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No. 347.-A South African development company will shortly require the services-of a mill superintendent, who has a general knowledge of concentration, particularly of flotation, and is able to take charge of a copper concentrator treating 15,000 tons per month and employing 200 natives and a small number of white men. Salary is £60 per month to start, and the company supplies furnished room or house, including free light, free water and free sanitary service, together with one native house servant. A contract will be made for 6 months, and notice of 3 months by 'either party will be required to terminate the engagement after 6 months. An allowance of £75 for-traveling expenses will be paid on arrival in South Africa to a single man, or £125 to a man who brings his family. Salary begins upon arrival in South Africa, and no allowance will be made for return traveling expenses. No. 349.-A Canadian university wishes to engage a man to teach non-ferrous metallurgy and ore-dressing as well as to direct research work. The instruction work covers 7 months but the research work is continued throughout the year. To a suitable man the rank of professor will be granted. Applicants are requested to state education, experience, salary desired and any other particulars that might assist in selecting a man for this position. No. 350.-Wanted, 60 engineers for ordnance training school, month's training. Salary for first three months $1200 to $1500. After 3 months, up to $2400.

Jan 11, 1918

By B. E. Eakin, A. L. Lee

Atmospheric pressure viscosity values For light hydrocarbons were calculated by a simple mixing rule based on the Sutherland constants for pure components. This method was further extended so that the atmospheric pressure viscosity of a mixture may be calculated based on the molecular weight information only. INTRODUCTION A proven method for estimating the gas-phase viscosity of a mixture is the one by Herning and zipperer.l This mixing rule has the following form: One method for calculating the pure component viscosity i is the Sutherland equation,2 which has the following form: The Sutherland constants B and S are determined from experimental data. A set of Sutherland constants for light hydrocarbons based on the data of several investigators3-5 is presented in Table 1. APPLICATION The Herning-Zipperer equation and the Sutherland equation were used to obtain an equation for calculating the gas-phase viscosity of light hydrocarbons. This equation has the form, Eq. 3 was used successfully in the study of methane-n-butane mixtures.6 Further analysis indicated that the Sutherland constants are a function of molecular weight.7 The gas-phase viscosity may be calculated based on molecular weight information only. The following equation was developed: The atmospheric pressure viscosity of ethane, propane, n-butaneand four methane-propane mixtures calculated on the basis of Eq. 6 are compared with the data of other investigators in Tables 2, 3, 4 and 5, respectively. A plot of atmospheric pressure viscosity vs molecular weight based on Eq. 6 is presented in Fig. 1.

Jan 1, 1965

Oregon State Agricultural College, School of Mines, Corvallis, Ore Available publications of the old Bureau of Mines and Geology of Idaho have lately been distributed through the School of Mines of Oregon State College As the School of Mines was abolished in the summer of 1932, all of the bulletins and publications available have been turned over to the State College Library for distribution. At present plans have not been completed for further distribution For information on available publications, address: Director of Libraries, Oregon State College, Corvalhs, Oregon

Jan 1, 1933

Engineering Experiment Station, University of Arkansas, Fayetteville, Ark. W N Gladson, Dean and Director The Engineering Experiment Station has published a number of bulletins, only a few of which are of particular interest in this directory: Bulletin 3, Arkansas coal or oil for domestic heating; 4, Road materials of Arkansas, 5, A study of Arkansas coals, 6, Portland cement materials in Arkansas; 11, Natural gas versus Arkansas coal for house heating. Circular 3, Short cuts to combustion efficiency with natural gas Address the Engineering Experiment Station for any of these publications.

Jan 1, 1933

By Charles E. Mauk, H. William Prengle, Robert W. Legan

A process breakthrough was needed for the complete destruction of total cyanide influent as high as 100,000 mg per 1, or below 1 mg per 1, to produce an influent with total cyanide below the limit of detection. The process uses ozone for the total destruction of cyanide and metal cyanide complexes. It was found that while ozone alone reacted with the iron cyanide complexes too slowly for practical application, ozone at slightly elevated temperature became more effective, and ozone with ultraviolet light became effective enough to permit the design of a successful system.

Jan 1, 1977

Frank L. Bader has been appointed to the sales staff of Lehigh Navigation Coal Co. in the Philadelphia territory. H. C. Burrell, former coordinator of raw materials, Pittsburgh, Penna., has been made manager of raw materials for Columbia-Geneva Div. of U. S. Steel Co., San Francisco. J. H. Cazier has resigned as general superintendent of Bagdad Copper Corp., Bagdad, Ariz., to devote full time with E. A. Scholz to the operation of the Copper King, Phillips and Black Pearl Mines near Bagdad. They have operated the Copper King zinc mine for more than two years.. Production started from the Black Pearl and Phillips tungsten mines during the past year. Robert T. Chapman has resigned from Reynolds Mining Corp. to join Westmoreland Manganese Corp. as general superintendent. Annan Cook, with Kennecott Copper Corp.'s exploration dept. for the past three years, has been appointed district geologist for the eastern states.

Jan 1, 1952

At its meeting on February 21, 1933, the Board of Directors passed the following resolution defining and expressing the policy of the Institute with respect to official participation or action in controversial matters: WHEREAS, the Board of Directors at its last meeting passed the following resolution: "The Board of Directors, having been appealed to by several Local Sections for advice concerning the attitude and policy of the Institute relating to the endorsement of candidates for public office, the following statement of policy is formulated: "Whereas, the American Institute of Mining and Metallurgical Engineers is organized for purely professional and scientific purposes, and whereas diversity of opinion among its members on partisan or political questions is inevitable, it is the expressed policy of the Institute to refrain from official participation or action, in political and semi-political matters." AND WHEREAS, appeals for additional advice have been received: NOW, THEREFORE, IT IS RE¬SOLVED: (1) That the policy of the Institute is to refrain from official participation or action in controversial non-technical economic subjects; further (2) That if any Local Section is in doubt as to the application of this policy to any particular subject, it should communicate with the Secretary of the Institute for advice.

Jan 1, 1946

IN presenting the medalist, Scott Turner, director of 'the Bureau of Mines, said in part: "Mr. Blaylock is a Canadian by birth, training, ex-perience and preference. He was born in the Province of Quebec, graduated from McGill University in 1899, and immediately thereafter became an employee of the company for which he is now general manager. His outstanding achievements have been the acquisition for his company of the Sullivan mine, and the organization of a metallurgical staff, which, under his leadership and personal direction, solved the difficult problems pre-sented by the extraordinarily complex lead-zinc-silver ores of the Sullivan mine. "By title only, I will suggest to you the high lights of his career: (1) Development, of the great mine at Kimberley, and a huge plant at Trail. (2) Discovery and application of a successful differential flotation process for Sullivan ore which had previously not re-sponded to any process. (3) Improvements in lead-blast-furnace and refinery practice. (4) Development of an electrolytic process for treatment of zinc concen-trates. (5) Development of an electric-furnace-smelt-ing-method for zinc-plant residues. Besides this, we recognize his great organizing ability, his gift of leader-ship, and the cooperative spirit he always displayed.

Jan 3, 1928

By J. A. Herbst, G. E. Agar

Beginning with the second paragraph in the second column of page 148, this paper should read: The Reynolds number in Fig. 6 was calculated from the inlet diam and it is evident from the graph that above NR = 5000 the value of K2 is as it should be, a constant. The data10 shown in Fig. 7 was obtained for fluids flowing in pipes of diam D with sharp edged orifices of diam d. To be consistent with the representation in Fig. 6 the Reynolds number was calculated with the orifice diam d. These two sets of data show similar patterns and the variation in the orifice coefficient C is believed to account for the variability of the cyclone coefficient K2. The values of C given in Table IV are derived from K2 by conversion of units. C more nearly represents an equivalent orifice coefficient for a cyclone. Armstrong1' showed that data reported by Chaston 12 and Elcox13 yielded values for C of 0.24 and 0.27, re- spectively, Dahlstrom's4 data gives a value of 0.22. As a consequence of the variability of the cyclone coefficient some caution must be exercised in substituting for Q in the split size equation.

Jan 1, 1967

By William Glenn

Almost beyond doubt, the most important contribution to the assaying of copper yet made, is that of Mr. Eustis (Bans., xi., 120) on the " Comparison of Various Methods of Copper Analysis," which indicates in a manner for which the assayer cannot but feel grateful, how a copper sample ought to be treated from the moment it enters the laboratory until the copper is finally weighed. Admitting, as the present writer is inclined to do, that this paper establishes, as the official standard, the method of electrolysis, we may note as one of the few details which it does not finally fix, the kind of battery most desirable for precipitating the copper upon platinum. In this respect each assayer appears to be a law unto himself, while all feel more or less " shaky " as to the results. Classsen seems to suggest a remedy when he directs the measuring of the -gases liberated by the battery employed. But, in fact, that measure is not a constant in the Bunsen elements which he prescribes for copper determination. Furthermore, measuring gases necessitates more machinery and labor than the average assayer has a stomach for. It is, however, but just to Classen, to whom we owe so much, to reeall that he wrote more especially for students in the schools.

Jan 1, 1889

By Kenneth Cottingham

The year 1941 brought a considerable increase in drilling activity in Ohio. In 1940, the total of wells completed was 1228, whereas in 1941 it was 1561, or an increase of approximately 27 per cent. Of the 1561 wells, 333 were oil wells, 701 gas wells and 527 dry holes. The completions for the past five years are shown in Table I; the number of productive oil or gas wells for the year 1941, arranged by producing formations, are given in Table 2; the number of wells, oil, gas or dry, completed in each county in 1941, in Table 3, and wells by sands in Table 4. The production of oil increased by about 500,000 bbl. in 1941, nearly all of the increase being in Pennsylvania grade. In 1940, the total production was 3,052,000 bbl. from 25,500 wells. In 1941 the total production was 3,547,534 bbl. from 24,801 wells. The increase in production is chiefly due to the Clinton pool in Clayton township, Perry County, which is briefly men- tioned later in this review. The number of oil wells, by grades of oil, and the total quantities produced are shown in Table ;. Annual oil production for five years is listed in Table 6. The average prices paid for crude in 1941 were slightly higher than in 1940 These 1941 prices, with dates of change, are shown in Table 7. The maximum production of natural gas in Ohio was in the year 1915, when the total was just under 80 billion cu. ft. The maximum consumption occurred in the year 1916, and was approximately 169 billion cu. ft. For the past several years, Ohio has ranged from eighth to eleventh, in order of gas production for the different states, being in tenth place in 1940. In the matter of consumption, however, Ohio remains in fifth place. Preliminary figures for 1940 indicate that production of natural gas increased II per

Jan 1, 1942

By Kenneth Cottingham

The year 1941 brought a considerable increase in drilling activity in Ohio. In 1940, the total of wells completed was 1228, whereas in 1941 it was 1561, or an increase of approximately 27 per cent. Of the 1561 wells, 333 were oil wells, 701 gas wells and 527 dry holes. The completions for the past five years are shown in Table I; the number of productive oil or gas wells for the year 1941, arranged by producing formations, are given in Table 2; the number of wells, oil, gas or dry, completed in each county in 1941, in Table 3, and wells by sands in Table 4. The production of oil increased by about 500,000 bbl. in 1941, nearly all of the increase being in Pennsylvania grade. In 1940, the total production was 3,052,000 bbl. from 25,500 wells. In 1941 the total production was 3,547,534 bbl. from 24,801 wells. The increase in production is chiefly due to the Clinton pool in Clayton township, Perry County, which is briefly men- tioned later in this review. The number of oil wells, by grades of oil, and the total quantities produced are shown in Table ;. Annual oil production for five years is listed in Table 6. The average prices paid for crude in 1941 were slightly higher than in 1940 These 1941 prices, with dates of change, are shown in Table 7. The maximum production of natural gas in Ohio was in the year 1915, when the total was just under 80 billion cu. ft. The maximum consumption occurred in the year 1916, and was approximately 169 billion cu. ft. For the past several years, Ohio has ranged from eighth to eleventh, in order of gas production for the different states, being in tenth place in 1940. In the matter of consumption, however, Ohio remains in fifth place. Preliminary figures for 1940 indicate that production of natural gas increased II per

Jan 1, 1942

By E. M. Boatman, S. J. Pirson, R. L. Nettle

More than a decade ago some theoretically derived relationships were proposed that permitted the prediction of the relative ability of reservoir fluids (oil, gas, water) to flow simultaneously within the porous structure of rocks. While many successful predictions of fluid-flow ratios from wells have been made from electric logs, the theoretical deductions have not been subjected to laboratory verifications. For the relative permeability to liquid and gas, simultaneous flow of water and air was used, employing the familiar external-gas-drive technique. While in the process or water desaturation, the resistivities of the test cores (Woodbine sand) were measured. Their permeabilities varied from 10 to 280 md. The laboratory results indicated the need for changing the values of exponents in the theoretically derived formulas, whereas the form of the functions of resistivities and saturations remained as derived by theory. For the relative permeability to oil and water, the three-core dynamic technique was used on six cores. In this case it was found that the formulas were valid with but slight modification as derived by theory, to a sufficient degree of accuracy for engineering use and for well productivity prediction from electric logs. INTRODUCTION Conventional quantitative well log interpretation generally stops after reasonable values for formation porosities and water saturations have been established. Yet such in formation is insufficient to predict either the outcome or the desirability of well tests and completion, let alone the economic aspect of producing oil- and gas-bearing sections which might have been established by conventional log analysis. To give an engineering answer to such questions, it is necessary to predict the expected fluid flow ratios, the productivity index and the ultimate recovery from potentially productive wells. This problem requires in part for its solution a determination of the relative permeability characteristics of the potentially producing formations, both to oil (or water) and gas, and to oil and water.

Jan 1, 1965

By R. W. Armstrong, P. C. Jindal

WE should like to point out that Hu and cline.1 in their study of the recrystallization of titanium, have obtained data which appear very important for accurately determining the dependence of hardness on grain size for this material. It has been proposed2,3 that the macrohardness. H. of a poly crystalline material should depend on its average grain diameter, l. in accordance with the relationship: H =H0 + kHl-1/2 [1] where Ho and kH are experimental constants. This relationship follows from the hardness dependence on yield stress or flow stress4 and. thence. the Hall-Petch stress-grain size relations.5'6 Fig. 1 shows the Diamond Pyramid Hardness. Dph. values vs the reciprocal square root of the average diameter of the recrystallized grains, taken from the titanium data reported by Hu and Cline. The data in this figure give a linear relationship for the hardness over a wider range of grain diameters than anyone has previously measured. The data are not linear, for example. on an I-1 or l-1/3 scale. At the very large grain sizes the data are in reasonable agreement with measurements earlier reported by Holden, Ogden, and Jaffee.7 For the grain sizes smaller than 1 µ, which correspond in Fig. 1 to hardness values greater than 150, the material was reported as not being completely recrystallized and, therefore, these data appear less meaningful as far as the hardness dependence on grain size is concerned. However. it has been suggested by other investigators that deformed materials exhibit strengthening due to an effective grain size refinement even in the unrecrys-tallized condition.8-10 Also. Hu and Cline have shown that a change in texture occurs for titanium during the recrystallization process and. especially. following it. The influence of this texture change on the hardness-grain size relation would be expected to be less than that reflected in the unidirectional stress-strain behavior, even for an hcp material. because of the actual combined stress system which applies for the hardness test. For, at least, certain combined stresses, average values of the orientation factors should still occur in the stress-grain size analysis of a material exhibiting a preferred orientation.' We previously suggested3 that the experimental constants. H0 and kH. from the Meyer hardness-grain size relation should be correlated with the Hall-Petch constants, uoy and ky.5,6 Our recent study" of the Hall-Petch relation and the hardness-grain size results which obtain for a number of polycrystalline materials shows that: The inequality [2] is explained by noting that the hardness should be correlated. perhaps, with the flow stress at some value of strain, as suggested by Dugdale,12 and. also, that the influence of strain on the Hall-Petch relation is to increase uo and not change k very much." Normally. Dph values and Brinell hardness values are nearly equivalent to each other and to the Meyer hardness number. For the case of titanium, then. the inequality [2] may be evaluated using the experimental values of ao = 8.0 kg per sq mm and ky = 1.3 kg per mm3/2 obtained from the experiment of Guard.6,13 Thus, (Ho/uo) = 12 and (kH/k3) = 1.3. This research has been supported at the University of Maryland through the Center of Materials Research by the Advanced Research Projects Agency of the U.S. Government.

Jan 1, 1969

By David Cornell

Back pressure test data on natural gas wells are short time test data of unsteady state nature. Performance curves from which unsteady state effects have been eliminated, called stabilized performance curves, are necessary for understanding the behavior of gas wells and for scheduling gas fields for periods up to 20 years. A calculation procedure has been developed whereby three day, seven day, 30 day, or other duration stabilized performance curves may be calculated from back pressure test data. Such curves are essential for correct gas deliverability calculations and gas field scheduling. I NTRODUCTION The manner in which a back pressure test is made will affect the slope of the back pressure curve because the radius of drainage changes with the length of time that the well is allowed to flow. The reciprocal of the slope of the back pressure curve is defined as n in Equation 1 and varies from 0.5 to 1.0. If the flow is viscous and the radius of drainage constant, n will have a value of 1.0. Because of turbulence in the formation near the wellbore, the pressure drop is usually greater than the viscous flow pressure drop and the exponent n is frequently less than 1.0. In addition, since the radius of drainage moves away from the well-bore during the test, the gas flows a greater and greater distance as the test proceeds, with a resulting increased pressure drop at the high flow rates, and, again, n for the test tends to be less than 1.O. The effect of the changes in the radius of drainage may be calculated and the results used in preparing stabilized performance curves for fixed values of the radius of drainage. Such curves can be made for a defi- nite time period, such as three day, seven day, or 30 day stabilized performance curves. These cukes will show the effect of turbulence near the wellbore and can be used to predict the performance of the gas well at any flow rate or for any production period. In order to discuss the importance of the radius of drainage quantitatively, it should be defined. Muskat" defines the radius of drainage as follows: "... the radius of drainage gives the distance from the well to which the approximately steady state condition has been established ... it being assumed that no gas is removed from any point until the radius of drainage has passed that uoint." An eauivalent definition of the radius of drainage is that radius at which the extrapolated portion of the steady state portion of the pressure gradient gives a pressure equal to the shut-in reservoir pressure. This definition is also implied in the back pressure equation. The radius of drainage is, then, the distance into the reservoir from which the gas appears to originate at any time. It is, however, only a useful concept and does not actually exist. Fig. 1 illustrates the definition of the radius of drainage. At the end of each flow period the radius of drainage may depend on three factors: (1) the duration of each flow period; (2) the rate of gas production; and (3) the rate and duration of the previous flow periods. In general, back pressure tests are conducted with various lengths of production time and at various flow rates. Each individual back pressure test, therefore, requires an individual analysis. The calculations of the change in the radius of drainage have been made, however, for the case of equal flow periods for all four production rates and several sets of increasing flow rates. Fig. 2 illustrates the results of such calculations made by the method of Cornell and Katz2 for the case of 8, = 50,000 and the flow rate increasing in the ratio 1.0:2.0:3.0:4.0 for each flow period. The increase in the radius of drainage during the test is apparent.

Jan 1, 1956

LEAD and tin mixed together make an alloy through an attachment of natural affinity which they have with each other, so that when they are mixed it is difficult to recognize by the sight which one it is, if the essences of their qualities are not surpassed by more than half. If, indeed, one can be recognized, it is the tin which gives off a certain sharp odor to the sense of smell, besides having a greater hardness and whiteness. The best of these is the one that is the purest in its kind. In the alloy of tin it is the one that is the whitest and hardest, or, when it is bent or some thin end of it is held tightly by the teeth, is heard to crackle as frozen water does. Because this happens more with this than with other metals, I do not wish now to inquire into it. It is enough that it be a sign for recognizing when tin is pure or mixed. Pewterers say that it should be joined in alloy with lead and that it is better for working when it contains four or six pounds to the hundred because it makes it softer to the hammer and more fluid in casting. But I do not like to hear this, even if all they say is true, for I see that the tin that comes from England, when worked as well as in cakes that show it to be pure, is much more beautiful and better in all works than is that made in Venice. And I believe that it is not better for any work when mixed than when pure, except for the advantage of the master who, if he does nothing else, sells lead that is worth little for tin that is worth much. I find that when mixed it serves in only two things. One is when it is wished to make a solder for copper, for use when it is not worth while to solder the bottoms and large pieces of vessels with low-grade silver as should be done. The other is when master potters calcine it in order to make glazes and to apply white to their vases. I consider lead to be useless in all other works of any kind of metal, since it unites with none of the other metals of good company except tin.

Jan 1, 1942

By J. T. Norton, A. L. Mowry

S. J. SINDEBAND*—(1) Discussing the properties of the powders used, Mr. Rostoker mentioned a silicon powder as being between 150 and 325 mesh. We always had much difficulty in measuring particle size of silicon powder by screen analysis, because of its tendency to agglomerate. I would be interested in the method used to measure these particle sizes. (2) Mr. Rostoker maintains that the measurement of magnetic properties is more accurate in determining complete homogenization of an alloy, than is the X ray diffraction technique. I wonder whether this is really true. Even when diffusion is complete, magnetic properties will change during continuation of the heat treatment, due to change in density and pore shapes, as has been demonstrated by Mr. Rostoker himself. Which effect is faster, the diffusion of the alloy components or the attainment of final density, will, in my opinion, depend very much on initial material and sintering conditions used. For magnetic applications, of course, the magnetic measurements are most suited for determining the point at which equilibrium conditions are reached. (3) I was glad to see that Mr. Rostoker had used sample sizes which are similar to those I had used previously, and I believe that ring samples of about 2 in. od will become more or less standard samples for the determination of magnetic properties of powder metallurgy products. I should like to ask how the density was changed for the samples on which the effect of porosity was investi- gated, and, further, why the sintering temperature used for this series of experiments was so low. It is somewhat surprising that a 24-hr treatment at 850°C acts so much more to spheroidize the pores than a treatment for 1 hr at 1100°C. But the effect seems to be indisputable. I have made an investigation of the influence of sintering temperature for longer times on the maximum permeabilities of iron powder compacts which was presented at the International Powder Metallurgy Conference in Graz, in 1948, and I hope that these results will be published here within a short time. The results of this investigation are confirmed by Mr. Rostoker's findings that the change of time from 1 to 24 hr changes the permeability behavior considerably in the direction as indicated by Polder and Van Santen for spheroidiza-tion of pores. I do not quite understand Mr. Rostoker's explanation of the influ-

Jan 1, 1950

By John Henry Harden

THIS shaft, located in the northern anthracite coal-field about 2300 feet southwest from the court-house at Wilkes-Barre, in the County of Luzerne, Pa., is the property of the Lehigh & Wilkes¬Barre Coal Company. The sinking and cribbing to the solid rock (see isometrical view on Plate IX) was conducted by Mr. W. W. Kenrick. Dimensions of the earthwork to the foundation of the cribbing, 51' 1/2" long, 17' 4" wide, 31' deep. Total amount of excavation in cubic yards, 998.5. Dimensions within the permanent cribbing, 45' 4" long, 11' 16" wide, 31' deep, divided into six parts by buttons 8" x 12", each division, 7' x 11’ 16". Permanent cribbing 12" x 12"; temporary cribbing 8" x 10"; backing, 3" thick ; clay puddle to ex¬clude surface water, 12" thick; conductors, 8" x 5"; lining, 1" thick from top to bottom of the shaft. In the latter part of the year 1871, Mr. H. Murray & Son contracted with the company for the continuation of the work at the rate of four hundred dollars per yard in depth, to a point 100 feet below the Hillman seam of coal ; for the succeeding 100 feet the price to be increased twenty-five dollars per yard, and so on until the bottom rock of the Baltimore seam of coal was found. The size of the shaft within the cribbing timbers is 45 feet 4 inches by 11 feet 6 inches, having six divisions of equal dimensions, 7 feet by 11 feet 6 inches, giving room for what is known as the" standard diamond" car, whose capacity when level full is 100 cubic feet, but when loaded by the miner 4 inches above the top contains 112 cubic feet.* Two divisions of this shaft are intended for hoisting coal from the Hillman seam, two from the Baltimore seam, one for ventilation, and one for pumps. The works were planned for two pairs of direct-acting, high-pres¬sure engines, twenty-four boilers, and for an estimated output of 2500 tons of coal per day from the two seams. * Size of the "standard diamond" car, 8' 10” x 4' 3" x 2’ 8” = 100.1.4; loaded 4 inches above the top, 8' 10” x 4’ 3” x 3’ “0"= 112.7.6.

Jan 1, 1877

By L. F. Stutzman, George Thodos

The friction factor plot presented by Cornell and Katz4 and developed for the flow of fluids through consolidated formations has been directly adapted for handling fluid flow problems involvitrg both linear and radial flow. In this adaptation the friction factor plot is used directly for the solution of problems and thereby eliminates the use of conventional equations which are specific to laminar (Darcy) or turbutent flow. This upproach overcomes the disadvantages inherent in the use of these conventional equations. It eliminates the necessity of checking the type of flow occurring in order to identify the specific equation which must be used. In radial flow problems, because of the increasing mass velocity of the fluids as they approach the wellbore. the type of flow may no longer remain laminar. Consequently, it is necessary to use more than one equation in a problem and to identify the range over which each equation should be applied. Finally, in practice it has been found that much of the flow of gases through consolidated media occurs in a range that is neither laminar or turbulent. For this transitional region, no convenient equations are available. The method and presented friction factor plot are appficahle to both liquids and gases. INTRODUCTION The flow of fluids through unconsolidated media in packed beds has been treated extensively by a number of investigatorsl,2,3,5,7,8 Most of these studies present friction factors as a function of modified Reynolds number similar to those developed for conventional fluid flow through pipes. These friction factor plots are presented for linear flow; however, Elenbaas and Katz have extended these concepts to apply to radial flow. All of these studies on unconsolidated materials require a knowledge of packing properties such as sphericity. porosity, and particle diameter. Sphericity and particle diameter cannot be defined at the present time for consolidated formations such as those commonly found in gas or oil reservoirs. As a result many investigators have not utilized friction factors and Reynolds number in the study of fluid flow through consolidated media. However, Cornell and Katz4 present a plot (Fig. 1) for the flow of fluids through consolidated porous media, in which the friction factor defined as: The turbulence coefficient, P, is related to the formation permeability, K, as presented in Fig. 2. Three different types of flow may exist in the flow ot

Jan 1, 1957

By K. E. Manchester, A. H. Clark

Hall measurements have been made on three groups of silicon samples, which were implanted with boron, aluininunz, and phosphorus ions. Boron and phosphorus implants show essentially bulk properties when annealed under previously determined conditions, i.e., 15 min at 80O°C for boron and 10 mirz at 600°C for phosphorus. Bulk properties were also observed in alu?rrilzum-implanted samples when ion concentrations were below 1015 cm-'; however, strange low- terrzperalure behavior and a falloff in cavrier concenlralion was observed for sarnples with ion concenlration abozle loL5 ern-'. This can be attributed to solid-solubility effects since the average bulk concentration f0.r the sample exhibiting bulk properties was below the reported solubility limit for aluminum, while the other samples were above the limit. A detailed study of the annealirzg process indicates that mobilities reach bulk c~alues in phosphorus implants at 250DC, in alutninurn ivnplanls a1 500°C, and in boron implants at 700°C. A simple rnodel has been proposed to fit the annealing data. THE technique of semiconductor doping by direct injection of energetic ions is being actively investigated at this Center. Previously published results from this laboratory have been concerned with the investigation of implanted profiles in silicon and the electrical properties of the resultant p-n structures.1'2 Diode properties have been reported for junctions produced by implantation of boron ions and aluminum ions in n-type silicon and phosphorus ions in p-type silicon. Reverse current characteristics, as well as electron diffraction data, have indicated that the damage to the structure produced by the energetic ions during the stopping process can be minimized by a gentle anneal. The time-temperature conditions for this process have been determined by sheet resistivity studies.3 Electrical profiles of implanted phosphorus ions which have been determined by a differential sheet conductivity technique are based on the assumption that the carrier mobilities and activation energies for ionization are the same as in bulk silicon. These assumptions have been substantiated experimentally by measurement of Hall constants and resistivities of these implanted structures and the results are presented herein. After establishing the bulk property equivalence of the annealed layers, a more detailed examination of the annealing process was undertaken. The sheet resistivity technique initially used to determine anneal conditions has been broadened to include Hall constants and mobility behavior with anneal conditions. PROCEDURE The three groups of samples prepared for Hall measurements were implanted with mass-separated beams of boron, aluminum, and phosphorus ions. Ion concentrations are equivalent surface concentration and they have been determined from beam current measurements during implantation. Implant conditions for the samples are shown in Table I. In all cases, the samples had previously been angle-lapped on one edge and the junction delineated with an HF-copper sulfate solution. The surfaces of the implanted regions of the samples were exposed to the delineating solution and in the case of the "n"-type phosphorus-implanted areas it was later discovered that a finite amount of surface could be etched by this solution. This is discussed in the section on results. The implanted samples were ultrasonically cut into the conventional six-probe configuration shown in Fig. l.* In the annealing studies, for which the meas- urements were taken at room temperature, the sample holder was a Bakelite jig incorporating tungsten mechanical probes. The other measurements were taken using a conventional liquid-nitrogen cryostat, in which the temperature could be varied from 77" to about 400°K. For these measurements, 10-mil aluminum dots were evaporated onto the samples and alloyed with the silicon at 530°C for 15 min. The samples were then mounted in flat-packs, and gold wires were bonded to the aluminum dots. The electrical measurements were made with either a Leeds & Northrup K-5 Potentiometer, a Keithley 147 Nanovolt Null Detector, or a Keithley 601 Electrometer. No external bias was applied to the substrate. There is an inherent self-biasing arrangement at one or the other of the current contacts (depending upon the polarity), and this suffices to limit the current flow to the implanted layer. The magnetic field was generated by an A. D. Little electromagnet. Except for occasional checks of linearity of the Hall voltage with

Jan 1, 1969