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By F. S. Turneaure, R. Gibson

The tin deposit of Monserrat, Bolivia, consists of one major vein 1600 m in length. The ore is unusual because of the notable quantity of teallite, even though cassiterite is the principal tin mineral. The deposit, formed at shallow depth under a wide range in temperature, may be classed as xenothermal. Polished sections reveal a complex history of replacement, with low-temperature minerals deposited before high-temperature minerals. THE Monserrat mine1'2 of the Compania Minera Monserrat is located 11 km east of Callipampa, a station on the Antofagasta and Bolivia Railway some 55 km south of Oruro. The mine lies in a group of low hills on the east slope of a broad valley of northerly trend. The valley is separated from the altiplano to the west by a prominent ridge that rises several hundred meters above the surrounding country (fig. 1). Callipampa is situated a short distance west of the ridge, near the east margin of the altiplano. The elevation at Callipampa is 3700 m and at the mine 4100 m. Monserrat is near the northeast limit of what may be called the Poopo-Pazna district, an area of northwesterly trend about 25 km in length and 15 km in width. The district includes the tin-silver prospects of Poopo to the north, the zinc-tin deposits of Salvador to the southwest, and the tin-tourmaline veins of Avicaya to the south. Along the prominent ridge already mentioned, which forms the western limit of the district, there are several tin and antimony prospects including the Trinacria mine, which is famous for its fine specimens of cylindrite. Although the principal ore mineral is cassiterite, the tin deposit of Monserrat contains an unusual amount of teallite. Cassiterite occurs in part as a finely granular mixture with sulphides of iron and zinc and in part as needle tin of late hypogene age. The regional structure is dominated by broad folds typical of the Andes of Central Bolivia and similar to those of the Llallagua district. The area adjacent to the Monserrat mine is underlain by thin-bedded shale somewhat variable in color but predominantly dark grey to black. The beds strike northwest and dip at low angles southwest, forming part of the northeast limb of a major syncline. A resistant sandstone formation, which underlies the black shale, crops out along a ridge east of the mine and also accounts for the high ridge to the west that was previously mentioned. No igneous rock of any kind is found at Monserrat. The nearest intrusive bodies known are the irregular dikes and masses of quartz porphyry at Avicaya about 10 km to the south. Mine Workings The Monserrat property includes one main vein, which can be followed on the surface for 1600 m, and two or three branch veins of distinctly minor importance. The principal haulage tunnel, referred to as the San Carlos adit or level III, extends northeasterly for 1700 m, following the main vein throughout most of this distance. Above the adit, there are

Jan 1, 1951

By Edward H. Robie

SUBJECT to formal Board approval in September, AIME dues will continue indefinitely at the present scale of $20 for Members and Associate Members; and $12 for Junior Members for the first six years of such membership, thereafter $17. That is the wish of the Board of Directors and the will of the membership, as expressed in the recent referendum. Though the official returns, as reported by the tellers, are not available as this is written, the data are sufficiently complete to give the results to the nearest percent. The total vote was approximately 93 pct for continuance of the present scale. Metals Branch members voted about 94 pet for continuance; Mining Branch members slightly less than that; and Petroleum Branch members about 91 pct. As in the referendum of 1949, there was no particular difference of opinion on the question of dues as between the three Branches. The percentage of ballots returned was about 61 pct, only slightly more than in the 1949 referendum. But the affirmative vote was much greater, 93 pct against 78 pet in the earlier referendum. Looked at another way, a majority of those to whom ballots were sent, 56 pct, voted to continue the present scale of dues, whereas only 46 1/2 pct of those canvassed voted to raise the dues in the previous referendum. But approximately 600 , members expressed their opinion that the dues should go back to $15 for Members and Associate Members and to $10 and $15 for Junior Members. This is a substantial group of members who either do not think they are getting their money's worth from AIME membership, or believe that a more businesslike conduct of Institute affairs should provide current services at less cost, or believe that more service is being provided for their dues than they need. As to the first point, it is probable that some members are not getting their money's worth. They perhaps have only a fringe interest in. AIME activities, or they do not or cannot participate in such activities at the Local Section, divisional, or national level, so that all they get out of the Institute is the monthly journal, which they do not have time to read. If they did read it intelligently, and acted upon the professional information thus gained, it is difficult to understand how one or more ideas cannot be gained that would be worth $20 to them professionally. But the 600 members who want lower dues offer a challenge to the Directors and to the staff to do a better job; to make Institute membership so rewarding that every. member will be thoroughly satisfied. Twenty 1935 to 1939 dollars are worth only $11.60 now, according to the latest government data, but that makes it all the more necessary for us all to appraise the value of what we buy. To the 93 pct of Institute members who expressed a vote of confidence, so to speak, the staff, and we feel sure the Directors as well, are most appreciative and thankful.

Jan 1, 1952

By J. O. Brittain, E. Lautenschlager

An investigation was conducted on fine grained airon wire to measure the influence of the temperature of deformation on strain aging near room temperature. Specimens were deformed various amounts at 77°, 195°, or 273°K and aged. The strain aging was followed by either internal friction or return of the yield-point measurements. The results show that strain aging occurs in three stages. During the first stage there is small, almost immediate return of the yield point. The solute carbon concentration, as mesured by internal friction, remains constant in stage I but is lower than the concentration in the unstrained condition. In the second stage, the solute concentration decreases while the magnitude of the yield point increases. In the third stage, the solute atoms continue to drain from the solution, the yield point approaches a maximum, and the strain-hardening coefficient and flow curve increase. The kinetics of the strain aging reaction are not the same for the two sets of measurements since the internal friction results lag behind the yield-point measurements. However, the strain-aging kinetics measured at 44° and 64°C showed no effect due to the difference in initial deformation temperature; nor were the strain aging kinetics influenced by low-temperature anneals at 77°, 195°, and 273°K. 1 HE object of this investigation was to measure the effect of initial deformation temperature on the strain aging of a-iron by tensile tests (i.e., return of the yield point) and internal friction methods, to correlate the results of the two measuring methods, and to measure the effect of low-temperature annealing (<273°K) after low-temperature deformation upon strain aging. The experiments were performed on fine-grained a-iron wire containing 0.02 wt pct c.l According to Thomas and Leak,&apos; return of the yield point and internal friction are similar measures of strain aging since both are dependent on solute atoms leaving the solid solution. The decrease in internal friction as a function of aging time is indicative of the removal of solute atoms from the solid solution, while the return of the yield point as a function of the aging time gives the rate of arrival of solute atoms at the dislocations. According to Cottrell and Bilby,3 during aging the solute atoms create an "atmosphere" which locks the dislocations and causes a return of the yield point on subsequent testing. It has been shown that after low-temperature neutron bombardment, a-iron goes through a stage of recovery at low temperatures which can be attributed to the annealing of iron interstitials&apos; and/or vacancies.4 If, after low-temperature deformation, there is an interaction during a low-temperature anneal between mobile point defects and the solute atoms (i.e., carbon atom interaction with vacancy or iron interstitial), it is possible that some solute atoms will be found at defect sites other than dislocations. Such changes in the sinks for the carbon atoms might be expected to alter the strain-aging kinetics sufficiently to be detected by either inter-

Jan 1, 1962

By T. D. Tiemann

The caustic extraction of silica from Wisconsin and Minnesota taconite was investigated by bomb digestion over the temperature range from 312 to 40S°F at caustic concentrations from 25 to 500 gpl. Residual concentrates containing as much as 65 pct iron were obtained. The high rate of silica extraction is related to a microcrystalline variety of quartz, since it is shown that the rate of extraction of silica from quartz is directly proportional to its surface area. Increasing dependence on foreign ore reserves makes the need for developing the technology necessary for treatment of our low grade ores even greater than it was at the time of World War 11, when much research was conducted on the extraction of alumina from clays. Representative of these were the studies carried on at the University of Illinois.&apos; More recently, the U. S. Bureau of Mines investigated the production of alumina from anorthosite, and currently the aluminum industry is showing renewed research interest in this field. The studies reported here are part of a continuing research program based on the above concepts and aimed at the eventual development of processes for the treatment of low grade ores, particularly those of iron. The fact that large reserves 3 of low grade nonmagnetic taconite are contained in the iron formation of the Wisconsin Gogebic range have made this ore an important and attractive target for investigation. The idea of removing silica by caustic extraction is not new.495 The digestion in caustic solution of ground flint, diatomite, and other forms of chalcedonic silica is the basis for the production of soluble sodium silicates by the wet-process. Upgrading bauxites by the caustic extraction of silica has been investigated6 and is the subject of a German patent.7 Although mention is made by Roe&apos; of the caustic extraction of silica from low grade Michigan and Wisconsin iron ores, and he lists a number of patents and references on the subject, recent work in the field does not appear to be extensive. As far as the author knows, there has been no work in this field on these particular ores. It is hoped that this paper will stimulate further investigation which will eventually lead to an econclmic means of processing these large low grade reserbes. TACONITES The taconites investigated in this study were from Minnesota and Wisconsin. That from Minnesota, a semi-taconite, Nas obtained from the Oliver Iron Mining Division, U. S. Steel Corporation, and represents a sample of an oxidized iron formation from their King Mine on the Mesabi range. The Wisconsin taconite came originally from the trench sampling of the U. S. Bureau of Mines, and represents a composite of the Norrie, Pabst, Yale, Plymouth, and Pence members of the Gogebic iron formation. Assays on these samples are given in Table I. A typical calcu1atr:d average analysis of the Wisconsin taconite is given in Table 11. Chemically, the Minnesota semi-taconite sample contains about 39 pct iron and 39 pct silica, while the Wisconsin taconite contains 30 pct iron and 53 pct silica, both on the dry basis.

Jan 1, 1962

By J. B. Conway

RECENT studies of first-stage creep data have led to a special least-squares procedure for use in calculating the Andrade creep-equation constants. This procedure is easy to apply, uses only experimental data, and yields results which do not vary with the individual making the analysis. Taking logarithms of the Andrade equation I = lo(1 +ßl1/3)ekt leads to In l = In lo + In(1 + ßl1/3) + kt A residual can then be defined as the difference between the logarithm of an experimental length value and the logarithm of a calculated length value. Following the usual least-squares approach differentiation with respect to 10 and k of the expression for the sum of the squares of the residuals leads to two equations which cannot be solved directly for the three constants involved. However, values of ß can be assumed and corresponding values of lo and k can then be calculated. Then the sum of the squares of the residuals can be calculated. For a certain value of ß this sum will exhibit a minimum value to identify the least-squares values for ß, lo, and k. An illustration of the application of the above least-squares approach is obtained by employing the creep data for lead originally presented by Andrade&apos; in the development of the one-third creep law. A plot of the sum of the squares of the residuals as a function of ß is shown in Fig. 1 along with the corresponding lo and k values. The minimum is seen to occur at ß = 0.0143 from which lo = 39.149 and k = 7.27 x 10-5. Based on these results the Andrade equation for these lead data is 1 = 39.149(1 + 0.0143 t1/3)e7.27 x 10-5t compared to the equation I = 39.13(1 + 0.01457/l/3)e6.95 X 10-5t developed by Andrade (calculation procedure not given but was probably a graphical solution). Calculating length values using the above equations and comparing with the experimental length values, residuals corresponding to the difference between experimental and calculated length values can be obtained. The sum of the squares of the residuals can then be calculated. For the case of the least-squares approach a value for this sum was found to be 2.37 x 10-3 compared to a value of 3.47 x 10" for the equation originally proposed by Andrade. In other words, while the constants proposed by Andrade provide an excellent fit for the lead data, a still better representation is afforded by applying the least-squares approach discussed above. A similar result was obtained for the lead data at 162oc.l The least-squares approach led to 1 = 9.866(1 + 0.0497 t1/3)el.011 x 10-2t compared to the equation I = 9.94(1 + 0.0433 l1/3)e1.06 X 10-2t given by Andrade. In this case, too, the sum of the squares of the residuals is slightly smaller for the equation based on the least-squares approach. It should be pointed out that a double trial and er-

Jan 1, 1965

By H. T. Bowman

For more than 80 years the Bessemer process has depended upon the ability, skill, and judgment of the blower, although as early as the I860&apos;s it was recognized that the process would benefit by some type of instrumental contro1.l IIowever, instruments with sufficient recording speeds did not exist, so the end-point determination was always dependent upon the blower&apos;s eye. This placed an obstacle in the way of precise experimental work, because of the absence of the necessary records and reference points as reported by Work.2 The use of the photocell provided the instantaneous record of the blow that made this experimental work possible and provided more scientific control for the process as discussed by Graham,3 A brief description of the progress of the blow will illustrate the recording function of the instrument. The silicon in the iron is being oxidized during the first minutes of the blow, as pointed out by Henning4 in a table showing the order of metalloid elimination. The product of this oxidation is a solid that remains in the converter, so there is virtually no flame during this part of the blow. This low flame luminosity is illustrated by the flame recording shown in Fig. I, where the silicon blow is plainly marked. The dull flame of the silicon blow gradually gives way to the brilliant carbon flame as the increasing quantities of carbon monoxide formed inside the converter burn to dioxide upon contact with the atmosphere above the vessel. When the carbon reaches some low value under 0.20 per cent, there is insufficient menoxide formed to maintain the dioxide flame, so its intensity drops. Throughout the flame drop carbon continues to burn, until at some value around 0.05 per cent an arrest occurs in the recorded drop. This point has been designated as the end point. The period of time from this end point until the vessel is turned upon its side and blowing has stopped has been called the afterblow. This afterblow is used as a measure of the degree of metal oxidation, and uniformity demands that it be controlled within narrow limits. Iron and blowing conditions are likely to change several times during a turn, necessitating corresponding changes in end-point control. It is the purpose of this paper to discuss these changes, the factors that make them necessary, and their bearing upon the quality of steel. Carbon-FeO Relationship In the Bessemer process oxidation relationships are precise. Fig. 2 shows a graph of the carbon-FeO relationship. The familiar "bomb-test" method, described by Mccutcheon and Rautio,5 was used for obtaining these and all other dissolved FeO values herein reported, all tests being taken from the converter before deoxidation unless otherwise noted. All tests of 0.10 per. cent carbon and above were obtained from metal blown for duplexing. McGinley and Woodworth6 reported iron oxide values for blown metal, but their tests were obtained by a . different method than were those

Jan 1, 1942

By H. T. Bowman

For more than 80 years the Bessemer process has depended upon the ability, skill, and judgment of the blower, although as early as the I860&apos;s it was recognized that the process would benefit by some type of instrumental contro1.l IIowever, instruments with sufficient recording speeds did not exist, so the end-point determination was always dependent upon the blower&apos;s eye. This placed an obstacle in the way of precise experimental work, because of the absence of the necessary records and reference points as reported by Work.2 The use of the photocell provided the instantaneous record of the blow that made this experimental work possible and provided more scientific control for the process as discussed by Graham,3 A brief description of the progress of the blow will illustrate the recording function of the instrument. The silicon in the iron is being oxidized during the first minutes of the blow, as pointed out by Henning4 in a table showing the order of metalloid elimination. The product of this oxidation is a solid that remains in the converter, so there is virtually no flame during this part of the blow. This low flame luminosity is illustrated by the flame recording shown in Fig. I, where the silicon blow is plainly marked. The dull flame of the silicon blow gradually gives way to the brilliant carbon flame as the increasing quantities of carbon monoxide formed inside the converter burn to dioxide upon contact with the atmosphere above the vessel. When the carbon reaches some low value under 0.20 per cent, there is insufficient menoxide formed to maintain the dioxide flame, so its intensity drops. Throughout the flame drop carbon continues to burn, until at some value around 0.05 per cent an arrest occurs in the recorded drop. This point has been designated as the end point. The period of time from this end point until the vessel is turned upon its side and blowing has stopped has been called the afterblow. This afterblow is used as a measure of the degree of metal oxidation, and uniformity demands that it be controlled within narrow limits. Iron and blowing conditions are likely to change several times during a turn, necessitating corresponding changes in end-point control. It is the purpose of this paper to discuss these changes, the factors that make them necessary, and their bearing upon the quality of steel. Carbon-FeO Relationship In the Bessemer process oxidation relationships are precise. Fig. 2 shows a graph of the carbon-FeO relationship. The familiar "bomb-test" method, described by Mccutcheon and Rautio,5 was used for obtaining these and all other dissolved FeO values herein reported, all tests being taken from the converter before deoxidation unless otherwise noted. All tests of 0.10 per. cent carbon and above were obtained from metal blown for duplexing. McGinley and Woodworth6 reported iron oxide values for blown metal, but their tests were obtained by a . different method than were those

Jan 1, 1942

By R. L. Perrine

This paper shows how stability theory can be used to optimize solvent recovery of oil. Application of the theory leads to definition of the limiting conditions required for stable displacement to occur. One of these conditions is that the size of a solvent "slug" must at least equal a prescribed minimum. The criteria to be satisfied are miscibil-ity and stability. Stability implies that no viscous fingering will occur and that mixing will be caused only by a dispersion process. Miscibility implies that complete recovery will be obtained from the swept regions. Thus, for any specified set of reservoir conditions, an optimum use of solvent is defined. INTRODUCTION The early outlook for solvent flooding as a means to increase oil recovery was very favorable. Some laboratory results indicated that a "slug" containing perhaps 2 to 3 per cent of a hydrocarbon pore volume could be successful. However, other data suggested as much as 30 per cent would be required. The difference is of considerable economic importance. A theoretical explanation for these divergent results has been advanced by the author.1,2 Stability theory defines conditions for two distinct flow regimes. In stable displacement, solvent and oil become mixed by a dispersion process, and the solvent requirement is small. On the other hand, unstable displacement can degenerate into viscous fingering. The practical result is a considerable increase in the extent of mixing and, thus, in the solvent required. The present paper shows how to use stability theory to optimize solvent recovery of oil. Oil is usually considered to be displaced by a small amount, or a slug, of solvent. Gas in turn follows solvent. Any fingering will permit contact of nearly solvent-free gas and oil, leading to immiscibility and reduced recovery. Thus, our optimum is defined by two restrictions — stable flow and miscibility. Although an immiscible solvent process could prove more profitable than any miscible process, such processes lie outside the selected definition of an optimum. The usefulness of computations based on the present work will depend on the validity of the general theory. Because the important idealizations required tend to minimize the predicted solvent requirement, the results should state correctly the limiting conditions required. Therefore, theoretical calculations should have practical value. This paper first reviews several principles that result from stability theory. The following section describes use of these ideas in relatively simple systems which symmetry makes appear one-dimensional. Of particular importance is the step-by-step design of 3 stable minimum-solvent slug. The use of stability theory in cases of multi-dimensional displacement is discussed and, finally, suggestions are given for simplified practical application of the theoretical results. PRINCIPLES OF STABILITY THEORY The use of perturbation methods to derive stability conditions has been shown by the author.l The discussion is presented in terms of the fractional concentration of solvent in the single hydrocarbon phase. Quite generally, any disturbance can be represented as a Fourier series, of which only the least stable term need be considered. Denoting this term at time t = 0 by cn,

By R. F. Krueger, L. C. Vogel

A design is presented for an electrical analog computer which can solve non-steady state heat transfer problems in an extensive radial forrnation containing a moving cylindrical source. The computer is used to simulate a .simplified thermal oil recovery process in which heat transfer from a moving, constant temperature source takes place radially by conduction only. Temperature distribution curves are .shown for several different assumed modes of travel for the heat source. The data are used to estimate the residual fuel requirements necessary to maintain a self-propagating isotherma1 front for the particular system being studied. Although the computer is designed to represent an unique system. conversion factors can he adjusted to show the effects of changing the assumed values of system constants, such as thermal conductivity of the formation and temperature of the source isotherm. Examples are given to illustrate the relative influence the assumed values of these variab1es will have upon the quantity of fuel required to maintain the source. The maximum effect of heat transfer by the flowing air stream is estimated mathematically, and full requirements for this system are shown to he markedly reduced. Inasmuch as the examples discussrd refer to a simplified process, the results are not directly applicable to a practical field operation. It is believed, however, that the data il1ustr-ate some general trends which are important in thermal recovery processes. Data from laboratory and field experimentation can he used to modify the computer to take into account the influence of heat transfer by various mechanisms, for example, by injected air and by fluids ahead of the hot zone. With .such refinements it would be possible to estimate more accurately the limiting values for the rate of travel of the high temperature front and for the required air- injection rates. Use of this computer should aid in evaluating the economic feasibility of oil recovery by various thermal processes. It is hoped this paper will stimulate further work by others to help accomplish this objective. As the costs of exploration for and development of new oil fields rise. increasing the recovery of oil from established fields becomes more and more important. In fields containing low gravity crude oil, ultimate recoveries by primary means are sometimes less than 10 per cent and often total only 10 to 20 per cent of the oil in place. Conventional secondary recovery methods are not always effective in increasing this total. Methods which have been proposed for increasing the recovery of viscous oils include thermal processes for increasing the mobility of the oil. One method is to provide a moving heat source generated within the formation to heat the oil and a flowing gaseous medium (for example, air) to sweep the oil to the producing wells. The possibility of such a process has intrigued engineers for many years.&apos;. &apos;." but little or no information has been available in the literature relative to the technical or economic feasibility of this method. Recently, however, interest has been revived by publication of laboratory and field test results indicating the feasibility of maintaining

Jan 1, 1956

By D. G. Swarthout, J. W. Savage, R. W. Guard

The Nb-N constitution diagvam has been examined from 1100° to 1450°C at 1 atm N2 pressure. On the basis of- our work plus that of Brauer and coworkers the stable nitvide Phases are: a) a solid solutlion, basic niobium (bcc) with nitrogen contained interstitially; NbN,, x = <0.40; b) ß NhNx,x = 0.39 to 0.45; hexagonal (W2C type) (NbzN); a =3.058A,c = 4.961 + 0.001A c) y NbNx x = 0.75 to 0.80; tetragonal (distorted NaCl type) (Nb4N3); a = 4.386A,c = 4.332 + 0.001A; d) 6 NbN,, x = 0.88 to 0.91; cubic (NaCl type); a = 4.3885 + 0.0007A; e) E NbNx x = 0.92 to 1.00; hexagonal (Tip type); a = 2.958A, c = 11.272 * 0.0015A. In addition, a metastuble transition phase 6&apos; has been observed and occurs only during the transition 6 — E. 6&apos; NbN has these distinguishing parameters: NbNx,x = 0.96; hexagonal (anti-NiAs type); a = 2.94A, c = 5 .46A. The high-temperature phase fields in the system are governed by two reactions: a) 6 + Y + E, a entectoid reaction occurring at 1270" ± 20° C; b) o + N2 = E, a 2 012 1 reaction occurring at 1370" ± 20° C. As part of a study of the electronic low-temperature. properties of transition metal nitrides, a number of specimens of niobium nitride were prepared. Preliminary observations on these specimens showed several points of disagreement with data already in the literature. It was, therefore, decided to determine the constitution diagram for the Nb-N system between 1100" and 1450°C. The objective of this research was to define the temperature and composition regions of stability of the various phases and to explain the differences among previously proposed diagrams. Review of Previous Literature. The research on the Nb-N system to 1964 has been summarized by storms.&apos; Although he does not present a phase diagram, his review covers the research on the system thoroughly. One of the earliest works on NbN is that of Ascher-mann and coworkers2 who studied the superconductivity of the cubic 6 NbN. Subsequent work by Horn and ziegler,3 Cook, Zemansky, and Boorse,1 Rögener:5 Schroder6 and sellmaier7 has qualitatively confirmed the first results on superconductivity, although their methods of preparation differed considerably. The constitution diagrams proposed for the system by Brauer and Esselborn8 and Elliott9 are shown in Fig. l(a)and (b). The diagram in l(a) has been modified by more recent results in Brauer&apos;s laboratory (private communication). Although 6&apos; is shown on this diagram, Brauer has indicated that he now believes 6&apos; to be a metastable phase in the temperature range shown. The diagram of Elliott, Fig. l(b), is based primarily on the results of Elliott and Komjathy10 on ni-trided niobium strip or rod specimens examined by X-ray diffraction and metallography. It will be noted that these proposed diagrams are in conflict with respect to the temperature and composition ranges of

Jan 1, 1968

By N. L. Hancox

Previous researchers have used the cutting and rejoining model to represent a porous body when attempting to place Archie&apos;s law on a theoretical basis and calculate rock permeabilities (F = Ø-m, where F = formation factor, = - porosity and m = a constant). In using the model, a porous solid is assumed to consist of sections with parallel sides containing straight. continuous pores of total porosity 4 (pore to total volume or, for a homogeneous body, pore to total area). The joining of pores at an interface between two sections is assumed to be random which results in a common pore area Ø2. This reduced area Ø2 is then taken as that area which limits electrical conduction or fluid flow in the body. Agreement between experimental results and results calculated using a model is not always good Because of this, various modifications of the model are presented — for instance, the random nature of the joining is questioned. Formation factor measurements on specially constructed porous specimens are described in this paper. it is concluded that the common pore area limits flow completely only if sections containing straight pores are very thin, and that, in most natural materials, the common pore area at an interface must be greater than that given by random joining. However, the model is still useful in permeability calculations, provided that the fractional area limiting flow is determined from formation factor measurements. INTRODUCTION Two important properties of porous media are permeability k, which describes the ease with which a fluid can flow through a porous medium, and formation factor F, defined as the ratio of the resistivity of a saturated specimen to the resistivity of the saturating liquid which describes the electrical properties of the saturated material. k is defined by Darcy&apos;s law,l k= µqL/P Ae . . . . . . . . . . . . . . . [1] where µ = liquid viscosity, q = flow rate, L = length of specimen, p = pressure across the specimen and = - the effective area over which flow occurs, F is given experimentally by Archie&apos;s law,2 F = Ø-m ,..............(2) where 4 is porosity defined as the pore to total volume or, for a homogeneous body, the pore to total area; and m lies between 1.3 for loose sand and 2 for cemented sand. Consider a porous body of total cross-sectional area A and length L, saturated with a liquid of resistivity R and with an effective area for conduction of Ae. Then, from the definition of F given previously, F=A/Ae , ................(3) or, from Eqs. 2 and 3, Ae = A Øm ..............(4) Thus, in any attempt to calculate k or F, some assumptions must be made concerning the pore structure of the body and a value derived for A,. To determine Ae, Childs and George3 and Wyllie and Gardner4 suggested an elementary statistical representation often referred to as the cutting and rejoining model of a porous body. The body is assumed to be composed of two or more parallel-sided sections of porosity 4, containing straight, continuous pores with a common pore area of Ø2 at an interface between two sections. The value is given by a random joining of the pores in either section. Two such sections,

Jan 1, 1969

By Arthur B. Yates

DIAMOND drilling has advanced and expanded during the past few years. Along with this increase there has been a marked trend to rely more and more upon drilling for the outlining of ore for reserve purposes. This is especially true underground, where men have not been available for opening up ore by crosscuts, drifts and raises. During the recent heavy call upon known ore reserves, more drilling has been done for exploration and it has become expedient to drill longer lateral holes from underground and deeper holes both from surface and from exploration headings in the mines. Furthermore, these deeper holes have to be drilled closely enough to warrant calculation of "probable" if not "proven" ore, from the results obtained therefrom. Interpretation of diamond-drill results has become more precise and reliable with the growing knowledge and understanding of the geologic structures that control the geometry of ore distribution, and this has broadened the field of usefulness of the drill. All of this has created a necessity and a demand for more accurate control of the hole as to direction, a more precise and reliable method of surveying for position, and a need for better and more complete core recovery, as well as larger cores, to provide an adequate sample. At depth the control becomes more difficult and, at the same time, more important. CONTROL A close study of drilling in various parts of the world for a period of more than 20 years has brought to light one definite rule, practically invariable; namely, that diamond-drill holes tend to deviate into a position normal to any structure existing in the rocks, such as bedding, schistosity, gneissosity, or even parting or jointing-even if the hole is started at almost any angle other than parallel with the structure. It also appears that the better developed the structure is, the more quickly will the hole get into a position perpendicular to it. It has often been said that there is a tendency for holes to "drift" in the direction of rotation. This is obviously untrue, for in a vertical hole the measure of deviation would depend upon the azimuth chosen as zero, and there is an infinite number of choices. It has been proved, however, that in homogeneous rocks there is a tendency for the hole to corkscrew, and that the direction of the spiral is the same as the direction of rotation. This may account for the belief that holes drift in that direction. Some tests have been made using right-hand and left-hand rods, and these show that no matter what the direction of rotation the hole will swing into a position perpendicular to the structure. Methods of Control The foregoing empirical rule may be used as an indirect method of control. If the prevailing structure is known, it may be advantageous to start the hole as nearly normal to it as possible, for the nearer the direction of the hole is to this ideal, the straighter it will remain. This, of course, is not always practical and in some cases is impossible. Usually such a

Jan 1, 1946

By James J. Bean

HE task of measuring the specific gravity of the -*- operating medium in a heavy-media separation system has never presented a particularly difficult problem because the medium is fairly stable and the overflow of the separatory vessel, as well as its underflow, can be sampled easily and accurately and the specific gravity of the suspension determined easily by weighing a known volume. However, while this method is simple and accurate it does require the operator to take the sample by hand and to weigh it and there is considerable temptation to avoid the periodic sampling if everything seems to be going well, or if something is occupying the attention of the operator. Furthermore all operators do not sample in exactly the same manner and considerable practice is required for two operators to be able to "check" each other to the last few hundredths, particularly if the sample is cut underneath the drainage screen where location of the point of sampling and load on the screens tends to influence the determination. While none of the above presents much of a problem, we have all recognized that some mechanical method of continuous measurement and recording would be advantageous since the operator would merely have to glance at the meter to check the gravity and to have an indication of the trend of any changes. Also if the instrument were of the recording type, a permanent record would be available for the guidance of the superintendent. The Eagle-Picher Mining and Smelting Co. was the first heavy-media user to actually install such a recording meter. In 1946 they installed in their Central Mill at Cardin, Okla., a specific gravity recorder manufactured by the Bristol Co. of Water-bury, Conn. R. A. Barnes, of the Bristol Co., working with E. H. Crabtree, Jr. and Elmer Isern, of Eagle-Picher, made the application and worked out the problems of sampling and measuring. Their attempts to measure the specific gravity of the medium in the cone itself were not entirely successful and they resorted to an outside sample tube for actually making the determination. Because of the particular flowsheet used, it was possible to tap off from the medium return pipeline a stream of medium and divert it into the sampling tube, which was provided with a constant level overflow and a spigot underflow, and into which the bubbler tubes dipped. The Eagle-Picher installation was successful and its possibilities were recognized by the Mineral Dressing Laboratory of the American Cyanamid Co. It was decided to install a similar unit in the heavy-media pilot plant to investigate further its possibilities. Chief among these was the continuous record which it was felt would be proof of the steadiness of the gravity in a heavy-media cone, something which is not always appreciated by POtential users. Because the heavy-media pilot plant is required to operate at a wide range of specific gravities, it was realized that the unit would have to record all gravities from 1.25 to 3.50, and do it to the nearest 0.01. It would not be necessary to record all of this wide range on a single chart and the method selected was to have 4 bands, each band range overlapping the other a small amount and calibrated so that with standard charts one division would represent 0.01 sp gr. A shift from one band to another could be arranged without alteration of the instrument itself, being accomplished by a simple change in the bubble-tube lengths, as described later. Accordingly, a recording type instrument was purchased and installed. Because there were some advantages in doing so, the first installation attempted to measure the gravity of the cone proper by placing the bubble tubes in the cone. This was not at all satisfactory and the second scheme utilized a fixed vertical screen at the surface of the cone, and an external sample-tube arrangement. We were particularly anxious to make this work as we felt it would be advantageous to measure the top level of medium where the separation was actually being made, but we were doomed to disappointment because it was impossible to keep the screen clean of float. Since the top gravity of the cone is the most convenient place to sample for control, a launder about 2 in. wide was installed longitudinally beneath the

Jan 1, 1951

By James J. Bean

HE task of measuring the specific gravity of the -*- operating medium in a heavy-media separation system has never presented a particularly difficult problem because the medium is fairly stable and the overflow of the separatory vessel, as well as its underflow, can be sampled easily and accurately and the specific gravity of the suspension determined easily by weighing a known volume. However, while this method is simple and accurate it does require the operator to take the sample by hand and to weigh it and there is considerable temptation to avoid the periodic sampling if everything seems to be going well, or if something is occupying the attention of the operator. Furthermore all operators do not sample in exactly the same manner and considerable practice is required for two operators to be able to "check" each other to the last few hundredths, particularly if the sample is cut underneath the drainage screen where location of the point of sampling and load on the screens tends to influence the determination. While none of the above presents much of a problem, we have all recognized that some mechanical method of continuous measurement and recording would be advantageous since the operator would merely have to glance at the meter to check the gravity and to have an indication of the trend of any changes. Also if the instrument were of the recording type, a permanent record would be available for the guidance of the superintendent. The Eagle-Picher Mining and Smelting Co. was the first heavy-media user to actually install such a recording meter. In 1946 they installed in their Central Mill at Cardin, Okla., a specific gravity recorder manufactured by the Bristol Co. of Water-bury, Conn. R. A. Barnes, of the Bristol Co., working with E. H. Crabtree, Jr. and Elmer Isern, of Eagle-Picher, made the application and worked out the problems of sampling and measuring. Their attempts to measure the specific gravity of the medium in the cone itself were not entirely successful and they resorted to an outside sample tube for actually making the determination. Because of the particular flowsheet used, it was possible to tap off from the medium return pipeline a stream of medium and divert it into the sampling tube, which was provided with a constant level overflow and a spigot underflow, and into which the bubbler tubes dipped. The Eagle-Picher installation was successful and its possibilities were recognized by the Mineral Dressing Laboratory of the American Cyanamid Co. It was decided to install a similar unit in the heavy-media pilot plant to investigate further its possibilities. Chief among these was the continuous record which it was felt would be proof of the steadiness of the gravity in a heavy-media cone, something which is not always appreciated by POtential users. Because the heavy-media pilot plant is required to operate at a wide range of specific gravities, it was realized that the unit would have to record all gravities from 1.25 to 3.50, and do it to the nearest 0.01. It would not be necessary to record all of this wide range on a single chart and the method selected was to have 4 bands, each band range overlapping the other a small amount and calibrated so that with standard charts one division would represent 0.01 sp gr. A shift from one band to another could be arranged without alteration of the instrument itself, being accomplished by a simple change in the bubble-tube lengths, as described later. Accordingly, a recording type instrument was purchased and installed. Because there were some advantages in doing so, the first installation attempted to measure the gravity of the cone proper by placing the bubble tubes in the cone. This was not at all satisfactory and the second scheme utilized a fixed vertical screen at the surface of the cone, and an external sample-tube arrangement. We were particularly anxious to make this work as we felt it would be advantageous to measure the top level of medium where the separation was actually being made, but we were doomed to disappointment because it was impossible to keep the screen clean of float. Since the top gravity of the cone is the most convenient place to sample for control, a launder about 2 in. wide was installed longitudinally beneath the

Jan 1, 1951

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

THE technique of concentrating valuable minerals from lean ores by flotation depends upon the creation of a finite contact angle at the three-phase contact, mineral-water-air. If the mineral is completely wetted by the water phase, contact angle zero, there is no tendency for air bubbles to attach themselves to the mineral. However, when the contact angle is finite, the surface free energy of the system, water-air bubble-mineral particle, can be diminished by contact between the bubble and the particle, and if not too heavy the mineral will be levitated in the froth. With a few exceptions, all clean minerals are completely wetted by pure water. Thus the art of flotation consists in adding substances to the water to make a finite contact angle with the mineral to be floated, but to leave the other minerals with a zero contact angle. The contact angle concept and experimental measurements of contact angles have played important roles in flotation research for several decades.&apos;-" Nevertheless, there remain unanswered some basic questions as to the scientific significance of the contact angle and the nature of the processes by which flotation reagents affect contact angles. The contact angle is a complex quantity because the properties of three different phases, or rather of three different interfaces, control its magnitude. Considering the interfaces close to the region of ternary contact to be plane, the relation among the contact angle and the three binary interfacial tensions is easily derived. The condition for equilibrium among the three surface tensions, Fig. 1, or the requirement of minimum total surface free energy leads to Young&apos;s equation, Eq. I: ysa — ysl = yLA cos 0 [1] According to this equation, the contact angle has one well-defined value. Actually it is found in many experiments that the value of the contact angle depends on whether the air is replacing liquid over the solid (receding angle) or the liquid is replacing air (advancing angle). The receding angle is always the smaller of the two.4 Two explanations have been offered for this experimental fact. According to some investigators,5-8 roughness of the surface causes apparent contact angles that are different for the receding and the advancing cases although the actual local contact angle may be completely determined by Eq. 1. The other explanation involves the hypothesis that the solid-air interface after the liquid has just receded is different from the same interface when no liquid has previously covered it.1,4 Adsorption of constituents of the air or liquid might play a role here. In this discussion the difference between advancing and receding contact angle will be neglected and plane surfaces where Eq. 1 describes the situation will be considered. But there is still a fundamental obstacle to the application of Young&apos;s equation. The surface tension of the liquid (rla) can easily be determined, but the two surface tensions of the solid (rsa and ySL) cannot be measured directly. Eq. 1, however, is not without value. By contact angle measurements it is possible to establish how ysl — ysl varies with the addition of solutes to the liquid phase. Also, Eq. 1 affords a convenient starting point for calculating net forces and energy changes involved in the process of bubble-particle attachment.1,2 . If for the moment surface tension of the liquid (yLa) is considered a constant, an increase in ysa — ysL, will tend to decrease the contact angle. A decrease in ySA — ysl, corresponds to an increase of the contact angle. In cases where ySA — ySL > yLa the contact angle is zero; it will only reach finite values when ysa — ysa has been decreased below YLA. Thus on the basis of Young&apos;s equation and contact angle measurements alone, it can be learned how flotation reagents affect the difference Ysa — ysl, but no conclusions can be drawn as to the effects of reagents on the individual surface tensions ysa, and ysL, not even as to signs or directions of the surface tension changes resulting from reagent additions. A quantitative relationship between the surface tension or interfacial tension and the adsorption occurring at a surface or an interface is given by the Gibbs equation, which for constant temperature and pressure reads dy = — 2 T, du, [2] where dy is the infinitesimal change in surface tension accompanying a change in chemical potential

Jan 1, 1955

By O. G. Paasche, Yuan-Shou Shen

THERE is a disagreement among the various authors about the exact manner of transformation of ZrCr2. Rostokerl and others2 stated that ZrCr2 had a C-14 (MgZn2) type of structure below 1000°C and a C-15 (MgCu2) type of structure at temperatures above 1000°C. Alisova3 and others4 reached the opposite conclusion and stated that the transformation temperature is close to the melting point of ZrCr2. A literature survey shows that various investigators3&apos;= who homogenized the specimens at a temperature higher than 1000°C have concluded that ZrCr2 had the C-15 structure at room temperature. Meanwhile, Jordan et al.4 reached similar conclusions without annealing the specimen. Other investigators1,2,6,7 who X-rayed the specimens in the as-cast condition without annealing reached different conclusions. The investigation reported herein was conducted with the aim of exploring the exact manner of transformation of ZrCr2 by various heat treatment tests. The alloys for this examination were prepared from iodide-reduced zirconium crystal bars, 99.9 pct purity, and electrolytic chromium, 99.9 pct purity. They were melted in a nonconsumable electrode arc furnace with water-cooled copper crucible in a helium atmosphere. The melting loss of each alloy was less than 1.5 pct by weight. Chemical analysis of a randomly selected specimen indicated that there was a very close agreement between calculated and analyzed compositions. Before being heat-treated each specimen was encapsulated in a vycor or quartz tube inside which an argon atmosphere was maintained at a pressure of lower than 1 atm. In determining the crystal structure of each specimen with a Debye-Scherrer camera, the standard procedure8 for X-ray quality analysis (Hanawalt method) was followed. The different series of heat treatment tests in this investigation are tabulated in Tables I and 11. The tests in Series I, specimens from 1-1 to 1-9, which were similar to Rostoker&apos;s experiment1 indicated that the transformation temperature seemed to fall between 870° and 900°C and that the crystal structure of ZrCr2 at lower temperature seemed to be of the C-14 type. However, once the compound is transformed to C-15 type, it is impossible to reverse the transformation back to the C-14 type by first heating the specimen above 900°C and then annealing it slowly below 900°C as shown in Experiments II-1 to II-3. Thus, it appears that the specimen of ZrCr2 will transform from C-14 to C-15 structure when heated above 900°C but will not transform from C-15 to C-14 when annealed slowly passing 900° C even after the extremely slow cooling process such as indicated in the experiment of Specimen II-3. As a valid transformation temperature is a temperature at which the transformation is reversible, therefore the temperature 900°C (or other temperature close to 900°C) is not the transformation temperature for ZrCr2 and the C-14 structure is not the stable structure of ZrCr2 at lower temperatures. The C-14 structure is retained at room temperature because the transformation to C-15 structure is very sluggish and the fast cooling after melting does not allow enough time for the transformation to take place. Additional energy is required to alter the metastable condition of the C-14 structure. The sluggishness of this transformation was again demonstrated through another series of experiments. Four specimens with C-14 structure were taken. Then they were annealed at 900°C but each specimen was soaked for a different period of time, Table 11. X-ray diffraction patterns of this group indicated that the C-14 structure gradually disappeared as the soaking period was lengthened. The figures listed under the column "C-14 Structure, pct" were estimated from the intensity of the d = 2.330 line of the diffraction pattern corresponding to the structure. Notice that the intensity of this line became weaker for longer soaking periods. To determine the transformation temperature of ZrCr2, specimens with C-14 structure (as-cast condition) were annealed at 1300°, 1400°, 1500°, 1550°, and 1600°C, respectively. A final specimen was first heat-treated to 1500°C in order to transform it to C-15 structure, then heat-treated at 1600°C again. From the X-ray analyses of this series of tests, Specimen Nos. III-1 to III-6, it is evident that a transition from C-15 structure at lower temperatures to the C-14 structure occurs at some temperature between 1550° and 1600°C.

Jan 1, 1969

By S. L. Craig, C. Orr, H. G. Blocker

WITHIN recent years gas adsorption methods have been developed for measuring the surface area of finely divided materials and have become extremely valuable in research on the corrosion and the catalytic activity of metals. Rather elaborate apparatus is required, and a single determination is so time-consuming that these methods have not been utilized to the fullest extent; the methods are un-suited for most routine control work such as that encountered in powder metallurgical operations and in processes employing metal catalysts. These difficulties are largely eliminated, and surface area is reduced to a routine determination if the liquid-phase adsorption of a surface-active agent such as a fatty acid can be used. When the affinity of the fatty acid carboxyl group for the solid surface is greater than its affinity for the solvent, a unimolec-ular layer of orientated fatty acid molecules will be formed at the solid-liquid interface in a manner similar to that of a compressed fatty acid film on a water surface. The measurement of surface area is then reduced to a measurement of fatty acid adsorption. This propitious circumstance, first investigated by Harkins and Gans,¹ has been employed with somewhat inconclusive results by a number of investigators in evaluating the surface properties of metals, metal catalysts, and metal oxides. The specific surface area values for nickel and platinum catalysts, determined from the adsorption of a number of fatty acids from various solvents, were found by Smith and Fuzek² to agree with values calculated by the gas adsorption technique of Brunauer, Emmett, and Teller," he so-called BET technique. And recently Orr and Bankston4 have also reported good agreement between nitrogen gas and stearic acid adsorption results in the measurement of the surface areas of clay materials. On the other hand, Ries, Johnson, and Melik5 found only order-of-magnitude agreement between these two methods in studying supported, cobalt catalysts having specific surface areas as great as 420 sq m per g; the reason is partially attributable to the very porous nature of the materials. Greenhill,6 investigating the adsorption of long-chain, polar compounds in organic solvents on a number of metal powders, concluded that a uni-molecular layer of stearic acid was formed on exposure of the solid to the acid solution and that the presence of an oxide or another film did not alter this result. Furthermore, the adsorption process appeared to be the same whether or not the sample was degassed prior to exposure to the solution. Greenhill estimated the surface area of one of the powders he investigated from microscopic diameter measurements, and obtained a rough check with surface area evaluation. Russell and Cochran7 found moderate agreement for alumina surface area results by fatty acid and gas adsorption methods. In addition, they also found that the prolonged heating and evacuating pretreatments previously used by investigators were unnecessary. The present work, however, considerably extends these previous investigations, shows that fatty acid adsorption can be used to determine the surface area of a variety of metals and metal compounds, offers further confirmation of the correctness of gas adsorption methods, and presents a simplified technique for the determination of the metal surface area which is suitable for routine work. Experimental Technique Basically, the fatty acid adsorption method is quite simple. It consists of exposing a sample of the material of which the surface area is desired to a fatty acid solution of known concentration. By analysis of an aliquot of the solution, the concentration after adsorption has occurred may be determined. The difference between the initial quantity of acid in solution and the final quantity is that quantity of acid adsorbed by the sample. The specific surface area of the adsorbent material may be calculated from the quantity adsorbed and the weight of the sample. In agreement with the findings of others as outlined above, it was found entirely unnecessary to degas or pretreat the nonporous materials employed other than by drying them thoroughly. However, precaution was necessary so that the dried sample entered the fatty acid solution with little exposure to moisture. The effect of moisture on the interaction of stearic acid with finely divided materials has been thoroughly investigated by Hirst and Lancaster." They found the presence of water merely reduced the amount of acid adsorbed by powders such as TiO2, SiO2, Tic, and Sic. With reactive materials such as Cu, Cu2O, CuO, Zn, and ZnO, however, water was found to initiate chemical reaction. Only with ZnO was reaction observed when the solid and the solu-

Jan 1, 1953

By K. A. Slagle

Hydraulic analysis of the wellbore has become increasingly inzportant for designing cementing operations and selecting equipment, materials and techniques to complenzent modern well-c-ompletion practices. Non-Newtonian fluid technology has advanced beyond the point where former empirical methods of analysis adequately define the hydraulic system and fluid properties. In view of these factors, this paper describes a series of rheological calculations which have been found practical, through field usage, for assistance in selecting a cementing program. A relatively simple laboratory method using standard viscometric equipment is suggested for determination of the rheological properties of slurries, and clrrta are presented on some of the more common cementitrg conzposition.A. A criterion for divergence from laminar-flow characteristics has been proposed. Usefulness of the calculations is indicated by examples of cementing operations where they have been used. INTRODUCTION With the changing aspects of well-completion practices during the past few years, it has been increasingly important to have a relatively simple method of analyzing the flow conditions existing in the well during cementing operations. This is particularly true in view of the improved economics toward which most of the changes have been directed. Rheological characteristics of slurries used for cementing should be a major consideration in the trend toward smaller casing sizes, either single or multiple strings. Receiving increased attention is the practice advocated in 1948 by Howard and Clark&apos; of attaining turbulent flow with the fluids circulated during a primary cementing operation. While there may still be a difference of opinion concerning this technique, most available information indicates that superior primary-cementing results are generally obtained when high displacement rates are employed. Fluid properties of the slurry to be used must be available, as well as calculation methods, to determine what flow rates should be attained and the probable consequences in terms of frictional pressure and horsepower utilization. It would certainly be inappropriate to attempt high displacement velocities if sufficient pressure might be developed to create lost circulation. Since cementing slurries are non-Newtonian fluids, it is not possible to define their rheological or fluid properties by the single factor of viscosity and then make calculations for the quantities just described. Because the shear stress-shear rate ratio is not constant: it becomes necessary to establish at least two parameters for adequate fluid-flow calculations. It is not the purpose of this paper to delve into the mathematical development of non-Newtonian technology, nor to discuss the arbitrary classification system under which a single fluid may resemble two or three different classes depending upon experimental conditions. Rather, the intention is to present a useful series of calculations based on a concept applicable to both Newtonian fluids and to the preponderance of non-Newtonian fluids encountered in the oil-producing industry. Development of this approach was begun some 32 years ago,&apos; and has most recently been brought to fruition by Metzner and his co-workers at the U. of Deleware. Some non-Newtonian fluids encountered in the petroleum industry, other than cementing slurries, have also had the benefit of this method of analysis."&apos; The two parameters required to define the fluid are usually denoted by the symbols n&apos; and K&apos; and, for the purposes of this discussion, are called "flow behavior index" and "consistency index", respectively. These two slurry properties permit calculation of the Reynolds&apos; number and the "critical" velocity, or the velocity at which departure from laminar flow begins. EXPERIMENTAL DETERMINATIONS The two principal instruments used for rheological studies are the pipeline (capillary-tube) viscometer and the rotational viscometer. When conveniently possible, a capillary-tube viscometer (where the pressure drop and flow rate of the material can be measured) is the better method for rigorous determination of the flow behavior index and consistency index for non-Newtonian fluids. With pressure-drop data at various flow rates, it is then possible to prepare a logarithmic plot of shear rate as the abscissa-shear stress as the ordinate. For fluids which do not exhibit time-dependency, these data will usually produce a straight line. The flow behavior index n&apos; represents the slope of this line, while the consistency index K&apos; becomes the intercept of this line at unity shear rate in accordance with the mathematical derivations associated with this concept of rheology. Due to the difficulties anticipated in maintaining a uniform, pumpable cement slurry for the time interval required to obtain measurements from the pipe viscometer, the n&apos; and K&apos; data reported herein were obtained using a direct-indicating rotational viscometer (Fig. 2). The

By E. F. Poncelet

Forty years ago A. A. Griffith developed a theory explaining why brittle materials displayed such low tensile strengths.&apos; He based his views on two points. First, he found himself compelled to assume that all brittle materials are replete with flaws, cracks, and other defects that act, although quite invisible, as large stress raisers. Second, he applied the "theorem of minimum potential energy," which says that the total potential energy of a system must pass from the unbroken to the broken condition by a process involving a continuous decrease in potential energy. By this means he satisfactorily accounted for the noted low strength of such solids and also for the wide spread obtained in experimental measurement of these strengths. So successful has the theory been that it is favored by some to this day. Unfortunately this theory is of limited use beyond the explanation of these two noted phenomena and it is keenly felt that a better theoretical insight into the physics of the fracturing process is needed as the volume of experimental evidence accumulates. The author proposes in the following to build on the fundamentally sound concepts of Griffith and, with the help of increased theoretical knowledge over that available to Griffith, develop a mechanism for frac-ture which will provide far greater understanding of the experimental evidence accumulated to date than is possible from the original Griffith idea. THE GRlFFlTH THEORY Very little progress indeed can be made without accepting the first postulate of Griffith which supposes all brittle solids to be full of microcracks. It would be difficult indeed to find a better mechanism for the small strength of such brittle materials, in conjunction with the fact that the energy that must be expended for comminution is by no means small. The postulate of the existence of the microcracks permits the breakup of the various bonds a few at a time by concentrating the stress at the tip of the progressing crack, while the total energy expended is the same as if they all had been ruptured simultaneously. The only flaw in the argument is that no reasonable explanation has been proposed to account for the genesis of such cracks. Indeed their very presence is in violation of the Griffith second postulate, the potential energy theorem. This theorem is straightforward for isothermal processes, and, in spite of Griffith, there is some doubt that treating the problem isothermally is legitimate. The surface energy of bodies is a free energy, not a potential energy as stated by Griffith, and the production of new surface free energies is not necessarily an isothermal process. There is ample evidence to the contrary. Generally speaking, if heating a body increases its surface area, then, by virtue of Le Chatelier&apos;s principle, any increase of that area by other means will tend to lower its surface temperature. Lord Kelvin calculated the actual cooling that resulted in drawing out a film of liquid.2 R. A. Houston calculated the surface cooling that resulted in stretching a metal wire.3 These calculations were made by applying the Carnot cycle to the process and evaluating the thermodynamics thereof. IRREVERSIBILITY OF THE FRACTURING PROCESS While Griffith was very careful not to say so, the impression gained from studying his papers is that he considered the fracturing process as reversible, that is, a succession of quasi-equilibrium states. There is ample evidence that it is not. The indication that the new surfaces produced by the propagation of a crack are cooler than the original body points to an irreversible heat flow from the interior to the new surfaces to equalize the temperatures. If the process be reversible, any crack accidentally formed should immediately close up as, in the absence of any strain energy, the potential energy would thereby be lowered. The fact that they do not, constitutes a paradox. Such paradoxes are nothing new where certain phenomena that propagate from minuscule nuclei are assumed to be reversible. Such is, for instance, the condensation of a pure saturated vapor that is suddenly chilled by adiabatic expansion. At the beginning the tiny droplets that are formed should be only a few angstroms in size, but the vapor pressure at such droplets is so high that they should evaporate at once. A similar situation arises if a saturated pure solution becomes super-saturated upon cooling; the first tiny crystal nuclei should dissolve as fast as

Jan 1, 1964

By W. B. Braden

This paper presents a suitable method for predicting gas-free oil viscosities at temperatures up to 500F knowing only the API gravity of the oil at 60F and the viscosity of the oil measured at any relatively low temperature. The API pravity and the one viscosity value are used as parameters to determine the slope of a straight line on the ASTM slanaord viscosity-temperature chart. Then, knowing the slope of the line and one point on the line, the vrscosities at higher temperatures can be determined. The line slope correlations were developed at I00 and 210F since viscosity data are frequently measured at these temperatures. A procedure is given for predicting line slopes from measurements at other tetnperatures. A nomogram is furnished for solving the relationship. The correlation has been evaluated at temperatures up to 5OOF for oils varyzng in gravity from 10 to 33 " API. The correiution is applicable only to Newtonian fluids. Comparison at 500F of true viscosities and those predicted from values at 100F shows an average deviation of 3.0 per cent (maximum deviation of 6.0 per cent). Predictions from the values at 21 0F for the same oils how an average deviation of 1.5 per cent (maximum deviation of 3.4 per cent). INTRODUCTION Correlations have been developed by Beal&apos; and by Chew and Connally&apos; for predicting viscosities of gas-saturated oils at reservoir conditions. Each of these correlations requires a knowledge of the solution gas-oil ratio and the viscosity of the gas-free oil at the reservoir temperature. For temperatures below 350F, measurements of the gas-free oil viscosities can be made easily using commercially available equipment. In thermal recovery processes, however, reservoir temperatures well in excess of 350F are encountered. Viscosity measurements at such conditions are more difficult and time consuming and require modification of existing equipment or the construction of new equipment. Measurements are further complicated by the difficulty of handling highly viscous oils associated with thermal recovery processes. Therefore, it is desirable to have a correlation which allows accurate prediction of viscosities at high temperatures. A commonly used technique for predicting viscosities at high temperatures is to measure the viscosities at two lower temperatures, plot the values on ASTM standard viscosity-temperature charts and extrapolate to the temperatures desired. If either of the values is slightly in error, the extrapolated value can be significantly in error. To justify an extrapolation, three points are actually necessary. This procedure can consume much time, particularly with heavy oils. Considering the cost of viscosity measurements, it would be desirable to eliminate the need for direct measurements by having correlations which would allow viscosity predictions from other physical or chemical properties. Beal1 investigated the possibility of correlating viscosity with oil gravity at temperatures from 100 to 220F. While showing that a general relationship exists, he also found significant deviations. It is possible that correlations will be developed based on oil composition as more information becomes available. While not eliminating the need for viscosity rneasurements, the method presented herein requires that only one viscosity measurement be made. The API gravity must also be known. The theory is based on the fact that the viscosity of paraffins (high gravity) changes less with temperature than does the viscosity of naph-thenes or aromatics (low gravity). The gravity. therefore, is used as a parameter to determine the slope of a straight line on the ASTM standard viscosity-temperature charts. The correlation is applicable only to Newtonian oils, and deviations due to thermal decomposition and nonhomo-geneity cannot be predicted. Oils containing additives have not been evaluated. PROCEDURE Fifteen oils were used in developing the correlation; eight were crudes and seven were processed oils. Oil gravities varied from 9.9" API (naphthene base) to 32.7&apos; API (paraffin base). The temperature range studied was 81 to 516F. Each oil used had a minimum of three viscosity measurements and each plotted essentially as a straight line on the ASTM charts. In all, 91 viscosity measurements were used in the correlation. Saybolt, rolling ball and capillary tube viscometers were used for the measurements. Viscosity data for Samples 1, 2, 4, 7, 10, 11 and 14 were obtained in Texaco, Inc. laboratories. The data for Samples 3, 5, 6, 8, 9, 12 and 15 were from Fortsch and Wilson,3 and data for Sample 13 were from Dean and Lane.&apos; All data points used in the correlation are plotted in Fig. 1. It is seen that some of the viscosity values deviated slightly from the straight-line plots at the higher temperatures. Properties of the oils after exposure to the

Jan 1, 1967