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STANFORD UNIVERSITY, CALIFORNIA Our activities for the year 1918-19 have closed with the coming of summer. It has been a most successful year in many respects, especially in the reorganization necessary after the war conditions had passed. An INITIATION SCENE AT STANFORD UNIVERSITY. "old-days" initiation was held on the Stanford campus by the Society a few weeks ago. The accompanying picture explains some of what took place when the following men were taken into the membership: W. P. Winham, Salinas, Calif. ; T. L. Wark, Long Beach, Calif.; P. L. Henderson, Greeley, Colo.; T. E. Bassett, Palo Alto, Calif.; and R. G. Wheelton, Long Beach, Calif. CHAS. A. DOBBEL, Secretary.

Jan 8, 1919

By F. S. Peabody

ANYTHING that may be said about "too much coal" must seem rather incongruous just at this time when two-thirds of the mines in the United States have been idle for nearly four months and a temporary coal shortage looms as more and more of a possibility. It is the purpose of this article, however, to deal primarily with the fundamental ills of the bituminous-coal industry, which, when summed up, can be expressed in one word-overdevelopment. During recent years the bituminous-coal industry in the United States has been seldom, almost never, in a state of normal business health with production run-ning evenly, prices steady and the market absorbing the output from week to week. There has been either a condition of feverish activity or apathetic sluggish-ness. We have had, for example, the intense strain on production during the war years with heatless days and lightless nights, followed by the slump late in 1918 which lasted through the greater part of 1919 when coal was a drug on the market. Then came the panicky demand of 1920. Competitive buying forced prices up to the highest levels in history. This demand in turn fell off suddenly in November, 1920, and the market remained apparently paralyzed all through 1921. During the latter year, lack of buying forced intermit-tent suspension of mining in all fields and prices averaged less than actual cost of production.

Jan 8, 1922

By H. S. Munroe

The dressing-works of the St. Joseph Lead Company were destroyed by fire, February 26th, 1883. Within about four months, or on July 5th, 1883, the new mill, with a capacity of 500 tons per day, was built and in active operation. The capacity of the new mill has since been increased to 800 tons per day. The old mill was built in 1867, by Mr. C. B. Parsons, the present superintendent. It was a curious rambling old structure, which had grown with the demands of the business; a few jigs having been added in one place, a table or two in another and wings and sheds added to the main buildings, from time to time, as it was found necessary to increase the efficiency or the capacity of the mill. The old mill was, moreover, a most interesting place to the student, a perfect "museum of ore-dressing." Nearly every form of dressing apparatus known to the art had, at one time or another, found a place under its roof, jigs of many kinds, concave, convex, side-bump and stationary tables, tyes, buddles, dolly-tubs, etc., etc. The method of dressing followed in the main the lines of English practice, but with many modifications, both in the machinery and the methods of working, due to the inventive genius of Mr. Parsons. Different forms of crushing apparatus were tried, and the best method of handling the ore and the different products of

Jan 1, 1889

By Edward L. Wilson, Keshavan Nair, Ranbir S. Sandhu

In planning and designing of underground excavations and construction, it is of considerable importance that the stresses and displacements in the rock mass subjected to arbitrary sequences of unloading and loading be within allowable limits. For determination of the stress and displacement fields, the usual approach is to treat the rock as an elastic material and to apply the principles of the theory of elasticity. However, analytic solutions are available only for a limited class of problems of simple geometry and idealized material properties. Nonhomogeneity and anisotropy of material coupled with complex geometrical configuration and initial stress fields that are almost always preexistent in rock masses at great depths, render the problem intractable by analytical methods. Approximate solution techniques using numerical procedures have, therefore, to be resorted to. The finite element method as applied to plane stress analysis was introduced by Clough.1 It has developed into a powerful tool for the analysis of various field problems in structural and continuum mechanics. The method is well documented in the literature2-6 and, therefore, its historical development will not be discussed here. Wilson's analysis of the plane stress/strain problem has found extensive use in the area of soil and rock mechanics including stresses around underground openings; stresses and displacements in dams, foundations, etc.7-11 In his analysis of the axisymmetric solid,3 Wilson proposed a procedure to allow for certain cases of nonlinear material properties. In this chapter, the develop-

Jan 1, 1972

By R. H. Lynn, T. C. Craig

During the year 1933, in the Texas Panhandle, 113 oil wells were completed, adding 33,337 bbl. to the daily potential of the field. The field potential on Jan. 1, 1933, as determined by the Texas Railroad Commission, was 149,260 bbl., with a daily allowable production of 41,000 bbl. The potential was raised gradually, until on July 16, 1933, it reached 155,344 bbl. with a daily allowable of 55,000 bbl. This potential and allowable was maintained over a period from July 16, 1933, to Sept. 8, 1933, when the potential was reduced to 136,893, with a daily allowable of 43,727 bbl. Since Sept. 8, 1933, there has been a gradual increase, until on Jan. 1, 1934, the field potential reached 159,740 bbl. with a daily allowable of 42,000 bbl. Of this amount 26,429 bbl. arc "marginal oil" and 2682 bbl. are exempt on account of water. Deepening of Wells During the year 64 wells were deepened, increasing their total oil production 9631 bbl. per day. Of this amount the Gray County granite wash contributed 9256 bbl. from 57 wells. It has been found in many places that the granite wash carries an additional oil pay from 50 to 75 ft. below sea level. The majority of the wells that were .drilled during the early development in Gray County encountered their oil above sea level. When the wells producing from the upper horizon have become unprofit-

Jan 1, 1934

By J. L. Jorstad

The hypereutectic Al-Si alloys 390 and A390 have wear characteristics superior to any of the more common aluminum casting alloys. This excellent wear resistance, coupled with good mechanical properties, high hardness, and low coefficient of thermal expansion, has made these alloys candidates for the all-aluminum internal combustion engine, the application for which they were primarily developed. A390 alloy is intended for sand and permanent mold casting, and requires a lower iron ccxltent (0.5 pct maximum) than its die casting companion 390 alloy (0.6 to 1.1 pct Fe). The 17 pct nominal silicon in these alloys provides sufficient quantities of the hard primary silicon phase to assure a high degree of wear resistance, yet little enough of this phase, to minimize the casting and m achining problems associated in the past with the hypereutectic alloys. The mechanical and physical properties of 390 and A390 alloys are competitive with the best of the common aluminum casting alloys with the exception of low ductility. This low ductility is not considered a detriment, since in many applications these alloys replace cast iron. Corrosion resistance is similar to the standard alloys 380 and 333. Numerous parts, of varying degrees of complexity, have been cast of alloys 390 and A390, including engine blocks and heads. The deviations from normal good handling and casting practices that are required for the alloys are those associated with the presence of the primary silicon. To obtain optimum strength and machinability, the molten alloys should be treated with phosphorus to refine the primary silicon phase. Care must be exercised to properly control the pouring temperature and rate in order to minimize primary silicon growth and segregation. AUTOMOTIVE engineers have for years recognized the advantages of lighter weight and better heat transfer that aluminum could offer as material of construction for engine blocks. These advantages alone, however, are insufficient justification for acceptance of aluminum engines by the automotive industry. To be acceptable, an aluminum engine first must pass all tests to which cast-iron engines are subjected, and, in addition, must represent no cost penalty in manufacturing. None of the conventional aluminum casting alloys have sufficient wear resistance to withstand the tests to which cast iron is subjected as a cylinder bore material, and recent attempts to manufacture aluminum engines with cast-in-place iron sleeves could not compete costwise with the equivalent cast-iron engine. The prerequisite to an acceptable aluminum engine seemed to be a casting alloy with a high degree of wear resistance that would eliminate the necessity of cast-in iron sleeves or liners. The hypereutectic A1-Si alloys 390 and A390 have met this challenge.' Combined with modified pistons and a patented cylinder bore surface finish,2 the performance of these alloys in more than 1300 cold start and cold scuff tests, over 3500 hr of dynamometer wear and endurance tests, and more than 350,000 miles of road tests leaves no doubt as to the feasibility of running on bare aluminum cylinder bores. ALLOY DEVELOPMENT The desirable characteristics of the hypereutectic A1-Si alloys have been recognized for some time. Their excellent wear resistance and low coefficient of thermal expansions have been used to advantage in the production of diesel-type pistons in Europe and to a limited extent in this country. The major contributor to the good wear resistance of these alloys is the extremely hard primary silicon phase in the microstructure. Although the percent silicon used experimentally has been much higher, most commercial alloys have ranged from about 14 to 25 pct. Generally, as the silicon content is increased, wear resistance increases, and the coefficient of thermal expansion decreases. With increases in silicon, however, machinability and cast-ability tend to suffer. The development of a satisfactory aluminum engine block material at Reynolds involved the testing and evaluation of many alloys, covering a wide range of silicon contents and numerous variations of iron, copper, magnesium, manganese, and other alloying additions. Castability, mechanical and physical prop-

Jan 1, 1969

By Vsevolod Krivobok

THE re-crystallization of metals has been the subject of much scientific investigation, some of which has resulted in a better understanding of this extremely important and interesting phenomenon. Unfortunately, while many have propounded theories of re-crystallization, but a few have presented experimental evidence as to how it takes place. If this can be determined the question, why re-crystallization occurs, may be answered more definitely. Re-crystallization in single phase metals consists of a complete rearrangement and re-sizing of the grains, of which the structure is composed, while the type of structure remains the same. That is to say, if the structure before re-crystallization is composed of a number of polyhedral grains of different shape and size, a particular spot after re-crystallization will be seen to consist of grains in no way different from the original except in size and shape. The re-crystallized grains may be smaller or larger, depending on the treatment received; and, while the re-crystallization may be brought about by means of heat treatment only in passing through a critical range, yet it is common knowledge that single phase metals subjected to cold working are possessed of a tendency toward re-crystallization, even if the heating does not reach critical range. The study of re-crystallization would, of course, be much easier if we had single crystals of any metal as the original material with which to study the phenomenon of re-crystallization, since it would permit the observation of structural changes at what amounts to enormous magnification, by changing the scale of the specimen. In metals of more normal grain size the crystal boundaries introduce complications, but the process, it may be assumed, is essentially the same. Such an opportunity

Jan 2, 1926

[Secretary's Note.—The following official tables, prepared by the government of the State of Nuevo Leon, and presented to the Institute at the fifth seseion of its Mexican meeting, held at Monterrey, November 26, 1901, present in compact form a general summary of the mineral and metallurgical industry of the State for the preceding calendar year, together with a statement of the railway-shipments of ores from January 1 to October 31, 1901, which, in the absence of direct official mining and metallurgical statistics (not yet available for that year), clearly indicates an increased activity and productiveness of these industries. In other words, the mines are reported to have yielded in 1900 a total product of 83,960,169 kilos of ore; whereas, the railway is reported to have carried, in 10 months of 1901, a total of 108,318,647 kilos of ore. At this rate, the railway-shipments for 1901 mould amount to nearly 130,000,000 kilos. It is, of course, possible that the railwaystatistics include other freight than ores, or that they include duplications, such as would be involved in the record, first of certain ores transported, and afterwards of the " base bullion " produced therefrom. An accurate comparison is therefore impossible ; yet, after making all reasonable allowances for such items as have been named, it seems safe to infer that the mining and metallurgical industry of this State accomplished in 1901 a substantial progress.]

Jan 1, 1902

Coal Division Industrial Minerals Division Minerals Beneficiation Division Mining, Geology and Geophysics Division Council Will Mitchell, Jr, Chairman (MBD), Kenneth L Cook, Vice-Chairman (MGGD). Edward L Clark (MGGD), Raymond B Ladoo (Ind Min Div), Sandford S Cole (Ind Mm Div), Norman L Weiss (MBD), C T Hayden (Coal), H F Yancey (Coal), Clayton G Ball (MED), P De Bruyn (MIED), Arnold Buzzalini, Secretary, AIME, 29 West 39th Street, New York 18, N Y Mining Branch Advisory Committee Will Mitchell, Jr, Chairman, Grover J Holt, J B Morrow, J L Gillson, Edward G Fox, S S Cole, Roger V Pierce, Norman L Weiss. H C Weed. J R Van Pelt

Jan 1, 1956

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8 27 Montreal, Canada Sept, ?79 8 28 New York, N.Y. Feb, ?80 9 29 Lake Superior, Mich Aug, ?80 9 30 Philadelphia, Pa. Feb, 81 9 31 Staunton, Va May, 81 10

Jan 1, 1923

By P. W. Ramsey, G. L. Werley

THERE have been numerous examples in recent years of the similarity between aging behavior and diffusion behavior, where a plot of the logarithm of the aging rate versus the reciprocal of the absolute temperature yields an approximate straight line, analogous to a similar plot of the diffusion coefficient D (log D vs. 1/T). Austin and Rickettl have pointed out that this linear relationship holds empirically for the de- composition of austenite into pearlite and bainite in carbon steels, and Robertson' has shown similar trends in the aging of 24S-type aluminum alloys. Jenkins and Bucknall³ have also demonstrated the association between aging and diffusion rates for nickel-silicon-copper alloys. Jetter and Mehl,4 however, have shown that the maximum rate of dilation of a series of aluminum-silicon alloys does not show this linear relation and Mehl5 has pointed out that careful study of available knowledge indicates that "aging rates increase with temperature approximately exponentially, whereas D increases precisely exponentially." He further notes that "the rate of aging at a given temperature is the greater the lower the melting point of the alloy, which is also true for D." This paper describes the aging changes occurring in a zinc-25 pct manganese-15 pct copper-0.1 pct aluminum die casting alloy. It was found that this alloy does show this linear relationship and use was made of this relationship to estimate aging rates at low temperatures from data acquired at elevated temperatures. It should be noted that the aging reaction is being studied only indirectly, using changes in certain properties as criteria of the progress of the phenomenon. This alloy is purely an experimental one and is not available commercially. Zinc-Manganese-Copper System: The zinc-rich portion of the zinc-manganese-copper diagram which is of significance in the present work is quite uncertain. X ray examination of the alloy as die cast shows a phase similar to the epsilon phase (hexagonal close packed) of the copper-zinc system. All of the data accumulated indicate that the epsilon phase of the zinc-manganese-copper alloy is stable at high temperatures; that is, 500°C or above. Below this temperature a new phase is precipitated on annealing, and a decrease in specific volume occurs. At elevated temperatures this phase change occurs quite rapidly, while at room temperature the alloy has shown no change after several years. According to X ray data, this precipitated phase resembles the gamma phase (cubic) of the copper-zinc system, a hard and brittle structure. From examination of the microstructure and from X ray examination of the alloys annealed at

Jan 1, 1951

Idaho Bureau of Mines and Geology, University of Idaho, Moscow, Ida. John W. Finch, Director. A list of publications will be sent upon application. A series of Bulletins and Pamphlets have been issued by the Bureau to date since 1920 Of the Bulletins, six are out of print, and a charge is made for eight. Each of the Bulletins, in the main, treats of the geology and resources of a particular district in Idaho, as follows (only available Bulletins listed): Bulletin 1, South central Idaho (1920), 15 cents, 7, North central Idaho (1924), 50 cents, 8, Bonneville, Bingham and Caribou counties (1924), 50 cents, 9, Boise Basin (1924), 50 cents; 10, Boundary County (1926), 50 cents; 11, Region about Silver City (1926), 50 cents; 12, Clark Fork district (1930), 50 cents, 14, Eastern Cassia County (1931), 50 cents, Press Bulletin 15, Teton County (1927), Bulletin 16, Melon Valley near Buhl (1927); 17, Concerning land slips near Whitebird, Idaho (1928) The 37 Pamphlets are issued free of cost, and each treats, also, in the main of the geology and resources of a particular district in Idaho Nos 1, 2, 3, 4, 5, 7, 8, 10, 17, 18, 20, 22, 25, 26, 30 and 35 are out of print Of those available, attention may be called to Pamphlet 6, Reported platinum occurrences near Coeur d' Alene (1925), 11, Bruneau River Basin, 12, Power and Oneida

Jan 1, 1933

By J. C. Bradley

THE relation of annealing temperature to conductivity of copper wire has been determined.1 Conductivity hard was 98.26 per cent. After a 10-min. heating at 200° C. it was 98.69. By annealing 10 min. at 300° C. a large increase, to 100.93, occurred. Maximum conductivity, 101.15, was attained after a 500° C. anneal; thereafter it decreased to 100.53 after a 950° C. anneal. If copper is gassed the decrease is much more than this. MATERIAL AND METHOD The work was done on high grade electrolytic copper, 99.942 per cent. copper-plus silver, silver 0.0008 per cent. It was hot-rolled to 3 in., then cold drawn to 0.080 in. The wire was cut into 25 5-ft. lengths and numbered 1 to 25 as cut. Four samples were tested hard. The others were wound into 5-in. diameter coils. For the 100° C. heating a coil was put into water, the water brought to boiling, and the wire kept at this temperature for 10 min. For the higher temperatures the coils were placed in envelopes of sheet copper, a little water added, and the envelopes sealed by folding over the edges twice, and hammering them together. This kept the air out very well. The envelope and wire were brought to the desired temperature; this was maintained for 10 min., then the whole was water-quenched.

Jan 1, 1927

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8 27 Montreal, Canada Sept, ?79 8 28 New York, N.Y. Feb, ?80 9 29 Lake Superior, Mich Aug, ?80 9 30 Philadelphia, Pa. Feb, 81 9

Jan 1, 1923

LIST OF THE MEETINGS OF THE INSTITUTE AND THEIR LOCALITIES FROM ITS ORGANIZATION Transactions Number Place Date Vol Page 1 Wilkes-Barre, Pa May, ?71 1 3 2 Bethlehem, Pa August, ?71 1 10 3 Troy, N Y November, ?71 1 13 4 Philadelphia, Pa February, ?72 1 17 5 New York, N Y May, ?72 1 20 6 Pittsburg, Pa October, ?72 1 25 7 Boston, Mass February, ?73 1 28 8 Philadelphia, Pa May, ?73 2 3 9 Easton, Pa October, ?73 2 7 10 New York, N Y February, ?74 211 11 St Louis, Mo May, ?74 3 3 12 Hazleton, Pa October, ?74 3 8 13 New Haven, Conn February, ?75 3 15 14 Dover, N J May, ?75 4 3 15 Cleveland, 0 October, ?75 4 9 16 Washington, D C February, ?76 4 18 17 Philadelphia, Pat June, ?76, 5 3 18 Philadelphia, Pa October, ?76 5 9 19 New York, N Y February, ?77 5 27 20 Wilkes-Barre, Pa May, ?77 6 3 21 Amenia, N Y October, ?77 6 10 22 Philadelphia, Pa. May, ?78 6 18 23 Chattanooga, Tenn May ?78 7 3 24 Lake George, N.Y. Oct. ?78 7 25 Baltimore, Md. Feb. ?79 7 26 Pittsburgh Pa, May ?79 8 27 Montreal, Canada Sept, ?79 8 28 New York, N.Y. Feb, ?80 9 29 Lake Superior, Mich Aug, ?80

Jan 1, 1923

By C. E. Shoenfelt

Operations ill Colorado oil fields in 1934 were not quite so extensive as in 1933, but much better results were obtained and one new oil field was discovered. In all, 26 wells were drilled, of which 9 were oil wells, 1 was a gas well, and 16 were dry holes. New oil production totaled 10,220 bbl. and new gas production totaled 33,714,000 cu. ft. This compares with new oil production in 1933 of 1238 bbl. and new gas production of 14,307,000 cu. ft. Dry holes in 1933 totaled 29 as conlpared with 16 in 1934. Oil was discovered in the Hiawatha gas field, Moffat County, in 1934 in the Mountain Fuel Supply Company's No. 4B Wilson, C. NE. NW. of sec. 23, 12N., 100W. This well was completed in a sand in the Wasatch (Tertiary) at 2304 to 2337 ft., after plugging back from 3797 ft. It made 20 bbl. of oil initially. No. 4B Wilson is the first well in the Rocky Mountain region to discover oil in commercial amounts in rocks younger than Cretaceous, and while it is not expected that Hiawatha will develop into an oil field of important proportions, eventually it may produce a considerable amount of oil as the gas pressure declines. The Hiawatha gas field was discovered in 1926, on one of six structures in what is known as the Vermillion Creek gas area. It is a northeast-

Jan 1, 1935

By Frank Marotta, Louis B. Lesem, Frank Greytok, John J. McKetta

Although one of the primary variables in the calculation of the flowing bottom-hole pressure in gas wells from surface measurements is the temperature at any point and its distribution in the flow-string, only few experimental data are available in the literature and little attention has been given to analysis of the problem. Virtually all of the recently published methods of calculating flowing bottom-hole pressures depend on the assumption that either the temperature is constant at some average value or that the variation is linear with depth. The purposes of this work are to analyze the problem theoretically and to verify the analysis by comparison with experimental data so that practical problems in the analysis of the behavior of gas wells can be solved with greater accuracy, reliability, and ease. MATHEMATICAL OUTLINE OF PROBLEM Assuming that: 1. The mass velocity and chemical composition of the gas stream are constant and in normal gas well operations, the change in linear velocity in the entire flow-string is trivial, 2. The product of the density and heat capacity of the gas is constant, 3. No horizontal temperature gradient exists in the gas stream, 4. Net flow of heat by conduction within the formation and in the gas stream in the vertical direction is trivial in magnitude and can be neglected, 5. The regional vertical geothermal gradient is constant, and 6. The temperature of the gas entering the borehole is constant, and equal to that of the reservoir, a set of two simultaneous, linear partial differential equations with appropriate boundary conditions was derived to describe the temperature distribution in the gas stream and the surrounding formation. These equations were solved by operational techniques for the distribution of temperature in the gas stream. The resulting integrals were evaluated numerically on an IBM 604 at the Machine Accounting Div. of the Railroad Commission of Texas. DERIVATION OF FUNCTIONS FOR THE DISTRIBUTION OF TEMPERATURE The physical system is a circular hole of radius a in an infinite medium with thermal conductivity K, density p8, and heat capacity c,. Under shut-in conditions the well is in thermal equilibrium with the surroundings and the increment in temperature is given by - ?T3/L x. Gas of density pg and heat capacity c.. flows upwardly through this hole in the direction of increasing x with a linear velocity W. Writing a heat balance on an element of gas ?x in thickness, convective heat transfer + conductive heat transfer + energy required to lift a unit mass of fluid = change in energy content. pa2W po Co To - pa2Wpo Co To x+xx - 2apK?x ?T8/?r r=a - Wpa2 po?x/778 = CoPopa2?x?To/?t... Dividing by (copopa2?x) and taking the limit as ?x tends to zero, -W (?To/?x + 1/778Co) + 2 K/a Po Co ?T3/?r r=u = ?To/?t

Jan 1, 1958

By D. D. Smith, D. P. Squier, E. L. Dougherty

A system of differential equations describing the temperature behavior of fluid injected at constant surface temperature in a well is derived and .solved analytically. A formula for the fluid temperature at any time and depth is given, as well us a special formula valid for very large times. These formulas are used to calculate temperatures for several typical cases. The results indicate that, initially, the temperature of the water entering the formation is considerably lower than the injection temperature. This condition lasts for only a short period— less than three days for most cases of practical interest. Following this highly transient period, during which the temperature of the fluid entering the formation builds up to about 50 to 75 per cent of the injection temperature. the system enters a quasi-steady state in which the temperature changes are very slow. After severl years, the bottom-hole temperature will still be 50" to 100°F lower than the injection temperature, hilt the heat losses may he tolerable. INTRODUCTION Predicting the behavior of a hot-water flood requires that the temperature of the water entering the injection interval be estimated. This report describes the development and solution of a system of equations which describes the temperature behavior of the injected water in the wellbore with certain simplifying assumptions. The only previous means known to the authors for describing such a process is that of Moss and White.' Their results appear to be close to those obtained by our method in the practical cases which were compared; this agreement is largely due to the fact that in our method temperature soon approaches a quasi-steady state, as was assumed in their method throughout. However, our model covers all times, is continuous (whereas the Moss-White model depends on breaking the depth into discrete intervals) and. we feel. more closely describes the physical problem. FORMULATION OF THE PROBLEM PHYSICAL SYSTEM AND ASSUMPTIONS The injection procedure consists of pumping water at a fixed surface temperature T., down an infinitely long cylindrical well or tubing of inner radius Any material exterior to the water column such as mud, casing, or cement is regarded as part of the formation. The general behavior of the system may be described qualitatively as follows. When the hot water is first introduced into the system, the temperature difference between the formation and the water is large, resulting in a high rate of heat transfer. As a result, the temperature adjacent to the wellbore rises very quickly. Because the segment of the formation adjacent to the wellbore largely controls the heat transfer rate, the heat transfer rate will become relatively constant when this portion has reached a temperature close to that of the water opposite it. The temperature of the water and formation then increase very slowly with time. The length of the initial highly transient period and the temperature of the water at its conclusion will be functions of depth, injection rate, injection-string radius, surface injection temperature and the physical properties associated with the water-formation system. The following additional assumptions were made. 1. There is no heat transfer by radiation in the system. 2. There is no heat transfer by conduction in the vertical direction in either the injection stream or the formation. 3. The linear volumetric and mass flow rate of the water is constant throughout the injection stream. 4. No horizontal temperature gradient exists in the injection stream. 5. The product of density and heat capacity is constant for both the water and the formation, and the formation thermal conductivity is constant. 6. Initially, both the water in the wellbore and the reservoir are at a temperature given by the (constant) ambient surface temperature plus the product of depth and geothermal gradient (assumed constant). At large distances for the wellbore (r m), the formation will remain at this temperature. 7. The water temperature and the formation temperature at r — r,, are equal for all depths D. DERIVATION OF EQUATIONS The differential equation satisfied by the fluid temperature T,(D, t), which is obtained by writing a heat balance on a cylindrical differential of volume dV of the injection string between the depths D and D i dD, is

LIST OF MEMBERS AND ASSOCIATES ARRANGED ACCORDING TO STATES AND TOWNS. ALABAMA. Aldrich, Aldrich, W. F. Anniston, Noble, A. E Bessemer, Fergusson, V. Bir¬mingham, Aldrich, T. H., Jr, Bowron, C. E, Bowron, J., Davis, F H, Dimmick, F. D., Hillman, Ludwig, C. P., McCarthy, M. E, McCormack, G B., McCrery, Ramsay, E, Shook, A. M. Ensley, McDonald, S., Shook, J. W. Gadsden, Lee, R. H., Jr. Gannts Quarry, Hiller, E Helena, Squire, J. Huntsvalle, Moss Le¬high, Toulmin. Ozmoor, Greenamyer, A. G. Rock Run, Garvin, J M. Selma, Saylor, B. F. A. Sheffield, Miller, D, I. Tuscaloosa, Lodge, J. Woodward, Wood¬ward, A. H. ALASKA Coppermount, Wiswell, H. J. Douglas Island, Macdonald, J Ellamar, Stevens, B. Fairbanks, Hamilton, A L Haines, Le Wald, E A. Jualin, Hoggatt, W. B. Juneau, Denby, Hampton, W. H , Thane, B L , Whipple, J. R. Ketchikan, Bar¬ber, J C , Parker, J. L., Reid, G D Nome, Garfield, C D. Snettwham, Tisdale. Teller, Hirshberg, M. R. Treadwell Caty, Kinzie, Stow, H. P. Valdez, Esterly, G. M, Hazelet.

Jan 1, 1910

[Admissions: B. M. Gottlieb, Chairman Edmond F. Egan K. Marshall Fagin John S. Fuller Edward E. Monteith T. A. Pollard Howard J. Ritts, Jr. Kenneth W. Robbins Harold E. Wright Advertising and Exhibits: Bernard F. Klein, Chairman Bob Diggs Brown R. E. Howard H. M. Krause, Jr. R. G. Parker Mrs. Evelyn R. Robertson]

Jan 1, 1961