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By K. S. Seljesater

SINCE the development of dispersion-hardenable lead-antimony alloys1 in the laboratories of the Western Electric Co., Inc., studies have been made of the effect of various third constituents on these alloys.2 This paper covers a study of the effect of small amounts of arsenic. This element is important since it occurs as an impurity in many commercial antimonial leads and the results obtained are particularly interesting as indicating a class of addition agents which exert a stabilizing effect on dispersion-hardened alloys. EXPERIMENTAL In order to-study the effect ,of increasing amounts of arsenic, a series of alloys were made up containing 1 per cent. antimony, and arsenic varying from 0. to 0.10 per cent., the balance Doe Run lead (99.997 per FIG. 1..-CHANGE OF MICRO-BRINELL HARDNESS WITH TIME OF 1 PER CENT. LEAD-ANTIMONY ALLOY. cent. lead). The alloys were cast into bars 1 ½ in. wide by ¾ in. thick and cold-rolled to about 1/8 in. thickness. Three samples of each composition were annealed 1 hr. at 225° C. and quenched in water. One set was aged at room temperature, one at 50° C., and the third at 100° C., the

Jan 1, 1929

University of Alabama University, Alabama Mining and Metallurgical Society WILLIAM R. HIGGS, President ROBERT E. MEAD, Secretary J. R. CUDWORTH, Faculty Sponsor MILTON H. FIBS, Counselor University of Arizona Tucson, Arizona Miners' Society LEE BLESSING, President R. W. CORY, Secretary E. P. MATHEWSON, Faculty Sponsor B. R. HATCHER, Counselor University of California at Los Angeles Los Angeles, California Student Chapter, A.I.M.E. ARCHER WARNE, President ROBERT JOHNSTON, Secretary E. K. SOPER, Faculty Sponsor EMILE HUGUENIN, Counselor Colorado School of Mines Golden, Colorado Student Chapter, A.I.M.E. J. Ross REED, President ANDREW PERRY, JR., Secretary J. BURNS READ, Faculty Sponsor A. W. NEWBERRY, Counselor

Jan 1, 1936

In 1973, US Borax & Chemical Corp. began investing three days wages and about $20 in training materials in every new employee before having him report to his first job. The result? Accidents involving new employees in the past two years have dropped by more than half from the 1972 level. What made this success possible was safety training done with programmed instruction materials-which, incidentally, US Borax also uses for vocational training.

Jan 4, 1976

Executive SCOTT TURNER, Chairman FREDERICK M. BECKET JOHN A. MATHEWS H. A. GUESS WILLIAM WRAITH Finance HENRY KRUMB, Chairman PAUL D. MERICA ROBERT E. TALLY Admissions JOHN M. LovEJOY, Chairman GEORGE D. BARRON ERLE V. DAVELER WILLIAM H. BASSETT W. D. B. MOTTER, JR. Alternates HENRY B. FERNALD F. JULIUS Polls AMOR F. KEENE

Jan 1, 1932

By R. W. Vieth, S. A. Bradford

THE orientations of tetragonal tin crystals are commonly examined by either the transmission Laue method or the back-reflection Laue method. The predominant planes and zone axes of the pattern are plotted on a Wulff net and indexed by measuring the angles between planes and directions. The problem of identifying the Laue spots has been approached in several different ways. Nicholas 1 tabulated interplanar angles for ten planes but did not relate the angles to permutation of indices or sign. A table of angles between adjacent planes and of angles between adjacent zones was published by Chandrasekhar and veal.' These tables are very helpful, provided the film shows all the low-order zones that occur within about 20 deg of each other. Frounfelker and Hirthe's compilation3 of angles between the (001) plane and twenty-nine other planes is useful for the indexing, only if the (001) spot can be found on the film. For all but the simplest orientations, however, more information is needed to index the diffraction spots. Standard stereographic projections, such as those published by Bicelli, 4 provide part of the information required. By their nature, these projections show the positions of only a few zone axes. In the tetragonal system many low-order zone axes are not normal to the planes having the same indices. Consequently, planes and directions can have entirely different positions on a stereographic projection. For example, the [011] zone axis is 33 deg from the normal to the (011) plane. The crystallographic orientation usually has to be deduced from a combination of the predominant zone axes and a few low-order planes that appear on the film. In addition to a standard stereographic projection of the planes, a stereographic projection of the directions is needed. Such a projection can be constructed from the angles given in Table I. To provide more information about angles between planes and directions, we have calculated interplanar angles up to (332) and angles between planes and directions up to [332] on an IBM 1620 computer. The angles are differentiated according to permutations of sign and indices. Those doing research on tin single crystals are welcome to request a copy of these tables from the authors.

Jan 1, 1967

By C. A. Worner

THE meeting of the Petroleum Division at the Annual Meeting of the Institute maintained the high standard set in previous years, and attendance of member: of the Division was at a new high. The impact of the war was evident not only in the tone of many of die papers but also in the presence at the meeting of many of our members now serving in the armed forces of our-country. Ken interest was manifested in all papers presented and the discussions which followed developed many additional facts of interist and importance. The first activity of the Division was the joint meeting of the Papers and Programs and the Publications Committees on Monday afternoon; at which time definite plans were formulated for a simplification and co-ordination of the work of the committees.

Jan 1, 1944

By J. L. Gillson

The word "other" in paragraph 4, line 11, column 1, page 205, should read "over;" the correct version of reason 2, this paragraph, is: 'L. . . 2) to evaluate the usefulness of certain geo-chemical techniques, V. C. Kennedy and S. W. Hobbs of the USGS had already studied the distribution of copper, lead, and zinc in the soils (both in background areas and over veins) and in the water and plants, providing a criterion for measuring the magnitude and effect of soil contamination; ...9 On page 206, in the top left hand corner of Fig. 1 (in the area bounded by 47°35' and 116°10), the reference to Fig. 3 is incorrect. The area of Pine Creek, South Fork Coeur d'Alene River, and portion of Big Creek (the area which includes, from left to right, Kingston, Pinehurst, Smelterville, and Kellogg) should be identified as that of Fig. 2A. The headings for columns 1, 3, and 4, Tables I and 11, page 209, column 2, were reversed when the paper was printed. The corrected tables are:

Jan 1, 1961

By Robert Pack

INTRODUCTION SOONER or later in the development of any natural resource it becomes highly desirable to know the quantity of this resource in the country as a whole, as well as of the part that is being developed, for the general course and. conduct of the development work must be governed to some extent by the total supply available. An accurate estimate of the quantity of any natural resource is difficult to make; yet if one is diligent enough one can obtain a pretty accurate idea of the quantity of marketable timber, the acreage of tillable land, or the horsepower that may be developed from the streams, for these are things that may be measured. But any attempt to estimate the quantity of some mineral in the ground appears to enter the realm of imagination and it seems that the estimate can be nothing more than a blind guess. It may appear to be especially futile to attempt to determine the quantity of oil and gas that is available in the ground, for these minerals are so vagrant that even if the quantity now available should be known quite exactly, the quantity that will eventually be obtained may be much less, for certain losses in the extraction of both oil and gas are unavoidable, and just what these losses will be cannot be predicted. Though necessarily inaccurate, estimates of such mineral reserves are, however, of distinct value, for they summarize the existing knowledge of the deposits of the mineral and thus enable those who are interested in some industry that depends in one way or another on this mineral to formulate a rational commercial policy. Some time ago, when the price of gasoline suddenly rose in a rather spectacular manner, the writer was one of the U. S. Geological Survey geologists called upon to help to estimate the quantity of oil that could be obtained in the United States, for the fear had become widespread that perhaps the rate of increase in the price of gasoline was a measure of the rate of depletion of the supply of petroleum. It thus became his

Jan 8, 1917

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By W. E. Stiles

A method is presented for predicting the performance of water flooding operations in depleted, or nearly depleted, petroleum reservoirs. The method makes use of permeability variations and the vertical distribution of productive capacity. From these two parameters can be calculated the produced water cut versus the oil recovery. Derivations of the mathematical analogy is shown and sample calculations and curves of prediction are presented. Comparison is made of the predicted and actual performance of a typical 5-spot in an Illinois water flood. INTRODUCTION The use of water as a flooding medium in both depleted and "flush" oil reservoirs is gaining greater recognition and acceptance. Many of the shallower fields, depleted by primary production, have been and are being subjected to water injection in order to obtain some part of the large volume of oil remaining after primary production. Some of the earlier water flood installation proved highly discouraging and the value of water flooding was often questioned. Many of these earlier floods were haphazardly selected and developed as little was known of the physical characteristics and contents of the producing formations. The prior evaluation of the flood performance was impossible. During the past decade the development of the required reservoir engineering tools-—core analysis, reservoir fluid analysis, electric logs, fluid flow formulae, etc.—has allowed the engineer to construct and apply the methods which are presently being used to evaluate the economic and mechanical susceptibility of a reservoir to flooding. This discussion will present a method for taking into account the effect of permeability variations in predicting the performance of water floods in depleted reservoirs. PERMEABILITY AND CAPACITY DISTRIBUTION It is generally agreed by most investigators that in a single phase system fluid will flow in a porous and permeable medium in proportion to the permeability of the medium. Producing formations are usually highly irregular in permeability, both vertically and horizontally. However, zones of higher or lower permeability are often found to exhibit lateral continuity. Thus, while structurally comparable stringers in adjacent wells may differ several fold in permeability values, they usually bear resemblance as being part of a general continuous higher or lower permeability section. It is generally agreed that where such stratification of permeability exists, injected water sweeps first the zones of higher permeability, and it is in these zones that "break-through" first occurs in the producing well. It is a basic assurnption of the presently described method that penetration of a water front follows the individual permeability variations as if such variations were continuous from input to producing well. This is admittedly not rigorously true, but can be justified as making possible a simplifying mathematical approach to an otherwise extremely complicated three dimensional flow problem. As a basis for study of the lateral flow of fluids in formations of irregular permeability, the irregularities may be conveniently represented by a permeability distribution curve and a capacity distribution curve. In obtaining these curves, the permeability values, regardless of their structural position in the formation, are rearranged in order of decreasing permeability. If these permeability values so arranged are plotted against the cumulative thickness, a permeability distribu- tion curve is obtained. This curve may then be likened to a "smoothed" permeability profile of the formation. In making comparison between different distribution curves it is convenient to state the permeabilities in terms of the ratio of the actual permeability values to the average permeability of the formation. These ratios termed "dimensionless permeabilities", are used in this paper rather than the permeabilities in terms of millidarcys. The capacity distribution curve is a lot of the cumulative capacity (starting with the highest permeabilities) versus the cumulative thickness. The capacity and thickness are given as fractions of the total capacity and thickness. Mathematically, the capacity distribution is the intergration of the permeability distribution curve. In practice it is convenient to first obtain the capacity distribution curve and derive from it a smoothed dimen-sionaless permeability curve. The method of obtaining the capacity distribution curve is illustrated in the successive column of Table 1, in which capacity and thickness are derived as fractions of their respective totals. If only a small number of permeability values are available, it is generally desirable to smooth the resultant curve. This has been done to give the capacity distribution curve shown in Figure 1. The differentiation of the capacity distribution curve to obtain the permeability distribution curve is shown in Table 2. Here, the capacity values are read from the smoothed curve at intervals of cumulative thickness, and the increments of capacity are divided by the increments of thickness to obtain the dimensionless permeability, K. Due to this stepwise procedure of calculation these premeability values must be plotted at the midpoints of the successive increments of thickness. The curve so obtained from these data is shown in Figure 1. The total area under the K' curve is equal to unity.

Jan 1, 1949

By E. J. Bonet, P. B. Crawford

It is fairly common practice to reinject water into the aquifer near the oil-water interface in water-drive reservoirs. There have been many studies of aquifer behavior without reinjection,l-5 but apparently no analytical studies have been made to indicate performance when injection wells are present in the aquifer. The diffusivity equation may be used to describe the pressure behavior in an aquifer. When sources are present it can be written as A general solution of Eq. 1 may be obtained as the sum of two solutions. One is a general solution of the homogeneous equation, obtained by dropping the source term in Eq. 1 and still satisfying the required boundary conditions. Another is a general solution of Eq. 1 satisfying homogeneous boundary conditions.1° The first solution, which corresponds to the aquifer without reinjection, has been given quantitative and qualitative treatment in the literature.l-5,8,9 The latter solution will be treated here. Solutions with variable injection rates are obtained by superimposing solutions with constant rates, so we have considered only the latter. Five cases have been treated here: 1. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The pressure along the line x = 0 is maintained at zero pressure. (See Fig. 1.) Equations showing the pressure distribution, rates, velocity and cumulative influx have been developed. Certain numerical results are shown. 2. A linear aquifer of finite width and extent. Water is injected into the aquifer at point xo, yo at constant rate. The rate of production along the oil-water water contact is maintained constant. Equations showing the pressure distribution inside the aquifer are presented. 3. A linear aquifer of finite width and extent. Constant pressures are maintained at opposite ends of the aquifer. Water is injected at constant rates at point xo, yo. Equations showing the pressure distribution are shown. 4. A linear aquifer of finite width and infinite extent. The pressure is maintained constant at the oil-water contact. Water is injected at a constant rate at point xo, YO. 5. A linear aquifer of finite width and finite extent. The pressure at the oil-water contact is maintained constant. Water is injected at constant rate per unit length along a line x,. The Linear Aquifer The linear closed aquifer, performing at constant terminal pressure was selected as the first case to be analyzed. The development of the equations is based on uniform injection per unit of thickness, and gravity effects are neglected. In practical application this condition is probably most closely achieved when the

Jan 1, 1970

Jan 1, 1967

By Walter O. Snelling

Discussion of the paper of WALTER 0. SNELLING, presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 100, April, 1915, pp. 695 to 704. A. C. McLAUGHLIN, San Francisco, Cal.-It seems to me that Mr. Snelling's work, if it is what it appears to be, is one of the most important contributions to petroleum technology that has been brought out iii the last 25 years. If his end products are what they seem to be, he has made a discovery, which, in my judgment, will revolutionize the petroleum industry. As to industrially carrying out these processes I do not think there is the slightest difficulty, for I have had some work recently where crude oils were handled successfully at a temperature of 750°F. and pressure of 750 lb. per square inch. WILLIAM A. WILLIAMS, San Francisco, Cal.-What metal did you use, Mr. McLaughlin? - A. C. McLAUGHLIN.-Ordinary seamless tubing, extra strong. WILLIAM A. WILLIAMS.-Tests were made in Dr. Rittman's experimental plant at Pittsburgh, upon samples of residuum furnished by Mr. Bell, the residuum being the remainder of the crude oil after the lighter fractions had been removed. After the material had been run through Dr. Rittman's plant, yields of from 43 to 58 per cent. of material, boiling under 150°C. were obtained. The distillate had a peculiar odor, due to the presence of benzene, toluene, and other unsaturated hydrocarbons. W. N. BEST, New York, N. Y.-What is the difference between the Rittman and the Snelling process or system? WILLIAM A. WILLIAMs.-The fundamental difference is that reactions take place under relatively higher temperatures and pressures and with none of the oil present in its original or liquid state, while the reactions secured by Mr. Snelling and other investigators have been from the liquids in the presence of some vapors. Under such conditions as Mr. Snelling operates, the temperatures and pressures used are limited and the flexibility in the control of these variables is extremely limited when compared with the Rittman process.

Jan 1, 1916

By Sherwin F. Kelly

Twenty five years of exploration has shown that the "geophysical dollar" is worth $1780 in the Orange Free State, $1488 on the Witwatersrand, $85 in Sweden, $28,000 in the Transvaal and $3500 or more in the U.S.

Jan 6, 1951

By E. Hornbogen

The deformation mechanisms of a iron-phosphorus alloys were compared at 20oand —196°C. Alloying with phosphorus increases the resistance to slip, but has little effect on the resistance to twinning. The stress for onset of twinning is nearly independent of temperature, but there is an increasing tendency for cleavage along (112) twin boundaries with decreasing temperature and increasing phosphorus content. FIVE iron-phosphorus alloys and one high-purity iron (0.004 pct C, 0.004 pct N, 0.05 pct O) were vacuum melted and cast, then homogenized for 6 hr at 1100oC and water-quenched. Single crystals were cleaved from the coarse grains produced in this manner. The hardness was measured* on polished (100) surfaces of the crystals at 20" and -196°C. Laue back-reflection patterns indicated a deviation of not more than 3 deg from coincidence of the {100} plane with the surface. The deformation mechanisms were studied by relief effects on the polished surfaces. Yield points in compression (0.5 pct offset) were measured with polycrystalline material. At 20°C the addition of phosphorus to a iron leads to a change from slip to twinning as the main deformation mechanism, Figs. 1(a), (b). Between 2 and 4 at. pct P slip and twinning occur simultaneously. In alloys with more than 4 at. pct P twinning is the main deformation mechanism and slip was observed only in the neighborhood of twin intersections. All cracks at 20oC were on (100) planes, some initiated by twins.' From measurements made at-196oC, hardness and yield points of all the alloys were nearly constant and the same as the hardness of high phosphorus alloys that deformed by twinning at 20°C, Figs. 2 and 3. In the high-purity iron, plastic deformation at -196°C occurred by both slip and twinning, but deformation in the iron-phosphorus alloys appeared to be entirely by twinning. In the high phosphorus alloys a large number of cracks formed along the (112) twin boundaries and at intersections of twins, in addition to the (100) cleavage, Fig. 1(c). DISCUSSION In , iron, plastic deformation can occur either by slip or by twinning, depending upon composition,

Jan 1, 1961

By Carl F. Floe, Michael B. Bever

ACCELERATED by the demands of war, research and development work in nonferrous physical metallurgy has continued at a rapid pace during the past year. In particular, advances have been made in processing and fabrication, especially of the light alloys, and in the surface treatment of metals. Theoretical physical metallurgy, although less active, has not been neglected and the year has brought forth some -notable contributions to our understanding of the fundamental structure of metals and their behavior in service. Of course, much work that has been done cannot be publicly discussed because of wartime restrictions.

Jan 1, 1945

By Rudolph G. Wuerker

THE Krupp-Renn Process,[1] has been successfully used to treat low-grade iron ores, laterites, titaniferous sands, and other minerals, and before World War I1 25 units were built by the Krupp-Grusonwerk, Magdeburg, Germany. J. J. Howard[2] has shown theoretical advantages of the pyro-metallurgical treatment over conventional approaches; and the process was described by R. Durrer[3].

Jan 1, 1951

By W. Hurst

The authors of this paper, in substituting values in a material balance equation associated with a gas reserve and a water drive, cannot find sustainment of what the gas in place should be; therefore, their conclusion is that this type of problem dealing with gas reservoirs is insoluble. They have introduced the word, "cybernetics," based on the work of Norbert Wiener, that further extends this line of reasoning, namely, to the effect that the system is a "black box", and that the gas reservoir and aquifer can take on infinite aspects 'based upon their past performance, to quote the authors. The inference is that this black box is an unknown. which permits in computer programming to subscribe as many variables as possible to observe by adjustment of one to another those combinations of conditions that fit field behavior. This may satisfy those in this discipline whose dedication is to programming, but to the others this is a comparison to the rationalization of the combinational results of the throwing of dice—a probability procedure. In reservoir engineering we are more direct. We learn from the examination of individual we'll and field data exactly what is in this black box. I now come to the impasse that has confronted these authors in their machine calculations. In this I have reproduced from their own production data (Tables 1 and 2 of their paper) pressure vs cumulative gas produced. shown as Figs. D-1 through D-5. A perusal of any of these five plots, for the corresponding fields in the Po Valley, shows the straight-line relation of pressure vs gas produced, evidencing pressure depletion. The point I make is that in their fundamental production data, there is no variance from a straight line that can support a water drive.

By Warren E. Wilson

THE transportation of solids in pipe lines is a matter of deep concern in many fields of engineering. Much experimental and theoretical work has been done in an effort to devise means of designing pipe lines that will satisfactorily transport given solid loads, but there remain many unanswered questions in this field. The present discussion will be confined to a rather narrow portion of this field and will endeavor to point out certain factors that may well be considered when comparing the relative economy of various installations. The data have been presented previously but a new interpretation was prompted by a suggestion in a paper by Professor O'Brien,1 of the University of California, that the friction work per pound of dry material should be considered in determining the relative efficiency of various installations. This method of considering relative economy in various pipe lines leads to some rather unexpected conclusions, especially with reference to the economy of large pipe sizes. A previous suggestion by the writer3 concerning the economy of a rather peculiar type of installation is strengthened. It is not believed that the considerations set forth herein apply directly in the case of dredge lines, where economy is largely a matter of a high rate of pumping in order to reduce the unit overhead charge. However, it is believed that some value may be gained from these considerations in cases involving the disposal of a fixed amount of solids per unit time with a minimum expenditure of energy and at a low cost for replacement of worn pipes. Such situations are not uncommon in the disposal of mill tailings and the disposal of solids deposited from irrigation waters. It was found that data leading to general conclusions for various pipe sizes were not available but certain definite trends are indicated and methods of analyzing available data are presented in the hope that they may be of assistance in preparing engineering estimates on designs of pipe lines of the type described above. ENERGY. REQUIREMENTS Carrying out the idea contained in Professor O'Brien's paper concerning the method of computing energy required to transport solids, the following analysis leads to some rather interesting conclusions. Let us represent: [Solids load in terms of mass per unit time by W Ratio of mass of suspended solids to total mass of mixture flowing by p Volume rate of flow of mixture by Q Length of pipe by L Slope of energy grade line by s Mass per unit volume of solids by m, Mass per unit volume of liquid by ml Mass per unit volume of mixture by m,,, We then have as an expression for the solids load: W = pQm¬] The work done per unit mass, P, on the mixture to move it along the pipe the

Jan 1, 1945

By R. I. Jaffee, J. G. Dunleavy, W. Hodge, H. R. Ogden

Jan 1, 1949