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By B. R. Hollebone

The chemical action of molten anhydrous pyridinium chloride (pyridine hydrochloride) on oxy salts and ores of some Group IV and V metals are discussed-in particular zirconium, hafnium, niobium (columbium) , and tantalum. Laboratory-scale experiments are described whose results suggest that this reaction might provide a practicable means of converting ores of these metals to the anhydrous metal chlorides. Experimental results are given which provide some insight into the nature of the reactions and some of the compounds which could be present at intermediate stages. The treatment of ores of the more refractory metals is difficult and expensive and often demands the use of gaseous chlorine, hydrogen fluoride, or other reagents which are, if nothing else, expensive and dangerous to use. This situation is, of course, due to the strong metal-oxygen affinity resulting from the high charge and the small size of the metal ion which combine to produce such high lattice energy in the metal oxide as to defeat standard reduction methods. Thus, the characteristic of these metals which leads to one of their most important properties—corrosion resistance—is the main hurdle in obtaining the metal. Many common methods' for treating ores of zirconium and niobium (columbium), for example, proceed as directly as possible to the preparation of anhydrous halides. These halides are purified by now standard processes of solvent extraction, fractional distillation, and so on. This paper reports on preliminary stages in the development of a method of treating these ores—particularly of niobium—so as to prepare the anhydrous, volatile halides by the use of chemical reagents which are much more easily handled than those used at present. CHEMICAL PRINCIPLES The solvent action of aminium halides has been referred to periodically in the literature over several decades. The chemistry of pyridinium chloride has been discussed particularly by Audreith2 and Starke.3 However, since this is not familiar chemistry in its nonaqueous setting, it is perhaps well to point out some general metallurgical principles and applications. One can use, as point of departure, the fact that HC1 dissolved in pyridine is an acid very much the same as aqueous HC1. It thus gives essentially all the reactions of the HC1 with which we are familiar. However, when the ratio of HC1:pyridine reaches 1:l (a ratio far higher than is possible with H2O) the solution becomes solid C5F5NHC1, pyridinium chloride.* Inter- estingly, the acidic properties of HC1 persist in this medium, although they are manifest only in the molten state of the compound. Some typical reactions of divalent metal compounds which we have carried out in our laboratories are the following: 2PyHCl + Zn — (ZnCl2) + H2 + 2Py 2PyHCl + MnO — (MnCl2) + H2O + 2Py 2PyHCl + CuS — (CuCl2) + H2S + 2Py 2PyHCl + CaCO3 — (CaCl2) + H2O + CO2 + 2Py In these equations, the parentheses indicate a solvated compound which in water would be predominantly a hydra ted cation but which in molten PyHCl will more likely be a complex chloro-anion of the type MC14-. Some important physical properties of pyridinium chloride (PyHCl) are given in Table I. One sees from the data in Table I that at the temperature of molten pyridinium chloride both water and pyridine will boil away. Thus the system will be kept anhydrous. For this reason the reaction 2NbCl5 + 5H2O— Nb2O5 + 10HC1 has no counterpart in molten PyHCl. Instead, the chloride is made even more stable by the formation of a hexachloro complex: Nb2O5 + 12PyHC1 — 2PyHNbC16 + 5H2O + 10Py One interesting property of these complexes is their thermal instability which for the case of niobium can be illustrated as PyHNbCl6 — PyHCl + NbCl5 With a view to possible use of this chemistry in ore treatment, we have attempted to dissolve Pyrochlore (essentially FeO - Nb2O5) and recover the NbC15 from it.

Jan 1, 1968

By F. R. Hensel

THE absorption of oxygen by molten metals is a quick and convincing method to determine the metallurgical characteristics of various types of furnaces.1 The investigation was restricted to the use of coreless induction furnaces. A major variable in induction furnace practice is the frequency and its influence was studied by comparing melts made in a 5000-cycle and a 60-cycle induction furnace respectively.2 The authors are not aware that such a comparative study has been made before and therefore present this paper in the belief that the results will be of general interest. ANALYTICAL METHODS FOR DETERMINATION OF OXYGEN IN NICKEL An analytical procedure for determining NiO by a quick and simple, laboratory method has been worked out in collaboration with Dr. Herty, of the Pittsburgh Station of the Bureau of Mines. It was found that Dr. Herty's aluminum method as used for the. determination of FeO in iron and steel was very suitable for use with nickel if instead of hydrochloric acid a 10 per cent solution of nitric acid is used for bringing the metal into solution. Essentially this method involves deoxidizing the nickel-oxygen alloy with aluminum (2Al + 3NiO = Al203 + 3Ni) and determining the resulting Al203 by a residue analysis. The original oxygen content can then be calculated from the amount of Al-20,. The method as suggested by Dr. Herty3 is referred to in the present paper as method B. A slight modification of method Bled to the application of method A, a description of which is given below according to F. W. Beiter?:3

Jan 1, 1932

By Rollyn P. Jacobson

THE town of Pacific, in Jefferson County, Mo., is 127 miles west of St. Louis. Since the area lies entirely on the flood plain of a cutoff meander of the Meramac River, it was considered a likely environment for accumulation of commercial quantities of sand and gravel. Excellent transportation facilities are afforded by two major railways to St. Louis, and ample water supply for washing and separation is assured by the proximity of the river. As a large washing and separation plant was planned, the property was evaluated in detail to justify the high initial expenditure. An intensive testing program using both geophysical and drilling methods was designed and carried out. The prospect was surveyed topographically and a 200-ft grid staked on which electrical resistivity depth profiles were observed at 130 points. The Wenner 4-electrode configuration and earth resistivity apparatus" were used. In all but a few cases, the electrode spacing, A, was increased in increments of 11/2 ft to a spread of 30 ft and in increments of 3 ft thereafter. Initial drilling was done with a rig designated as the California Earth Boring Machine, which uses a bucket-shaped bit and produces a hole 3 ft in diam. Because of excessive water conditions and lack of consolidation in the gravel there was considerable loss of hole with this type of equipment. A standard churn drill was employed, therefore, to penetrate to bedrock. Eighteen bucket-drill holes and eight churn-drill holes were drilled at widely scattered locations on the grill. The depth to bedrock and the configuration will not be discussed, as this parameter is not the primary concern. Thickness of overburden overlying the gravel beds or lenses became the important economic criterion of the prospect.** The wide variety and gradational character of the geologic conditions prevailing in this area are illustrated by sample sections on Fig. 2. Depth profiles at stations E-3 and J-7 are very similar in shape and numerical range, but as shown by drilling, they are measures of very different geologic sequences. At 5-7 the gravel is overlain by 15 ft of overburden, but at E-3 bedrock is overlain by about 5 ft of soil and mantle. Stations L-8 and H-18 are representative of areas where gravel lies within 10 ft of surface. In most profiles of this type it was very difficult to locate the resistivity breaks denoting the overburden-gravel interface. In a number of cases, as shown by stations M-4 and H-18, the anomaly produced by the water table or the moisture line often obscured the anomaly due to gravel or was mistaken for it. In any case, the precise determination of depth to gravel was prevented by the gradual transition from sand to sandy gravel to gravel. In spite of these difficulties, errors involved in the interpretation were not greatly out of order. However, results indicated that the prospect was very nearly marginal from an economic point of view, and to justify expenditures for plant facilities a more precise evaluation was undertaken. The most favorable sections of the property were tested with hand augers. The original grid was followed. In all, 46 hand auger holes were drilled to gravel or refusal and the results made available to the writer for further analysis and interpretation. When data for this survey was studied, it immediately became apparent that a very definite correlation existed between the numerical value of the apparent resistivity at some constant depth and the thickness of the overburden. Such a correlation is seldom regarded in interpretation in more than a very qualitative way, except in the various theoretical methods developed by Hummel, Tagg (Ref. 1, pp. 136-139), Roman (Ref. 2, pp. 6-12), Rosenzweig (Ref. 3, pp. 408-417), and Wilcox (Ref. 4, pp. 36-46). Various statistical procedures were used to place this relationship on a quantitative basis. The large amount of drilling information available made such an approach feasible. The thickness of overburden was plotted against the apparent resistivity at a constant depth less than the depth of bedrock for the 65 stations where drilling information was available. A curve of best fit was drawn through these points and the equation of the curve determined. For this relationship the curve was found to be of the form p = b D where p is the apparent resistivity, D the thickness of overburden, and b a constant. The equation is of the power type and plots as a straight line on log-log paper. The statistical validity of this equation was analyzed by computation of a parameter called Pearson's correlation coefficient for several different depths of measurements, see Ref. 5, pp. 196-241. In all but those measurements taken at relatively shallow depths, the correlation as given by this general equation was found to have a high order of validity on the basis of statistical theory.

Jan 1, 1956

By Charles E. Mann, Douglas J. Lootens, Rufino B. Bomasang

INTRODUCTION The economy of the Philippines, like that of many other developing nations, has been severely strained by the rapid escalation of imported crude oil prices over the past decade. In an effort to reduce its dependence on imported crude, significantly increased emphasis, both in the public and private sectors, is being placed on the rapid development of Philippine coal resources. This paper is designed to present an overview of the Philippine coal industry, its historical development, present status, and future potential. COAL RESOURCES AND RESERVES In 1977, a British consulting firm collated all available data on Philippine coal resources and estimated the total coals potential at about 0.9 to 1.4 billion metric tons (mt). In 1981, using more recent data the Philippine Bureau of Energy Development (BED) estimated the potential at 1.7 billion mt. The BED estimated the proven coal reserves at 257 million mt. These coal resources are scattered throughout the major islands comprising the Philippine archipelago. However, about 52 percent of the currently proven reserves are located in the tiny island of Semirara between the islands of Mindoro and Panay. About 25 percent is located in the Cagayan Valley in northeastern Luzon while 13 percent is located in Mindanao. The remaining 10 percent is scattered in the islands of Cebu, Samar, Mindoro, Negros, Polillo, Batan, and Catanduanes. The bulk of Philippine coal is sub-bituminous in rank. Some bituminous coal with coking properties has been reported in Malangas, Zamboanga del Sur in western Mindanao, and in Catanduanes, but the exact tonnages have not been accurately established. It is believed, however, to be at most 5 million tons. A little semi-anthracite coal exists in Malangas with the remaining unmined reserves estimated at a little more than one million tons. Table 1 shows the quality ranges of Philippine coal deposits.. Figure 1 shows the distribution of known Philippine coal resources PHILIPPINE COAL PRODUCTION In 1981, total coal production was 330,720 mt. Though modest by world standards, this was the highest production figure in Philippine coal mining history. This came from 25 mines, mainly small scale underground mines of capacities varying from 10 to 100 tons per day (tpd). The actual production capability was about 800,000 mt in 1981, but the producers had to scale down production to the level of local demand. Even then, some 50,000 tons of coal remained unused by year-end. The 1981 production came from the following areas: Cebu 224,751 mt (68%) Zamboanga del Sur 57,095 mt (17%) Semirara 13,222 mt (4%) Polillo 17,132 mt (5%) Cebu has always been the main source of Philippine coal production. Coal mining has been carried out in Cebu for the last 50 years, although it has been characterized by a very crude mining technology. Due to the limited size of coal deposits and complicated geology, however, Cebu's share of the total national production is expected to go down to only 10 percent by 1985. Except for Semirara's open-pit production, the balance of Philippine coal production comes from underground mines. These underground mines generally use room-and-pillar methods, except for those at Zamboanga del Sur and Polillo which use modified longwall methods patterned after those used in Taiwan. Due to the much higher mining recovery, most underground mines are now planning on switching to longwall. At Semirara, an open pit mine is now being developed for a one million ton per year capacity by 1984, and will then be the largest Philippine coal mine. While present earthmoving work is done with bulldozers, loaders, and trucks, the main coal extraction equipment will be bucket wheel excavators imported from Austria. PRESENT COAL UTILIZATION Existing coal production is sold mainly to coal- fired cement plants and power plants. The balance is sold to a sugar central, a coconut oil mill, a food processing plant, and two plants producing carbide and ferro-silicon alloys.

Jan 1, 1982

By Eduardo Martinez Baca

Although Mexico has always been justly considered by the whole world essentially a mining country, this reputation is due principally to the richness of the deposits which have been worked. In reality, the majority of the States have been little

Jan 1, 1902

By C. E. Wood, E. P. Barrett, T. L. Joseph

The United States Bureau of Mines has been studying the blastfurnace process for about ten years. An experimental furnace was developed by the Burcau in cooperation with the Minnesota School of Mines Experiment Station, University of Minnesota. Many data have been obtained and published.' Royster, Joseph and Kinney §(48) found that the particle size of ore had an important effect upon the blast-furnace process. Kinne(28) stated: Economy in blast-furnace practice depends largely upon efficient gas-solid contact in the shaft of the furnace. If efficient work is not done in the shaft, the hearth and bosh will not function properly. A condition may be readily imagined where the particles of ore in the shaft are so large that the time entailed in the descent of these materials into the bosh is not sufficient to permit proper reduction and preparation prior to the time the ore enters the bosh of the furnace. Another condition may be pictured where the density of theatock column and the flow of stock is such that the ore will take one course and the gas another. Both of these examples will result in insufficient contact between the gas and the ore. Unreduced ore will reach the hearth, and the gas which has not been efficiently oxidized will reach the stock line. The result is the use of an excess of carbon in the smelting process. It is obvious that fine ore particles occurring in the ore as charged, or formed in the furnace due to heat and mechanical action, place a definite limitation upon the efficiency of the operation. There is also an economic loss of fine material as dust. Effect of Size of Material Kinney reported (p. 83(29)) the reduction of iron oxides between planes at three furnaces as given in Table 1. The Chicago furnace was operated on Lake ores. Distribution of gas was not good and much of the charge passed into the hearth before the iron oxide was reduced. The Holt furnace was operated on coarse ore. Distribution of gas was fairly uni-

Jan 1, 1930

By W. J. Carlson, S. M. Parmerter, I. Iwasaki

This article discusses the effect of physical and chemical modifications of starches on the anionic and cationic flotation of silica from oxidized iron ores and magnetite-taconite concentrates. It also deals with the results of the interaction of starch, pH, and calcium ions on the flocculation, clarification, and filtration of iron ore slimes and magnetite-taconite tailings. Starches, particularly when an-ionically modified, were found to be effective depressants in anionic silica flotation. British gums and dextrins were beneficial for oxidized iron ores, but none of the starches or starch derivatives appeared to have any effect on magnetite-taconite concentrates. The flocculation and filtration of iron ore slimes were affected most strongly by the level of starch, to a lesser degree by the pH, and virtually not at all by the level of calcium chloride. The clarification of iron ore slimes was complexly dependent on these three factors. The flocculation of magnetite-taconite tailings depended mainly on the level of starch, whereas their clarification depended on the level of lime. As previously reported in the literature, selective flocculation and partial upgrading of a semitaconite could be readily attained with starch and calcium chloride. A previous article discussed some of the parameters that are important when various corn starches are applied to the soap flotation of activated silica from iron ores and to the flocculation of iron ore slimes.' Methods of solubilizing the starches and the molecular size after mechanical and thermal treatments, as inferred from the viscosity measurements, were shown to influence the adsorption characteristics on iron ores, and the residual concentrations of both calcium ion and starch in the pulp liquor were in direct correlation with the flotation and flocculation behavior.2-4 The present article summarizes the results of more recent tests conducted to ascertain the role of starches and starch derivatives in various phases of iron ore beneficiation. The scope of this investigation has been extended to include not only anionic and cationic flotation, but also the flocculation and filtration of iron oxide slimes, the selective flocculation and partial upgrading of semitaconites, and the flocculation and clarification of magnetite-taconite tailings —all problems that are of vital importance to the iron ore industry of Minnesota. By combining a practical approach with adsorption studies and by using single-mineral systems5 in these research efforts, it is believed that the ultimate goal of developing a suitable modification of starch structure may be realized. The topics covered in this article are limited to the empirical aspects of the research program on the depressant activity of starches and products in the cationic and anionic flotation of silica and of their role in flocculation, water clarification and filtration. ANIONIC SILICA FLOTATION In the soap flotation of activated silica from iron

Jan 1, 1970

By A. D. Hodges

The process to be described, whatever other merits (or demerits) it may have possessed, certainly proved a financial success under the conditions of the locality where it was introduced and where a refining process had been sought previously in vain. I have ventured to bring it to the notice of the Institute in the hope that it may prove of some interest as a solution of a practical problem, such as is often presented to the metallurgist in the remote mining regions of the West. The method was used first at the Lyon Mill at Dayton, Nevada, and has been adopted at other tailings-mills on the Cornstock. These mills treat two classes of tailings: "sand," or; material which has passed previously through the pans of the ore-mills; and " slimes," or the fine clayey material which, coming from the battery, is too light to settle in the tanks inside of the mills but is

Jan 1, 1886

By H. Foster Bain

Probably no more significant change has come into the lives of men in the past two hundred years than their shift from major dependence on plants and animals to major dependence on minerals. From the dawn of history, nay from long before that dawn, food and clothing had been man's main concern. The wandering of the tribes in pastoral ages was in search of grass for their cattle; the patient work of the "man with the hoe" has ever been to supply food for himself and family and if he accomplished so much he had little strength, energy, or ambition for other things. The great civilizations of the past arose in the fertile valleys where food supply was abundant or on shores where by grace of the wind and primitive wooden ships food could, if needed, be imported. Provision for the "seven lean years" by storing the abundance of the seven fat years was long held up as the highest example of statesmanship and the ambitions of the Roman populace did not go beyond bread and circuses, the former the product of a plant and the latter involving essentially contests of men and other animals. Through all those centuries of want, misery, and warfare it was, for example, an axiom that "an army fights oh its belly." Now an army rides to the battle line in trucks; its members stand up and fight with tons and tons of metal and other minerals. Food supply is assumed, and rightly so, for in this modern world of ours shortage of food is chargeable at once to poor organization or deficiency of transport. The areas in which famines occur are those in which the one or the other

Jan 1, 1932

By J. Price Wetherill

The coal-seams that are worked vary from 3 1/2 to 100 feet in thickness, and occur at all angles of inclination, but are never flat for any great extent. They contain coal, slate, and an unsolidified coal, called dirt by the miners, in various proportions, a uniform seam of coal alone being rare. The upper walls are composed of conglomerate, sandstone, or slate; the first two hard and solid in texture, and withstanding the action of the atmosphere and moisture sufficiently well to offer but little trouble to the mining operations; while the latter crumbles rapidly, owing, in part, to the decomposition of iron pyrites which it contains in large quantities, and in part to its own friable character, and requires constant care to avoid accidents to the men working below it, and to prevent its mixing with the coal mined. The floors are composed of slate. As in all mining operations, the general system pursued is to reach with a permanent outlet such a point in the seam as will

By N. A. Ziegler

A CERTAIN amount of interest has been indicated recently in the resistance to oxidation at high temperatures of iron-aluminum alloys (rich in iron). Hautman1 published a paper in. which some interesting results are given. According to his paper, only alloys containing at least 8 per cent aluminum indicate a marked improvement in their resistance to oxidation. At about this aluminum content, however, alloys become brittle, which considerably reduces their commercial value. About two years ago the author, performed a series of experiments, the results of which are presented here. A series of iron-aluminum-carbon alloys was prepared by melting electrolytic iron, aluminum and high-carbon iron alloy in an induction vacuum furnace.2 The list of these alloys is given in Table 1. Each alloy was forged in the ordinary way to

Jan 1, 1932

By F. M. Lyon, F. J. Chernosky

Research efforts have not developed techniques for the complete desulfurization of coal that is needed to reduce air pollution caused by burning coal and to reduce the sulfur in metallurgical coke. Sulfur in coal occurs in three forms and of these, the pyritic sulfur occurs as discrete mineral particles and, at least theoretically, should be subject to physical rejection. Pyrite occurring in hard rock mining is concentrated by froth flotation; therefore, the possibility of removal of pyrite from coal by flotation does exist. With this possibility in mind, the flotation and adsorption characteristics of ore and coal-pyrite were compared while using potassium ethyl xanthate as the collector.

Jan 1, 1973

New York Meets first Wednesday after first Tuesday of each month. DAVID H.-BROWNE, Chairman, JOHN H. JANEWAY, Vice-Chairman. F. E. PIERCE, Secretary, 35 Nassau St., New York, N. Y. P. A. MOSMAN, Treasurer. LEWIS W. FRANCIS. Boston Meets first Monday of each winter month. HENRY L. SMYTH, Chairman. . ALFRED C. LANE, Vice-Chairman. HENRY A. WENTWORTH, Secretary-Treasurer, 60 India St., Boston, Mass. ROBERT H. RICHARDS, ALBERT SAUVEUR. Columbia Holds four sessions during year. Annual meeting in September or October. FRANK A. ROSS, Chairman. RUSH J. WHITE, Vice-Chairman. LYNDON K. ARMSTRONG, Secretary-Treasurer, P O. Drawer 2154, Spokane, Wash. FREDERIC KEFFER, FRANCIS A. THOMSON.

Jan 11, 1915

By Walter B. Devereux

Metallic copper is a product of native metallurgy in various parts of Mexico, and by somewhat varied processes. While recently examining copper mines in the State of Jalisko, I had an opportunity of witnessing Mexican copper smelting by a process which I have not seen described, and which is interesting from the fact, that a fine quality of copper is produced from sulphurous ores in three metallurgical operations, and apparently without excessive loss. The process was carried on in buildings which were part of a plant erected by an American more than twenty-five years ago for the purpose of smelting and working copper. After a few years this man met with accidental death, and the works have been but little used since. Located in the centre of a high range of mountains, far from any town or seaport, and inaccessible except over difficult mule trails, these substantial buildings, filled with furnaces and heavy machinery,

Jan 1, 1883

By G. M. Schwartz, J. N. Gundersen

John W. Gruner (Professor Emeritus, College of Science, Literature, and the Arts, Dept. of Geology, University of Minnesota, Minneapolis) — It is surprising that two men as well acquainted with the taconite rocks of the Mesabi District as Drs. J. N. Gundersen and G. M. Schwartz should have concluded that the taconite of the Eastern Mesabi before the intrusion of the Duluth gabbro consisted largely of quartz and magnetite. These minerals were "locally reconstituted" into "a wide variety of silicate mineral assemblages" by the gabbro. It is well known, of course, that the silicate mineralogy of the Eastern Mesabi ('about 14 miles in length) is quite different from that of the Main Mesabi which is over 60 miles long. The change from one to the other is abrupt and cannot be attributed to any other cause than the thermal effects of the gabbro. Are we to assume or believe that the taconite of the Eastern Mesabi was radically different from that of the Main range before the gabbro metamorphosed it?

Jan 1, 1962

POSITIONS VACANT (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons.) Opening for man as head of laboratory of large brass manufacturing plant in Ohio; must also be competent to manage foundry making brass castings, following practice of malleable iron castings and insulating materials. Good opportunity for right man. No. 36. Professorship in Mining at a Western university; requires man competent to give instruction in ore dressing, in metal and coal mining, and in zinc smelting, and capable of gaining confidence of mining interests. Salary $2,200 to $3,000. No. 37. ENGINEERS AVAILABLE (Under this heading will be published notes sent to the Secretary of - the Institute by members or other persons introduced by members.) Member, graduate engineer, aged 44, with over 20 years' experience in connection with large coal and coke operations in different parts of the country, desires position as general superintendent of large coal company, or will take an interest with the management in a smaller company. No. 206.

Jan 6, 1915

By Nathaniel Arbiter

THE separation of minerals by flotation can be regarded as a rate process, with the extraction of any one mineral determined by its flotation rate, and the grade of concentrate by the relative rates for all the minerals. So regarded, the significant variables for the process are those that control the rates. These variables are of two types, the first describing the ore and its physical and chemical treatment prior to flotation and the second characterizing the separation process in the cells. This paper will examine the variation in rates for a group of separations, will show that a simple rate law appears to govern, and will consider the relation of the control variables to the rates. The use of rate constants for evaluation of performance and efficiency will be discussed.

Jan 9, 1951

[America,-Dear, G. C. Anniston.-Klugh, B. G. Auburn. *Poor, R. S. Bankhead.-Armstrong, W. D. Bessemer.-Creveling, J. G. Lindstrom, W. A. McKenzie, W. C. Mitchell, F. R. Birmingham.-Abbott, C. E. Armstrong, G. R. Austin, W. W., Jr. Ball, T. L. Beard, A. H. Benjamin, F. S. Blackburn, E. C. Blair, A. J. Blair, C. S. Blair. H. W.]

Jan 1, 1946

By J. P. Matoney, E. J. Sandy, D. A. Dahlstorm

INTRODUCTION Before an understandable discussion concerning coal dewatering processes can be initiated, it is necessary to define some terms of usage. The many different meanings and interpretations of terms preclude development of standard definitions so the terms defined in this chapter should be regarded primarily as working terms intended to facilitate communication.

Jan 1, 1979

By L. G. Jones

An approximate method of calculation is developed in this paper which allows duplication of radial unsteady-state gas flow computer results where Darcy's law applies, such as those reported by Aronofsky and Jenkins and Bruce, Peaceman, Rachford, and Rice. Moreover, the new calculation method can be used to obtain results for radial unsteady-state gas flow obeying the quadratic flow law proposed by Duwez and Green. Means are discussed for predicting well behavior at single or superimposed flow rates in finite or infinite reservoirs, determining reservoir rock properties from well-test data, reproducing and interpreting back-pressure test data, and determining the radial extent and reserves of gas reservoirs from well-test data. Example calculations are presented for gas flow following both Darcy's law and the quadratic flow law. INTRODUCTION Since the publishing of U. S. Bureau of Mines Monograph 7,1 most gas-well testing methods have been based on the equation q = y (pl2 - pw2)a, where q = production rate, pl and pw, are formation pressure and sandface pressure, respectively, and y and a are constants to be obtained from test data. These methods, used for predicting both deliverability and "open-flow" capacity of gas wells, have been useful and accurate in many cases but unsatisfactory in others. Even at best, however, they do not supply information about the formation or lead to an understanding of nonsteady-state gas flow in porous media. Many theoretically based studies2-4 of gas flow obeying Darcy's law have been made.' Since the partial differential equations which result from combining Darcy's flow law with the continuity equation are nonlinear, most of the published research consists of either numerical solutions or analytical solutions for linear approximating equations. Such solutions have been of limited value in field work due to their unhandy form and their failure to correlate most field data. There is evidence5,6 which indicates that Darcy's law is inadequate to describe gas flow at some flow rates of practical interest. A quadratic flow law: which reduces to Darcy's law at low rates, is more successful in accounting for experimentally observed behavior. This flow law has been applied successfully to a few hypothetical reservoir cases in work which has recently been published.10 However, these numerical solutions of the equations involved have been successful only on a special analog computer. Routine applications to field cases would be awkward and have not been attempted. The present paper describes an approximate method for computing nonsteady-state gas flow solutions which has been completely successful in predicting the results for both Darcy flow and quadratic flow obtained by elaborate numerical methods. The new calculation method allows determination of the observable variables in gas-well testing at constant rates. It is similar to the scheme of using a succession of steady states suggested by Muskat7 in that it makes use of steady-state and material-balance equations. It also is similar to the work of Aronofsky and Jenkins2 in that the new method includes Aronofsky and Jenkins' stabilized flow equation as a special case. It improves upon both of these calculation schemes in that it accurately describes all portions of reservoir history and suggests means of determining reservoir rock properties from well-test data. This paper deals only with production from a reservoir, in which case the rate is defined as being negative. The reservoir studied here is a homogeneous, disk-shaped porous body of uniform thickness, with all boundaries sealed except the inner radial boundary of the well.