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By B. S. Blakeney, E. P. Abrahamson II

The effect of the transition elements in binary solid-solution additions upon the recrystallization temperature of iron has been investigated. All these elements immediately raised the temperature, the majority having their greatest effect in less than 0.10 at. pct. A correlation is noted between the rate of change of recrystallization temperature with atomic percent solute and the electron configuration of the solute element. THE work of Abrahamson and rant' on binary chromium-base alloys indicated that a correspondence existed between the effect of each solute element on the brittle-to-ductile transition temperature of chromium and the ground-state electron configuration of the element added. This was felt to be a bonding phenomenon and would be expected to be observed in measurements of other properties involving the breaking or exchange of atomic bonds. From this work it was postulated that a like correspondence should be found for other properties of binary alloys, such as recrystallization. This study is an effort to check this postulation using binary solid-solution iron-base alloys. Previously, the majority of recrystallization studies were carried out on steels. However, Tammann2 investigated the recrystallization of iron as effected by Co, Ni, Si, Mn, Mo, and Cr and stated that elements with the same crystal structure at room temperature as iron appeared to be more effective in raising the recrystallization temperature. Austin, Luini, and Lindsay3 studied the effects of Ni, Cr, Mn, Co, Si, and Mo on cold rolling and annealing, but noted no trend. Abrahamson and rant,' in their work on the effect of both substitutional and interstitial elements upon the brittle-to-ductile transition of chromium, have shown that the outer electron configuration in the ground state of the solute element appears to be the prime determinant of the transition temperature. PROCEDURE All alloys were made using 99.95 + pct Fe with 0.02 wt pct 0, 0.004 pct C, and 0.001 pct N. All alloying elements were 99.9 + percent pure. Metal-lographically the alloys, out to at least 0.1 at. pct, appeared to be in solid solution. Though several published phase diagrams tend to dispute this.4 All alloys were arc melted six times and cast into square 400-g ingots under an argon atmosphere.

Jan 1, 1961

THE 127th meeting of the Institute was held in New York, Feb. 19 to 22, 1923. In addition to the usual large volume of technical matters under consideration, the meeting was particularly noteworthy for the amount of attention given to its business session; the convention of local section representatives also was full of interest. The total registration was 1201. The annual business meeting on Feb. 20, President Dwight presiding, was attended by 125 members, who listened with marked attention to the reports and addresses of the several officers. The chairman departed from the stipulated order of business in order to allow more time for the presentation of remarks on the state of Institute affairs. The previously pub-lished reports of the officers were accepted, as printed. On the report of the tellers, the following officers were declared elected: E. P. Mathewson, Director and President-District 0 T. T. Brewster, Director and Vice-president-District 6 Frank M. Smith, Director and Vice-president-District 11 W. H. Aldridge, Director-District 0 G. H. Clevenger, Director-District 1 A. N. Diehl, Director-District 3 Reno H. Sales, Director-District 7 Seeley W. Mudd, Director-District 10

Jan 3, 1923

By George M. Fowler, R. E. Illidge

Part I. Developing BY GEORGE M. FOWL INTRODUCTION The Tri-State district comprises an area of about 2000 square miles in southwestern Missouri, southeastern Kansas, and north [ ] eastern Oklahoma. The part that is in and contiguous to Missouri is still sometimes designated as the Joplin district (Fig. I). EARLY OPERATIONS Mining operations in what is now the Tri-State district date from about 1848 and have been continuous to the present. Apparently the first discoveries of ore were made about the same time near the present sites of Joplin, Oronogo, and Granby. Lead minerals were found at grass roots, probably in shattered rock in shallow excavations, then these minerals were followed in shear zones to deeper horizons. The mining of zinc followed. Before 1874, zinc ore was worthless and discarded as waste. According to published records, the total production of lead to that date was 49,000 tons of metal from 70,000 tons of concentrates. PRODUCTION The aggregate ore production from the Tri-State district was recorded at interval

Jan 1, 1943

By F. Brons, V. E. Marting

In the past, other authors.1, 2 have studied the influence of a skin effect on the productivity of a well. This skin effect, expressed by the skin factor S, is considered to be caused by a thin layer of impaired permeability immediately around the wellbore and extending vertically over the whole productive interval penetrated by the well. The skin factor S is defined as follows. Based on this, the impairment in productivity caused by a skin can be expressed by the fractional loss in productivity I, which is the loss in productivity divided by the total unimpaired productivity. For compressible flow in a stabilized well which drains a circular area of radius re, 1 is given by The present paper deals with a different kind of productivity impairment. Consider a well in which part of the productive formation is blocked off completely, either by incomplete penetration or by exclusion of parts of the productive zone by blank casing. In Fig. 1 (A, B and C), three examples are shown. Fig. 1(A) shows the situation where a well only partially penetrates the formation. This often is done to combat the actual or imagined danger of bottom-water coning. Fig. 1(B) shows a well producing from only the central portion of a productive interval. This type of completion is sometimes used where both water and gas coning are a problem. Although the case of a well producing through perforated casing cannot be treated in a manner similar to the previous two cases (where radial flow in the horizontal plane is assumed), Fig. 1(C) shows several intervals open to production and qualitatively describes this case (as will be discussed later). To study the loss in productivity in all these cases, two parameters are introduced which fully determine the impairment. The first is the penetration ratio "b," i.e., the total interval open to fluid entry divided by the total thickness of the productive zone. The second is the ratio hlrw. In this ratio, rw is the wellbore radius. The definition of h is more cumbersome. In Fig. 1(A), h is the thickness of the total productive interval. The streamline configuration for this case of partial penetration is basic to the other two cases considered (Views B and C of Fig. 1). It will be obvious from Fig. i (A) that the flow lines in the uppermost portion of the formation will be essentially horizontal, while those in the lower portion will curve upward toward the well. In Fig. 1(B), with only the middle portion of the zone open to production, the streamline configuration. of the upper half will be an exact mirror image of that in the lower half of the zone. Hence, for the case illustrated in Fig. 1(B), h is defined as one-half the total sand thickness. It follows, then, that in Fig. 1(C) h is one-half the distance between corresponding points in adjacent intervals. (In gun-perforated casing, h would be one-half the distance between perforations.) In a paper by Nisle4 and a paper given by the present authors5, the mathematical theory was developed for the cases under consideration. In the present publication, the emphasis is put on the results of these studies; consequently, the equations derived in Refs. 4 and 5 will be omitted, for the most part. The pressure drop p in a well producing from only a portion of the total formation thickness can, in analogy with Eq. 1, be expressed by Numerical solution of Eq. 5 by use of the IBM 650 leads to the following important conclusions. First, during a short period after starting production (usually on the order of a few minutes), the function p(b) is given by

By W. H. Andrews

THE constantly increasing consumption of Portland cement in the State makes the above subject of partlcular interest at this time. The increasing demand is due to the rapid settling of the country and the fact that new uses are being found frequently for the above named commercial article. The industry is one that is bound to grow as the population increases, and this being the case, it may be well ,it this time to consider briefly- the matter of the chemical and physical com-position of proper raw materials. A cement mixture is one that contains approximately 75 per cent. carbonate of lime, 15 per cent. Silica, and 5 to 7 per cent. alumina, and iron oxides; the other elements being magnesium carbonate and small quantities of the rarer elements general associated with limestone deposits. It call be readily seen from the above composition that it is possible to build up this mixture from a number of different materials. First.-A rock high in carbonate of lime can be mixed with clay or shale in such proportions as to bring about the desired composition ; the chief difficulty in the building up of such a mixture is that it is hard to find a clay or shale in which the silica-alumina, ratio lies .between 4 to 1 and 3 to 1 and at the same time shows physical characteristics which will make certain its adaptability to the practical manufacture of Portland cement. Very often clays or shales are found which are right chemically but contain large quantities of grit or free silica. Such clays or shale must be ground to extreme fineness in the mixture in order to make the silica and alumina combine with the lime when the mixture is burned. On the other hand, clays or shales are often found that have the proper physical characteristics but in which the amount of alumina, is too great.

Jan 9, 1913

By Carl A. Holley

Agglomeration is very closely identified with the mining industry. Ores must be crushed finer and finer to separate minerals from gauge and the fine ore concentrates must be agglomerated so they can be handled for further processing. This paper reviews each type of agglomeration device and summarizes the areas of usage for each type of agglomerator.

Jan 1, 1980

By W. A. Clark

The production of sand in an oil well increases operating costs because of abnormal wear in subsurface equipment, the necessity for frequent cleanouts, and the need for a means of disposing of the sand. Moreover, removal of sand from the zone can bring about the creation of cavities from which bodies of formation, sand or shale, may slough into the hole, endangering the shutoff, impeding production or collapsing the liner. The procedure known as gravel packing is attracting attention as a means of controlling these factors and contributing to the productive life of a well. That gravel packing is now substantially beyond the preliminary stage on the Pacific Coast is reflected in the 191,000 bbl. of oil produced monthly by the 66 gravel-packed wells in 11 different producing sectors. Reasons fob Gravel Packing Gravel packing, if properly carried out, can be expected to provide the following benefits: 1. Prevent the movement of sand and thus eliminate sand production and sand fills, and prevent the formation of cavities. 2. Provide a practical, relatively inexpensive, large-diameter hole, which will provide well-known theoretical advantages. 3. Support the walls of the hole by completely filling the space between the liner and the formation, regardless of its irregularities, and afford a support for liners. 4. Provide for more efficient pumping operations in wells by: (a) possibly utilizing the gravel as a gas trap in pumping gaseous fluids, (b) allowing deep submergence of the pump into the oil zone. In a conventional well—that is, where the liner is set in an open hole-. even though perforation sizes are chosen according to known rules based on analysis of sand grains from samples from the zone, there is likely to be some production of sand. This may be due to the miscalculation of

Jan 1, 1940

By W. A. Clark

The production of sand in an oil well increases operating costs because of abnormal wear in subsurface equipment, the necessity for frequent cleanouts, and the need for a means of disposing of the sand. Moreover, removal of sand from the zone can bring about the creation of cavities from which bodies of formation, sand or shale, may slough into the hole, endangering the shutoff, impeding production or collapsing the liner. The procedure known as gravel packing is attracting attention as a means of controlling these factors and contributing to the productive life of a well. That gravel packing is now substantially beyond the preliminary stage on the Pacific Coast is reflected in the 191,000 bbl. of oil produced monthly by the 66 gravel-packed wells in 11 different producing sectors. Reasons fob Gravel Packing Gravel packing, if properly carried out, can be expected to provide the following benefits: 1. Prevent the movement of sand and thus eliminate sand production and sand fills, and prevent the formation of cavities. 2. Provide a practical, relatively inexpensive, large-diameter hole, which will provide well-known theoretical advantages. 3. Support the walls of the hole by completely filling the space between the liner and the formation, regardless of its irregularities, and afford a support for liners. 4. Provide for more efficient pumping operations in wells by: (a) possibly utilizing the gravel as a gas trap in pumping gaseous fluids, (b) allowing deep submergence of the pump into the oil zone. In a conventional well—that is, where the liner is set in an open hole-. even though perforation sizes are chosen according to known rules based on analysis of sand grains from samples from the zone, there is likely to be some production of sand. This may be due to the miscalculation of

Jan 1, 1940

The sum of $250 was appropriated to the Chicago Section. The President was authorized to appoint five members of the Board of Directors, including himself as Chairman, to discuss with other technical societies the proper organization for handling all matters of joint interest to the profession of engineering as distinct from purely technical activities, and to submit its findings in the form of recommendations to the Board of-Directors. Charles F. Rand was appointed a Trustee of the United Engineering Society to succeed himself. John H. Janeway was elected a member of the Library Board, vice Karl Eilers, resigned. Alexander C. Humphreys was elected a member of the Library Board to succeed himself.

Jan 1, 1917

By M. H. Forester, John D. Cooner

ALTHOUGH the unmined anthracite will last for approximately 150 years, most of the thicker and cleaner coal beds have been almost entirely first-mined and pretty well robbed, leaving much of the present and future production to come from thin and dirtier beds. Herewith is a section of one of the dirty beds being mined in the Wyoming region [ ] This section shows that 45.8 per cent of the bed is made up of impurities and that the 45 in. of coal in the bed is in five benches, the thickest of which is 19 in. In some localities of the anthracite region there are 14 beds of minable coal. Orderly and proper mining of the coal makes it necessary to rob or second-mine--almost all beds have already been first-mined-in sequence from the top downward. Therefore the robbing of the few remaining portions of the thicker and cleaner beds is in many instances being held up by the mining of the overlying thin and dirtier coal beds. Impurities Impurities consist of fire clay, slate, rock, and bone. The latter, which is black, contains 40 to 60 per cent carbon and often resembles good coal. In some beds there are also bands of "blue" coal, which, as the name implies,

Jan 1, 1950

By Cuppam Dasarathy

THE object of this note is to report briefly certain results of investigations on the Fe-In phase diagram. BISRA-high purity H-iron and 99.9 pct pure indium were used to prepare the alloys. The experimental techniques consisted of thermal analysis, optical metallography, and X-ray diffraction. A phase diagram based on the present results as well as those reported earlier by the author' is shown in Fig. 1. It is seen that the liquidus points fall on a smooth line which meets the monotectic isotherm at 1470°C. The liquidus extends up to 3.4 at. pct In. The phase boundary separating the two liquidus L1 and L2 is shown dotted. The experimental solidus meets the monotectic isotherm at -0.9 at. pct In. The 6/6 + L2 boundary drops steeply to the 6 + La/y + L2 boundary at -1350°C. In this region, it is impossible to detect satisfactory thermal arrests because of the steep phase boundary. The present diagram shows that indium lowers the temperature of the d/y transforma-tion and raises the temperature of the y/a transfor-mation. The y +d region is found to be very narrow. Indium gives rise to a restricted y field when alloyed with iron. The width of this field is between 0.4 and 0.5 at. pct In. Details of the alloys containing 40 and 50 at. pct In have already been reported by the author' and the transformation temperatures of these alloys are included in Fig. 1. It appeared from optical metallography and X-ray diffraction that the room temperature solubility of indium in a iron is less than 0.28 at. pct since alloys of 0.28 at. pct In and above, slow cooled to room temperature, contained dark etching second phase particles situated both in the matrix and grain boundaries of the a-grains, see Figs. 2 and 3. These particles were identified to be unalloyed indium by X-ray diffraction. The lattice parameter of the a phase reached a maximum of 2.8672A at the indium level of -0.28 at. pct. The present diagram, Fig. 1, is in substantial agreement with that of Stadelmaier and Fiedler' except for certain differences in detail. For example, they found the monotectic composition and temperature to be 7.0 at. pct In and 1443oC, respectively, while the present work indicates them to be 3.4 at. pct In and 1470°C. The 6 + L2/y + L2 transformation is indicated in the present work to occur at -1350°C, whereas Stadelmaier and Fiedler find this to occur at -1320°C. They also claim that the width of the y field is 0.2 at. pct In while the present work shows the width to be between 0.4 and 0.5 at. pct In. 1) Indium, when alloyed with iron, gives rise to a restricted y field, the width being >0.5 at. pct In.

Jan 1, 1970

By George A. Desborough, Forrest G. Poole

Marine black-shale samples of Paleozoic age in the western United States that exceed 10 wt % organic carbon contain as much as 5000 ppm vanadium, 5000 ppm molybdenum, 1300 ppm nickel, 600 pprn cobalt, 16 ppm silver, 11,700 ppm chromium, 18,800 pprn zinc, 280 pprn cadmium, and 350 ppm selenium. Depositional set- tings include: (I) continental-rise and marginal- ocean basins, (2) continental-shelf and foreland basins, and (3) cratonic-platform embayments. Most of these metalliferous organic-rich shales have not been examined for resources because rapid weathering and poor exposures preclude easy sampling of unoxidized rock necessary to determine actual concentration and residence of indigenous metals. Generally, when interval thickness is considered, the marine black shales of Paleozoic age in the western United States are richer in metals than marine upper Paleozoic black shales in the eastern United States.

Jan 1, 1983

By Ralph H. Phelps

WHAT information do you have on precision investment casting? Please send me all available information on the removal of paraffin from oil wells and pipe lines. How can I find out how to remove magnesium oxide from lime? I want a good book on the pickling of steel. Can liquid oxygen be used as an explosive in a mine? Where can I get a bibliography on the plasticity of metals? These questions, selected from the scores of questions asked the Engineering Societies Library staff every day, indicate some of the diversity of the requests received. The samples chosen relate to interests of AIME members but the questions that come to the Library by mail, telephone, telegraph, and in person cover all fields of engineering, science, and technology. Some questions can be answered quickly; others require extensive searching. Those that can be answered in a few minutes or ten, twenty, or even thirty minutes are usually done without charge. For the more difficult questions a charge is made. In this way those requiring considerable service pay for it and the Library finds it possible to serve more persons.

Jan 1, 1948

By C. A. Heberlein

The present war in Europe seems to have stimulated the demand for quicksilver. In July last, the price ranged around $35 per flask of 75 Ib., while to-day it seems to fluctuate between $47.50 and $50. The use of quicksilver in the form of fulminate, containing 70 per cent., and as corrosive sublimate, containing 73.8 per cent., must be extensive and a further market advance may be expected. With such an advance, some revival in quicksilver mining may be looked for, particularly in California, where many abandoned properties exist. What can be done with low-grade quicksilver ores under favorable conditions, particularly with low mining cost, may be seen from the following description of the Oceanic mine, near San Luis Obispo, Cal. Its operations date back to 1876, when rich sand ores were discovered. In three years 7,400 flasks of quicksilver were produced, but since then the deposit has been worked only sporadically . Until two years ago various attempts had been made by the Oceanic Quicksilver Co. to mine the more refractory "mud rock," which was encountered lying beyond the " sand rock." Mud and sand rock in varying quantities were treated together, with poor results, but operations were successful with sand rock of fair percentage. About two years ago, when all the sand rock had been exhausted, Murray Innes purchased the Oceanic mine. He found large quantities of low-grade mud rock, varying from 6 to 8 Ib. of quicksilver per ton, which at the prevailing low price of quicksilver demanded very cheap mining costs, in conjunction with high but cheap metallurgical extraction. At that time the extraction of quicksilver from mud rock ranged between 40 and 50 per cent., as far as I am able to learn. Mining The low cost of mining was the principal consideration, since, with mercury at 50c. per pound, the total gross value of the ore did not exceed

Jan 1, 1915

By R. O. Williams

A study utilizing neutron diffraction, electrical resistance, and chemical extraction has been carried out to clarify the chromium-rich part of the miscibility gap previously proposed for this system. This gap appears to be more symmetrical than previously supposed and is very flat. This flatness is believed to be the result of a cooperative phenomenon perhaps of magnetic origin; in particular, it is believed that the chromium-rich phase is antiferromagnetic. The presence of antiferromagnetism is believed to result in an additional strengthening mechanism very sinzilar to that for ordered precipitates. Likewise, it is proposed that the quenched alloys which are known to be ferromagnetic have antiferromagnetic regions which accounts for the maximum in hardness around 75 pct Cr. It is also believed that the existence of antiferromagnetism in other alloys of transition elements might explain some of their anomolous characteristics. THE iron-chromium phase diagram at low temper atures has recently been constructed as shown in Fig. 1(a)1 based upon that work and the work of Fisher, et al2 This system exhibits a number of extraordinary features but perhaps the most striking is the odd shape of the miscibility gap (in the

Jan 1, 1959

By S. Leber, R. F. Hehemann

Diffusion coefficients for the Cb-W system were measured using couples prepared from poly crystalline, commercially pure metals. The diffusion coefficients, measured in the temperature range between 1700° and 2300°C, decreased exponentially as the tungsten concentration was increased from 0 to 50 at. pct, then decreased abruptly at higher concentrations. A decrease of two orders of magnitude was observed over the entin? compositional range. The diffusion coefficients were in the range defined by the self-difiusion coefficients of the individual elements, indicating their general validity. An activation energy of 60,500 cal per mole was measured for the 20 pct W composition. Such low values, when compared with energies over 100,000 cal per mole for the pure constituent elements, indicated that transport mechanisnzs more rapid than volume diffusion were contributing substantially to inter dijfusion. Difference should, therefore, be expected between these data and the intrinsic diffusion coefficients. These differences should be significant in the kinetics of 'transport phenomena in practical systems. CONSIDERABLE attention has been devoted in recent years to the mechanical behavior and other properties of the refractory metals and their alloys. The Cb-W system has been of special interest as a base for the development of more complex compositions of commercial interest. In spite of the importance of mass transport to all aspects of elevated-temperature behavior, and especially to the production of alloys by powder-metallurgy techniques, little attention has been paid to diffusion in the Cb-W system. Results from a previous study of this system1 appeared to be anomalously high. The present investigation is, therefore, an attempt to obtain more accurate diffusion coefficients in this system. Intrinsic diffusion coefficients, of primary importance from the theoretical viewpoint, can only be obtained accurately from studies utilizing compositional gradients approaching zero. However, many practical problems involve diffusion under significant concentration gradients. The diffusion coefficients determined in this investigation were, therefore, obtained from couples prepared from elemental metals. The data obtained should be of value in the analysis of problems such as homogenization during powder-metallurgy alloying or reactions between base and clad in coated structures. In this vein, the investigation was conducted on poly crystalline materials of commercial purity. PROCEDURE Diffusion couples were prepared by sandwiching a columbium sheet between two sheets of tungsten. The composite was welded around all edges, the tungsten forming a protective can for the columbium. The composite was soaked for 4 min at 1600°C in a hydrogen-atmosphere furnace, quickly forged to 40 pct reduction in thickness, and then rapidly cooled to room tempera-

Jan 1, 1967

By F. P. Dewey

The subject of this paper does not embrace the consideration of ways and means for the increase of analytical accuracy, or the question what could or should be attained in that direction. I desire simply to call attention to the degree of accuracy exhibited in actual every-day practice. In estimating this, little weight will be given to the evidence afforded by the agreement of duplicate or multiple determinations by the same chemist; for I am convinced that such agreement is a delusion and a snare. Nor will special importance be attached to the agreement of two or even three analyses in special cases, or to the agreement between two methods practiced by the same analyst. I propose to compare the results obtained by several chemists, working upon the same sample and by various methods, in order to exhibit, as I have said, the actual condition of practice. The available material for illustrating this phase of the question is unfortunately scanty; but something has been done; and I hope, by calling attention to some of the work in this line, to stimulate further work in the same direction by inducing others to prepare suitable samples and submit them to various chemists who are competent and willing to make the necessary determinations, and fully describe the methods they employ. I draw most of my illustrations from the Transactions of the Institute, the Proceedings of the Association of Official Agricultural Chemists, and from personal experience. Manganese in Steel.—In May, 1881, Mr. William Kent presented a paper to the Institute entitled " Manganese Deter-

Jan 1, 1897

By Bailey, Lewis Newton

Bailey, Lewis Newton, Master Engineer, Senior Grade, 4th Regiment, U. S. Engineers, Headquarters Company, died of pneumonia at Camp Merritt, N. J., on Apr. 30, 1918. Baird, Louis, Lieut., Royal Field Artillery, British Army, died on the battlefield in 1915. Ballamy, John H., Capt., 103d Engineers, killed in action near Fismes, Aug. 9, 1918. Bowles, Martin F., 2d Lieut., Co. B, 355th Infantry, killed in action, Sept. 3, 1918. Burt, Andrew, died in active service, 1916. Cobeldick, William Morley, Royal Engineers, died from gas poisoning on Oct. 7, 1915. Dougall, Ralph, 4th University Co., Princess Patricia Regiment, killed in action early in the war. Evans, Alfred Winter, Lieut.-Col., New Zealand Rifle Brigade, D. S. 0., D. C. M., killed in action on Oct. 12, 1917.

Jan 3, 1919

By C. W. Kempton

IF New England were located in some distant and almost inaccessible region, there is no doubt that its mineral resources would have been ere this well developed and generally acknowledged, but laboring under the disadvantage of nearness, it has been neglected. Its surface, moreover, is not cut up by mountains and canons, and the remnants of many of the old ridges are extensively covered by glacial drift. Having for the past ten months been engaged in the development of a. mineral district in Southeastern Maine, I would take this opportunity to lay before the Institute sketches of results, and try to give some idea of the formations as found. The Sullivan Mining District extends from the town of Franklin, through Hancock, Sullivan, and Gouldsborough, from northwest to southeast, about sixteen miles. A general idea of this locality may be gathered from the map accompanying. (Fig. 1).

Jan 1, 1879

By Fred H. Poettmann

An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of the compressibility factor of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. Comparison of calculated results with field measured results were made on 20 dry gas wells from a given field and 11 distillate wells from different fields. The agreement between calculated and observed results is good. In addition to their use in the calculation of sandface pressures of flowing wells, the factors can be used in the direct calculation of the static bottom hole pressure of gas wells, the capacity of gas transmission lines, and in the calculation of the theoretical isothermal horsepower necessary to compress a natural gas. Examples demonstrating the use of various equations are given. INTRODUCTION Many of the equations used to calculate the sandface pressures of flowing gas wells from well head data do not take into consideration rigorously the deviation of the natural gas from ideal gas behavior. For low pressure wells this error is not serious. For high pressure wells flowing at high rates this error call be serious. Sandface pressures are used to determine the producing capacity of gas wells as shown in the U. S. Bureau of Mines' Monograph 7.' An equation has been derived for use in calculating the sandface pressure of flowing gas wells in which the variation of compressibility of the gas with pressure is taken into consideration. This variation due to compressibility has been put into both graphical and tabular form. In addition to their use in the calculation of sandface pressures, these "factors" can also be used to give a direct solution in the calculation of the static bottom hole pressure of gas wells, the calculation of the capacity of gas transmission lines, and the calculation of the isothermal horsepower necessary to compress a gas. CALCULATION OF SANDFACE PRESSURE OF FLOWING GAS WELLS The starting point in the derivation of any specific flow equation is an energy balance on the fluid flowing between any two points in the system. This energy balance based on one pound of flowing fluid is expressed by the well known general flow equation: jp~- vdP+ Ah + -— + wt + r. = o . . (i) P, 2 g. where V = specific volume of flowing fluid in cu ft/lb P = pressure in Ib per sq ft ah = difference in height above datum plane in, ft ------ = kinetic energy change of one lb of flowing fluid, v equals velocity in ft/sec and g. = 32.174 Ws = Work done by fluid while in flow (similar to shaft work in driving a turbine) W, = Znergy losses due to the irreversibilities of the flowing fluid This equation contains no limiting assumptions and can be made the basis of any fluid flow relationship by limitations or substitutions. The energy units are usually expressed in term* of foot-pounds of energy per pound of mass. Considering the vertical flow of gas through tubing or annu-lus, the external work W, done by the gas is zero. Let us also assume that the value of the kinetic energy function is small and can be neglected. Equation (1) is reduced to: /P: VdP + Ah+Wt = 0 .......(2) Pi The energy loszes PI can be expressed in terms of the well known Fanning equatinn: 4/Lf: rf = —— ............(3) 2g,D where L = the integrated average velocity in ft/sec of vertical flow in a uniform flow string -~h = L v = the integrated average velocity in ft/sec / = dimensionless correlating function

Jan 1, 1951