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By M. R. Tek, K. H. Coats, D. L. Katz

A large number of boundary value problems encountcred in unsteady-state heat transfer, fluid flow through porous media, neutron diffusion and mass transfer involve the solution of a linear, parabolic partial differential equation commonly refcrred to as the diffusivity equation, where U is the dependent potential variable. K is the diffusivity (hydraulic, thermal, neutron, etc.) and 1 is the time variablc. Solutions to Eq. I are available in the literature for a wide variety of initial and houndary conditions. The great majority of these solutions are ohtained for geometric boundaries corresponding to linear. cylindrical or spherical flow models. A typical engineering application where the solution to Eq. 1 is required is the calculation of underground water encroachment across the boundaries of oil or natural gas reservoirs, In this particular area of application, the reservoir boundary is invariably approximated by circular geometry. However. the areal shape of many reservoirs can be better approximated by elliptic rather than circular boundaries. Thus the need for a general method of solving the diffusivity equation in elliptic coordinates arises in this problem as well as in other engineering applications involving elliptic boundaries. The solution to the diffusivity equation usually in volves the Error Function for the linear flow model, Bessel functions for the radial flow model and trigonometric or Legendre functions for the spherical flow model. It is well known that the general solution to the diffusivity equation in elliptic coordinates involves Mathieu functions. The significance of Mathieu functions in the analytical treatment of the diffusivity equation in elliptic coordinates is discussed in the literature However, these references do not providc analytical solutions useful in practical engineering problems. The objectives of this papcr are the development of the equations describing the unsteady-state liquid flow through a porous medium with an elliptic inner boun- dary, the development of a numerical method of solving these equations and, finally, a comparison of the water encroachment quantities calculated from the elliptic flow equation with those calculated from the radial flow equation. While the specific problem treated in this paper relates to unsteady-state liquid flow through a porous medium, the basic equations and computational techniques devcloped will apply equally well to problems occurring in the other areas of engincering interest mentioned previously. The solution given here is limited to a single case in which thc outer boundary encloses an area 100 times that of the inner boundary. DESCRIPTION OF THE FLOW MODEL Fig. 1 shows the flow model upon which the calcu lations presented in this paper are based. The inncr and outer houndaries of the flow model are represented by two confocal ellipses with major and minor axes, respectively, equal to 2a1, 2b1, and 2a, and 26,. The height of the elliptic cylinder flow model is denoted by 17. The following assumptions are employed in the development 01 the equations governing the unsteady-state liquid flow through the described flow model. 1. Uniform porosity and permeability throughout the flow model

By H. M. Morse

This report covers the period from Jan. I, 1943 to Dec. 31, 1943. During the year, II2 wells were drilled in Mississippi, as foilows: wildcats drilled and abandoned, 54; wildcats producing oil, 4; oil wells drilled in oil fields, 26; oil wells drilled in fields, dry and abandoned, 10; sulphur-test wells drilled, 14; salt-water-disposal wells, 3; core tests, I. Prospecting Geophysical work in Mississippi during 1943 amounted to 1127 crew weeks, divided as follows: reflection seismograph, 809 weeks; gravity meter, 285; magnotometer, 30; torsion balance, 3. A considerable amount of core drilling was done over a large part of the state. The complete data on this activity are not available at the present time. Salt Domes To date, the following salt domes have been discovered in Mississippi: Midway, Edwards, Glass, Newman, Tatum, Oak-vale, Kings, Halifax, D'Lo, Hazlehurst, Byrd, Leedo, Prentiss, Carson, Moselle, Monticello, Ruth, Keno, Taylorsville. New Oil Fields Lincoln County.—On March 10, 1943, the California Company completed its Smith No. I in sec. 4, T. 7 N., R. 7 E., Lincoln County, as an oil well and produced 29 bbl. of 25" gravity oil in 24 hr. through a fi-in. choke. Two outpost wells have been drilled in this area by the California Company, and both have been abandoned as dry holes. Madison County. —Love Petroleum Co. completed its J. R. Anderson No. 2, sec. 2, T. 8 N., R. I W., Madison County, on Sept. 7, 1943. This well produced 135 bbl. of approximately 30" gravity- oil in 24 hr. through a )/4-in. choke. The production comes from a sand or porosity in the upper part of the Chalk formation of the Cretaceous age. Adams County.—The California Company drilled its National Gasoline Co. of Louisiana No. I in sec. 52, T. 7 N., R. I W., to a total depth of 10,383 ft., and at 10,280 ft, it perforated and obtained gas and a condensate. The well had several showings in the Wilcox of the Eocene age. Several of these showings were tested and the well finally was completed at 5888 ft. on Oct. 6, 1943, producing 44" gravity oil in the second sand in this formation. No other wells were completed in this field during the year. However, a number of wells are contemplated in the near future, and locations have been staked by the California Company. The Oklahoma Pipe Line Co. will market the oil through its pipe-line facilities. Wayne County.—The Gulf Refining Co. drilled Davis No. I in sec. 2, T. 9 N., R. 9 W. in Wayne County. After several stem tests 545'-in. casing was set at 6850 ft. and production was obtained in the so-called Massive Sand of the Lower Tuscaloosa. The well produced 359 bbl. of oil in 24 hr., and it Was completed on Oct. 4, 1943. Other locations have been staked ill this area and probably will be drilled in 1944 by

Jan 1, 1944

By B. W. Dyer

In 1924, the Crescent Eagle Oil Co., while drilling the salt section of the Paradox formation in Grand County, Utah, encountered a salt that did not appear to be sodium chloride. This salt was analyzed and showed the presence of potash minerals, both sylvite (KCl) and carnallite (KMgC12.6H2O). Because of the high potash content of the sample, there was considerable speculation: (I) as to whether the hole had been salted, and (2), if not, the extent, richness, and the depth at which the deposit occurred. The discovery caused a large amount of activity in the area. During the next few years, 68 potash prospecting permits were issued by the Government, 24 under the Act of 1917 and 44 under the Act of Feb. 7, 1927, each including about four sections of land. Several holes, all shallow, were drilled for potash. A number of holes were drilled for oil into the salt horizon and the cuttings collected at the oil wells were examined petrographically and chemically. The shallow test holes were not sufficiently deep to reach the potash horizon and revealed nothing of value, but several of the oil test holes gave some indication of where potash might be found. Location and Geology of Deposits The potassium and magnesium salts have been found in various places from the Denver and Rio Grande Western Railroad tracks about seven miles west of Thompsons, in eastern Utah, to Cane Creek, a tributary of the Colorado River— a distance north and south of about 35 miles. In this locality, there appear to be five separate deposits: the Crescent Eagle area, which is in T. 22 S., R. 19 E.; the Salt Valley area, in the vicinity of the north-south line of T. 23 S., between R. 20 E. and R. 21 E.; the Seven Mile area, in the eastern part of T. 25 S., R. 20 E.; the Cane Creek area, on the Colorado River, in T. 26 S. and T. 27 S., R. 20 E. and R. 21 E.; and the Salt Wash area, in T. 22 S. and T. 23 S., R. 16 E. and R. 17 E. (Fig. I.) The Crescent Eagle and Salt Valley areas are in the Salt Valley anticline, some of the wells being in the fault graben and others outside. Structurally, the Salt Valley anticline is very complex, and can be described in general terms as a northwesterly plunging collapsed anticline about 15 miles long. In the Crescent Eagle area, the valley graben is about 1 1/2 mile wide and the salt probably forms a plug, the apex of which is in the vicinity of the Crescent Eagle well. Owing to the complex structure, there has been every opportunity for flowage in the salt to cause local thinning or thickening of beds. The regular succession of formations in the general area* is: Cretaceous Mancos Dakota Jurassic Morrison Summerville Entrada Carmel

Jan 1, 1948

By B. W. Dyer

In 1924, the Crescent Eagle Oil Co., while drilling the salt section of the Paradox formation in Grand County, Utah, encountered a salt that did not appear to be sodium chloride. This salt was analyzed and showed the presence of potash minerals, both sylvite (KCl) and carnallite (KMgC12.6H2O). Because of the high potash content of the sample, there was considerable speculation: (I) as to whether the hole had been salted, and (2), if not, the extent, richness, and the depth at which the deposit occurred. The discovery caused a large amount of activity in the area. During the next few years, 68 potash prospecting permits were issued by the Government, 24 under the Act of 1917 and 44 under the Act of Feb. 7, 1927, each including about four sections of land. Several holes, all shallow, were drilled for potash. A number of holes were drilled for oil into the salt horizon and the cuttings collected at the oil wells were examined petrographically and chemically. The shallow test holes were not sufficiently deep to reach the potash horizon and revealed nothing of value, but several of the oil test holes gave some indication of where potash might be found. Location and Geology of Deposits The potassium and magnesium salts have been found in various places from the Denver and Rio Grande Western Railroad tracks about seven miles west of Thompsons, in eastern Utah, to Cane Creek, a tributary of the Colorado River— a distance north and south of about 35 miles. In this locality, there appear to be five separate deposits: the Crescent Eagle area, which is in T. 22 S., R. 19 E.; the Salt Valley area, in the vicinity of the north-south line of T. 23 S., between R. 20 E. and R. 21 E.; the Seven Mile area, in the eastern part of T. 25 S., R. 20 E.; the Cane Creek area, on the Colorado River, in T. 26 S. and T. 27 S., R. 20 E. and R. 21 E.; and the Salt Wash area, in T. 22 S. and T. 23 S., R. 16 E. and R. 17 E. (Fig. I.) The Crescent Eagle and Salt Valley areas are in the Salt Valley anticline, some of the wells being in the fault graben and others outside. Structurally, the Salt Valley anticline is very complex, and can be described in general terms as a northwesterly plunging collapsed anticline about 15 miles long. In the Crescent Eagle area, the valley graben is about 1 1/2 mile wide and the salt probably forms a plug, the apex of which is in the vicinity of the Crescent Eagle well. Owing to the complex structure, there has been every opportunity for flowage in the salt to cause local thinning or thickening of beds. The regular succession of formations in the general area* is: Cretaceous Mancos Dakota Jurassic Morrison Summerville Entrada Carmel

Jan 1, 1948

By H. M. Morse

This report covers the period from Jan. I, 1943 to Dec. 31, 1943. During the year, II2 wells were drilled in Mississippi, as foilows: wildcats drilled and abandoned, 54; wildcats producing oil, 4; oil wells drilled in oil fields, 26; oil wells drilled in fields, dry and abandoned, 10; sulphur-test wells drilled, 14; salt-water-disposal wells, 3; core tests, I. Prospecting Geophysical work in Mississippi during 1943 amounted to 1127 crew weeks, divided as follows: reflection seismograph, 809 weeks; gravity meter, 285; magnotometer, 30; torsion balance, 3. A considerable amount of core drilling was done over a large part of the state. The complete data on this activity are not available at the present time. Salt Domes To date, the following salt domes have been discovered in Mississippi: Midway, Edwards, Glass, Newman, Tatum, Oak-vale, Kings, Halifax, D'Lo, Hazlehurst, Byrd, Leedo, Prentiss, Carson, Moselle, Monticello, Ruth, Keno, Taylorsville. New Oil Fields Lincoln County.—On March 10, 1943, the California Company completed its Smith No. I in sec. 4, T. 7 N., R. 7 E., Lincoln County, as an oil well and produced 29 bbl. of 25" gravity oil in 24 hr. through a fi-in. choke. Two outpost wells have been drilled in this area by the California Company, and both have been abandoned as dry holes. Madison County. —Love Petroleum Co. completed its J. R. Anderson No. 2, sec. 2, T. 8 N., R. I W., Madison County, on Sept. 7, 1943. This well produced 135 bbl. of approximately 30" gravity- oil in 24 hr. through a )/4-in. choke. The production comes from a sand or porosity in the upper part of the Chalk formation of the Cretaceous age. Adams County.—The California Company drilled its National Gasoline Co. of Louisiana No. I in sec. 52, T. 7 N., R. I W., to a total depth of 10,383 ft., and at 10,280 ft, it perforated and obtained gas and a condensate. The well had several showings in the Wilcox of the Eocene age. Several of these showings were tested and the well finally was completed at 5888 ft. on Oct. 6, 1943, producing 44" gravity oil in the second sand in this formation. No other wells were completed in this field during the year. However, a number of wells are contemplated in the near future, and locations have been staked by the California Company. The Oklahoma Pipe Line Co. will market the oil through its pipe-line facilities. Wayne County.—The Gulf Refining Co. drilled Davis No. I in sec. 2, T. 9 N., R. 9 W. in Wayne County. After several stem tests 545'-in. casing was set at 6850 ft. and production was obtained in the so-called Massive Sand of the Lower Tuscaloosa. The well produced 359 bbl. of oil in 24 hr., and it Was completed on Oct. 4, 1943. Other locations have been staked ill this area and probably will be drilled in 1944 by

Jan 1, 1944

By F. S. White, E. L. Kinsella

THE solids fluidization process brought out by the Standard Oil Development Co. in the early forties for catalytic cracking of petroleum enabled rapid transfer of large quantities of heat from gases to solids under closely controlled temperature conditions. As the technique developed, it was natural that applications for the process outside the petroleum industry would be sought. The calcination of limestone to ' quicklime requires the transfer of a large quantity of heat at high and closely controlled temperatures. For these reasons, this possible application was one of the first to be investigated. Laboratory work conducted by the Dorr Co. indicated that lime produced by solids fluidization would be of exceptional quality. Calculation of theoretical heat balances showed that savings in fuel could be expected. Accordingly, a pilot plant of 10 tons per day capacity was erected by the New England Lime Co. at Adams, Mass., to substantiate the process. Operation of the pilot plant, previously described,1 showed that excellent lime could be produced with a saving in fuel. The work also indicated the necessity of preparing feed to remove the finer fractions if dust losses were to be held to a tolerable level. A single-stage fluidized solids drier-stripper was developed to accomplish this sizing.2 Subsequently a commercial lime reactor was erected at Adams, beginning operation in June 1949, followed by air sizer facilities completed in November 1951. This paper will describe these two applications of solids fluidization. The raw material for preparation of lime by the fluidizing process is a high calcium crystalline lime stone having the approximate chemical composition shown in Table I. The stone is first prepared by crushing and grinding in conventional equipment to pass a 6-mesh sieve. After crushing, the material is sent to the FluoDry unit for drying and dedusting. Fluidized Drying and Sizing As shown in Fig. 1, the FluoDry unit consists of a 1/4-in. cylindrical steel shell, 9-ft ID by 22-ft 6-in. overall height. Attached horizontally at the bottom is a 6-ft diam combustion chamber, approximately 7 ft 6 in. long. A refractory constriction dome, consisting of first-quality fire brick shapes, partitions the inside into two sections. The lower section is called the windbox and the upper the bed compartment. The vertical wall of the shell is lined with 6-in. first-quality rotary kiln blocks. In the bottom of the windbox a hoppered section is formed with castable refractory to permit the windbox to be readily cleaned via a 6-in. screw conveyor. The combustion chamber is similarly lined with refractory shapes. On the 6-in. diam section, 4 1/2 in. of insulating brick, HW-26, are used. The inner combustion chamber is lined with 4 1/2-in. Korundal brick to withstand the high flame temperatures encountered. An 8-in. steel feed pipe, entering vertically through the top and fitted with an air-operated cone valve,

Jan 1, 1952

By D. V. Carter, D. C. Williams

Four oil discoveries were made in east and east central Texas during 1940, three of which represented new fields. In the Chapel Hill field, Smith County, oil was found where formerly only gas and distillate were produced. The three oil fields discovered are: Hawkins, Wood County; Pittsburg, Camp County; and Tehuacana, Limestone County. Important extensions were made to the following fields: Bazette, Navarro County; Long Lake, Anderson and Leon Counties; Cayuga, Anderson, Freestone and Henderson Counties; Opelika, Henderson County; and Talco, Titus and Franklin Counties. At the close of the year 54 oil and gas fields were producing in the district. There were 13 other fields, 11 oil and 2 gas, which have been abandoned. The East Texas field led the district in the number of completions for the year. During the year about 622 wells (oil and distillate wells included) were completed and 80 wildcats were drilled. Production and Proration During the year 170,424,685 bbl. of oil (distillate production included) were produced in the district—a decrease of 2.6 per cent from the 175,053,729 bbl. (distillate production included) during the preceding year. The district's production for the year 1938 was 182,369,484 bhl. As usual, most of the district's annual production was in the East Texas field, which produced 139,095,694 bbl. (distillate production in- cluded) during 1940, or 81.6 per cent of the total oil produced as compared with 141,333,317 bbl. (80.7 per cent) for 1939. The December estimated daily average production in the district was 424,565 bbl. The district accounted for 34.9 per cent of the state's annual production, compared to 36.7 pcr cent of the state's 1939 production. The decrease in production for 1940 may be attributed to changes made in proration schedules. Any material changes in the district's annual production may be considered for the most part as a reflection of proration-schedule changes affecting the East Texas field, since it is by far the most important field in the area. The entire state was subject to 71 shutdown days for the year; the East Texas field to 131; and the Rodessa field (Cass County, Texas, portion) to 5 days. No important changes were made in field rules and regulations during the year regarding the allocation of oil in individual fields in this district. Discoveries The Hawkins field is in southeastern Wood County in and principally north of the town of Hawkins. Development to date indicates that the field is somewhat of an elongated anticline trending slightly east of north and the proved oil area appears at this time to cover approximately 4000 acres. The oil production has been secured from the Woodbine sand, Upper Cretaceous; a considerable quantity of gas has been encountered in the Sub-Clarksville formation (Eagleford shale) in the higher part of the structure. It appears that a free gas

Jan 1, 1941

By D. C. Williams, D. V. Carter

Four oil discoveries were made in east and east central Texas during 1940, three of which represented new fields. In the Chapel Hill field, Smith County, oil was found where formerly only gas and distillate were produced. The three oil fields discovered are: Hawkins, Wood County; Pittsburg, Camp County; and Tehuacana, Limestone County. Important extensions were made to the following fields: Bazette, Navarro County; Long Lake, Anderson and Leon Counties; Cayuga, Anderson, Freestone and Henderson Counties; Opelika, Henderson County; and Talco, Titus and Franklin Counties. At the close of the year 54 oil and gas fields were producing in the district. There were 13 other fields, 11 oil and 2 gas, which have been abandoned. The East Texas field led the district in the number of completions for the year. During the year about 622 wells (oil and distillate wells included) were completed and 80 wildcats were drilled. Production and Proration During the year 170,424,685 bbl. of oil (distillate production included) were produced in the district—a decrease of 2.6 per cent from the 175,053,729 bbl. (distillate production included) during the preceding year. The district's production for the year 1938 was 182,369,484 bhl. As usual, most of the district's annual production was in the East Texas field, which produced 139,095,694 bbl. (distillate production in- cluded) during 1940, or 81.6 per cent of the total oil produced as compared with 141,333,317 bbl. (80.7 per cent) for 1939. The December estimated daily average production in the district was 424,565 bbl. The district accounted for 34.9 per cent of the state's annual production, compared to 36.7 pcr cent of the state's 1939 production. The decrease in production for 1940 may be attributed to changes made in proration schedules. Any material changes in the district's annual production may be considered for the most part as a reflection of proration-schedule changes affecting the East Texas field, since it is by far the most important field in the area. The entire state was subject to 71 shutdown days for the year; the East Texas field to 131; and the Rodessa field (Cass County, Texas, portion) to 5 days. No important changes were made in field rules and regulations during the year regarding the allocation of oil in individual fields in this district. Discoveries The Hawkins field is in southeastern Wood County in and principally north of the town of Hawkins. Development to date indicates that the field is somewhat of an elongated anticline trending slightly east of north and the proved oil area appears at this time to cover approximately 4000 acres. The oil production has been secured from the Woodbine sand, Upper Cretaceous; a considerable quantity of gas has been encountered in the Sub-Clarksville formation (Eagleford shale) in the higher part of the structure. It appears that a free gas

Jan 1, 1941

By L. E. Young

LOADING machines may be classified in several ways: (1) Machines which cut or break down and load .the coal; (2) machines which simply load the coal; (3) devices which load and transport the coal; (4) de-vices which elevate; (5) devices which transport the coal after it has been shoveled onto the device. There are many types of mechanical loading devices, Bull. 17, Coal Mining Investigations, under the auspices of Carnegie Institute' of Technology, U. S. Bureau of Mines, and the Advisory Board, listing 31 exclusive. of -the large shovels used in thick coal seams. Mechanical loading of coal is not in its infancy; I think some of the early patents go back to 1890. One large coal company, properly called the early leader in this field of mechani-zation, has about 26 large machines at work. This company spent about thirty years in developing a ma-chine, and at the present time is loading approximately two million tons of coal a year in its mines. The chair-man directed a question at the previous speaker; inquir-ing if real progress was being made in mechanical load-ing. The experience of the company just referred to is in itself an adequate answer. A review of a list of mines using mechanical loading devices shows that there are 28 mines which we may say are 100 per cent mechanical. There are four more mines which have been 100 per cent mechanical, but which are idle at this time on account of labor condi-tions. There are at least 25 more at which the tonnage is more than 50 per cent mechanical. In speaking of a 100 per cent mine I do not mean that every pit car of coal is loaded by machine, because when complete, re-covery of the coal is attempted it is not practical to load all the coal at, the break line. In order to load the last 5 to 10 per cent of coal with a minimum of gob material and in order to keep the. working places along the break line timbered in a safe manner it is generally desirable to use a few hand loaders. At a certain mine operat-ing on the block system 90 percent of the coal is being loaded by what is properly a mechanical loading: device, and about 10 per cent -is being loaded by hand. This 10 percent is right off the break line, out of what might be called, the screen pillar. The mines referred to are scattered over the country, . in seven different' States, and the equipment used is produced by ten different machinery companies. As to size, these mines vary from small mines of 500 tons mining capacity-up. In one instance a company with one loading machine is producing an, average of 450 tons per day. One of the large mines that is idle pro-duced at the. rate of 4300 tons per day, of which 97 per cent was actually loaded by machinery.

Jan 8, 1928

By William P. Blake

(Canal Zone Meeting, November, 1910.) A DEPOSIT of manganese-ore near Tucson, Ariz., merits notice by reason of the peculiar form in which it occurs, and as a striking. example of ore-deposition by vadose upward capillary flow of metal-bearing solutions with concentration at the surface of the country-rock. This deposit occurs at the northern end of the Coyote mountains, about 40 miles west of Tucson, upon the outcropping beds of porphyritic rock, which appear to be partly-metamorphosed strata of volcanic tufa, probably of late Secondary or of Tertiary age. The strata dip northward at a low angle, and present a series of basset-edges in parallel lines of outcrop, east and west, facing the south and extending over many acres. Successive groups of these outcrops, from 5 to 20 ft. in breadth, are coated with oxides of manganese in lustrous black films and crusts, shining in the sunlight like polished ebony, and covering the whole surface of the rock above the soil. Seen at a little distance, these croppings look like solid ledges of massive and pure ore; but closer inspection and a few blows of the hammer reveal their true nature as a superficial coating allied in origin to the blackened shining surface of rocks exposed in desert-regions, familiarly known as " desert paint" or "desert varnish,"' similar to the phenomena described by me in a former paper, but much thicker and heavier. * By reason of the death of the distinguished author, this communication, probably his last communication to technical literature, is published without revision of the proofs by him. A term first given y G. K. Gilbert. See Rocks, Rock-Weathering, and Soil; by George P. Merrill, p. 256 (New York, 1897). Superficial Blackening and Discoloration of Rocks, Especially in Desert Regions, Trans., xxxv., 371 (1905).

Sep 1, 1910

By T. R. A. Davey

A Survey of current and recent research and developmental work is supplemented by predictions for processes which should be developed over the reminder of this century.

Jan 1, 1970

By K. E. J. Rapperport, C. S. Hartley

The only slip system observed in zirconium crystals deformed at 77", 575", and 1075OK was (1010) [1210] with a critical resolved shear stress in tension of 1.0 kg per sq mm at 77°K; 0.2 kg per sq mm at 575 °K; and 0.02 kg per sq mm at 1075 OK. The active twin planes were {1012}, (1121}, (11221, and (11233) with varying temperature dependence. A detailed analysis for the slip direction using Laue spot asterism is appended. NeARLY all metals of the hexagonal close-packed structure exhibit basal slip, i. e.,(0002)<1120>- type slip. This is true of magnesium,&apos; zinc,&apos; cadmium,3 beryllium,4 titanium,= yttrium,6 and rhenium.Many of these such as titanium 5&apos;8-&apos;0beryllium,4&apos;" magnesium, and zinc13&apos;14 display other slip modes even at room temperature, and nearly all have been reported to slip on other systems under particular loading or temperature conditions of testing. As is shown in this paper, basal slip was not found at any of four test temperatures from 77" to 1075°K in hexagonal close-packed zirconium under the simple loading conditions of tension and compression, even though in one case the resolved shear stress on the inactive (0002) <llgO> system was twenty-five times higher than the critical resolved shear stress on the active (1010) [1210] system. This result is consistent with prior studies on the active deformation processes in zirconium deformed at room temperature. &apos;&apos;-I7 SPECIMEN PREPARATION A) Material—The zirconium used in this work was of two types: 1) as-deposited reactor grade crystal-bar, and 2) arc-melted and forged reactor grade crystal-bar. Typical chemical and spectrographic analyses of these materials as received, and after hydrogen removal and crystal growth are given in Ref. 17. Crystals of type 1) above have the letter prefix (A) and those of type 2) have the prefix (B) throughout this paper. B) Crystal Growth— he zirconium was machined into rectangular parallelepipeds about 0.2-in. scl in cross section and 2 in. iong. These were hand polished through 4/0 abrasive paper, electropolished, given a hydrogen removal anneal, and subjected to long-time anneals at 840 °C in vacuo to produce usable crystals.&apos;7 A second technique used to obtain large crystals was to cycle the samples two or three times between 1200" and 840°C, allowing them to remain at the higher temperature for about 4 hr and at the lower temperature for 5 days.17 These techniques yielded some grains which occupied the entire cross section of the bar and were as long as 3/4 in. C) Orientation Determination—After the growth of large crystals by thermal cycling, the samples were repolished with extreme care through 4/0 abrasive paper and electropolished. Metallographic examination after polishing showed the surfaces to be free of visible deformation traces. Standard Laue back-reflection X-ray techniques were used to find the crystallographic orientations of selected large grains with respect to a specimen face and edge. Fig. 1 shows the stereographic projections of the stress axes for the crystals used. The sharpness of the spots on the Laue photographs indicated that the crystals were of good quality. EXPERIMENTAL METHODS Nine crystals were deformed in tension at 77"K, nine in tension and five in compression at 300°K in previous tests,17 fifteen in tension at 575"K, and eleven in tension at 1075°K. All specimens were stressed by load increments. After a predetermined load was applied, the specimen was removed from the loading appratus and metallographically examined for deformation traces. An attempt was made to initially stress each bar so that some crystals slipped a small amount and others not at all. This was done to bracket the critical resolved shear stress. One bar of special orientation (B-11) was repolished and annealed at 1075°K for 1 hr after lower temperature deformation, before final deformation at 1075°K. In the other bars the loading by increments, followed by metallographic examination, was continued until the surface distortion would interfere with analysis, or until fracture. One example of a crystal pulled to fracture is shown in Fig. 2. This photograph shows a crystal (B-14C) which was pulled at 1075°K and failed by slip on two (10i0) planes. The approximate orientation of this crystal is illustrated in the figure. Specimens were deformed at 77°K in liquid nitrogen on a tensile machine using an insulated bucket with an internal hook to accept a clamped specimen.

Jan 1, 1961

By L. D. Jaffe, F. W. Cotter, E. Cordon

The hardenability of titanium-base alloys was studied by metallographic examination and hardness survey of Jominy specimens end-quenched from the B range. Analyses of the data led to the equation log J = -0.57 + 0.25 @ct Fe + pct Mn + pct Mo) + 0.19 @ct Cr) +0.16 @ct V) + 0.03 @ct Zr). Here J is the distance, in sixteenths of an inch, from the quenched end of a Jominy hardenability specimen in the position of peak hardness, for material quenched from the B range. This equation fitted the experimental data with a standard deviation of approximately 0.29. The effects of the elements Al, Sn, W, Cu, Ni, B, C, N, 0, and H, and of pain size, were not statistically significant or not practically significant. A check against hardenability measurements in the literature showed agreement within the stated standard deviation. The equation should be useful in estimating hardenability of new or modified titanium alloys. HARDENABILITY in a titanium-base alloy is the ability of the alloy to retain the B structure on quenching. An alloy with high hardenability will retain the /3 structure even when cooled relatively slowly from a temperature at which B or P plus a is stable. A low hardenability material will retain P only if quenched extremely rapidly from the range of p or 0-plus-a stability, or will not retain it at all, at room temperature. High hardenability is desirable in titanium alloys to be heat-treated to high-strength levels. Its value is by no means limited to large section sizes. With high hardenability, a material can be solution-treated and cooled at a variety of rates, either to give high strength directly or, more generally, to give a soft ductile condition from which high strength can be obtained by subsequent aging. With low hardenability, high strength can be obtained, if at all, only by very rapid quenching, and there will generally be little increase in hardness on subsequent aging; an alloy of this type is limited in its applicability. On the other hand, alloys of very low hardenability have some advantages in weldability; essentially, they are always in the annealed condition, after welding as well as before. For commercial alloys, hardenability data are usually available, in the form either of property data after cooling from the solution temperature at various rates, with or without subsequent aging, or of results of a standard hardenability test, such as that originally developed for steels by Jominy and Boegehold.&apos; When modifications of an available alloy are considered, or preparation of new alloy compositions, it would be Very convenient to be able to estimate the hardenability of the new material without having to make and test it. A method of estimating hardenability of titanium alloys from their composition was suggested by one of the authors some time ago, on a preliminary basis, utilizing scattered data found in the literature.&apos; It seemed worthwhile to carry out a systematic experimental study of the effect of composition upon hardenability. EXPERIMENTAL PROCEDURE Approximately fifty heats of various compositions, weighing 8 to 10 Ib apiece, were melted in a small inert-gas tungsten-arc furnace with water-cooled copper walls. The starting material was 110 Brine11 titanium sponge, with high-purity metals added for alloying. Each heat was bottom-poured under vacuum through a molybdenum burnout strip into a cold graphite mold, to form an ingot approximately 4-1/2 by 3-1/2 by 3 in.* From each ingot were cut *The material was melted and cast by Pitman-Dunn Laboratory, Frankford Arsenal, to whom the authors must express their thanks. two pieces 4-1/2 by 1-1/2 by 1-1/2 in. These were forged, at temperatures adjusted to the composition, into 1-1/4-in. rounds, from which standard 1-in.-diam hardenability specimens3 were machined. A number of small samples were also prepared from forged materials of each heat, annealed, quenched from various temperatures, and examined metallographically. The P-transus temperature was determined by observation of the degree of resolution of primary a in these pieces. samples for chemical analyses were also taken from the forgings. One hardenability specimen of each heat was solution-treated for 1 hr approximately 50°F above the measured transus temperature, and the other for 1 hr approximately 250°F above the transus. (An additional hour was allowed for the specimens to reach furnace temperature.) These are not necessarily the temperatures that would be selected for

Jan 1, 1964

By R. F. Mehl, J. K. Stanley

THE recrystallization of cold-worked metals is studied ordinarily by determining the temperatures required for complete recrystallization to occur within a given arbitrary time period, usually within 15 min. to 2 hr. The results obtained are conventionally assembled in a three-dimensional diagram relating this temperature to the amount of cold-work (percentage deformation) and the resultant grain size, though sometimes other modes of representation are employed.1 Such three-dimensional diagrams are not complete, for the number of variables exceeds the number represented. The process of recrystallization is characterized by a time-rate, a fact that is not portrayed upon ordinary recrystallization diagrams. It is known that recrystallization consists in the formation of new nuclei and the growth of these nuclei, a process that continues until the matrix is completely consumed and the original set of grains entirely replaced by the new. This knowledge is old.2 Truly heterogeneous reactions invariably proceed by nucleation and growth; the decomposition of eutectoid solid solutions provides an example about which much is known,3 and freezing, originally studied by Tammann, provides the classic example. Although recrystallization is not a heterogeneous reaction within the orthodox meaning of the term, the mechanism of the process is the same. As in eutectoid inversion and freezing, it should be possible to study the rate of isothermal recrystallization as a function of time, and it should also be possible to analyze the isothermal reaction curve into the component rates of nucleation and growth that determine them.* Other methods, not employing the rates of nucleation and growth, have been used to represent the rates of such reactions, but these in general have been artificial and have not led to progress .4,5† The theory of recrystallization is not in advanced state; if recrystallization data were obtained in terms of the rate of isothermal recrystallization, and in terms of the rate of nucleation and the rate of growth of recrystallized grains, and in particular if the temperature coefficients of these rates were measured accurately, an adequate theory should be more readily developed .27 Such an effort requires proper experimental technique, but especially requires suitable methods of mathematical analysis to convert measurements made upon a surface of polish into values for the rate of nucleation and the rate of growth and to combine these into a rate of isothermal recrystallization. These methods are now

Jan 1, 1942

Accurate modeling of the semivariogram is an extremely important step in the geostatistical analysis of mineral deposits. Automatic fitting of a mathematical model is often possible but not necessarily desirable. Significant geologic and statistical information must be taken into account in the fitting process, which is not always available to the computer. Manual model fitting is, on the other hand, extremely time consuming. Interactive graphics are best suited to optimize the process. Many interactive methods are described, which are adapted to modeling semivariogram in one-, two-, or three- dimensional environments.

Jan 1, 1985

By G. H. Kesler, J. E. Oberele, C. E. Dryden, J. H. Oxley

Heat-transfer rates were measured in a model of a multifilament vapor-deposition bulb fo the preparation of high-purzty metals. Local transfer coefficients for heat transfer frow the filaments to the circuates process stream were determined as a functiol of gas flow rates and bulb, inlet, and filament, geowzetvies. These results a-e then convertted to n mass-t7,ansfer basis to provide a method of correlating vapor-deposition rates and to predict the performance of commercial urzits. The firm1 cor?,elating equation for mass transfer was found to be- wheve k, is the mass-transfer coefficient; D, is bze gas difficsivity : P is the system pressure; R is the gas constant; T is the gas temperature; Df, DB, and Di ave tlze diameters of the filament, bulb, and inlet, respectively; k is the gas conductivity; C, is the specific heat of the gas, M is the wzolecular zleight of the gas; Npr . N,,, NRe a7&apos;e the Prandtl, Schmidt, and Reynolds numbem of the system, respectively; LB is the height of the bulb; and SB and Sf are the total suyiace area of the bulb and filaments, respectively. ONE of the more conventional methods of preparing very high-purity metals is the vapor deposition of the metal upon heated filaments. The reactions which can be employed in such a process generally fall into two classes: 1) Pyrolysis of a volatile metal compound. Generally because of their instabilities, metal iodides are used; however, other metal halides and hydrides have been employed. These processes are frequently carried out under vacuum conditions, and the filaments are maintained at high temperatures. 2) Hydrogen reduction of a volatile metal compound. A metal chloride is normally the preferred feed for these processes, but other halides are sometimes used under special conditions. These hydro- gen-reduction processes are usually operated at atmospheric pressure. Many of the current processes for the production of semiconductor materials are actually vapor-deposition processes. However, the vapor-deposition process itself is relatively old, and almost all metals can be prepared in a state of very high purity by the use of vapor-deposition techniques. Loonam has recently given an excellent review of the iodide process for metal deposition,&apos; and Owen has started some detailed studies with a carbonyl system.&apos; A more general treatment of all vapor-deposition processes has been outlined by Powell, Campbell, and Gonser.3 Despite the fact that vapor-deposition techniques have been employed since 1890, there is a surprising lack of fundamental information regarding the transport characteristics of even the simplest deposition system, the heated filament. The purpose of the investigation described in this paper was to extend some of the earlier data obtained at Battelle to predict deposition rates and the uniformity of deposition in large-diameter, multifilament deposition bulbs under forced convection conditions.4&apos;5 A number of other investigators have already presented a simplified treatment of the deposition process under non-flow conditions, i.e., pure diffusion.6"9 To obtain information on the transport characteristics of a deposition bulb, a model of a typical plant deposition unit was constructed, and local heat-transfer coefficients from the filaments to a circulating air stream were determined under various conditions of air-flow rates and bulb, inlet, and filament geometries. These results were then converted to a mass-transfer basis, and consequently provided a method to correlate experimental vapor-deposition rates and to design commercial deposition units. EXPERIMENTAL WORK Description of Model. The apparatus which was used in this work was a scaled model of one type of deposition bulb. It was constructed of Lucite and was easily altered to give several combinations of diameter of bulb liner, inlet size and location, number of filaments, and outlet geometry. The model is shown in Figs. 1 and 2. The bulb shell was made octagonal for convenience in construction and observation, and the bulb liners were cylindrical. Air, introduced through one of several different jet inlets, was used as the test fluid in these model studies. Filaments for deposition of metal were simulated by metal rods 1/4-in. in diam. Two of the rods could be heated by passing electrical current through them ¦ while the remaining rods could not be heated. This procedure minimized the amount of heat which was

Jan 1, 1962

By Young C. Kim, Francis Martino, Ish Chopra

For the past two and one-half years, various emission control strategies were jointly developed by the University of Arizona and the Homer City Owners to com- ply with the clean air requirements at its Homer City Power Plant. Some of the available options for the SO2 emission control by the Homer City Owners were:l)cleaning of run-of-mine coal,2) scheduling of mining operations at its captive mines, 3) blending the captive mine coal with externally purchased low sulfur coa1,and 4) placing a partial FGD system. This paper describes two specific emission control strategies developed and implemented. These are: 1) production scheduling at the mining face to minimize sulfur variability, and 2) external purchasing of low sulfur coal for further blending. The main objective of this paper is to share our experiences on implementing the developed strategies. This paper emphasizesthe need for proper mine planning on a short-term basis, if the power plant is to meet the desired objective.

Jan 1, 1983

By E. W. Johnson, M. L. Hill

Cold working of iron-carbon alloys was found to increase greatly the hydrogen solubility and to decrease the diffusivity at temperatures up to 400° C. These effects are increasing functions of both the carbon content and the degree of deformation. The hydrogen behavior is consistent with the idea that cotd working creates "traps", which are concluded to be microcracks in which the hydrogen is chemisorbed. Hydrogen embrittlement is explained by the Petch theory of metal crack surface energy loss due to hydrogen adsorption. HYDROGEN embrittlement of steel has been studied for many years and has been the subject of an extensive literature, but the mechanism of the effect has not been completely understood. The embrittlement is unusual in that the ductility loss is not accompanied by an increase of the yield strength, being primarily a decrease of the fracture strength alone. The loss of fracture strength is usually most severe in the temperature range between 0°and 100°C. Here the solubility of hydrogen in the iron lattice at ordinary H2 pressures is extremely low while the diffusivity is still quite high. From the relationships between the ductility and the hydrogen content, test temperature and strain rate, it is apparent that the hydrogen atoms causing the ductility loss difbse to and concentrate in small regions of the metal which are especially susceptible to the initiation and propagation of fracture. This hydrogen segregation apparently occurs after plastic straining has begun. Below 0°C the ductility loss persists only at low strain rates in confirmation of the view that the embrittlement is diffusion .controlled. The tendency of the embrittlement to disappear above 100°C can be explained by the increasing lattice solubility of hydrogen with rising temperature. A common view of hydrogen embrittlement of steel is that the hydrogen initially dissolved in the metal lattice diffuses to structural discontinuities and there precipitates as H2 gas at very high pressures which assist the external stress in causing premature failure.1,2 The idea of a high H2 pressure in equilibrium with ordinary amounts of hydrogen in steel at room temperature is due to observations of hydrogen behavior in fully annealed material, for which the Sieverts&apos; law constant relating solute concentration to H2 pressure is extremely small. Hydrogen-embrittled steel, however, is always plastically deformed to some extent, and therefore it is important that hydrogen embrittlement be explained primarily in terms of hydrogen behavior in plastically deformed material. Such an explanation is attempted in this paper. Previous studies of hydrogen in cold-worked steel have shown that both the solubility and the diffusion rate are significantly chaned when the steel is cold worked. Darken and Smith discovered that the amount of hydrogen absorbed from acid by cold-rolled steel at 35°C is many times greater than that absorbed by hot-rolled steel. They found also that the hydrogen permeability of the steel is unaffected by cold working. Keeler and Davis4 confirmed the high apparent solubility of hydrogen in cold-worked iron-carbon alloys at temperatures up to and even beyond the recrystallization temperature. They also found that this solubility increase accompanying cold work is a sensitive function of the carbon content, being absent when no carbon is present. The present experimental study was undertaken primarily to obtain an improved understanding of the behavior of hydrogen in cold-worked steel. Data were obtained on the effects of temperature, H, pressure, carbon content, and degree of cold work on the hydrogen solubility and diffusivity in iron-carbon alloys. These data have been helpful in elucidating the nature of the cold-worked steel structure as well as in providing information on the mechanism of hydrogen embrittlement of steel. EXPERIMENTAL Cylindrical specimens for hydrogen absorption and diffusion rate measurements were prepared from three iron-carbon binary alloys and a commercial SAE 1010 steel. The iron-carbon alloys were prepared by vacuum melting electrolytic iron with graphite in a magnesia crucible. The alloys were cast in vacuum as 2 1/2-in. sq ingots weighing about 20 lb each. The ingots were hot rolled (above 1900°F) to 5/8-in.-diam round bars and then cooled in air to room temperature. The resulting metallographic structure consisted of islands of fine pearlite surrounded by free ferrite. Chemical analyses of the materials are given in Table I. The 5/8-in. diam bars were turned to diameters such that cold reduction to the desired final specimen diameters would result in either 30 or 60 pct reduction in area (RA). The machined bars were then cold worked by swaging at room temperature

Jan 1, 1960

By William R. Barton

It is generally conceded as axiomatic that the aggregate producer and the average urban resident have mutually incompatible goals. The producer wants to be near his mass market and the average resident wants him as far away as possible. The traditional economic decision to mine local material to avoid transportation costs is increasingly challenged by zoning and planning bodies and by citizens&apos; groups. This conflict generated much written and spoken word and offered opportunity for great flights of rhetoric. The pressure on the producer also has forced re¬appraisal of the need for the classic confrontation with indications that much of the conflict is more apparent than substantive. In New England several factors combine to increase complexity of the siting problem. It is a region of high land values and population density. Due to the proximity of metropolitan areas, even rural communities have experienced a prolif¬eration of environmental groups with concomitant enthusiastic regional planning and critical watch over land use. In New England where there is little public understanding of the necessity for, and the realities of, mineral production a sophisticated approach to aggregate production site location is required.

Jan 1, 1975

By Robert W. Zimmerman

POROUS SOLID COMPRESSIBILITIES There are four different compressibilities associated with porous solids, each relating the fractional change in either bulk volume or pore volume with the change in either pore pressure or confining pressure. These will be referred to as Cbc, Cbp, Cpc, and Cpp, with the first subscript denoting the relevant volume, and the second subscript denoting the relevant pressure. They are defined as: [ ] Note that minus signs are included in two of the definitions so that each of the compressibilities will always have a positive value. In general, each compressibility depends on the elastic moduli of the matrix material, the porosity, and the exact geometry of the pores. Taking the latter factor into account calls for separate analysis for each different pore shape, which of course can only be attempted for a few relatively simple cases. But lower bounds for each of the four compressibilities can be found, independant of pore structure, in terms of only the porosity (0) and the elastic moduli of the matrix material (any pair chosen from K, E, G and V). The first step is to find relationships between the four compressibilities, starting with the following observation: If a porous solid made of a linear elastic, isotropic and homogeneous matrix material is subjected to uniform hydrostatic pressure of magnitude P on its external and all of its internal (pore) surfaces, the state of stress in the solid will be exactly the same as that which would occur

Jan 1, 1982