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By J. T. Shimmin

THE past twenty-five years has been a period of unparalleled improvement in all lines of mining and metallurgical equipment, but probably none has undergone greater refinement and development than the vacuum filter. Beginning a quarter of a century ago, there has been steady advancement in the art of vacu-um filtration until today its use has become virtually standard practice for dewatering throughout the entire metallurgical industry as well as in important parts of the chemical and industrial processing fields. The credit for the first successful application of vacuum filtration 'at the Consolidated Mercury mines in Utah in 1902 undoubtedly belongs to George Moore. There, it is said, his filter reduced the loss of gold in the slime and sand from $1.25 to 40c. per ton. Successful applications were subsequently made by Mr. Moore at the Liberty Bell mines, Telluride, Colo., the Lundberg, Dorr &Wilson mill at Terry, S. D., and elsewhere. E. L. Oliver is generally credited with, having done the most to work out the necessary continuity of op-eration exemplified in the well-known continuous vacu-um filter which bears his name. Others made improve-ments also, but in my opinion all the new ideas advanced in recent years are modifications of the fundamental principles originated by the two pioneers, Moore and Oliver. Considerable interest has been shown recently in the new type of continuous internal-type vacuum filter which is associated with my own name1. In response to frequent inquiries regarding it and the steps which led up to its invention, I am giving herewith a brief account of the early history of this development and some of the more important installations which have been made during the last year or so. A. M. Nicholas (now deceased), an Australian engi-neer, conceived the idea, several years ago, of manu-facturing a continuous vacuum filter with the filter medium applied upon the inside of the drum, as con-trasted with existing drum filters in which the medium is applied externally. Nicholas recognized that a ma-chine of this type would be simpler than one with a tank and would overcome some of the difficulties en-countered with tank filters on certain classes of pulps, and he appreciated the value of having filtration take place in the same direction as the gravitational settle-ment of the solid particles in the pulp, the pulp being retained within the drum instead of being held against the outside surface. The ease of starting up after a shut down was likewise realized by Nicholas. It was tried in the United States, but was not entirely success-ful primarily due to mechanical defects.

Jan 5, 1928

By Lewis W. MacNaughton

The North Texas district, as herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wil-barger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature are in traps, which, although localized by structures incident to the regional uplift, are usually modified by stratigraphic changes in the sediments. Excepting the fields in southeastern Baylor, southern Archer, and southwestern Clay Counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsylvanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1940 The encouraging outcome of exploration and development in Montague and Cooke Counties and generally greater activity throughout the district resulted in the drilling of some 1700 wells during 1940, about 350 more wells than were drilled in 1939. Approximately 1250 of these tests were completed as oil wells. Production likewise increased during I940 to the extent of 8 million barrels more than the 25 1/2 million barrels produced in 1939. In spite of this large increase in production, known oil reserves again increased substantially. As is usually characteristic of this district, the new reserves were from a large number of fields, none of which were of such magnitude as to be important to the oil industry. Nevertheless, the Fargo field, Wilbarger County, deserves mention as one of the more important discoveries in this district during 1940. Following seismic surveys, the hmerada Petroleum Corporation located its No. I Goodpasture in sec. 35, block IS, H. and T. C. R. R. Co. survey, and drilled it to a total depth of 6717 ft. This well was completed in July 1940 through perforations in the casing from a pay between 3230 and 3252 ft. for an initial production of 241.5 bbl. on an 8-hr. pumping test. Other potential producing horizons were found in the Pennsyl-vanian at depths of 3960 to 3995 ft., 4208 to 11.234 ft., 4407 to 4422 ft., and in the Ordovician at 6300 ft. Wells completed to date in the several Pennsylvanian horizons have an average daily potential of 600 bbl. of oil. Although no wells have yet been completed in the Ellenburger dolomite (Ordovician), the discovery well swabbed I5 bbl. per hour from this formation before plugging back for completion in an upper horizon.

Jan 1, 1941

By Lewis W. MacNaughton

The North Texas district, as herein defined, includes the counties of Archer, Baylor, Clay, Cooke, Foard, Hardeman, Knox, Montague, Wichita, and Wil-barger. This area covers generally the crest and south flank of a system of buried mountains known as the Red River uplift. The oil and gas accumulations along this feature are in traps, which, although localized by structures incident to the regional uplift, are usually modified by stratigraphic changes in the sediments. Excepting the fields in southeastern Baylor, southern Archer, and southwestern Clay Counties, all the fields within the district are on this Red River uplift. These exceptions, which have the same type of oil and gas accumulation as the other fields, are on the extreme north end of the Bend arch, which is a broad anticline plunging northward from the Llano uplift in central Texas to Archer County. The larger part of past oil and gas production has come from Pennsylvanian strata, with less important amounts from the Permian, and minor but increasingly important quantities from the Ordovician. Developments during 1940 The encouraging outcome of exploration and development in Montague and Cooke Counties and generally greater activity throughout the district resulted in the drilling of some 1700 wells during 1940, about 350 more wells than were drilled in 1939. Approximately 1250 of these tests were completed as oil wells. Production likewise increased during I940 to the extent of 8 million barrels more than the 25 1/2 million barrels produced in 1939. In spite of this large increase in production, known oil reserves again increased substantially. As is usually characteristic of this district, the new reserves were from a large number of fields, none of which were of such magnitude as to be important to the oil industry. Nevertheless, the Fargo field, Wilbarger County, deserves mention as one of the more important discoveries in this district during 1940. Following seismic surveys, the hmerada Petroleum Corporation located its No. I Goodpasture in sec. 35, block IS, H. and T. C. R. R. Co. survey, and drilled it to a total depth of 6717 ft. This well was completed in July 1940 through perforations in the casing from a pay between 3230 and 3252 ft. for an initial production of 241.5 bbl. on an 8-hr. pumping test. Other potential producing horizons were found in the Pennsyl-vanian at depths of 3960 to 3995 ft., 4208 to 11.234 ft., 4407 to 4422 ft., and in the Ordovician at 6300 ft. Wells completed to date in the several Pennsylvanian horizons have an average daily potential of 600 bbl. of oil. Although no wells have yet been completed in the Ellenburger dolomite (Ordovician), the discovery well swabbed I5 bbl. per hour from this formation before plugging back for completion in an upper horizon.

Jan 1, 1941

While coal was undoubtedly seen by the Spanish explorers in Texas, no mention can be found of it in any of their available published records; it was likely noticed by the first Americans, and coal along the Rio Grande River was reported in 1834.1 The next record is that of brown coal in Bastrop County in 1837 by James Nicholson and Judge Pinckney Hill? Dr. Riddell saw brown coal along the Trinity River in 1839 and described it as follows: "In the banks of the Trinity, associated with the iron ore, and overlying the brown coal, whole trees and fragments of trees, piled sometimes one upon another, present themselves completely transformed into stone. In some logs a diversified metamorphosis is observable; one portion of the vegetable structure having been replaced with silex, another with brown oxide of iron, and a third is bitumenized or converted into coal. "In concern with Dr. F. B. Page, I took considerable pains in the exploration of the Trinity brown coal formation., As no excavations for working have yet been made, the best places for inspecting the formation are where the Trinity cuts its way through the highlands, or where its banks present themselves in bold high bluffs, as at New Cincinnati, and near the site of the projected town of Osceola. The coal lies in horizontal strata, dipping one foot in thirty to the northwest. The main stratum at the latter place, just above Bedias creek; is represented by the concurrent statement of W. C. Brookfield, surveyor, Mr. James S. Hunter, of Huntsville, Texas, Dr. Page, and some other persons whom I consulted, as between six and seven feet in thickness, the lower portion being between three and four feet above low water mark. Unfortunately, during my sojourn there, the river was unusually high and turbid for the season of year; I could not consequently verify the same by personal observation and measurements. The most considerable coal beds which I had opportunity fully to inspect, were in the Trinity bluffs, southwest side, at New Cincinnati, six miles lower down, and just below the mouth of Salt creek, near six miles above. The workable stratum of brown coal in each of these localities is about five feet thick, and situated some fifteen feet or so above low water mark. In quality it is said to be precisely similar to the coal in the seven feet bed."2 . Moore in 1840 mentioned coal in the vicinity of Great Salt Lake, through which the Brazos flows; lignite in Bastrop County; lignite in the banks of the Colorado River a few miles above Lagrange in Fayette County; a deposit of excellent coal in the bed of the Sabine River, 30 miles above the

Jan 1, 1942

FRED TURRELL GREENE Fred Turrell Greene was born in Brooklyn, N. Y., Nov. 22, 1872. His father, William A. Greene, was born in Providence, R. I., and his mother, Angenora Semlear, was born in Brooklyn, N. Y. Fred's early school clays were spent in Boston, whence his father moved to Canada in 1882. Attending first the Collegiate Institute in Toronto, .then the High School at Berlin (now Kitchener), Ontario, where he graduated, Fred progressed to the Toronto University and the Michigan College of Mines, at Houghton, where lie graduated in 1897. He secured employment almost immediately at Butte with the engineering force of the Boston & Montana Consolidated Silver Mining Co., under Chas. S. Batterman. In 1899 he went to Rossland, B. C., where he spent more than a year as mining engineer and assistant superintendent of the War Eagle Consolidated Mining and Development Co. and the Center Star Mining Company Ltd. Returning to Butte in 1900, he acted as assistant geologist for the Anaconda Copper Mining Co. until 1906, when he filled a similar position in St. Paul with the Great Northern Railway for about two years. From 1908 until his tragic death on Christmas day, 1917, his headquarters were in Butte, where he enjoyed an excellent reputation -as consulting mining engineer, with a rapidly widening circle of clients. During the past four years he had been consulting engineer for the Elm Orlu and other mines controlled by Hon. W. A. Clark, and was in charge of underground developments and law-suit preparations for the celebrated apex case between the Elm Orlu and the Butte & Superior companies. At the time of his death he was in charge of similar work for the Utah Metals Co., in connection with their mines at Bingham, Utah. He was also for some years active in the Coeur d'Alenes, as consulting geologist for the Federal and other companies there, and was considered an authority on this as well as the Butte district. Mr. Greene was unmarried, and is survived by his parents, a younger brother, who is in the army, and one sister, Mrs. James A. Hatch, of New York. Some of the most important and valuable ideas regarding the nature and origin of copper ores have originated in Butte, since that district is not only one of the greatest examples of mineralization known in any land, but has gone through a long course of mining litigation, and was, one of the first to be studied intensively by geologists. In connection with the early investigations, as well as with the most recent in that camp, Mr. Greene played an important part. His conscientious devotion to his duties and his intelligent handling of the problems presented for solution sufficiently explain the esteem in which he was held by his employers and his professional associates.

Jan 5, 1918

C. P. BOWIE, San Francisco, Cal.-In my work with the U.S. Bureau of Mines, I have been detailed to report on oil storage containers, and in going around the country I have, been much interested in, the possibilities in the use of concrete for such containers. In talking with a good many people, I have discovered that concrete is being used A good deal for a wide variety of oils ranging from 14° to as high as 40° Bé., especially, by some of the western railroads:, If any member has had experience, in storing gasoline in concrete, I should like to learn of it. DORSEY HAGER, Tulsa, Okla.-Mr. M J. Munn, formerly .with the U. S. Geological Survey, acid connected with the Gypsy Oil Co., until a short time ago, has invented a invented a method for the application of concrete to the storage not only of crude oil but of refined products:. The Cosden Oil Co., of Tulsa, is now working on that plan, and, expects to store refined products in concrete tanks. THE CHAIRMAN (I.N. KNAPP, Ardmore Pa.).-I have had considerable experience in building masonry tanks for gas Holders. I do not believe it is possible to build a concrete or masonry tank of any kind. With hydraulic cement, mortar, which will be absolutely water-tight, unless the bottom and inner wall, after completion are waterproofed with some impervious material. The same will be true of oil tanks, the bottom and inner face of which must be made impervious to oil. Masonry tanks are intended to be sunk in the ground. All that the wall of the tank then amounts to is a retaining wall to keep the excavation in shape and to receive an impervious coating. The bottom of, a; tank, when empty, must be protected by a relief valve from any hydraulic: pressure acting from below. At ordinary prices, for sheets, a tank 100 ft. diam by 20 ft. deep can be built of steel much quicker and cheaper than of masonry. Several years, ago I saw very large oil storage tank under construction in California the bottom and sides being concrete. The sides were, sloped at about the single of repose for the material excavated: If you build a steel oil tank, you can get. .men for the work who do nothing else, and you, are likely to get a satisfactory job; but if you wish to build a concrete or masonry tank it is almost: impossible to find men skilled in building absolutely water-tight masonry Work. The general idea is that any laborer can mix up concrete in any old way and make a,

Jan 1, 1918

By Henry S. Drinker

THE Butler Mine property is situated in the vicinity of Pittston, in the Wyoming coal-field of Pennsylvania. The coal has been worked out from the fourteen-foot or Baltimore vein for a number of years on part of the tract, the old chambers remaining open as when originally abandoned. This vein outcrops on the Butler property, and is nowhere more than sixty feet below the surface of the ground on the line of the cut-off to be described. Above the fourteen-foot vein and about, say midway, between it and the surface of the ground, there is another small vein or rider of coal, about twelve inches in thickness. The rock between the two veins is a carbonaceous slate, about twenty-five feet in thickness. Above the smaller vein is a bed of sandstone, varying in thickness, but generally not less than from eight to ten feet. This sandstone is also carbonaceous, but the proportion of carbon is much less than in the slate below. Both rocks have been analyzed, and before the next Institute meeting, the writer hopes to be able to furnish the exact proportions. The sandstone is overlaid with debris up to the surface of the ground. Some time during the spring of 1876, it was found that the coal left in the worked-out mine had been set on fire, and that the fire was gradually spreading. Inquiry developed the fact that the fire had originally been started by a woman, who had taken up her abode in an old tunnel leading into the workings. Owing to some delay in the early attempts made to extinguish the fire, it finally gained such headway that no ordinary means were found to be effectual. Finally, Mr. C. F. Conrad, civil and mining engineer, of Pittston, Penna., was called in as consulting engineer. He advised the making of a thorough cut through such portion of the old workings as had not been reached by the fire. It was found by survey that this cut could be limited to a length of about one thousand two hundred feet, as the vein faulted on both sides, and that the greatest depth of the cut would be about sixty feet. Subsequently it was decided to tunnel part of the way, thus saving the deepest portion of the cut. In 1856-7, there occurred a fire in the same mine. Two stone-walls in V-shape running from the apex of the V towards the outcrop, were built to cut the fire off, and these walls were carried as far as the vein had at that time been worked. After the walls were finished

Jan 1, 1879

By Henry S. Drinker

The Butler Mine property is situated in the vicinity of Pittston, in the Wyoming coal-field of Pennsylvania. The coal has been ' worked out from the fourteen-foot or Baltimore vein for a number of years on part of the tract, the old chambers remaining open as when originally abandoned. This vein outcrops on the Butler prop erty, and is nowhere more than sixty feet below the surface of the ground on the line of the cut-off to be described. Above the four teen-foot vein and about, say midway, between it and the surface of the ground, there is another small vein or rider of coal, about twelve inches in thickness. The rock between the two veins is a carbon aceous slate, about twenty-five feet in thickness. Above the smaller vein is a bed of sandstone, varying in thickness, but generally not less than from eight to ten feet. This sandstone is also carbonaceous, but the proportion of carbon is much less than in the slate below. Both rocks have been analyzed, and before the next Institute meet ing, the writer hopes to be able to furnish the exact proportions. The sandstone is overlaid with debris up to the surface of the ground. Some time during the spring of 1876, it was found that the coal left in the worked-out mine had been set on fire, and that the fire was gradually spreading. Inquiry developed the fact that the fire had originally been started by a woman, who had taken up her abode in an old tunnel leading into the workings. Owing to some delay in the early attempts made to extinguish the fire, it finally gained such headway that no ordinary means were found to be effectual. Finally, Mr. C. F. Conrad, civil and mining engineer, of Pittston, Penna., was called in as consulting engineer. He advised the making of a thorough cut through such portion of the old workings as had not been reached by the fire. It was found by survey that this cut could be limited to a length of about one thousand two hundred feet, as the vein faulted on both sides, and that the greatest depth of the cut would be about sixty feet. Subsequently it was decided to tunnel part of the way, thus saving the deepest portion of the cut. In 1856-7, there occurred a fire in the same mine. Two stone walls in V-shape running from the apex of the V towards the out crop, were built to cot the fire 06 and these walls were carried as far as the vein had at that time been worked. After the walls were finished

Jan 1, 1879

By J. R. Coulter, F. O. Case, H. G. Satterthwaite, B. Harden

During the two years that the Henderson plant has been in operation, a number of technical improvements have been made by the staff of Basic Magnesium, Inc., the effects of which were realized subsequent to the writing of the paper by Major C. J. P. Ball (p. 28j, this volume). Pellet Mix The process as originally installed required the use of peat moss in the mixture going to the chlorinators. This had to be imported from Canada at a considerable cost, and, besides being expensive, constituted a serious fire hazard in the dry climate of Nevada. Experimentation looking toward its elimination had been going on for some time and was actively pushed as soon as operations commenced. It was found that a pellet mix containing no peat, which would chlorinate at a satisfactory rate, could be cast as a fluid slurry, which would set up into a hard mass having the desired porosity. For carrying out this operation, equipment similar to that used in the manufacture of phosphate fertilizer at Anaconda, Mont., was installed and proved eminently successful. The dry materials, with peat moss and raw concentrates entirely eliminated, are mixed with magnesium chloride solution in two Pratt phosphate mixers and the resultant slurry is poured onto two 48-in. slowly moving rubber conveyor belts. By the time the slurry has reached the head pulley, the material has set su4iciently to be broken and sized as desired. The discharge from the casting belts is fed to the four rotary kilns in the preparation plant, where it is dried and coked to the proper degree for subsequent chlorination. With the peatless feed the capacity of the kilns was found to be about double what it had been before, so that the four rotaries suffice for a 10-unit operation, thus making it unnecessary to operate the extruders and tunnel kilns. In addition to saving the cost of the peat, the new system can be operated with about 85 per cent less labor than was formerly required in the preparation plant. The new pellet production system has also made it feasible to install centralized crushing equipment with suitable conveyors and a loading station. Containers of 8000 lb. capacity were substituted for small cubicles of 1000 lb. capacity which formerly were used for charging the chlorinators, and trailer trucks were substituted for the small trains originally provided for transportation from the preparation plant to the chlorinators. These changes resulted in a considerable saving in handling and transportation charges. Handling Molten Metal The molten magnesium originally was ladled from the electrolytic cells into small gas-fired brick-lined cars standing between the cell rows. From these cars the metal nes ium. into ''cheeses'' weighing from 150 to 300 lb. After solidification the

Jan 1, 1944

By C. Fairhurst, A. M. Starfield

As a practicing mining engineer, I face many rock mechanics' problems daily and would like to mention one or two examples to illustrate the current gap between laboratory investigations and actual field problems. I would like to endorse Dr. Obert's suggestion that more field measurements and observations should be undertaken. There is an ever-increasing body of data beginning with Hast's results in Sweden,l then measurements at Elliot Lake, Canada, and so on, including our own measurements at White Pine, which clearly indicate that the horizontal stresses underground are often at least as large as the vertical stresses. Visual obsenation of the deformation of roof and pillars (including failure due to horizontal compression) also demonstrates that the horizontal stresses are often most important. Yet almost every laboratory investigation begins with the assumption that the only stresses acting are vertical. Roof spans in layered formations. for example, are calculated on the assumption that the rock behaves as a gravity loaded beam. This is all too often unrealistic. Roof bolts are also often considered to be simply means of suspending the gravity loaded beams. As Dr. Reed has mentioned they are probably, in fact, acting to restrain a beam which is attempting to buckle due to lateral pressure. The fact that moisture can reduce the strengths of some rocks as much as 50 percent has been known for many years. In the mine me are almost always faced with wet rock, yet no one has investigated ways in which this wakening effect can be overcome. as, for example, by waterproofing the rock. C. Fairhurst, University of Minnesota I would like to mention that we have found,2 from stress-relief determinations, that appreciable (over 1000 lb per sq in.) horizontal pressures occur also at the surface in granites quarried in central Minnesota. Whilst I agree that more field measurements are desirable, it is important to point out that most university research is undertaken by graduate students who must attend classes daily. Their research is therefore restricted to the laboratory. A.M. Starfield, University of Minnesota No one denies the importance of obtaining: data from field measurements. It is equally important, however, that field measurements be guided by theory. Much time and money can be wasted by indiscriminate measurement. An example of the value of theory in interpreting measurements is given in Dr. Obert's comments on the time dependent strain observed in a salt mine. He anticipated that the stress at the wall of the opening would change with time because salt is viscoelastic rather than elastic. It can be shown from theory that if an excavation in a viscoelastic medium is unsupported, then the stress at the wall does

Jan 1, 1967

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By W. R. Purcell

An apparatus is described whereby capillary pressure curves for porous media may be determined by a technique that involves forcing mercury under pressure into the evacuated pores of solids. The data so obtained are compared with capillary pressure curves determined by the porous diaphragm method, and the advantages of the mercury injection method are stated. Based upon a simplified working hypothesis, an equation is derived to show the relationship of the permeability of a porous medium to its porosity and capillary pressure curve, and experimental data are presented to support its validity. A procedure is outlined whereby an estimate of the permeability of drill cuttings may be made with sufficient acuracy to meet most engineering requirements. INTRODUCTION The nature of capillary pressures and the role they play in reservoir behavior have been lucidly discussed by Lev-rett', Hassler, Brunner, and Deah12, and others. As a result of these publications the value of determining capillary pressure curves for cores has come to be generally recognized within the oil industry. While considerable attention has been directed toward the subject in an effort to provide a reliable method of estimating percentages of connate water, it has been recognized that capillary pressure data may prove of value in other equally important applications. This paper describes a method and procedure for determining capillary pressure curves for porous media wherein mercury is forced under pressure into the evacuated pores of the solids. The pressure-volume relationships ob- tained are reasonably similar to capillary pressure curves determined by the generally accepted porous diaphragm method. The advantages of the method lie in the rapidity with which the experimental data can be obtained and in the fact that small, irregularly shaped samples, e.g., drill cuttings, can be handled in the same manner as larger pieces of regular shape such as cores or permeability plugs. Based upon a simplified working hypothesis, a theoretical equation will be derived which relates the capillary pressure curve to the porosity and permeability of a porous solid, and experimental data will be presented to support its validity. This relationship aplied to capillary pressure data obtained for drill cuttings by the procedure described provides a means for predicting the permeability of drill cuttings. METHODS FOR DETERMINING CAPILLARY PRESSURES Several techniques have so far been employed in determining capillary pressure curves and these fall into two principal categories: (1) Liquid is removed from, or imbibed by, the core through the medium of a high displacement pressure porous diaphragm (2) Liquid is removed from the core which is subjected to high centrifugal forces in a centrifuge4,'. There are? however, certain limitations inherent in both methods. The greatest capillary pressure which can be observed by method (I), above, is determined by the maximum displacement pressure procurable in a permeable diaphragm which at the present time appears to be less than 100 psi. An even more serious limitation of the diaphragm method is imposed hy the fact that several days may be required to reach saturation equilibrium at a given pressure; hence, the time re- quired to obtain a well-defined curve may be measured in terms of weeks. Furthermore, to date, no suitable technique for handling relatively small, irregularly shaped pieces of rock, such as drill cuttings, has been reported and, therefore, measurements must be made, in general, on cores, or portions thereof. The centrifuge method offers the distinct advantage over the porous diaphragm method of arriving at saturation equilibrium in a relatively short time by virtue of the elimination of the transfer medium for the liquid. The calculation of capillary pressures from centrifuge speeds is somewhat tediousa, however, and the equipment required is fairly elaborate. While there exists the possibility that this method might be adaptable to the determination of the capillary pressures of cuttings, this particular ramification has not been investigated, as far as is known. In view of the limitations of the two principal methods for determining capillary pressures, the apparatus described in the following sections has been devised in order that difficulties previously encountered might be circumvented. MERCURY INJECTION METHOD FOR DETERMINING CAPILLARY PRESSURES Theory The methods described above for determining capillary pressures are characterized by the fact that one of the fluids present within the pore spaces of the solid is a liquid which "wets" the solid, i.e., the contact angle which the liquid forms against the solid is less than 90" as measured through that phase. For these "wetting" liquids the action of surface forces is such that the fluid spontaneously fills the voids within the solid. These forces likewise oppose the withdrawal of the fluid from the pores of the solid.

Jan 1, 1949

By P. B. Baxendell, R. Thomas

Work on the calculation of vertical two-phase flow gradients by Cia. Shell de Venezuela has been based mainly on the "energy-loss" method proposed by Poett-mann and Carpenter in 1952. The "energy-loss-factor" correlation proposed by Poettmann and Carpenter was based on relatively low-rate flow data. This correlation proved inapplicable to high-rate flow conditions. In an attempt to establish a satisfactory correlation for high rates, a series of experiments was carried out at rates up to 5,000 BID in Cia. Shell de Venezuela's La Paz field in Venezuela, using tubing strings fitted with electronic surface-recording pressure elements. As a result of these experiments a correlation between energy-loss factor and mass flow rate was established which is believed to be applicable to a wide range of conduit sizes and crude types at high flow rates (e.g., above 900 BID for 27/8-in. OD tubing). It is anticipated that the resulting gradient calculations will have an accuracy of the order of % 5 per cent. At lower flow rates the energy-loss factor cannot be considered as constant for any mass rate of flow, but varies with the free gas in place and the mixture velocity. No satisfactory correlating parameter was obtained. As a practical compromise for low flow rates, a modification of the curve proposed by Poettmann and Carpenter was used. In practice this was found to give gradient accuracies of approxirnately ± 10 per cent clown to flow rates as low as 300 B/D in 27/8-in. tubing. INTRODUCTION Production operations in Cia. Shell de Venezuela's light- and medium-crude fields are principally concerned with high-rate flowing or gas-lift wells. Under these conditions the analysis of well performance, the selection of production strings and the design of gas-lift installations are vitally dependent on an accurate knowledge of the pressure gradients involved in vertical two-phase flow. Initially, attempts were made to establish the gradients empirically as done by Gilbert,' but the results were not reliable due to scarcity of data over a full range of rates and gas-oil ratios. Several methods of calculation based on energy-balance considerations were attempted, but the computations were cumbersome and the results cliscouraging. In 1952 a paper was published by Poettmann and Carpenter' which proposed a new approach. Their method was also based on an energy-balance equation. but it was original in that no attempt was made to evaluate the various components making up the total energy losses. Instead, they proposed a form of analysis which assumed that all the significant energy losses for mutiphase flow could be correlated in a form similar to that of the Fanning equation for frictional 1osses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The basic method was applied in Venezuela to the problem of annular flow gradients in the La Paz and Mara fields" This involved establishing a new energy-loss-factor correlation to cover high flow rates and, also, some adaptation of the method to permit mechanized calculation using punch-card machines. The final result was 1 set of gradient curves for La Paz and Mara conditions which proved to be surprisingly accurate. With the encouraging results of the annular flow calculations, several attempts were made to obtain a corresponding set of curves for tubing flow. Here, unfortunately, little progress could be made. The original correlation of Poettmann and Carpenter was based on rather 1imited data derived from low-rate observations in 23/8- and 27/8-in. OD tubing. It did not cover the higher range of production rates, and extrapolation proved unsuccessful. A new correlation covering high flow rates was required, but this proved to be extremely difficult to establish since tubing flow pressure measurements at high rates did not exist—due to the difficulty of running pressure bombs against high-velocity flow. The necessity for reliable tubing flow data increased with the development of the new concessions in Lake Maracaibo, where high-rate tubing flow from depths of 10,500 ft became routine. Thus. it was decided to set up a full-scale test to establish a reliable energy-loss factor for tubing flow conditions. A La. Paz field light-oil producer with a potential of approximately 12,000 B/D on annular flow was chosen. To obtain full pressure gradients, a special tubing string was installed which was equipped with electronic surface-recording pressure measuring devices,

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By R. M. Hays

At the present time, oxidized taconite and semitaconite are not processed on the Mesabi Range except in vely limited tonnages. However, it is estimated that by 1990 shipments from the Range will approach 75 million tons of iron ore per year. To achieve this and future production, either additional magnetic taconite reserves must be proven or oxidized taconite and semitaconite must be processed. One beneficiation process which uses high-intensity magnetic separation and flotation for concentrating oxidized taconite and semitaconite is described. Detailed metallurgical results are given and an economic evaluation of the process is presented with comparison to other processes. The results of the present study indicate that the high-intensity magnetic separation and flotation process appears nearer commercialization for the processing of Mesabi Range semitaconite. The disadvantages of the process are nearer solution and are being solved by well-defined programs. During the twentieth century, the Mesabi Range in northeastern Minnesota has been the main source of iron ore for American steel mills. The Mesabi Range, which is about 120 miles long and up to 3 miles wide, is the pre-glacial outcrop of a group of sedimentary iron-bearing rocks known as the Biwabik formation. The formation, which is 200 to 650 ft thick and dips 50 to 10° to the southeast, is divided into four stratigraphic units. From top to bottom, these are the Upper Slaty, Upper Cherty, Lower Slaty, and Lower Cherty. Since its deposition in Precambrian time, most of the original Biwabik formation has been subject to alteration. Thus, although the iron content of the original formation was quite uniform, major variations in mineral composition now occur both laterally along the length of the formation and vertically within its units. Details of the mineralogical variations in the Biwabik formation have been described by Wolff,' Gruner, 2 and White.3 The unaltered portion of the Biwabik formation includes the magnetite taconites which are being commercially processed by Reserve Mining, Erie Mining, Eveleth Taconite, National Steel, Butler Taconite, and U.S. Steel. These six operations have a capacity of 32 million tons of iron ore pellets per year and have produced approximately 170milion tons of pellets since 1956. Capacity for another 30 million tons of pellets per year is being considered by the industry for the next ten years. This increase will be obtained by constructing new plants and by expanding present operations. Thus, by ! 978, it is estimated that approximately 60 million tons of iron ore vellets will be produced each vear from the magnetite taconites of the Biwabik formation. The portions of the Biwabik formation subjected to intense alteration resulted in direct shipping, wash, and heavy-media ores. Since 1892, 1.8 billion tons of direct shipping ore have been shipped from the Mesabi Range. This ore has been the major source of iron ore for American steel mills. In 1967, about 11 million tons of direct shipping ore and 13 million tons of wash, jig, heavy-media, and other gravity concentrates were shipped from the Mesabi Range.4 These products generally have poorer physical and chemical properties than the iron pellets produced from magnetic taconite. It is predicted that the shipment of these materials will decrease from 24 million tons in 1967 to 6 to 8 million tons in 1975.' This decrease will

Jan 1, 1970

By C. D. Stahl, S. M. Farouq Ali

This investigation attempts to describe and simulate the alcohol displacement process by means of a cell model, as employed in chemical engineering practice. The proposed model is more simple than previously proposed models. and utilizes parameters chosen on a theoretical basis. The model successfully reproduced the formation of the stabilized bank and the breakthrough of alcohol, the latter depending on one of the model parameters, which may be correlated with the length of the porous medium. Moreover, the effects of the phase behavior of the liquid system involved, as observed in experimental studies, were reproduced. Several variations of the basic model were devised and tested on a digital computer. These included the cases in which: (1) the actual value of fractional flow was used in cell-to-cell computations; (2) the number of cells was varied within the same run; and (3) incomplete rather than complete phase equilibrium was assumed within each cell. The proposed cell model clarifies the basic mechanism of the process. Detailed concentration profiles obtained for each cell, for instance, showed the mechanism of bank formation in relation to the phase behavior characteristics. The results obtained indicated a varying degree of phase equilibrium concommitant with changes in the velocities of the phases in an actual alcohol displacement. This condition was approximated by changing the number of cells during the simulation. Interesting information was obtained on the influence of path length on the efficiency of alcohol displacement, which has been the subject of some controversy. Certain limitations preclude the use of the proposed model as a substitute for experimental studies. The results obtained were, nevertheless, of value in interpreting the experimental results. INTRODUCTION During recent years considerable effort has been directed toward an understanding of alcohol displacement, the process whereby oil and water are recovered from a porous medium by the continuous injection of a solvent. The complex nature of the physical process involved has so far defied a complete mathematical treatment. Other methods of approach, amounting to an overall material balance, have been proposed, yielding useful information on certain aspects of the process.1-3 Taber et al, in particular, defined the displacement mechanism in terms of the phase behavior of the alcohol-oil-brine system invoIved.2 Wachmann reported a mathematical treatment of alcohol displacement subject to certain simplifying assumptions? Donohue proposed the use of a "cell model" for simulating alcohol disPlacement.5 The nature of the assumptions involved limited the utility of the model. The present work attempts to examine the variables involved in the simulation of alcohol displacement and discusses several possible versions of the basic cell model. Under certain conditions the model results are similar to the experimental results. In particular, the spontaneous formation of of the stabilized bank and the effects of the system phase behavior were successfully reproduced. PREVIOUS WORK ON CELL MODELS Cell models and the theoretical plate concept are often used in solving chemical engineering problems in which an explicit mathematical solution may be difficult or impossible to obtain. Examples of such applications occur in distillation, gas-liquid chroma tography,6 reactor technology, absorption, etc. In petroleum engineering, such a model was used by Attra7 to describe non-equilibrium gas drive, and by Higgins and Leigh ton8 to calculate sweep efficiency in water flooding. Aris and Amundsen pointed out the equivalence between the diffusion model and perfectly mixed cells connected in series.9 Deans proposed a three-parameter cell model to simulate two-component

Jan 1, 1966

By Wieland D. R., Hurst R. E., A. R. Hendrickson

Analysis of acidizing techniques, in correlation with reservoir data and a backlog of past treatments, has resulted in the development of a valuable engineering guide for planning acidizing treatments. Such treatments fall into three categories: (I) acid injection into the pores of the matrix; (2) acid injection into natural formation fractures at less than parting pressure; and (3) combination acidizing-fracturing treatments in which acid solutions (without propping agents) are injected at treating pressures sufficient to open and extend fractures through which the acid flows. Because the spending tirnze of acid during a specific well treatment does not change appreciably, maximunl penetration is attained when the first increment of injected acid is completely spent. Additional acid injection cannot be expected to further extend the benefits of the treatment. Depth of penetration will depend upon the reaction rate of the acid under treatment conditions, the injection rate of the acid into the matrix or fractures and the area-volume relationship existing in the flow channels. Based on Darcy's flow formula, extremely low injection rates must be used in order to keep bottom-hole injection pressures below formation fracturing pressure. As a result, only limited penetration of unspent acid will occur. Treatment records indicate that, in most acidizing treatments, formation parting pressures are exceeded, greatly extending acid penetration. Under these conditions, stimulation benefits are limited to the fracture area produced during the spending time of the first increment of acid injected into the formation. This area may be calculated from laboratory and well data to estimate depth of penetration. This, in turn, may be correlated with productivity data to assist The art of gas and oil well acidizing has been characterized by many changes in treating materials and techniques since its inception. These developments have been designed to provide greater production increases. prolong production declines and shorten payout time. Such improvements have been based primarily on data derived from laboratory research and field experience. As more of the variables influencing these treatments have been recognized and evaluated, acidizing has become less of an art and more of a science. Recent studies of fracturing treatments,' in light of individual well conditions and the results of thousands of fracturing treatments, made possible the formulation of an engineering guide that is now being used to select optimum treating techniques and to forecast probable results of such treatments. A similar analysis of the factors controlling acidizing treatments has been made and is the basis for this paper, The findings herein can be used as a guide in the selection of acidizing solutions and techniques, tailored to fit specific well conditions and to provide optimum stimulation per dollar cost. Acidizing treatments may be classified into three basic categories—(1) treatments in which the acid is injected uniformly into the pores and flow channels of the matrix, (2) treatments in which the acid enters natural fissures and fractures in the formation at less than fracturing pressures and (3) injection of acid into the formation at a pressure sufficient to open and extend fractures into the rock through which the acid penetrates (without the inclusion of a propping agent). TYPE 1 — MATRIX ACIDIZING This category consists of treatments in which acid solutions are injected into a homogeneous carbonate

By F. H. Bunge, W. H. Jr. Dailey

This paper covers an investigation of the magnetic roasting characteristics of several iron ores when treated in the form of small pebbles (1/8" to 1/2" in size), and in the form of balled fines. The roasting treatment was carried out with apparatus capable of very close control of time, temperature, face velocity, and per cent combustible in the reaction gas. The effect of rapid initial heating was not studied although it is believed that this has a major effect on the results when processing solid pebbles. The test equipment is a fixed bed type, with such a wide range of gas velocities, temperature, combustible content and etc., that the results obtained can be made to approximate those from various commercial roasting processes. The data presented in this report covers reaction rates, effect of processing variables on silica in the concentrate, flow resistance of beds, and to a limited extent, the effect of particle size. The work is far from complete and raises many more problems than it gives answers for. We believe, however, that much of the information will be useful to those engaged in investigation of magnetic roasting processes. We measured the time required for various degrees of completion of the reaction of hematite to magnetite, for finely pound material in balled form and for carefully sized crushed ore. Measurements were made for a variety of Minnesota and Labrador ores. This report covers an ore requiring fine ginding (-325 M) for liberation (Lower Kevin) and an ore requiring coarser grinding (-100 M) for liberation (Upper Olson). These ores represent approximately the range of characteristics for a group in the west end of the Mesabi Range. Our data shows that the reaction rate is very fast for the finely ground material and that tests are readily reproducible. The reaction rate of the larger size material, in the range of 1/8" to 1/2", is much slower and the results more erratic. We found that for the ores tested, the percentage of silica in the Davis tube magnetic concentrate was a function of iron recovery. Normally the concentrate had a low and relatively uniform percentage of silica up to a critical value of recovery. Above this critical recovery value the percentage of silica increased very rapidly. For example, for one particular ore roasted in the form of 3/8" diameter balls made from -28 mesh fines, the silica remained at about 7% to 8% until the recovery exceeded about 93%. Increasing the recovery beyond 93% resulted in over 25% silica with the additional recovery. The degree of conversion of hematite to magnetite (% completion of roast) required to obtain 93% recovery for balled material, varied inversely with the gas flow rate. Percentage silica in the concentrate resulting from roasting 3/16" and 1/2" solid material was relatively erratic. However, for varying degrees of iron recovery the lowest silica percentages corresponded to those obtainable when roasting fines. It is thought the probable reason for the erratic values was the variation in shattering or cracking of the pebbles during initial heating and roasting. There is some indication that very fast initial heating will greatly increase the permeability of the individual particles of ore to gas flow so that the reaction rate for coarse sizes will approach that obtainable with balled fine material.

Jan 1, 1961

By J. B. Dorsey, T. W. Brinkley

Performance of a high-pressure, vaporizing gas-drive project in a volatile oil reservoir is discussed. The project has been in operation for over 8 years. Present recovery from the over-all displaced portion of the reservoir is 40 percent, and an ultimate recovery of 60 percent is indicated. Calculations reflect an over-all displacement volume of 50 percent for the entire reservoir; therefore, ultimate oil recovery will be 30 percent of the entire reservoir oil originally in place. Laboratory vaporization tests conducted prior to project initiation also are presented and discussed, along with an analytical method of determining stock-tank oil production and gar injection requirements related to over-all volumetric displacement efficiency from these data. Introduction The Shoats Creek field is located in Beauregard Parish, La., in the extreme western part of the state (Fig. 1). Discovered in 1956, the field is productive in three Cockfield sand zones, ranging in depth from 8,000 to 9.000 ft. The upper two zones, 1st and 2nd Cockfield, are condensate-bearing gas reservoirs. The lowest zone, the 5th Cockfield, is a volatile-oil reservoir. Laboratory work conducted on crude oil from the 5th Cockfield zone shortly after field discovery demonstrated that, when contacted with dry gas, signidcant volumes of the oil could be vaporized at reservoir temperature and at an appropriately high reservoir pressure. Further study led to the conclusion that early initiation of a crude vaporization project in the 5th Cockfield zone would be superior economically to other methods of reservoir depletion. Consequently, the zone was unitized and gas injection operations started late in 1958. This paper discusses laboratory work performed in conjunction with the project, and project performance to the present. History of Development The 5th Cockfield zone in Shoats Creek is composed of a thin, very shaly, low-permeability sandstone. Oil accumulation is controlled by a structural trap bounded by faults along the north and west and by a water contact on the southern boundary (Fig. 2). The zone covers a productive area of 1,550 acres at an average depth of 9,000 ft. The net sand section is thin, having a maximum thickness of 10 ft and an average thickness of 5.5 ft (Fig. 3). Average reservoir rock properties, as determined from core analysis are presented in Table 1. Shaliness of the zone is illustrated by the typical electric log of the 5th Cockfield section in Fig. 4. Because of the thinness and poor quality of the sand, the 5th Cockfield was developed on a wide spacing. Eleven completions were made in the zone between 1956 and 1961 for an average density of 140 productive acres per completion, with the majority of wells being dually completed in the 2nd and 5th Cockfield. Average initial potential for producers in the 5th Cockfield was 130 BOPD. Oil from the 5th Cockfield has a stock-tank gravity of 50.5" API; with a bubble-point pressure of 3,515 psia, the oil was highly undersaturated at the original reservoir pressure of 4,675 psia. Pertinent properties of the oil as determined in the laboratory are presented in Table 2. Because of the volatile nature of the crude, laboratory studies of its susceptibility to vaporization, as well as a vapor-liquid phase study, were conducted in addition to a standard PVT analysis. The vaporization study was conducted in a visual cell; a stepwise illustration of this work and laboratory measurements are presented in Fig. 5. Field

Jan 1, 1969

By L. J. Kashar

By means of a continuum-mechanics approach, the following equation for calculuting the pressure for axisymmetric cold forging has been derived: where P is the extrusion pressure; K and n are the strength coefficient and the strain-hardening exponent of the steel, respectively; a and b are strain factors, primarily dependent on the die design; and R is the extrusion ratio. Data from compression and backward-extrusion tests performed at a crosshead speed of 0.5 in. per min on a nonwork-hardening material pure lead) and on a work-hardening material (1018 steel) indicate that the predicted extrusion pressures obtained from the derived equation agree very closely with the actual extrusion pressures. Therefore, the equation can be used to predict backward-extrusion pressures from standard mechanical-test data. The decision to cold-forge a part is based on several considerations, most of them related to economics. However, the production feasibility is usually determined by the pressure needed to extrude the part and the availability of tooling that can repeatedly sustain this pressure for over several hundred thousand cycles. A major contribution to the cold forging of steel would result from the development of steels that could be forged at reduced pressures and from the development of techniques that permit the accurate prediction of the pressure necessary to cold-forge the part. The ability to predict extrusion pressures is necessary to properly design the tooling required for the cold-forging process. Attempts to theoretically predict the cold-forging pressure, especially for work-hardening materials, have been unsuccessful in previous investigations of the cold-forging process.1-3 Many empirical relations have, therefore, been proposed relating the extrusion pressure to the chemical composition,' the extrusion ratio,2 the tensile strength,273 and hard- ness, 2 and the yield strength3 of the material being extruded. However, these empirical relations are valid only for the specific conditions used in their development, and, in some cases, the empirical relations had a scatter band greater than * 10 pct. A study of the extrusion process was undertaken with the objective of developing predictor equations for extrusion pressure by using a continuum-mechanics approach to the problem of metal flow. The derivation of such an equation is summarized in this paper, and data are presented that confirm the validity of the derived equation. DERIVATION OF THE EXTRUSION EQUATION If the extrusion of a material through a die is considered in terms of a work balance, it has been shown that it is possible to derive an equation relating the work necessary to move the material through the die to the deformation work undergone by the material. The work done, W, in moving the material is given by where F is the extrusion force, I, is the distance the material was moved, A, is the original cross-sectional area of the material, P is the extrusion pressure acting on A,, Ap is the cross-sectional area of the extrusion punch, and Pp is the punch pressure acting on Ap. The deformation work, WD, is given by where V is the volume of metal deformed, ay is the flow stress of the metal, and E is the total strain undergone in the extrusion. If there are no frictional losses, the work done, W, is equal to the deformation work, WD; therefore, Since the volume of a metal does not change during deformation,

Jan 1, 1968