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By T. K. Prentice

The January-February number of the Journal of the Chemical Metallurgical and Mining Society of South Africa, 1943, is made up entirely of a discussion of Ball Wear in Cylindrical Mills. Following the principal paper by T. K. Prentice are several remarkably pertinent and carefully prepared discussions. Few persons in this country would be likely to see this publication, and since the information presented is new and of current interest, it seems desirable to abstract and review this publication for the benefit of the members of the A.I.M.E. The purpose of the investigation is stated in the first two paragraphs of Prentice's paper, as follows: Early in 1941, The Chamber of Mines Steel Products, Limited, initiated a series of tests under semi-working scale conditions to determine, if possible, those physical and chemical properties of a ball which make it resistant to wear when used in a cylindrical mill as a grinding medium, with the primary object of incorporating those beneficial qualities in the balls being produced at their works. This paper describes the tests carried out and discusses the results obtained. From these results it was possible to formulate a new theory relating to ball wear in cylindrical mills. This theory is presented in the second portion of this paper. Practical Ball-mill Tests in a Cylindrical Mill Part I of the paper begins with a discussion of the methods used for the manu- facture of grinding balls in South Africa. The following paragraph is of particular interest. The cast steel ingots, 4¼ in. square by 3 ft. 6 in. long, are re-heated in a gas-fired sloping stationary-hearth furnace and then rolled in a six-pass continuous mill into 25/8 in. round billets. Some of these billets are then removed and cut into suitable lengths for forging into 4 in., 3¼ in. , 3 in. or 2½ in. balls by means of three Drop and two Beche hammers, but the greater number, whilst still at about 1,000, pass directly into a set of scroll rolls which produce, in an ingenious manner, finished 3 in. balls direct from the 25/8 in. billets. Except in special cases, all balls are allowed to cool in the atmosphere and are not water quenched. Details of the Tests In order to enable the reader to evaluate properly the results and conclusions in the rest of the paper and in the discussions following the paper, most of the information presented by the author under this heading is quoted: The testing unit was a nominal 30 in. diameter and 18 in. long centre discharge Denver Ball Mill. The ore pulp to the ball mill comprised a small portion of the normal feed to one of the fourteen City Deep 5 ft. 6 in. X 22 ft. tube mills, and the grinding media consisted of the balls under test plus other balls to give the desired load. The running time of the test-mill was divided into approximately equal periods of five days 13½ hours each. The usual procedure was to examine and make up the load

Jan 1, 1947

By R. A. Stauffer

The chief ore of lithium is spodumene, a lithium-aluminum silicate containing up to 3 pct lithium. The preparation of lithium salts from spodumene is costly because of the low concentration of the metal and the difficulty of separating it from the other alkali metals present. Dr. Kroll's and Dr. Schlecten's recent paper1 has reviewed various methods proposed for preparation of lithium. It will be seen from this paper that the methods proposed to date have required one or another of the lithium salts as a raw material. The high cost of these salts has been the chief item of expense in the lithium metal produced. This situation has made it interesting to investigate the possibility of producing the metal directly from spodumene. When spodumene is calcined at 1000ºC in the presence of lime, lithium oxide is replaced in the ore as is evidenced by the fact that it may be leached from the reaction mixture with water.2 Free energy calculations suggested that lithium oxide might be reduced with aluminum or silicon and the lithium produced distilled from the reaction mixture by heating-to about 1000ºC in a vacuum. These facts taken together suggested that it might be possible to prepare lithium metal directly from spodumene by heating a mixture of the ore, lime, and a suitable reducing agent in vacuum and distilling off the lithium metal as formed. The Replacement of Li2O in Spodumene A series of experiments were undertaken to determine the ratio of lime to spodumene necessary to free substantially all the lithium oxide Present in the Ore. The spodumene used in these experiments was supplied by Foote Mineral Co. in the form of powder of about 200 mesh' Analysis of the spodumene was as follows: PCT SiO2......................... 62.7 Al2O3........................ 29.9 Li2o......................... 4.9 Na2O........................ 0.89 CaO......................... 0.75 MgO........................ 0.49 K2O......................... 0.44 Lime (cp —200 mesh) was added in various ratios to spodumene and thoroughly mixed in a ball mill. Two hundred gram samples of spodumene-lime mixtures were charged loosely in fireclay crucibles and held at 1000ºC in a gas-fired furnace for 5 hrs. The product in each case was ground to pass 140 mesh and then placed in a thimble in a soxhlet extractor. Extraction with water was carried on for 6 hrs. After this period the extract was reduced in volume by evaporation in order to precipitate dissolved lime and was then filtered and titrated with 1/4 normal hydrochloric acid. After correcting for residual calcium oxide in solution, the alkali present was calculated as lithium oxide. The results of these experiments are shown in Table I and Fig I. At lime-spodumene ratios less than 1.5, the products were invariably fused. At the ratio of 1.5 and above, the product was loosely sintered with little evidence of fusion. When the ratio of lime to spodumene was three, replacement of alkali oxides in the

Jan 1, 1949

By D. Havlena, A. S. Odeh

The use of the straight-line method of solving the material balance equation is illustrated by means of six field cases. Also, the application of statistical criteria to arrive at the most probable answer is shown. The theory underlying the straight-line method of solution and the applicability of the statistical criteria was presented in a previous paper.' The field cases include saturated and undersaturated oil reservoirs with and without water drive. The aquifers discussed are: limited radial, infinite radial, very small aquifer and infinite linear. The field cases also include a gas reservoir producing under water drive. INTRODUCTION In a previous paper,' the authors presented the theory underlying the solution of the material balance as an equation of a straight line. The appropriate equations for various material balance cases as well as the methods of analysis and interpretation with comments and discussion were also included. To illustrate the various theoretical cases treated previously, five field cases are analyzed in this paper by employing the straight-line method of solving the material balance equation (MBE) and one example previously published is referred to. The use of statistical criteria to arrive at the most probable answer is also shown. All the field examples presented, except Case 2, are excerpts from complete reservoir studies. To illustrate the method, only sections specifically dealing with the material balance principles are included. Additional geologic information and basic data are reported to better acquire an understanding of the cases and thus to better follow the reasoning that suggested the successful application of the straight-line method of solving the MBE. The six cases are: (1) saturated reservoir, small gas cap, limited aquifer; (2) saturated reservoir, very small gas cap, infinite aquifer; (3) undersaturated-saturated reservoir, very small aquifer; (4) highly undersaturated reservoir, no water drive; (5) high undersaturated one-well reservoir, limited aquifer; and (6) gas reservoir, infinite linear aquifer. THE D4 SAND, GUICO FIELD, VENEZUELA The D, sand, which was discovered in 1943, is presently in a depleted state. Since its discovery it has produced under water drive, gas-cap-gas expansion, and solution gas drive. In Nov., 1947, water injection was initiated to arrest further pressure decline. When discovered, the D, sand was a saturated reservoir with a gas cap /oil zone volume ratio m estimated volu-metrically at 0.0731, an average permeability of 500 md, a porosity value of 25 per cent, and an oil viscosity at reservoir conditions of 0.3 cp. The volumetrically determined stock-tank oil initially in place was 23.1 million bbl. The volumetrically weighted physical data and production data available until Nov., 1953 are reported in Table 1. In Ref. 1, the effects on the straight-line plot of various values of ro/r for a constant ?to, or of various dimen-sionless times for a constant r8/r10 were theorized and were illustrated in Fig. 3A of that reference. In this field case, the previously theoretically predicted effects are established. Thus, the MBE calculations using Eq. 3c of Ref. 1 were performed for various r6/r10 and dimension-less time values. Eq. 3c of Ref. 1 is:

Jan 1, 1965

By R. T. Hukki

The purpose of this paper is to present an analysis of the unit operation of grinding and the circulating load, of the unit operation of classification and the circulating load, and of the two superimposed into one operation to clarify the overall trend of events relating the circulating load to the capacity of the closed circuit grinding system, to the specific surface area of the final fine product, and to the energy consumption in the closed circuit grinding process. The capacity of the closed circuit is frequently, if not always, determined by the classifier, not by the mill." With these words a startling idea was expressed in 1934 by Dorr and Anable.1 Today, some 30 years later, grinding in closed circuit is universally accepted. The basic curve presenting the capacity factor versus circulating load by Dorr and Anable has obviously been so convincing that not a single authoritative investigation regarding its validity seems to have been conducted. The only major subject of discussion appears to have been the relative merits of the 'high' and 'low' circulating loads. It seems to be universally agreed that much still remains to be hoped for regarding sharpness of classification. BASIC CURVES FOR CONSTANT MILL LOADING Fig. 1 presents a series of basic curves for constant mill loadings in function of new feed rate and circulating load. The mill loading indicated by each curve is the sum of hourly tonnages of new feed and circulating load. For example, at point 0 where the new feed rate is 100 t/h and the circulating load 300%, or 300 t/h, the mill loading is 400 t/h. In closed circuit grinding, the new feed rate corresponds to the rate of finished classified material produced. Although at this stage the effect of classification is excluded in construction of the basic curves, the trend indicated by these curves is strongly in favor of closed circuit operation under relatively small circulating loads. A study of the curves reveals that, e.g., a mill operating under a load of 200 t/h at point P where the new feed rate is 50 t/h and the circulating load 300% will also operate under the same total load at point Q where the new feed rate is 100 t/h and the circulating load 100%. In other words, a reduction of circulating load from 300% to 100% would lead to doubling of the new feed rate and doubling of the rate of production of finished material, without a change in the total mill loading. The obvious question is, is it also possible by a reduction of the circulating load in a closed industrial grinding circuit to increase the production of finished classified material and, if so, how and to what extent? GRINDING TESTS BY DORR AND ANABLE In a series of open circuit grinding tests reported by Dorr and Anable1 limestone was ground at various feed rates in a 3-ft ball mill. The original data are reproduced in Table I. It can be seen that with the increased feed rate production of -65-mesh material increased and the energy consumption per unit weight of the -65-mesh product decreased in the reverse ratio. The data shown in Table I have been reproduced for our purposes in Table II for a scale corresponding to grinding in a large industrial mill. This reproduction

Jan 1, 1968

By M. T. Hepworth, A. K. Stewart

Iron containing 0.1 pct A1 and -0.9 pct P by weight was internally oxidized in the temperature range 900° to 1300° C, where the bcc structure is stabilized by phosphorous. By measuring the depth of penetration of oxygen with time in an internally oxidized zone for an imposed surface oxygen potential, oxygen permeability was determined. The dgfusion coefficient of oxygen in iron was then calculated using known solubility data, yielding the expression: where Do is the diffusion coefficient of oxygen in bcc iron in sq cm per sec and T is temperature in OK. RECENTLY Hepworth, Smith, and Turkdoganl measured the diffusivity of oxygen in bcc iron and reported the temperature dependence of diffusivity from data determined in the a, and 6 temperature ranges. Subsequently Swisher and Turkdogan' have measured the diffusivity of oxygen in fcc iron. Internal oxidation techniques were employed by these investigators and in this current study. The analysis of this technique is developed by wagner3 (presented in English by Hauffe4 and Rapp 5). In this present study bcc iron stabilized by phosphorous was used to determine oxygen diffusivity in the temperature range 900° to 1300°C. Meijerin 6 has studied oxygen permeability in this temperature range using bcc iron stabilized with 5 pct Sn. Other inves- tigators who have studied oxygen permeability in bcc iron at other temperatures are Schenck et al., 7 Bohen-kamp and Engell, 8 and Bradford. EXPERIMENTAL Electrolytic iron of 99.99 pct purity was alloyed to contain 0.897 pct P and 0.093 pct Al. The maximum weight percent phosphorous required to stabilize bcc iron between 910" and 1392°C is 0.51 pct as determined by Haughton,10 0.42 pct by Roquet and jegaden," and 0.58 pct by vogel,12 with the latter value preferred by Hansen.13 Microprobe analysis indicated that there was no segregation of the phosphorous either before or after permeability studies; therefore, the quantity of phosphorous added was assumed to be sufficient to stabilize the bcc structure. Furthermore, the permeability results of studies on this alloy agreed substantially with interpolated values from previous data on bcc iron.' An ingot of the Fe-P-A1 alloy was hot-rolled to a l-in.-thick slab. Specimens were machined to dimensions: 13/8 by $ by 1/4 in. The experimental apparatus and procedure used have been described before.' A constant oxygen potential was established by passing argon and hydrogen through a column of oxalic acid dihydrate, which has a water vapor pressure which is well-known as a function of temperature. Slab specimens were exposed to a gas mixture sufficiently lean in oxygen to prevent the formation of a surface oxide for predetermined temperature for selected times. The specimens were then quenched, sectioned, and examined metallo-graphically. All quenched specimens were iron-plated to provide protection from the outside sample edge during polishing. Fig. 1 shows a typical microstruc-ture for a specimen oxidized at 953°C for 48.00 hr at a water vapor-to-hydrogen pressure ratio of 0.20. DISCUSSION AND RESULTS The following equation was derived by Hepworth et al.' from Wagner's kinetic expressions for internal oxidation:

Jan 1, 1969

By W. C. Ellis

IN an ingot of germanium solidified progressively from the bottom by a method' devised by J. H. Scaff and H. C. Theuerer, examination discloses ex- IH. C. Torrey and C. A. Whitmer, Crystal Rectifiers. p. 364. 1948. New York. McGraw-Hill Pub. Co. tensive twin relationships. A slice taken about midway in a cylindrical ingot approximately 3/4 in. in diameter and 1 1/2 in. in length, after etching and polishing to delineate different orientations, is shown in fig. la. The orientations of the regions designated with letters were determined by Laue X-ray back-reflection methods and plotted on stereograms. The orientation relationships of the designated components were determined by comparing the values for the nine angles between the three respective cube poles of each orientation with the values calculated in a formal treatment of octahedral multiple twinning in cubic crystals. Germanium, diamond cubic in structure, has the octahedral twinning habit. I am indebted to K. H. Storks for the calculation of the angular relationships of cube poles in octahedral twinning to four orders. The set of values for the nine angles is distinctive of the order of twinning. Confirmation for a multiple twin relationship is obtained from the determined indices of the mirror planes. These exist for all orders of twinning through the third and for some of the fourth." If the orientations are not those for twinning, then the nine angles for the cube poles do not correspond in value and distribution to those formally calculated. Since all nine angles must correspond in values and distribution of values to the calculated ones, the Laue method with a precision of one or two degrees is adequate to establish or deny with confidence the existence of multiple twins. Regions of the same orientation can also frequently be identified by the optical reflections. For example, the narrow twin bands in A at 2: 00 o'clock have orientation B1. The interesting twin relationships shown schematically in fig. lb were found for the section in fig. la. Most of this slice was made up of orientation, A, appearing in widely separated regions. Of the four possible first order twins of A, three were present in this slice and are designated by B with subscripts. Four second order twins of A are designated by C with subscripts. It is worth emphasizing that two of these, C, and C,, are second orders of A through the first order missing in this section. Two regions, designated by D with subscripts are third order twins of A. D2 is a sixth order twin of D,. All orientations found were ascribable to multiple twinning, as if the orientations in this section originated earlier in solidification from a single nucleus. The presence of extensive multiple twinning to- gether with the absence of other orientations appears to be a characteristic result in many instances of solidification of germanium. Fertile conditions for twinning probably exist in the array of atoms in the diamond cubic structure. The high order twins in the section shown, it is reasonable to presume, are the result of progressive octahedral twinning through several generations in the material freezing earlier. Some of these generations do not appear in this section, it is suggested, because their orientations with respect to the growth direction were unfavorable for survival. The extensive twinning is probably promoted during solidification by constraint imposed by volume increase, and to an irregular growth front. Twinning may also be due, in part, to the attempt of the solidifying region to attain the orientation most favorable to the growth direction (maximum thermal gradient). The nucleus for a twinned orientation could have its origin in a "stacking fault" on the close-packed octahedral plane. Further work is being done in which the course of twinning throughout an ingot is being studied. The results appear to be important in the general theory of solidification.

Jan 1, 1951

By J. C. Savins

The practical analysis of the hydrodynamics of the wellbore has long been a subject of interest to engineers. This paper presents a simplified solution to the problem of computing the pressure drop for the flow of drilling mud in the annulus of the wellbore. This solution is, however, an exact and rigorous solution under the assumptions which have been imposed. These assumptions are that the drilling fluid is a Bingham plastic fluid* and that the annulus is formed by two concentric, stationary, cylindrical pipes. It is further assumed that the fluid is incompressible and that its motion is isothermal and in a steady state. This problem under the same assumptions has been attacked by previous authors. Beck, Nuss and Dunn' proposed that the equation for the flow of a Bingham plastic fluid in a cylindrical pipe could be applied to an annulus if the pipe radius were replaced in the equation by the hydraulic radius. This equation, known as the Buckingham-Reiner equation' (see Appendix 1), was also used in an approximate form. Van Olphen pointed out that even for a simple or Newtonian- fluid the pipe equation (Poiseuille's law) could not be converted to the Lamb equation escriptive of flow in an annulus (see Appendix 1) by using the hydraulic radius. Van Olphen further attempted to give a solution for the annular flow of a Bingham plastic fluid by introducing approximations similar to those which have been used in the case of the Buckingham-Reiner equation. Other attempts to provide approximate or exact solutions have been made by Grodde' and by Mori and Ototakeq. The present authors some years ago in unpublished work derived the correct expressions relating the pressure drop and flow rate for this problem. It was found that the solution consisted of two simultaneous equations, one of which contained a logarithmic term. Thus, obtaining numerical results for any particular case of interest involves very tedious trial-and-error computations. Very recently Laird presented the correct derivation of the two equations which are given in full detail in Appendix 1. In order to reduce the amount of calculation time which would be involved in providing a complete tabular or graphical solution to the problem, a high-speed electronic digital computer has been utilized. For this purpose the two simultaneous equations were transformed into more compact expressions by introducing reduced variables. These expressions are given in the following theoretical section. A similar procedure in this problem has been developed by Fredrickson and Bird1" Their tabular results, however, are very incomplete in the range of practical interest for problems of wellbore hydrodynamics. We have furthermore been able to express our graphical results in terms of convenient and familiar dimensionless groups. THEORETICAL DEVELOPMENT Use of Reduced Variables In terms of reduced variables the two simultaneous equations just discussed take the following form, The reduced variables q, x, a and z are defined in terms of the various measured quantities, where Q is volumetric flow rate, AP/L is pressure gradient, Dl is OD of inner pipe, D, is ID of outer pipe, is plastic viscosity, and is yield point. Thus, we have a dimensionless volume flux, a dimensionless reciprocal pressure gradient, and the ratio of the pipe diameters Before introducing the fourth reduced variable, z, it is of interest to consider the physical significance of the parameter x. As may 'be seen from the velocity profile of Fig. 1 the Bingham plastic fluid has the interesting property that a portion of the stream flows at a uniform velocity without shearing action. This section of the stream is situated approximately in the center of the conduit and is known as the "plug flow" region. Its existence is due to the fact that the shearing stresses within the region do not exceed the yield point, which is one of the two flow properties characterizing the fluid. The parameter x then turns out to be the ratio of the

By M. P. Dalton

THE problem at the Morning mill is to separate the galena, which contains a great percentage of the silver, from the sphalerite, making each into a commercial product. The ore as received from the nine is dumped into hopper-bottomed bins of 1200 tons capacity. These are divided into five sections, the first section being the regularly used section and the re-mainder used as a reserve bin. The ore is first passed through a 9 by 15-in. Blake jaw-crusher with an opening of 4 in. This allows a ham-mer head to pass through without damage. The crusher discharges to a conveyor that delivers the ore into a two-section punched-plate trommel screen with 1 ½ and 2-in. openings. The undersize is carried by means of conveyors to the mill bins. The oversize passes over a shaking feeder and through a spray or high-pressure water to a picking-belt, where waste and crude ore is hand-sorted. About 4 per cent of the ore by weight is picked out as waste, assaying about 0.6 per cent lead, and this is discarded over the dump. About 4 per cent of the ore by weight is removed as crude ore, assaying 10 oz. silver, 30 per cent lead, and S per cent zinc, and is shipped direct to the smelter. The remainder of the oversize from the picking-belt is con-veyed to a 4-ft. Symons cone crusher with 1-in. opening, which is interesting as a new introduction in this dis-trict. The machine consumes approximately 40 hp. and the pinion shaft travels 555 r.p.m. The horsepower is rather high, but the machine has an extraordinarily large capacity, and, due to the unique construction, there is no danger of tramp steel causing any damage, as in that case the discharge "opening" is automatically

Jan 7, 1927

By Frank C. Greene

The principal event in the development of oil and gas in Missouri in 1942 was the drilling of the Cities Service Oil Company's No. I Jim Cook, in the northwest corner, NW. 1/4 sec. 32, T. 65 N., R. 39 W., Atchison County, in the northwest corner of Missouri. This well, not yet completed, bailed several barrels of free oil in about 27° Baume from a sand called the Bartlesville by those in charge, at a depth of 1450 ft. The well is on a block of leases obtained after the area, which is covered by several hundred feet of glacial drift, had been prospected by core drilling. Earlier in the year the same company drilled a well on the Glen Gray farm in the southwest corner, SW. 1/4 sec. 29, T. 65 N., R. 39 w., to a depth of 2427 ft. in the Hunton lime with a rotary drill. Oil stains in this hole led to the drilling of the second well. Table i .—-Wells Drilled for Oil and Gas in Missouri in 1942 Country Number of Number of County Oil Wells Gas Wells Dry Andrew.......... Atchison.......... I Bates............ 2 6 Caldwell.......... I 3 Cass............. I Clinton........... I Holt............. I Jackson.......... I I Knox............ I Nodaway......... I Platte............ 4 4 Ray.............. 5 Sullivan.......... I Totals.......... I 7 28 Otherwise drilling in Missouri was uneventful, with a total of only 36 Completions, of which one was a very small oil well, Seven were small gas wells and 28 were dry holes. The total footage drilled was 24,7541/2 ft., of which 14,0281/2 was by cable tools and 10,726 ft. by rotary. Twelve of the dry holes were drilled into Mississip-pian or older beds. Table I gives a summary of activities by counties.

Jan 1, 1943

By Frank C. Greene

The principal event in the development of oil and gas in Missouri in 1942 was the drilling of the Cities Service Oil Company's No. I Jim Cook, in the northwest corner, NW. 1/4 sec. 32, T. 65 N., R. 39 W., Atchison County, in the northwest corner of Missouri. This well, not yet completed, bailed several barrels of free oil in about 27° Baume from a sand called the Bartlesville by those in charge, at a depth of 1450 ft. The well is on a block of leases obtained after the area, which is covered by several hundred feet of glacial drift, had been prospected by core drilling. Earlier in the year the same company drilled a well on the Glen Gray farm in the southwest corner, SW. 1/4 sec. 29, T. 65 N., R. 39 w., to a depth of 2427 ft. in the Hunton lime with a rotary drill. Oil stains in this hole led to the drilling of the second well. Table i .—-Wells Drilled for Oil and Gas in Missouri in 1942 Country Number of Number of County Oil Wells Gas Wells Dry Andrew.......... Atchison.......... I Bates............ 2 6 Caldwell.......... I 3 Cass............. I Clinton........... I Holt............. I Jackson.......... I I Knox............ I Nodaway......... I Platte............ 4 4 Ray.............. 5 Sullivan.......... I Totals.......... I 7 28 Otherwise drilling in Missouri was uneventful, with a total of only 36 Completions, of which one was a very small oil well, Seven were small gas wells and 28 were dry holes. The total footage drilled was 24,7541/2 ft., of which 14,0281/2 was by cable tools and 10,726 ft. by rotary. Twelve of the dry holes were drilled into Mississip-pian or older beds. Table I gives a summary of activities by counties.

Jan 1, 1943

By R. A. Swalin, B. W. Roberts

ONSIDERABLE controversy has centered about the existence of an order-disorder transformation in alloys in the composition vicinity of 75 atomic pct Ni and 25 atomic pct Cr. All the evidence to date for such a transformation is of a rather indirect nature, since direct X-ray confirmation is difficult to obtain as a result of the small difference in X-ray scattering factors between nickel and chromium. As a result, superlattice lines would be very faint if present. Several investigators1-5 have observed anomalies in the electrical resistivity vs temperature curves of alloys in the vicinity of 25 atomic pct Cr. The observed change is characterized by a rather broad resistivity peak at about 540°C. A discontinuous drop in resistivity is normally associated with ordering. However, Taylor and Hin-ton4 have rationalized that the discrepancy could conceivably be caused by changes in the Brillouin zones upon ordering. The same investigators measured the specific heat as a function of temperature and have also observed anomalies in the vicinity of 540°C. Nordheim and Grant5 have proposed, because of the absence of superlattice lines and the absence of a discontinuity in the resistivity vs temperature curve, that long-range order is improbable and that the results could be better explained by short-range ordering. To date, however, the question has not been resolved satisfactorily. Neutron diffraction techniques provide a method for partially resolving the question since nickel and chromium have considerably different atomic scattering factors in the case of neutrons and, therefore, superlattice peaks, if ordering occurs, should be readily discernable. The results of a neutron diffraction investigation* coupled with a dilatometric in- vestigation are reported here. An alloy containing 28.0 atomic pct Cr was prepared from carbonyl nickel and electrolytic chromium in the form of a 1-in. diam x 10-in. ingot. Melting was done in an alumina crucible and casting in a graphite mold. The ingot was homogenized at 1250°C for seven days, after which a 5-in. long piece was cut into shavings in order to obtain a suitable neutron diffraction sample. Hardness samples and samples suitable for dilatometric analysis (% in. diam x 2 in.) were prepared from the remainlng piece. The neutron diffraction sample, along with a hardness sample, was annealed at 501°C for seven days, at which time the temperature was lowered to 479°C and held at this temperature for twenty-four more days. The hardness was observed to increase from 133 to 147 Vhn during the course of the annealing treatment, in qualitative agreement with Nordheim and Grant." Neutron diffraction traces taken at room temperature and at 42 °K are shown in Fig. 1. The insert shows the trace taken at room temperature with short counting times and thus only fair statistical accuracy. No evidence for superstructure reflections of Cu3Au-type ordering is observed. The statistical accuracy of the 4.2°K trace was improved by using longer counting periods. Several weak intensities are observed at small angles, including an aluminum reflection from the cryostat assembly and a very

Jan 1, 1958

By Kendall E. Born

Production of crude oil in Tennessee during 1940 was slightly more than 15,000 bbl., a decrease from 1939 of about 36,000 bbl. This sharp decline has been caused largely by curtailed activities in the shallow pools in Clay County, where approximately 3000 bbl. was marketed off the lease during the year as against more than 37,000 bbl. in 1939. The flashy production found in 1938 in the Celina area has been short-lived and the area is essentially abandoned. Failure to find steady production has been the major factor retarding developments in the northeastern Highland Rim area. The Mississippi lime production in Scott and Morgan Counties continued to show a steady decline. The Tennessee production by counties is shown in Table I. Table i.—Oil Production in Tennessee it1 1940 Production. Bbl. Number of County Wells Pumped 1939 1940 Scott............ 4 4,332 3.596 Morgan.......... I: 6,479 5,751 Fentress.......... 3 I,2XX 1,5xz Pickett........... 1 1.2XX Clay............. 8 37.200 3,XXX Developments There were 32 wells spudded in during 1940, four of which were drilling or only temporarily suspended on Dec. 31, 1940. Twenty-eight wells were completed during the year, four of which were commercial producers. The total footage drilled was 3I,214 ft. The more important wildcats are listed in Table 2; the distribution of 1940 oil and gas tests according to physiographic divisions is given in Table 3. Cumberland Platenu.—Thcre was one completion in the coal area of the state, a test that attempted to extend the Mississippi lime production in the Coon Hollow pool to the southeast in Morgan County. This test encountered only slight shows of oil in the producing horizons of the near-by Coon Hollow and Boone Camp pools. Some surface work was carried on by private interests during the year in Scott and Morgan Counties and two wells were spudded in early in 1941 The revival of interest in the Kentucky portion of the plateau will probably result in increased activity in this part of Tennessee during 1941. Several sizable blocks of acreage, some by major oil companies, are held in Scott, Morgan, and Cumberland Counties. Middle Tennessee.—The northeastern Highland Rim continued to be the most active area in the state with 20 completions, although this figure is about one third of the number drilled in 1939. Four oil wells, none with initial productions of more than I00 bbl., were completed in Clay, Fentress, and Pickett Counties. The producing horizons discovered in Pickett and Fentress Counties were in the "Sunny-brookJ' pays of Trenton age. The Clay County producer was an old test drilled deeper in which oil was found at 671 ft. in the upper part of the Stones River group of limestones, a common pay in this area. All four wells were drilled in or close to old shallow production. Deeper testing into the Knox dolomite group in this area was not particularly encouraging, although one well in Fentress County encountered some saturation at 1860 to 1869 ft. in the upper

Jan 1, 1941

By D. H. Polonis, J. G. Parr

IN a recent paper on titanium-rich Ti-Fe alloys,' the hardness of quenched powder specimens was given, together with the amounts of martensitic a they contained. The values disagreed in two respects with previous determinations that Worner² made on lump specimens: 1—Some martensitic a' is formed in powder specimens of alloys containing up to 12 atomic pct Fe. On the other hand, Worner reports that, although his results on quenched lumps are not conclusive, alloys containing more than about 4 pct Fe "appear to consist of retained ß'' although they "may not be strictly unaltered solid solutions." 2—According to Worner, quenched lump specimens show a maximum hardness at a composition about 3.5 pct Fe. Earlier -experiments by the authors showed a maximum hardness of martensitic alloys in powder form at 10 pct Fe. Accordingly, more experiments have been conducted in order to confirm these differences and to determine with more accuracy the minimum composition of quenched lump specimens that consist entirely of retained ß. Lump samples?x?x1/20 in. were quenched from 1000°C in helium and, on the whole, showed similar hardness values to the specimens that Worner water-quenched from 950°C. The hardness curve the authors obtained shows a more pronounced peak, but in other respects it is very similar to Worner's curve (Fig. 1). While it was possible to make fairly reliable measurements of the percentage of martensitic a in quenched powders (by Geiger spectrometer), the solid samples allowed only approximate estimates to be made from visual observation of line intensities on film. Retained ? begins to appear in quenched lumps containing 0.2 pct Fe; at 2.2 pct Fe there are approximately equal quantities of ß and a'; in a 4.7 pct Fe alloy only a trace of a' appears. These results are represented as a curve on Fig. 1. The hardness and constitution of powder samples were verified by repeating both types of quenching experiment described in the earlier paper.' Identical results were obtained by the two methods, and they agreed with the figures published previously (Fig. 1). The appearance of the martensitic structure under the microscope is shown in Figs. 2 and 3. The mar-tensite needles are coarser in the lump; otherwise the structures are similar. Three conclusions are made at this juncture: 1— The properties of quenched lumps reported by Worner are confirmed, on the whole. The differences between them and the properties of powders are probably due to an effect of specimen size. Differences of behavior in various sizes of specimen have been observed previously in martensite reactions in Fe-Mn alloys3 and in Cu-A1 alloys. 2—The maximum hardness of both quenched lumps and quenched powders appears at a composition where martensite formation has all but ceased. In this respect, powders and lumps behave similarly. 3—Martensitic a' has essentially the same microscopic appearance both in powders and lumps. Acknowledgment This work is part of a program sponsored by the Defegce Research Board of Canada, Project No. 425.

Jan 1, 1956

By Kendall E. Born

Production of crude oil in Tennessee during 1940 was slightly more than 15,000 bbl., a decrease from 1939 of about 36,000 bbl. This sharp decline has been caused largely by curtailed activities in the shallow pools in Clay County, where approximately 3000 bbl. was marketed off the lease during the year as against more than 37,000 bbl. in 1939. The flashy production found in 1938 in the Celina area has been short-lived and the area is essentially abandoned. Failure to find steady production has been the major factor retarding developments in the northeastern Highland Rim area. The Mississippi lime production in Scott and Morgan Counties continued to show a steady decline. The Tennessee production by counties is shown in Table I. Table i.—Oil Production in Tennessee it1 1940 Production. Bbl. Number of County Wells Pumped 1939 1940 Scott............ 4 4,332 3.596 Morgan.......... I: 6,479 5,751 Fentress.......... 3 I,2XX 1,5xz Pickett........... 1 1.2XX Clay............. 8 37.200 3,XXX Developments There were 32 wells spudded in during 1940, four of which were drilling or only temporarily suspended on Dec. 31, 1940. Twenty-eight wells were completed during the year, four of which were commercial producers. The total footage drilled was 3I,214 ft. The more important wildcats are listed in Table 2; the distribution of 1940 oil and gas tests according to physiographic divisions is given in Table 3. Cumberland Platenu.—Thcre was one completion in the coal area of the state, a test that attempted to extend the Mississippi lime production in the Coon Hollow pool to the southeast in Morgan County. This test encountered only slight shows of oil in the producing horizons of the near-by Coon Hollow and Boone Camp pools. Some surface work was carried on by private interests during the year in Scott and Morgan Counties and two wells were spudded in early in 1941 The revival of interest in the Kentucky portion of the plateau will probably result in increased activity in this part of Tennessee during 1941. Several sizable blocks of acreage, some by major oil companies, are held in Scott, Morgan, and Cumberland Counties. Middle Tennessee.—The northeastern Highland Rim continued to be the most active area in the state with 20 completions, although this figure is about one third of the number drilled in 1939. Four oil wells, none with initial productions of more than I00 bbl., were completed in Clay, Fentress, and Pickett Counties. The producing horizons discovered in Pickett and Fentress Counties were in the "Sunny-brookJ' pays of Trenton age. The Clay County producer was an old test drilled deeper in which oil was found at 671 ft. in the upper part of the Stones River group of limestones, a common pay in this area. All four wells were drilled in or close to old shallow production. Deeper testing into the Knox dolomite group in this area was not particularly encouraging, although one well in Fentress County encountered some saturation at 1860 to 1869 ft. in the upper

Jan 1, 1941

By John L. Miles

John L. Miles (Arthur D. Little, 1nc.)—Pollack and orris" have reported measurements on electron tunneling through A1-A12O3-A1 sandwiches in which the oxide was formed by gaseous oxidation in a glow discharge. From these measurements they deduced the asymmetry of the barrier and, since this is small, conclude that the mechanism suggested by Mott19 for the growth of oxide in thin A12O3 films is inapplicable. In earlier papers20 Pollack and Morris report similar work for oxide films grown thermally. In this case they find a greater asymmetry and conclude that the Mott mechanism is valid. I would like to point out that both these conclusions are quite unjustified. Mott suggests that the growth of the oxide film on aluminum results from the passage of ions through the already present film of oxide under the action of an electric field. This field results from a constant voltage which is in effect a contact potential between metal on one side of the barrier and adsorbed oxygen ions on the other side of the barrier. The theory does not require that the oxide grown is nonuniform either in stoichiometry or structure. It does however specifically assume that the partial layer of ionized oxygen on the surface remains adsorbed on the surface of the growing oxide. In other words, the so-called "built-in field" remains in the oxide only as long as the ionized oxygen is present. When a counter electrode of aluminum is deposited on the oxide, it will react with the adsorbed oxygen on the surface of the oxide, thus forming a small additional amount of oxide. It is clear, then, that there is no requirement in the Mott theory of oxide growth which would necessitate tunneling currents through an Al-A1203-A1 sample to be different when the polarity is reversed. Neither does the theory eliminate the possibility that some additional mechanism could cause the tunneling barrier to be asymmetric and hence tunneling currents to be a function of polarity in such a sandwich. Thus these tunneling-currents measurements are not germane to the question of whether the Mott mechanism is the true method of growth of aluminum oxide films. In fact, it is not surprising that there should be a difference between the oxide properties at the two interfaces (with resulting asymmetry in the tunneling barrier) since the growth conditions and growth rates must have been quite different at these two positions. S. R. Pollack and C. E. Morris (authors' reply)— The point raised by Miles above is one has caused some confusion in the past. The following is an attempt to clarify this point. The built-in field which is responsible for the growth of the thermal oxide at low temperatures arises, according to Mott, because of the passage of electrons from the Fermi surface of the oxidizing metal to surface states introduced by the adsorbed oxygen. It is assumed that the energy of these surface states lies below the Fermi energy of the metal. Electrons therefore continue to flow from the metal to the surface until the built-in electric field raises the potential energy of the surface states to the value of the Fermi energy in the metal, at which time equilibrium is obtained between the surface states and the metal. That is in equilibrium as many excess electrons pass from the metal to the surface per unit time as vice versa. The surface of the oxide prior to deposition of a metallic counterelectrode can then be pictured as follows. The Fermi energy lies in the energy gap of the oxide and is essentially pinned at the energy of the oxygen surface states. The vacuum work function of the oxide is then given by the sum of the electron affinity of the oxide (i.e., the difference in energy between the vacuum and the conduction-band minimum) plus the energy difference between the conduction-band minimum and the Fermi energy. The deposition of a metal onto the surface of the oxide can result in a transfer of electrons across the extremely thin oxide only if there is a contact potential difference between the deposited metal and the parent metal or oxide. That is if the vacuum work function of the deposited metal differs from that of the parent metal, then charge can be redistributed across the oxide in order to equilibriate the Fermi energy across the structure. (It should be

Jan 1, 1965

By J. S. Pascover, J. K. Abraham

The influence of the early stages of precipitation on the kinetics and structure of martensite formation in Fe-27Ni and Fe-29.5Ni alloys containing from 0 to 10 pct Ti was examined with X-ray and electron microscopy techniques. The formation of a coherent, ordered preprecipitate had a profound stabilizing effect on the austenite. The Ms was decreased by increased titanium content and aging time up to a critical time. When the critical aging time was exceeded, the Ms was observed to increase markedly. The formation of the clusters was insuppressible and the volume fraction of clusters formed during the quench was a function of the titanium content. Martensite resulting from transformation of the clustered austenite is tetragonal with the c/a ratio increasing with titanium content. A model for the tetragonality is suggested. The morphology and substructure of the m artensite is inter-preted in terms of the above information and the cur-rent models of twinned martensite. ThE ramifications of precipitation in austenite to the properties of austenite have been the subject of numerous investigations. The current research is concerned with the influence of precipitation in austenite on the kinetics and structure of subsequent marten-site formation. In a previous investigation, Abraham et al.1 followed the aging reaction in an Fe-29.5Ni-4.2Ti* (at. pct) alloy using an X-ray diffraction technique. This technique, employing a Guinier camera, provided kinetic measurements through observation of the side band position as a function of aging time. The salient results of this work were: 1) The initiation of precipitation was not suppressed by quenching, i.e., there was a finite cluster zone size at zero aging time; and 2) The hardness of the aged austenite correlated extremely well with the zone size. During the previous work it was noted that the mar-tensite formed after aging was tetragonal, substanti-ating an earlier observation.2 Systematic investiga-tion revealed that the martensite was tetragonal in both the solution-treated then quenched, and the solu-tion-treated, aged, and quenched condition, and, furthermore, that a marked stabilization of the austenite occurred as a function of aging time. The present work is concerned with documenting the tetragonality and the stabilization phenomena as well as the ob- served microstruction with a suggested rationale for the behavior noted. EXPERIMENTAL PROCEDURE The compositions of the alloys are listed in Table I. The analyses were performed after the solution treatment of the strip material. Nickel was determined using the standard dimethy1-glyoxime procedure whereas titanium was determined colorimetrically with hydrogen peroxide and volumetrically by titrating with ferric iron. The materials were melted in a 5-lb vacuum induction furnace, cast into 2-in.-diam ingots, and forged in a temperature range of 950. to 1200°C to 1/2-in. slabs. The three higher titanium containing materials cracked during forging; therefore, to get the alloys into strip form, slices 1/8 in. thick were cut from the slab, homogenized 4 hr at 1150°C, then cold-rolled to a 0.04-in. thickness. The remaining slabs were hot-rolled, homogenized 4 hr at 1065"C, then cold-rolled to a final thickness of 0.03 in. All of the heat treatments were performed under a protective atmosphere of argon. The Ms temperature for most of the alloys is below room temperature; therefore, it was possible to solution treat, quench to room temperature, polish, and then observe the transformation optically on a cold-stage microscope. To determine the effect of aus-tenitizing temperature on Ms, eight of the alloys were treated at two temperatures, 1025" and 1120°C. No measurable variations in Ms were noticed. The remaining alloys were treated at 1025°C. The specimens, : by 5/16 by 0.03 in., were austeni-tized in a vertical tube furnace under a dynamic argon atmosphere. The bottom of the tube was submerged in water for quenching purposes. The question of stabilization that may be operating at room temperature was investigated and found to be negligible. Many of the specimens were held at room

Jan 1, 1970

By T. P. Chen, F. W. Bowdish

Studies made with a captive bubble apparatus on the sulfidization and collection by amyl xanthate of true chrysocolla specimens have defined the ranges of pH value and sulfide concentration which permit contact between the bubble and the mineral surface. Titanium compounds were the most effective of the materials found to activate the sulfidization of chrysocolla. With titanium activation, the contact angles and the ranges of pH value and sulfide wncentration giving bubble contact were all increased. Chrysocolla ores were concentrated by flotation. Chrysocolla ores occur at many localities in grade and quantity sufficient to make mining and millin feasible, but no satisfactory method of concentratio has been found. Although chrysocolla may be leached with acid, only those ores without acid-consuming gangue may be leached economically. Because of its potential importance, a study of the conditions nece sary for flotation of chrysocolla has been carried ou The literature contains a few references to flotation of chrysocolla. Two methods were developed by the U. S. Bureau of Mines.1,2 The first consisted of a fatty acid soap and a high xanthate as collectors of chrysocolla from a synthetic ore, while the second involved the use of hydrogen sulfide and xanthate. Ludt and DeWitt3 demonstrated the difference in adsorptive powers of chrysocolla and quartz for bas triphenyl methane dyes and suggested the use of butyl, hexyl or octyl-substituted malachite green as collector. Jackel4 emphasized the effects of combin tions of reagents such as Aerofloat 31, pine oil, and Reagents 404 and 425 with sodium sulfide and zinc hydrosulfite as conditioning agents. Although he reported recoveries of 89% from a synthetic ore and 98% from a natural ore containing azurite, malachite, chalcopyrite and chrysocolla, careful application of Jackel's method to chrysocolla from Tyrone, N.M., failed to give a high recovery. MATERIALS AND TECHNIQUE Samples from Inspiration, Ariz., and Tyrone and Magdalena, N. M., were used for experimentation and verified as true chrysocolla by leaching tests, specific gravity tests and X-ray diffraction. Chrysocolla does not dissolve at pH 4, although malachite and azurite do. Chrysocolla is about half as dense as the copper carbonates. X-ray diffraction analyses by the powder camera method confirmed the samples as true chrysocolla. A captive bubble apparatus, which cast an enlarged image of the air bubble and the mineral surface upon a screen, was used to check on the character of the surfaces. The specimens were prepared by grinding a flat surface on a glass plate using fine abrasive; then they were washed and kept in distilled water until they were to be treated with reagents. Before each reagent treatment, the specimen was carefully checked for cleanliness in the captive bubble apparatus. It was assumed that the surface was clean if, after fine grinding and washing of the specimen, the bubble would not stick. Specimens were handled with glass forceps, and precautions were taken to avoid contamination of the mineral surfaces. Contact angle measurements were carefully made several times on each treated specimen to obtain reliable average values. EFFECT OF pH VALUE AND SODIUM SULFIDE CONCENTRATION In each experiment, a specimen with a freshly ground surface was immersed for 10 min in a solution of sodium sulfide, washed and immersed for 15 min in a solution containing 30 mg per 1 of potassium amyl xanthate. The specimen was then washed again in distilled water and tested for contact angle in the captive bubble apparatus while submerged in distilled water. In this series of experiments, the pH of the sulfidizing solution was varied from 3 to 7, and the concentration of sodium sulfide, containing 60% Na2S, was varied from 50 to 650 mg per 1. Many combinations of pH value and sulfide concentration resulted in no contact between the bubble and the surface, but over a limited range of conditions, contact angles varying from 24ºto 52ºwere obtained. The data in Fig. 1 show sulfidization conditions that lead to bubble contact and those that do not. The region of contact is surprisingly small, which may indicate why flotation of chrysocolla involving sulfidization has proven so difficult in practice. Several features of the system are illustrated in Fig. 1. In the region between pH values of 4 and 6 with sodium sulfide concentrations below about 350

Jan 1, 1963

By J. T. Norton, Pekka Rautala

The phases and equilibria in the W-Co-C system have been studied by X-ray diffraction methods, metallographic technique, and thermal analysis. In addition to the 7 phase, two double carbides, called 8 and have been revealed. The compositions correspond to CO3 W6C2 and Co3-W10C4. The reactions leading to these phases have been explained and tentative diagrams of stable and metastable equilibria proposed. The basic reactions in sintering cobalt cemented tungsten carbides are discussed. THE W-Co-C system is of fundamental importance in practical carbide manufacturing as well as for the understanding of the sintering mechanism. Surprisingly little is known about this system, for the probable reason that all the important alloys are of two-phase structure and that the diagram Co-WC has been treated as a quasi-binary. This obviously is incorrect, because WC decomposes before melting. One ternary phase, 7, of composition Co3W3C has long been known. It was first studied by Adelskold, Sundelin, and Westgren,1 although the isomorphous iron-tungsten carbide was known earlier. There have been in the literature several reports of two 7 phases.' " Also the 7 phase has been considered unstable by Takeda4 and Westgren.1 The Co-WC diagram has been studied by Wyman and Kelley5 and a quasi-binary diagram has been published by Sandford and Trent.2 Takeda has published a tentative Co-W-C diagram, considering both metastable and stable equilibria. However, the lines of two-fold saturation are shown only partially and it seems impossible to complete the diagram without violating the phase theory. Therefore it seemed desirable to examine the system in more detail. Experimental Procedure The alloys used in the present investigation were made of powders of tungsten, tungsten monocarbide, cobalt, and carbon and were of the grade used in manufacture of commercial cemented carbides. The powders were ground and mixed in small stainless steel ball mills, using balls of the same material. Benzene was used as a dispersing agent. The mixing period was 1 hr, since this was shown to give suffi- ciently good mixing of the powders without too great a contamination from the mill. After ball milling, the specimens were pressed in cylindrical or rectangular dies. No paraffin or other lubricant was used and the small compacts had sufficient green strength to be handled without difficulty. Several sintering furnaces were employed. The most satisfactory arrangement was a vacuum furnace based on the Arsem principle which employed a graphite helix as the resistance heating element. Specimens were placed on graphite stands and there was generally a slight carburization or decarburiza-tion of the specimen surface, depending on the carbon content of the alloy. The evaporation of the cobalt at a sintering temperature of 1400°C was not significant, but became severe at 1500°C and higher. The sintering time was 1 hr at 2000°C and 2 to 4 hr at lower temperatures. It was not possible to quench the specimens, but the cooling rates were rather fast, greater than 300°C in the first minute. In the system under investigation, the reactions are sluggish, and it is believed that the high temperature structures are satisfactorily retained. The principal method of investigating the sintered specimens was X-ray diffraction by the Norelco recording spectrometer. Approximate determinations of the phase boundaries were made by the disappearing phase method. Ternary Phases To study the phase formation in W-Co-C system, a series of specimens was sintered at 1400°C. In this experiment two ternary phases, called here ? and k were formed in addition to the well-known 7 phase. The 7 phase, which has been completely described by Westgren: showed a range of homogeneity from 7 to 20 pct C and from 38 to 48 pct Co. At 1400°C the 7 phase was found to be in equilibrium with monotungsten carbide, 8, tungsten, 8, #?, and liquid. The boundaries toward #? and liquid were difficult to determine and appeared to be very temperature sensitive. The other boundaries are believed to be well fixed. The homogeneity range of 7, as measured in this work, is considerably smaller than the one

Jan 1, 1953

By D. Havlena, A. S. Odeh

The material balance equation used by reservoir engineers is arranged algebraically, resulting in an equation of a straight line. The straight line method of analysis imposes an additional necessary condition that a successful solution of the material balance equatiott should meet. In addition, this algebraic arrangement attaches a dynamic ineuning to the otherwise static material balance equation. The straight line method requires the plotting of one variable group vs mother variable group. The sequence of the plotted points as well as the general shape of the resulting plot is of utmost importance. Therefore, one cannot progrm the method entirely on a digital computer ar is usually done in the routine solution of the material balance equation. If this method is applied, then plotting and anaIysis are asential. Only the appropriate equations and the method of analysis and interpremtion with comments and discussion are presented in this paper. Illustrative field examples for the various cases treated are deferred to a subsequent writing. INTRODUCTION One of the fundamental principles utilized in engineering work is the law of conservation of matter. The application of this principle to hydrocarbon reservoirs for the purpose of quantitative deductions and prediction is termed "the material balance method of reservoir analysis". While the construction of the material balance equation (MBE) and the computations that go with its application are not difficult tasks, the criteria that a successful solution of the MBE should fulfill have always been a problem facing the reservoir engineer. True and complete criteria should embody necessary and dcient conditions. The criteria which the reservoir engineer uses possess a few necessary but no sufficient conditions. Because of this, the answers obtained from the MBB are always open to question. However, the degree of their acceptability should increase with the increase in the number of the necessary conditions that they should satisfy. Generally, the necessary conditions commonly used are (1) an unspecified consistency of the results and (2) the agreement between the MBE results and those determined volumetrically. This second criterion is usually overemphasized. Actually, the volumetrically determined results are based on geological and petrophysical data of unknown accuracy. In addition, the oil-in-place obtained by the MBE is that oil which contributes to the pressure-production history,' while the volumetrically calculated oil-in-place refers to the total oil, part of which may not contribute to said history. Because of this difference, the disagreement between the two answers might be of paramount importance, and the concordance between them should not be overemphasized as the measure of correctness of either one. In this paper, a third necessary condition of mathematical as well as physical significance is discussed. It is not subject to any geological or petrophysical interpretation, and as such, it is probably the most important necessary condition. It consists essentially of rearranging the MBE to result in an equation of a straight line. This straight line method of the MBE solution has invalidated a few long time accepted concepts. For instance, it has always been advocated that if a water drive exists, but one neglects to take it into account in the MBE, the calculated oil-in-place should increase with time. The straight line method shows that in some cases, depending on the size of the neglected aquifer, the calculated oil-in-place might decrease with time. The straight line method requires the plotting of a variable group vs another variable group, with the variable group selection depending on the mechanism of production under which the reservoir is producing. The most important aspect of this method of solution is that it attaches a significance to the sequence of the plotted points, the direction in which they plot, and to the shape of the resulting plot. Thus, a dynamic meaning has been introduced into the picture in arriving at the final answer. Since the emphasis of this method is placed on the interpretation of the sequence of the points and the shape of the plot, one cannot completely automate the whole sequence to obtain "the best value" as normally done in the routine application of the MBE. If one uses the straight line method, then plotting and analysis are musts. The straight line method was first recognized by van Everdingen, et al,2 but for some reason it was never fully exploited. The advantages and the elegance of this method can be more appreciated after a few cases are carefully treated and worked out by it. SOLUTION OF THE MATERIAL BALANCE EQUATION SATURATED RESERVOIRS The MBE for saturated reservoirs written in AIME symbols is

By Jack Washburn, E. R. Parker

Kinking in zinc single-crystal tension specimens was observed under conditions of low stress and high temperature. Kinking is discussed in relation to other plastic bending phenomena on the basis of dislocation theory. Experiments on the stress-induced motion of small angle boundaries are reported. KINKING was first reported by Orowan1 as a new deformation mechanism. He observed the phenomenon in cadmium single crystals loaded in compression. Glide lamellae in a local region of the rod were observed to snap over suddenly to a tilted position, resulting in a sudden shortening of the specimen. Between the tilted portion and the rest of the crystal there were fairly sharp boundaries, with the slip plane assuming approximately mirror image positions on opposite sides of these boundaries. Orowan considered the boundaries to be regions where dislocations had concentrated. Hess and Barrett' observed the formation of kinks in critically oriented zinc compression specimens. It was found that the sudden snapping over of the tilted region was not an essential part of the kinking phenomenon but rather was associated with the method of loading. Kinking was explained on the basis of the accepted mechanisms of slip and flexural glide. It was also suggested that a kink can be considered as a special type of deformation band. During a recent investigation of the effect of surface condition on creep of zinc single crystals," a similar phenomenon was observed in crystals which were loaded in tension. The specimens were 0.4 in. diam cylindrical rods with a free length of 4 in. between end connections. All of the crystals were tested at a constant load. adjusted to give an extension rate of approximately 0.05 pct per hr. Kinking, as shown in Fig. 1, occurred in some of the tests performed at temperatures above 200°C. Kinking was observed in specimens varying widely in initial orientation, scattering about a 45" angle between the slip plane and the specimen axis. The condition leading to kinking in tension appeared to be non-uniform distribution of flow along the gage length combined with the restraint imposed by the tensile load. At low temperatures and fast strain rates, the distribution of strain throughout the midsection of tension specimens was generally quite uniform; therefore, bend planes developed only near the ends as described by Miller.4 However, at high temperatures under creep conditions it was difficult to obtain specimens in which the distribution of flow was uniform. Some of the factors which may have caused differences in flow stress along the length of the crystals are: Nonuniform distribution of impurities, accidents of growth (lineage structure), slight bending or other damage during handling, surface conditions, and strain-aging characteristics due to dissolved nitrogen." Plastic flow, once started in a local region, often continued to a relatively large strain before other parts of the gage length became active. Under these conditions a series of kinks, such as those in Fig. 1, were produced. Fig. 2 illustrates how a nonuniform distribution of slip produces bending moments which- are responsible for kink formation. If no plastic bending were to occur while the rod extended by pure slip in two separate sections of the rod, it would assume a shape such as that in Fig. 2a. A specimen having this shape and being subjected to a tension load would have concentrations of stress at the concave surfaces C and lower than average stress would exist at the convex surfaces D. Therefore a bending moment is superimposed on the average stress in the regions between C and D. The positions of potential bend planes under these conditions are shown as dotted lines. Actually no such shape as Fig. 2a develops because plastic bending in the region C-D occurs simultaneously with pure slip in the intervening regions. The observed structure of a tension kink is indicated by Fig. 2b. Perhaps the best approach to an understanding of kinking as well as other related plastic bending phenomena, such as the bend planes discussed by Miller,' cell formation studied by Wood et al.,6 and polygonization,7 is consideration of the dislocation model of a bent lattice. Current theories of the slip process postulate generation or multiplication of dislocations at certain lattice imperfections. The mechanism proposed by Frank and Read8 results in continuous generation of concentric dislocation loops which spread out

Jan 1, 1953