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By Michael B. Kahle, Fred J. Scheaffer

Production scheduling, along with production planning, provides projections of future mining progress and time requirements for the development and extraction of a resource. These schedules and plans are used by management as a means of attaining the following objectives (1) maintaining or maximizing expected profit, (2) determining future investment in mining, (3) optimizing return on investment, (4) evaluating alternative Investments, and (5) conserving and developing owned resources. The first four goals are generally concerned with mining costs, both capital and operating requirements, and as such, play an important role in production planning. However, this chapter is concerned with the fifth management objective of resource development in order to conserve and perpetuate the corporate entity. The following discussion is based on the premise that detailed economic evaluations and market surveys have been performed and analyzed and that the results indi¬cate a viable project.

Jan 1, 1979

Receipts General Funds: Initiation fees ' 6,008.50 Arrears of dues 1,772.69 Current dues 46,576.56 Advance dues 1,820.97 Sale of binding 10,554.43 Sale of advertising 6,003.42 Sale of Transactions 3,237.07 Sale of special editions ' 1,722.50 Sale of Bulletins and. pamphlets ' 2,263.95 Miscellaneous Receipts; Interest on investments and deposits 450.06 Sale of pins and fobs 312.80 For the collection of checks 161.84 From Finance Committee, Feb., 1916, Meeting 101.02. Subscriptions to the land fund 86.14 Arizona Meeting refund from N. Y. Central Railroad.. 52.48 Local Section refund from N. Y. Central Railroad.... 31.85 Miscellaneous 425.68 Total Receipts General Funds 81,611.96 Cash balance Dec. 31, 1913 1,063.39 $82,675.35

Jan 2, 1917

By Theron Wasson

The Central Michigan area held first place in the state during the year. Midland and Isabella, the leading counties in 1932, produced most of the oil in 1933. The Porter field southeast of Mt. Pleasant and along the same structural trend saw the greatest drilling activity. In Porter during the year 117 new wells were drilled. Under proration these wells produced 3,583,617 bbl., or nearly one-half the total for the state, which has been estimated at 7,947,695 bbl. The Porter field is already outlined on all sides except the northwest. It probably reached its peak in 1933. Unless a new field of some magnitude is developed in 1934, Michigan will see a continuous decline. The Greendale extension to the old Mt. Pleasant field furnished the new flush for 1932. In 1933

Jan 1, 1934

Recognizing the fact that the problems of the committee named by the Board to prepare the "official ticket" for officers and Directors of the Institute are various and difficult; and desiring to assist this committee by setting forth some of the principles that should guide the committee and some of the qualifications that should be required of candidates, the following instructions are formulated and the Secretary is directed to publish them in MINING AND METALLURGY concurrently with the publication of the names of each newly appointed Nominating Committee and to send a copy to each member of the Committee. Each year the Nominating Committee is to select "official" candidates for eight places, as follows:, (1) President and Director (2) Vice-President and Director (3) Vice-President and Director (4) Director (5) Director (6) Director (7) Director (8) Director

Jan 1, 1939

EXPLORATION U.S. 4,065,972 - Exploration for subsurface ore bodies of uranium. mercury or other inorganic or organic minerals having specific gases associated thereto Small gas sample containers are planted in a plurality of shallow holes in the surface of the earth in a predetermined pattern and left in place for a period of time sufficient to collect migrating gases. Each container includes a gas collection chamber and means for admitting gases at a predetermined flow rate. Strips of detector material which is sensitive to specific gases are mounted in the collection chamber. Recovered containers are subjected to qualitative and quantitative analysis. F. W Holub and H. W. Alter, assigned to Terradex Corp Jan. 3, 1978. 9 pp (73-421 5R) Filed 5-24-76 (689,710) Same. British 1,498,737, dated Jan. 25, 1978

Jan 1, 1979

Dues: Arrears........................................... $ 4.878.18 Current........................................... 96.174.46 New Members..................................... 6.281.50 Dues for future periods received in advance........... 1.745.28 $109.079.42 Initiation Fees.................................................. 7,879.00 Magazine Receipts: Advertising Gross Receipts.......................... $39,247.77 Magazine Sales.................................... 3,820.04 43.067.81 Sale of Transactions Volumes 75 and 76............; .... $ 2,525.93 Sale of Transactions and Special Editions............... 7,586.00 Sale of Year Book.................................... 141.60 Sale of Authors' Reprints............................. 2,032.97 Sale of Pamphlets.................................... 1,346.29 Sale of Bindings...................................... 4,551.90 18,184.69 Interest Received: On Bank Balance and Temporary Investments......... $ 2,780.75 On Life Membership Fund.......................... 2,106.43 On James Douglas Library Fund..................... 5,399.45 On General Reserve Fund........................... 1,995.33 12.381.96 Miscellaneous Receipts........................................... 131.16 Total Receipts................................................ $190,624.04

Jan 1, 1929

By A. Werenfels

After discussing the geology of the Limagne, the surface indications of petroleum, and the recent exploration, the author states that none of the wells were properly located and that oil possibilities of the Limagne have not been adequately tested. NO PETROLEUM, in commercial quantities, is found in France except the small production of the Pechelbronn field (Fig. 1) in Alsace, which produced 75,000 tons in 1923; therefore the test of the petroleum FIG. 1.-KEY MAP. prospects of the Limagne is most interesting. Under the superintendence of M. Termier, chief engineer of the French mines, a well near Crouelle (Fig. 2) was drilled in 1921 to a depth of 856.3 m. (2808 ft.); at different depths favorable showings were encountered. The well, however, was abandoned because of drilling difficulties. A second one is now being drilled near the same place.

Jan 12, 1924

By Michael G. Schill, Mark C. Fischer

Since its introduction several years ago in the United States, the high pressure belt filter press has proven to be a highly cost-effective dewatering device in a number of mining and industrial applications. To evaluate the process and economic factors associated with the dewatering of coal refuse, a comprehensive program of laboratory and on-site pilot studies has been conducted. This paper will summarize findings of this study and discuss advantages of the belt filter press over conventional dewatering methods. The conventional means of dewatering thickened coal refuse involves the use of vacuum disc filters or centrifuges. Due to the high amount of energy used to dewater refuse with these devices it was a logical course of action to apply belt filter press technology to this application, since a belt filter press will require less than 3.7 kW (connected).

Jan 1, 1982

By J. E. Schaffer

Drilling activity in Ohio increased slightly in 1939. There were 1020 completions as compared to 910 in 1938. During the past six years the number of completions has varied little (Table 1). Oil production in Ohio has been gradually declining since 1896, when the peak production of 23,941,000 bbl. was reached (Fig. 1). Since that date production has slowly declined to an estimated production in 1939 of 3,144,134 bbl., the lowest in 53 years. This total production is divided approximately into the following grades of crude oil: Pennsylvania, 1,185,456 bbl.; Corning, 1,261,615 Flg 1. bbl.; Lima, 578,500 bbl.; Lodi, Based on figures of U. S. .Bureau of 104,740 bbl.; Cleveland, 13,823 Mines and Oil andGas Journal bbl. Table 2 shows the prices paid for the various grades of crude oil.

Jan 1, 1940

By J. E. Schaffer

Drilling activity in Ohio increased slightly in 1939. There were 1020 completions as compared to 910 in 1938. During the past six years the number of completions has varied little (Table 1). Oil production in Ohio has been gradually declining since 1896, when the peak production of 23,941,000 bbl. was reached (Fig. 1). Since that date production has slowly declined to an estimated production in 1939 of 3,144,134 bbl., the lowest in 53 years. This total production is divided approximately into the following grades of crude oil: Pennsylvania, 1,185,456 bbl.; Corning, 1,261,615 Flg 1. bbl.; Lima, 578,500 bbl.; Lodi, Based on figures of U. S. .Bureau of 104,740 bbl.; Cleveland, 13,823 Mines and Oil andGas Journal bbl. Table 2 shows the prices paid for the various grades of crude oil.

Jan 1, 1940

1. Healthy and active Local Section organizations are vital factors in promoting the vigor and growth of the Institute. 2. Activity on the part of Local Sections should be recognized and stimulated by appropriation of funds from the Insti¬tute's treasury; and these appropriations should be as large as is consistent with the relative needs for other activities. 3. As between different Sections, the amount of such appropriations should be based primarily on the extent of activities as reflected in the number and character of meetings held and the attendance of the members at such meetings. 4. In making a request for funds for any year, the officers of a Local Section should submit a report on the printed form approved by the Directors at their meeting on November 19, 1937. 5. A standing Committee on Local See-

Jan 1, 1942

By D. M. Urich

New plant construction for pyrolysis and agglomeration during 1969 has been relatively quiet in the North American scene. U.S. pellet capacity approximates 52 million long tons and that of Canada 25.3 million tons. The foreign scene, however, has been extremely active during 1969, and this is expected to continue for the next several years. Changes in sinter practice have not been reported, other than a few changes towards increased bed depths and the increased use of screening facilities to size the product more closely. Interest in the field of briquetting in fields other than iron ore is high with a new fluorspar briquetting plant under construction at Brownsville, Texas. Considerable research appears to be pointed towards solving the problem of reclaiming steelmill waste products (flue dust, BOF dust, mill scale) by means other than sintering.

Jan 1, 1970

1 Healthy and active Local Section organizations are vital factors in promoting the vigor and growth of the Institute 2 Activity on the part of Local Sections should be recognized and stimulated by appropriation of funds from the Institute's treasury, and these appropriations should be as large as is consistent with the relative needs for other activities 3 As between different Sections, the amount of such appropriations should be based primarily on the extent of activities as reflected in the number and character of meetings held and the attendance of the members at such meetings 4 In making a request for funds for any year, the officers of a Local Section should submit a report on the printed form approved by the Directors at their meeting on November 19, 1937 5 A standing Committee on Local See-

Jan 1, 1952

By W. R. Hansen, F. W. Boulger

Twenty-nine laboratory steels were studied to determine the effects of composition and ferrite grain size on drop-weight and Charpy V-notch transition temperatures. The experimental steels covered the following ranges in composition.. 0.10 to 0.32 pct C, 0.30 to 1.31 pct Mn, 0.02 to 0.43 pct Si, md nil to 0.136 pct acid-soluble Al. Although most of the data were obtained on hot-rolled samples, some plates were heat-treated in order to cover a wider range in ferrite grain size. The experimental data were used for a multiple-correlation analysis conducted with the aid of an electronic computer. The study showed that carbon raises and that manganese, silicon, aluminum, and finer ferrite grains lower both drop-weight and Charpy transition temperatures. Quantitatively, variations in composition and grain size have a more marked effect on V15 Charpy transition temperatures than on the drop-weight transition temperature. Useful correlations were found between transition temperatures in drop-weight tests and those defined by seven different criteria for Charpy tests. Evidence was accumulated that the conditions ordinarily used for drop-weight tests are more severe for 1-1/4-in. -thick plate than for 5/8- to 1-in. -thickplate. PROJECT SR-151, to study quantitatively the effects of metallurgical variables on performance in the drop-weight test, was established by the Ship Structure Committee late in 1958 on recommendation of the National Academy of Sciences, National Research Council. This project was initiated as a result of the increasing use of the drop-weight (nil-ductility) test in predicting the ductile-to-brittle behavior of steel. Qualitative data indicated the drop-weight was not as sensitive to metallurgical variables as the Charpy V-notch test. Furthermore, the available information indicated that the drop-weight test did not show the superiority of killed steels over semikilled steels reflected by Charpy tests. This difference in sensitivity to brittle fracture is considered important because the drop-weight transition temperature has been reported1 to correlate better with service-temperature failures than the V-notch test does at a constant energy level. Therefore, this project was concerned with establishing quantitatively the effects of metallurgical variables in the drop-weight test. For comparison, Charpy V-notch data were obtained for the steels investigated. This paper summarizes the results of the investigation. Most of the steels used for the study were made and processed in the laboratory. However, some tests were also made on commercial killed steels available from Project SR-139 (SSC-141). During the course of the investigation, data were obtained on the effects of carbon, silicon, manganese, and aluminum on transition temperatures of drop-weight and Charpy specimens. In addition, the effects of heat treatment which changed the ferrite grain size and the transition temperatures were also investigated. Finally a few exploratory studies were made on commercial killed steels to evaluate the effects of plate thickness, grain size, and heat treatment on the performance of drop-weight specimens. EXPERIMENTAL PROCEDURES Preparation of Materials. A total of twenty-nine 500-lb induction-furnace heats were made and processed in the laboratory for the investigation. Carbon, manganese, silicon, and aluminum contents were systematically varied. Melting and rolling techniques proven satisfactory in a previous project2 were used as a guide for the current investigation. Composition. The composition of the twenty-nine laboratory heats made for this project are given in Table I. The steels are divided into three groups. The first group consists of ten aluminum-killed steels similar in composition to Class C ship-plate steel. The second group consists of ten semikilled or Class B type steels. In both of these groups the carbon and manganese contents were intentionally varied over a wide range. This wide range in composition was helpful in obtaining quantitative data from a limited number of steels. The primary purposes of these two groups of steels was to determine the effects of carbon, manganese, and deoxidation practice. In addition, one steel in each group (Steels 2-2 and 9-2) were made about 1 year after the start of the program in order to check consistency of melting practice. The third group of nine steels listed in Table I was intended for studies on the effects of silicon and aluminum. In eight of these steels carbon and manganese were held relatively constant at levels of about 0.2 and 0.8 pct, respectively, while silicon and

Jan 1, 1963

By K. A. Jackson, G. A. Chadwick, A. Klugert

The diffusion field ahead of a lamellar interfnce is analyzed using an electrical analog. A self-consistent solution is obtained for the shape of the interfnce and the diffusion field by an iterative process. The solutions presented here are for a 50-50 eutectoid or eutectic, The shape of the interface is found to he independent of growth velocity and lamellar spacing, and to depend on the relative values of interfacial free energies at the phase houndaries . The mode of growth of lamellar eutectics and eutectoids has been a subject of much interest for many years.1-4 Mehl and Hagel 1 have shown photomicrographs taken by Tardif when he attempted to determine experimentally the shape of an advancing pearlite interface; the results are completely ambiguous. Brandt' and schei13 have made approximate calculations of the composition ahead of a lamellar growth front. The shape of the advancing front and the composition distribution ahead of the front are difficult to calculate because one depends on the other. It is the purpose of the present paper to describe a method by which this calculation has been done. Lamellar-eutectic growth usually occurs under conditions where the growth is fairly rapid, and the interface temperature is close to the eutectic temperature. The growth rate is usually determined by heat flow. Eutectoid growth, on the other hand, can best be studied by quenching to some temperature, and allowing growth to proceed isother-mally. In both cases the growth is believed to be controlled by diffusion* rather than by the atomic kinetics of the transformation. This being the case, a single treatment of the diffusion equation will apply to both cases, provided the region of the interface in a eutectic may be considered to be isothermal. If a part of the interface could appreciably change its thermodynamic driving force by advancing ahead of or lagging behind the mean interface, then the two cases would not be similar. Eutectics normally grow in temperature gradients of the or-der of a few degrees per centimeter. The normal eutectic spacing is the order of a few microns. Part of the interface would have to extend many lamellar spacings ahead of the mean interface before it experienced sensibly different conditions. The interface temperature is usually a few tenths of a degree below the eutectic temperature so that temperature differences of the order of one-thousandths of a degree (a displacement of one lamellar spacing) would be unimportant. Protrusions large compared to the mean spacing do occur when one phase only grows into a eutectic liquid. This is usually a dendritic type of growth, and easily distinguishable from the lamellar mode of growth. A single treatment of lamellar growth will apply equally well to both eutectic and eutectoid decomposition. At the interface, which as shown above is essentially isothermal, the difference between the equilibrium eutectic temperature Teu and the actual interface temperature Ti, can be divided into two parts: 1) the composition varies across the interface, so that the local equilibrium temperature is not Teu; and 2) the interface is curved, so that the local equilibrium temperature is depressed according to the Gibbs-Thompson relationship. This undercooling can be written as Teu-Ti =?T = mAC(x) + a/r(x) [1] where ?C(X) is the departure of the composition at a point x on the interface from the eutectic composition, see Fig. 1, r(x) is the local radius of curvature at a point x on the interface, m is the slope of the liquidus line on the phase diagram, and a is a constant given by where s is the interfacial free energy, TE is the equilibrium temperature, and L is the latent heat of fusion. The calculations in this paper will be made only for the case where the phase diagram is symmetric, that is, the eutectic occurs at 50 pct, the liquidi have the same magnitude slope m at the eutectic temperature, and C,, the amount of B rejected when unit volume of a freezes, see Fig. 2(a), is the same for both phases. As shown in Fig. 2(b), the composition ahead of the a phase will be rich in B, the composition ahead of the ß phase will be rich in A. The composition at the phase boundary is the eutectic composition. The difference between the local liquidus temperature and the actual tempera-

Jan 1, 1964

By G. W. Nabor, A. S. Odeh

The effect of production history of a well on the results of two-rate flow tests, and conventional build-up analyses was investigated. The effect was examined by means of digital computers and an R-C network model, respectively, for wells with infinite and finite radii of drainage. For systems which behave as infinite, it was found that production history and the duration of production at constant rate prior to the initiation of the test have important effects on the results. During build-up time equal to about one-fourth of the stabilized time, correct permeability-thickness product calculations can be made. For wells with finite radii of drainage, the time was determined during which the straight line can be satisfactorily used for permeability-thickness product calculations in case of drawdowns and build-ups. On build-ups, the dimensionless time (based on the external radius) during which the straight line gives reliable results was detertriined to be about 1/12. This is one-fourth as long as that of the drawdown. The investigation was done theoretically, and subsequently was verified by R-C network model runs. General interpretive rules were formulated which, if not followed, could lead to serious errors. Moreover, a recommended testing procedure is reported. INTRODUCTION The method used by most reservoir engineers for estimating formation characteristics in a producing well is the analysis of pressure build-up data. The method originally devised by Horner' makes use of the point source solution to the diffusion equation. This solution is approximated by a logarithmic function and the superposition principle is employed to arrive at the well known pressure build-up equation:where q, the flow rate, is in reservoir B/D; ft is in cp; kh is in md-ft; At is the shut-in time; and t is the producing time. At and t are in any consistent time units. Ey. 1 is applicable to a well of unlimited drainage radius which produces at a constant rate q from zero to time t and is then shut in. Such a constant production rate seldom obtains in practice. Therefore. a correction term must be applied to Eq. I to account for the varying rate. Two theoretically accurate methods are available for treating the variable rate case. The first, originally derived by Horner,' is based on the application of the superposition theorem. It requires knowlege of production history of the well as a function of time and results in lengthy and laborious calculations. The second t*q* niethod is suited for short production tests and requires that the shut-in time be at least one and one-half times the production time. A third method which is not based on any theoretical justification and which was suggested by Horner as a "good working approximation" is the one used by the majority of reservoir analysts. especially when the well has been producing for a long time and the t*q* method is not practicable. The key to this method is in choosing or determining the t that appears in Eq. 1. Horner suggested using a corrected time t, in place of t. t, is calculated by dividing the total cumulative production by the last established rate. Therefore, a normal procedure of pressure build-up testing is to stabilize the well at a constant rate for at least 24 hours before shut in and to use the stabilized rate to calculate t,. The analysis is then made by plotting either or P. and examining the resulting plot for the expected straight line to calculate kh and the original reservoir pressure. Recently, Russell" proposed a method for determining formation characteristics from two-rate flow tests. His method reduces to pressure build-up if the second flow rate is zero. Russell uses the Horner simplified procedure for calculating a corrected t,. His method also requires the stabilization of the well at a constant rate q which is used to calculate t,. Theoretically, the above procedure is valid for a well with an unlimited radius of drainage or with a limited radius as long as the boundary effect has not been felt by the well. Several authors'' derived formulas which allow the estimation of time during which limited reservoirs behave as infinite ones and, thus, can be treated by unsteady-state mechanics. One equation derived by Swift and Kiel' terminates the application of unsteady-state theory when the drainage radius reaches one-half the reservoir radius. Thereafter, steady-state behavior obtains. Another equation derived by Jones'" initiates steady-state

Jan 1, 1967

By Lloyd Pollish, Robert N. Breckenridge

SUCCESS in any underground mining operation is determined by accessibility of the orebody, which in turn is dependent upon maintenance of passageways to the mining zones and temporary support of the voids caused by extraction of ore. This is accomplished by one or a combination of the following methods: timbering, back-filling, pillaring, or, more recently, rock bolting. Timbering has usually been the principal means of maintaining these underground openings necessary for mining operations. Timber, however, does not prevent ground movement beyond the scope of localized sloughing, which is indicated by the gradual failing of the timber itself. Besides this, timbering has always been a costly process, and with the decline of available supplies of timber close to the mining areas, mining men have constantly sought other methods of controlling ground. Rock bolting is now replacing timbering at an ever increasing rate. Experience has proved that this form of ground support is just as applicable to blocky igneous rock as to stratified rock. Besides preventing sloughing of the walls and back of underground openings, Fig. 1, rock bolting has a stabilizing effect on the surrounding ground in much the same manner that steel reinforcing rods add to the strength of concrete structures. Further, rock bolting is flexible and may be applied to any shaped excavation, whereas timber sets are in a fixed pattern and the ground must often be changed to conform with this pattern. Rock-bolting installations were made in metal mines of the Northwest as early as 1939. An exhaust air crosscut was driven that year in one of the Butte mines of the Anaconda Copper Mining Co. The crosscut was rock-bolted and gunited at the time it was driven and is still being used to exhaust hot humid air from the 3400 level of the Belmont mine. It is interesting to note that no sloughing or caving has taken place in the 14 years it has been open. Even though these early installations of rock bolts were successful, few men recognized their potentiality until recent years, when the coal mines started their programs of mechanization and the great trend toward roof bolting began. In some areas of the Northwest stopes that previously required heavy timbering and close backfilling are now being mined by the more economical cut-and-fill and shrinkage methods. When used in conjunction with timbering, rock bolting increases the efficiency of the operation by decreasing hanging wall dilution and by making it possible to blast larger rounds. Most of the rock bolts installed to date in mines of the Northwest have been the 1-in. diam slot and wedge type, but there has been a recent trend to- ward using the 3/4-in. diam expansion shell bolt shown in Fig. 2. In addition to these commercially manufactured steel bolts, wooden bolts have been used with considerable success by the Day Mines of Wall'ace, Idaho. Installation of the slot and wedge type requires three distinct operations, with tools for each operation: 1—drilling the hole to proper diameter and depth, 2—setting the bolt, and 3—tightening the nut. Holes are drilled and bolts set with pneumatic rock drills. A number of setting or driving tools have been used successfully, but most follow the same general pattern. Usually the driving tool is designed to accommodate a short length of drill steel on one end and the rock bolt on the other end. In this manner the hammering effect of the rock drill is transmitted through the steel and driving tool to the bolt. When machines not having stop rotation are used, slippage is allowed between the driving tool and bolt or between the drill steel and driving tool. The rock bolt nuts are tightened either with pneumatic impact wrenches or with hand wrenches. Impact wrenches are desirable because they are faster and assure adequate tightness. Expansion shell bolts have the following advantages over slot and wedge rock bolts: 1—No special equipment other than a wrench is needed for their installation. 2—Installation is faster. 3—They are removable. 4—Holes need not be drilled to a specific depth as the expansion shell will anchor anywhere along the length of the hole. These advantages are offset somewhat by the lesser strength of the bolt, since expansion shell bolts are generally made from 3/4-in. diam steel as compared to 1-in. diam steel for the slot and wedge type. One manufacturer, however, is now fabricating expansion shell rock bolts from steel of high tensile strength, which gives this ¾-in. bolt a much greater strength than that of the mild steel bolt. Table I illustrates tests made by the Anaconda Copper Mining Co. to determine the proper hole size to use with various types of bolts and to determine

Jan 1, 1955

By H. E. Cline

Calculations of the formation and growth of faults caused by a variation in lumellar widths were made for a two-dimensioml three-plate problem. The angle between the a-ß boundary and the growth direction was allowed to vary and the time evolution was studied using a quasisteady state approach. At spacings smaller than a critical spacing given by X V = AO variations in the larrlellar widths grow in time to produce faults that coarsen the structure, while at spac-ings larger than this critical spacing, variations in the lamellar widths decay in time. If small plates are introduced into the structure they may grow only at large spacings to refine the structure. The time evolution and shape of faults were calculated for the three plate-problem and then the three dimensional problem and rod-like eutectic were qualitatively discussed. UNDERSTANDING of the mechanism by which the spacing of directionally solidified eutectics is determined may allow one to control their structure better. Steady state solutions for the growth of lamellar structures have been found for a range of lamellar spacings A and growth velocities V. To obtain a unique solution for the isothermal growth of pearlite, Zener1 assumed that growth occurs at a maximum velocity, while Tiller2 assumed that a eutectic alloy, grown under an imposed velocity, will choose a spacing corresponding to minimum undercooling. These assumptions are equivalent and have been referred to as "extremum growth". The extremum condition predicts the observed relation between velocity and spacing as given by V = constant [I] but does not provide a mechanism for changing the lamellar spacing. Jackson and Hunt3 calculated the interface shape by using solutions to the diffusion equation for a planar interface and a relation of the interface composition to the local curvature. If the spacing is much larger than the extremum spacing, the interface breaks down catastrophically to form forked plates. However, the catastrophic breakdown cannot account for the small adjustments in spacing that must occur in practice..3 Direct observations during the growth of organic eutectics4 and the Pb-Sn eutectic5 show that spacing changes occur by the formation of faults. A fault in a plate-like eutectic is the edge of a plate. Once the faults form, they may move to make small adjustments in the spacing.6,3 The motion of faults intersecting the growing interface was shown by an approximate analysis to give Eq. [I].6 A perfectly regular lamellar structure should be able to persist over a range of lamellar spacings. However, during growth small perturbations in the structure may occur. If the amplitude of the perturbation increases in time the structure is unstable, while if all possible perturbations decrease in time the structure is stable. In a previous paper7 variations in the shape of the solid-liquid interface were considered, while this paper considers only variations in lamellar widths while maintaining a macroscopically planar solid-liquid interface. Previously, theories of lamellar growth1"3 have artificially contrained the growth to give a regular periodic structure. To allow for a variation in spacing, the three phase intersections and groove angles were allowed to change with time as determined by assuming local equilibrium. THREE-PLATE PROBLEM Since the spacing changes in eutectics by local formation of faults,4'5 it is suggested that local variations in spacing are responsible. The interaction between neighboring plates will be greatest because they have the smallest diffusion distance. For simplicity, as a nearest neighbor approximation, a three-plate problem will be considered, as illustrated in Fig. 1. The structure consists of a periodic array in which all the plates are allowed to vary in width. As in steady state growth it is assumed that the average composition in the solid remains constant. A variation in plate widths, that maintains the composition in the solid, was introduced by making the first a-phase plate thinner by an amount A, keeping the width of the second B-phase plate constant, and increasing the width of the third a-phase plate. If the structure were not perturbed, as in the regular two-plate problem previously described,' then the groove angles at the three-phase junctions are the equilibrium angles, 0, and ? B, and the solid-solid boundary is normal to the interface. In the three-plate problem with a variation in plate widths the phase boundaries are assumed to be related to the three-phase junction by equilibrium angles, but the a/B boundaries may be rotated by an angle 0 from the growth direction. The angle H be-tween the tangent to the a/B boundary and the growth direction may vary during growth and determine the —> — — —.A_ Q-0 / 0 x, X2 Fig. 1—Schematic of the three-plate problem showing a variation in the spacing and the effect on the angles at the three phase intersections.

Jan 1, 1970

Now producing 35,000 tpd of coal from a deposit whose estimated reserves total 1.1 billion t, the Navajo mine of Utah International Inc. near Farmington, N. M., is the largest open-pit coal operation in the US. The history of this mine began in 1953 when, foreseeing the growing need for electrical power in the southwest, Utah International obtained a prospecting permit from the Navajo tribe. The lease, now covering 31,000 acres of the 12-million acre New Mexico-Utah-Arizona Navajo Indian reservation, was entered in 1957; in the next 3 years, Utah International negotiated with the State of New Mexico for water rights on the San Juan River, and finalized an agreement with the Arizona Public Service Co. to provide coal for the proposed Four Corners power-generating plant near Farmington.

Jan 10, 1974

By F. B. Eiseman

IT is desired -to determine the effect of the extent of bank repairs on the final slag volume in acid electric steel-melting practice. It is understood that the repairs stud- TABLE I-Summary of Effect of Bank Repairs on Slag Volume [ ] ied here are necessary and the amount of sand added is that needed to maintain hearth and banks in a satisfactory condition. In this way the effect of repair materials on the amount of slag tapped would be found with a reasonable degree of accuracy. Ten heats were made for this study with careful attention to a uniform charge. The steel was the usual grade B and melting was carried out in a 3 1/2-ton top-charge Lectromelt furnace. Melting practice in all cases was the same-complete oxidation, with recarbonization by means of low-silicon pig iron.

Jan 1, 1947