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By Clarence Zener

THE internal friction of nonferrous metals vibrating at low stress amplitudes has so far always been successfully interpreted in terms of inhomogeneities of one sort or another. Examples are the fluctuation of stress across a specimen vibrating transversely,1,2,3 the stress inhomogeneities due to the elastic anisotropy and partial random orientation of the individual crystallites,4,5 localized weak regions introduced by cold-working,6,7 grain boundaries and possibly twinning planes.8,9 Perfect single crystals are, by definition, homogeneous. Actual single crystals usually, perhaps always, contains some imperfections. The present investigation. was undertaken to determine whether the internal friction of single crystals may likewise be attributed to inhomogeneities. This study was made possible through the gift of a large single crystal of 70-30 alpha brass by H. L. Burghoff, of the Chase Brass and Copper Co. The specimen, ½ in. in diameter and 10 in. long, was similar to samples previously described by Mr. Burghoff.10 EXPERIMENTAL METHOD The experimental method used has previously been described in Institute papers.5,6,9 The measure of internal friction adopted here, 1/Q, is (1/p) X the logarithmic decrement, a measure used by some writers, and is also (1/2p) X the specific damping capacity, a measure used by other writers. In all measurements the stress level was kept so low that the measurements were independent of stress level. In all measurements in which the temperature was varied, observations were made as the specimen slowly cooled from its highest temperature. The specimen was vibrated transversely. Observations were made at the funda¬mental frequency and at the first overtone, of about 620 and 1710 cycles per second, respectively. No attempt was made to avoid acoustical losses. EXPERIMENTAL RESULTS The specimen was annealed for several hours at 450°C. The temperature dependence of the internal friction was then determined from room temperature to 400°C. As shown in Fig. 1, the internal friction increased by only a factor of 2 from room temperature to 300°C., then by a factor of l00 during the next 100° interval. These measurements are consistent with the view that the observed internal friction is the superposition of two distinct parts. One, dominant at room temperature, is nearly independent of temperature. This part may be accounted for by acoustical losses and by transverse thermal currents. It was not further investigated. The second part, when plotted in the manner of Fig. I, lies upon a straight line. Therefore it has a heat of activation H; i.e., it varies with temperature as Internal friction e~H/RT [I]

Jan 1, 1942

By A. W. Hale

IN a work published in 1838, De Morgan, the author of the article on "Probabilities,' in the Encyclopedia Metropolitana, says " The method of least squares is not yet introduced into the affairs of common life,….that many things which are demonstrable only by the higher branches of mathematics are looked upon as useless." And he mentions an instance in which "a method was suggested for estimating the relative importance of boroughs, by considering their population and contributions to the revenue com-

Jan 1, 1881

By W. Spencer Reid

ALTHOUGH there have been some developments during the last five years which have had far- reaching and important bearing on lead smelting, it cannot be said that any basic principles of pyrometal-lurgy have been discovered. Eighteen or twenty years ago the Dwight & Lloyd sintering machine was intro-duced and literally turned the roasting end of lead smelting upside down. There has been nothing com-parable to the advent of the sintering machine during recent years. Actual blast-furnace practice today is slightly, if any, better than it was five years ago ; although immeas-urably better than it was twenty to thirty years ago. Some tell us that as far as cleanness of slags is con-cerned, it is no better today than in the days of the old Romans. The metallurgist of a generation ago did very good work, considering the equipment he had available. It is true he was working with the cream of the ores, the clean oxides and carbonates and the low-zinc sul-fides. He was troubled very little with high zinc and selected his type of slag according to preference of -some authority such as Eilers, Iles, Raht, Hahn, etc. As these free-smelting ores were depleted the complex ores were encountered, and the metallurgist gradually discovered that he had to forget the old type slags and run a slag according to the percentage of zinc on the charge. I believe it is now universally agreed that SiO2 and CaO must be lowered and FeO raised in a slag as the ZnO increases. The ratio of these variations is practically uniform and can be relied upon over wide fluctuations of the determining element, zinc. These "bastard" slags, as they are sometimes inappropriately designated, are actually in daily use, and the metallurgist of today has been forced to adopt certain standards, as a guide to successful operation. These slags practically refute the old Eilers' theory that all good slags are chemical combinations of SiO2 with FeO and MnO, and CaO and MgO. Eilers' and the other type-slag theories were based upon the assumption that a good slag must con-form to a definite formula, such as 3 (FeO)2 SiO2 + 2 (CaO)2 SiO2 or 2 (FeO)2 SiO2 + 2 (CaO)2 SiO2 which respectively figure 31.3 and 36 per cent SiO2. The SiO2 was supposed to remain constant even with the entrance of impurities such as Zn and A1,0? into the slag. The increasing amount of impurities, espe-cially Zn, soon discredited the theory, for in actual practice the slag failed to run freely.

Jan 1, 1927

By C. F. Jr. Tolman

IN February 1913, Prof. L. C. Graton and Dr. Joseph Murdoch1 presented to the American Institute of Mining Engineers a notable contribution to economic geology under the title The Sulphide Ores of Copper. The value of the work was recognized by mine operators, and Mr. Graton was assisted in his plan to extend his investigations,. by the organization of a commission to undertake a "secondary enrichment investigation." In this work lie secured the cooperation of the Geophysical Laboratory of the Carnegie Institution of Washington. Their report 2 on the chemical phases of the investigation has just been published. Incidental to investigations 3 carried on in my laboratory by advanced

Jan 2, 1916

The Committee on Nominations begs to submit the following names as its nominees for the respective offices indicated: For President, SIDNEY J. JENNINGS, New York. For Vice-Presidents. C. W. GOODALE,* Butte, Mont.; MARK, L. REQUA, San Francisco. For Directors, J. E. JOHNSON, JR., New York; ALLEN H. ROGERS, Boston; HOWARD N. EAVENSON, West Virginia; ROBERT AI. RAYMOND, New York; WILLET G. MILLER, Canada. The nomination for President has attracted the attention of a large number of members, as is evidenced by the receipt of many hundreds of letters and postcards. Most of these favored either Sidney J. Jennings or Philip N. Moore, each of whom received many cordial endorsements. Such a wide interest on the part of the members is a very wholesome sign, but where there is so much activity it is natural to expect a certain amount of criticism. Some of the letters indicate that the authors feel that the nomination of President should be left entirely to the Committee on Nominations without any effort by the members at large to influence them. Others feel that the nominations are largely controlled by a small group and that the members at large can have little influence. As the result; of the experience of the last few months; a majority of the Committee on Nominations begs leave to suggest that the method of making nominations be changed so that two candidates, at least, for the various offices to be nominated, and suggests that the Directors appoint a committee to investigate this question thoroughly with. a view to making definite recommendations. In accordance with its opinion that the best interests of the Institute would be served by a change in the Constitution, allowing the nomination of two candidates, and in view of the fact that this Committee has no authority to make more than a single nomination for each office, considering the high standing of both Mr. Jennings and Mr. Moore and the large number of members favoring each of these gentlemen, this Committee respectfully suggests the desirability of ,the immediate nomination of Philip N. Moore by a petition of 25 members in accordance with the present Constitution. This Committee regrets, its inability to make two nominations. Respectfully submitted, S. W. MUDD, Chairman.

Jan 1, 1917

(There are 70 Student Chapters in the United States, 2 in Canada) University of Alabama-University, Alabama, Mining and Metallurgical Society, Win L Mason University of Alaska-College, Alaska, Mining Society of the University of Alaska, E H Beistline University of Arizona-Tucson, Arizona, Miners Society Birmingham-Southern College-Birmingham, Alabama, Pick and Hammer Club, Daniel D Arden University of British Columbia-Vancouver, British Columbia, G M Dawson Club, H C Gunning University of California-Berkeley, California, Mineral Technology Association, W H Somerton Carnegie Institute of Teehnology-Pittsburgh, Pennsylvania, The Metals Club, Gerhard Derge Case Institute of -Technology-Cleveland, Ohio, Case Metallurgical Engineering Society, Robert F Hehemann

Jan 1, 1956

By Thomas Brownfield

Development and production activity in Oklahoma during the year 1940 was of routine nature. Production, according to the Corporation Commission's figures, averaged 409,100 bbl. daily as compared with 421,000 bbl. for the year 1939. Discoveries were of minor importance except for the Cumberland pool in Marshall and Bryan Counties, in the southern part of the state. Maintenance of a relatively stable producing rate is attributable to the drilling of new wells and the recompletion of many old wells in the previously established producing areas. During the year 1785 new wells were drilled, a decline of approximately 10 per cent as compared with the previous year. Of the wells drilled, 962 were oil wells with a combined initial production of 241,000 bbl. daily, 172 were gas wells having aggregate capacities of 1205 million cu. ft., and 651 were dry holes. Wildcat activity increased 20 per cent over 1939 and 227 such wells were completed during the year; that isl 43 oil wells, 16 gas wells, and 168 dry holes. In addition to the new work completed, 603 wells were recorded as having been drilled deeper or plugged back to test new horizons; included were 334 producing wells with total initial production of 65,000 bbl. daily, 37 gas wells with initial aggregating 305 million cu. ft., and 232 abandonments. Footage drilled amounted to 4,730,000 ft., an average of 2650 ft. per well as com-pared with an average depth of 2600 ft. recorded the previous year. The principal new pools discovered as a result of the exploratory drilling were Cumberland; East Cromwell, in Okfuskee County, and Prague, in Lincoln County. At the end of the year Cumberland had 13 completed wells, which averaged 700 bbl. initial through tubing from the Simpson Bromide formation (Ordovician) at 4750 ft. East Cromwell had 10 wells with average initial of 435 bbl. in the Cromwell sand (Pennsylvanian) at 3460 ft. Prague had II wells with an initial average of 220 bbl. from the Senora sand (Pennsylvanian) at 3260 ft. There were notable extensions to the Dill pool, Okfuskee County, and to the Hewitt pool, Carter County. At the end of the year, 19 producing wells had been drilled in the former, with initials averaging 1000 bbl., and 63 wells averaging 150 bbl. daily in the latter. There were no notable changes in the policy of State conservation authorities with respect to proration. The Bureau of Mines recommendations for the year averaged 413,000 bbl. daily; the State author-ities fixed allowables at an average of 406,000 bbl. daily, while, as noted above, production averaged 409,100 barrels. The most important development in the older areas occurred in the following pools: Billings.—Seven oil wells with an average initial production of 2500 bbl. and two dry holes were completed during the year. Production from the Simpson horizon averaged 6025 bbl. daily as compared with 5950 the previous year. Production from this field has been almost steady since reaching its peak early in 1937. The major portion of the pool is efficiently operated as

Jan 1, 1941

By Thomas Brownfield

Development and production activity in Oklahoma during the year 1940 was of routine nature. Production, according to the Corporation Commission's figures, averaged 409,100 bbl. daily as compared with 421,000 bbl. for the year 1939. Discoveries were of minor importance except for the Cumberland pool in Marshall and Bryan Counties, in the southern part of the state. Maintenance of a relatively stable producing rate is attributable to the drilling of new wells and the recompletion of many old wells in the previously established producing areas. During the year 1785 new wells were drilled, a decline of approximately 10 per cent as compared with the previous year. Of the wells drilled, 962 were oil wells with a combined initial production of 241,000 bbl. daily, 172 were gas wells having aggregate capacities of 1205 million cu. ft., and 651 were dry holes. Wildcat activity increased 20 per cent over 1939 and 227 such wells were completed during the year; that isl 43 oil wells, 16 gas wells, and 168 dry holes. In addition to the new work completed, 603 wells were recorded as having been drilled deeper or plugged back to test new horizons; included were 334 producing wells with total initial production of 65,000 bbl. daily, 37 gas wells with initial aggregating 305 million cu. ft., and 232 abandonments. Footage drilled amounted to 4,730,000 ft., an average of 2650 ft. per well as com-pared with an average depth of 2600 ft. recorded the previous year. The principal new pools discovered as a result of the exploratory drilling were Cumberland; East Cromwell, in Okfuskee County, and Prague, in Lincoln County. At the end of the year Cumberland had 13 completed wells, which averaged 700 bbl. initial through tubing from the Simpson Bromide formation (Ordovician) at 4750 ft. East Cromwell had 10 wells with average initial of 435 bbl. in the Cromwell sand (Pennsylvanian) at 3460 ft. Prague had II wells with an initial average of 220 bbl. from the Senora sand (Pennsylvanian) at 3260 ft. There were notable extensions to the Dill pool, Okfuskee County, and to the Hewitt pool, Carter County. At the end of the year, 19 producing wells had been drilled in the former, with initials averaging 1000 bbl., and 63 wells averaging 150 bbl. daily in the latter. There were no notable changes in the policy of State conservation authorities with respect to proration. The Bureau of Mines recommendations for the year averaged 413,000 bbl. daily; the State author-ities fixed allowables at an average of 406,000 bbl. daily, while, as noted above, production averaged 409,100 barrels. The most important development in the older areas occurred in the following pools: Billings.—Seven oil wells with an average initial production of 2500 bbl. and two dry holes were completed during the year. Production from the Simpson horizon averaged 6025 bbl. daily as compared with 5950 the previous year. Production from this field has been almost steady since reaching its peak early in 1937. The major portion of the pool is efficiently operated as

Jan 1, 1941

By W. L. Crentz, E. E. Donath, D. Doherty

Maurice Rey—The influence of cyclone diameter upon the fineness of separation is an important point which, however, cannot be discussed adequately if the injection pressure or the rate of flow are not specified. Perhaps some light can be thrown on the matter by using the formulas derived by Dahlstrom. Let us consider several geometrically similar cyclones where the apertures e and b are equal and proportional to the diameter D and which are operated with the same pressure drop. Eq 8 of Dahlstrom's paper can be written: Q Q = K D'. " or. if F is constant: Q = K D18 K is a constant of proportionality. Introducing this value of Q in eq 13 gives elimination efficiency = K D0' " Elimination efficiency, in the terminology of Dahlstrom, means the diameter of particles, in microns, which divide equally between the underflow and the overflow. This denomination is regrettable and it would be preferable to call it diameter of separation or characteristic size or any other name connoting a size rather than an efficiency. Whatever the name used, the above equation shows a slow increase in the fineness of separation when the diameter of the cyclone decreases. For example, if a 14-in. cyclone gives a 400-mesh separation (37 microns), geometrically similar cyclones, having the same pressure drop will give separations at the sizes shown below.

Jan 1, 1951

By E. E. Donath, W. L. Crentz, D. Doherty

Maurice Rey—The influence of cyclone diameter upon the fineness of separation is an important point which, however, cannot be discussed adequately if the injection pressure or the rate of flow are not specified. Perhaps some light can be thrown on the matter by using the formulas derived by Dahlstrom. Let us consider several geometrically similar cyclones where the apertures e and b are equal and proportional to the diameter D and which are operated with the same pressure drop. Eq 8 of Dahlstrom's paper can be written: Q Q = K D'. " or. if F is constant: Q = K D18 K is a constant of proportionality. Introducing this value of Q in eq 13 gives elimination efficiency = K D0' " Elimination efficiency, in the terminology of Dahlstrom, means the diameter of particles, in microns, which divide equally between the underflow and the overflow. This denomination is regrettable and it would be preferable to call it diameter of separation or characteristic size or any other name connoting a size rather than an efficiency. Whatever the name used, the above equation shows a slow increase in the fineness of separation when the diameter of the cyclone decreases. For example, if a 14-in. cyclone gives a 400-mesh separation (37 microns), geometrically similar cyclones, having the same pressure drop will give separations at the sizes shown below.

Jan 1, 1951

Addicks, L Ambler, J O Anderson, F B Armstrong, T Allen, L M, Jr Arnold, C E Adams, C E Adams, R E Anderson, A J Booth, E L Bernhardt, D I Boyd, W S Browning, W C Blake, D E Black, T B Bergman, Julius Bowen, H P Beckett, P G Blickensdefer, F C Bond, Josiah Butler, P P Bondlas. Y

Jan 1, 1923

By J. P. Heller

The purpose of this discussion is to comment briefly on one of the points raised in the paper. The topic is that referred to in the Conclusion 2, in which the authors note a "disproportionate increase in mixing rate" as they proceed from a displacement performed at viscosity ratio 0.998 to one at 1.002. The recovery curve of this displacement, Fig.2A, shows a quite noticeable difference between the two runs in which displaced and displacing liquids were interchanged. This difference is ascribed by the authors to the change in viscosity ratio between the two experiments. This interpretation of the experimental results must certainly be based on rather precise measurements of the fluid viscosities or, at least, of the ratio of their viscosities. The ordinary Ostwald viscometer, employed in the usual way, is only just able to distinguish between liquids whose viscosities differ by two or three parts per thousand. The experimental refinements which then must have been necessary to measure with any precision a viscosity ratio of 1.002 would be worthy of mention. Indeed, one would have expected the authors to devote at least a paragraph to the display of this technique. For the same reason - to emphasize that the details of such unusually critical experimental work should be reported and discussed in the literature — I would have liked to see some comment by the authors on the requirements for temperature control during both the viscosity measurements and the displacement experiments. The temperature coefficient of viscosity of Soltrol C at room temperature has been measured in this laboratory at about - 1.9%/1°C. How much did the coefficients for the fluid mixtures used in the experiment differ from this and from each other Even if the two fluids were identical in this respect, it would appear that a temperature difference of .l°C between them in the flow system would produce a viscosity con- trast equal to that imposed by their composition. Reference to the experimental solutions of these problems would render Conclusion 2 more credible. Published theoretical work on the stability problem contains no indication of such extreme sensitivity to the viscosity ratio in the immediate neighborhood of unity. On the contrary, perturbation calculations such as those made by Chuoke1 and Perrine2 lead to initial finger growth rates proportional to the first power of the viscosity difference. The later instability growth calculated by Scheidegger,3 using the assumption of zero pressure gradient perpendicular to the average flow, is also simply proportional to the viscosity difference. The conflict regarding the sensitivity of the dependence of instability growth or mixing rate on the viscosity contrast needs explicit recognition in the literature. In particular, it would seem that the experimental work reported here should be supported by a more detailed description of the viscosity controls. Further discussion of possible alternative interpretations of the data would also be in order. For instance, is it possible that the unconsolidstted bead pack used changed its characteristics between the runs (due, perhaps, to the handling and inverting involved in the injection of the front) Or, are the data points of Fig. 2A averages from several runs performed in a series in which the two liquids alternated as displaced and displacing fluids? To summarize, it seems to me that the relationship asserted by Conclusion 2 in the paper needs the support of more detailed experimental evidence. REFERENCES 1. Chouke, R. L., van Mews, P. and van der Poel, C.: "The Instability of Slow Immiscible Viscous Liquid-Liquid Displacements in Porous Media", Trans., AIME (1959) Vol. 216, 188.

By HENRY FA

HENRY FAY (communication to the Secretary*).-In reply to the discussion of my paper, I wish to take this opportunity to express my appreciation to the Chairman and the various gentlemen who have taken part. I regret that others have not offered criticism, for honest differences of opinion often lead to the truth, and suggest new lines of work. An experiment has been made which bears on Prof. Sauveur's discussion and which helps to emphasize the conclusion that cementation is not a factor in the hardening of: the surface. Dr. Langenberg, of the Watertown Arsenal, has heated for me, in vacuo at 1,000° C., a piece of the metal containing a hard surface. The microstructure shows uniform distribution of carbon throughout the metal, showing that no carbon has been added to .the surface and heating in vacuo has prevented any oxidation of the surface.

Jan 6, 1917

By L. R. Raymond, J. L. Hudson

This paper proposes a comparatively short-term (8 to 10 hours) well test for detecting and characterizing well-bore damage and for measuring mean formation permeability. The proposed test is made by injecting fluid at constant pressure, recording injection rate as a function of injection time. After one to four hours of injection, the well is shut in and fall-off of bottom-hole pressure is obtained as a function of shut-in time. Formation permeability is estimated by an iterative technique. First, a value of formation permeability is assumed. Then, a plot of the recorded injection rate as a function of dimensionless time is made, using the assumed pertneability value. From the slope of the injection-rate curve. a new value of formation permeability is calculated. If the new value agrees with the original assumed value, the assumption was the correct formation permeability. If the values do not agree, the process is repeated using the new permeability value in the calculation. Convergence is rapid, and a reliable permeability value results. Pressure fall-off data are used to check the result. Graphs of pressure and injection rate us functions of time given in the paper show that changes in permeability of the formation in the neighborhood of the wellbore are disclosed by this technique. Thus, the short-term test can he used to detect formation damage. Also, a rough measure of the radial extent of damage can be inferred, which is helpful in designing stimulation treatments. The mathematical model used for this work was a single-zone, horizontal reservoir with a damaged zone in which permeability decreased continuously as radial distance to the wellbore decreased. This model is more realistic than the usual two-zone, discontinuous permeability model used in published works; calculations indicate the realistic model is valid. Vertical variations in horizontal permeability were studied with this model, and results indicate that the permeability measured by the short-term test is the mean horizontal permeability for the vertical interval tested. The proposed short-term test thus should be useful in detecting and characterizing formation damage and in measuring formation permeability needed in calculating reservoir transmissibility. INTRODUCTION To plan the most efficient production or injection schedule for a well and to design or evaluate the optimal stimu- lation treatment, it is necessary to know the properties of the reservoir adjacent to the well, particularly the reservoir transmissibility and characteristics of a damaged zone, if one exists. Several techniques for determining reservoir transmissi-bility from well tests have been presented in the literature. 1,2,3,4 All these techniques rely on conducting constant-rate well tests that often are difficult to execute. A constant-pressure well test is generally easier to carry Out. and this paper contains the first available method for the analysis of constant-pressure well tests. Determination of wellbore damage from transient well tests has been the subject of several papers."" From these studies it is apparent that information necessary for determination of the characteristics of a damaged zone is available shortly after the transient well test is initiated. Consequently, it may not be necessary to carry out an extensive well test (for example, a pressure build-up test) if the primary purpose of the test is to detect the existence of wellbore damage. All previous studies of well testing to determine wellbore damage have been based on the two-zone perrneability model. In this model the damaged zone has a permeability k,, extending to a radius r,,, and the formation permeability k obtains from r, to the drainage radius r,.. Consequently, there is a discontinuity in permeability at r = r,,. This discontinuity can be eliminated by assuming a continuous variation in permeability through the damaged zone. The effect of this assumption on transient well tests is discussed in following sections of this paper. In addition, all formations have within them vertical permeability variations associated with lithology changes throughout the zone of interest. This paper also considers the effect of these variations on transient well tests. ANALYSIS OF CONSTANT-PRESSURE WELL TESTS The mathematical analysis associated with the injection of fluid at constant wellbore pressure into a single-zone, horizontal reservoir completely filled with a fluid of small and constant compressibility and constant viscosity is given in Appendix A. In this analysis it is assumed that the well is located at the center of an undamaged, circular drainage area. From this analysis, the formation permeability can be obtained as follows. 1, Estimate a value for the formation permeability k. 2. Prepare a plot of injection rate q vs

Jan 1, 1967

By Y. Jeannin, C. Mannerskantz, F. D. Richardson

Measurements have been made between 1040o and 1300°C of the equilibrium between chromium metal, chromic oxide, hydrogen, and water. The results are in closer agreement with those deduced from recent thermal data than with previous equilibrium values. They lead to the equation ?G°1300°-1600°k = -266,700 + 59.95T ± 300 cal for the formzation of a mole of Cr2O3 from chromium and oxygen. This same equilibrium has been studied with the chromium dissolved in solid iron, and in this way chromium activities in Fe + Cr alloys have been established. The measuremenis show that there are substantial positive deviations from ideality in the a, and b phases, and support the results obtained by Heymer and Kubaschewski against those of other investigators. There is considerable disagreement between existing data,1"4 which is referred to in the Discussion, concerning the equilibrium Cr2O3 + 3H2 = 2Cr + 3H2O [l] There is also substantial disagreement between the results obtained by various investigators5-' who have measured the activities of chromium in its alloys with iron by the Knudsen effusion vapor pressure method. In view of the importance in metallurgical processes of chromium and its oxide and of Fe-Cr alloys, an attempt has been made to study equilib- rium [I] both with pure chormium metal and with chromium alloyed with iron, at temperatures between 1040o and 1300oC. From the work with the alloys it is possible to derive the chromium activities from the relationship

Jan 1, 1963

By R. Schuhmann, J. Th. Overbeek, P. L. De Bruyn

W. E. Ewers (Commonwealth Scientific and Industrial Research organization, Melbourne, Australia)— Any attempt to elucidate further the meaning of the contact angle, particularly if it deals with the magnitudes of those mysterious quantities rsa and YRL, is certain to receive attention from those interested in the fundamentals of flotation. It is imperative, therefore, that attention should be drawn to a serious defect in the treatment by de Bruyn, Overbeek, and Schuhmann. Their Eq. 5 dy = — ld/u — Th2odiH2n states correctly the relationship between the change in surface free energy dy, the surface excesses Tx and Th2o of the components x and H2O and the changes du, and dph2o in the chemical potentials of these components. This equation applies for constant pressure and con- stant temperature and for the interface of the solid in contact with the solution of X. The relation remains valid when 1.1 is defined so that TH2O becomes zero and the equation becomes dr = — r:dur [17] From this equation de Bruyn et al. correctly concluded that increased adsorption of the collector at the liquid solid interface would reduce the interfacial energy ysl. Their second conclusion, however, that an increase in the contact angle, corresponding to a greater decrease in rsa than in rsL can be attributed to greater adsorption of X at the solid-air interface than at the solid-liquid interface is quite unjustified. The portion of the solid surface from which the collector solution has been displaced by air must be considered in terms of the equilibria between the gaseous phase and the surface. If the pressure and temperature

Jan 1, 1955

By R. J. Bethancourt, D. M. Collingwood

The use: of a pilot waterflood is very desirable where all of the pertinent data necessary to initiate a full scale waterflood are not. available. This paper attempts to take a specific case and .show the step by step process of starting with a pilot waterflood and progressing to a full wale flood as results are obtained. INTRODUCTION Many of the older fields of Soutlwest Texas are approaching depletion by primary produrtion methods. As primary protlllc:inp operations on individual properties approach their economic limit. conflicting considerations face management: cm the one hand. plugging and abandonment of wells for equipment salvage; on the other hand, further investment in secondary recovery installtions, equilent, and well workovers in the interests of conservation anal additional oil reserves. In main instances, where primary production by pressure depletion and gas solution drive has been comparatively good, there still exists the possibility of an economic secondary recovery by waterflood. This is not necessarily true to the same degrre of all such fields. nor all portions of large fields. To properly evaluate the economics of a prospective water-11ot1cI requires a considerable amount of precise geological. statitical. and physical data Such information on the older field.; is often very limited. and in the case of the property discussed in this paper was considered inadequate to justify investment in an overall waterflood. Primary production was estimated at :39 per cent of the original oil in place, yet sand conditions of permeability and homogeneity, and position in the field appeared to be favorable for a limited margin of profit from a carefully controlled waterflood. Thus a pilot waterflood, with its minimum initial financial risk, followed by extension as favorable results were obtained, seemed to be the answer for the Sun Oil Co L. Wiederkehr lease in the Nortl Government Wells Field, Duval County. Texas DESCRIPTION OF RESERVOIR Approxinately 8,200 wells have been drilled in Duval County. As of March 1, 1952, there were 3,350 producing oil wells in 92 different fields, with very few flowing wells (Fig. 1.) Sun Oil Co. operates the I.. Wiederkehr lease located in the North Government Wells Field in Duval Countv. 85 mile. west of Corpus Chriti and 100 miles south of San Antonio. The lease has been subjected in part to a controlled five spot waterflood. The North Government Wells Field is roughly 7 miles long and 3 miles wide, with numerous overlapping producing zones. The L. Wiederkehr lease of 3.085 acres. Has seven producing zones from 700 to 7.500 ft. The lease is in the northern section of the field where it is widest, and has 710 acres productive from the North Government Wells .and. (Fig. 2.) The North Government Wells sand, Jackson group. Eocene age, at an average depth of 2.250 ft (minus 1.750 subsea). has a thickness range of 25 ft on the east side of the L. Wiederkehr lease to 4 ft on the west side. It has a slight overall dip to the North and East of some 33 ft to the mile.

Jan 1, 1953

By R. L. Fullman

IN the investigation of metallurgical transformations and the relationships between microstructure and properties of metals, it frequently is desirable to obtain a measurement of the relative amounts of the various phases present and of the mean size of particles into which each phase is dispersed. The relative amounts of the phases can be measured by the classical methods of area, lineal, and point analysis,1-5 in accordance with the principle that the volume fraction of a phase, the fraction of a polished cross section occupied by the phase, the fraction of a random line occupied by the phase, and the fraction of randomly arrayed points occupied by the phase are all equal. The validity of this relationship depends only on the attainment of a truly random sample of area, length, or points, and not on the size, shape, or distribution of the particles constituting the phase. Smith and Guttman8 have derived a relationship between the interface area per unit volume S, and the measurable quantities L., the interface length per unit area on a cross section, and NL, the number of interfaces per unit length intersected by a random line. Their equation, Sv = — L8 = 2NL is also valid regardless of the distribution of particle sizes and shapes. In contrast to the situation concerning measurement of relative fractions of phases and of interface area, the measurement of particle sizes in opaque samples has not been subjected to a complete analysis. It has been common to measure some lineal or area dimension of particles on a polished cross section and to use the mean value as a qualitative measure of particle size. In the present paper, quantitative relationships are established among the various mean dimensions on a polished cross section and the actual dimensions of the particles present. Particles of Uniform Size Spheres: If a metal sample contains particles of a phase a dispersed in the form of spheres of uniform size, a polished cross section through the sample will reveal circular areas of phase a with radii from 0 to ?, the radius of the spheres. Consider a cube of unit dimensions to be cut from the sample. If a cross section parallel to one of the cube faces is examined, the average number of particles per unit area (N,) equals the number of particles per unit volume (Nv) times the probability p1 that the plane would intersect a single sphere positioned at random within the unit cube. Since, of the various possible positions for the cross-sectional plane over the unit length from top to bottom of the cube, only those positions existing over the length 2r would lead to the plane intersecting the sphere, the probability of intersecting a single sphere is just 2r. N8= Nvp1 = Nd-2r [1] Applying the equality of area and volume fractions, the relationship is found between sphere size and average area s of uniform spheres intersected by a random cross section, 4 - f = NV V = Nr . — pra = N s = Nd . 2rs S = —pr2 [2] A similar analysis reveals the average traverse length across spheres of uniform size when random lines are passed through the sample. If a randomly oriented unit cube is cut from the sample and a randomly positioned line is passed through the cube parallel to a cube edge, the number of spheres intersected by the line (Nl) equals the number of spheres per unit volume times the probability p1 of the line hitting a single randomly placed sphere in the cube. Since possible positions of the line occupy unit area, and possible positions for which it will pass through the sphere occupy an area of pr2, the probability of the line hitting a randomly placed single sphere is pr2. NL = Nv p1 = Nvpr2 [3] Combining this relationship with the equality of volume and lineal fraction, the desired relationship is obtained between radius and mean lineal traverse length -i, for spheres of uniform size. 4 - - 3 l=4/3r [4] Circular Plates: Consider a sample containing particles of a phase a in the form of circular plates of uniform radius r and thickness t, where r >> t. If the plates are randomly oriented, as in a sufficiently large sample of a fine grained polycrystalline material, area and lineal analysis may be carried out with parallel cross-sectional planes and lineal traverses. If the plates are not randomly oriented, it is necessary to randomize the orientation of the cross-sectional planes and traverse directions. Let a unit cube be cut from the sample, and a cross-section plane be passed through the cube parallel to one of the cube faces. The number of plates cut by the cross-sectional plane per unit area is equal to the number of plates per unit volume times the probability of a plate intersecting a single randomly positioned and randomly oriented plate in the cube. If J is the component of the plate diameter in the direction normal to the cross-sectional planes, the probability of a plane cutting a single randomly oriented plate is equal to J, the mean value of J for all possible orientations of the plate. Let 4 be the dihedral angle between a plate and the cross-sectional plane, and let p?, d? be the probability that a plate makes an angle between 4 and ? + d? with the cross-sectional plane. Then for ran-

Jan 1, 1954

By David L. Holt, Walter A. Backofen, Anwar-uI Karim

Specimens of a hydrided Mg-0.5 Zr alloy were strained in tension at 500°C and constant rates of 2 x10-3 5 x 10-3, and 2 X 10" min-1. Hydride-denuded zones formed at grain boundaries normal to the tensile-stress direction as a result of magnesium transport during difusional flow. The width of the zones could be measured and the measurement used for calculating the diffusional component of the imposed tensile strain. The strain from diffusional flow was found to increase with imposed strain at a diminishing rate, tending to saturate at approximately 12 pct. Strain rate sensitivity of flow stress was low. The apparent non Newtonian character of the diffusional flow is attributed to a non Newtonian process acting in parallel with it which could be boundary shear. Fracture grows out of voids that form in the denuded zones. DEFORMATION of a grain by diffusion of atoms from boundaries stressed in compression to boundaries stressed in tension is Newtonian viscous,1-3 and evidence has accumulated in recent years that such a process may be responsible for the high strain-rate sensitivity of the flow stress of super-plastic alloys.4"7 One piece of evidence is that experimental stress: strain-rate relationships can be quantitatively explained.5-7 There is also metallo-graphic evidence of diffusional flow in superplas-ticity, but in a limited amount. The formation of striated bands on the surface of superplastically deformed specimens has been attributed to diffusional flow.5"7 The basis of that attribution came from experiments on a coarse-grained, nonsuperplastic and hydrided Mg-½ wt pct Zr alloy which formed hydride-denuded, light etching zones at tension-stressed boundaries when strained in tension at 270?C.6 The origin of these zones had already been traced to the diffusional flow of magnesium atoms to the boundaries.' The particular observations in the more recent work were of striated-band formation on the surface and denuded-zone formation internally, with both the bands and zones having the same width and appearing at tension-stressed boundaries. It was argued that the bands were a surface manifestation of the zones and hence of diffusional flow. Of course in superplastic alloys which do not contain internal metallographic "markers", the surface bands can be the only metallographic indication. In the present work, denuded-zone formation was utilized, as it has been by others,9-11 to extend the observations of diffusional flow and to measure the strain, ed, resulting from it. Grain size had to be large to measure ed with accuracy. The grain size chosen for this study was -30 , and with that a strain of 10 pct from diffusional flow produces a denuded zone only 3 µ in width. The large grain size naturally precludes superplasticity. The observations of diffusional flow were complemented by determining the strain from the other operative deformation modes: slip, e,, and grain boundary shear, egb. An incremental specimen extension is the sum of increments from slip, and grain boundary shear as well as diffusional flow. Division by a common length is required to convert to strain. If this length is taken as the initial specimen length, then imposed engineering strain, e, is given in terms of the component engineering strains by e = ed + es + egb [1] Stress:strain-rate relationships are determined by the way in which this "strain balance" is made up. EXPERIMENTAL Material. Zirconium hydride markers were introduced into the Mg-0.5Zr alloy by annealing in hydrogen at 450°C for 30 min. The hydride concentration was particularly high at zirconium rich stringers, which was fortunate in that the transverse boundaries at which denuded zones form lie perpendicular to the stringers. Grain size after annealing was 30 µ. Photomicrographs of unstrained and strained material are shown in Fig. 1. Procedure. Specimens were strained in tension with an Instron machine at crosshead velocities of either 2 x 10"3, 5 x X or 1 x 10-2 in. min-'. Specimen length and diameter were 1.0 and 0.2 in., respectively, so that initial strain rates in tests at constant crosshead speed were 2 x 10"3, 5 x X and 1 X l0-2 min-1. Tests were made at 500°C which is a compromise temperature at which diffusional flow is still measurable but grain growth is not active enough to interfere with metallographic measurements. The tests were made in a hydrogen atmosphere. Strain Balance. An equation additional to [I] is eg = ed + es [2] where eg is strain measured from grain elongation. Measurement was made of ed, eg, and, of course, e, which enabled all the strains in Eq. [I] to be determined. For this purpose, strained specimens were sectioned longitudinally, polished, and etched. The strain from diffusional flow, ed, was computed by measuring on photomicrographs the width in the tensile direction of denuded zones at either end of a grain XI, X2, adding them, and dividing by twice the initial longitudinal grain dimension L0, Fig. 2. Reported values are the results of measurements on seventy randomly selected grains; 95 pct confidence limits on ed were +1.5 pct strain. To measure eg, the maximum length, L, and the maximum width, W,

Jan 1, 1970

By Albert L. Toenges

C. P. HEINER*—I would like to ask Mr. Toenges about the highest rank coal. I did not get that clearly. What kind of coal is that? A. L. TOENGES (author's reply)— The coal in the Matanuska field ranges from high volatile "B" bituminus to anthracite. It all depends on which direction you go in the Matanuska field. C. P. HEINER—Is it a large reserve. A. L. TOENGES—That is what we hope. That is what we are trying to find out. B. W. DYER*—In those strip beds, I wonder how far back the coal would weather ? A. L. TOENGES—I never noticed particularly. B. W. DYER—The weathering does not extend back like it does in this country ? A. L. TOENGES—No, it does not. B. W. DYER—Is that due to the freezing ? A. L. TOENGES—Probably so. B. W. DYER—In this country, you would expect nothing but weathered coal. R. H. SWALLOW*—Along that line, you mentioned some of the seams were on fire. Did you ever know how far back they burned, or was it hard to tell ? A. L. TOENGES—The fires occurred in the mine. That one you refer to was from an inside fire.

Jan 1, 1950