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By H. D. Outmans

The mechanics of filtration are described by a theoretical-empirical nonlinear diffusion equation which, under certain circumstances, may,be linearized and then solved explicitly. For filtration under static conditions linearization leads to a boundary value problem analogous to a heat flow problem with a known explicit solution. The corresponding solution for static filtration is compared with published experimental data. Under dynamic conditions filtration takes place in three successive stages. During each of these the rate of filtration and/or the thickness of the filter cake are different functions of the filtration time. The proposed mechanism explains the observed high resistance of dynamically deposited filter cakes against erosion and also the connection between filtration rate and viscosity of the drilling fluid. Several of the quantities governing dynamic filtration have no counterpart in the static filtration mechanism. The static filtration rate is, therefore, not a reliable measure for the dynamic rate and vice versa. INTRODUCTION Filtration under simulated borehole conditions, i.e.. either from a static suspension or from a suspension flowing parallel to the filter cake (dynamic filtration), has been the subject of several laboratory studies.1-7 This experimental and theoretical work showed that many aspects of the filtration mechanism cannot be explained by an elementary filtration theory based on the assumption that the filter cake is incompressible. For a more satisfactory theory compressibility should be taken into account. This has been done. at least to some extent, in the filtration theory developed for the chemical industry. Surveying the literature (see Ref. 8 for a bibliography) it becomes apparent that, although several properties of filter cakes deposited from many different suspensions have been measured, including compressibility, the filtration equations are essentially empirical in nature. No attempt has been made, for instance, to develop filtration theory along the lines of consolidation theory.12 This theory, upon which a highly successful development in soil mechanics rests, would appear to be an excellent starting point for a filtration theory since the compressibility concept is an essential part of it. As we will use this theory in the following development it is well to state the four assumptions on which it is based: 1. The fluid flow through a compressible porous medium is governed by Darcy's law. 2. The rate of change in fluid content of an element of the porous medium is proportional to the rate of change of solid pressure between the particles. 3. The solid particles are incompressible within the range of pressures considered. 4. The total pressure on a surface normal to the line of flow is equal to the sum of the fluid pressure and the pressure between the particles (solid pressure) at that surface. To calculate the rate of filtration and other quantities of interest it is necessary to know the filter cake compressibility and the permeability as a function of the solid pressure. It has not been possible to calculate these functions from theoretical considerations and they will therefore be introduced in this paper as empirical expressions. Both are determined in a compression cell where the cake is subjected to a mechanical load. Permeability and compressibility are measured after the solid pressure has stabilized, i.e., after the excess fluid pressure has been dissipated and the uniform pressure is transmitted entirely by the solids. The permeability and compressibility thus determined are not the same as during filtration in the borehole, under either static or dynamic conditions, because then, due to frictional drag, the solid pressure and hence also the permeability and compressibility vary along a line normal to the direction of the mean flow and can only be defined locally. DERIVATION OF THE FILTRATION EQUATION FOR COMPRESSIBLE FILTER CAKES As the filter cake in the borehole is thin compared to the radius of the hole the filtration may be considered as linear. Taking the x-axis normal to the wall, with its origin at the formation, we have, according to Darcy's law,

By E. J. Harris

Mathematical solutions to complex mine ventilation problems are possible, but often the airway network is so complex that the mathematical solution becomes tedious and impractical. A fluid network analyzer, designed and built for analyzing mine ventilation problems has been in service at the Bureau of Mines' Pittsburgh station for approximately nine years. Using this analogue as a model, the mine ventilation network is simulated electrically by a combination of series and parallel circruits laid out to conform with actual mine airways. A tungsten filament lamp, referred to as a Fluistor, is used to simulate mine airway resistance. With the analogue ventilation model established, voltages of the proper amplitude to represent ventilating pressures are impressed across the circuit at points where mine fans and airshafts are located. Comparison of mathematical solutions of complex systems against analogue results showed a maximum variance of 3% for pressures and 2% for quantities. An electrical fluid network analyzer, designed and built especially for analyzing mine ventilation distribution problems, has been in service at the Bureau of Mines, Pittsburgh, for approximately nine years. It is a nonlinear, low voltage, fluid network analyzer of the type developed by the late Malcolm S. McIlroy, Professor of Electrical Engineering, Cornell University, who cooperated with G. E. McElroy, of the Bureau of Mines, in adapting the instrument to mine ventilation systems. Several modifications have been made since the original installation, but a considerable part of this paper is drawn from G. E. McElroy's original description of the analogue.' The analysis of water or gas distribution systems2,3 led to the development of this type of network analyzer. Several similar units are now employed by utility companies for this purpose; however, the Bureau of Mines unit is the only one designed specifically for mine airflow problems. Other airflow analogues employing a similar principle have been used at the Central Research Station of the Netherlands State Mines,4 in England,5 and in South Africa.6 Information on these devices indicated they were somewhat inflexible because commercial lamps with a sufficient range of resistance are difficult to obtain. Computers for mine ventilation analysis have been developed in Germany which instead of lamps use a variable resistance to adjust for turbulent flow laws. These units are expensive, but excellent results have been reported in their application. THE ANALYZER Theory of Application: As airflow generally follows the law of turbulent fluid flow, resistance to flow is nonlinear; consequently, the problem has been to find a nonlinear resistance element of suitable range that can be used for electrically simulated airflow. Tungsten filament lamps operated on alternating or direct current approximate the square-law resistance characteristics of mine airflow over a large range below maximum or rated voltage; that is, the voltage drop varies approximately as the square of the current. Consequently, the heart of the network analyzer is a nonlinear resistor known as a Fluistor, which is simply a custom-made low voltage, tungsten filament lamp that is available in a progressive series of relative resistance values ranging from 0.05 to 500 in nominal 5% steps. However, variations in manufacturing large groups result in differences of 1 to 3%, but series arrangements required for high-loss branches can be matched within about 1%. Utilizing a combination of Fluistors and load circuits, the mine ventilation system is duplicated electrically. Intake load circuits are connected from power intake to primary points of the circuit network; segments of unregulated flow along intakes and returns are represented by Fluistors, regulated splits and leakage paths are represented by load circuits and Fluistors of proper capacity; and mine exhausts are connected to ground from the last point of the network to complete the circuit. For the special purpose of representing booster fans or natural draft conditions, boosters or separate source circuits are provided that can be inserted between any two points of a network to increase voltage to the required value. Physical Layout: The analyzer consists of three 42

Jan 1, 1963

By Charles H. Thurman

The data given herein were first included in a paper read before San Francisco Section, A.I.M.E., in October 1940, and are applicable to conditions existing until the gold-dredging industry was temporarily suspended by Order L-208 of the War Production Board in the fall of 1942. There is no doubt that gold dredging will be resumed at some future time, and on a scale equivalent to that of the recent past, but the cost data given herein will be affected to some extent by conditions existing at that time, and by labor rates and prices for materials then prevailing. Dragline vs. Bucket-line Dragline dredges should not be considered for mining large areas of low-grade placer gravel. In such deposits a dragline operator with a 5-cu. yd. dragline would be doing well to maintain an operating cost of 6¢ per cu. yd., while a bucket-line dredge with buckets no smaller than 7 cu. ft. each could be operated for less than 4¢ per cu. yd. By operating costs, I mean only field charges such as direct operating and overhead, which includes pay roll, power or fuel, repairs and maintenance, insurance, land clearing and general expenses, but not including such items as prospecting, depletion, depreciation of equipment, State Franchise Tax, or Federal Income Tax. It is not to be inferred that a dragline dredge cannot make a profit in small low-grade deposits, where the extent of a given property is too small to justify the use of the more costly bucket-line dredge. Consider small deposits of 106 gravel. It is obvious that a deposit of 5,000,000 cu. yd. of such gravel could not be mined profitably with a new 7-cu. ft, bucket-line dredge, costing upward of $250,000, and in operation costs at 4¢ per cu. yd., paying for land or royalties out of earnings; nor could a new combination 5-cu. yd. dragline and washing plant, worth upward of $125,000 and working at 6¢ Per cu. yd., make a profit. These comparisons are made because the hourly capacity of both types of dredges is nearly the same. The bucket-line dredge averages 93 per cent operating time in 24 hr., as against about 80 per cent or less for the dragline dredge. These Percentages of operating time are important factors in making a comparison of this kind- The bucket-line dredge has greater efficiency in cleaning soft bedrock, usually characteristic of dredging deposits, and a 7-cu. ft. bucket-line dredge can be efficient to a total digging depth of 80 ft- (65 ft. below water, 15 ft. above). A 5-cu. Yd. dragline dredge is limited to about 30 ft. of efficient digging depth, 5 ft. of which could be above water. In small areas of gravel not over 30 ft. deep, a 5-cu. yd. dragline dredge could make a profit where a bucket-line dredge could not do so. As an example: compare the dredging of 3,000,000 cu. yd. of 10 gravel 28 ft. deep with bucket line, costin 4¢ Per cu. yd., and with a 5-cu. yd. dragline dredge operating at 6¢ Per cu. yd. Because of small yardage, new equipment is not warranted, therefore we can assume that the dredges of both types are used equip-ment, fully depreciated. Dismantling, mov-

Jan 1, 1946

By P. B. Leavenworth

Twenty-six fields were found in the Texas Gulf Coast in 1940 as compared to 17 fields in 1939. Of these, 14 were oil fields and 12 were gas and distillate. About 150 wells were drilling at the end of the year. Production for the year 1940 amounted to 104,127,247 bbl. as compared to 100,-253,937 bbl. for 1939. Considerable wildcatting for Wilcox production featured the exploration, but discoveries were few and the type of fields found mainly gas and distillate. On the whole, the program was discouraging. New Fields Alta Lomu. Galveston County.—The Alta Loma field was discovered on May 20, 1940, by the Stanolind Oil and Gas Company's No. I John A. Hulen, which blew out at a depth of 9166 it. and ran wild for several days, with an estimated production of 400 bbl. per hour of 36" gravity oil from a sand in the top of the Frio. Water soon appeared but the well produced more than I3o,ooo bbl. of oil between May 20 and June 10, together with a large amount of salt water. Later the well was killed and recompleted on Nov. 23, for 276 bbl. of 34" gravity oil per day. Probably this was the most sensational discovery of the year, although development to the end of the year was disappointing. The discovery was the result of reflection seismograph work of the Stano-End Oil and Gas Co., the principal leaseholders. Bailey's Prairie, Brazoria County.— Glenn H. McCarthy9s No. I W. B. Munson was completed in a lower Frio sand from perforations 11,345 to II,349 ft. for 8 bbl. of fluid (50 per cent black oil, 27" gravity, and 50 per cent B. S. and W.) on Sept. 24, 1940. It was finally recompleted as a gas well from perforations 11,631 to 11,651 ft., on Oct. 9, 1940. The well had been drilled to a total depth of 11,860 ft. This well produced for only a short time and the area is at present inactive. Blessing, Matagorda County.—The Texas Company's No. I A. B. Pierce was completed from a Frio sand from 8265 to 8300 ft. on July 8, 1940, for an initial production of 29 bbl. of distillate, I 1/2 million cu. ft. of gas. One other gas and distillate well was completed in 1940. Borden, Wharlon County.—J. F. Hutch-ins' No. 2 A. P. Borden Estate was completed on Feb. 11, 1940, for 108 bbl. of 35,6° gravity oil, from a Frio sand at 4758 to 4771 ft. This is the second well drilled in the area by Hutchins. Two other wells in 1940 were failures and there was no activity at the end of the year. Dyersdale, Harris County.-The Dyers-dale field was opened by the completion, on Sept. 15, 1940, of H. C. Cockburn's No. I G. Burkitt from a sand in the top of the Frio, through perforations from 4067-4072 ft., for 240 bbl. of low-gravity oil. By the end of the year the field had been fairly well outlined and did not appear to be a major discovery. Duck Bay, Calhoun County.—Coronado Oil Company's No. I Welder, alter having drilled to 10,002 ft., perforated casing from 5654 1/2 to 5659 it. and was completed for 60 bbl. of 36.8° gravity oil On July 27, 1940, from a Miocene sand.

Jan 1, 1941

By P. B. Leavenworth

Twenty-six fields were found in the Texas Gulf Coast in 1940 as compared to 17 fields in 1939. Of these, 14 were oil fields and 12 were gas and distillate. About 150 wells were drilling at the end of the year. Production for the year 1940 amounted to 104,127,247 bbl. as compared to 100,-253,937 bbl. for 1939. Considerable wildcatting for Wilcox production featured the exploration, but discoveries were few and the type of fields found mainly gas and distillate. On the whole, the program was discouraging. New Fields Alta Lomu. Galveston County.—The Alta Loma field was discovered on May 20, 1940, by the Stanolind Oil and Gas Company's No. I John A. Hulen, which blew out at a depth of 9166 it. and ran wild for several days, with an estimated production of 400 bbl. per hour of 36" gravity oil from a sand in the top of the Frio. Water soon appeared but the well produced more than I3o,ooo bbl. of oil between May 20 and June 10, together with a large amount of salt water. Later the well was killed and recompleted on Nov. 23, for 276 bbl. of 34" gravity oil per day. Probably this was the most sensational discovery of the year, although development to the end of the year was disappointing. The discovery was the result of reflection seismograph work of the Stano-End Oil and Gas Co., the principal leaseholders. Bailey's Prairie, Brazoria County.— Glenn H. McCarthy9s No. I W. B. Munson was completed in a lower Frio sand from perforations 11,345 to II,349 ft. for 8 bbl. of fluid (50 per cent black oil, 27" gravity, and 50 per cent B. S. and W.) on Sept. 24, 1940. It was finally recompleted as a gas well from perforations 11,631 to 11,651 ft., on Oct. 9, 1940. The well had been drilled to a total depth of 11,860 ft. This well produced for only a short time and the area is at present inactive. Blessing, Matagorda County.—The Texas Company's No. I A. B. Pierce was completed from a Frio sand from 8265 to 8300 ft. on July 8, 1940, for an initial production of 29 bbl. of distillate, I 1/2 million cu. ft. of gas. One other gas and distillate well was completed in 1940. Borden, Wharlon County.—J. F. Hutch-ins' No. 2 A. P. Borden Estate was completed on Feb. 11, 1940, for 108 bbl. of 35,6° gravity oil, from a Frio sand at 4758 to 4771 ft. This is the second well drilled in the area by Hutchins. Two other wells in 1940 were failures and there was no activity at the end of the year. Dyersdale, Harris County.-The Dyers-dale field was opened by the completion, on Sept. 15, 1940, of H. C. Cockburn's No. I G. Burkitt from a sand in the top of the Frio, through perforations from 4067-4072 ft., for 240 bbl. of low-gravity oil. By the end of the year the field had been fairly well outlined and did not appear to be a major discovery. Duck Bay, Calhoun County.—Coronado Oil Company's No. I Welder, alter having drilled to 10,002 ft., perforated casing from 5654 1/2 to 5659 it. and was completed for 60 bbl. of 36.8° gravity oil On July 27, 1940, from a Miocene sand.

Jan 1, 1941

By R. L. Fleischer, R. S. Davis

BICRYSTAL specimens grown from the melt have been used extensively for investigations of the influence of grain boundaries on plastic deformation. The bicrystals are usually of predetermined orientation prepared by seeded growth from the melt in milled graphite boats. This technique has been described in detail by Chalmers.' Since the direction that the grain boundary follows during growth is affected by both thermal conditions and crystallography, a difficulty arises in maintaining the grain boundary position constant along the length of the specimen. This problem is particularly

Jan 1, 1960

R. W. Raymond, New Pork, N. Y.:—I think Mr. Bache has put his finger on the chief source of the danger of dust-, or gas-and-dust, explosions in collieries. 1 mean the persistent determination of the miners' unions to increase their weekly wages by the excessive use of explosives. This would not be feasible if coal-miners were paid by the day; but this form of payment is, for many reasons, not economically practicable; and the universal practice is to pay for the winning of coal according to the quantity produced. If the miner, by using a large amount of powder, can throw down a large amount of coal without corresponding labor on his own part in undercutting and drilling, he will receive more money for less work, provided he is paid for everything—merchantable coal, worth-less dust, slate, and " bone "—resulting from such a method. My attention was called to this matter many years ago by an admirable report of Prof. W. B. Potter, a past- President of the Institute, on the conditions obtaining in this respect in the Illinois coal-field. It was made very clear in that report that considerations of danger to workmen or loyalty to employers could not be relied upon to prevent miners from employing this perilous and wasteful method of increasing their own immediate receipts. So far as I know, only three remedies have been attempted, namely: the enforcement of discipline as to the methods of mining; the refusal to pay for dust, etc., produced by the miners'methods; and restriction upon the use of explosives, effected by requiring the miner to purchase them from the employer, at a price so high as to make it unprofitable for him to use them in excess. All of these attempted remedies have encountered the bitter opposition of the miners' unions. The enforcement of discipline has become almost impossible, if discipline be (as it should be) understood to involve punishment for the violation of rules when no disaster has followed. I

Jan 1, 1910

` LAWRENCE ADDICKS, New York, N. Y.-We have really two competitive processes for the production of electrolytic zinc. In the process used at Great Falls, the ore is roasted and the calcines leached, leaving a residue which has to be smelted; in the other method, the ore is burned, the zinc and lead fumed off, and the condensed fumes are leached. I do not think that we can yet come to any decision as to which is the better way to attack the problem. Of course if we roast first and then leach, various substances remain in the calcines which may consume sulphuric acid; whereas if we do the burning first, we obtain simply the zinc and lead oxides, with considerable sulphate, in the fume, and there is no shortage of acid. It also depends partly on the complexity of the ore. The one that Mr. Hall is treating and the ore they are treating at Great Falls are not quite alike, but I think they are sufficiently similar to make a comparison of the two methods, working in competition, on different parts of the country, very interesting. C. E. SCHWARTZ, Miami, Okla.-Mr. Hall states that the Joplin conditions are not suitable for the manufacture of electrolytic zinc. When we speak of Joplin ore in general, we consider, of course, a 60-per cent: concentrate with comparatively low iron, but if a low-grade concentrate could be made from tailings and so-called chats, then the problem would be quite different. A Joplin ore is comparatively simple to treat electrolytically, and I believe the electrolytic process would open a field for the treatment of such ores as would not be ordinarily smeltable; that is,

Jan 1, 1918

By HOWARD I. YOUNG

F. W. SPERR, Houghton, Mich.-Why does 10 to 20 per cent. of the ore formation have to he lost? It is not clear to me why it should not all be taken out, from the conditions as I saw them underground this afternoon. H. I. YOUNG.-The grade of our ore is so low that we cannot stand the expense of timbering to support the roof, which, in a sheet-ground mine, would be from 25 to 50 per cent. of our total mining cost at present. After the orebody is mined out, we can often recover 10 to 20 per cent. of the material that is left. F. W. SPERR.-I think it should be a very simple mining engineering problem to mine all of that mineral without the use of a stick of timber. Similar work has been done in the mines of Grand Rapids Plaster Co. The usual operation in deposits of this kind is to open up and excavate as far as the roof will stand; when it caves, start in and dig somewhere else. But in the case I referred to they learned that by working the ground more systematically and leaving in a sufficient amount of pillar, they could later draw those pillars and get them all, and avoid uncon¬trolled breakages which would be likely to occur if they tried to hold up the overburden permanently. From the point of view of safety and also from the financial point of view, I contend that it is better to keep the caving under control and make it do what you want it to do, rather than to take out what you can conveniently for the time being and after a while be compelled to let the overburden do what it pleases.

Jan 1, 1918

By J. T. Burwell, J. Wulff

As is well known, the alloys of iron containing 18 ± per cent chromium, 8* per cent nickel and less than 1.2 per cent carbon exhibit the same allotropic modifications as iron. The face-centered cubic or gamma phase is stable at high temperatures and the body-centered cubic or alpha ferrite is presumably stable at room temperature. The transformation from the gamma phase to the alpha phase in alloys of the above composition (18-8 or stainless steel) is sluggish; even moderately rapid cooling permits the retention of the gamma phase. Cold-work, however, causes the transformation from gamma to alpha to occur at room temperatures. It is difficult, nevertheless, to induce complete transformation regardless of the method of cold-working. Since metallographic polishing is very effective in transforming the surface austenite to ferrite, as indicated by the magnetic studies of Buehl and Wulff,1 it was decided to investigate the phenomenon by electron diffraction methods. Apparatus The apparatus used (Fig. 1) was a hot-filament type employing movable slits, similar to that described by Germer.2 The sample-to-photographic plate distance was 69 cm. and the accelerating voltage 30 kv. Since electrons do not in general follow geometrical paths, it is necessary that either the electron source or the sample be movable in a plane normal to the beam. In this case the sample is fixed and the electron source is movable. The source is adjusted until the shadow of the sample appears in the brightest part of the beam as viewed on the fluorescent screen, then the slits composing the two pinholes are inoved into position one by one. The system is evacuated by means of a mercury diffusion pump backed up with a Cenco Hypervac oil pump. Pressures lower than 10- mm. of Hg are read on a calibrated ionization gauge.

Jan 1, 1939

By J. T. Burwell, J. Wulff

As is well known, the alloys of iron containing 18 ± per cent chromium, 8* per cent nickel and less than 1.2 per cent carbon exhibit the same allotropic modifications as iron. The face-centered cubic or gamma phase is stable at high temperatures and the body-centered cubic or alpha ferrite is presumably stable at room temperature. The transformation from the gamma phase to the alpha phase in alloys of the above composition (18-8 or stainless steel) is sluggish; even moderately rapid cooling permits the retention of the gamma phase. Cold-work, however, causes the transformation from gamma to alpha to occur at room temperatures. It is difficult, nevertheless, to induce complete transformation regardless of the method of cold-working. Since metallographic polishing is very effective in transforming the surface austenite to ferrite, as indicated by the magnetic studies of Buehl and Wulff,1 it was decided to investigate the phenomenon by electron diffraction methods. Apparatus The apparatus used (Fig. 1) was a hot-filament type employing movable slits, similar to that described by Germer.2 The sample-to-photographic plate distance was 69 cm. and the accelerating voltage 30 kv. Since electrons do not in general follow geometrical paths, it is necessary that either the electron source or the sample be movable in a plane normal to the beam. In this case the sample is fixed and the electron source is movable. The source is adjusted until the shadow of the sample appears in the brightest part of the beam as viewed on the fluorescent screen, then the slits composing the two pinholes are inoved into position one by one. The system is evacuated by means of a mercury diffusion pump backed up with a Cenco Hypervac oil pump. Pressures lower than 10- mm. of Hg are read on a calibrated ionization gauge.

Jan 1, 1939

By W. R. Bean

Probably few, if any, of the many serious problems confronting malleable foundries have been more difficult of solution than the question as to why malleable that is ductile, black in fracture, and normal in all respects before galvanizing should, by that process, be rendered brittle, brilliantly crystalline or "white" in fracture, and of low resistance to shock. So far as we are aware, the technical literature contains no data or discussions on this subject, except two referencesl,2 of a general character. It is apparently a question that every one concerned, producer and consumer alike, has been willing to evade as far as possible. Various theories as to the cause of the deterioration have been given but such checking of these theories as we have done indicates that there was no sound basis for most of them. This work on the galvanizing of malleable was first undertaken in 1916, and has continued until the present time. We now feel that for all practical purposes we have reached a solution and are glad to be able to offer it in a form that can be readily applied to production processes. It is impossible to give here a detailed account of the early work done on this problem. A great number of tests were instituted and an enor-

Jan 1, 1923

By W. R. Bean

Probably few, if any, of the many serious problems confronting malleable foundries have been more difficult of solution than the question as to why malleable that is ductile, black in fracture, and normal in all respects before galvanizing should, by that process, be rendered brittle, brilliantly crystalline or "white" in fracture, and of low resistance to shock. So far as we are aware, the technical literature contains no data or discussions on this subject, except two referencesl,2 of a general character. It is apparently a question that every one concerned, producer and consumer alike, has been willing to evade as far as possible. Various theories as to the cause of the deterioration have been given but such checking of these theories as we have done indicates that there was no sound basis for most of them. This work on the galvanizing of malleable was first undertaken in 1916, and has continued until the present time. We now feel that for all practical purposes we have reached a solution and are glad to be able to offer it in a form that can be readily applied to production processes. It is impossible to give here a detailed account of the early work done on this problem. A great number of tests were instituted and an enor-

Jan 1, 1923

By William P. Blake

As the storage of water for agricultural and mining purposes in the arid regions of the West is now receiving much attention by the people and their representatives, some facts coucerning the greatest pioneer enterprise for the purpose should appear on our records. I refer to the dam and reservoir at Walnut Grove, in Yavapai county, Arizona Territory, which was finished in the winter of 1887, and is known as the Walnut Grove Dam, It is not my intention at this time to give a full description of

Jan 1, 1889

By D. W. Peaceman

In previous papers by this author on numerical calculations of multidimensional miscible displacement, some simplifying assumptions were made in writing the dispersion term of the differential equation. It was assumed that the flow vectors were essentially parallel to the x-axis. However, in most multidimensional miscible displacements, the flow vectors are not so simply oriented with respect to the coordinate axes. This paper derives the correct dispersion term /or the more general case; gives a difference approximation /or the dispersion tern; and derives the stability criterion for the corresponding explicit difference eguation.

Jan 1, 1967

By R. B. Sosman

INTRODUCTION WE have shown in the preceding paper that practically all natural oxides of iron contain a determinable percentage of ferrous iron, and in many cases the percentage approaches that in magnetite itself. Some of these oxides are true homogeneous solid solutions. Others are not homogeneous, and can be separated magnetically into fractions. The nature and cause of this inhomogeneity in certain special cases form the subject of the present paper. MAGNETIC FRACTIONATION OF OXIDES OF IRON The magnetic fractionation of a sample of oxide can be conveniently carried out by powdering the material very fine, and exposing it at various distances from the poles of an electromagnet. The magnet that we used was specially designed 1 to give a strong field together with a steep gradient outside of the poles. It is set in a frame, with the pole pieces directed downward. A glass plate can be adjusted at various distances beneath the poles. If the fine iron oxide powder is placed just beneath the glass plate, successive portions of the powder are picked up by the magnetic attraction and are caught against the glass plate, the most magnetic portions being taken up at the greatest distance from the poles. Some natural oxides can thus be separated into several-fractious of different magnetic susceptibilities. Among other natural iron oxides, we examined the powder obtained by crushing some crystals of hematite from Elba.2 We found that

Jan 6, 1917

By H. W. McCue, Henry Rogatz

Oil.—During the year 1939, there were 365 oil wells drilled in the Texas Panhandle, with a total daily initial production of 130,968 bb1.— that is, 69 fewer oil wells drilled than in the previous year, with a decrease. in total daily initial production of 61,738 bbl. The total daily potential of the field on Dec. 5, 1939, as determined by the Texas Railroad Commission, was 1,344,677 bbl., an increase of 94,032 bbl. over the previous year. On Dee. 5, 1939, a daily allowable of 130,527 bbl., which was an

Jan 1, 1940

By Frank Firmstone

The material described below was made at Furnace No. 2, Longdale, Va., Oct. 28, 1907, during a sudden derangement of working, in the course of which the furnace became entirely bridged over and for some time no solid material whatever descended into the hearth. This caused the hearth to become so completely emptied that, at the tuyere-level, a pricker put in at one tuyere could be seen by looking in at the opposite one. The tap-hole was opened and the iron got out with some difficulty. It ran sluggishly, throwing many sparks, but was not

Jan 1, 1909

By Henry Rogatz, H. W. McCue

Oil.—During the year 1939, there were 365 oil wells drilled in the Texas Panhandle, with a total daily initial production of 130,968 bb1.— that is, 69 fewer oil wells drilled than in the previous year, with a decrease. in total daily initial production of 61,738 bbl. The total daily potential of the field on Dec. 5, 1939, as determined by the Texas Railroad Commission, was 1,344,677 bbl., an increase of 94,032 bbl. over the previous year. On Dee. 5, 1939, a daily allowable of 130,527 bbl., which was an

Jan 1, 1940

By H. Sevim, T. M. Yegulalp

This paper summarizes recent developments in modeling of underground coal slurry haulage networks to determine optimum design and operating parameters. The model presented is based on a stochastic dynamic program¬ming formulation. It is applicable in any typical room-and-pillar or longwall mining configuration commonly practiced in the US. The formulation and structure of the model is general enough to handle design problems involving more than one face and mining method. Given the stochastic operating characteristics and a system layout, the model can be used to determine the equipment configuration and operating regimes that minimize the overall unit cost of coal haulage.

Jan 1, 1985