Search Documents

By D. R. Parrish, W. E. Lamoreaux, W. W. Owens

Several methods are now being used by the industry for determining the gas-oil flow characteristics of reservoir rock samples. Most of the laboratory experirnerltal rlzethods can be classified either as steady-state, unsteady-state, or Hassler-type tests. Although the validity of the results obtained by any specific method is not questiorzed, in general, the complexity of these methods leaves much to be desired. This investigation dealt primarily with the development of a simplified unsteady-state (gas drive) laboratory test method for measuring kg/ko re1ationships of small core samples. A procedure for selecting uniform and representative sandstone rock samples was developetl since it was observed that the reliability of the test resu1ts was dependent upon having a sample which was uniform in porosity and permeability. The importance of factors known to influence the results of this type test, such as oil viscosity, gas expansion, and pressure differential were eva/uated. The method of calculating the test results was found to give valid data over a wide range of gas expansion. The limits of pressure differential and oil viscosity which would insure reliable results were defined. In cornparisorz with other presently used testing methods, the gar drive method requires considerably less apparatus, is less time consuming, and is more readily adaptable to a routine type core test. INTRODUCTION The detcrmination of the gas-oil flow characteristics of reservoir rocks has been given concentrated study by the oil industry for the past decade. Both analytical and experimental methods have been considered. The analytical methods have generally relied on a simplified characterization of porous materials in order that the fundamental laws of fluid flow and capillarity could be utilized. More direct experimental methods have been proposed by numerous production research laboratories with the primary goal being a simple and inexpensive, yet reliable method for measuring the gas-oil flow characteristics of reservoir rock samples. The experimental methods which have been reported in the literature generally can be grouped into one of the following classifications: 1. Steady state1,2,3,4 in which a fixed ratio of flowing fluids is forced through the test sample until equilibrium conditions of saturation and pressure gradient are established. 2. Hassler or stationary liquid method5,6,7 in which a uniform liquid saturation is attained, usually through capillary desaturation, then gas or oil is flowed through the sample at a pressure drop insufficient to disturb the pre-established saturation. :. Non-steady state method1,8,9,10 In which only the gas phase is injected into the sample, causing displacement of the oil phase and resulting in a system of continually changing average saturation and saturation gradient. The steady-state and Hassler methods have been most popular because, no doubt, of the simplicity of the actual relative permeability calculations. The problems involved in these methods were limited to apparatus design and measurement techniques. In the steady-state method, for instance, a constant flowing fluid ratio is established which, at equilibrium, results in an essentially uniform saturation over the entire length of the test sample. Therefore, the basic flow characteristics could be obtained by correlating the average saturation of the test sample with the kg/ko determined at various flowing gas-oil ratios.

Jan 1, 1957

By F. M. F. Cazin

Some twenty years ago the author of a book,* by which, for the first time, molecular action was made to account for nearly all phenomena in hydrodynamics, began his preface as follows: " It is contrary to all experience, that any branch of science should suddenly cut short its own line of reasoning, and drop all connection with its past, and yet as quickly re-establish itself on an entirely new basis. It is, therefore, not without justification that this book should be met with caution and even distrust." When the newly-discovered natural facts and laws presented in this paper were, in 1891, first laid before the officers of the American Institute of Mining Engineers, they might have been preceded by a preface to the same effect; and the expression would have found its justification by the actual experience these facts and laws met with. Since then, as the result of their publication in one of the most prominent

Jan 1, 1895

By W. C. Elmore

THE magnetic powder method, long used for roughly mapping mag-netic fields, has recently been refined 1,2 for investigating the microscopic variations in the surface magnetization of ferromagnetic crystals. Bitter2 first discovered regular powder patterns connected with the crystal structure of such specimens. Several other investigators3 have used Bitter's original technique, with slight modifications, to study the varia-tion of the patterns with variations in the magnetizing field applied parallel to the surface, and their dependence upon the state of strain, of polish and of crystal cut. All of the explanations of these patterns on metallic ferromagnetics have been couched in general terms. In a preliminary report we have described an improvement in the powder technique which led us to the discovery of a new effect throwing con-siderable light on the magnetic secondary structure of alpha iron4 and of nickel5 single crystals. We now report additional evidence confirming the existence and stability of a magnetic block secondary structure.

Jan 1, 1936

By A. S. M’Creath, E. V. d’Invilliers

The rapid development of the southern coal and iron-ore fields during the past few years, and especially in the latter half of the year 1886, and the avidity with which everything relating to the industrial situation there is read and absorbed by the professional and non-professional public, has led to the preparation of a brief paper for the Institute upon a comparison of the raw materials available on or about January 1st, 1887, at three prominent centers of consumption. While disclaiming any originality or priority in the treatment of the resources of these districts, where so much valuable and interesting work has been performed in the past by several members of the Institute, we hope that the presentation of some analyses of samples personally secured by us in the several districts selected, and prepared for a comparative study of the character of the materials actually used and to be used by the furnaces of the "New

Jan 1, 1887

By Fred C. Bond, Jen-Tung Wang

Comminution energy is principally energy of deformation before break-age, which appears as heat. An empirical equation is presented which covers the entire comminution range. The new strain-energy theory considers comminution from the known principles of mechanics and the reduction ratio. Energy requirements according to the different theories are compared.

Jan 8, 1950

Energy conservation has been the keyword in many plant expansions. Far many years, most of the phosphate industry has been dry grinding their phosphate rock. Agrico Chemical in Florida has recently been evaluating the wet grinding of phosphate rock, a process which eliminates a pre-dry stage for mill feed while allowing higher through- puts. This same company also plans to open a new phosphate facility in Louisiana that will use wet grinding in both ball mills. The Eveleth Expansion Co.'s Fairlane concentrator will have the largest rod and ball mills in the US mining industry. The plant will consist of three lines, each with one rod mill and one ball mill, and will process 464 ltph. The rod mills will be 15 x 20% ft, drawing 2035 hp. The ball mills will be 17 x 41½ ft, drawing 6900 hp and driven by dual 3000- hp motors. The plant is scheduled for startup in the fall of 1976.

Jan 2, 1975

By Benjamin Smith Lyman

The question of the original extent of the anthracite-beds of Pennsylvania has often been raised; and even discussed with reference to the probability of their present existence under the New Red, a matter of immense practical importance. So high an authority as my revered master, J. P. Lesley, Honorary

Jan 1, 1903

By Harvey P. Knudsen, Young C. Kim, Edward Mueller

Abstract-This paper describes the results of a comparative study of the geostatistical ore reserve estimation method over three conventional methods; the polygon method, the inverse of the distance squared (IDS) method, and ELIP which is similar to IDS. Each method was evaluated on its ability to accurately predict individual block grades for one bench of the Pima mine, located near Tucson, Ariz. Results at the Pima mine indicate that the geostatistical method is no better or worse in predicting block grades and total tonnage than the ELIP or IDS methods. In contrast, the polygon method is clearly inferior. All of the methods would have given better results if geology had been included in the block model. At already producing mines ELIP or IDS may be good choices since they involve substantially less cost in computer time. For prospective or new properties the geostatistical model is more attractive due to its ability to construct confidence limits on the estimates.

Jan 1, 1978

By J. R. Linney

Demand for eastern magnetite in 1948 necessitated practically all eastern magnetite industries to operate on a six-day week, with the result that over 11,000,000 long tons of crude ore were mined, and the shipping products amounted to approximately 5,000,. 000 long tons. Reports indicate that operating on a six-day week and doing maintenance work on the seventh day was satisfactory and resulted in excellent continuity of operation. In the Port Henry district, Republic Steel Corp. once again set new all-time records for the production of crude ore and total shipping product; 1,868,000 long tons of crude ore were mined, 945,000 from the Old Bed mine, 408,500 from the Harmony mine, and 514,500 from the Fisher Hill mine. Of the 969,000 long tons of shipping products, 663,800 long tons were sinter, 181,000 lump ore, and 115,200 con¬centrates.

Jan 1, 1949

By F. E. Luborsky, K. T. Aust

RECENT interest has been shown in utilizing solid-state techniques for obtaining large oriented grains in the Alnico Alloys.1-4 Unfortunately, due to the inherent brittleness of these materials it is difficult to introduce sufficient imperfections by deformation to support the nucleation and growth of new, recrystallized grains. As a result, recrystal-lization methods for obtaining large grains, such as the strain-anneal technique, do not appear to be feasible. Steinort et a1.2 used a combination of a thermal gradient and internal strains to obtain large single crystals of Alnico 5 from a poly crystalline casting by annealing at temperatures above 1200°C. It was suggested that the strains were the result of the precipitation of the y phase which exists between -850° and 1200°C. The purpose of the present study was to determine if the grain size of the cast Alnico alloys can be markedly increased by solid state techniques involv-

Jan 1, 1963

By E. Amott

A test is described in which the wellubility of porous rock is measured as a function of the displacement properties of the rock-water-oil system. Four displacemet operations are carried out: (I) sponlaneous displaceti?ent of water by oil, (2) forced displacement of water by oil oil in the same system using a centrifuging procetllrre, (3) spontaneous displacement of oil by water. and (4) forced displacment of oil by water. Ratios of the spontaneous displacement volumes to the total displucenlent volumes are used as wettability indicates. Cores having clean mineral surfaces (strongly preferentially water-wet) show displacement-by-waler ratios approaching 1.00 and displacement-by-oil ratios of zero. Cores which ([re. strongly preferentinlly oil-wet give the reverse resu1ts. Neutral wellability cores show zero values for both ratios Fresh cores from different oil reservoirs have shown wettabiltties in tlris te.st covering rrlti~ost 111e conlplrtt, range of thr: te.st. Notvever, nlo.s/ of tlle fresh California cores tested were slightly prcfere111icrlly wclter-\vet. The chrrnge.~ in coro u ('liabilities, as indicated hy this te.st, r~.sril/ing from various CO~P hanrlling procedures tt,ere oh.served. In sonie ca.sc,s /Ire ~,cttahilitio.c. of fresh cores were changell by drxi:~g or 11y e.x/rclct ing with iolcreiii~ or. dioxunc~; in o/h~r cases they were 1101 changed. Co~ltrrc/ of cort,.s ~.ith filtrc~t~c. from water-base rlrilling rilrrrls crlrc.sed littlc change in we/ /ahility ivhile contnct with filtrates frorii oil-hus~ ri1rlcl.s tlecrrascrl the prefcrerlcc, of the, cores for )I.NI Usitig thi,s test to ri.crl~lute n~r~ttubili~y, N .vt~ldy was iilarle of /lie correlmtio~i of wettability with wa/erfloocl nil recovery for orttcrop Ohio sand.stone and for Al~ln-tlunl. Resul/.v indicate thml no single correlatioti between these factors applies to different porous rock syste~n. It is thought that diflerences in pore gen~netry resrrlt in diflrrerrce.~ in this correlurio~z. INTRODUCTTON Most investigators who have reported on the wettahility of porous rock have described such rock as prcferentially water-wet or preferentially oil-wet. In some cases a third classification, neutral wettability. has been used. The efficiency of water floods in each of these wettability groups has been described in numerous publications. Several methods for characterizing porous rock wet tability more precisely have been reported,' " but it appears that because of one weakness or another. none of these has been generally accepted. Early in our studies in this field, it was found that the displacement efficiency of oil by water in a particular porous rock having a strong preference for water was quite different from that in a similar rock having only a moderate preference for water. Thus, there appeared to be a need for a practical, reasonably precise wet tability test. one which could classify porous rocks into 10 to 20 different groups rather than the two or three broad groups listed above. The test developed to meet this need is described in this paper. Also, changes in wettability, as indicated hy this test, resulting from various core handling procedures are discussed. Finally, data showing the corrclation of wettability with waterflood oil recovery for two different types of cores are presented and discussed. Some confusion has resulted from the failure of certain writers to define clearly some of the wettability terms they have used. Accordingly, the following commcnts concerning definitions are offered. The wc t ta-hility of a solid surface is the relative preference of that surface to be covered by one of the fluids under consideration. It is felt that this is the generally accepted definition. The fluids being considered must bc specified (or understood) before the term wettability has any significance. In the work reported here these fluids are water (3 per cent brine) and oil (kerosene). The term preferential wettability is sometimes used, but we think that the word preferential is redundant here and should not be used. Tn line with the definitions of Jennings', a preferentially oil-wet solid surface is regarded as a surface which will show an oil advancing contact angle less than 90" (measured through the oil) in the water-oil-solid system. Oil will spontaneously displace water, if both are at the same pressure, from such a surface. A preferentially water-wet surface is analogous. This is consistent with the wettability definition above. As Jennings has said, frequently the term oil-wet is used to mean the same thing as preferentially oil-wet. However, oil-wet also has been used occasionally referring to an oil-covered surface when the availability of water was limited. To avoid confusion from this source, we do not use the terms oil-wet and water-wet. DESCRIPTION OF WETTABTLITY TEST The following points were considered desirable in a wettability test for our purpose. 1. The test should be a displacement test resembling

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

By F. C. Pittman, D. W. Harriman, J. C. St. John

This paper mentions briefly the history of hydraulic jetting as applied to perforating and fracture initiation. It points out the advantages of hydraulic perforation and undercutting as an aid for creating a fracture at the point desired rather than depending upon the weakest point in the formation for breakdown. It describes early experimental work with jet nozzles in search of better nozzle materials. The effect of splash-back damage and its subsequent influence on jet body and tool design during this work is discussed. A series of cutting-rate curves for jets cutting steel and steel-cement-formation combinations is presented to show the effect of hydrostatic head and the point of diminishing returns with respect to cutting time. There is a series of photographs showing various types of rock formation in which perforation and undercutting tests were made. These stones were drilled and the casing cemented in place as in an actual well. The casing was perforated and circularly cut as if preparing for a fracturing job. The conclusion reached in the paper is that hydraulic jetting with sand-laden fluid can be used for perforating and undercutting casing, cement and formation rock for the intended purpose of inducing the formation to fracture at a desired point. INTRODUCTION Hydraulic jetting as a means of cleaning a formation during acidizing has been used for many years. The acid-jet gun was used to clean formation and for drilling cement from casing with acid. This tool was dropped to a seating ring installed on the tubing and could be retrieved by reverse circulation or wire line. In this process, the fluids were directed against the formation to clean and penetrate beyond the mud-damaged area. After the development of the hydraulic fracturing process, interest in jetting the formation with abrasive-laden fluid was renewed. The cutting action of abrasive fluid on pumping equipment, which is a well known problem, has been utilized to perforate and undercut casing, tubing and formation. In this process, surface areas are provided in the formation on which the frac- turing pressures may work to produce a fracture at the location desired. EQUIPMENT The tools used consist of bodies containing two, three or four jets in a single horizontal plane equally spaced around the circumference. The body is threaded to the end of a string of tubing and run into the well. In addition, an expendable tool is available that may be left in the hole after perforating and produced through until necessary to remove the tubing. The bottom of each tool is equipped with a ball-type back-pressure valve. The ball can be reversed to the surface and recovered. This allows reverse circulation so that loose sand which accumulated below the tool while jetting may be removed before the fracturing job. The present jetting tools are of such length that, when screwed together, the jets fall on 12-in. spacing. ANALYSIS OF THE PROBLEM Early work with nozzles indicated that hardened steel was not a suitable material for jets and that more durable material would be required. Ceramics were tried and found to be superior to steel but still too shortlived for most applications. Tungsten carbide, which was tried and found to be the best material available, is now being used for jet nozzles. Analysis of the problems presented by this process indicated that the following information was needed. 1. The effect of submergence on a jet stream and the effect of submergence on the cutting rate of a jet stream. 2. The cutting rate and depth of a jet stream in steel. 3. The cutting rate in various formations and point of diminishing returns. 4. Size of hole or slot cut in a pipe by a given jet. 5. Fluids and sands used. 6. The flow of various weight fluids through the jet nozzle and the discharge coefficients. 7. The type cut formed in the formation by the jet stream. 8. The stretch and contraction of tubing due to temperature and pressure. The cutting effect of a jet stream on a target in the atmosphere is rapid and spectacular as most of the

By John W. Gruner

On account of the tremendous increase in the production of steel there has been much speculation as to the reserves of iron ore. A number of estimates of world scope have been published, which show that these reserves are definitely limited if a long range view is taken. There are, however, optimists who believe that in perhaps two generations the metallurgy of iron will have advanced to the point where any kind of iron mineral combination of perhaps 20 pct iron will be usable. This thinking has been particularly applied to the new taconite developments of the Mesabi Range, for here is an iron formation of such vast extent that its iron could almost last forever. Let us briefly examine this most favorable of all low grade ore reserves in North America. Nothing will be said about the 1,000 million long tons of material now classified as ore, for they will be largely gone in less than 20 years.

Jan 3, 1954

By John Hays Hammond

IT was but a few years ago that the mining engineer, and his confreres, the civil, mechanical and electrical engineer, were stigmatized by politicians of the parish? pump variety as advance agents of unprincipled exploiters of backward countries. Today he is recognized as a most important missionary of civilization in opening up new territory to contribute its mineral wealth and incidentally its other resources for the needs of mankind. An engineer, it is now conceded, is not only a benefactor of the world at large, but is a primary factor in the betterment of conditions of the inhabitants of those countries developed by his skill and indomitable courage-for courage is requisite in pioneering and his indefatigable industry. The engineer will, I believe, become a real "Ambassador of Good Will," when the slow-consenting academic mind realizes as it must that beneficent deeds are more enduring and more convincing than mere gestures of professed amity.

Jan 1, 1929

By Leroy W. Weeks, Peter B. Nalle

The rapid growth of the modern electronic computer industry during the past 15 years is, perhaps, the greatest phenomenon that has occurred in American business in this century. This growth is due in part to the new, and in some instances, revolutionary applications of computers instigated and developed by both the manufacturers of such equipment and their customers who search for easier, faster, more accurate methods of conducting their business operations. As in other industries, modern computers are becoming more common in the field of mining. The adaptation of computer analysis to the unique problems of mining companies is undergoing research and development by both electronic and mining companies. However, for those of us in mining who are interested in the possibilities of computer analysis and control, the basic question is Where can a computer system be of use in a mining operation today? Some ideas of such applications follow, as well as a specific example of computer control at the Riverside Cement Co.

Jan 9, 1960

By J. W. Whalen

The design, operation and evaluation of an instrumental method for the determination of fluid saturation in porous materials during multiphase flow studies is described. The presence of a magnetic tracer comprising approximately 20 per cent by weight of the aqueous phase is necessary in the utilization of this method. The results of two-phase relative permeability studies on two samples of porous media are presented. The realizable accuracy of the magnetic susceptibility apparatus in fluid saturation determination is estimated to be 2 saturation per cent. The response characteristics of the instrument, together with its simplicity of operation and maintenance are sufficient to recommend its use in routine laboratory studies. INTRODUCTION The problem of fluid saturation determination in laboratory multiphase flow studies characterizing oil recovery processes is one which has been given exhaustive study. Briefly the requirements which are considered essential for a method sewing this purpose are: (1) that the measurement be made external to the porous rock sample under study with no interruption of the fluid flow pattern, (2) the saturation indication must be independent of fluid distribution in the volume scanned by the measuring device, (3) the sensing element should have a small field of definition enabling several independent measurements to be made along the length of a core sample, and (4) the properties of the fluid phases should not be too greatly influenced by required tracer substances. Several methods of saturation determination have found acceptance as meeting most of the above requirements. These include resistivity,1 X-Ray absorption,2,3,4 radiotracers,5,6,7 and neutron8 diffraction The merits of these techniques have been discussed elsewhere in detail and will not be considered here. It may, however. be pointed out that the elaborate instrumentation required by the methods mentioned above, with the exception of the resistivity method (which is undesirable from other standpoints) encourages the development of methods of saturation determination which, while meeting the requirements listed, are simple to operate and maintain. It is the purpose of this paper to describe the instrumentation and evaluation of a technique for the determination of fluid saturation which combines relative simplicity with an accuracy and applicability comparable with methods now in practice. DESCRIPTION OF THE METHOD If the magnetic susceptibility of one of the fluid phases contained within a porous material is sufficiently greater than that of the remaining phases, the fluid content of the material with respect to that phase may be determined by an induction measurement. This may be accomplished by measuring the induced voltage in the secondary of a transformer which contains the porous sample and its interstitial fluids as a portion of the magnetic flux path. Since the fluids used in multiphase flow studies involving petroleum reservoir samples possess uniformly low magnetic susceptibilities, the use of a magnetic tracer in one of the fluid phases is required. In view of the relatively high paramagnetic susceptibility of salts of the transition elements, together with their high water solubility. these compounds become logical choices as tracer materials. Cobaltous chloride, having a specific magnetic susceptibility of 17.5 x 106 cgs electromagnetic units, was used as the tracer material throughout this work, in a concentration of approximately 20 per cent by weight in the aqueous phase. MAGNETIC SUSCEPTIBILITY APPARATUS Basically, the magnetic susceptibility apparatus consists of a transformer serving as the detecting head, a

Jan 1, 1955

By Samuel L. Hoyt

This paper gives a brief description of an investigation made several years ago on the diffusion of zinc into copper. The material for that study was furnished in the form of thin copper strips coated with zinc. The result was required rather quickly and at not too great an expense, and especially information was desired as to the rate at which zinc would diffuse from the zinc coating into the copper and the temperature at which the operation should be carried out. A study of the requirements of this problem indicated that the solution might be secured by means of six determinations. This is the smallest number that will give the information desired and, at the same time, furnish checks on the accuracy of the determinations which justify an abbreviated experimental program. This does not count a preliminary test which was designed to give some idea of the correct temperature to use. The minimum number of temperatures that can be used is two. Knowing the rates of diffusion of zinc into copper at two properly chosen temperatures, it is possible to calculate the rate for any other temperature, and also to check the accuracy of the determination by means of the heat of diffusion, which is calculated from the effect of temperature on the rate of diffusion. The minimum number of determinations at any one temperature is three. The amount of diffusion which occurs at a fixed temperature is definitely related to the time of diffusion, so that by determining the amount of diffusion for three different time intervals, this relationship may be established and possibly a check on the accuracy may be secured. This accounts for the six determinations or experiments, and suggests the logical plan of the work. The check used here is not generally applicable to diffusion phenomena, but it seems to hold closely enough for the limited amount of diffusion in this investigation to justify its use. The samples used were 5 to 6 mils thick and about 1 in. square. They were placed between iron blocks and set in the hot zone of a nichrome furnace which had been brought to the desired temperature Time was taken from the moment the samples reached the furnace

Jan 1, 1929

By Samuel L. Hoyt

This paper gives a brief description of an investigation made several years ago on the diffusion of zinc into copper. The material for that study was furnished in the form of thin copper strips coated with zinc. The result was required rather quickly and at not too great an expense, and especially information was desired as to the rate at which zinc would diffuse from the zinc coating into the copper and the temperature at which the operation should be carried out. A study of the requirements of this problem indicated that the solution might be secured by means of six determinations. This is the smallest number that will give the information desired and, at the same time, furnish checks on the accuracy of the determinations which justify an abbreviated experimental program. This does not count a preliminary test which was designed to give some idea of the correct temperature to use. The minimum number of temperatures that can be used is two. Knowing the rates of diffusion of zinc into copper at two properly chosen temperatures, it is possible to calculate the rate for any other temperature, and also to check the accuracy of the determination by means of the heat of diffusion, which is calculated from the effect of temperature on the rate of diffusion. The minimum number of determinations at any one temperature is three. The amount of diffusion which occurs at a fixed temperature is definitely related to the time of diffusion, so that by determining the amount of diffusion for three different time intervals, this relationship may be established and possibly a check on the accuracy may be secured. This accounts for the six determinations or experiments, and suggests the logical plan of the work. The check used here is not generally applicable to diffusion phenomena, but it seems to hold closely enough for the limited amount of diffusion in this investigation to justify its use. The samples used were 5 to 6 mils thick and about 1 in. square. They were placed between iron blocks and set in the hot zone of a nichrome furnace which had been brought to the desired temperature Time was taken from the moment the samples reached the furnace

Jan 1, 1929