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By William N. Poundstone

To forecast the future of coal intelligently, one must first consider the market outlook. Coal can be used for many purposes, but currently about 25% of it goes into metallurgical coke, while 75% serves as fuel. Coal for metallurgical coke should show a modest growth for at least the next decade, primarily because of increased exports, but the important factor in the coal outlook is energy. Today, this country faces a serious shortage of energy, and its requirements are growing at an almost unbelievable rate. Last year the United States consumed 68 quadrillion Btu, or double the energy it consumed in 1950, and, if projections are correct, this figure will grow to 150 quadrillion Btu by 1990. Thus, in one working lifetime, the nation's energy consumption is expected to increase by roughly five times. The future of coal hinges on its degree of participation in meeting this energy need. The Federal Power Commission predicts that coal consumed by electric utilities will increase about 4-576 per yr, reaching 472 million tons by 1980 and 615 million tons by 1990. If this projection proves correct, 1980 consumption will be double that of last year and, even more startling, the utility industry alone will use more coal in 1990 than the entire coal industry produced in 1970. This is a tremendous increase, but in view of the projected energy growth, it is difficult to see how this country's needs can be satisfied with- out a coal contribution of this magnitude. Unless some new source such as solar energy is discovered, it must be assumed that the projected energy will come principally from the present-day sources-oil, gas, nuclear materials and coal.

Jan 1, 1971

By Leo H. Glanville

Until 1934, natural ventilation was depended upon in the mine of the Climax Molybdenum Co. at Climax, Colorado. In that year a 7-ft. axial-flow, low-pressure fan was installed as an exhausting unit. In 1936, three more fans of the same kind were installed, all as exhausting units, with a total capacity of 115 000 cu, ft. per min., and since then fans and sprays have been added as required. Atmospheric Conditions Adverse atmospheric conditions at this elevation of 11,500 ft. account in part for difficulty in maintaining adequate ventilation throughout the mine. Barometric pressures range from 18.99 to 20.01 in. of mercury; the norma1 average being 19.70 in. Air weight is 0.051 lb. per cu. ft., and humidity is low—about a 30 per cent yearly average. This makes the use of mechanical humidity aids mandatory the Year around to prevent excessive dryness of the mine workings and the resultant dust hazard. The yearly temperature range is from minus 24" to 75°F.; typically, in February 1942 the mean low was minus 3.25°F. and the mean high, 21.3°F. In August the mean low was 34.8°F.; the mean high, 64.26°F. Even during the summer month air filtration through the openings of the cave area is 32°F., owing to accumulation of snow in the glory hole and in Part to glacial ice, which, combined with a rock temperature of 39°F. on the upper levels (elevation 11,945 ft.) and 42°F. on the main haulage level (elevation 11,470 ft.], makes it difficult to maintain a comfortable working temperature. The one advantage in ventilation of mine workings at the altitude of the Climax mine is that the power required to circulate a given air volume is 32 per cent less than would be required at sea level. Problems since 1936 the mine management has studied intensively plans for providing adequate ventilation for the entire mine for its expected life. As the ore breaks into large pieces, much secondary blasting is necessary, therefore there is a considerable amount of smoke, gas and dust, which requires circulation of a large amount of air to remove the contamination, It is undesirable to use haulage drifts and manways as air passages because some would be passageways for contaminated air also, and there would be undesirable high velocities in some drifts. High velocities and large volumes of subfreezing air dry out the passageways through which they pass, and thus increase the amount of dust. Regulating doors in haulage drifts are difficult of upkeep and interfere with production. It was decided as a general principle to distribute fresh air to each working place at low velocities and low pressures and to remove contaminated air as soon as possible with a minimum of travel through working places.

Jan 1, 1943

By Leo H. Glanville

Until 1934, natural ventilation was depended upon in the mine of the Climax Molybdenum Co. at Climax, Colorado. In that year a 7-ft. axial-flow, low-pressure fan was installed as an exhausting unit. In 1936, three more fans of the same kind were installed, all as exhausting units, with a total capacity of 115 000 cu, ft. per min., and since then fans and sprays have been added as required. Atmospheric Conditions Adverse atmospheric conditions at this elevation of 11,500 ft. account in part for difficulty in maintaining adequate ventilation throughout the mine. Barometric pressures range from 18.99 to 20.01 in. of mercury; the norma1 average being 19.70 in. Air weight is 0.051 lb. per cu. ft., and humidity is low—about a 30 per cent yearly average. This makes the use of mechanical humidity aids mandatory the Year around to prevent excessive dryness of the mine workings and the resultant dust hazard. The yearly temperature range is from minus 24" to 75°F.; typically, in February 1942 the mean low was minus 3.25°F. and the mean high, 21.3°F. In August the mean low was 34.8°F.; the mean high, 64.26°F. Even during the summer month air filtration through the openings of the cave area is 32°F., owing to accumulation of snow in the glory hole and in Part to glacial ice, which, combined with a rock temperature of 39°F. on the upper levels (elevation 11,945 ft.) and 42°F. on the main haulage level (elevation 11,470 ft.], makes it difficult to maintain a comfortable working temperature. The one advantage in ventilation of mine workings at the altitude of the Climax mine is that the power required to circulate a given air volume is 32 per cent less than would be required at sea level. Problems since 1936 the mine management has studied intensively plans for providing adequate ventilation for the entire mine for its expected life. As the ore breaks into large pieces, much secondary blasting is necessary, therefore there is a considerable amount of smoke, gas and dust, which requires circulation of a large amount of air to remove the contamination, It is undesirable to use haulage drifts and manways as air passages because some would be passageways for contaminated air also, and there would be undesirable high velocities in some drifts. High velocities and large volumes of subfreezing air dry out the passageways through which they pass, and thus increase the amount of dust. Regulating doors in haulage drifts are difficult of upkeep and interfere with production. It was decided as a general principle to distribute fresh air to each working place at low velocities and low pressures and to remove contaminated air as soon as possible with a minimum of travel through working places.

Jan 1, 1943

By L. S. Richardson, N. J. Grant

REACTIONS of oxygen and nitrogen at low pressures with titanium have recently been studied by a number of investigators.1-3 Gulbransen and Andrew' noted that the reaction with nitrogen followed the parabolic rate law whereas the reaction with oxygen deviated slightly from this law in the temperature range 300° to 800°C. In the work reported here, commercial titanium (75 A) was used as the test material. Cylinders 2.5 in. long and 0.25 in. in diameter were machined from heavier bar stock. The test pieces were given a metallographic finish, immersed for 30 min in cold concentrated HC1, washed in water, then acetone, and dried with lint-free cloth. Reaction rates were determined in a modified Sieverts type apparatus by measuring the decrease in gas pressure of the reacting gas contained in a constant volume. The amount of gas added could be measured in a calibrated gas burette to an accuracy of 0.01 mm. During the course of a run the temperature never varied by more than 10°C and then only for brief moments. After placing the specimen in the furnace, the system was first evacuated for 12 hr at room temperature, and then flushed with purified argon five times, adsorbed gases being discharged during this period from the glass system with a high frequency spark coil. The flushing and discharging were repeated at 400°C. This rather involved procedure was found necessary after a number of trial runs indicated extraneous effects traceable to the system. Reaction periods up to 2 hr were used, at initial gas pressures of 0.2 to 0.5 atm. Experimental Results Fig. 1 shows the decrease in oxygen pressure for tests at 0.5 atm at various temperatures as a function of the square root of the time. Deviations from linearity are minor and the parabolic rate law is obeyed. Fig. 2 shows the same plot for the nitrogen reaction. A definite deviation from linearity is noted; however, it is probable that the higher initial rates are caused by the presence of small amounts of oxygen contamination, the initial faster rate changing to the slower rate after about 5 to 10 min. Calculations of the rate constants were made on the basis of the latter portion of the curves. The parabolic rate law constants calculated from these curves are shown for oxygen and nitrogen in Fig. 3. In spite of some scatter the average curves are quite definite. Changes in gas pressure of the order of 20 pct did not result in a measurable change in the rate law constants. The activation energy for the oxygen reaction was calculated to be 47,400 cal per mol (above 700°C), which is not in agreement with the value quoted by Gulbransen and Andrew' for lower temperatures, their value being 26,000 cal below 600°C. The activation energy for the nitrogen reaction was calculated to be 45,400 cal per mol above about

Jan 1, 1955

By G. S. Hume

Production of petroleum and natural .gas increased in Canada in 1940 over the previous year. Alberta produced more than 97 per cent of the total Canadian production of 8,718,053 bbl. of oil, an increase for this province of nearly 12 per cent, whereas in Ontario and New Brunswick, where the production is relatively small, there was a slight decline. In Alberta the main producing field is Turner Valley, on the eastern edge of the foothills southwest of Calgary, and development continued in this field in 1940 with the completion of 36 wells, all of which obtained production. In the Red Coulce field, close to the International Boundary, near Coutts, no new wells were drilled and the seven producing wells showed a decline of 900 bbl. below the previous year. Also, in the Wainwright field of east central Alberta, four wells, yielding heavy crude oil, produced 4000 bbl. less oil than in 1939, owing possibly rather to discontinuous operation than to actual decline in potential yield. This decline was more than offset by production from a new field 40 miles northeast of Wainwright, at Borradaile, producing oil of 14" to I 5° A.P.1. There was a small increase in production during 1940 from the Del Bonita field, in southern Alberta, where the production is from two wells. The outstanding development of the year was the completion of Standard Oil Princess No. 2 well in the Steveville area, on the Plains 100 miles east of Calgary. This well was completed late in December with an initial flow1 of 520 bbl. of 26.3" A.P,I. oil, and 12,750 M cu. ft. of gas from the upper part of the Mississippian limestone. It has opened up a new field and given a further proof of the potentialities of the Southern Plains. The production of petroleum in Canada is shown in Table I. Since most of the yield comes from Alberta, the production is shown from the various fields in Table 2. The sale value of the petroleum produced in Canada in 1940 exceeded 11.1 million dollars, which is still somewhat less than the value of the natural gas production, shown in Table 3. Table i.—Production of Petroleum in Canada" Barrels Province 1939 1940 New Brunswick........ 20,101 21,161 Ontario............... 206,196 186,471 Alberta............... 7,595,000 8,493,237 Northwest Territories. . 17,013 8,493,23717.184 Total............... 7,838,310 8,718,053 Value............... $10,353,351 $11.113,000 0 Bureau of Statistics, Ottawa. Turner Valley, Alberta Turner Valley continues to be by far the largest producing field in Canada (details are given in Table 4), The limits of the Pr in- field are now Known. On the east the oil area is bounded by the gas cap, which in turn is cut off on its east side by a major overthrust fault; on the west, ii is defined by edge water at a level of 4roc

Jan 1, 1941

By Leo H. Glanville

UNTIL 1934, natural ventilation was depended upon in the mine of the Climax Molybdenum Co. at Climax, Colorado. In that year a 7-ft. axial-flow, low-pressure fan was installed as an exhausting unit. In 1936, three more fans of the same kind were installed, all as exhausting units, with a total capacity of 115,000 cu. ft. per min., and since then fans and sprays have been added as required. ATMOSPHERIC CONDITIONS Adverse atmospheric conditions at this elevation of 11,500 ft. account in part for difficulty in maintaining adequate ventilation throughout the mine. Barometric pressures range from 18.99 to 20.01 in. of mercury; the normal average being 19.70 in. Air weight is 0.051 lb. per cu. ft., and humidity is low-about a 30 per cent yearly average. This makes the use of mechanical humidity aids mandatory the year around to prevent excessive dryness of the mine workings and the resultant dust hazard. The yearly temperature range is from minus 24° to 95°F.; typically, in February 1942 the mean low was minus 3.25°F. and the mean high, 21.3°F. In August the mean low was 34.8°F.; the mean high, 64.26°F. Even during the summer month air filtration through the openings of the cave area is 32°F., owing to accumulation of snow in the glory hole and in part to glacial ice, which, combined with a rock temperature of 39°F. on the upper levels (elevation 11,945 ft.) and 42°F. on the main haulage level (elevation 11,490 ft.), makes it difficult to maintain a comfortable working temperature. The one advantage in ventilation of mine workings at the altitude of the Climax mine is that the power required to circulate a given air volume is 32 per cent less than would be required at sea level. PROBLEMS Since 1936 the mine management has studied intensively plans for providing adequate ventilation for the entire mine for its expected life. As the ore breaks into large pieces, much secondary blasting is necessary, therefore there is a considerable amount of smoke, gas and dust, which requires circulation of a large amount of air to remove the contamination. It is undesirable to use haulage drifts and manways as air passages because some would be passageways for contaminated air also, and there would be undesirable high velocities in some drifts. High velocities and large volumes of subfreezing air dry out the passageways through which they pass, and thus increase the amount of dust. Regulating doors in haulage drifts are difficult of upkeep and interfere with production. It was decided as a general principle to distribute fresh air to each working place at low velocities and low pressures and to remove contaminated air as soon as possible with a minimum of travel through working places.

Jan 1, 1943

By G. S. Hume

Production of petroleum and natural .gas increased in Canada in 1940 over the previous year. Alberta produced more than 97 per cent of the total Canadian production of 8,718,053 bbl. of oil, an increase for this province of nearly 12 per cent, whereas in Ontario and New Brunswick, where the production is relatively small, there was a slight decline. In Alberta the main producing field is Turner Valley, on the eastern edge of the foothills southwest of Calgary, and development continued in this field in 1940 with the completion of 36 wells, all of which obtained production. In the Red Coulce field, close to the International Boundary, near Coutts, no new wells were drilled and the seven producing wells showed a decline of 900 bbl. below the previous year. Also, in the Wainwright field of east central Alberta, four wells, yielding heavy crude oil, produced 4000 bbl. less oil than in 1939, owing possibly rather to discontinuous operation than to actual decline in potential yield. This decline was more than offset by production from a new field 40 miles northeast of Wainwright, at Borradaile, producing oil of 14" to I 5° A.P.1. There was a small increase in production during 1940 from the Del Bonita field, in southern Alberta, where the production is from two wells. The outstanding development of the year was the completion of Standard Oil Princess No. 2 well in the Steveville area, on the Plains 100 miles east of Calgary. This well was completed late in December with an initial flow1 of 520 bbl. of 26.3" A.P,I. oil, and 12,750 M cu. ft. of gas from the upper part of the Mississippian limestone. It has opened up a new field and given a further proof of the potentialities of the Southern Plains. The production of petroleum in Canada is shown in Table I. Since most of the yield comes from Alberta, the production is shown from the various fields in Table 2. The sale value of the petroleum produced in Canada in 1940 exceeded 11.1 million dollars, which is still somewhat less than the value of the natural gas production, shown in Table 3. Table i.—Production of Petroleum in Canada" Barrels Province 1939 1940 New Brunswick........ 20,101 21,161 Ontario............... 206,196 186,471 Alberta............... 7,595,000 8,493,237 Northwest Territories. . 17,013 8,493,23717.184 Total............... 7,838,310 8,718,053 Value............... $10,353,351 $11.113,000 0 Bureau of Statistics, Ottawa. Turner Valley, Alberta Turner Valley continues to be by far the largest producing field in Canada (details are given in Table 4), The limits of the Pr in- field are now Known. On the east the oil area is bounded by the gas cap, which in turn is cut off on its east side by a major overthrust fault; on the west, ii is defined by edge water at a level of 4roc

Jan 1, 1941

By H. M. Morse

This report covers the period from Jan. I, 1943 to Dec. 31, 1943. During the year, II2 wells were drilled in Mississippi, as foilows: wildcats drilled and abandoned, 54; wildcats producing oil, 4; oil wells drilled in oil fields, 26; oil wells drilled in fields, dry and abandoned, 10; sulphur-test wells drilled, 14; salt-water-disposal wells, 3; core tests, I. Prospecting Geophysical work in Mississippi during 1943 amounted to 1127 crew weeks, divided as follows: reflection seismograph, 809 weeks; gravity meter, 285; magnotometer, 30; torsion balance, 3. A considerable amount of core drilling was done over a large part of the state. The complete data on this activity are not available at the present time. Salt Domes To date, the following salt domes have been discovered in Mississippi: Midway, Edwards, Glass, Newman, Tatum, Oak-vale, Kings, Halifax, D'Lo, Hazlehurst, Byrd, Leedo, Prentiss, Carson, Moselle, Monticello, Ruth, Keno, Taylorsville. New Oil Fields Lincoln County.—On March 10, 1943, the California Company completed its Smith No. I in sec. 4, T. 7 N., R. 7 E., Lincoln County, as an oil well and produced 29 bbl. of 25" gravity oil in 24 hr. through a fi-in. choke. Two outpost wells have been drilled in this area by the California Company, and both have been abandoned as dry holes. Madison County. —Love Petroleum Co. completed its J. R. Anderson No. 2, sec. 2, T. 8 N., R. I W., Madison County, on Sept. 7, 1943. This well produced 135 bbl. of approximately 30" gravity- oil in 24 hr. through a )/4-in. choke. The production comes from a sand or porosity in the upper part of the Chalk formation of the Cretaceous age. Adams County.—The California Company drilled its National Gasoline Co. of Louisiana No. I in sec. 52, T. 7 N., R. I W., to a total depth of 10,383 ft., and at 10,280 ft, it perforated and obtained gas and a condensate. The well had several showings in the Wilcox of the Eocene age. Several of these showings were tested and the well finally was completed at 5888 ft. on Oct. 6, 1943, producing 44" gravity oil in the second sand in this formation. No other wells were completed in this field during the year. However, a number of wells are contemplated in the near future, and locations have been staked by the California Company. The Oklahoma Pipe Line Co. will market the oil through its pipe-line facilities. Wayne County.—The Gulf Refining Co. drilled Davis No. I in sec. 2, T. 9 N., R. 9 W. in Wayne County. After several stem tests 545'-in. casing was set at 6850 ft. and production was obtained in the so-called Massive Sand of the Lower Tuscaloosa. The well produced 359 bbl. of oil in 24 hr., and it Was completed on Oct. 4, 1943. Other locations have been staked ill this area and probably will be drilled in 1944 by

Jan 1, 1944

By H. M. Morse

This report covers the period from Jan. I, 1943 to Dec. 31, 1943. During the year, II2 wells were drilled in Mississippi, as foilows: wildcats drilled and abandoned, 54; wildcats producing oil, 4; oil wells drilled in oil fields, 26; oil wells drilled in fields, dry and abandoned, 10; sulphur-test wells drilled, 14; salt-water-disposal wells, 3; core tests, I. Prospecting Geophysical work in Mississippi during 1943 amounted to 1127 crew weeks, divided as follows: reflection seismograph, 809 weeks; gravity meter, 285; magnotometer, 30; torsion balance, 3. A considerable amount of core drilling was done over a large part of the state. The complete data on this activity are not available at the present time. Salt Domes To date, the following salt domes have been discovered in Mississippi: Midway, Edwards, Glass, Newman, Tatum, Oak-vale, Kings, Halifax, D'Lo, Hazlehurst, Byrd, Leedo, Prentiss, Carson, Moselle, Monticello, Ruth, Keno, Taylorsville. New Oil Fields Lincoln County.—On March 10, 1943, the California Company completed its Smith No. I in sec. 4, T. 7 N., R. 7 E., Lincoln County, as an oil well and produced 29 bbl. of 25" gravity oil in 24 hr. through a fi-in. choke. Two outpost wells have been drilled in this area by the California Company, and both have been abandoned as dry holes. Madison County. —Love Petroleum Co. completed its J. R. Anderson No. 2, sec. 2, T. 8 N., R. I W., Madison County, on Sept. 7, 1943. This well produced 135 bbl. of approximately 30" gravity- oil in 24 hr. through a )/4-in. choke. The production comes from a sand or porosity in the upper part of the Chalk formation of the Cretaceous age. Adams County.—The California Company drilled its National Gasoline Co. of Louisiana No. I in sec. 52, T. 7 N., R. I W., to a total depth of 10,383 ft., and at 10,280 ft, it perforated and obtained gas and a condensate. The well had several showings in the Wilcox of the Eocene age. Several of these showings were tested and the well finally was completed at 5888 ft. on Oct. 6, 1943, producing 44" gravity oil in the second sand in this formation. No other wells were completed in this field during the year. However, a number of wells are contemplated in the near future, and locations have been staked by the California Company. The Oklahoma Pipe Line Co. will market the oil through its pipe-line facilities. Wayne County.—The Gulf Refining Co. drilled Davis No. I in sec. 2, T. 9 N., R. 9 W. in Wayne County. After several stem tests 545'-in. casing was set at 6850 ft. and production was obtained in the so-called Massive Sand of the Lower Tuscaloosa. The well produced 359 bbl. of oil in 24 hr., and it Was completed on Oct. 4, 1943. Other locations have been staked ill this area and probably will be drilled in 1944 by

Jan 1, 1944

By W. I. Duvall, L. D. Sadwin

Three explosives with different detonation characteristics were tested by studying their cratering ability in a granite-gneiss. The strain wave generating characteristics of these explosives were also studied in the same rock medium. Correlations between the relative performance of three explosives as evaluated by crater studies and other methods of evaluation are indicated. Numerous test methods have been employed to evaluate the output performance of explosives; for example, the underwater explosion method, the airblast method and the ballistic pendulum method.'*' For blasting applications, the study of explosion produced craters and explosion generated strain waves are the most meaningful. This laboratory has employed these techniques extensively for many years and has shown that the detonation properties of explosives and their ability to generate strain waves in rock are related and that the amplitude and shape of the strain wave is related to some of the crater parameters such as slab thickness and fly rock velocity.3'11 However, a good comparison between the relative performance of explosives as determined by the crater and strain wave methods had not been made. The purpose of this investigation was to determine if the relative performance of three explosives as determined by the crater method shows a correlation with the relative performance as determined by the strain wave method. If a good correlation exists between these two sets of relative performance, it should then be possible to relate the detonation properties of an explosive to its ability to break rock in a crater test. In most commercial blasting operations, the diameter of the blast hole remains constant even though the type of explosive may change. In general, it is the explosive volume rather than the weight which remains constant when two or more explosives of different density are compared. Therefore all tests in this investigation were conducted on a constant volume basis rather than on a constant weight basis. TEST SITE AND ROCK PROPERTIES The tests described in this paper were conducted at a granite quarry owned and operated by the Consolidated Quarries Div. of the Georgia Marble Co. at Lithonia, Ga. The tests were performed in an area where the exposed rock surface was nearly horizontal and where the general rock mass had few joints or faults. The rock has an apparent sp gr of 2.6 and a longitudinal propagation velocity of 18,000 fps. The characteristic impedance of Lithonia granite gneiss is 53(lb - sec/in3). EXPERIMENTAL PROCEDURE There are many parameters which must be considered in the study of explosion-produced craters. The role played by each variable in the explosive-rock-crater system can be determined by experimental techniques in which one parameter is varied while others are maintained constant. In this investigation, the crater geometry was studied as the depth was varied for each of three explosives. The explosive volume and rock-type were held constant for all crater tests. The experimental arrangement used in performing the crater tests is illustrated schematically in Fig. 1.

Jan 1, 1965

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 Guy N. Bjorge

HOMESTAKE'S mining methods today are of necessity controlled to a considerable extent by that which has been done in the past. This may be shown by the fact that our two main operating shafts now, the B. & M. and Ellison, were begun in 1878 and 1896 respectively, so that-the loca-tions of shafts, locations of all the drifts on the upper levels, and a great deal of sloping was done before any of us now connected with the mine had anything to do- with it. Anything that I may say is not to be construed as criticism of those who have gone before for it would be a sad commentary indeed on us if we had not learned something from their experience. The levels down to the 1100 in the Homestake mine are spaced at 100-ft. intervals, and below that at 150-ft. intervals. The general plan of develop-

Jan 1, 1934

By J. E. Harris

The metallic elements, beryllium, calcium, cerium, lithium, manganese, titanium, vanadium and zirconium are used in metallurgical practice in relatively small percentages for the purpose of improving the physical properties of various alloys. No important uses for any of these elements have thus far been developed either in the pure form or in alloys of which they constitute the major constituent.

Jan 1, 1935

By Selma Hermann

For the past century, the so-called aluminum bronzes have been assuming a role of ever-increasing importance in the metallurgical field. The last quarter of that century has marked many efforts to find alloying elements that would alleviate some of the undesirable qualities of the aluminum bronzes-for example, the heterogeneity of the alpha solid solution and the extreme hardness of the beta. Much of this work, however, has been rather haphazard-compositions and heat treatment are usually so much at variance as to make comparison impossible. It is the object of this research to study the effect of certain percentages of common alloying elements on aluminum bronzes of analogous compositions and heat treatments. It is hoped that the material gathered here will at least serve as a basis for further systematic study.

Jan 1, 1930

By W. A. STERLING

IN the opencut iron mines of the Mesabi Range in Minnesota, the trend in mining is in the development of mining equipment and mining methods which will move surface overburden and ore-bearing materials with less labor and at a cheaper cost. This is a must for most of the independent operators. Their reserves of direct-shipping ore are extremely small and their operations are being conducted in small, or intermediate pits, with a high stripping ratio in the outer fringes, or shore lines of older pits. and in ore bodies passing from direct shipping to the washing and the intermediate, or retreat ore state. The trend is toward deeper stripping, longer and steeper hauls, and the necessity of moving a total of from three to five or six tons of overburden and ore material for each ton of shipping-grade ore produced. This naturally calls for greater production, with larger shovels, or draglines. cheaper drilling and blasting costs through the drilling of larger-diameter blastholes, and cheaper haulage through the use of trucks of larger capacity and more extensive use of belt-conveyor systems. This trend is notable both in stripping and mining.

Jan 1, 1948

By Eugene A. Stephenson

NUMBER of noteworthy events in the petroleum industry may be reported for 1941, of which the most spectacular was doubtless the rise in the daily rate of crude-oil production to a peak of approximately 4,300,000 barrels. This enormous daily rate did not ensue from the furor of flush pools but represented for the most part merely a slight additional daily delivery from many wells that had previously been operated on a more restricted basis, in line with good conservation practice and also from the adroit increase in the number of days per week by the Texas Railroad Commission. Another important fact was the increase in price throughout the Mid-Continent area from the static level of $1.02 for 36°, A.P.I., crude, to $1.17 per barrel. Efforts to elevate the price above this point have met with severe opposition from the O.P.A.. as has also a similar effort by the PennsyIvania Crude Oil Producers' Association, but the vastly increased costs for materials and labor may shortly give the industry the enhanced price which it has long deserved.

Jan 1, 1942

By C. A. Mitke

In the Southwest, mcchanical ventilation of metal mines has been receiving consideration for many years. The United Verde Copper Co., in Jerome, has used large mine fans for ventilation and fire-fighting purposes for at lcast 15 years, while the Copper Qucen Branch of the Phelps Dodge Corpn. commenced installing mechanical ventilation in its various divisions 10 years ago.' Since then, with few exceptions, every large mine in this part of the country has installed and put in operation a mechanical ventilating system. The properties of some of these companies consist of from two to six divisions, or separate mines, each of which requires an independent ventilating system. In other words, thirteen copper mining companies, with an aggregate tonnage, when operating at capacity, of approximately 50,000 tons a day, have installed mechanical ventilating systems in their mines. All these mines are within a radius of approximately 200 miles, which constitutes the largest copper-producing area in the world. The capacities of mechanical ventilating installations in these mines range from 100,000 to 300,000 cu. ft. of air per minute, depending on the size of the mine, character of the workings, tonnage produced, etc. The latter varies from 300 to 20,000 tons per day. The mines include both high- and low-grade deposits, the greatest depth of the former, at present, being approximately 2500 ft.; and of the latter, 1200 ft. The volumes of air at present being coursed through the mines are from 60,000 up to 225,000 cu. ft. of air per minute,which, in their relation to the undcrground working force, range from 200 to 800 cu. ft. of air per man, per minute. While not to be taken as criteria, these figures are indicative of the character of the ventilation furnished.

Jan 1, 1923

By C. A. Mitke

In the Southwest, mcchanical ventilation of metal mines has been receiving consideration for many years. The United Verde Copper Co., in Jerome, has used large mine fans for ventilation and fire-fighting purposes for at lcast 15 years, while the Copper Qucen Branch of the Phelps Dodge Corpn. commenced installing mechanical ventilation in its various divisions 10 years ago.' Since then, with few exceptions, every large mine in this part of the country has installed and put in operation a mechanical ventilating system. The properties of some of these companies consist of from two to six divisions, or separate mines, each of which requires an independent ventilating system. In other words, thirteen copper mining companies, with an aggregate tonnage, when operating at capacity, of approximately 50,000 tons a day, have installed mechanical ventilating systems in their mines. All these mines are within a radius of approximately 200 miles, which constitutes the largest copper-producing area in the world. The capacities of mechanical ventilating installations in these mines range from 100,000 to 300,000 cu. ft. of air per minute, depending on the size of the mine, character of the workings, tonnage produced, etc. The latter varies from 300 to 20,000 tons per day. The mines include both high- and low-grade deposits, the greatest depth of the former, at present, being approximately 2500 ft.; and of the latter, 1200 ft. The volumes of air at present being coursed through the mines are from 60,000 up to 225,000 cu. ft. of air per minute,which, in their relation to the undcrground working force, range from 200 to 800 cu. ft. of air per man, per minute. While not to be taken as criteria, these figures are indicative of the character of the ventilation furnished.

Jan 1, 1923

By Henry Howe

§1. FOUR ASPECTS OF FLOW in the plastic deformation of steel by overstrain, such as punching, wire-drawing, tensile rupture, etc., are: (1) The inter-granular, i.e., the relative movements of the several grains, each as a whole; (2) the intra-granular, i.e., the relative movements of the masses of ferrite or cementite and pearlite within those grains; (3) the intra-pearlitic, i.e., the relative movements of the pearlitic ferrite and cementite; and (4) the crystal unit slipping, i.e., the travel of the minute units past each other, along the slipping planes, giving rise to the slip bands of Ewing and Rosenhain. It may be objected justly that (2), (3), and (4) are in a sense "intra-granular," and that (4) is in a sense "intra-pearlitic." Hence clearness may be gained at times by calling these "Movements of the 2d, 3d, and 4th orders" respectively.

Jan 4, 1914