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By J. B. Umpleby

The subject of reservoir energy and its efficient utilization has been well explored in many papers. The present effort, therefore, is limited to a summary of existing information combined with an emphasis of the probability that the relative importance of controlling factors will change with advancing knowledge. Consequently the necessity for flexibility in laws and regulations, inherent in the problem, is emphasized. Definitions Many terms have been widely used in the literature without having been specifically defined. For example, confusion exists in the use of ((reservoir energy" and "gas energy." The latter is much more limited in meaning than the former. Other terms have been variously used. Consequently, I shall preface my remarks with definitions of a few of the more pertinent terms. Reservoir energy is that force or forces, active or potential, that is native to the reservoir and has the power to move oil through the reservoir rock. The energy may result from expanding gas, from hydrostatic head, from the weight of overburden, or from any other source. Gas energy is the expansive power of gas when pressure is reduced. It is one type of reservoir energy. An oil reservoir is that part of a geologic formation or formations in which oil occurs in commercial quantities wholly surrounded by nonproductive rock. The essence of this definition is effective separation rather than remoteness and under it oil reservoirs may be superimposed in the same oil pool. Conservation of reservoir energy means primarily its maximum use in the production of oil. Unit operation is a plan of development and production, which embraces an entire oil reservoir under a unity of engineering control. It is distinct from unitization, which has to do with arrangements of organization and equities to make unit operation possible in areas of divided ownership.

Jan 1, 1934

By Daniel R. Hull

IN 1026 Genders' reviewed the existing theories of this subject and stated his views in support of the gas-pressure theory. Again, in 1937, the subject was thoroughly reviewed by N. B. Vaughan,3 and by Phillips and Brick,2 so that no resume is called for here. The purpose of this paper is to describe certain observations made in the course of mill work, and to point out that they mostly tend to confirm the gas theory of Genders. VAPOR SEGREGATION There is, however, one type of inverse segregation that can be accounted for by considering the volatility of one of the constituents of an alloy. The most familiar case is ordinary brass, which is subject to a zinc enrichment of a few tenths of a per cent at the surface of a chill casting. This has been noted in 70-30 brass by Genders, and a typical example of it is given in Table I, which represents a [ ] cylindrical billet 7 in. in diameter by 5; in. long. After lathe-turning 1/32 in. from the surface, the remaining distance to the center was sampled at six equally spaced intervals. The lead, which is essentially the same throughout, will be mentioned later. Consider a brass-mill mold, either round or rectangular in cross section, standing several feet high. It may require a minute or two for pouring. Before it is full, the metal in the lower end has partly solidified and contracted somewhat away from the mold. The initial shell of solidification follows not far behind the top of the column, even if the central portion is liquid for a long way down. There is, then, a space between metal and mold that is filled with zinc vapor. The vapor has no exit, because the liquid at the top of the rising column is not only in contact with the mold but keeps up a fresh supply of zinc vapor, which has, perhaps, already begun to condense in the lower portion. The cycle is short. Within a minute or two after the mold is full the bar has cooled enough to condense all the zinc. Some of it may condense on the mold; it might be expected that most of it would condense there, but the mold at that time is well coated with a velvety carbon residue from the oil dressing, overlain by fluffy zinc oxide that commenced covering the inside of the mold as soon as pouring began. The clean skin of the freshly cast brass offers a preferred surface for condensation. Reabsorption is quick and inevitable. A simple experiment indicates that a surprisingly large quantity of zinc vapor is trapped in the space between mold and

Jan 1, 1941

By Daniel R. Hull

In 1926 Gendersl reviewed the existing theories of this subject and stated his views in support of the gas-pressure theory. Again, in 1937, the subject was thoroughly reviewed by N. B. Vaughan3 and by Phillips and Brick,2 so that no résumé is called for here. The purpose of this paper is to describe certain observations made in the course of mill work, and to point out that they mostly tend to confirm the gas theory of Genders. Vapor Segregation There is, however, one type of inverse segregation that can be accounted for by considering the volatility of one of the constituents of an alloy. The most familiar case is ordinary brass, which is subject to a zinc enrichment of a few tenths of a per cent at the surface of a chill casting. This has been noted in 70-30 brass by Genders, and a typical example of it is given in Table 1, which represents a cylindrical billet 7 in. in diameter by 55 in. long. After lathe-turning 1/32 in. from the surface, the remaining distance to the center was sampled at six equally spaced intervals. the lead, which is essentially the same throughout, will be mentioned later. Consider a brass-mill mold, either round or rectangular in cross section, standing several feet high. It may require a minute or two for pouring. Before it is full, the metal in the lower end has partly solidified and contracted somewhat away from the mold. The initial shell of solidification follows not far behind the top of the column, even if the central portion is liquid for a long way down. There is, then, a space between metal and mold that is filled with zinc vapor. The vapor has no exit, because the liquid at the top of the rising column is not only in contact with the mold but keeps UP a fresh supply of zinc vapor, which has, perhaps, already begun to condense in the lower portion. The cycle is short. Within a minute or two after the mold is full the bar has cooled enough to condense all the zinc. Some of it may condense on the mold; it might be expected that most of it would condense there, but the mold at that time is well coated with a velvety carbon residue from the oil dressing, overlain by fluffy zinc oxide that commenced covering the inside of the mold as soon as pouring began. The clean skin of the freshly cast brass offers a preferred surface for condensation. Reabsorption is quick and inevitable. A simple experiment indicates that a surprisingly large quantity of zinc vapor is trapped in the space between mold and

Jan 1, 1941

By Daniel R. Hull

In 1926 Gendersl reviewed the existing theories of this subject and stated his views in support of the gas-pressure theory. Again, in 1937, the subject was thoroughly reviewed by N. B. Vaughan3 and by Phillips and Brick,2 so that no résumé is called for here. The purpose of this paper is to describe certain observations made in the course of mill work, and to point out that they mostly tend to confirm the gas theory of Genders. Vapor Segregation There is, however, one type of inverse segregation that can be accounted for by considering the volatility of one of the constituents of an alloy. The most familiar case is ordinary brass, which is subject to a zinc enrichment of a few tenths of a per cent at the surface of a chill casting. This has been noted in 70-30 brass by Genders, and a typical example of it is given in Table 1, which represents a cylindrical billet 7 in. in diameter by 55 in. long. After lathe-turning 1/32 in. from the surface, the remaining distance to the center was sampled at six equally spaced intervals. the lead, which is essentially the same throughout, will be mentioned later. Consider a brass-mill mold, either round or rectangular in cross section, standing several feet high. It may require a minute or two for pouring. Before it is full, the metal in the lower end has partly solidified and contracted somewhat away from the mold. The initial shell of solidification follows not far behind the top of the column, even if the central portion is liquid for a long way down. There is, then, a space between metal and mold that is filled with zinc vapor. The vapor has no exit, because the liquid at the top of the rising column is not only in contact with the mold but keeps UP a fresh supply of zinc vapor, which has, perhaps, already begun to condense in the lower portion. The cycle is short. Within a minute or two after the mold is full the bar has cooled enough to condense all the zinc. Some of it may condense on the mold; it might be expected that most of it would condense there, but the mold at that time is well coated with a velvety carbon residue from the oil dressing, overlain by fluffy zinc oxide that commenced covering the inside of the mold as soon as pouring began. The clean skin of the freshly cast brass offers a preferred surface for condensation. Reabsorption is quick and inevitable. A simple experiment indicates that a surprisingly large quantity of zinc vapor is trapped in the space between mold and

Jan 1, 1941

By Roy D. McLellan

Electrolytic production of cadmium at the Great Falls plant started in the first part of the year 1925. Prior to that time, an experimental unit had been in operation for a few months during the year 1922. At present the plant is the largest producer of cadmium, not only in the United States but in the world. Electrolytic cadmium is characterized by its very low content of impurities. The main impurities, which are lead, copper, zinc and iron, do not aggregate more than 0.05 per cent., leaving a cadmium content better than 99.95 per cent. The consumption of cadmium has increased rapidly since the war, with the growing use in the plating industry. Cadmium plating has come into prominence because of its connection with the automobile and radio industries. As a protective coating, a deposit of cadmium is superior to zinc. Cadmium is also used extensively in alloys. Important among these is the alloy with copper used in telephone and trolley wire. In proportion of 0.5 to 1.2 per cent., cadmium adds materially to the strength and wearing qualities. Practically all commercial zinc concentrates contain a small amount of cadmium. In the electrolytic zinc process, the cadmium that is dissolved in the regular leaching operation is removed from solution with metallic zinc, generally added in the form of zinc dust. This precipitate also contains the copper taken into solution and the excess of zinc dust, which is required in order to insure a complete removal of all impurities. The precipitate is treated by a separate process to recover the copper, cadmium and excess zinc. In order to make the metals more soluble and to render insoluble such impurities as iron, arsenic and antimony, the precipitate is roasted. The roasting is carried out in gas-fired McDougall furnaces, with a roasting temperature of about 700' C. The roasted residue is leached with dilute sulfuric acid, spent electrolyte from the zinc electrolyzing, containing 10 to 12 per cent. free H2S04. The leaching is done in cylindrical tanks of 30 tons capacity, agitated

Jan 1, 1930

By W. T. Lundy

THE forms in which sulphur is commonly found-native sulphur, sulphides of many metals and sulphates-are widely distributed throughout the world. The two first mentioned are the principal sources of sulphur. Substantial amounts of sulphur in some form are recovered from gases from industrial plants and from gases from smelters treating other minerals. In recent years, plants have been installed in the United States to recover sulphur in elemental form from sour gases."' The amount of sulphur so produced is small at the present time but undoubtedly will increase in the future. The recovery of sulphur from gases is not covered in this chapter, which is confined to: (1) native sulphur deposits of Texas and Louisiana; (2) those of Italy; (3) other scattered deposits of native sulphur; and (4) pyrites deposits found in many countries of the world.30 Sulphur, a nonmetallic element, occurs normally in well developed bipyramidal or tabular crystals of the orthorhombic system, as well as in stalactitic and earthy masses. The mineral has a distinctive yellow color, which may be dark and discolored by impurities; the streak is white; the luster is resinous; and the fracture is conchoidal to uneven. Sulphur is translucent to opaque; has a hardness of 1.5 to 2.5, a specific gravity of 2.05, and an atomic weight of 32.06.16 The molecular weight of the solid is expressed by the symbol SS and that of the liquid and vapor ranges from S2 to S8, depending on the temperature. Sulphur melts at a temperature between 2340 and 248°F, depending on its crystalline state, to a liquid of dark amber color, the boiling point of which is 832°F. The viscosity near the melting point is about that of water and increases to 50,000 times that of water at a temperature of 380°F, subsequently falling rapidly to a low figure at the boiling point. Crystallization changes slowly from rhombic to monoclinic above 205 °F and in cooling the transformation is reversed. The mineral is a very poor conductor of heat and electricity; it is insoluble in water and nearly all acids and is soluble in cold carbon bisulphide and carbon tetrachloride. It ignites in air at a temperature of 478°F, burning with a distinctive blue flame with evolution of sulphur dioxide.47

Jan 1, 1949

The function of a preposition is to show the relation of one thing to another; it is necessary therefore for the writer to select the preposition that indicates the particular relation, otherwise he will fail to express himself clearly. Is it against common sense &o suggest that a Government is justified, morally as well as constitutionally, in preventing the decay of an industry by insisting upon the amalgamation of the prosperous with the needy? All these seven prepositions are used correctly. With the first dredge introduced in Russia, of Werf Conrad, Haarlem, make, this method of alluvial mining became important. Here the prepositions "with", "in", and "of" are used wrongly. He means: "This method of alluvial mining sprang into importance shortly after the first dredge, made at the Werf Conrad, Haarlem, was introduced into Russia." The statement itself is not true, but for that I am not responsible. Once, while I was serving with him, we were frozen in out of sight of land in the Gulf of Pichili in the North of China. Admiral Fisher wrote thus. He has used nine prepositions in making this brief statement. The sequence of three prepositions "in out of" is particularly awkward. Lounsbury says : One might fairly infer from the way in which it [newspaper English] is often spoken of that with the steadily increasing circulation of this sort of periodical literature there is no hope whatever for our speech. "Of that with" is lamentable. The construction is thoroughly bad, and it is bad mainly because the misplaced prepositions have tangled the meaning. I suggest:

Jan 1, 1931

By W. A. Cole, E. L. Derby, J. F. Wolff

Exploration of Lake Superior iron ores is done principally by drilling. The soft iron ores are churn drilled and the harder ores are diamond drilled. The churn drill used is the Mesabi type and its operation should be described as "water jetting." The drill rods are washed down by the combination action of the water jetting from the bit at the lower end of the rods and the churning motion given the line of rods. The water, which is forced down through the rods, comes up between the wash rods and the casing, bringing the choppings to the surface. It is caught in three or more barrels, each of which has a stoppered hole 8-10 in. from the bottom. These barrels are successively filled, allowed to settle, and drained to the hole, until the desired depth is drilled. The sediment from each barrel is transferred to a settling tub in which it is allowed to settle; the water is then drawn off and the wet sample is collected and dried. The number of barrels used depends on the character of the ore. For example, when drilling sandy ores, all the wash water is caught and settled for the proper length of time without refilling any of the barrels. Thus, the sediment held below the stoppered hole in any one barrel is not disturbed. The casing is kept as near the bottom of the hole as practicable to prevent the caving of the hole from jeopardizing the sample. While the casing is being driven down and the hole is being washed clean after casing, the return water is not run into the sample barrels. In exploratory work in the harder formations, where the diamond drill is used, the sample comprises both core and cuttings. The care given in handling and preserving the core depends on the importance that may be attached to certain characteristic strata in different formations. The following instructions for the care of core samples are issued by the Ogle-bay Norton Co. for diamond drill work done for them on the Gogebic Range of Michigan:

Jan 1, 1925

By L. G. Jones, A. S. Odeh

A theoretical developtment is presented which provides a straightforward method of handling the drawdown analysis for both oil and gas wells flowing at variable rates. In the past our inability to analyze variable-rate drawdowns has been a major obstacle in using them for formation evaluation. This method should permit wider use of these tests in the future. INTRODUCTION Pressure build-up analyses are widely used to obtain reservoir data such as the effective flow capacity of the formation. On the other hand. although pressure drawdowns have been run for a long time, they have not been used extensively to evaluate reservoirs because they are difficult to analyze. One of the difficulties in analyzing pressure drawdowns has been that the theory developed until now has required the test to be run at a constant rate. For both oil and gas wells this is a difficult requirement to satisfy. especially during the early period of a well's life when drawdown tests are usually run. In spite of this limitation, drawdown tests are often run with build-ups as a check. In this paper a theory, which handles the drawdown analysis for variable rates, is presented for both oil and gas wells. Thus, one of the biggest deterrents to running drawdowns is removed, and they should become a much more useful engineering tool in the future. THEORETICAL CONSIDERATIONS 011, RESERVOIRS The general equation used for describing the unsteady-state radial flow of slightly compressible fluids in homogeneous porous media can be written in cylindrical coordinates as where r is the radial distance in cm, t is the time in seconds, p is the pressure at r and t in atmospheres, + is the fractional porosity, p is the viscosity in cp, c is the compressibility in vol/vol/atm, and k is the permeability in darcies. There are a number of solutions of Eq. 1 for various boundary conditions. One of these is the so-called "point-source" solution, which approximates the case of an infinite oil reservoir with a well located at r = 0 and produced at a constant rate. The point-source solution of Eq. 1 is

Jan 1, 1966

By J. H. Jensen

Bromine is the intermediate member of the halogen family of elements between iodine, a solid: and chlorine, a gas. The name is derived from the Greek "bromos," meaning stench. Bromine is the only nonmetallic element that is liquid at room temperatures with a melting point of -7.2" C and a boiling point of 58.78" C. Reddish brown in color, it dissolves easily in water to yield a red solution. Bromine volatilizes at ordinary temperatures to a red vapor that is very irritating to the eyes, nose, and throat. Density of the liquid is 3.12 and gas weighs 7.59 gpl at standard conditions. As the element is highly active, it exists in nature only as bromide compounds. Bromine was discovered by Antoine Jerome Balard in seawater bitterns in 1826 and first prepared in quantity in 1860. Distribution Bromine is widely distributed in nature and compounds occur in solution in natural brines, in seawater, saline lakes, oil and gas well brines, and in evaporite chloride minerals. The concentration of bromine salts ranges from 60- 65 ppm in seawater to several thousand ppm in oil well brines and saline lakes. The distribution of bromine in marine evaporite minerals and in the solutions from which they crystallized was determined many years ago by H. E. Boeke (1 908). Theoretical aspects regarding the geochemistry of bromine have been published in numerous papers (Raup and Mite, 1969). Bromine occurs in solid solution in carnallite and sylvite associated in potash de- posits; in halite in salt beds; salt in oil shales; and in trona deposits. Its presence is useful as a guide in geochemical exploration. The analysis of small amounts of bromides in the presence of large amounts of chlorides is discussed by W. Schwerdtner (1963). Manganese, iron, and iodine may interfere with the determination. Other analytical methods are discussed at length in the literature (Stenger and Atchison, 1964). Sources and Reserves The sources and reserves of bromine, given in [Table 1], appear ample to meet present and foreseeable requirements in all producing countries. With the occurrence of bromine salts in sea-water and other brines, the potential for bromine production is worldwide. It has been estimated that 99% of all commercially recoverable bromine is in the ocean. However, actual subterranean brines having a higher bromine content than seawater will continue to be the preferred sources of bromine for the foreseeable future. Markets and Prices About 17% (1968) of bromine produced is used in its elemental form, with the balance consumed as bromides and bromates. The largest use for bromine is ethylene dibromide which, together with tetraethyl lead, are used as an antiknock additive in gasoline. Tetra-ethyl lead is the antiknock agent. Ethylene dibromide combines with the lead after combustion in the engine to form a volatile com- pound that escapes from the engine with the exhaust gases.

Jan 1, 1975

By G. Richards Gwinn

THE mineral graphite has been known for hundreds of years and was first used commercially as a coloring agent. Its true identity, however, was not recognized until the end of the eighteenth century and its commercial development did not become extensive until near the close of the nineteenth century. The common names for this mineral are graphite, plumbago, and black lead; others less frequently used are potelot, crayon noir, carbo mineralis, and kish. Graphite was named by Johann Gottlieb Werner in 1789 from the Greek word graphein, to write, and this name was applied primarily to the large crystalline, flake variety. Plumbago is a trade term used primarily for massive graphite as found in Ceylon. Black lead is also a trade term and, like plumbago, is based upon the idea that prevailed throughout the Middle Ages that graphite was a form of lead, or at least contained that metal. Graphite is a soft, black, unctuous form of carbon that crystallizes in the hexagonal system with rhombohedra1 symmetry. It occurs occasionally in six-sided tabular crystals but usually is found in foliated masses, minute disseminated scales, or earthy lumps. It has perfect basal cleavage, is gray to black, has a metallic luster and a gray streak. The specific gravity is 2.1 and hardness is 1 to 2. It is opaque even in finest particles; extremely resistant to the action of acid or heat; and a good conductor of both heat and electricity. Graphite may be separated into three classes: ( ) natural, (2) manufactured (which is sometime called artificial), and (3) colloidal. Natural graphite is divided into two classes, "crystalline" and "amorphous." Crystalline graphite may occur as flake, lump, chip or dust. Amorphous graphite is a commercial term only, as all graphite is crystalline, but grades in which the individual grains cannot be distinguished are classified by the trade as amorphous. Natural mixtures of crystalline and amorphous occur in all proportions. The term "artificial graphite" is a misnomer; "manufactured graphite" is a better term, because it actually is pure crystalline graphite,

Jan 1, 1949

By Walter L. Maxson, Fred C. Bond

SINCE the last publication of tabulated results of grindability tests by the authors1 the total number of ball-mill tests made has more than doubled, and rod-mill tests have become increasingly important. Nearly all of the standard closed-circuit ball-mill and rod-mill tests made to date are included in the present tabulation, together with additional information not previously published. STANDARD BALL-MILL GRINDABILITY TESTS The method of conducting these closed-circuit tests has not been altered. A sample of the ore or other material is stage-crushed in rolls set at 1/16-in. opening with a 6-mesh screen until all of it has passed the screen. The combined minus 6-mesh screen undersize is mixed, sampled and screen-analyzed, and its apparent specific gravity is determined by packing and shaking in a standard container, and weighing. The apparent specific gravity ordinarily is about 60 per cent of the true specific gravity. The unit volume present in the mill in all tests is 700 c.c. of the packed minus 6-mesh roll product, and the number of grams occupying 700 c.c. is the unit test weight. This weight is placed in the mill dry, ground for the number of revolutions estimated to be necessary, discharged, and screened mechanically in three testing sieves of the mesh size at which the test is to be conducted. The oversize, or circulating load, is weighed, sufficient fresh minus 6-mesh feed is added to bring the total weight up to that of 700 c.c., and the charge is returned to the mill for a second grinding period. All standard ball-mill tests are conducted at 250 per cent circulating load, and the number of revolutions in the mill necessary to obtain this circulating load at any grinding period is estimated from the results of the previous period. The number of net grams of screen undersize produced per revolution of the mill approaches its final equilibrium value after several grinding periods, and this is recorded as the grindability, or relative ease of grinding, of the sample. A cylindrical ball mill, 12 by 12 in. inside, with a smooth lining and rounded corners, is used with a revolution counter. Under standard grinding conditions it runs at 70 r.p.m., and contains a charge of 285 iron balls weighing 20,125 grams, ranging from I ½ to ¾ in. in diameter. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the capacity to be expected from a given mill is calculated by comparing the

Jan 1, 1943

By George L. Reiter, George B. Clark

Commercial strip mining of coal was first begun in the state of Illinois in 1911.l The annual tonnage of coal produced from coal strip mines in the state was very small until 1924, when the strip mines shipped 1.68 pct of the total state shipping mine tonnage. Since then, strip mines have gradually come into their own by producing a sizable percentage of the coal produced in the state. Table 1 shows the coal tonnage shipped from both underground and strip coal mines in the state of Illinois for selected years. The table illustrates the major role that strip mines play in the state's coal industry. Today, strip mining is generally conducted in areas where the coal seams lie so close to the surface of earth that a stripping method of mining the coal seam is cheaper than an underground method. Strip mining not only recovers 100 pct of the coal deposit, but may also be used as a method of mining large acreages of coal abandoned by the closing of underground mines. Open cut or strip mining is a very highly mechanized method of producing coal and is carried on in three distinct and separate operations. The first of these is uncovering or exposing the coal seam so that the coal is made available for mining. The second operation is that of actually mining the coal. The third operation is the washing, crushing and grading of the coal according to the producer's market. Description of Shovel The Marion 5560 power shovel is used in the first of these three operations. The large electric-powered shovel works forward and back across the coal deposits, removing the overburden of dirt, rock, and clay in successive cuts of 30 to 60 ft deep and 40 to 80 ft wide. The shovel has a maximum cutting height of 95 ft, but around 60 ft is considered to be the maximum economical cutting height by the operators. The smaller the depth of cut, the more economically the shovel will operate until a minimum cut of 15 ft is reached, below which the efficiency decreases rapidly. The Marion shovel may be used in tandem stripping in excessive depths of overburden. The other type of excavating equipment used in the tandem team is generally a dragline with a long boom of about 180 ft. In tandem stripping, the dragline is used to remove the upper portion of the cut and to place it at a maximum dumping radius from the place of removal. The Marion 5560 power shovel is then used to remove the overburden left above the coal seam and to deposit it at the shovel's maximum dumping radius. The Marion 5560 power shovel is of gigantic proportions. It has a 102 ft 6 in. boom and 32 cu yd dipper and is

Jan 1, 1950

By Maurice Rey, Victor Formanek, Paul Chataignon

IT is found when floating oxidized lead ores by sulphidization, that the presence of calcium salts in the water is usually detrimental and lowers the recovery. This effect is particularly marked in dry countries such as North Africa, where the waters often carry large amounts of calcium sulphate and where the ore may even contain gypsum. This effect is particularly marked in dry countries such as North Africa, where the waters often carry large amounts of calcium sulphate and where the ore may even contain gypsum. The effect of calcium salts is readily visible. Whereas in their absence cerussite is quickly stained brown and then .black by sodium sulphide, in their presence the mineral remains very light in color. A similar- effect is produced when barium sulphide is used as a sulphidizing agent instead of sodium- sulphide. Magnesium salts have little or no effect and even tend to reduce the detrimental effect of calcium salts. A study of this phenomenon indicates that it is due to the precipitation of calcium or barium carbonate in contact ,with the mineral simultaneously with the formation of lead sulphide.

Jan 1, 1950

By G. P. Connell, R. E. Gilmore, J. H. H. Nicolls

The purpose of this paper is to suggest a procedure for indicating the dividing line between noncaking coals and those that have weakly caking properties. A laboratory agglomerating test as an aid in classifying weakly caking coals is outlined and its merits in comparison with the standard agglutinating method advanced by the U. S. Bureau of Mines are discussed. No attempt, however, is made to discuss in detail either the different methods for determining "caking" and "agglutinating" indices or the various systems of classification. Two methods, differing somewhat in procedure, have been employed and recognized as suitable for determining the caking or agglutinating values of coals; namely, those in which an inert material such as sand, electrode carbon, etc., has been mixed with the coal before being heated, and those in which the coal is carbonized alone. In all such methods, the coal with or without the inert material is in the finely divided state and the index or value sought is derived from the examination of the residue after heating in a closed crucible or other container. The procedure outlined by Selvig, Beattie and Clellandl is the most recent representative of the method using sand as inert material, while the agglomerating test described below is representative of the method in which the coal is carbonized alone. The standard volatile-matter determination affords a means for observing the coking properties of a coal, and this has been described by Rose2 as the simplest of all coking tests. According to him, "the resulting coke button will indicate whether the coal is noncoking, feebly coking or strongly coking," despite the fact that "almost every condition in this test is at variance with large-scale carbonizing practice." Lessing,3 the

Jan 1, 1934

By Herman Dykstra, R. L. Parsons

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By R. L. Parsons, Herman Dykstra

A numerical method for solving partial differential equations in steady state fluid flow is described. This method, known as the "relaxation method," has two advantages over analytical methods: (1) practically any problem can be solved, and (2) a solution can be obtained quickly. A disadvautage is that the solution is not general. The method is applied to core analysis and relative permeability measurement to calculate constriction effects and to calculate the true pressure drop measured by a center tap in a Hassler type relative permeability apparatus. Further applications are suggested. INTRODUCTION Many problems in fluid flow cannot be solved analytically because of the nature of the boundary conditions. For many problems, however. an exact answer is not necessary because boundary conditions are not exactly defined or the parameters describing the porous medium are not accurately known. The relaxation method can be used to obtain an approximate answer easily and quickly for the flow of incompressible fluids in porous media. The method can also be used for other types of problems, such as determining the stress in a shaft under load. or the temperature distribution during steady state heat flow. In this discussion only calculations concerned with the flow of fluids in porous media will be considered. The method was introduced by R. V. Southwell in 1935.' THEORY The treatment given here follows that given by Enimons.2 Consider a porous medium to be replaced entirely by a net of tubes of equal length and uniform cross-sectional area as shown in part in Fig. 1. Assume that the net of tubes behaves exactly like the porous medium which it replaces; that is, the net can be made fine enough to reproduce exactly the porous medium. Assume also that Darcy's Law can be used to calculate the flow from one point to another point through these tubes. The flow from point 1 to point 0 is KA . ------ P-P) .......(11 where a is the distance between points: K is the "permeability" of a tube; A is the cross-sectional area of a tube; is the viscosity of the liquid in the porous medium; and (P1 — P0) is the pressure difference between point 1 and point 0. In like manner the flow can be calculated from points 2, 3, and 4 to point 0. The net flow into point 0 is Qo = KA/µa (P1 + P2 + P33 + P4-4P0) . . (2) MB For an incompressible fluid the net flow into point 0 will be zero or, Q. = 0. This says that at point 0 fluid is neither being accumulated nor depleted. 'Therefore. P1 + P2 + P3 + P4 - 4P0 = 0 .... (3) . If. now. with specified boundary conditions. the pressure i.; known at a finite number of points in a given region, as at the points shown in Fig. 1, Equation (3) will be satisfied at every point. If, on the other hand, the pressure is not known, the pressure can be guessed at these points. Then. unless the guess is perfect. Equation (3) will not be satisfied at all of the points. When Equatiol~ (3,) is not satisfietl. let d = P1 + I?, + P, + P, - If' .,....(4) where 6 is an apparent error and is called the residual at point 0. Equation (4) shows how much the pressure guess is in error at point 0 with respect to the surrounding points. A positive residual means that the pressure is too low, and a negative residual means that the pressure is too high. To bring the residual, 6. to zero in order to satisfy Equation (3). it is necessary to make changes in the pressure guesses. Equation (4) shows that a +1 change in Po will change the residual at point 0 by -4. A +1 change in the pressure at any of the four surrounding points will change the residual at point 0 by +l. Thus it can be seen that a change at any point will affect the residual at that point and the four surrounding points. By changing the pressure from point to point, all of the residuals can eventually be brought nearly to zero and the problem will be solved. This procedure is the essence of relaxation methods and is used to relax the residuals so that Equation (3) is satisfied at every point. The procedure can be most easily explained in detail by solving a simple problem. as Southwell says, "To explain every detail of a practical technique is to risk an appearance of complexity and difficulty which may repel the reader. A

Jan 1, 1951

By W. H. Meyer

Although an aerial photograph is not a map, most of the information that is necessary for compiling a map is recorded in the photograph provided some form of radial-line method is used to determine the true position of images. The slotted- templet method, which is based on the well-established radial-line principle, has made it possible to construct accurate mosaic maps at a cost comparable with that formerly charged for the average mosaic. It makes possible the securing of these results with far less ground control, which is always expensive. It has expanded widely the possible use of aerial photographs for mapping. ALTHOUGH a vertical or oblique aerial photograph is not a map, most of the information that is necessary for compiling a map is recorded in the photograph. Some ground controls or data are needed, the number and accuracy to be governed by the mapping method to be used and the scale and final accuracy desired in the finished map. RADIAL-LINE CONTROL It is essential that the principle of radial-line control in the use of vertical aerial photographs be understood and accepted before any confidence in the slotted-templet method can be gained. A simple sketch and some enlargements showing the Empire State Building will serve to illustrate the cause of displacement of an image that is above the datum plane as recorded in the photograph. The top of the tower of the Empire State Building is directly above the base, and when the image of the top is shown almost two blocks away from the center of the base, it is evident that the image of the top of the tower is not the true location, and in this particular case we know where the true location is; namely, over the center of the base of the tower. If the top of the tower were the top of a hill 1250 ft. high, we would have no way of knowing by inspection the true position of the top of the hill, so it is very important to have a method whereby the true location of any such point can be determined, and thereby make it possible to convert the detail of an aerial photograph into accurate information for mapmaking.

Jan 1, 1939

By W. H. Meyer

Although an aerial photograph is not a map, most of the information that is necessary for compiling a map is recorded in the photograph provided some form of radial-line method is used to determine the true position of images. The slotted-templet method, which is based on the well-established radial-line principle, has made it possible to construct accurate mosaic maps at a cost comparable with that formerly charged for the average mosaic. It makes possible the securing of these results with far less ground control, which is always expensive. It has expanded widely the possible use of aerial photographs for mapping. Although a vertical or oblique aerial photograph is not a map, most of the information that is necessary for compiling a map is recorded in the photograph. Some ground controls or data are needed, the number and accuracy to be governed by the mapping method to be used and the scale and final accuracy desired in the finished map. Radial-line Control It is essential that the principle of radial-line control in the use of vertical aerial photographs be understood and accepted before any confidence in the slotted-templet method can be gained. A simple sketch and some enlargements showing the Empire Stale Building will serve to illustrate the cause of displacement of an image that is above the datum plane as recorded in the photograph. The top of the tower of the Empire State Building is directly above the base, and when the image of the top is shown almost two blocks away from the center of the base, it is evident that the image of the top of the tower is not the true location, and in this particular case we know where the true location is; namely, over the center of the base of the tower. If the top of the tower were the top of a hill 1250 ft. high, we would have no way of knowing by inspection the true position of the top of the hill, so it is very important to have a method whereby the true location of any such point can be determined, and thereby make it possible to convert the detail of an aerial photograph into accurate information for mapmaking.

Jan 1, 1941

By W. H. Meyer

Although an aerial photograph is not a map, most of the information that is necessary for compiling a map is recorded in the photograph provided some form of radial-line method is used to determine the true position of images. The slotted-templet method, which is based on the well-established radial-line principle, has made it possible to construct accurate mosaic maps at a cost comparable with that formerly charged for the average mosaic. It makes possible the securing of these results with far less ground control, which is always expensive. It has expanded widely the possible use of aerial photographs for mapping. Although a vertical or oblique aerial photograph is not a map, most of the information that is necessary for compiling a map is recorded in the photograph. Some ground controls or data are needed, the number and accuracy to be governed by the mapping method to be used and the scale and final accuracy desired in the finished map. Radial-line Control It is essential that the principle of radial-line control in the use of vertical aerial photographs be understood and accepted before any confidence in the slotted-templet method can be gained. A simple sketch and some enlargements showing the Empire Stale Building will serve to illustrate the cause of displacement of an image that is above the datum plane as recorded in the photograph. The top of the tower of the Empire State Building is directly above the base, and when the image of the top is shown almost two blocks away from the center of the base, it is evident that the image of the top of the tower is not the true location, and in this particular case we know where the true location is; namely, over the center of the base of the tower. If the top of the tower were the top of a hill 1250 ft. high, we would have no way of knowing by inspection the true position of the top of the hill, so it is very important to have a method whereby the true location of any such point can be determined, and thereby make it possible to convert the detail of an aerial photograph into accurate information for mapmaking.

Jan 1, 1941