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By Fred A. Krafft

The time allotted to this paper will permit only the sketching of general principles and practice as generally employed in the industry to maintain and preserve the physical well-being of the miner and his family. Let it be emphasized on behalf of the industry that coal opera- . tors, individually and collectively, have given primary consideration to the appointment of a mine or community physician who is charged with the responsibility of caring for the sick and injured. However, it too frequently happens that with the selection or appointment of the camp doctor many operators wash their hands of further responsibility toward the health and the working efficiency of their employees. The coal industry is so organized in most of the coal-producing areas that not only is the health of the individual miner an important production problem but the collective health of the entire mining community is a fundamental operating problem. This is particularly demonstrated when epidemics of communicable diseases attack entire communities, with resultant loss of life and production and general community distress. The problem and responsibility of maintaining high health standards among miners and their families should be given as much consideration as safety, economical production and efficient distribution are given in the successful operation of coal mines. Company Policy In the inauguration or administration of a medical program for a large mining operation or for an individual mine, the first question to be solved is what the company policy is to be with respect to the following factors pertinent to a medical program: 1. On what basis will the company and the employees finance the program ? 2. Should a contract doctor or a full-time doctor on salary be employed ? 3. What measure of service is to be rendered the employee and his family in return for his monthly contribution to the medical program?

Jan 1, 1936

By V. F. Parry, S. P. Burke

The presence of gas in coal mines necessitates the use of costly ventilation arrangements and the use of expensive mining methods. On the other hand, the gas itself in many instances is of considerable intrinsic value, and its separate recovery might conceivably be a profitable undertaking. This paper is concerned with a study of the movement of gas in coal strata with the object of determining the laws governing gas movement and thus making at least a preliminary step toward the solution of the more practical problem of its control or recovery. Naturally, so important a subject has received much attention from scientists and engineers. In most cases, however, the studies have been concerned with the origin1$, the amount" the composition3 and the method of retention4 of the gas in coal; or, from the more practical side, have been concerned with the phenonlena and conditions associated with outbursts5 or explosions and their control. Numerous studies also have been made of the permeability of coal to gas" of gas pressures measured in coal seams, etc. The authors are unaware, however, of any attempt to present a consistent or complete picture of the laws governing the movement of gas through the coal. Study in West Virginia A recent study conducted at this University7 gives the first presentation of the distribution of pressures in a small section of a coal seam. Holes were drilled into the coal rib to various depths and at various distances from the coal face. The location selected for study was as remote as possible from disturbing influences of mining operations, faults, "wants," etc. The pipes extending into the coal that were used to determine pressures were grouted into the borehole for the entire depth of the hole, and great precaution was taken to insure accurate pressure readings. A map of the geology of the region, a map of the probable boundary and extent of the coal seam, a current map of the mine and a

Jan 1, 1936

By V. F. Parry, S. P. Burke

The presence of gas in coal mines necessitates the use of costly ventilation arrangements and the use of expensive mining methods. On the other hand, the gas itself in many instances is of considerable intrinsic value, and its separate recovery might conceivably be a profitable undertaking. This paper is concerned with a study of the movement of gas in coal strata with the object of determining the laws governing gas movement and thus making at least a preliminary step toward the solution of the more practical problem of its control or recovery. Naturally, so important a subject has received much attention from scientists and engineers. In most cases, however, the studies have been concerned with the origin1$, the amount" the composition3 and the method of retention4 of the gas in coal; or, from the more practical side, have been concerned with the phenonlena and conditions associated with outbursts5 or explosions and their control. Numerous studies also have been made of the permeability of coal to gas" of gas pressures measured in coal seams, etc. The authors are unaware, however, of any attempt to present a consistent or complete picture of the laws governing the movement of gas through the coal. Study in West Virginia A recent study conducted at this University7 gives the first presentation of the distribution of pressures in a small section of a coal seam. Holes were drilled into the coal rib to various depths and at various distances from the coal face. The location selected for study was as remote as possible from disturbing influences of mining operations, faults, "wants," etc. The pipes extending into the coal that were used to determine pressures were grouted into the borehole for the entire depth of the hole, and great precaution was taken to insure accurate pressure readings. A map of the geology of the region, a map of the probable boundary and extent of the coal seam, a current map of the mine and a

Jan 1, 1936

By C. M. Young

This is an attempt to bring together some of the knowledge of the coal-forming conditions obtaining during the Pennsylvanian period in the Western Interior Coal Province, to sketch briefly the present extent and character of the coals produced, and to show the beginning of correlation of beds over wide areas. Coals of later age than the Pennsylvanian are not included and, for reasons that will appear later, little attempt is made to cover the districts of eastern Oklahoma and western Arkansas, and northern Texas is omitted entirely. Geological Conditions The conditions that made possible the formation of large coal beds in the United States were most favorable in the Pennsylvanian period, formerly known as the Upper Carboniferous. The geological conditions can be determined from the records, but not the reasons for them. Preceding the Pennsylvanian was the Mississippian, formerly known as the lower Carboniferous and still later as the sub-Carboniferous. During this time, large bodies of limestone were deposited and at the close of the Mississippian they were warped upward and for a long period were eroded. Then there began a period of subsidence, more or less interrupted at times, during which the Pennsylvanian strata were deposited (see table on next page). These consist of sandstones, limestones and shales, with occasional coal beds. At the beginning of the Pennsylvanian there was subsidence, which allowed the sea to extend over the eroded Mississippian surface to the north and east. It passed over eastern and central Texas, a large part of Oklahoma, with a projection into Arkansas, over Kansas and part of Nebraska, all the northern and western part of Missouri, a large part of Iowa except a strip in the north, most of Illinois, practically all of Kentucky, northern Tennessee, most of Indiana, all of the eastern part of Ohio, practically all of West Virginia, western Maryland, the west end of Virginia, and a large part of Pennsylvania. The Ozarks were already up and separated the main body of this sea, which covered the northern

Jan 1, 1936

By C. M. Young

This is an attempt to bring together some of the knowledge of the coal-forming conditions obtaining during the Pennsylvanian period in the Western Interior Coal Province, to sketch briefly the present extent and character of the coals produced, and to show the beginning of correlation of beds over wide areas. Coals of later age than the Pennsylvanian are not included and, for reasons that will appear later, little attempt is made to cover the districts of eastern Oklahoma and western Arkansas, and northern Texas is omitted entirely. Geological Conditions The conditions that made possible the formation of large coal beds in the United States were most favorable in the Pennsylvanian period, formerly known as the Upper Carboniferous. The geological conditions can be determined from the records, but not the reasons for them. Preceding the Pennsylvanian was the Mississippian, formerly known as the lower Carboniferous and still later as the sub-Carboniferous. During this time, large bodies of limestone were deposited and at the close of the Mississippian they were warped upward and for a long period were eroded. Then there began a period of subsidence, more or less interrupted at times, during which the Pennsylvanian strata were deposited (see table on next page). These consist of sandstones, limestones and shales, with occasional coal beds. At the beginning of the Pennsylvanian there was subsidence, which allowed the sea to extend over the eroded Mississippian surface to the north and east. It passed over eastern and central Texas, a large part of Oklahoma, with a projection into Arkansas, over Kansas and part of Nebraska, all the northern and western part of Missouri, a large part of Iowa except a strip in the north, most of Illinois, practically all of Kentucky, northern Tennessee, most of Indiana, all of the eastern part of Ohio, practically all of West Virginia, western Maryland, the west end of Virginia, and a large part of Pennsylvania. The Ozarks were already up and separated the main body of this sea, which covered the northern

Jan 1, 1936

By Maurice Ewing, J. A. Peoples, J. W. Peoples, A. P. Craby

The purpose of this paper is to present the results of the application of the earth-resistivity method of subsurface investigation to the problem of locating seams of anthracite coal beneath a mantle of soil and subsoil. Details are given of the successful use of this method in locating the outcrops of anthracite seams in actual prospecting. The presence of the outcrop of an anthracite seam is indicated at points where electrical resistivity tests showed relatively low readings. The reason for this is that in some localities the resistivity of anthracite was found to be about 0.0001 megohm-cm. compared to 1 to 200 megohm-cm. for shales and sandstones. For two reasons it is believed that the data summarized in this paper should be of particular interest. In the first place, most of the interpretations of the resistivity survey have been checked by subsequent drilling and some by the removal of the overburden and the exposing of the anthracite seams. It is infrequent that the opportunity for checking results so thoroughly is given. In the second place, the fact that recent commentatorsl,2,3 on the application of geophysical methods to mining have concluded that direct prospecting for anthracite and other types of coal is not promising makes the good results obtained more significant. So far as the authors can learn, the only previous experiment with electrical methods in the Pennsylvania anthracite field was one made by Sherwin F. Kelly in 1921, when he used the self-potential method at Wilkes-Barre4. The profile he made does not show a very marked correlation with the geologic cross section. Kelly points out that stray currents from electric motors in the mines undoubtedly affected 'his results, but the experience of the present authors with stray currents from mining machinery suggests the possibility that the potentials measured by Kelly were due almost entirely to this effect.

Jan 1, 1936

By Maurice Ewing, A. P. Craby, J. W. Peoples, J. A. Peoples

The purpose of this paper is to present the results of the application of the earth-resistivity method of subsurface investigation to the problem of locating seams of anthracite coal beneath a mantle of soil and subsoil. Details are given of the successful use of this method in locating the outcrops of anthracite seams in actual prospecting. The presence of the outcrop of an anthracite seam is indicated at points where electrical resistivity tests showed relatively low readings. The reason for this is that in some localities the resistivity of anthracite was found to be about 0.0001 megohm-cm. compared to 1 to 200 megohm-cm. for shales and sandstones. For two reasons it is believed that the data summarized in this paper should be of particular interest. In the first place, most of the interpretations of the resistivity survey have been checked by subsequent drilling and some by the removal of the overburden and the exposing of the anthracite seams. It is infrequent that the opportunity for checking results so thoroughly is given. In the second place, the fact that recent commentatorsl,2,3 on the application of geophysical methods to mining have concluded that direct prospecting for anthracite and other types of coal is not promising makes the good results obtained more significant. So far as the authors can learn, the only previous experiment with electrical methods in the Pennsylvania anthracite field was one made by Sherwin F. Kelly in 1921, when he used the self-potential method at Wilkes-Barre4. The profile he made does not show a very marked correlation with the geologic cross section. Kelly points out that stray currents from electric motors in the mines undoubtedly affected 'his results, but the experience of the present authors with stray currents from mining machinery suggests the possibility that the potentials measured by Kelly were due almost entirely to this effect.

Jan 1, 1936

MISCELLANEOUS U.S. 0,029,598 - Extraction of vanadium values from vanadiferous iron oxide ore. A pelletized mixture of ore, limestone and bentonite is roasted in an oxidizing atmosphere to form calcium vanadates, the calcine ground, the ground material leached with aqueous ammonium carbonate or sodium carbonate to produce a vanadium-rich solution while leaving an insoluble residue of calcium carbonate and/or calcium bicarbonate along with undissolved iron values, and the solution separated and treated for its vanadium content. This patent is a reissue of U.S. Patent No. 3,853,982, dated Dec. 10, 1974. C. B. Bare and J. W. Pasquali, assigned to Bethlehem Steel Corp. Mar. 28, 1978. 7 pp. (423-68). Filed: 3-3 1-77 (783,352).

Jan 1, 1979

US 4,135,913-Extraction of nickel values from iron-containing nickel sulfide ore, particularly pentlandite or nickeliferous pyrrhotite A mixture of raw ore, roasted ore, or iron powder, and coal as a reductant is heated to a temperature of 800- 1000° C in a nonoxidizing atmosphere to convert the bulk of the iron content to metallic iron while diffusing into the iron the bulk of the nickel, the mixture cooled, and the cool material separated into a magnetic fraction containing most of the nickel and a non-magnetic gangue fraction A Illis arid L S Renzoni, assigned to International Nickel Co, Inc Jan 23, 1979 7 pp (75-21) Filed 10-10-75 (621,343) Priority Canada, 10-27-72 (155,032) Same Canadian 981,910, dated Jan 20, 1976 Same British 1,389,145, dated Apr 3, 1975 US 4,135,917-In the recovery of gallium from a solution obtained by the digestion of bauxite or nepheline in an alkali solution for the production of alumina, the digestion solution is neutralized, the neutralized solution evaporated to an op¬timum caustic alkali concentration and adjusted to a ratio of alkali metal oxide to alumina of above 2, the corrected solu¬tion contacted with a gallium-aluminum alloy, arid high-purity gallium recovered from the solution by electrolysis or cemen¬tation K A Badaliants, et al Jan 23, 1979 6 pp (75-109) Filed 12-19-77 (862,201) Priority USSR, 12-22-76 (2,428,¬006) US 4,135,918-Extraction of copper from copper sulfide ore containing also one or more of the metals iron, nickel, arid cobalt Ore is roasted at a temperature of 750-800° C to expel sulfur, the sulfur-free calcine slurried in water containing a sufficient amount of sulfuric acid to supplement any sulfuric acid formed in situ, the slurry heated at 150-165° C in the presence of a reducing gas to form soluble sulfates of metals other than copper while reducing copper to elemental form, arid the slurry filtered to recover copper solids Any precious metals present in the ore will report with the copper solids V A Ettel, A P Devuyst, R Sridhar, arid C. E O'Neill, as¬signed to International Nickel Co, Inc Jan 23, 1979 5 pp (75-117) Filed 3-2-78 (882,610) Priority Canada, 5-13-77 (278,360)

Jan 1, 1980

US 4,181,588 - Direct extraction of lead from lead sulflde ore. Ore is leached with a solution of ferric chloride and sodium chloride. The leach liquor is filtered to remove sulfur and gangue, then cooled in a crystallizer to precipitate lead chloride The slurry from the crystallizer is subjected to electrolysis to deposit lead chloride on the cathode plate. Solution from the electrolysis cell is used in the leaching step. M.M. Wong and F.P. Haver, assigned to US Secretary of the Interior Jan 1, 1980. 6 pp. (204-115). Filed: 1-4-79 (1,026).

Jan 1, 1982

By Fathi Habashi

At the Duisburger Kupferhütte plant in Germany, pyrite cinder is collected from the sulfuric acid manufacturers in that country and processed to recover the nonferrous metals contained in the cinder, before charging it to the blast furnace for iron recovery. A typical analysis of the cinder is given in Table 9-1. The pyrite cinder is mixed with NaCl and treated continuously in a multiple hearth furnace. The evolved gases are scrubbed with water to form a weak acid which is used for the leaching process. Each batch requires about 2 days for leaching. The concentrated leaching solution obtained in the first 15 to 20 hr is sent for copper recovery, while that subsequently obtained, being poor ill metal content, is recycled. The residue, called purple ore, now a high-grade iron ore (61-63 % Fe); is sintered and delivered to the blast furnace.

Jan 1, 1970

By P. G. Nahin, A. Grenall, R. S. Crog, W. C. Merrill

A progress report of an experimental investigation into the role of clay in reservoir performance is presented. The Paper gives some of the reasons for considering clay as a significant component and outlines the objectives of a broad field of stud) which it is intended to pursue. Descriptions of the analytical methods used are given; these include X-ray diffraction. elec tron miscroscopy, thin section petrography, infrared spec-troscopy, and cation exchange analysis. A suite of the more important clay minerals has been assembled and characterized l~y these methods for use as standards in core analysis. From the data obtained it appears that although no one method of analysis is diagnostic for all of the clay minerals the infrared technique shows considerable promise in this direction. For the present, one or more supplementary methods should be used to confirm the clay mineral identifications. The methods of analysis are applied to field cores taken from repesentative and widely differing strata especially as regards their susceptibility to damage by fresh water. well.; completed in the stevens and Gatchell zones in San Joaquin valley are I,articularly clear-cut examples of this behavior with stevens zone wells being more adversely affected by fresh water. cores from these zones have been studied and are discussed. It appears that differences in this behavior can be ascribed to differences in the nature of the contained clays. The value of the infrarecl spectra of the clay fractions in establishing the identity of the predominant clay minerals is given particular emphasis. INTRODUCTION It is a challenge to the technical resources of the petroleum industry that when the economic limit of production is reached, from 40 to 70 per cent of the oil in California reservoirs remains unproduced even by use of the best presently known methods of recovery. The magnitude of this abandoned volume of oil can be appreciated when it is considered that to 1950 in excess of 8 billion bbll has been produced from California reservoirs with estimated economically recoverable reserves in known fields and pools totaling nearly 4 billion bbl.24 If for every barrel of oil produced there is at least another barrel still in place, it is evident that the revenue obtained from the recovery of only a .few per cent of this volume would repay the cost of the required research manyfold. From well completion experience. production behavior, and a growing body of laboratory data it now appears certain that the mineral composition of a producing stratum has an important bearing on the productivity and ultimate yield. In addition to the organic component and water, the cores con,ist of gravel, sand. silt, and clay" in diverse variety of (a, composition and (b) texture. It is the composite effect of these two factors which is probably responsible in large measure for the way in which the oil flows to the well. The role of the clay and fine-size accessory minerals is not clear but there is a growing opinion, based on their physical and chemical properties, that it is a significant one. of particular importance are the prime facts: 1. The silt and clay fractions of the reservoir matrix possess the highest surface area per gram, and 2. The silt and especially the clay fractions are the most chemically reactive of the inorganic constituents present. Only within the last few years has the knowledge of clay mineralogy and the techniques of identifying the clay minerals reached such a stage as to enable reliable inquiry into the composition of argillaceous sediments.2,8,10,11,12,16,26 It is the purpox of this and succeeding papers to add to the fund of information on the role which these materials play in the production of petroleum from California formations by correlating their presence and associated properties with observed reservoir behavior. In the present paper attention is directed to their possible influence on damage by fresh water. OBJECTIVES The attack on this problem divides naturally into two broad phases: 1. Determination of the nature of the clays and their relationships to the other mineral components, and 2. Determination of the physico-chemical relationships between the clays and the interstitial fluids. In the work described in this paper the emphasis has been on phase 1, which stems logically from the necessity of identifying and understanding the materials to be dealt with in Phase 2. Based on the authors' present opinion that not all of the minerals which occur in oil-bearing formation are of equal importance in their effects on the flow and recovery of oil, it was decided to focus attention first upon the clay minerals content and then. later perhaps. work into the field of the normally larger size non-clay minerals and fractions. The

Jan 1, 1951

By W. C. Merrill, P. G. Nahin, A. Grenall, R. S. Crog

A progress report of an experimental investigation into the role of clay in reservoir performance is presented. The Paper gives some of the reasons for considering clay as a significant component and outlines the objectives of a broad field of stud) which it is intended to pursue. Descriptions of the analytical methods used are given; these include X-ray diffraction. elec tron miscroscopy, thin section petrography, infrared spec-troscopy, and cation exchange analysis. A suite of the more important clay minerals has been assembled and characterized l~y these methods for use as standards in core analysis. From the data obtained it appears that although no one method of analysis is diagnostic for all of the clay minerals the infrared technique shows considerable promise in this direction. For the present, one or more supplementary methods should be used to confirm the clay mineral identifications. The methods of analysis are applied to field cores taken from repesentative and widely differing strata especially as regards their susceptibility to damage by fresh water. well.; completed in the stevens and Gatchell zones in San Joaquin valley are I,articularly clear-cut examples of this behavior with stevens zone wells being more adversely affected by fresh water. cores from these zones have been studied and are discussed. It appears that differences in this behavior can be ascribed to differences in the nature of the contained clays. The value of the infrarecl spectra of the clay fractions in establishing the identity of the predominant clay minerals is given particular emphasis. INTRODUCTION It is a challenge to the technical resources of the petroleum industry that when the economic limit of production is reached, from 40 to 70 per cent of the oil in California reservoirs remains unproduced even by use of the best presently known methods of recovery. The magnitude of this abandoned volume of oil can be appreciated when it is considered that to 1950 in excess of 8 billion bbll has been produced from California reservoirs with estimated economically recoverable reserves in known fields and pools totaling nearly 4 billion bbl.24 If for every barrel of oil produced there is at least another barrel still in place, it is evident that the revenue obtained from the recovery of only a .few per cent of this volume would repay the cost of the required research manyfold. From well completion experience. production behavior, and a growing body of laboratory data it now appears certain that the mineral composition of a producing stratum has an important bearing on the productivity and ultimate yield. In addition to the organic component and water, the cores con,ist of gravel, sand. silt, and clay" in diverse variety of (a, composition and (b) texture. It is the composite effect of these two factors which is probably responsible in large measure for the way in which the oil flows to the well. The role of the clay and fine-size accessory minerals is not clear but there is a growing opinion, based on their physical and chemical properties, that it is a significant one. of particular importance are the prime facts: 1. The silt and clay fractions of the reservoir matrix possess the highest surface area per gram, and 2. The silt and especially the clay fractions are the most chemically reactive of the inorganic constituents present. Only within the last few years has the knowledge of clay mineralogy and the techniques of identifying the clay minerals reached such a stage as to enable reliable inquiry into the composition of argillaceous sediments.2,8,10,11,12,16,26 It is the purpox of this and succeeding papers to add to the fund of information on the role which these materials play in the production of petroleum from California formations by correlating their presence and associated properties with observed reservoir behavior. In the present paper attention is directed to their possible influence on damage by fresh water. OBJECTIVES The attack on this problem divides naturally into two broad phases: 1. Determination of the nature of the clays and their relationships to the other mineral components, and 2. Determination of the physico-chemical relationships between the clays and the interstitial fluids. In the work described in this paper the emphasis has been on phase 1, which stems logically from the necessity of identifying and understanding the materials to be dealt with in Phase 2. Based on the authors' present opinion that not all of the minerals which occur in oil-bearing formation are of equal importance in their effects on the flow and recovery of oil, it was decided to focus attention first upon the clay minerals content and then. later perhaps. work into the field of the normally larger size non-clay minerals and fractions. The

Jan 1, 1951

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 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

The Board of Directors has authorized the following offers of sets of back volumes of the Transactions, at considerably reduced prices, to Members, Libraries, and Scientific Societies Per Set. I. Five volumes, bound in half-morocco, from No. 36 (1906) to No. 40 (1910), . $20 II. Ten volumes, bound in half-morocco, from No. 31 (1902) to No. 40 (1910), including Mexican Volume, 35 III. Twenty volumes, bound in half-morocco, from No. 21 (1893) to No. 40 (1910), 50

Jan 4, 1913

C. R. CORNING, Chairman. ADOLPHE E. BORIE, First- Vice-Chairman. THOMAS T. READ, Secretary, Woolworth Bldg., New York, N. Y. Vice-Chairmen. JOHN H. ALLEN, GEORGE M. COLVOCORESSES, RICHARD M. ATWATER, JR., -ROBERT PEELE, GEORGE D. BARRON, CHARLES P. PERIN, A. CHESTER BEATTY, JOSEPH A. VAN MATER, J. PARKE CHANNING, ARTHUR L. WALKER. D. C. Bard, Howard Eckfeldt, Milton H. McLean, W. de L. Benedict, R. C.Gemmell, ' Philip N. Moore, John C. Branner, F. Louis Grammer, T. H. O'Brien, Palmer Carter, Ernest A. Hersam, James J. Ormsbee, Allan J. Clark, Edwin C. Holden, Edward W. Parker, F. Crabtree, William L. Honnold, John B. Porter, George G. Crawford, Reginald E.. Hore, R. M. Raymond, O. C. Davidson, C. Colcock Jones; Robert B. Richard's, E. V. D'Invilliers, Eugene P. Kennedy, LeRoy Salsich, James S. Douglas, Chester F. Lee, Henry L. Smyth, Walter Douglas, Richard S. McCaffery, F. W. Traphagen, Howard N. Eavenson, James F. McClelland, Elton W. Walker. Meetings of this committee were held at the Institute headquarters on April 18, May, 3 and 15, and June 19.. At the meeting of June 19, the Secretary reported that letters of invitation to apply for membership in the Institute had been sent to all the alumni of the School of Mines of Columbia University and also to all State Mine Inspectors and their deputies. He also reported the securing of lists of the alumni of the Harvard Engineering Schools, and of the Mining Schools at Houghton, Mich. ; Butte, Mont. ; State College, Pa. ; Seattle, Wash. ; Fayetteville, Ark.; Laramie, Wyo.; Montreal, Canada, and Wor-cester and Rensselaer Polytechnic Institutes. Arrangements were made to invite all these to join the Institute. It was suggested that a. member' of the Institute resident in Australia be appointed to this Committee, also one from Japan. Attention of the members of the Committee was drawn to the fact that letters requesting, others to join the Institute will be written in the offices of the Institute if desired. The applications for membership received recently have been as follows March, 30; April, 02; May, 70; June, 54. The next meeting will be held July 17. THOMAS T. READ, Secretary.

Jan 7, 1913

INTERNATIONAL GEOLOGICAL CONGRESS. (For further particulars apply to the Secretary, 12th International Geological Congress, Victoria Memorial Museum, Ottawa, Canada ; cable address, Geocong, Ottawa.) The Coal Resources of the World.-Three quarto volumes of about 400 pages each, 8 1/4 by 10 3/4 in., and an atlas of about 70 maps in colors, 13 1/3 by 19 1/2 in., bound in heavy paper cover. Edition limited to 3,000 copies, One thousand copies will be reserved for members of the International Geological Congress, and the remainder of the edition will be distributed in the order in which applications are received. Price, $35 per set. Ready in July, 1913. This book is an inquiry made upon the initiative of the Executive Committee of the Twelfth International Geological Congress, with the assistance of geological surveys and mining geologists of different countries, published by: Morang & Co., Ltd., Toronto, Canada. Headquarters During Session at Toronto. The headquarters will be a t the University of Toronto, where there will be a branch post-office open at all hours and at which registered mail may be received or despatched, money orders sent or cashed, etc. A hank will be established at which money may be exchanged. A typewriting service will be maintained, also a telephone service and messenger service. Railway and steamship agents will also be in attendance. A restaurant service providing luncheon in the middle of the day will be arranged.

Jan 8, 1913

COMMITTEE ON INCREASE OF. MEMBERSHIP. C. R. CORNING, Chairman. ADOLPHE E. BORIS, First Vice-Chairman. THOMAS T. READ, .Secretary, Woolworth Bldg., New York, N. Y. Vice-Chairmen. JOHN H. ALLEN, GEORGE M. COLVOCORESSES, RICHARD AL ATWATER, JR., ROBERT PEELS, GEORGE D. BARRON, CHARLES P. PERIN, A. CHESTER BEATTY, JOSEPH A. VAN MATER, J. PARKE CHANNING, ARTHUR L. WALKER. D. C. Bard, Howard Eckfeldt, Philip N, Moore, W. de L. Benedict, R. C. Gemmell, T. H. O'Brien, John C. Branner, F. Louis Grammer, James J. Ormsbee, Palmer Carter, Ernest A. Hersam, Edward W. Parker, Allen J. Clark, Edwin C. Holden, John B. Porter, F. Crabtree, William L. Honnold, R. M. Raymond, George G. Crawford, Reginald E. Hore, Robert H. Richards, O. C. Davidson, C. Colcock Jones, LeRoy Salsich, E. V. D' Invilliers, Eugene P. Kennedy, Frederick H. Sexton, James S. Douglas, Chester F. Lee, Henry L. Smyth, Walter Douglas, - Richard S. McCaffery, F. W. Traphagen, Howard N. Eavenson, James F. McClelland, Elton W. Walker. Milton H. McLean, Meetings of this committee were held at the Institute headquarters on April 18, and May 2 and 15. It was resolved that meetings shall be held monthly on the third Friday of each month.

Jan 6, 1913