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By THOMAS G. FEAR

THE COAL DIVISION started its share of the annual meeting Monday morning with a study of coal classi fication. A. C. Fieldner was in the chair. The report of the tellers of the ballot for division chairman, stating that Thomas G. Fear had been elected to that office, was read by M. D. Cooper. Mr. Fear acknowledged the honor in a few words. In reviewing the history of the Coal Classification Committee the chairman pointed out that this was its third symposium, the last previous one having been held at the 1930 Annual Meeting. Throughout its work the com¬mittee has had the active cooperation of the Canadian workers who are interested in the subject which should result in a uniform scheme of classification in Canada and the United States. F. E. Lathe, of the National Research Council, Ottawa, abstracted the first two papers of the session entitled "Determination of the Alkali-Soluble Ulmins in Coal," by Edgar Stansfield and K. C. Gilbart, and "Moisture Determination for Coal Classification," by the same authors. The third paper "Condition of Water in Coals of Various Ranks"' was presented by its author, A. W. Gauger. Written discussions of these papers were presented by H. C. Porter and Gilbert H. Cady. In the oral discussion which followed, W. T. Thom, Jr., brought out the advisability of considering age as a factor in classification. Mr. Fieldner favored retaining bed moisture as a partial classification basis, stating that a review of many coal analyses revealed a remarkable consistency in this item in samples from a given mine particularly where the moisture content was not high. Mr. Porter pointed out that the structure and porosity of coal often have much to do with its moisture content and that these vary in different parts of a seam, particularly in anthracite. Mr. Gauger expressed doubt as to whether the Stansfield method gives the true moisture content of coal, which is needed for classification purposes.

Jan 1, 1932

By G. B. WATERHOUSE

THE year 1929 was exceedingly busy and prosperous for the iron and steel industry in the United States. The lake shipments of ore were approximately 65,000,000 tons, steel ingots produced were about 57,000,000 tons. Plants were very active. operating for many months well over their rated capacity, slowing down during the last quarter following the severe break in the stock market. The ore tonnage mentioned above was the greatest ever shipped by lake from the Lake Superior region. The trend at the ore mines has been to supplement manual labor by mechanical appliances as much as possible. Mining methods have been greatly improved along the lines of safety as well as to increase the percentage of ore recovery. Crushing and grading of iron ores continued to gain in popularity inasmuch as remarkable blast-furnace operations and records were obtained with sizing and uniformity of raw materials. Progress was made along other lines. The Bradley process for the separation of manganese osicle and iron oside from siliceous manganiferous iron ore was cleuelopecl; also considerable work was clone on a process for the beneficiation of the Cuban laterite ores. Sintering of ores and concentrates increased in popularity. A new analytical method for the deter- mination of sulfur in iron ore was worked out which reduced the time required appreciably. The ore re- serves of the Lake Superior district continued to receive considerable attention and played an important part in the recent mergers which have taken place in the iron ancl steel industry.

Jan 1, 1930

Separates of all the Technical Publications published in 1931 are available at Institute headquarters. All the papers are on file in public, university and technical libraries, and when so indicated in the list, may be found in the Transactions. Copies of these papers have been mailed to those members of the Institute who are registered in the different classes: A-Metal Mining; B-Milling and Concentration; C-Iron and Steel Division; D-Nonferrous Metallurgy; E-Institute of Metals Division; F-Coal Division; G-Petroleum Division; H-Nonmetallic Minerals; I-Mining Geology; K-Mining Administration; L-Geophysical Prospecting. Other members may obtain copies by writing to the Secretary. Additional copies are sold at the rate of I cent per page; minimum charge, 25 cents. Metal Mining Tech-nical Publi- Title Author Meeting TRanb. cation Volume No. and Page* 411-A.43 Ventilation at the Portovelo Mines, J. P. Harmon New York. T31, 83 Ecuador (18) Feb., 1931 425-A.44 Use of Models for the Study of Mining P. B. Bucky New York, Problems (28) Feb., 1931 Milling and Concentration 375-B.32 Ball Mill Studies, I (53) A. W. Fahrenwald New York, H. E. Lee Feb.. 1931 401-B.33 Experimental Flotation of Oxidized H. S. Gieser New York. Silver Ores (9) Feb., 1931 410-B.34 Flotation of Minor Gold in Large-scale E. S. Leaver New York, Copper Concentrators (32) J. A. Woolf Feb., 1931 414-B.35 Effect of Particle Size on Flotation A. M. Gaudin New York, (23) J. 0. Groh Feb., 1931 H. B. Henderson 416-B.36 Ball Mill Studies, 11.—Thermal A. W. Fahrenwald New York. Determinations of Ball Mill Effi- G. W. Hammar Feb., 1931 ciency (13) H. E. Lee W. W. Staley Iron and Steel Division 38QC.59 Open-hearth Steel Process as a Prob- E. R. Jette New York, C31, 80, 111 Iem in Chemical Kinetics (34) Feb., 1931 381-C.60 Thermodynamic Study of the Phasial Yap, Chu-Phay New York. Equi1ibriain the System Iron-car- Feb., 1931 bon (26) 382-(3.61 Influence of Dissolved Carbide on the Yap, Chu-Phay New York, Equilibria of the System Iron-car- Feb., 1931 ban (19) 383-C.62 Research on Blast-furnace Slags. R. S. McCaffery New York, Three papers (88) Co-workers Feb., 1931 384-C.63 Statistical Analysis of Blast-furnace K. S. McCaffery New York, C31, 60, 70 Data (13) R. G. Stephenson Feb., 1931

Jan 1, 1931

By F. C. Noyes

DAME Nature was in a generous mood when she distributed widely over the face of the globe numerous deposits of phosphate rock from which man can make phosphatic festiIizer to replace the phosphate re- moved from the soil by crops. The principal deposits are readily accessible to the world's greatest consuming areas and most of them are such that mining operations can be carried on at relatively low cost. The world's known reserves shown in Table 1 are sufficient to last well over 2000 gears at the present rate of consumption. Before giving a brief outline of the phosphate rock industry of foreign countries let us try to get a picture of the movement of phosphate rock throughout the world in 1938, the last full normal calendar year where it came from and where it was consumed. Table 2 shows the origin and finial destination of world shipments in 1938 by grand divisions. Table 3 (p. 499) shows shipment9 of phosphte rock to each country in Europe. Europe is seen to be by far the world's greatest market and the French North African mines the world's most important producers outside of the U. S. A.

Jan 1, 1944

A regular general meeting of the Canadian Mining Institute will be held in Vancouver, B. C., on Nov. 26-28. The Council extends a cordial invitation to all members of the American Institute of Mining and Metallurgical Engineers to attend.

Jan 11, 1919

By Charles Jackson Abrams

MINING is one of the major industries of the Rocky Mountain region and since the United States became involved in the present World War, all mines have been called upon by the Government for the maximum production of the strategic metals necessary. Operating under the most adverse conditions, such as priority requirements, slow delivery of necessary material and equipment, labor shortages, and freezing of all wages, which still permitted some industries to pay higher rates than were allowable in the mines, thereby drawing labor from the mines; and the United States Employment Service continually giving mine labor certificates of availability; these and many other problems made mine operation particularly difficult. Yet, in spite of these obstacles, the mining industry, either through its own resources or through Government subsidies in the form of loans or premium prices for strategic metal, have and still are making an all-out effort to meet Government demands. They, without question, have played a major role in assisting the war effort.

Jan 1, 1945

By Julian Avery

IN its dual role of pig-iron smelter and gas producer, the blast furnace is a remarkably satisfactory and efficient apparatus. Many metallurgists and engineers have pointed out, however, that since the primary function of the blast furnace is to produce pig iron at the lowest possible cost, its function as a gas producer should be subordinated to this primary pur-pose. During the past 10 years or more, improvements in blast-furnace technique and economy have, in fact, been directed primarily to increasing efficiency in the use of the reducing power of the gases produced by com-bustion of coke at the tuyeres, to reduce iron ore within the furnace. The net over-all result is a decrease in the fuel value of the top gas per unit of volume, and per ton of pig iron, which is evidently more than offset in value by the corollary saving in coke and the possibility of increased furnace capacity, for otherwise there would be no point in making such improvements. The purpose of the present paper is to suggest that, while progress has been made in this direction, there is another approach to the problem of increasing the chemical and thermal efficiency of the blast furnace in its primary role as a pig-iron smelter, which appears to offer possibilities of improvement in over-all economy of a different order of magnitude than results thus far obtained by the use of other expedients. The present argument is based in large part upon the hypothesis that the effi-ciency and economics of pig-iron smelting are seriously and adversely affected by the phenomenon known as "solution loss," and that the problem of solution loss can be successfully attacked by increasing the over-all pressure; i.e., the "top pressure" under which the furnace is operated. It is indicated that pressure operation may also be expected to result in concomitant benefits, which may be summed up as generally improved operating conditions, together with a substantial saving in fuel and/or a substantial increase in furnace capacity.

Jan 1, 1938

By A. B. Parsons

AT the outset, the authors of this paper desire to file a disclaimer and an, explanation. They have no inside information from occult sources; neither of them feigns clairvoyant powers in the slightest degree. It is true that they have indicated on be graphs an approximate trend for the consumption of seven important mineral commodities up to the year 1954. At best this is a risky business; the figures do not pretend to be any- thing more than reasoned conjectures that are predicated on an attempt to evaluate some of the more obvious of the many factors that are likely to have a bearing on the future.

Jan 1, 1937

By William H. Hallahan

The Friedensville zinc mine of The New Jersey Zinc Company is located about four miles south of Bethlehem, Pennsylvania in the Saucon Valley, an infolded and down faulted block of Cambro-Ordovician carbonate sediments surrounded by hills of pre-Cambrian gneiss and Cambrian quartzite except where breached by Saucon Creek at its entrance into the Lehigh River. The Beekmantown formation of lower Ordovician age is the host for zinc and limonite ores, the former occurring in the lower dolomitic portion thereof and the latter in the upper interbedded dolomite and limestone portion of the section. The Beekmantown is overlain unconformably by the Jacksonburg of middle Ordovician age and according to Miller (2) underlain conformably by about 2500 feet of Cambrian dolomites and 200 feet of the basal Cambrian Hardyston quartzite. Igneous rocks, younger than the Cambro-Ordovician carbonate rocks, are absent in the vicinity of the ore deposits. The major structure is a N60°E-trending saddle-shaped doubly plunging anticline overturned to the north. A syncline lies to the north of the anticline. A thrust fault of substantial displacement repeats the south limb of the anticline. The ore consists of sphalerite and pyrite, along with gangue dolomite and quartz, filling and replacing the sedimentary type matrix of a strata-bound solution collapse breccia in the dolomitic portion of the lower Beekmantown. This breccia was produced in pre-Jacksonburg time as a consequence of uplift, erosion, and development of a karst topography and subsurface drainage system in the Beekmantown. Deposits of both zinc and limonite are present on the vertical north limb, on the crest and on the gently dipping (25°) south limb of the Friedensville anticline; consequently, there is no preferred structural setting for mineralization. Rather this distribution supports the view that the folding is post-ore. Features confirming this view are the development of flow cleavage in the breccia matrix, the deformation of some of the sphalerite, and the fracturing of the pyrite mineralization therein. There is nothing to indicate that the age of mineralization is other than Ordovician and older than Taconic deformation. In the absence of intrusive igneous activity younger than the ore host, the writer suggests that submarine volcanic exhalations associated with the volcanic activity recorded in the eastern eugeosynclinal facies of the Ordovician may be the source of the metal ions.

Jan 1, 1968

By Carle Hayward

THIS work was first undertaken in the metallurgical laboratory of the Massachusetts Institute of Technology in 1907 by L. A. Dickinson, E. Phelps, and V. S. Rood, under the author's direction. They attempted to determine the diagram for the system Cu2S-NiS, but several inexplicable results were obtained. The following year, P. H. Mayer with Mr. Dickinson carried, on some experiments with nickel sulphide and found that the molten material slowly lost sulphur until it reached a composition corresponding to the compound Ni3S2, established by Bornemann.1 At this point the composition remained stable. The freezing points of the mixtures gradually fell off with the loss of sulphur. Since the above facts seemed to explain the erratic results obtained in the first experiments, Mr. Mayer with F. Jaeger attempted in 1910 to establish a correct equilibrium diagram for the Cu2S-Ni3S2 series. They prepared pure Cu2S and Ni3S2 and determined the cooling curves for various mixtures. The fusions were made in a platinum resistance furnace and the temperatures were measured with a platinum-iridium thermocouple connected with a Sullivan galvanometer. The curve was established for mixtures containing more than 40 per cent. Cu2S, but they were unable to determine certainly the direction of the curve beyond that point. Nothing further was attempted with this series until the present year, when the work was carried to a successful conclusion with the assistance of A. Butts, Jr., and E. H. Weil. The results of this work are given in the following pages.

Jan 1, 1914

Resistant Tape A new oil-resistant tape for rapid insulation build-up on splices in large power cables has been announced by Minnesota Mining & Mfg. Co. Designated Scotch brand electrical tape No. 25 is made of synthetic rubber providing greater dielectric strength and resistance to high temperatures. The chemical-resistant qualities of the tape make it suitable for use in oil drilling, mining and underground [ ] cable operations, while the 40-mil thickness and extreme stretch (1500 pct breaking point) make possible smooth insulation wraps on irregular surfaces. Dielectric strength is 15,000 v and 10,000 v at 500 pct elongation. It has an electrolytic corrosion factor of 1.0 and an insulation resistance of 100,000 megohms. Circle No. 1 Hydra-Lift The Pitman Mfg. Co. announces that is now has in production a new model of the Pitman hydra-lift, recently-developed crane with hydraulically-powered boom that can be mounted on the frame of any truck, 1 ½ tons or larger. According to the manufacturer, the new model hydralift model B features a variety of improvements over the original production model, introduced late in 1950. Changes incorporated in the new model, according to officials, not only have resulted in improved crane, but also have given the unit a new profile which distinguishes it sharply from the original model. The two chief improvements in the new model are: a big increase in the unit's safety margin and the fact that it is now shipped almost completely preassembled, cutting the time and cost of installation. Rated capacities of the hydra-lift are based on the tipping factor of a 1 1/2 ton truck, with outriggers down, and thus have not been increased. Circle No. 2

Jan 1, 1952

By Ralph H. Sweetser

MUCH progress in -blast-furnace construction and in the manufacture of firebrick for furnace linings has been made since the publication of Bulletin 130 of the U. S. Bureau of Mines on "Blast-Furnace Breakouts, Explosions and Slips, and Methods of Prevention," by F. H. Willcox in 1917. At the time of publishing this report comparatively little information was available to blast-furnace men as to the fundamental facts relating to the character of blast-furnace refractories. Some of the accepted theories of only a few years ago have been completely reversed. The mortality of blast-furnace linings used to be so great that nearly every furnace plant had one or more complete linings in the brick shed ready for use in case of a lining suddenly "going out"; it was generally accepted that a furnace could not "keep her lines" more than two or three years at best, and often a hot spot in the shell would develop, or a breakout occur in the hearth or bosh within a year or two after blowing in on a new lining. In some respects these frequent relinings were not so detrimental as to he a complete loss because they afforded opportunities to take advantage of advances in blast-furnace practice. At present the cost of relining has greatly increased, but the life of a lining has also increased. Anything less than five years on a lining is now considered a short blast.

Jan 1, 1932

By J. P. Zannaras

Referring to the article by R. J. Charles and P. L. de Bruyn, let us assume that W = weight of glass bar; P = weight of hammer; e = total deformation; K = unit of deformation; K = potential stress energy; E = modulus of elasticity; L = length of the bar; 7 = coefficient of inertia; h = height, ft; V = velocity, fps; and a = cross section area. The portion of kinetic energy which is effective in producing stress energy in a fixed bar struck horizontally is given by the formula" 1 + 1/3 W/P K =1+1/3w/p/(1+1/2w/p)2 P.V2/2g = Ph where 1 + 1/3 W/P ? (1 + 3W/P/(1=1/2w/p)2 [8] Putting e e = W/P =------------ From the above equation it can be seen that the maximum transfer of kinetic energy to stress energy is when e = 0 or W/P = 0 which indicates that the weight of the hammer must be very large as compared with the weight of the impacted rod. Eq. 8 diametrically opposes the conclusions reached by the authors of this article. In fact, if their suggestions were followed to the extreme when e = co when P = 0, there would be no transfer of kinetic energy to stress energy at all, as 7, becomes zero. Eq. 8 presumes that the velocity with which the stress is propagated through the bar is infinite, whereas the authors claim that the compression waves reflected are reaching the struck end of the bar prior to the complete transfer of the kinetic energy to cause such modification of the conditions there as to make them reach the reverse conclusions demonstrated by the above formula. That such interference exists is unquestionably demonstrated by the authors and others. However, if my observations are correct, such interference for this specific experiment and also for practical comminu- tion is insignificant, and the conclusions of the authors are in error and must be reversed to comply with Eq. 8. Eq. 5, w. = AE 2/2, given by the authors on page 51, is derived from the following equation (Eq. 9): K = 1/2Pe, where P = Sa, S = ?E, e = EL, and L = 1. The above formula, Eq. 9, cannot be applied in this case. This formula is applicable for static loads where the load increases from zero up to its final value, P, in such a way that the deformation at different instants is proportional to the loads acting at those instants and actually represents the area of a right triangle in the strain load diagram of base e and height P. The typical photographs shown in Figs. 3 and 4 represent the familiar strain load diagrams, and since the line of the wave marks the existence and intensity of the strain with the unquestionable conclusion that such strain has been caused by the action of a load acting continuously all along the wave until it reached the horizontal axis, the work stored at this point is represented by the area under the wave line and the horizontal axis and not by the area of the fictitious triangle given by the authors. Then if this is correct, even visual estimation of these areas at gage stations given in the typical photographs of Figs. 3 and 4 suffice to contradict the authors' calculation given in Figs. 6a and 6b and Figs. 7a and 7b. The typical photographs presented by Charles and de Bruyn show a considerable variation of the intensity of the strain at different stations but very small variation of areas which actually represent the stress energy at the corresponding stations. And, apparently, by squaring the small quantities, the authors magnified their error tenfold. J. M. Frankland's paperV iscusses the relative strain intensity and not the total energy for different types of impact loading. He states in his paper, "The reader is explicitly warned not to confuse the results in this report with those obtained when the load is applied by a blow as from a hammer. In this case the peak load rises to very large but mostly unknown values. The accompanying large deflections and stresses are the result of high values of P, not of the dynamic load factor n. According to Frankland "the dynamic load factor" is the numerical maximum of the response factor. It therefore appears that the authors followed the same procedure in obtaining the relative strain energy ab-

Jan 1, 1957

By R. HAYDEN, H. B. HALLOWELL, H. O. Hofman

THE object of refining copper in the reverberatory furnace is to obtain a metal which will have the highest attainable degree of malleability, ductility and electric conductivity, and present at the same time a level surface when it solidifies in the mold after casting. These desirable physical properties are governed by the character of the impurities and the forms in which they are present, by the amount of cuprous oxide retained by the copper, by the quantity of gas held in solid solution, by the casting-temperature, and by the thickness of the casting. The effects of impurities, of cuprous oxide and of gases upon the mechanical properties of copper have been studied by Hampe in his classical paper "Contributions to the Metallurgy of Copper." The most recent research into the effect of metals upon the electrical conductivity of copper is that of Addicks.2 The influence of cuprous oxide upon the electrical conductivity has been investigated by Walker' and Addicks.4 The absorption of gases has received' attention by Hampe,5 Stahl 6 and Heyn.7 The effects of casting-temperature have been noted by Stahl.8

Mar 1, 1907

By Edward B. Cook

INTRODUCTION. THE installation of the Gayley Dry-Air process appealed specially to the management of the Warwick Iron & Steel Co., for the. reason that for fifteen years records had been kept at the works of the company, showing the amount of water entering the furnace in the form of aqueous vapor, and careful observations had been made of its effect upon the working of the furnace. Some years had proved much worse in their effect than others, on account, not only of excessive moisture, but also of great variation in the moisture from day to day, and sometimes within a few hours. It had been found impossible to. make a satisfactory percentage of high-silicon foundry-iron in summer, even on high fuel; and for some years the endeavor had been made so to arrange the sales that, during July and August, only a small percentage of the iron produced would be required to carry more than 2 per cent. of silicon. Our larger furnace, running on basic iron, year after year, produced in February a tonnage 20 per cent. higher than in August, on a much lower fuel-consumption, while, at the same time, the summer months were marked by ? messes," tuyeres closed by slips, and other irregularities, constituting serious additional business losses. It will be easily understood, therefore, that the records made at the Isabella furnace after the installation of the dry blast in 1904 possessed special interest, and were closely watched by us. On the basis of our own experience, we argued that if the moisture could be kept low, and also uniform, the cost of installation would be more than justified. The subject was brought before our Board of Directors in the fall of 1905; and in the spring of 1906 it was decided to install a plant of sufficient capacity to treat 70,000 cu. ft. of air per min., an amount

Nov 1, 1908

By AIME AIME

DREAMS do come true at times, although it is evidently better to believe in engineers than to "believe in fairies" if most dreams are to be translated into fact. It was a fine dream that David H. Moffat had when he projected a railway directly west from Denver; a dream of opening a new empire in northwestern Colorado, and of quickening transportation from the Middle West to the Pacific slope. But Moffat had been a miner and had become a banker. He knew that dreams, untranslated into works, benefit no one and pleasure only the dreamer, so he employed an engineer, H. A. Sumner, to study and plan the route to be followed by the rails. Previous main lines had run to the north, the Union Pacific, or the south, the Santa Fe. The Denver and Rio Grande, it is true, wriggled its way bravely across Colorado but, in order to reach a point 74 miles in an airline west of- Denver, travelled 281 miles following two canyons and crossing Tennessee Pass at 10,240 ft. Valuable as such a road is, it could never accomplish what Moffat had in mind. It was known that no low pass could be found directly west of Denver but up to 9000 ft. the topog-

Jan 1, 1925

By L. G. Jones, A. S. Odeh

A theoretical developtment is presented which provides a straightforward method of handling the drawdown analysis for both oil and gas wells flowing at variable rates. In the past our inability to analyze variable-rate drawdowns has been a major obstacle in using them for formation evaluation. This method should permit wider use of these tests in the future. INTRODUCTION Pressure build-up analyses are widely used to obtain reservoir data such as the effective flow capacity of the formation. On the other hand. although pressure drawdowns have been run for a long time, they have not been used extensively to evaluate reservoirs because they are difficult to analyze. One of the difficulties in analyzing pressure drawdowns has been that the theory developed until now has required the test to be run at a constant rate. For both oil and gas wells this is a difficult requirement to satisfy. especially during the early period of a well's life when drawdown tests are usually run. In spite of this limitation, drawdown tests are often run with build-ups as a check. In this paper a theory, which handles the drawdown analysis for variable rates, is presented for both oil and gas wells. Thus, one of the biggest deterrents to running drawdowns is removed, and they should become a much more useful engineering tool in the future. THEORETICAL CONSIDERATIONS 011, RESERVOIRS The general equation used for describing the unsteady-state radial flow of slightly compressible fluids in homogeneous porous media can be written in cylindrical coordinates as where r is the radial distance in cm, t is the time in seconds, p is the pressure at r and t in atmospheres, + is the fractional porosity, p is the viscosity in cp, c is the compressibility in vol/vol/atm, and k is the permeability in darcies. There are a number of solutions of Eq. 1 for various boundary conditions. One of these is the so-called "point-source" solution, which approximates the case of an infinite oil reservoir with a well located at r = 0 and produced at a constant rate. The point-source solution of Eq. 1 is

Jan 1, 1966

By James P. Kimball

Jan 1, 1881

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

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