O. P. Puri

The magnetostrictia of nickel after increasing amounts of plastic elongation was measured at field strengths up to 1500 oe. In addition, the residual stress was measured by means of X-ray line shifts. The observed decrease in magnetostriction following plastic strain is shown to be associated with residual compressive stress. If a metal bar, whose longitudinal axis is taken as the x direction, is plastically elongated in the x direction and then unloaded, X-ray diffraction measurements will indicate the presence of a residual compressive macrostress 0%. However, stress measurement by means of mechanical relaxation does not reveal any macrostress. In a previous paper1 the fictitious macrostress indicated by X-rays was ascribed to a particular distribution of micro-stress, namely, one in which the bulk of the material was stressed more or less uniformly in compression and a very small portion in tension. It was shown that this distribution would account for Neurath&apos;s measurements2 of magnetic losses in silicon steel, because of the effect of residual stress on magnetostriction. The present paper is concerned directly with magnetostriction, in nickel, and with the effect on magnetostriction of the residual stress created by plastic elongation. The residual stress was determined by measurements of X-ray line shifts. MATERIAL AND METHODS Commercially pure "A" nickel was investigated. Its nominal composition, in weight percent, is 99.4 Ni + Co, 0.2 Mn, 0.15 Fe, 0.1 Cu, 0.1 C, 0.05 Si, and 0.005 S. Magnetostriction was measured by means of SR-4 electrical-resistance strain gages mounted on specimens 1/4 in. sq and 8 in. long. Magnetic fields up to about 1500 ce were provided by a multilayer, non-cooled solenoid. A considerable amount of heat was developed at the higher field strengths, and, to avoid errors due to changes in the specimen temperature, the following procedure was adopted. Each measurement of the magnetostriction X at a particular field strength H was preceded by demagnetization and an adjustment of the strain indicator to zero; the field H was then quickly switched on and the strain read immediately. Curves of ? vs H were flat for field strengths above about 750 oe for all specimens, and this constant value of X was accordingly taken as the saturation magnetostriction ?s The X-ray measurements of residual stress were made with a Norelco diffractometer on specimens cut from flat bars 1 1/4 in. wide, 1/8 in. thick, and 12 in. long. These measurements were confined to lattice planes parallel to the surface of the specimen. Two reflections were studied: the 311 CrKß line at 28 = 157 deg, and the 420 CuKal line at 28 = 155 deg. The line centers were determined by fitting a parabola to the peak of the line, as suggested by Ogilvie3 and as modified by Koistinen and Marburger.4 The CuKa doublet from the plastically elongated specimens was first resolved by the Rachinger method5. All X-ray measurements were made by counting at fixed angular positions. RESULTS The results of the magnetostriction measurements are shown in Fig. 1 and Table 1. The magnitude of

Jan 1, 1963

By A. T. Robinson, J. E. Dorn

The electrical resistivities of aluminum alloys containing CU, Ge, Zn, Ag, Cd, and Mg were found to increase linearly with the atomic percentage of the solute atoms. Application of Linde&apos;s rule to these data suggests that each aluminum atom contributes 2.5 electrons to the metallic bond. ALTHOUGH aluminum invariably exhibits a Jt\. valence of three in ionic solids, it does not follow necessarily that its valence in the metallic state is also three. As a matter of record, many properties suggest that the number of bonding electrons in metallic aluminum is less than three. For example, as shown in Fig. 1, the atomic radii1 of the metallic elements in the solid state decrease with increasing atomic number at the beginning of any one period. The atomic radius of aluminum, however, is greater than that which would result from a regular decrease in atomic radius with increasing atomic number, suggesting that the number of bonding electrons in aluminum is somewhat less than three. Correlated with the anomalously large atomic radius of aluminum is its abnormally low melting temperature. As the atomic numbers increase in any one period, the melting temperatures of the metallic elements increase.&apos; As shown in Fig. 2, however, the melting temperature of aluminum (13) is only slightly greater than that of magnesium (12). Again the number of bonding electrons in metallic aluminum appears to be nearer two than the expected value of three. In addition Ageev and Ageeva3 alculated the electron density distribution in the aluminum lattice. A comparison of such electron density curves for various assumed valence states of aluminum with experimentally determined curves suggests that the actual number of bonding electrons in metallic aluminum is between two and three. Hume-Rothery and Raynor&apos;, " have suggested that the above-mentioned abnormalities are associated with the overlapping of the Brillouin zones of metallic aluminum when it is in the usual face-centered cubic structure. The importance of the number of bonding electrons in metals has been extended recently into the field of mechanical properties. While formerly it was thought that the plastic properties of alpha solid solutions were primarily dependent upon the lattice strain induced in the solvent by the solute, it is now known that the difference in the number of bonding electrons of the solute and solvent also has its influence on the plastic properties."1&apos; In order to achieve a satisfactory correlation of the effect of alloying elements on the plastic properties of aluminum alloys,"&apos;T however, it was necessary to assume that the number of bonding electrons contributed by aluminum was about two rather than the expected value of three. It appeared to be desirable, therefore, to seek other criteria for evaluating the number of bonding electrons contributed by aluminum to its alpha solid solutions, especially in view of the practical as well as the theoretical importance of the effect of valency on the plastic properties. Norbury&apos; was perhaps the first to illustrate that the increase in resistance of alpha solid solutions is associated with the differences in valence of the solute and solvent metals. In a series of illuminating investigations Linden-&apos;&apos; has shown that the electrical

Jan 1, 1952

By H. J. Beach, W. C. Goins

The laboratory development and field use of oil well cement compositions* with high resistance to drilling mud contamination are described. Resistance is obtained by adding a I-lb mixture composed of three parts paraformaldehyde to two parts sodium chromate tetra-hydrate for each sack of cement. This mixture neutralizes the cement-retarding properties of quebracho and other tannins, starch, sodium carboxymethylcellu-lose, Ignite, and monovalent salts of lignosulfonic acid. The retarding properties of calcium lignosulfonate are unaffected. The decontaminating mixture may be used in common cement (designated Type I by ASTM specifica-tions,&apos; Class A by API Std. 10A2) or in a slow set slurry prepared from common cement by addition of calcium lignosulfonate. No changes in slurry viscosities or thickening times are caused by the protecting reagents. The method has been used in 185 field jobs where an improved success ratio has been obtained in plug setting. INTRODUCTION Field experience and laboratory investigations have established contamination by drilling mud as a major factor in oil well cement failures. During 1955, 12 attempts were required to set six open-hole cement plugs in the Timbalier Bay field, La. Eighteen to 30 hours elapsed between placing and testing the plugs in preparation for sidetracking operations. Considerations of rig time expense required immediate resetting where soft cement was drilled after a reasonable waiting period. Sea water drilling mud was used in each well and daily additions of thinners, usually lignites, had been required. Sodium carboxymethylcellulose had been added regularly to control fluid loss. The 50 per cent plug failures were attributed primarily to contamination by the mud. Similar experiences can be found in other fields along the Texas and Louisiana coasts where drilling muds normally contain large quantities of organic treating materials. Cement contamination was the subject of a survey by the Mid-Continent District Study Committee on Cementing Practices and Testing of Oil-Well Cements of the API.3 Data collected from member laboratories and released in Sept., 1951, reported the effects of a number of drilling mud treating chemicals on cement. The study revealed that many of the additives, notably the organic materials in relatively small quantities, had marked effects on the properties of cements tested. Severe losses in strength and erratic thickening time resulted from small additions of mud treating chemicals such as quebracho, starch, sodium carboxymethylcellulose, and lignite. The report included no recommendations of methods for overcoming the problem. One investigation of the contamination problem reported the successful use of activated charcoal in setting cement plugs after conventional slurries had failed.4,5 The investigation indicated that an optimum concentration of 5 per cent activated charcoal was effective in combating contamination from 16.7 volume per cent of treated mud. Laboratory and field muds were included in tests and contained varied quantities of ode or more of the following: quebracho, caustic, starch, lime, and calcium lignosulfonate. The function of the charcoal appears to be physical, removing the organic materials by adsorption. The method may be employed in API Class A or Class D (unretarded slow set) cements. The chemical approach presented here is based on

Jan 1, 1958

By Joseph L. Gillson

Bentonite, designating a distinct type of clay, is a young name in mineral nomenclature in the light of the age-old names of most other useful nonmetallics. The earliest references in literature are to "soap clay" (1873) "taylorite" (1888) and finally "bentonite" in 1897, from its occurrence in the Fort Benton series of rocks near Rock Creek, Albany County, Wyoming. Bentonite is a rock term and consists largely of montmorillonite clay. The latter name was proposed in 1847 for a plastic clay found at Montmorillon, France. A clay of apparently identical properties was described by Cronstedt of Sweden in 1788 and a number of other similar clays found in France were given other names in publications from 1853 to 1856. The mineral name montmorillonite was recognized by Dana in 1892. The recognition of "clay mineral" distinctions which led to the present-day classifications of clays by their chief mineral content, dawned in the early part of the twentieth century. Grim6 has aptly said: About 1924, Ross10 and some colleagues of the U. S. Geological Survey began a study of the mineral composition of clays that led to a series of monumental papers on the subject. By the early 1930&apos;s what has come to be known as the clay-mineral concept became firmly established in the minds of a great many people actively studying clay materials. The clay mineral concept designates the major clays as kaolins, montmorillonites and illites and by this concept bentonites are now defined as "fine-grained clays containing not less than 85 pct montmorillonite" and a wide variety of clays found all over the world are included in that classification. They could all properly be called "montmorillonite clays" but the common commercial name is bentonite. For a period of over forty years from the time of the earlier discoveries, bentonite was thought to be only the sodium type highswelling clay produced principally in Wyoming. By the clay mineral concept, non-swelling montmorillonite clays also became known as bentonite. In the trade there are two broad divisions-sodium bentonite, often called Wyoming or "western," which expands in water and carries sodium as its predominant exchangeable ion, and calcium bentonite often called "southern," which has negligible swelling and carries calcium as its principal exchangeable ion. There are many intermediate gradations. Properties The mineralogy and chemistry of the clays are so complex that the subject cannot be summarized briefly. The reader is referred to Chapter 12 of this volume in which the subject is treated at some length. Grim6 gave the formula for montmorillonite as (OH)4Si8AL4020.nH2O. He wrote: Montmorillonite is composed of units made up of two silica tetrahedral sheets with a central alumina octahedral sheet. . . . Exchangeable rations occur between the silicate layers. . . . The words "tetrahedral" and "octahedral" refer to the coordination number of the cations in the unit cell in the crystallographic lattice. Carroll5a stated: That the montmorillonite structure is the same as that of mica, but the layers are not held together by K+ ions; and water and other polar molecules, such as organic molecules, can enter between the unit layers and cause expansion. Ex-

Jan 1, 1960

By W. C. Ellis, E. S. Greiner

METALLIC titanium has been prepared in small quantities since the beginning of the century. Hunter1 reported in 1910 that he obtained a malleable product of 99.9 pct purity by the reduction of the tetrachloride by sodium in a closed container. Later Van Arkel2 and Fast3 prepared small quantities of malleable titanium by thermal decomposition of titanium iodide. Another method for producing malleable titanium from tetrachloride was reported by Kroll4 who used magnesium as the reducing agent. More recently Dean, Long, Wartman, and Anderson5 working at the U.S. Bureau of Mines have reported the preparation of the metal on a pilot plant scale by the reduction of titanium tetrachloride by magnesium in an atmosphere of helium. Their product, which is malleable, was used in the present investigation. Early in 1948 after the work of this paper: was completed Campbell, Jaffee, Blocher, Gurland, and Gonser6 described the strength and working characteristics of pure titanium which was prepared by the iodide method on a scale producing 300 to 600 g per run, in the form of 0.3- to 0.4-in. diam rods. Their product is characterized by low hardness and large capacity for cold work which they attribute to a high degree of purity with respect to oxygen, nitrogen, and carbon. Titanium has a melting point of about 1725°C5 it may be classed as a light metal since the specific gravity is 4.5 g per cc-1. The crystal structure is close-packed hexagonal from room temperature t0 885°C. Above this temperature the structure is reported7 as body-centered cubic. The change in crystal structure has been associated with discontinuities in specific heat8 electric resistance9 and thermoelectric force10 at temperatures near 890°C. It is reported11 that annealed titanium has a tensile strength 0f 78,700 psi which can be increased by cold-work to 123,000 psi. In the present investigation, the lattice constants at room temperature, the thermal expansivity between 30 and 800°C, as well as the electrical resistivity and thermoelectric force against platinum between - 200 and 1000°C have been determined. MATERIALS For the measurements, two series of specimens were prepared from titanium furnished by the U. S. Bureau of Mines. The first was lade from an annealed sintered compact, 0.38 in. thick. Sections of the compact were cold-swaged with intermediate anneals in vacuum to the sizes used. Sizes over 0.25-in. diam were annealed at 1000°C and smaller sizes at 800°C. Specimens originating from the sintered compact are designated in this paper as A. The second series of specimens was lade from a rod of titanium, 0.19 in. in dial, which was cold-swaged with the necessary intermediate anneals to the required sizes. This series of specimens is designated B. The impurities in the specimens of titanium, determined by chemical analysis, are given in Table I. Oxygen and nitrogen which were not determined by analysis, are probably present although in small quantities in view of the ductility of the material.

Jan 1, 1948

By S. A. Herres, A. R. Elsea

Temper brittleness refers to the loss in the notched-bar impact resistance encountered in most medium- or low-alloy steels when they are tempered within the temperature range of 700 to ll00°F or slowly cooled from a higher tempering temperature. Temper brittleness is important because it impairs the service properties of otherwise suitable steels over the range of hardnesses obtained at medium tempering temperatures and because it is impractical to cool pieces of large section rapidly enough from higher tempering temperatures to prevent temper brittleness. The problem of temper brittleness has always been closely associated with ordnance manufacture because armor plate and gun steels require good shock resistance and are often heat treated in heavy section. However, it is now realized that many brittle failures in structural alloy steel parts are attributable to temper brittleness, and there is little question that it contributes to the low impact resistance of alloy steels used in the hot-rolled or normalized condition which are slowly cooled from the hot-rolling or normalizing temperature. Recently Hollomonl has presented a comprehensive summary of the literature on the subject and an excellent description of the manner in which temper brittleness affects the notched-bar impact resistance and other mechanical properties of steel. Carpenter and Robertson2 have given a good analysis of the probable mechanism of temper brittleness, which is similar in many respects to the precipitation-hardening phenomenon. Fig 1 is their diagram illustrating the response to tempering of a susceptible steel. Three changes are recognized as the temperature of tempering a previously quenched steel is raised: (1) pre- cipitation occurs more rapidly and to a greater extent and the notched-bar impact value falls to a minimum; (2) coalescence of the precipitated particles begins to be effective and the impact values for both rapidly cooled and slowly cooled specimens increase; (3) the precipitate goes back into solution at higher tempering temperatures and the impact values of specimens cooled rapidly enough to retain the solution increase, while reprecipitation occurs in slowly cooled specimens and their impact values decrease again. No change must proceed to completion before the following one begins and there is overlapping in temperature ranges. Although there have been a large number of experimental investigations of temper brittleness, insufficient evidence has been accumulated to permit definite identification of the precipitate wnich causes temper brittleness nor have the specific effects on it of various alloy elements and impurities in steel been definitely established. This lack of evidence is largely a result of the lack of a suitable measure for temper brittleness. Temper brittleness is evidenced by an increase in the temperature of brittle failure of notched-bar impact specimens, but most of the data are in the form of an arbitrary susceptibility ratio of the room-temperature impact value for specimens quenched from a high tempering temper to that of similar specimens furnace cooled from the temper. It is obvious that this numerical ratio is dependent upon the type of specimen used and the specific conditions of testing rather than the characteristics of the steel. In general, manganese, chromium, and nickel alloy steels are most susceptible to temper brittleness and molybdenum has heen used to decrease

Jan 1, 1950

By G. W. Healy, N. R. Griffing

The activity coefficient of sulfur in Cr-Fe-S melts was determined by measuring the values of Ph3Rh,in equilibrium with such melts. The results showed that chromium has a pronounced negative effect on the activity coefficient of sulfur, which up to about 20 pct Cr may be represented by the equation: log f; = - 0.019 pct Cr It was also found that the influence of chromium was not altered by the presence of appreciable amounts of carbon or silicon. The influence of alloying elements on the activity of sulfur in molten iron has been the subject of many investigations; however the effect of one important alloying element, chromium, has not been reported, and the object of the present investigation was to determine its effect on the activity coefficient of sulfur in liquid Fe-Cr-S alloys both in the absence and in the presence of carbon and/or silicon. EXPERIMENTAL PROCEDURE The general method employed consisted of passing mixtures of hydrogen and hydrogen sulfide over the sulfur-containing melt of interest and analyzing the outgoing gas to determine the equilibrium value of which resulted from the reaction shown in Eq. 111. H, (gas) + S (dissolved in melt) = H,S (gas) 111 The activity coefficient of sulfur, fs, was then calculated with Eq. [2] in which K, is the known equilibrium constant of Eq. [I] for dilute solutions of sulfur in iron. Raw materials used in the preparation of the charges included commercial grades of electrolytic iron and chromium and carbon-reduced, acid-treated silicon of 99.9 pct purity. Oxygen in the former presented no problem since it was removed by hydrogen in the normal course of an experiment. Carbon was added in the form of premelted iron-carbon and chromium-carbon master alloys. Sulfur was charged as iron sulfide prepared by first heating powdered iron and sulfur in air in an alumina dish until reaction occurred, and then deoxidizing by melting in a hydrogen atmosphere. Commercially bottled hydrogen and hydrogen sulfide were used after being passed through purification systems containing palladium, "Drierite," and magnesium perchlorate in the case of hydrogen, and "Drierite" alone in the case of hydrogen sulfide. Lamp-grade cylinder argon served as a flushing agent without further purification. Charges weighing from 300 to 500 g were placed in a high-purity alumina crucible of 0250-ml capacity and heated in an argon atmosphere in the induction-heated carbon-tube furnace illustrated in Fig. 1. During heating, a dry hydrogen atmosphere was substituted for argon in order that deoxidation of the charge and flushing out of argon would be accomplished sooner. After the charge melted, a Pt-Pt 10 pct Rh thermocouple contained in an alumina protection tube was immersed in the melt, and the desired melt temperature (usually 1600°C) was established. Higher temperatures up to 1760°C were required for some chromium-rich alloys because of their higher melting points, and in these cases a Pt 6 pct Rh-Pt 30 pct Rh thermocouple was used. The thermocouple output was fed to an automatic controller which provided straight line temperature

Jan 1, 1961

By H. E. Stamm, H. H. Spain, R. C. Rumble

This paper presents a reservoir analyzer study of the performance of the Woodbine formation in the East Texas basin. The study was made possible by the compilation of available information on the configuration. thickness and the pressure drawdown of the formation. The investigation was made of the pressure variations in the basin incident to production from the several Woodbine reservoirs. In addition, the apparent compressibility of Woodbine water was evaluated so that the potential water yield of the formation could be determined. The distribution of permeability of the Woodbine sand and the interference between producing areas were also investigated. In conjunction with this basic study of the Woodbine sand, an acceptable match of the production-pressure relationship in the East Texas Field was established on the analyzer. INTRODUCTION When production is taken from a reservoir contiguous to an aquifer, the resultant pressure gradient causes a water influx into the reservoir. For some years it has been the practice to predict the performance of water drive reservoirs with mathematical equations that relate the water influx into reservoirs to their pressure behavior. A rigorous solution of these equations is quite complex: hence, the conventional method requires the simplifying assumptions that the formation have constant thickness, permeability and poiosity, and that it have a known and regular shape. It is necessary to use performance records of the reservoir in question to determine the equation constants that make the results of the mathematical calculations duplicate the reservoir history. The values of the constants determined in this manner sometimes differ so greatly from theoretical or measured values that the constants appear unreasonable. The equation constants comprise such factors as the thickness, porosity and permeability of the formation, and the viscosity and compressibility of water. Usually the thickness, porosity and viscosity are known within a reasonable degree of certainty. whereas the formation permeability and the water compressibility are known with considerably less certainty. Hence. permeability and compressibility values are arbitrarily selected that will make the mathematical equations duplicate the reservoir behavior. In many reservoir studies the value of the compressibility of water thus selected has exceeded the reported value by a factor of from severalfold to manyfold. Whether this excessive value results from the inadequacy of the mathematical approach to take into account the shape irregularities and the heterogeneities of the aquifer, or is due to some type of formation compaction and decrease of porosity has not been established. Because of the significance of the potential water yield of formations with reference not only to oil reservoirs but to water resources as well, it is very important that a representative value for the effective water compressibility be determined. One of the best known examples of a field for which it has been possible in the past to predict the future reservoir pressure is the East Texas Field. Until about 1943 it was possible by means of mathematical equations to duplicate past pressure behavior and to predict with a high degree of accuracy the reservoir pressure of the field. Since 1943, however, the calculated pressures have deviated progressively from the observed pressures to such a degree that in recent years, it has

Jan 1, 1951