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By John Norton

IN recent years, the damping capacity of metals has come to be recognized as an important index of certain types of structural change. In a number of instances, this property has proved to be particularly sensitive, but insufficient work has been done to permit a general inter-pretation. There is considerable question at the present time as to just what factors are responsible for the internal dissipation of energy when a metal is carried through a cycle of stress, and these factors must be ascertained if the value of the damping method as a metallurgical tool is to be determined. Since internal stresses are among the chief causes of dissipation of internal energy, or damping capacity, it was thought that a study of the changes in damping during the recovery and recrystalliza-tion of a cold-worked metal might throw some light upon the subject, particularly if the damping changes were correlated with other properties that are better understood. Probably more work has been done on the recrystallization phenomena of alpha brass than on any other metal, so this was chosen as the material for the present investigation. Damping measurements on brass have been made by Förster and Köster.1 They showed that the annealing of a brass that had been cold-drawn to 50 per cent reduction produced a rapid fall in the damping, a flat minimum occurring at approximately the temperature of recrystal-lization. The damping remained at a low value until grain growth was well under way and then it increased rapidly with increasing grain size. Köster and Rosenthal2 continued the work in greater detail. They pointed out that the damping decrease does not correspond to the hard-ness drop but occurs at a lower temperature, suggesting that the relief or redistribution of internal stresses has a large effect while the actual recrystallization effect is small. They also show the increase in damping at the higher annealing temperatures. Their curves are reproduced in Fig. 1.

Jan 1, 1940

By Kenneth N. McLeod, Donald W. McGlashan

In the use of free bubbles with precise temperature control and continuous pH measurement, the contact angle apparatus differs from all previous equipment. Experimental procedures differ sharply from the captive bubble method of introducing the gaseous phase in the three-phase system. When freed from the tube and captured by a solid surface, a bubble more closely conforms to the spherical ideal set up by the usual mathematical analysis of surface free energy or surface tensional relationships of the forces involved. The assembled equipment, Fig. 1, departs from the usual contact angle apparatus in providing: 1) water circulation for fixing temperature, 2) instruments to measure and record pH during testing, and 3) a system for producing and using free bubbles. The apparatus allows testing over a broad range of closely controlled conditions, and the use of free bubbles gives contact angles independent of operator manipulation, which was unavoidable in the older captive bubble method. A bubble released below the specimen rises through the liquid and contacts the mineral. If the mineral is gas-avid the bubble adheres, developing a finite contact angle.

Mar 1, 1956

By Research Staff ? Verde Copper Mines

FLOTATION is now commonly practiced in alkaline ore pulps, yet little is known regarding the action of the alkaline solutions on the ore particles beyond the fact that films of oxidized material form. We wish to chronicle our discovery of the presence of soluble reducing agents in alkaline ore pulps of the United Verde, and present some data on lime consumption. During the grinding and flotation of a pyritic ore containing small amounts of ferrous sulfate and other soluble salts, an excess of lime was added to precipitate the salts, and filtered samples of the solution were titrated with standard permanganate solution. Even in pulps of high causticity an appreciable permanganate titration was always obtained, in spite of the fact that the solutions were shown to contain little iron. Investigation of the cause brought about the discovery of several previously unsuspected compounds in flotation pulps made from pyritic ore. Not only the reducing agents present had to be identified, but also the amount of dissolved oxygen, and a survey was finally made of the free oxygen content and reducing agents of the mill pulp in the concentrating mill at Clarkdale. A great many. compounds might form, caused by oxidation of pyrite or other metal sulfides or by reaction between a lime solution and pyrite. The most probable compounds considered were calcium sulfides, polysulfides, thiosulfates, and polythionates. Later it was discovered in the literature that in alkaline pulp polythionates do not exist and if introduced are decomposed into sulfites and thiosulfates.1 Any precipitated sulfur is changed by alkali into thiosulfate and polysulfide. Sulfites and sulfides react to form thiosulfate, so that in the end it is possible to have in an alkaline solution only thiosulfate and an excess either of sulfide or sulfite. Confirmatory tests were made and it was finally established that the alkaline mill pulps made from the United Verde ore contained

Jan 1, 1929

By Peter McKellar

The district around Bag bay in Shoal lake, meat of Lake of the Woods, in the Ontario western gold-fields, is attracting considerable attention at the present time as a gold-producer. A large number of gold-bearing veins have been prospected and mined to a considerable extent in the locality. On the whole they make a fair showing, considering the work done ; and some are undoubtedly rich—the Mikado, for instance. The principal mining companies that have been operating here are the Yum-Yum, Ontario Limited, Cornucopia, Engledue Concession, Tycoon, Toronto and Western and Mikado Cos. I will confine my remarks chiefly to the three companies last

Jan 1, 1900

By J. C. Osler

The design of a tailings dam is a geotechnical engineering project of considerable scope. For the design, it is necessary to establish the engineering properties of the soil or rock strata which will support the dam and the tailings or other fill which will be used to construct the dam. The various field and laboratory investigations which are necessary to obtain the required design parameters are discussed in the paper and the use of these parameters to compute stability, settlement, and seepage are considered. The designer of a tailings dam can never assume an absolute knowledge of the properties of the foundation strata. Further, initial design assumptions are often approximate, particularly with regard to the distribution of pore pressures through and beneath the dam. Thus, the installation of performance monitoring instruments is recommended, since data obtained from such instrumentation can be used to check the stability of the structure both during construction and after its completion.

Jan 1, 1972

By I. C. White

Only two factors appear to be directly responsible for the geographic distribution of sulfur in the coal fields of West Virginia: these are the stratigraphic position of the coals in question, and the eastward or westward location of the deposits. There appears to be a progressive increase in the sulfur content of West Virginia coals from the oldest Peqnsylvanian deposits in the Pocahontas, New River, and Kanawha Groups of the Pottsville Series up through the Allegheny, Conemaugh, and

Jan 1, 1920

By Z. M. Zavodni

The stability of waste dumps depends to a great extent on the physical properties of the underlying foundation. These physical properties are evaluated through surface geotechnical surveys, subsurface exploration, and field and laboratory testing. Sufficient information must be obtained to define and assess the strength, consolidation, distribution, topographic and hydrogeologic properties for these materials. Important foundation data collected in the field include: surface infiltration rates, downhole hydraulic conductivities, ground water levels, bedrock structural parameters, soil types and soil thickness. Laboratory testing should identify the classification, strength, moisture content, hydraulic conductivity, attenuation and consolidation characteristics. Summarized in this paper are procedures and typical results of porphyry copper leach dump foundation investigations. Laboratory properties and design recommendations for potenia1 foundation liner materials are described. Back analysis and laboratory foundation strengths are compared. The topographic effect of the foundation on dump behavior is discussed and a foundation pore pressure monitoring experiment at the toe of an active waste dump is described.

Jan 1, 1985

By Joseph Kuti

Longwall mining is the term used for the underground extraction of a wide and deep panel of coal. Such a panel may be blocked out by one or more entries on either side ("head" and "tail") of a longwall face. If all the entries are pre-driven, the panel extraction is termed longwall retreat mining. With one exception, all the longwall faces in the United States are of this type3 Prior to the general decline in the rates of production with Continuous Miners, the development of the multiple entries generally kept ahead of the longwall extraction rate. This is no longer the case: longwall extraction rates far exceed the rate of development. In addition to this problem, in newly established mines, the development of a haulage and bleeder system based on multiple entries results in a lead-time of three years or more before longwall mining can be applied. This is one reason why earlier projections and much of the optimism attached to longwall mining as a principal "savior" in the energy crisis should be viewed with some caution. The alternatives to retreat mining with multiple entries are: Modified retreat mining- where the tail-entry is being formed during the mining of-the panel ("2"-system). Some form of advance mining-where the head-entry or both head and tail entries are being formed as part of the longwall extraction process. These methods are well-known and well-established. Variants of them are being practiced in Canada, Central and South America, but not in the US. It is primarily the laws governing ventilation-conceived for room and pillar mining which prevent the rapid development of these techniques. Another aspect of longwall mining is that it requires a systematic and consistent approach in organization, roof control, ventilation and transport. It is for this reason that compliance with health and safety regulation is fairly well ensured if the longwall system has been well laid out and is subsequently well-run. Nevertheless, a management mentality raised in the great flexibility of the room and pillar system cannot always come to terms with the degree of forward planning and rigid discipline required to successful longwall mining. Research, development and other investments in the partial aspects of longwall mining are always of interest, but no massive trend to longwall can be expected realistically unless these major stumbling blocks in the basic law and basic approach are effectively removed.

Jan 1, 1980

By P. B. Bucky

THE purpose of this paper is to present a scientific method for deter-mining the proper span and shape of roof for safe and economical mining; at present, these two vital factors wherever pillars are left to support the roof are determined by local practice or general experience. To develop the method described here, experimental laboratory work was done. The arch adopted was a segment of a circle, a flat roof being considered an arch with an infinite radius. Hitherto, arches have been used underground without the background of stress analysis that generally precedes arch construction on the surface. In many cases results have not been as expected, because of the lack of knowledge of the factors affecting its strength and behavior. A theoretical and experimental study of arches should furnish informa-tion that will make it possible to design safe and economical surface structures as well as underground openings. For example, on the subject of mine drifts and tunnels, the present idea is that arching their backs increases their strength; this paper will indicate that this is not always true, and if it can be shown that under certain conditions arching becomes unnecessary an economic saving will result. In room-and-pillar work a question may arise as to whether arching the roof and gobbing the excavated material will result in timber saving, and a decrease in the dan¬gers from falls of roof. It is to be distinctly understood that each mine must be treated as an individual problem, and that answers to these ques-tions and many others can now be found after experimental laboratory data have been obtained.

Jan 1, 1934

By J. Skrove, C. R. Boardman

In situ permeability of the rock outside the Hardhat chimney was determined by pressurization of long holes with air. Experimental data indicated a remarkable difference between fracture permeability of the rock near the chimney and that at a considerable distance. Although permeable fault zones were known to exist in the granite stock, the measurements of background permeability were quite low, on the order of tenths to several millidarcies. The observed difference is about two or three orders of magnitude above this background in the region 125 to 215 ft radially from the shot point, or 80 to 165 ft radially from the vertical axis of the chimney. The presence of a collapsed drift immediately beyond this region precluded measurements which could have defined the maximum extent of the zone of high permeabilily. INTRODUCTION Previous exploration has revealed that contained nu-clear explosions create cavities which generally collapse, resulting in rubble-filled chimneys and annular fractured zones. These geometries have been shown to result in complex flow regimes which should increase the production rate from hydrocarbon reservoirs.' Empirical scaling equations have been developed for estimatina chimney radii and heights for a variet; of rock media.' The exten; of the annular fractured zone has been documented and associated permeability changes have been observed qualitatively for several explosions. This study was begun to establish the nature and magnitude of the permeability of the latter region. It is anticipated that results will be useful in estimating permeability changes and consequent production stimulation which might ensue from a contained explosion in a hydrocarbon reservoir. The post-shot environment of the Hardhat event (a 5-kt contained nuclear explosion in granitic rock) was c'hosen for the experimental measurements. The Hardhat device was detonated at a depth of 939 ft, and subsequent exploration revealed a chimney of broken rock with a radius of 65 to 70 ft and a height above shot point of 281 ft.' BeFore the explosion, the Hardhat medium was highly jointed and fractured (Fig. I). Jt was expected that differential rock motion along these and other weaknesses induced during cavity growth and collapse would significantly alter the permeability of the rock mass. EXPERIMENTAL METHOD Initially, three 2-in. diameter holes (Nos. 10, 12 and 19) were drilled about 25 ft outward through the walls of the 500-ft level drift (elevation 4,253 ft, Fig. 2). One was drilled near the chimney and two holes, one vertical and the other horizontal, were drilled near the shaft. Order-of-magnitude differences in permeability obtained by pressurization measurements indicated further: investigation was warranted. A series of 3-in. diameter holes was then drilled with water as a coolant into the walls and roof of the drift (Fig. 2). An 11-in. long packer was set from 1 to 8 Et inside each hole and air was injected at measured Row rates. Hole pressures were monitored at the collar. Permeability was low enough in the holes near the access shaft that pressure could be maintained long enough to obtain good pressure decay rates. In the vicinity of the chimney, however, permeability was so high that this was not possible and air was injected under steady-state conditions. About one year later, these same holes were retested to

Jan 1, 1967

By N. M. Macmillan, R. S. Kalyoncu, A. R. C. Westwood

The environment-sensitive hardness and laboratory-scale rotary drilling behavior of granite, quartz, and feldspar have been studied. By controlling the chemistry of the drilling environment, it is possible to triple the rate of drilling granite. Pre-existing flaws or other microstructural features play a minor role.

Jan 1, 1975

By Arthur Foote

AT THE end of the year 1914, the main North Star incline shaft had reached the 6300-ft. level, and encountered a vein dipping Southwest, or, exactly opposite to the North Star. Subsequent development failed to find the North Star vein continuing beyond this intersection, so the 6300-ft. level proved to be the bottom level of the North. Star vein, and very little ore was found below the 5300-ft. level. The new vein was called No. 1 vein. Development work carried on for the next 10 years discovered a third vein, called No. 2, branching off about 1200-ft. to the east, with a North-south strike and a west dip. No. 1 vein had about 900 ft. of backs above the 6300-ft. level before reaching the boundary line of the property, and No. 2 vein died out about 800 ft. above. During these 10 years, the money spent on development was increased from $54,000 in 1914 to $184,000 in 1924; the ore reserves steadily diminished until it was evident that the mine must close down unless by some means a large tonnage of ore could be developed quickly.

Jan 1, 1930

By Charles MacDowell

Up to 1909 the American public had little knowledge of, or interest in, potash. Some remembered that it had to do with soft soap and sore throat, but further they knew not. In 1909-10, the German-American potash war, and the publicity attending hostilities, brought home to America the knowledge that potash was an important article of commerce; that Germany monopolized its production and distribution, and exercised all the prerogatives attending complete control. The present war, with its transportation embargo, has again directed attention to Germany's strength as a potash producer and her present unfortunate situation as a distributor. As a consequence, the search for potash takes on new life and it again becomes a subject of general interest. My first knowledge of potash came from a study of the German potash exhibit at the World's Fair in 1893. This investigation led to the recommendation that Armour & Co. engage in the manufacture of commercial fertilizers and the fertilizer branch was organized early in 1894. From then to now "potash" has been a live subject. Two and eight-tenths per cent. of the earth's crust consists of potassium oxide. It is an important constituent of feldspar, granite, and other igneous rocks. Potash is valuable commercially in a water-soluble form. In igneous rocks it is locked in so tight that it is of little value and no utilization in a commercial way has been made of these insoluble forms. Potash in water-soluble form is found in large deposits in Germany; in smaller deposits in Austria and Spain; and in brines in some of our Western arid basins. The deposits in Germany, Austria, and Spain are concentrations from sea waters containing potash derived from the decomposition of potash-bearing rocks.

Jan 2, 1915

By G. M. Webster, G. E. Dawsongrove

The use of percussion-type side-wall cores as an aid in detection and evaluation of hydrocarbon shows and in examination of rock properties has become increasingly popular in recent years. Sidewall coring has an advantage over normal bottom-hole coring methods in that the zones may be surveyed with the electric log prior to selection of sample depths. This allows an efficient sampling of all zones of interest, a procedure not possible with bottom-hole coring techniques unless the costly procedure of continuous coring is utilized. Percussion sidewall coring presently provides the most rapid and lowest cost method of obtaining sidewall cores. It has been recognized for some time that certain discrepancies exist between core analysis data obtained from percussion cores and data obtained from other types of core Samples. This paper presents existing field and laboratory data that were available to the authors. Several examples of comparative core analysis data obtained from various fields are presented along with photomicrographs of thin sections of conventional and percussion cores. The results of this investigation are presented to throw more light on the possible disturbed condition of percussion sidewall cores. SAMPLE DISTURBANCE AND FRACTURING The principal cause of discrepancy between conventional core analysis data and percussion sidewall core analysis data is believed to be the shattering and re-adjustment of the grains due to the large impact shearing forces produced by mechanics of percussion coring. Figs. 1 through 5 are photomicrographs of thin section slides of formation samples obtained by means of diamond cores, conventional cores, and percussion sidewall cores. Figs. 1 and 2 show samples of the

By T. M. Geffen, F. F. Craig

Laboratory model flow tests have been made to simulate field conditions of partial pressure rnaintenance by dispersed gas drive on rocks having sandstone-type porosity. In this production method there is a significant saturation gradient between injection and production wells. A means of calculating relative permeability characteristics. from partial pressure rnaintenance flow tests has been developed. This method takes into account the saturation gradient. These kg/ko characteristics are identical to those for solution and external gas drives. This method of calculation, which has been proved experimentally, has limitations; however, it is valid for cases likely to be encountered in field prediction of partial pressure maintenance performance. The production performance of a hypothetical reservoir has been calculated for several different injection programs, involving both full and partial pressure maintenance. Results indicate that the maxinum oil recovery by these gas injection programs is obtained by full pressure mainte- nance at the original bubble point. Correspondingly lower oil recoveries are obtained by postponing gas injection and/or by reducing the degree of pressure maintenance. INTRODUCTION Dispersed gas injection is an important method of recovering additional oil beyond that obtainable by pressure depletion alone. The injected gas acts as a source of additional energy to displace oil from the rock formation as well as to retard oil shrinkage in the reservoir. In practice, gas injection is usually started after the reservoir pressure has fallen below the original bubble point. For various reasons sufficient gas is generally not injected to completely maintain the pressure in the reservoir. So, injecting gas at a declining reservoir pressure results in a combined external and solution gas drive. These two oil displacement processes are characterized by different gross saturation distributions in the reservoir. The external gas drive, like all frontal drive processes, inherently results in an oil saturation which increases from the injection wells to the producing wells. In the solution gas drive there is essentially a uniform oil saturation throughout the reservoir, provided the field is being depleted uniformly. It has been customary to predict oil recovery performance under partial pressure maintenance by a method which does not take into account the saturation gradient1. It has been shown2 that neglecting the presence of a saturation gradient can cause considerable error. It is the purpose of this paper to develop and present an improved method of predicting partial pressure maintenance performance of reservoirs including, where necessary. the effects of well arrangement. From the laboratory standpoint, this problem involves the measurement of the basic flow behavior (relative permeability characteristics) under partial pressure maintenance conditions. Recent research- as shown that for rocks having sandstone-type porosity, the relative permeability characteristics are identical for solution gas drive and complete pressure maintenance external gas drives. Since both solution and external drives have the same basic flow behavior, it was speculated that partial pressure maintenance, being a combination of the two, would also

Jan 1, 1957

By H. A. Coy

THE Mascot mines of the American Zinc Co. of Tennessee are situated in the Holston River valley, in Knox County, Tennessee, about 13 miles (20.9 km.) east of the city of Knoxville, and form a property of three operating shafts and one open pit. A second open pit is located at Jefferson City about 16 miles (25.8 km.) east of the Mascot mines. Geology Topography.-The principal topographical features of the region within which the zinc deposits occur is a series of parallel northeast and. southwest ridges which reach altitudes of 200 to 400 ft. (61 to 122 m.) above the valley. These ridges are formed of resistant formation such as sandstone, quartzites, etc., while the valleys are occupied principally by limestone, including Knox dolomite, and by shale and other formations subject to quick erosion. The Holston River valley is wide and open with a rolling surface. Sink holes are common to the limestone portion, the general aspect of the valley being that of well-rounded hills with low intervening valleys superimposed upon which is a characteristic sink-hole topography. General Geology.-According to Keith, the rock formation of the area extends from the lower Cambrian into the Silurian. The region has undergone severe deformation with heavy faulting, the underlying Cambrian having been brought to the surface by a series of low angle thrust faults, the strike of the faults and formations paralleling the general northeast and southwest direction of the topography and clipping at varying angles to the southeast. In general the Cambrian quartzites, sandstone, etc., occupy the ridges while the Cambro-Silurian dolomites, limestone and shales occur principally in the valleys. Of the latter, the Knox dolomite is of particular interest to this paper in that it is the ore carrier in the Mascot area. The ore is associated with more or less irregular breccia zones, the degree of brecciation varying from-a fine crushing to a breaking that involves blocks of large size. The breccia zones

Jan 9, 1917

By J. S. Westwater

The Mather mine of The Negaunee Mine Co. embraces nearly all of Sections 1 and 2, T47N, R27W, within the limits of the cities of Negaunee and Ishpeming on the Marquette iron range of Michigan's Upper Peninsula. Operations of the Negaunee Mine Co., the stock of which is jointly owned by Bethlehem Steel Co. and The Cleve-land-Cliffs Iron Co., are under the direction of the latter company. The opening of the Mather mine was described by C. W. Al1en.† Mather " A " shaft was completed to an initial depth of 2352 ft in early 1943. The shaft capacity of over one million tons yearly is in prospect of being realized by orderly development and mining, and sinking of the second or "B" shaft then started in accordance with previous planning. Mather "B," also a vertical shaft, was designed as a twin to Mather "A" shaft and the sinking technique developed at Mather "A" was utilized in "B" shaft operation. Shaft Sinking General Plan An average depth of 16 ft of sand overburden at the shaft site was cleared away by bulldozer, and the shaft approximately 15 by 20 ft in rock opening put down to an initial depth of 87 ft. Mucking of the broken rock to this depth was accomplished by an Insley excavator equipped with a 1/2 yard ca-pacity Owens clamshell bucket. Addition of 200 lb weight to each lip of the clam bucket provided adequate "bite" to dig the broken diorite and jasper rock. Temporary heavy wood bearers were placed across the shaft mouth to support the steel shaft sets which were hung in this initial 87 ft depth, aligned accurately and concreted in place from the lowest set upwards. The permanent steel headframe foundations and three service tunnel openings to the shaft were also concreted in the upper section to the shaft collar. A temporary wood headframe was then erected over the shaft mouth, and initial hoisting machinery assembled consisting of a Lake Shore 12 ft diam single drum grooved for a 1 3/8 in. rope and powered by two 400 hp motors to attain hoisting speed of 1100 fpm. Compressed air was obtained from a Nordberg 2 stage tandem horizontal type with a capacity of 1500 cfm. An enclosed landing platform at the shaft collar was equipped with a rotary dump and pocket for discharge of the rock into a Euclid 15 ton truck. On completing assembly of this equipment and installation of a special cage in the shaft, sinking was resumed on a three shift, six days per week

Jan 1, 1950

In March 1956 a conference on geochemical methods of prospecting for ore deposits was held in Moscow. This conference was the culmination of a ten-year period of extremely rapid increase in both research and routine application of geochemical prospecting methods in the USSR. This activity was divided among groups centered in extremely widely separated bases of operation, ranging from Moscow and Leningrad in the West, Yerevan in the Caucasus, and Alma-Ata in Central Asia to Chita near the Manchurian frontier in the Far-East. The All-Union Conference on Geochemical Methods of Prospecting for Ore Deposits, as the meeting was called, was the first opportunity for these scientists from many parts of the country to meet and exchange experiences. It also served to introduce members of the different research laboratories located in the city of Moscow itself, where adequate channels of technical communication had not yet been established. As a result of the Conference, it was resolved that a concerted effort should be made for the participants to publish the results of their work. Two books have appeared as a direct response to this resolution. I. I. Ginzburg prepared a synthesis of the field of geochemical prospecting for minerals based on the material presented at the Conference. This volume has been translated into English and is now available. In addition, the individual papers presented at the Conference were assembled into a symposium volume and published in 1957 under the editorship of V. I. Krasnikov. Unless otherwise noted, these two books have supplied the source material for the present appraisal of the status of geochemical prospecting in the USSR. It is thus about four to five years old. In the years following the conference, the literature has carried a substantial volume of technical papers, together with a few monographs pertaining to specialized aspects of geochemical prospecting.

Jan 6, 1960

By B. W. Gandrud

WET-PROCESS coal-washing tables as we know them today have been in use in this country for approximately 25 years. The literature records only a few table installations worthy of note prior to adoption of the present-day differential-motion table. According to Phillip,1 six Campbell bumping tables were being operated by the St. Bernard Coal Co., Earlington, Ky., in 1893. As late as 1923, according to Richardson, 2 such tables were in operation in the Rosedale washery of the Cambria Steel Co., at Johnstown, Pa. Bumping tables probably were not used to any considerable extent except in the plant at Earlington, and at two or three plants in Pennsylvania, but they may be considered as. forerunners of the present-day coal-washing table. The transition from bumping tables to the type of tables now in use signalized a revolutionary change in table design. The advantages of the new design over the old were so outstanding as to make its adoption inevitable. BUMPING TABLES Bumping tables, as the name implies, utilized a bumping action for conveying the refuse and discharging it over the refuse end. The tables were hung from rods attached to overhead supporting beams. A shaft and cam arrangement at one end of the table served as the actuating mechanism and imparted to the table an endwise, back-and-forth, swinging motion. A bumping block was fixed in the proper position at the shaft end, so that the table would strike against it at the end of each backward swing. The hanger rods or stirrups were so adjusted as to give the table a slight uphill slope toward the refuse end; that is, the end next to the driving mechanism. The feed box was near the upper end of the table and designed to spread the mixture of coal and water over the width of the table. Wash water was added a short distance below the feed box. With the table in motion and coal mixed kith water being fed to it through the feed box, a certain amount of stratification took place, depositing heavy refuse at the bottom of the bed in contact with the surface of the table. Constant bumping and a certain amount

Jan 1, 1950

By H. D. Outmans

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