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By Jack R. Elenbaas, Donald L. Katz

A radial turbulent flow formula has been developed which permits the computation of the pressure drop for radial flow in gas wells whether the flow is laminar, turbulent, or partially laminar and partially turbulent. Using the formula a complete back-pressure curve has been calculated and analyzed by a comparison with existing back-pressure curves. A procedure is presented for computing the permeability of the porous media when the porosity, sphericity and average particle diameter are known. Introduction Recent studies on the flow of fluids through porous media have provided new methods for computing flow under turbulent conditions. The present study was initiated as an investigation of pressure -drop computations for flow through porous sands in gas wells and as an analysis of present-day back-pressure tests. Although laminar flow exists in the producing formation of gas wells under normal flow rates, turbulent flow does take place adjacent to the well bore. As the flow rate is increased, turbulent flow exists further and further into the producing formation and under open-flow conditions in relatively deep wells a considerable portion of the flow through the sand will be turbulent. In order to calculate a complete backpressure curve for relatively deep wells without resorting to extrapolation of curves drawn from data obtained in back-pressure tests or calculations made in the completely laminar region, it was necessary to have some means of calculating pressure drop for flow through porous sands under turbulent conditions.4.6 As a result, a radial turbulent flow formula was derived from the equations recently presented by Brownell and Katz.1 A rigorous solution of this equation involves a trial and error graphical integration. By making the assumptions of average viscosity, temperature and compressibility factor of the flowing gas, it was possible to graphically integrate the relation for the general case of radial flow of gases through the porous sand of gas wells. A chart has been prepared relating the value of the integral to the radius of the well bore and to the Reynolds number of the flowing gas. The chart actually performs the graphical integration and the solution of the formula is then reduced to a simple trial and error calculation. A typical back-pressure curve is calculated to show the transition from laminar to turbulent flow. This paper will briefly describe the pro-cedurcs for computing flow through porous media, including a method for predicting sand permeability from porosity and grain size and shape. Flow through Porous Media Brownell and Katzl recently reported a correlation for computing flow of fluids through porous media by the use of an enlarged Reynolds number and friction factor in which the porosity of the bed is included as an additional prime variable. The enlargcd Reynolds number com-

Jan 1, 1948

By Donald L. Katz, Jack R. Elenbaas

A radial turbulent flow formula has been developed which permits the computation of the pressure drop for radial flow in gas wells whether the flow is laminar, turbulent, or partially laminar and partially turbulent. Using the formula a complete back-pressure curve has been calculated and analyzed by a comparison with existing back-pressure curves. A procedure is presented for computing the permeability of the porous media when the porosity, sphericity and average particle diameter are known. Introduction Recent studies on the flow of fluids through porous media have provided new methods for computing flow under turbulent conditions. The present study was initiated as an investigation of pressure -drop computations for flow through porous sands in gas wells and as an analysis of present-day back-pressure tests. Although laminar flow exists in the producing formation of gas wells under normal flow rates, turbulent flow does take place adjacent to the well bore. As the flow rate is increased, turbulent flow exists further and further into the producing formation and under open-flow conditions in relatively deep wells a considerable portion of the flow through the sand will be turbulent. In order to calculate a complete backpressure curve for relatively deep wells without resorting to extrapolation of curves drawn from data obtained in back-pressure tests or calculations made in the completely laminar region, it was necessary to have some means of calculating pressure drop for flow through porous sands under turbulent conditions.4.6 As a result, a radial turbulent flow formula was derived from the equations recently presented by Brownell and Katz.1 A rigorous solution of this equation involves a trial and error graphical integration. By making the assumptions of average viscosity, temperature and compressibility factor of the flowing gas, it was possible to graphically integrate the relation for the general case of radial flow of gases through the porous sand of gas wells. A chart has been prepared relating the value of the integral to the radius of the well bore and to the Reynolds number of the flowing gas. The chart actually performs the graphical integration and the solution of the formula is then reduced to a simple trial and error calculation. A typical back-pressure curve is calculated to show the transition from laminar to turbulent flow. This paper will briefly describe the pro-cedurcs for computing flow through porous media, including a method for predicting sand permeability from porosity and grain size and shape. Flow through Porous Media Brownell and Katzl recently reported a correlation for computing flow of fluids through porous media by the use of an enlarged Reynolds number and friction factor in which the porosity of the bed is included as an additional prime variable. The enlargcd Reynolds number com-

Jan 1, 1948

New Products Equipment

Jan 8, 1951

Jan 1, 1970

By Wilbur H. Somerton

W. H. Somerton is to be commended for his application of the methods of dimensional analysis in combination with the results of laboratory drilling tests to obtain a significant formula for the rate of penetration for the process of rotary drilling. This formula is shown to be a consequence of a more general formulation developed by the discussor as a result of his investigations of the basic action of most methods of rock drilling by mechanical means—the momentary loading of a chisel-shaped tool on the surface of the rock at the bottom of the hole. Some of the author's conclusions are re-examined in the light of this general formulation. DRILLING RATE FORMULA The author selects a minimum number of the most significant variables associated with the rotary drilling process to set up his two dimensionless parameters. Only one variable is associated with the geometry of the bit —the bit diameter, D; only one variable is associated with the properties of the rock pertinent to drilling— the drilling strength, S; and only two independent variables are associated with the conditions of operation the weight on the bit. F, and the rate of rotation, N. The dependent variahle of interest is, of course, the rate of penetration, R. The results of the author's drilling tests show that the variable R that appears in the dimensionless parameter, RIND is approximately proportioned to the square of the variable, F, that appears in the other dimension-less parameter, F/D2S. This establishes the functional relationship between these two simple parameters that leads to the formulation of a third dimensionless parameter, RD1T2/NF1. This last parameter is a significant one for the rotary drilling process, in general, although the author properly limits the validity of his equations to his present test conditions. The author realizes that the numerical value of this parameter, C, is not a constant but may be a function of one or more additional dimensionless groupings of the many other variables associated with the rotary drilling process, e.g. some dimensionless measure of bit wear. The author's parameter is shown to be a special case of a more general dimensionless parameter, developed by the discussor. that is applicable to practically all methods of rock drilling by mechanical means, namely. RD2S/P. P is the rate at which mechanical work is done on the rock, and S is the drilling strength, a term originated by the discussor. S is defined as the ratio of energy input to the rock to the volume of rock broken

Jan 1, 1936

United Engineering Trustees, Inc. W. D. B. MOTTER, JR., '40 A. L. QUENEAU, '41 ALBERT ROBERTS, '39 The Engineering Foundation GEORGE D. BARRON, '40 F. F. COLCORD. '42 A. L. QUENEAU, '41

Jan 1, 1939

By J. G. Thompson

IRON, iron everywhere, but hardly a particle of pure unadulterated iron for the metallurgist to use as a base for the protean characteristics that he develops in the alloys of iron-the modern steels. Iron, next to aluminum the most abundant metal in the crust of the earth; one of the oldest metals known to man and serving him as the most indispensable metal in both war and peace; yet man's knowledge of its properties is based on specimens that are not pure and hence probably differ considerably in their properties from the truly pure metal. Purification of iron has brought about startling changes in its electrical and magnetic properties and has modified its behavior in changing its crystal form with temperature, the basis of the heat-treatment of iron. So both the research metallurgist and the metallurgist of the steel plant are intrigued by the possibilities that might unfold were 100 per cent pure iron available in sufficient quantities to determine its properties.

Jan 1, 1940

By B. B. Gottsberger

A NOTABLE feature of the practice of the American mining engineer is the fact that 'his field has been world wide, and the results of his work may be found in all countries. For this reason, the mining engineer is particularly interested in any legislation tending to restrict his freedom in this respect. In their zeal to improve the status of the professional engineer, those responsible for the enactment of the registration laws now in effect in various of the United States may have introduced a practice that will result very much to the detriment of the American mining engineer. He is preeminently interested in the maintenance of the professional "open door," and fame may be the reward of him who calls the first "International Conference for the Limitation of Restrictive Legislation." There is no reason why these United States should be the only country to regulate the practice of professional engineering and, in fact, the movement is spreading beyond its borders. Already, it is necessary for the mining engineer to be thoroughly conversant with the various state laws in order to insure his right to pursue his calling. It may soon be necessary for him to make sure of his status in foreign countries before undertaking work in them.

Jan 1, 1921

Jan 1, 1933

References are in all cases to the earliest known editions. In the few cases where the first edition has been unavailable for consultation, the particular one studied is indicated. English translations are included when known, but not others. [ ]

Jan 1, 1942

Jan 1, 1929

Jan 1, 1931

By E. C. Pechin

AT the suggestion of some members of the Institute, attention is called to the record of the working of Dunbar Furnace during the twelve months ending in January, 1874. During this period, with a product of over eleven thousand gross tons, not a single ton of

Jan 1, 1874

Jan 1, 1920

By W. C. Ellis, M. E. Fine

WHEN certain binary Fe-Ni alloys are worked cold and then stabilized by a stress-relief anneal, their Young's moduli are nearly invariant over a substantial temperature range determined by composition and work-anneal history.' In the present investigation addition of molybdenum to such alloys (besides increasing the yield strength) was found to diminish the sensitivity of the thermal coefficient of Young's modulus to composition changes. Such alloys are of interest for applications requiring 1 a metal with controlled, low temperature coefficient of Young's modulus and substantial magnetic permeability.' Young's modulus ordinarily decreases with rising temperature. In ferromagnetic alloys a change in modulus on heating due to loss of ferromagnetism modifies the .temperature dependence. Far below the Curie temperature ferromagnetism alters the modulus in two ways: a—Addition of the energy of magnetization, a function of interatomic distance, changes the relation between interatomic energy and distance.' This lowers the modulus in the Fe-Ni and Fe-Ni-Mo alloys of this investigation. b—An applied stress changes the ferromagnetic domain arrangement so that linear magnetostriction contributes to the strain and further lowers the modulUs.~ Since in the alloys of this investigation both effects lower the modulus, loss of ferromagnetism on heating changes the slope of the modulus-temperature curve in a positive direction. With increasing temperature the slope of the modulus-temperature curve, due to progressive loss of ferromagnetism, becomes less negative, goes through zero (the modulus is minimum), becomes positive, and resumes its normal negative value above the Curie temperature.' The increase in modulus and decrease in curvature in the modulus-temperature curve occurring on work hardening have been attributed to a reduction in effect (b).'. Vn the absence of ferromagnetism work hardening through introduction of residual strains would be expected to decrease the modulus.' Alloy Preparation—Test Methods Four series of alloys having nominal molybdenum contents of 5, 7, 9, and 10 pct and containing 47 to 58 pct Fe (the analyzed compositions are given in Table I) were melted in air and cast as bars weighing from 2 to 6 lb. The charge consisted of electrolytic nickel, Armco iron, molybdenum (99+ pct) or ferromolybdenum (62 pct Mo), manganese, and aluminum as a deoxidizer. The bars were swaged cold to the desired diameters with intermediate anneals. Alloys in this composition range are reported" to be face-centered cubic and ferromagnetic at room temperature. The Curie temperatures" decrease with molybdenum. For example, keeping the Ni/Fe ratio at unity and increasing the molybdenum from 0 to 17 pct decreases the Curie tempera- ture from approximately 500°C to room temperature. (The 17 pct Mo alloy requires quenching to retain a single phase.~) Young's modulus at a series of temperatures from —50" to 100°C was determined by a dynamic method previously described.', " In this method Young's modulus is calculated from the resonant frequency (in this case approximately 50,000 cycles per second) of a rod sample (approximately 2 in. long) vibrating longitudinally in the first mode. The densities of the samples at room temperature, Table I, were determined by the standard method of weighing in air and reweighing in redistilled bromobenzene. The linear coefficients of expansion, Table I, needed to calculate the sample length and density at the temperature of measurement, were obtained by observing the change in length (22" to 100°C) of an 8 in. gage distance with a two microscope cathetometer. The values of density and coefficient of expansion in the few samples checked are independent of treatment to the accuracy reported. This was assumed to be general for all the samples. The modulus values are accurate to &0.05x101' dynes per sq cm. However, values of thermal change in modulus are accurate to 20.005~ 10" dynes per sq cm. Young's Modulus Values at 25°C: The modulus values of O', 5, and 10 pct Mo alloys at 25 °C are plotted in Fig. 1 as functions of nickel. After working cold, the samples were either recrystallized at 950" to 1000°C or given a low temperature stabilizing anneal at 400° C. The 400°C anneal does not reduce the hardness nor cause recrystallization. Annealing at 400 °C does

Jan 1, 1952

1913. FRANDKA WBONA DAMS Montreal, Canada. 1921. WILLIAM CUTHBERTB LACKETT Sacriston, Durham, England. 1923. GELASIOC AETANI. Rome, Italy. 1929. TAKUMAD AN Tokyo, Japan. 1920. HENRYS TURGISD RINKER. Merion Station, Pa. 1922. FEDERICGIOO LITTI. Torino, Italy. 1906. SIR ROBERTA . HADFIELD. London, England. 1928. JOHNHA YSH AMMON.D. New York, N. Y. 1921. FRANKW ILLIAMH ARBORD London, England. 1917. HERBERTH OOVER. Washington, D. C. 1906. HENRI LECHATELIER. Paris, France. 1900. WALDEMAR LNDGREN Cambridge, Mass. 1879. JOHNM ARKLE .New York, N. Y. 1921. C. MCDERMID London, England. 1913. EZEQUIELO RDONEZ Mexico City, Mexico. 1909. ALEXANDRPEO URCEL Paris, France. 1911. ROBERT H . RICHARDS Cambridge, Mass.

Jan 1, 1929

By Charles Catlett

Some years ago the writer was struck by what might be called the remarkable vitality of the Virginia furnaces during the panic of 1893; and attention was called to the fact in the American Manufacturer of February 8,1895. From the second half of 1892, which was a period of maximum output, to the second half of 1893, when the full effects of the depression had been reached, the output of pig-iron had fallen off in Illinois 85; in New York, 66; in Ohio, 51; in Tennessee, 44; in Pennsylvania, 28; and in Virginia only 15 per cent. It seemed a reasonable inference that the State which had thus shown its marked ability to meet hard times could make and market its product with a larger margin of profit than any of the other States. This was true at that time, and to a certain extent the reasoning still holds good; but my mistake was in not fully realizing the marked effect of the Mesabi development, combined with reduced economies in transportation, and the consequent advantage to those furnaces which were so situated as to utilize these new commercial factors. The effect of these factors is seen in comparing the second half of 1894 with the second half of 1892. New York had dropped off 44, Alabama 23, Tennessee 21, Illinois 19, and Virginia 16 per cent., while Pennsylvania had increased 5 and Ohio 10 per cent. While there is no question of the great economy which has been made possible for certain interests which are peculiarly situated with reference to the ores of the Northwest, it is yet too early to say what furnaces not so fortunate will have to pay for their raw material. Already an increase of twenty cents per ton of ore has been announced, based upon increased cost of production.

Jan 1, 1900

By J. M. Dahl, R. J. Warrick, O. K. Riegger, H. Van Vlack

A liquid which is rich in oxygen (and silicon) develops at steel rolling temperatures in resulfurized and plain-carbon steels. This liquid fluxes solid manganese sulfide. The composition of the liquid and the resulting microstructures vary with the manganese/silicon/oxygen ratios in the steel. The observations and conclusions zuhich are presented are used 1) to suggest a mechanism for MnS deformation in resulfurized steels, and 2) to rationulize hot-shortness anomalies between plain-carbon and resulfurized steels. 1 HIS is a summary of the dependence of sulfide inclusion microstructures upon steel composition, and an interpretation of the behavior of sulfide inclusions at steel-rolling temperatures. Sulfide inclusions are known to have several metallurgical effects upon steel. Their effects upon hot-shortness are best appreciated. Although hot-shortness is well known, it is questionable whether its mechanism is fully understood because there are several anomalies in our interpretation. For example, why should not high sulfur contents produce extensive hot-shortness in free-machining steels ? A second metallurgical consequence of sulfide inclusions appears because sulfide inclusions improve machinability. Furthermore, globular inclu- sions are to be desired over elongated inclusions. To date, we know that lower silicon contents (< 0.010 pct) favor the globular sulfides, but we do not know why this interrelationship between silicon content and inclusion shape exists. Finally, the evidence is strong that the surface quality of a hot-rolled steel is particularly sensitive to the sulfur content. SUMMARY OF PREVIOUS WORK The role of sulfur in hot-shortness was first suggested during the past century. It is uncertain who was the first to conclude that sulfur was less deleterious in the presence of manganese, and that manganese altered the sulfide phase from a liquid FeS to a solid MnS at steel-rolling temperatures. However, Urban and chipman&apos; emphasized that liquid FeS may accumulate as an interdendritic film during solidification. More recently, Keh and Van lack&apos; showed that the intergranular liquid does not completely surround the metal grains at all rolling temperatures. Rather, a small finite dihedral angle exists when geometric equilibration is attained at

Jan 1, 1962

By N. Van Wingen

EFFective sand permeabilities can be ascertained from core analysis if the laboratory data are compensated to allow for the presence of connate or residual water. Such adjustments can be made by applying empirically derived correction factors. Effective sand permeabilities can be estimated also from analytical studies of field depth-pressure measurements. In one method the time rate of pressure build-up after a well is shut in from steady-state flow is required, and in the other the direct measurement of a steady-state rate of flow and the corresponding equilibrium pressure. The results of the investigation discussed in this paper demonstrate that these methods for determining mean effective sand permeabilities can be correlated. Introduction In recent years many investigators have demonstrated the practical value of an accurate knowledge of the physical and dynamical characteristics of reservoir sands containing oil and gas. Of these factors, which serve to completely define a porous medium as a container or carrier of fluids, the dynamical characteristics are of particular interest to the production engineer because they afford a direct measure of the rate at which the oil or gas content of a reservoir will become available. The constant that defines dynamically the porous medium as the carrier of a homogeneous fluid in viscous motion is the "permeability." Coke-analysis Method The generally accepted practice in com-piling permeability data has been to analyze in the laboratory core samples taken in the course of drilling through the productive horizon, and to obtain the mean measure of the productive ability or permeability for the interval open to production by graphical integration of the permeability profile. An average permeability ascertained in this manner, however, is useful to the production engineer only for comparisons of wells drilled in the same horizon, as permeabilities determined in the laboratory are measures of only the ability of a porous medium to transmit a single fluid. As a result of many investigations, it has been shown, however, that under actual reservoir conditions water is coexistent with the petroleum and that its presence greatly reduces the permeability of the sand to oil. Empirical relationships showing the effect of the presence of any immiscible fluid A (such as water) in a porous medium on the permeability of the medium to a fluid B (such as oil) have been established separately by Hassler,1 Dunlap,2 and the writer (Fig. I),3 so that the average specific or dry-core permeability as determined in the laboratory can be corrected to give the true measure of the ability of the horizon penetrated to transmit oil, provided the percentage of pore space occupied by connate water is known accurately.

Jan 1, 1942