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By K. E. Brown, J. P. Brill, A. R. Hagedorn, T. C. Doerr

A recent correlation for multiphase vertical flow by Hagedorn and Brown1,7 has been used to examine the effect of numerous variables such as pipe size, gas-liquid ratio, liquid flow rate, liquid viscosity, liquid surface tension, oil API gravity, water cut, etc., on flowing pressure gradients. Most previous correlations were derived by using a form of the general energy equation which assumed negligible changes in kinetic energy. Under certain flow conditions this can lead to serious errors in predicting pressure traverses. Examples of traverses calculated both with and without the kinetic energy term are included here. The Chew and Connully correlation for calculating changes in viscosity with changing pressure and temperature has been extended so that the effect of a changing viscosity with depth on pressure gradients can also be predicted. Examples illustrating the effect of tubing size show the importance of this correlation in determining pipe sizes for initial well completions. Limitations on production rates in small pipe sizes from excessive friction losses can be predicted with greater accuracy. The combined use of a vertical-flow correlation with a horizontal-flow correlation provides a method for determining the maximum flow rate possible from both flowing and gas-lift wells. Examples are included to illustrate application of the combined use of vertical and horizontal-flow correlations in optimizing production rates and minimizing excessive costs from over injection of gas in gas-lift wells. INTRODUCTION The problems of multiphase vertical and horizontal flow are immediately encountered in any producing well. Fig. 1' shows three stages of production: flow in porous medium, vertical flow and horizontal flow. All three stages affect the production rate from a well. If we are confronted with a particular well and consider only the variables involved in the vertical and horizontal stages of Fig. 1, we should be capable of calculating the flowing bottom-hole pressure necessary to produce a particular flow rate. A change in any of the variables results in a new solution to the problem. Recent approaches in developing horizontal and vertical-flow correlations have improved to the extent that the solution can now be obtained with more confidence than previously. VERTICAL AND HORIZONTAL FLOW CORRELATIONS Since Poettmann and Carpenter's' original work in multiphase vertical flow, there have been many additional vertical-flow correlations developed which have greatly improved the accuracy of pressure-loss calculations. These

Jan 1, 1967

By Earl L. H. Sackett

Barite, although not a glamour mineral and probably little known to many of those in the mining business, is produced in the US. in very respectable quantities and is an important factor in the mineral economy of this country. The scope of the various uses of this mineral is perhaps one of the most misunderstood things about it, for it is surprising how many of those with a casual knowledge of the subject speak of its primary utilization in terms of paint pigments and barium chemicals. The life blood of barite utilization, however, is the petroleum industry by virtue of its dependence on this high specific gravity, inert mineral as the weighting material in its drilling fluids. From 80 to 85% of barite usage in the U. S. is accounted for in this manner-in fact, its role in oil well drilling is the only excuse for some of the large-scale barite production facilities which have been developed. Other uses are important and widely varied, but comparatively they are of small scale. They include fine crushed barite of low iron content as a component in glass manufacture, barite as a source material for manufacture of barium chemicals, finely divided barite as a component of some rubbers and ground, bleached barite in pigments. The formerly substantial use of barite in lithopone, however, has declined markedly because of replacement of lithopone by titanium pigments

Jan 5, 1962

By Edna A. Dancy, Gerhard J. Derge

Jan 1, 1963

By G. T. Engel, W. G. Gruzensky

Jan 1, 1960

[Separates of all the Technical Publications published in 1929 are available at lnstitute 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.] Metal Mining Technical Pdbli- Title Author Meeting Trans. cation . Volume No. and Page* 182-A-23 The Royal Commission on Mining Henry Louis New York Subsidence Feb., 1929 183-A-24 Cycles in Metal Production D. F. Hewett Nen. York T29, 65, 95 Feb., 1929 199-A-25 Ventilation at the United Verde Oscar A. Glaeser New York T29,- 114. Mine Feb., 1929 206-A-26 Air Conditioning In Deep Mines R. W. Waterfill New York T29. 99, 112 Feb., 1929 245-A-27 Bumps in No. 2 Mine, Springhill, Walter Herd New York Nova Scotia (with discussion) Feb., 1929 257-A-28 Misfires: Their Causes, Prevention New York and Treatment on Occurrence Feb., 1929 Misfires in Anthracite Coa1 T. D. Thomas Mines (With Discussion) Misfires in Bituminous Coal W. H. Forbes Mines (With Discussion) Misfires in Non-metallic Mining A. W. Worthington (Limestone) (With Discussion) Milling and Concentration 195-B-15 A Study of Differential Flotation C. R. Ince New York Feb., 1929 196-B-16 Elements of Operation of the Arthur F. Taggart New York Pneumatic Table H. L. Lechmereoertel Feb., 1929 202-B-18 Silver-bearing Minerals of Some A; W. Habn New York T29, 325 Ores from Tintic Mining District Feb., 1929 204-B-17 Experiments with Flotation Re- A. F. Taggart New York agents T. C. Taylor Feb., 1929 C. R. Ince 208-B-20 Cyanide Regeneration or Recov- C. W. Lawr Sun Francisco ety as Practiced by the Com- Oct., 1929 pania Beneficiadora de Pachuca, Mexico 214-B-19 Calculations in Ore Dressing W. Luyken New York E. Bierbraer Feb., 1929 217-B-21 Differential Grinding Applied to Leon M. Banks San Francisco Tailing Retreatment George A. Johnson Oct., 1929 224-B-22 Reducing and Oxidizing Agents Research Staff San Francisco and Lime Consumption in Flo- of United Verde Oct., 1929 tation Pulp Copper Co. 247-B-23 Copper Sulfate as Flotation Acti- 0. C. Ralaton San Francisco vator for Sphalerite 0. R. King Oct., 1929 F. X. Tartaron

Jan 1, 1929

By H. Kazemi, M. S. Seth

The effects of anisotropy and stratification on flow behavior and production performance of oil and gas wells have been studied by numerous authors.1-3 Lefkovits et al.l studied the performance of totally penetrated, stratified bounded reservoirs with no crossflow. Others have studied a similar problem, but with crossflow; Russell and Prats2 have summarized the findings of these papers. Muskat3 studied the steady-state behavior of liquid flow for a partially penetrating well in an anisotropic system and concluded that the productivity weakly depended on the directional permeability ratios (kz/kr>0.1). Nisle4 used the classical method of point source solution to the diffusivity equation to study the effect of partial penetration on pressure buildup of oil wells in an isotropic system. He found that the theoretical pressure buildup curves consisted of two straight lines, the one at early buildup times having a slope proportional to the flow capacity of the open interval (l-d)k, and the other having a slope proportional to the flow capacity of the entire formation hk,. Later Brons and Marting5 supplemented the findings of Nisle and concluded that partial penetration gave rise to a pseudo damage, which reflected itself as a skin factor in pressure buildup calculations. Using the pseudo skin, they calculated the impairment of productivity of the production wells, which agreed well with the results of Muskat.6 Pizzi et al.,? using an electrical analog of a stratified system, concluded that a high pseudo damage resulted if the reservoir was partially penetrated. Harriss studied the optimum spacing and arrangement of perforations in cased holes. Hantush9 derived an expression for pressure distribution in an unbounded reservoir with restricted flow entry. Seth10 extended Hantush's work to a bounded reservoir. Odehl1 has studied a similar problem for steady-state conditions. The purpose of this work was to investigate: (1) the combined effects of anisotropy, stratification with crossflow, and restricted flow entry on pressure transient analysis of flow and buildup tests, (2) the feasibility of calculating the horizontal permeabilities of intercommunicating stratified systems, and (3) the pressure interference tests in such systems. Theory The partial differential equation governing the isothermal flow of homogeneous fluids of constant compressibility is given by Eq. 1: The initial and the boundary conditions are: 1. The reservoir potential is initially constant, say 4v

Jan 1, 1970

By A. E. Chute

The shortage of sulfur is not only continuing but appears to be worsening, attended by steadily rising prices. At the same time emphasis on air-pollution abatement is also increasing. These two factors, a rising market and the growth of environmental attention, have encouraged producers to carefully review all possible sulfur sources. As a result, production of sulfur from hydrogen sulfide occurring in petroleum is receiving greater attention than ever before. Until about a decade ago, the practice of recovering sulfur from hydrogen sulfide separated from gases (either found naturally or generated in desulfurization of liquid petroleum) was wide1y recognized but contributed little to total free-world sulfur production. However, during the past ten years, the production of sulfur from this source has increased so rapidly that it now accounts for a substantial portion of total production. This trend shows no signs of slackening, and current forecasts predict that recovered sulfur may become the dominant source of supply within ten years, exceeding mined sulfur production. This paper is intended to list sulfur sources and relationships, and to discuss the potential of producing sulfur from petroleum. The processing involved, in addition to product storage and transportation will also be discussed along with important economic aspects of sulfur recovered from hydrogen sulfide. For many years, most of the world's elemental sulfur has been produced from salt domes, predominantly by the Frasch process. During the past decade, however, another production source has developed so quickly that it is expected to surpass the Frasch production sources within a short time. This new source lies in the petroleum gases and liquids from which dramatically increasing quantities of elemental sulfur are being recovered. In the phraseology of the trade, the sulfur so obtained is know as "recovered sulfur," a term which does not, as one might expect, include sulfur recovered from other sources such as smelter gases. The growth rate of recovered sulfur compared to that of Frasch sulfur, total elemental sulfur, and total Free World sulfur in all forms is shown in Fig. 1 Since 1963, sulfur consumption has exceeded production,with the natural result that the price of sulfurhas continually increased. The posted price reported for f.o.b. Port Sulphur, La., has risen from as low as $18 per ton in 1962 to $32.50 per ton in mid-1967. With freight and other charges, delivered prices have of course run much higher, amounting to $45 or $46 per ton on the east and west coasts. In some cases, spot sales for as much as $60 have been reported. Although it is playing an ever-increasing role in the sulfur market, recovered sulfur was originally a by-product of the removal of hydrogen sulfide from natural and petroleum refinery gases. Today, however, it is often the most valuable product of a multi-product processing facility. Since there are two major sources of recovered sulfur—production and refining processes —natural gas is included with liquid petroleum for purposes of this discussion. Sulfur from these sources is produced in the form of gaseous hydrogen sulfide which is removed from a gas stream and converted to elemental sulfur. Gases in which hydrogen sulfide occurs naturally are natural gas and the gas produced from a high=pres-sure crude=oil or condensate field.

Jan 1, 1969

By Ernest M. Spokes

For bituminous and lignite coals the economic picture continued to improve as it has each year since the low of 1961, with production at 480 mil- lion tons in 1964 compared with 1963's 459 million tons. The anthracite industry produced 16.3 million tons in 1964 and 18.3 million tons in 1963. The industry is looking toward a further expansion; among the new developments will be a mining wheel producing 3 million tons of lignite per year in South Dakota. It is expected that electric power generation will continue to provide the market for most of the increase in consumption, with exports second in importance in the expansion. Improvements in methods of mining and transporting coal underground and in strip mines, and the cooperation of carriers in finding ways to reduce transportation costs to distant markets, have made possible these expansions. Research continues to reduce costs of mining, transportation, steam generation of electric power and production of steam for space heating and manufacturing processes, to retain some markets and expand others. Other research seeks to expand markets by developing fuel from coal which will be more attractive than competing fuels, by reducing sulfur and other sources of air pollution. Public relations efforts of the industry are bearing fruit in a greater acceptance of coal as a modern fuel.

Jan 2, 1965

By J. Geertsma, F. de Klerk

During the hydraulic fracturing treatment of an oil or gas well the liquid pressure in the borehole is increased until tensile stress in the surrounding rock exceeds tensile strength. Once a tensile fracture is initiated, it is penetrated by liquid from the borehole and fracture propagation under continuous hydraulic action takes place. The fracturing liquid carries a propping agent to ensure a highly permeable flow channel after pressure release. Field results range from failure to obtain increased production to outstanding success. In all cases, however, it unfortunately remains uncertain whether the values chosen for the operational parameters, such as injection rate, pumping time and fluid viscosity, were in fact the ideal ones. Though experience provides a lead, a more satisfactory way to predict results would seem to be to subject the fracture propagation process to a theoretical analysis that (1) makes the maximum use of the relevant physical information and (2) so simplifies the resulting calculations that the field engineer gets practical data that he can handle comfortably. We are attempting here to do this in connection with the prediction of fracture width and areal extent before pressure release. What remains of the fracture afterwards depends on the distribution of the propping agent between the fracture walls, and that is a separate story. Idealization of the Problem To keep the problem tractable, a number of simplify- ing assumptions have had to be made: 1. The formation is homogeneous and isotropic as regards those of its properties that influence the fracture-propagation process. 2. The deformations of the formation during fracture propagation can be derived from linear elastic stress-strain relations. 3. The fracturing fluid behaves like a purely viscous liquid; i.e., any peculiar flow behavior due to the addition of gelling agents or other additives is neglected. Moreover, the effect of the propping agent distribution on the distribution of fluid viscosity in the fracture is not taken into account. 4. Fluid flow in the fracture is everywhere laminar. 5. Simple geometric fracture-extension patterns are assumed — either radially symmetrical propagation from a point source (Fig. 1A) or rectilinear propagation originating from a line source (Fig. 1B). In the first case the periphery of the fracture is circular, in the second case it is rectangular. 6. A rectilinear propagation mode can be accomplished only by injection over a large perforated interval, thus forming a line source. Such a rectilinear fracture must therefore be located in the vertical plane. A circular propagation mode might be expected from injection through a narrow band of perforations. This forms a point source. Because gravity effects are excluded from our considerations, the fracture propagation plane may in this case assume any angle with respect to the wellbore as far as the

Jan 1, 1970

By Arnulf Muan, Egil Aukrust

Activities of COO in the three solid solution series COO-MgO, COO-MnO, and COO-"FeO" have been determined at 1200°C by equilibrating oxide samples with a metal phase (cobalt or a Co-Fe alloy) in atmospheres of known oxygen activities. The systems COO-MgO and COO-MnO are ideal, within limits of experimental error, whereas the system COO-"FeO" shows a slight positive deviation from ideality at the temperature of this investigation. KNOWLEDGE of activities of oxide components in solid solutions is necessary for the calculation of the cation distribution among coexisting oxide phases in many important metallurgical, ceramic, and geochemical systems. Very few activity-composition curves are available for such systems at the present time. A start on the prodigious job of obtaining such data has been made by studies of solid solutions with simple sodium chloride type structure containing NiO or "FeO" as a component.1-3 The present paper describes similar studies for solid solutions with sodium chloride type structure containing COO as a component. For the systems COO-MgO and COO-MnO, the activity solid solution is determined by the equation Here po and are the oxygen activities of the gas phase in equilibrium with the phase assemblages metallic cobalt plus oxide solid solution, and metallic cobalt plus pure COO, respectively. In the system CoO-"Fe07', the metal phase is a Co-Fe alloy rather than pure cobalt. In this case the activity of COO in the oxide solid solution is calculated from the equation where a& is the activity of cobalt in the metal phase. Because the system Co-Fe is close to ideal4 and the metal phase appearing in the present work contains less iron than cobalt even at the lowest COO concentrations of the oxide phases used may be set equal to N . Hence, Eq. [2] becomes The value of Nc, can be estimated from the relative stabilities of the oxides COO (see below) and I) EXPERIMENTAL METHOD Two different but closely related procedures were used in the present investigation to determine the activity-composition curves. In one method, the oxide solid solutions were equilibrated against

Jan 1, 1963

By E. J. Ripling, M. W. Toaz

Tensile tests were conducted on pure magnesium and on four commercial alloys over a variety of temperatures and strain rates. The high positive slope of the ductility vs testing temperature curves that is found over a short range of testing temperatures for these materaturerials was shown to result from the fact that the microstructure was not stable at these testing temperatures. Pure magnesium did not display a transition temperature, although its sub-room temperature ductility was low. This poor ductility resulted from a grain boundary weakness. The aluminum-bearing commercial magnesium alloys had a higher ductility than the pure magnesium. ness.Thealuminum-bearingcommercialThese alloys did exhibit a transition temperature and grain boundaries that were stronger than the grain material. Both pure magnesium and the commercial alloys began initiating cracks at strains equal to one half of their fracture strain. MAGNESIUM base alloys' enormous potential as structural materials lies in their high strength to weight ratios. At present, the high strength magnesium base alloys such as AZ-80, which will be discussed later, have about as high a tensile strength to specific gravity ratio as the highest strength wrought aluminum alloy, 75s-T6, and, of course, a much higher strength to weight ratio than structural steel. Further, since the magnesium base alloys develop their high strength to weight ratios with moderate strengths and extremely light weights, the ratio of load carrying capacity to the weight of many structures is relatively higher for the magnesium base alloys than their strength to weight ratios would indicate. This results because judicious increases in section size, such as increasing the depth of bending members or adding reinforcing ribs, can frequently increase the weight of a structure linearly while the strength and stiffness increase as the second or third power of the added weight. Strength and rigidity must be designed into lightweight structures by those techniques which establish multiaxial stress states. Consequently, strong, lightweight structures frequently also possess a greater propensity toward brittle failures. In order to insure against these catastrophic failures, an extra premium must be placed on ductility and toughness in light alloys. Current knowledge of the ductility and toughness behaviors—notched behaviors—of magnesium base alloys is limited.* Most of the magnesium base alloys * The state of present knowledge regarding the effect of testing temperature on mechanical properties has recently been summar-ized by Pritchard.' crystallize in the hexagonal system, so that they are expected to exhibit a tough and ductile to brittle transition temperature. Actually, a transition temperature behavior has been reported for commercially pure magnesium in the literature, but the characteristics of this transition temperatureh uggest that it may not be a transition in the usual meaning, but simply the onset of some thermal softening, a performance much like that which face-centered-cubic lead might exhibit slightly below room temperature. If transition temperatures do exist, such important questions as the manner in which they are affected by internal variables such as chemical composition and grain size, or the effect of external variables such as rate of straining or notch severity have never been investigated. The investigation reported upon herein was undertaken in order to define some of the mechanical behaviors of the magnesium base alloys better, to gain a better understanding of the influence of some of the above listed variables, and particularly to understand their effect on ductility and toughness better. Material and Procedure Material-—Pure magnesium and four commercial alloys were used in this investigation. The alloys were selected so that chemically they made up a series with approximately the same minor alloying

Jan 1, 1957

By Waldemar Lindgren

THE following pages present data accepted by many geochemists and geologists regarding the succession of minerals and the temperatures of formation in ore deposits affiliated with igneous rocks. They also present the individual views of the author on the composition of the solutions that were active and on the mode of deposition. He does not regard these views as speculations or hypotheses but as forming a well motivated and consistent theory. It is not certain, however, that all investigators will subscribe to them.

Jan 1, 1936

Jan 1, 1967

The following is a list of members who died in 1928. It is compiled from reports to the Secretary's office. Biographical sketches published in Mining and Metallurgy are indicated in the last two columns. Issue Containing Year or Date or Biography Election Name Death 1928 Page 1914 Adams. David T.................... July 22 October 471 1905 Aguilera. Pedro................... May 3 October 469 1902 Althouse, H. W.................... NOV. 3 December 559 1920 Averill: C. C...................... July 9 October 471 1915 Baldwin, C. Kemble............... Aug. 9 October 471 1926 Barquist, Walter C............... NOV. 14 June 298 Barron,* Clarence Walker......... Oct. 2 November 511 1917 Beasley, Fred E.................... Aug. 31 October 471 1901 Belden, S. B....................... May 15 July 333 1927 Binney, Edwin, Jr.................. Dec. 29 February 96 1915 Bonsall, James Malcolm............ Feb. 12 June 284 1917 Boyle, John....................... July 12 December 561 1913 BradEn, Eugene B............. Jan. 29 March 157 1889 Bulkley, Frank.................... Mar. 25 May 240 1896 Callaghan, J. T., Jr............... Apr. 1 1892 Chalmers, George.................. Feb. 4 April 197 1898 Clark, Josiah H.................. May 7 July 333 1887 Copeland, F. K............. Nov. 10 December 561 1915 Cunningham, B. L11............... Dec. 6 August 294 1888 Dana, R. T........................ Aug. 20 December 559 1907 Dennis, Clifford G............... Dec. 28 March 1 1920 DeVenny, Thomas................ Feb. 13 April 197 1882 d'Invillier-, Edward V........... Jan. 4 March 157 1884 Duncan, M. M..................... Dec. 17 February 96 1924 Dyrssen, WaldemaR ............... Aug. 4 October 471 1906 Edmondson. H. W................ Dec. 21 February 1884 Emmerton, F. A.................. Oct. 9 June 298 1911 Eu, S. H............................ July 20 February 1917 Farrand, Ira W.................... Sept. 6 October 469 1900 Fell, E. Nelson...........•......... Mar. 25 May 231 1918 Fenton, Clarence M.............. October Junet 298 1908 Ferraris, Erminio................. Sept. 22 June 298 1914 Galloway. A. D. R............... December April 215 1924 Grant, A. W., Jr................... .4pr. 5 June 285 1917 Grant, Clifford G............... Jan. 26 January? 37 1918 Grant, Frank E.............. Jan. 14 September 417 1921 Gunderoth, C. J.................. Feb. 15 1897 Harms, Ernest..................... Aug. 12 November 512 1891 Hartrick, J. S..................... Feb. 9 June 285 1925 Hochschild, Berthold.............. Jan. 24 April 197 1917 Hutton, L. W...................... NOV. 3 January 37 1894 Jenning", S. J...................... NOV. 17 December 560 1925 Jones, J. Ravenscroft............... Jan. 29 March 157 1880 Jones, J. T......................... May 4 June 284

Jan 1, 1929

By F. D. Richardson

STAFF: Editor, Gerhard Derge Carnegie lnstitute of Technology Schenley Park Pittsburgh, Pa. 15213 Editorial Assistant, M. A. Redmerski Production Editor, Otto T. Johnson THE METALLURGICAL SOCIETY: Jack H. Scoff, President; Richard C. Cole, Past-President; Harold 0. Emerick, President-Elect; Ralph L. Hennebach, Treasurer; Robert W. Shearman, Secretary; Donald A. Parks, Assistant Secretary; Leslie S. Wilcoxson, Assistant Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: R. E. Lund, Chairman; T. E. Dancy, H. O. Emerick, P. R. Gouwens, R. E. Grace, J. H. Jackson, H. H. Johnson, A. E. Lee, Jr., R. R. Nosh, R. D. Pehlke, and Paul Queneau. Review and selection of manuscripts is under the supervision of the following Publications Committees: Extroctive Metallurgy Division: R. E. Grace, Choirmon; G. M. Bell, D. W. Bridges, J. M. Cigon, G. W. Heoly, T. A. Henrie, R. D. (Holli-doy, C. E. O'Neill, C. S. Somis, A. W. Schlech-ten, and Charles Shull. Iron and Steel Division: R. D. Pehlke, Choirmon; T. P. Floridis, Arnulf Muon, G. R. St. Pierre, E. T. Turkdogan, L. H.Von Vlock, and J. M. Uys. lnstitute of Metals Division: H. H. Johnson, Jr., Chairman; J. B. Clark, Vice Choirmon; M. R. Achter, G. F. Bolling. J. O. Brittoin, G. P. Conard, II, R. S. Davis, L. A. Girifolco, G. T. Hohn, J. P. Hirth, L. Himmel, G.T.horn, George Krauss, J. D. Livingston, R. D. Manning, H. M. Otte, S. V. Rodcliffe, R. E. Reed-Hill, H. C. Rogers, E. ScaIa, O. Sherby, M. T. Simnad, G. R. Speich, E. A. Steigerwald, R. A. Swolin, W. A. Tiller, W. R. Upthegrove, J. B. Wagner, Jr., Derek Wolton, H. W. Weart, W. W. Webb, and D. Published seven times yearly in February, March, April, June, August, October, and December by the American lnstitute of Mining, Metallurgical, and Petroleum Engineers, Inc., 345 East 47th Street New York, N. Y. 10017. Telephone PLAZA 2 -6800. Subscription $30 per year for non-AtME members m United States and North, South, and Central America; $32, foreign; $7.50 for AlME members Single copies, $6.00, single copier foreign, $6.50. The AiME is not responsible for any statement made or opinion expressed in its publications . . . Copyright 1964 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AiME New York Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts. Second dost postaas poid ot New York, N. Y.,ond Ann Arbor, Mich. Volume 230, Number 6.

Jan 1, 1964

By M. Felsenthal

Engineers are frequently faced with the problem of having to predict oil recovery from a solution gas drive reservoir in the early life of a field. This is often the time when actual laboratory or field-derived gas-oil permeability (kg/k0) data are not yet available. Although excellent collections of k0/k0 data for various types of rocks may be found in the literature,1,2,3 a need exists for a more detailed correlation of k0/k0 data with core properties such as porosity, permeability, clay content or pore-size distribution. It is the purpose of this article to present this type of correlation for sandstone material. The correlation is based on laboratory tests performed on over 300 core samples from 19 reservoirs in the United States and Canada. EXPERIMENTAL Cores were analyzed by routine procedures, using samples of conventional size (7/8-in. diameter, 7/8-in long) cut parallel to the bedding planes. Air permeability was measured at 1.67 atm mean pressure in a Hassler-type apparatus. Porosity was determined with the aid of a Ruska bulk volume meter and a Boyle's Law rock volume meter, An evaporation method' was used to evaluate irreducible water saturations. Core samples were saturated with 25,000 ppm NaCl brine. The brine was reduced to the irreducible saturation, and the remainder of the pore space was filled with kerosene. This was followed by multiphase flow tests using the so-called "dispersed feed" technique.5 n this technique, gas and oil (kerosene and kerosene-saturated air) were dispersed with the aid of a porous Alun-durn feed head, the face of which contained a waffle-shaped system of Lucite-lined grooves. Oil entered the back side of the feed head and emerged at the raised areas of the front face. Gas was introduced directly into the system of grooves at the front face. The gas-oil mixture then entered the test core which was kept in capillary contact with the feed head. Permeabilities were determined from rate and pressure measurements and saturations from weights. All determinations were performed at equilibrium or steady-state conditions. Pore-size distributions were determined on selected samples by a mercury injection technique.6 GENERAL CORRELATIVE TRENDS When examining data from a given reservoir, it was noted that k0/k0 vs saturation curves became generally less steep as specific air permeability increased, a development that has a favorable effect on oil displacement efficiency by solution gas drive. This trend has also been reported by others in the literature.' An effect of porosity on k0/k0 data was also noted. This effect was not generally discernible in a study of relative permeability data for a given reservoir but became apparent when data for sandstone reservoirs of similar lithology but differing average porosity were compared. For instance, in a comparison of argillaceous and/or calcareous sandstones from 11 reservoirs ranging in average porosities from 14 to 28 per cent, a definite trend was noted, indicating that for a given permeability k0/k0 curves became less favorable (i.e., steeper) as porosity increased. A similar trend was observed for a group of comparatively clean sandstones from five reservoirs ranging in average porosities from 15 to 21 per cent. For a given permeability and porosity, comparatively clean sandstones gave more favorable k0/k0 curves than argillaceous and/or calcareous sandstone or chert reservoirs. The laboratory studies also showed that least favorable k0/k0 curves were exhibited by shaly sandstone, conglomerate, and sandstone containing carbon inclusions. Table 1 lists the various source reservoirs classified by lithology types. To facilitate a correlation of k0/k0 data with core characteristcis, it was found expedient to work with

By D. N. Dietz

Jan 1, 1969

By A. A. Stripling

The Cretaceous limestone wells of the Mara/Maru-caibo Dist. of Venezuela are extremely prolific producers. To maintain production on cessation of natural flow, large scale gas-lift operations were commenced involving high production rates on caring Flow. For the design of these gas-lift installations it was essential to have some knowledge of the pressure gradients involved in casing flow, so that the required injection pressures, optimum gas injection raws, etc., could be forecast. This paper presents a method of calculating these annular pressure gradients. Basically the method makes use of an energy balance equation coupled with an empirical energy loss factor derived from field data. The calculations have been put in a form suitable for "punch card-type" calculating machines. A set of gradient curves for Mara/Maracaibo conditions covering flow rates up to 12,000 B/D, and GOR's of 500 to 2,000 cu fd/bbl is presented. From these curves the flowing BHP can be predicted from surface data and the vertical pow performance under varying conditions of gas injection can be estimated. The method has been applied to La Paz and Mam gas-lift operations for over three years and has given consistently accurate results. INTRODUCTION The Cretaceous limestone fields of the Mara/Maracaibo area in Venezuela are characterized by the presence of widely distributed fissure systems. Under these conditions individual wells frequently have extremely high potentials and such wells are generally flowed on the casing-tubing annulus in order to reduce the pressure loss in vertical flow. To maintain production on cessation of natural flow, an extensive gas-lift system was planned. As a first approach to this gas-lift design problem, an attempt was made to construct a set of empirical flowing gradient curves from the available subsurface pressure data. Such a method has been used successfully for tubing-flow conditions in California by Gilbert'. Unfortunately, the empirical construction of casing-flow gradient curves presents additional difficulties, as pres- sure bombs cannot bc run in the casing-tubing annulus against high rates of flow. Thus, the Full flowing gradients cannot be defined by actual measurement and the best that can be done is to obtain spot pressures at the tubing shoe. Under these conditions a vast accumulation of BHP data is required to construct a set of gradients. To the La Paz and Mara fields the majority of the available flowing pressure measurements fall into a relatively narrow GOR range, in the neighborhood of the solution ratio. While there appeared to be reasonable prospects of constructing gradient curves for this limited range, measurements at higher GOR's, which were of major interest for gas-lift operations, were relatively few and the prospects of constructing empirical curves cor~spondingly remote. As an alternative approach, the possibilities of a mathematical analysis of vertical flow conditions were investigated. May and Laird2fV n 1934 presented an excellent analysis of the vertical-flow conditions in the Anglo-Iranian Oil Co.'s fields. Their analysis was based on an energy-balance equation and calculated the losses due to kinetic energy, friction and slippage separately. By combining these losses with the total calculated available energy, the required depth-pressure traverse could be deduced. On applying the method to La Paz conditions, good results were obtained for tubing flow at high tubing-head pressures. However, for lower wellhead pressures (300 psi and under) the discrepancy between calculated and measured values increased appreciably. It was considered that this was probably due to energy losses caused by slippage or liquid hang-up in a continuous gas phase, for which it was difficult to visualize any analytical approach. In 1952 Poettmann and Carpenter4 presented a method of pressure gradient calculation which, while based on an energy-balance equation similar to that employed by May and Laird, made no attempt to evaluate the various components making up the total energy loss resulting from irreversibilities of flowing fluids. Instead, they proposed a method of analysis which assumed that all significant losses for multiphase flow could be correlated in a form similar to that of the Fanning equation for frictional losses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The total available

By H. Conrad

The strain hardening associated with the creep of magnesium single crystals at room temperatu.Je was investigated by shear tests in which the direction of stressing was reversed a number of times after creep in a <100> direction. The strain hardening was strongly anisotropic; the largest amount occurring in the direction of flow and the least 180 deg to this. The time law for creep changed from a parabolic type to logarithmic for the first and subsequent reversals of stress. For a given stress the creep strain decreased significantly for the first and second reversals and then only slightly for subsequent reversals. The logarithmic creep constant a changed in a similar manner. A linear relationship was observed between the creep strain for a given reversal and the stress. The slope for the third reversal yielded a strain hardening coefficient 12 to 16 times greater than that observed for unidirectional flow. Al-though no recovery was observed upon resting at room temperature, the hardening resulting from stress reversals could be completely removed by heating to 450" C. PREVIOUS work1.&apos; indicated that the creep rate of magnesium single crystals tested in the temperature range of 78" to 364°K decreased with time. This was attributed to an increase in internal stress resulting from an accumulation of dislocations at internal obstacles. The object of the present investigation was to further evaluate the nature of this hardening by conducting tests in which the direction of stressing is changed after previous creep in shear in a given slip direction. Previous to 1950 three investigations indicated that a Bauschinger effect3 occurred for single crystals as well as polycrystals brass in tension compression,

Jan 1, 1960

By Samuel Hoyt

SOME of the more important properties of finished materials are strength, ductility, toughness, resistance to alternating and repeated stresses, etc: Of these, the property that appears to have received the least consideration, at least in this country, is toughness, which is clue, possibly, to our regarding toughness as a qualitative property or, at any rate, as one that, parallels ductility. This arises out of our greater experience with the simple carbon steels in the rolled or forged (non-heat-treated) condition which, qualitatively, are tough if ductile and are not tough if brittle. In this way we have erroneously become, accustomed to judging the toughness of a material from its behavior in the tensile or similar test. The point of view presented in the present paper is that toughness, like hardness or tensile strength, should be regarded as an independent property and of sufficient importance to require, in so far as that may be possible, quantitative determinations. If such be true, it becomes at once necessary to devise experimental means for measuring, or valuating toughness, and the notched-bar impact test (the Charpy test) is advanced as the most logical test that has so far been developed for this purpose. It is further advanced, with particular emphasis, that we have two kinds of toughness to deal with and, accordingly, they will be dealt with independently. CLASSIFICATION OF MATERIALS ACCORDING TO TOUGHNESS Toughness has been defined somewhat as follows: Tough materials are those that offer considerable resistance to permanent deformation but which, once such resistance has been overcome, may&apos; be deformed plastically, but only by the expenditure of considerable energy. In other words; tough materials may be deformed plastically but they absorb a considerable amount of work in the process. This kind of toughness may be called "static" toughness when the rate of loading is reasonably slow or "dynamic" toughness when the rate of loading is

Jan 2, 1919