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By Gary P. Thomason

INTRODUCTION One may have heard about how various projects were financed or certain companies were successful in obtaining a bank loan, but there are many more projects and companies who fail to get the money they need. At least a portion of these failures, and a large percentage of the frustrations connected with even the successful financings, are a result of not understanding the process of obtaining money. Recent years have seen a proliferation of debt financing sources available to finance minerals operations (see the next Chapter 11), but these represent only a minor portion of the minerals financing market. The fundamental source of borrowed money to many minerals related companies remains the banks. Therefore, understanding the "Loan Approval Process" can easily mean the difference between getting the money or not. LOAN APPROVAL PROCESS The initial stages of the loan approval process should begin long before the bankers, and the organizations they represent, enter upon the scene. The loan approval can be broken down into six stages: 1) Generation 2) Preparation 3) Presentation 4) Evaluation 5) Approval 6) Documentation As you can see in Figure 1, the bank is only directly involved in the second half of the process. The perils in obtaining financing for the smaller minerals venture are primarily in the first three stages, not the last three. The minerals venture making application for a loan can, in almost every case, improve its chances of success by carefully planning and preparing itself and the information that will be required of it in the loan approval process. Generation This first step in the process is deciding on the need for a loan. (Earlier papers in this Book and in Chapter 11 provide some guidance.) It is surprising how many ventures confuse the need for money with the need for a loan. Suffice to say that the equity investor risks both the timing of the yield on his capital and, ultimately, his capital. The lender, on the other hand, advances temporary funds which he expects to be repaid on a specific schedule with a fixed

Jan 1, 1985

By G. K. Manning, W. E. Few

WORK on the effect of vacuum heat treatment of 0.040 in. diam sintered and wrought molybdenum wires has been sponsored by the Office of Naval Research at Battelle for the past several years. An electrical resistance furnace' capable of maintaining a vacuum of less than 0.1 micron of mercury at temperatures as high as 4000 °F was used for heat treating the wires. Early in the work, it was found that the introduction of a few microns pressure of oxygen into the furnace resulted in a rapid increase in the oxygen content of the wire specimens and the appearance of a discrete oxide phase. Subsequent elimination of the oxygen atmosphere caused the disappearance of the oxide phase. This was used to determine the solid solubility of oxygen in molybdenum over the temperature range of 2000" to 3000°F.2 It was observed that, with the disappearance of the oxide phase, the wires regained some ductility. Single-phased wires possessed from 5 to as much as 40 pct elongation in 2 in. Later, attention became centered on determining the cause of this wide range in ductility. Wires containing less than 0.002 pct C, less than 0.0007 pct 0, less than 0.0005 pct N, and less than 0.00003 pct H exhibited the erratic ductility noted above. These percentages represent approximately the limit of accuracy of presently available methods of analysis and thus it became apparent that chemical analysis would be of little help in the study. A number of possible explanations for the wide range in ductility were suggested during the course of the work. It was first suspected that variations in the grain size of the recrystallized wire specimens might be responsible. Wire from several lots of material was available. One of these lots tended to develop very large grains when recrystallized, the others all developed an ASTM grain size of 3 to 4 when heated above 2700°F. No correlation between grain size and ductility could be found. It was thought that back diffusion of oil from the diffusion pump might cause contamination of the wire, principally with carbon, but when wires were treated without cooling the cold trap in the pumping system,

Jan 1, 1956

By George Wendell

THE fact that a symposium on pyrometry is being held under the auspices of the American Institute of Mining and Metallurgical Engineers may very properly be taken as a recognition of the importance of temperature measurements and control in production and in the industries, and of the need for instruction in pyrometry in our schools of engineering. Though there may be general agreement as to the need of some instruction along this line, there will undoubtedly be divergence of opinion as to the amount of time that can be allowed to such instruction, as well as to its character. Those who have given little attention to the complexity of high-temperature measurements will be apt to think that a few simple experiments are all that is required. They fail to distinguish between the artisan, who merely has to learn how to use any piece of apparatus that is installed, and the technically trained man, who must be prepared to assume the responsibility for the supervision and maintenance of the pyrometric equipment, for the calibration of the instruments, and for the solution of any temperature problems that arise. In approaching this subject two questions present themselves: What should be the character of the instruction in pyrometry in an engineering school, and what can be expected of the students who have had this instruction? In brief, it may be said that the aims of a course in pyrometry should be to give: (1) A thorough grounding in the fundamental principles of thermoelectric, resistance, radiation, and optical pyrometry, and of liquid and gas thermometry; (2) practical instruction in the calibration of pyrometers; (3) acquaintance with the errors that are likely to arise and the precautions that must be observed in practice; (4) information regarding the limitations of the various classes of instruments, their relative reliability, and the accuracy attainable with them at different temperatures; (5) acquaintance with the commercial instruments on the market, their construction and relative merits; (6) a knowledge of the chief sources of information relating to the measurement of high and low temperatures. To sum up, the aim should be to turn out resourceful young men familiar with the leading instruments on the

Jan 9, 1919

By Ben-Zion Weiss, Melvin R. Meyerson

FATIGUE crack propagation in some aspects can be viewed as being a result of localized plastic deformation concentrated near the tip of the crack.' Deformation is influenced by microstructure which in turn can affect the fatigue crack growth significantly. To study the effect of localized microstructural changes on fatigue crack propagation, cantilever-type notched specimens were subjected to cyclic bending at constant load amplitude. The extent of fatigue crack propagation was obtained by measuring the length of the crack by periodic observation with a microscope on the polished side of the sample,2"4 and these data were used in preparing the curves in the figures which follow. Figs. 1 (solid lines) and 2 show experimental results obtained in austenitic type 302 stainless steel containing higher than standard carbon (0.24 pct C) and 310 stainless steel. Both steels were homogenized for 8 hr at 1120°C and then water-quenched in order to prevent the precipitation of carbides. Fig. 3 shows experimental results obtained on 9440 low alloy steel in the normalized condition and in the quenched and tempered (580°C) condition. Indications of microstructural influence can be seen in scattering of the experimental data. The degree of scattering depends on both the microstructure and the amount of cyclic stress applied to the sample. For microstructures which are more easily deformed plastically, e.g., normalized or annealed as compared with hardened and tempered structures, the scattering is greater. Similarly, higher stresses produce greater scattering in the results, regardless of whether the cause of the stress increase is due to initial loading conditions or the growth in crack length. Scattering is believed to be a result of partial redistribution in the stress field around the tip caused by plastic deformation. This opinion is borne out by much smaller scattering of experimental results in the austenitic 302 high-carbon (0.24 pct C) steel. In this steel, plastic deformation in the neighborhood of the crack causes partial mar-tensitic transformation of metastable austenite,5 which in turn restrains further plastic deformation. As a result, the stress redistribution around The tip is reduced. Partial martensitic transformation was confirmed

Jan 1, 1969

By AIME AIME

THE second meeting of 'the Open-Hearth Committee, 'sub-division of the Iron and Steel Committee of this Institute, was held at the Hotel Cleveland, Cleveland, Ohio; on Oct. 13-15. On Oct: 12, the Open-Hearth Superintendents visited the plants of the Youngstown Sheet and Tube Co. and. the Republic Iron and Steel Co. These men were courteously entertailled by the two companies and every facility for a thorough inspection was furnished. Luncheon was severed at the plant bf the Youngstown Sheet and Tube Co. The meeting was opened Tuesday morning with addresses by J. V. W. Reynders, President of the Institute, and Herbert M. Boylston, Chairman of the Ohio Section of the Institute. E. A. Whitworth, of the Gathmann Engineering Co., presided at the meeting and L. B. Lindeinuth was secretary.

Jan 1, 1925

By John B. Cook

Most of today's open pits take the form of conical-shaped excavations in the relatively flat or undulating terrain surrounding them. Ore is usually hauled uphill from the pit bottom by truck, rail, or skip to crushing, beneficiation, railroad loading, and stockpiling facilities near the edge of the pit. There are, however, a few orebodies whose locations in mountainous terrain causes special problems that generate different technical solutions. LAMCO's 10.5 million metric tons per year high-grade iron mine in the Nimba Range in tropical Liberia is probably one of the most extreme of these exceptions (Fig. 1). At Nimba there is a 2,000-ft difference in elevation between the upper- most levels of the orebodies and the start of the railroad below at the foot of the mountain. Haulage to the crusher is usually downhill at grades of up to 12% dictated by the topography of the rugged terrain. Ore is transported from the crusher down the mountainside by a conveyor sys- tem 10,096 ft long, whose average grade is 18%. The belt is braked by asynchronous generators, feeding power into the local network. The original crusher must be relocated at a lower elevation outside the final pit limit to allow that part of the mountain on which it now stands to be excavated. HISTORY The LAMCO Joint Venture is owned 75% by the Liberian-American- Swedish Minerals Co. (LAMCO) and 25% by Bethlehem Steel Corp. LAMCO is comprised of a 50% interest by the Liberian Government and 50% interest by Liberian Iron Ore Ltd (Fig. 2). This joint venture was launched to develop the high-grade iron ore deposits of the Nimba Range.

Jan 1, 1969

Extractive Metallurgy Division Institute of Metals Division Iron and Steel Division OFFICERS AND COMMITTEES John Chipman, President W R Hibbard, Jr, Past President C C Long, Vice-President T D Jones, Treasurer R W Shearman, Secretary AIME, 29 West 39th Street New York 18, N Y

Jan 1, 1959

By G. A. Beiswenger

The application of the law of supply and demand to the sale of crude oil is generally conceded, but the motives underlying the buyer's (refiner's) demands are not always obvious to the seller (producer). In some cases this obscurity has led to the conclusion that the refiner may be unnecessarily particular when he selects one crude and rejects another. This preference, however, is very largely the reflection of the refiner's product demands and the quality of the stocks obtainable from the selected crude. The purpose of this paper is to point out critical characteristies of the major classes of refined products and to show how crudes vary in their suitability for such products. With relatively few exceptions, available processing methods and addition agents make it theoretically possible to produce any type of refined product from any crude source, although it may not be economically sound to do so. The widespread application of thermal cracking for converting higher boiling stocks into gasoline is well known. More recently cracking and refining in the presence of catalysts9 have been developed, as well as various processes for polymerizing lighter hydrocarbons into gasolines having desirable characteristics.6 For several years, selective solvents have been applied commercially to refining inferior quality kerosene, Diesel fuel and lubricating oil distillates.3 Improved methods for refining lubricating oils from crude residual4 formerly suitable only for fuel, are now in use and a number of special solvent processes are available for dewaxing lubricating oils to low pour point.5 These improved refining methods have been developed not only to meet the demand for improved product quality but also to enable the refiner to obtain quality products from crude sources that would not yield such products by the older refining methods. In many cases, the utilization of these modern refining tools necessitates an appreciable expenditure for equipment as well as added manufacturing costs, and their application therefore must be justified economically. Despite the availability of such tools, the added processing costs involved and yields obtainable may render their application entirely impractical. To illustrate this point, inspections of typical cuts from various crudes

Jan 1, 1940

By A. K. Chakravarti, A. Lihiri, G. G. Sarkar

One primary objective of India's third Five Year Plan is the expansion of coal production. The goal: boost present output of 45 million tons to 95 million tons by 1965--an increase of more than 100 pct!

Jan 7, 1961

By Frederic H. Lahee

After abandoning two dry holes, on the Mrs. Daisy Bradford land, C. M. Joiner finally completed his No. 3 on Sept. 8, 1930, at a total depth of 3592 ft. This well is 735 miles somewhat north of west of the town of Henderson, in Rusk County. Between Oct. 2 and Oct. 6, this well made numerous heads which indicated that it would produce about 300 bbl. daily. By Nov. 27, two dry holes,' completed near the Joiner well, taken in conjunction with the small production from this well, served to dampen any enthusiasm among those who hoped for a major pool; but by December 18 three other producers had been completed. On Dec. 28, 1930, E. W. Bateman's Lois Della Crim No. 1 drilled itself in with an estimated daily yield of between 10,000 and 15,000 bbl. from a depth of 3650 ft. This well, 10 miles north of the Joiner well, also in Rusk County, initiated the leasing campaign that led to the later orgy of drilling. On Jan. 25, 1931, Moncrief, Farrell and others completed their J. K. Lathrop 1 as another big producer, 7 miles east of Gladewater in Gregg County and 14 miles N. 20" E. from the Bateman Crim well. The Lathrop well, 3574 ft. deep, flowed 320 bbl. in 1 hr. through a ½in. choke. The first well completed in Smith County was Cook No. 1, drilled by Guy Lewis et al. in the James Jordan Survey, 4.7 miles west of the Joiner discovery well. On Mar. 30, 1931, it flowed 137 bbl. in 33 min, through a ¾-in. choke. The top of the pay sand was found at 3672 ft. Finally, in Upshur County, on May 5, the Mudge Oil Co. et al. completed the Richardson No. 1, which flowed 274 bbl. through a 4 2/64-in. choke in 2 hr. This well is 4 miles northwest of the Lathrop producer. Development It is unnecessary to give a lengthy description of the rapid development of the area discovered in these five far-separated wells, or to discuss the speculations offered as to whether there were several pools or only one.

Jan 1, 1932

By John T. Galey

Oil and gas development in southern Pennsylvania during 1937 was marked by considerably increased activity in deep-sand drilling. Nine tests were completed to the Oriskany sand: one in Independence and three in South Beaver townships, Beaver County; one in Franklin township, Butler County, two in Slippery Rock township, Lawrence County; one in Mt. Pleasant township, Washington County, which is drilling below the Oriskany, and one in Fairfield township, Westmoreland County. Two of these wells, both of which were in the Blackhawk pool, South Beaver township, Beaver County, obtained wet gas with open-flow volumes of 1.5 million cu. ft. and 3.1 million cu. ft. and closed-in pressures of 1900 Ib. The remaining seven were unproductive in the Oriskany. Two wells, one in Hampton township, Allegheny County, which is shut down temporarily as a result of a gas pocket, and one in South Beaver township, Beaver County, are drilling to the Oriskany. One deep test on the Chestnut Ridge anticline, South Union township, Fayette County, was completed after considerable difficulty as a dry gas well in the Onondaga limestone. At this locality the cherty limestone is porous as a result of fracturing. Three additional tests are under way in the area, one in South Union township, a second in North Union township, and a third in Wharton township. Completions Oil.—Despite price cuts and production curtailment of Pennsylvania Grade crude, caused largely by a decreasing demand from export markets, operation in the shallow oil areas continued at a fairly high rate and a number of good wells were completed. Some of these were new wells in close proximity to old production and others were old wells drilled into deeper pays. One new well of a number of producers drilled to the Nineveh Thirty-foot sand in the Harvey pool, Center township, Green County, made 400 bbl. of oil and 500 million cu ft. of gas the first 24 hr. The Chambers dam pool of Amwell and South Franklin townships, Washington County, yielded a number of Fifth Sand producers with initials as high as 200 bbl. Several wells in the old Mars-Butler field

Jan 1, 1938

By M. A. Mosher

Most modern electrolytic copper refineries have found it expedient to build and operate a complete secondaries plant for the treatment of the electrolytic slime accumulated in the cells during the corrosion of the copper anodes. In the earlier years this was done for the sole purpose of promptly recovering in marketable form the silver and gold contained in the slime. Later, improvements in refining methods made possible the recovery of the more precious metals such as platinum, palladium, osmium and iridium, and in recent years, due largely to an increasing market, many secondaries plants have undertaken the commercial production of selenium and tellurium. The complete up-to-date secondaries plant, or silver refinery as it is usually called, is therefore equipped for the production in marketable form of from six to eight metals. The physical plant and operations may be separated into six main divisions: 1. Slime treatment, in which the raw slime is treated by wet methods for the removal of its high copper content and portions of other impurities such as arsenic, selenium and tellurium. 2. Furnace refining, in which the remainder of the base-metal content of the slime is removed by fluxing and fire-refining. 3. Electrolytic parting and refining, in which the silver and gold are parted and obtained in the pure state. 4. Melting of silver and gold into marketable form. 5. Recovery and refining of the more precious metals. 6. Recovery and refining of selenium and tellurium. The Silver Refinery of the Raritan Copper Works at Perth Amboy, N. J., is a complete secondaries plant and the following description of its equipment and processes is, in a general way, typical of other plants of its kind. Slime Treatment The raw slime, pumped with a minimum amount of cell solution from the electrolytic copper refinery, is discharged into the center of circular settling tanks 15 ft. in diameter by 8 ft. deep, where the slime settles out and the solution overflows peripherally to return to the copper refinery by gravity. The slime is then dropped through a bottom outlet to a

Jan 1, 1934

By G. E. Murray

Lead blast-furnace work at Trail is unique in that this is the only plant in the world where blast-furnace smelting on a large scale for both lead and zinc recovery is carried on under one management. On this account the factors that determine economic practice differ from those of other lead smelters. In addition to this different metallurgical outlook, a great deal of structural investigation has been carried on, which has resulted in the development of a furnace which should prove of interest to all who are faced with similar problems. This description may be conveniently divided into various heads as follows: (1) General—make-up of charge, etc.; (2) structural—(a) hoods and charging methods, (b) shaft construction, (c) crucible construction; (3) handling slag; (4) handling bullion; (5) metallurgy. The Charge The Trail plant is an old one, on a congested site. As with most old plants, this limits the method of charge preparation. In general, lead metallurgists will agree that sinter when it reaches the blast furnace should contain as small an amount as possible of actual fines. There would be some difference of opinion as to the maximum size as well as of the minimum required, but to obtain the optimum condition some form of screening is indicated. This screening should take place immediately before the blast furnace if possible, and because sinter deteriorates in storage there should be as little as possible. There should also be the minimum amount of handling between the sinter machines and the furnaces. Unfortunately, at Trail the sinter must be handled considerably before it is charged to the furnace, and no feasible scheme of screening has yet been devised. Trail practice, then, demands that the sinter be a strong one physically. Dependent upon the amount of lead in it, it has been found advantageous to incorporate granulated slag into the final sinter, the amount varying inversely as the lead content. The addition of this slag makes a harder sinter, which arrives at the blast furnace in a better condition, but it entails some lack of efficiency, because desulphuriza-tion is not so rapid nor so complete.

Jan 1, 1937

By Francis P. Sinn

LOW prices have made 1938 a difficult year for the zinc industry of the world. Particularly in the United States, output had to be radically curtailed to bring production into line with consumption. Despite these unfavorable conditions, some additional plant construction is contemplated. In Jugoslavia, through co-operation with the Government, Trepca Mines is lo build a zinc plant to produce 10,000 metric tons annually, the plant to be ready for operation in July, 1941). Cerro de Pasco is proceeding with its plans for an electrolytic plant in Peru. A pilot plant, to be ready next summer, is under construction. In eastern Canada an electrolytic plant is planned in Quebec to treat concentrates from Yoranda and other mines but no defi-

Jan 1, 1939

By H. V. Flagg

OPERATION of a modern steel plant presents a curious anomaly. Large-scale operations, in which large volumes or heavy weights of materials are involved, are not usually subject to close control or narrow specifications. On the other hand, operations that call for a high degree of precision are usually carried out under carefully controlled conditions with delicate, precise machinery and tools, and production is made secondary to quality. In a modern steel mill both extremes are taken as a matter of course. A strip mill making auto-body sheets must supply its customers with sheets that all come within a tolerance of plus or minus 0.003 in. in gauge at any point from side to side or end to end, and without blemishes either of color or surface. Sheets that were considered par excellence as recently as ten years ago could not even find a market today. Such exacting requirements have made necessary a nicety of control that approaches the watchmaker's art. Notwithstanding this necessity for precision, the scale of operation is stupendous.

Jan 1, 1940

By Mark Sheppard

DURING the winter of 1937, the writer visited a West Virginia stone, quarry at which the overburden is stripped hydraulically. The quarry is in a bed of limestone, about 200 ft. thick, which outcrops on a hillside above a small river; the quarry face is 175 ft. high. The top of the stone is cut in all directions by erosion channels, which are filled with a tough, red clay. Some of the larger channels are 30 ft. deep and 8 ft. wide, The thickness of the clay overburden ranges from a few inches to 10 ft., the average being estimated as less than 3 feet. The topography of the district is rugged, and the hillside above the quarry face is not suited to the use of the usual mechanical methods of moving dirt. Until hydraulicking was started 10 years ago, the over-burden was dug by hand labor, dumped to the quarry floor and trans-ported to the dump in quarry cars, Cleaning deep channels was a slow and expensive process. When hydraulicking was started, the top of the quarry face was over 200 ft. above the level of the river. The pipe line was carried in a semi-circle around the top of the quarry about 200 ft. from the face and about 50 ft, above it. As there is no adequate supply of water above the quarry, the water must be pumped from the river: As quarrying pro-gressed the pipe line was moved until the discharge points are now over 300 ft. above the river. Water is pumped from the river by a four-stage centrifugal pump having a 5-in. intake and a 4-in. discharge. It is direct-connected to a 200-hp,, 2300-volt, 1760-r.p.m. induction motor. At 1760 r.p.m. the rated capacity of the pump is 750 gal. per minute under a head of 600 ft. The pump is installed in a house of frame construction on the river bank, about 10 ft, above normal water level, which also houses the pump for the mill-water supply. Above the pumps are hoisting hays into which the motors are raised whenever the river reaches flood stage.

Jan 1, 1938

By John T. Crawford

Much has been written of late regarding the flotation of coal as a means of reclaiming the valuable portion of the fines encountered in nearly all methods of coal preparation. Whether the process be wet or dry, whether the dust be sent through the entire process or removed prior to the cleaning by some such method as screening or aspiration, one of the final products consists of a considerable proportion of — 48-mesh material. The percentage of this —48-mesh material depends upon the mining method, transportation, storage, and method of preparation. The tonnage of this dust material ranges from 1 to 10 per cent of the total output of the cleaning plants. Four methods of disposal are available for this coal: 1. Disposal with the refuse from the plant. 2. Addition, after being reclaimed from the wash water, or dust collectors, without cleaning to the larger sizes. 3. Separate disposal as a pulverized fuel. 4. Cleaning so that addition to the larger sizes benefits the product as a whole. It is also true that flotation in one form or another is the only known way to effectively clean this material. While some processes do a reasonable cleaning job down to and including +l00 mesh, by far the greater majority stop at or short of the + 48-mesh size. Much of the literature on coal flotation passes by the fred pulp density and size by merely stating that the feed varies from 20 to 30 per cent solids and that the size range is from — 1/4 in. or — 1/8 in. to 0. Small wonder then that some operators with entirely different conditions, and not knowing the machine capacity, throw up their hands in despair when flotation is mentioned. Too much parallel is drawn between flotation methods as applied to ores and as applied to coal, to the detriment of the latter. In the flotation of metalliferous ores the feed pulp density ranges from 20 to 30 per cent solids, depending upon the amount of mineral to be floated and upon the size analysis. Thus where 2 to 5 per cent of the

Jan 1, 1936

By John T. Crawford

Much has been written of late regarding the flotation of coal as a means of reclaiming the valuable portion of the fines encountered in nearly all methods of coal preparation. Whether the process be wet or dry, whether the dust be sent through the entire process or removed prior to the cleaning by some such method as screening or aspiration, one of the final products consists of a considerable proportion of — 48-mesh material. The percentage of this —48-mesh material depends upon the mining method, transportation, storage, and method of preparation. The tonnage of this dust material ranges from 1 to 10 per cent of the total output of the cleaning plants. Four methods of disposal are available for this coal: 1. Disposal with the refuse from the plant. 2. Addition, after being reclaimed from the wash water, or dust collectors, without cleaning to the larger sizes. 3. Separate disposal as a pulverized fuel. 4. Cleaning so that addition to the larger sizes benefits the product as a whole. It is also true that flotation in one form or another is the only known way to effectively clean this material. While some processes do a reasonable cleaning job down to and including +l00 mesh, by far the greater majority stop at or short of the + 48-mesh size. Much of the literature on coal flotation passes by the fred pulp density and size by merely stating that the feed varies from 20 to 30 per cent solids and that the size range is from — 1/4 in. or — 1/8 in. to 0. Small wonder then that some operators with entirely different conditions, and not knowing the machine capacity, throw up their hands in despair when flotation is mentioned. Too much parallel is drawn between flotation methods as applied to ores and as applied to coal, to the detriment of the latter. In the flotation of metalliferous ores the feed pulp density ranges from 20 to 30 per cent solids, depending upon the amount of mineral to be floated and upon the size analysis. Thus where 2 to 5 per cent of the

Jan 1, 1936

By R. E. Collins, Paul B. Crawford

Mathematical equations have been derived to show the effect of the slippage phenomomenon (Klinkenberg effect) on unsteady-state gas flow through porous media. The assumption is made that the slippage may be represented by an equation of the type It is pointed out that most of the existing data on unsteady gas flow may be corrected for slippage by a simple change in definition of the dimen-sionless groups. INTRODUCTION Several solutions to the various problems associated with the unsteady-state flow of gas through porous media have been recently presented in the literature.','" The cited publications have resented solutions for flow under ideal conditjons. The principal assumptions involved include: (a) the density of the gas obeys the perfect gas law; (b) the viscosity of the gas is constant; and (c) the gas permeability is constant. Few, if any, actual gases under reservoir conditions are believed to conform with the above, but the ideal solutions do provide the basis for making improved estimates on the performance of gas reservoirs. The purpose of this paper is to show the performance characteristics when assumption (c) is corrected for the slippage phenomenon or the Klinkenberg effect. This is believed to be a step nearer to reality. MATHEMATICAL DEVELOPMENT Case 1. Gas Flow — Ideal Conditions The equations describing the flow of gas under ideal conditions have been clearly presented in the cited literature; however, for completeness of this work they are repeated here. The basic differential equation describing the flow of gas is Equation (6). It may be derived as follows: The continuity equation, the perfect gas law and Darcy's law are combined to give: Manuscript received in the Petroleum Branch office Aug. 3, 1963 or If — is constant, Equation (5) is rewritten to form the basic Equation (6). or for the linear case A dimensionless equation is obtained by dividing through by (pl)z and making the substitutions shown below: The resulting equation is A similar procedure for the radial case leads to the following equations: where and Equations (11), (12), and (13) are those used by Bruce, et al., and Jenkins and Aronofsky for their computational work.

Jan 1, 1953

By J. B. Newkirk, R. W. Hendricks, R. Baro

STUDIES of the kinetics of precipitation in binary alkali halide systems are of interest from a theoretical point of view, because of the possibility of controlling diffusion rates by additions of aliovalent impurities. This note reports some preliminary results of a study of the kinetics of precipitation of AgCl from supersaturated solid solutions of AgCl in NaCl containing trace amounts of divalent cation impurities. In their study of the system NaC1- AgC1, Stokes and Li1 derived the phase diagram containing a mis-cibility gap with a broad maximum at approximately 170°C. They found that single crystals quenched from above the miscibility gap and aged at various temperatures within the two-phase region gradually turned light blue, then cloudy white, and finally opaque. The rate of transformation depended markedly on the aging temperature. The light-blue color in the early stages of aging was interpreted to be the result of Rayleigh scattering from precipitated particles less than 0.1 µ in diameter. These qualitative observations have been confirmed by us. However, a more precise tool was needed in order to quantitatively follow the growth kinetics of the precipitate particles. Because of the suspected small size of the precipitate particles and for other reasons, small-angle X-ray scattering was thought to be a suitable technique for this study. Small-angle X-ray intensities scattered from powder specimens were recorded on a General Electric XRD-5 diffractometer using the four-slit geometry described by Neynaber, Brammer, and Beeman.2 The slits were 0.08 mm wide by 10.00 mm high. It was found that, with very careful alignment, meaningful data could be obtained to within 3 min from the middle of the direct beam. Chromium radiation (?Ka = 2.29Å) was used in order to spread the scattered intensity to a relatively high angle, as indicated by Eq. [1]. A specimen containing 21.0 at. pet AgCl was prepared by melting analytic reagent-grade AgCl and NaCl under a chlorine atmosphere in a vycor cap-

Jan 1, 1964