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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 Leendert de Witte

Conventional resistivity logs consisting of a short normal, a long normal, and one or more long lateral curves do not give data that allow a complete quantitative interpretation in beds thinner than 20 ft. Reservoir rocks usually exhibit zones of continuous homogeneity of quite limited thickness where the long lateral curves become useless because of adjacent bed effects and boundary phenomena. If the beds are 12 ft or thicker, the short and long normals may be used for qualitative interpretation, which can be streamlined by the application of simplified departure curves. For beds of a thickness less than twice the long normal spacing, this procedure breaks down. The combination of the limestone curve, the later-olog or guard electrode log, and the microlaterolog permit quantitative interpretation for beds that are at least 10 ft thick, provided the mud resistivity and the hole diameter are known with sufficient accuracy. For beds thinner than 10 ft, combinations of the microlaterolog with short spaced laterologs and pseudo laterologs appear to be promising. Interpretation of these curves again requires the application of simplified departure curves. Resolution of various possible combinations was analyzed using departure curve data calculated on the Whirlwind I computer at the Massachusetts Institute of Technology. A field example is shown using the microlaterolog-microlog combination, and the combination of a 6-in. modified laterolog plus a 6-in. pseudo laterolog. INTRODUCTION For the purpose of quantitative interpretation of resistivity logs in porous formations, we want to obtain two essential quantities from the logs, namely, the true resistivity of the undisturbed formation, Rt, and the resistivity of the part of the formation invaded by mud filtrate, Rt. The apparent resistivities of all conventional logging devices are functions of these two parameters and are also influenced by a third unknown parameter, the diameter of the invaded zone, d. It has been shown' that from the normal curves alone it is impossible to arrive at a unique solution for the three unknowns, Rt, R1, and d1. In very thick homogeneous beds, if invasion is not too deep, we can obtain a fair approximation to Rt from the long lateral curves and then use the two normal curves to find Rt and d1 Even under the most favorable conditions, the resolution of this system is not very good. The short normal does not give a reasonable approximation to R1 unless invasion is very deep (dl>16 hole diameters). For very deep invasion, however, the long laterals no longer approximate Rt. For bed thickness between 20 and 40 ft, the long laterals are affected appreciably by the adjacent beds; and the curves are distorted by boundary anomalies to the extent that they lose their quantitative usefulness in most cases. For the same bed thicknesses, the normal curves still function reasonably well. Although it is impossible to find unique solutions Lor R1 and Rt using the normal curves alone, we can obtain a reasonable approximation for the ratio R1/Rt through the use of simplified departure curves. This fact was brought to our attention by A. J. de Witte, geologist with Continental Oil Co. As the magnitude of Rl/Rt is a major clue to the presence of oil in formations, this method can be used to good advantage for qualitative analysis and will be discussed in somewhat greater detail. With the aid of suitable bed thickness corrections, the analysis of the normal curves may be used for bed thicknesses larger than 12 ft. For thinner beds, the method rapidly loses its resolution; and we have to resort to different types of resistivity logs if we want to attempt to analyze the curves quantitatively. The inadequacy of conventional resistivity curves in thin beds is far more serious than generally realized. Fig. 1 shows a conventional E. S. with a 16-in. and 64-in. normal and a 16-ft lateral through a section of Lansing-Kansas City lime, in comparison to a guard electrode survey through the same section in a neighboring well. The porous zones, which show up as low resistivity breaks on the guard electrode log, are completely masked by adjacent bed effects and boundary anomalies on the conventional curves. Even the short normal shows most of the porous Zones only as Vague deflections and in many cases fails to register Their

Jan 1, 1955

ALABAMA Aldrich.-Lloyd, T. W. Anniston.-Carrington, F. G. Klugh, B. G. Bessemer.-Abbott, C. E. Dobbs, G. G. Ferguson V. Salmon, h. S. Stuart, Q. W. Birmingham.-Adams, J. H. Aldrich, T. H. Aldrich, T. H., Jr. Allen, A. W. Armstrong. W. D. Ball, E. M. Bonnyman, J. Bush, M. W. Carter, E. Crawford, G. G. Davis, C. B. Dryer. T. B.

Jan 1, 1923

By AIME AIME

COUNCIL PRESIDENT OF THE COUNCIL. CHARLES KIRCHHOFF NEW YORK, N. Y. (Term expires February, 1912.) VICE-PRESIDENTS OF THE COUNCIL. BENJAMIN B. LAWRENCE NEW YORK, N. Y. JOSEPH W. RICHARDS SOUTH BETHLEHEM, PA. ALBERT SAUVEUR CAMBRIDGE, MASS. (Term expires February, 1912.) S. B. CHRISTY BERKELEY, CAL. W. A. LATHROP PHILADELPHIA, PA. GARDNER F. WILLIAMS WASHINGTON, D. C. (Term expires February, 1913.)

Oct 1, 1911

By AIME AIME

Council. * PRESIDENT OF THE COUNCIL. JAMES F. KEMP NEW YORK, N.Y. (Term expires February, 1913.) VICE-PRESIDENTS OF THE COUNCIL. S. B. CHRISTY BERKELEY, CAL. W. A. LATHROP PHILADELPHIA, PA. GARDNER F. WILLIAMS WASHINGTON, D. C. (Term expires February, 1913.) KARL EILERS NEW YORK, N. Y. WALDEMAR LINDGREN WASHINGTON, D. C. BENJAMIN B. THAYER NEW YORK, N. Y. (Term expires February, 1914.)

Mar 1, 1912

NEW YORK SECTION ALLEN H. ROGERS, Chairman, H. C. PARMELEE, Vice-chairman, FOREST RUTHERFORD, Vice-chairman, W. S. DICKSON, Secretary, 71 Broadway, New York, N. Y. J. E. JOHNSON, JR. . F. T. RUBIDGE, Treasurer, P. G. SPILSBURY. The annual meeting of the New York Section, for the election of officers and other business, was held at the Machinery Club on May 23,

Jan 8, 1918

By AIME AIME

COUNCIL.* PRESIDENT OF THE COUNCIL. JAMES F. KEMP : NEW YORK, N. Y. (Term expires February, 1913.) VICE-PRESIDENTS OF THE COUNCIL. S. B. CHRISTY BERKELEY, CAL. W. A. LATHROP PHILADELPHIA, PA. GARDNER F. WILLIAMS WASHINGTON, D. C. (Term expires February, 1913.) KARL EILERS NEW YORK, N. Y. WALDEMAR LINDGREN WASHINGTON, D. C. BENJAMIN B. THAYER NEW YORK, N. Y. (Term expires February, 1914.)

Apr 1, 1912

ALABAMA Aldrich.-Lloyd, T W Anniston.-Carrington, F G Gerber, A B Heimrod, A A. White, H E Ashland.-Barton, J C Sturdevant, J C Bessemer.-Abbott, C E Ball, T L Hines, H K Hodgkin, W -0. Salmon, H S Thompson, N E Birmingham.-Adams, J H Adler, J. E Aldrich, T H Aldrich, T H, Jr. Ball, E M

Jan 1, 1923

By A. R. Powell

Four, general methods have been used in the study of the decomposition of coal. The first has been directed toward the processes of coal formation, the second has been by means of microscopic studies, the third from the data of destructive distillation, and the fourth has made use of various solvents. Applying these methods to the sulfur of coal, it has been found that the organic sulfur of plant and animal life enters into the formation of coal and remains in organic combination in the final product. The inorganic sulfur is almost entirely combined as iron pyrites and marcasite. The infiltration of hydrogen-sulfide waters is doubtless a large factor in these combinations. Sulfates are found in very small quantities except where free oxygen has entered the coal strata. The mechanical mixing of detritus with the early coal material is another source of sulfur. In this case the sulfur is distributed in microscopic particles throughout the mass. In destructive distillation, a part off the sulfur comes off as hydrogen sulfide and various thiophen compounds, but this furnishes little information as to the nature of the sulfur compounds in the coal itself. The use of solvents has given valuable data concerning the sulfur compounds in coal. Fremy1 and later E. Guignet2 noted the action of alkaline solutions on coal after treatment with nitric acid and Anderson and Roberts3 showed' the presence of large quantities of organic' sulfur in the extract so obtained. In a study of the phenol extract of coal, Parr and Hadley4 found organic sulfur in the soluble organic material. These investigations proved the presence of organic sulfur in coal in addition to the inorganic forms, such as iron pyrites and sulfates. T. M. Drown5

Jan 9, 1919

By R. W. Armstrong, P. C. Jindal

WE should like to point out that Hu and cline.1 in their study of the recrystallization of titanium, have obtained data which appear very important for accurately determining the dependence of hardness on grain size for this material. It has been proposed2,3 that the macrohardness. H. of a poly crystalline material should depend on its average grain diameter, l. in accordance with the relationship: H =H0 + kHl-1/2 [1] where Ho and kH are experimental constants. This relationship follows from the hardness dependence on yield stress or flow stress4 and. thence. the Hall-Petch stress-grain size relations.5'6 Fig. 1 shows the Diamond Pyramid Hardness. Dph. values vs the reciprocal square root of the average diameter of the recrystallized grains, taken from the titanium data reported by Hu and Cline. The data in this figure give a linear relationship for the hardness over a wider range of grain diameters than anyone has previously measured. The data are not linear, for example. on an I-1 or l-1/3 scale. At the very large grain sizes the data are in reasonable agreement with measurements earlier reported by Holden, Ogden, and Jaffee.7 For the grain sizes smaller than 1 µ, which correspond in Fig. 1 to hardness values greater than 150, the material was reported as not being completely recrystallized and, therefore, these data appear less meaningful as far as the hardness dependence on grain size is concerned. However. it has been suggested by other investigators that deformed materials exhibit strengthening due to an effective grain size refinement even in the unrecrys-tallized condition.8-10 Also. Hu and Cline have shown that a change in texture occurs for titanium during the recrystallization process and. especially. following it. The influence of this texture change on the hardness-grain size relation would be expected to be less than that reflected in the unidirectional stress-strain behavior, even for an hcp material. because of the actual combined stress system which applies for the hardness test. For, at least, certain combined stresses, average values of the orientation factors should still occur in the stress-grain size analysis of a material exhibiting a preferred orientation.' We previously suggested3 that the experimental constants. H0 and kH. from the Meyer hardness-grain size relation should be correlated with the Hall-Petch constants, uoy and ky.5,6 Our recent study" of the Hall-Petch relation and the hardness-grain size results which obtain for a number of polycrystalline materials shows that: The inequality [2] is explained by noting that the hardness should be correlated. perhaps, with the flow stress at some value of strain, as suggested by Dugdale,12 and. also, that the influence of strain on the Hall-Petch relation is to increase uo and not change k very much." Normally. Dph values and Brinell hardness values are nearly equivalent to each other and to the Meyer hardness number. For the case of titanium, then. the inequality [2] may be evaluated using the experimental values of ao = 8.0 kg per sq mm and ky = 1.3 kg per mm3/2 obtained from the experiment of Guard.6,13 Thus, (Ho/uo) = 12 and (kH/k3) = 1.3. This research has been supported at the University of Maryland through the Center of Materials Research by the Advanced Research Projects Agency of the U.S. Government.

Jan 1, 1969

ALABAMA Anniston.-Carrington, F. G. Auburn.-Brown, R. L. Battelle.-Green, G. G. Bessemer.-Abbott, C. E. Dobbs, G. G. Ferguson, V. Birmingham.-Adams, J. H. Aldrich, T. H. Aldrich, T. H., Jr. Allen, A. W. Bonnyman, J. Bowron, J. Bush, M. W. Crawford, G. G. Crockard, F. H. Ellis, E. E. Fairbairn, C. T. Gallacher, J. Geismer, H. S.

Jan 1, 1917

By Patricia J. Rand, Kailish Narayan

Atlantic Richfield Co. began operating a commercial uranium solution mining project in April 1975, in Live Oak County, Tex., 10 miles southwest of the town of George West. The operation is designed to produce 250,00 lb of U308 per year and is jointly owned by Atlantic Richfield Co., Dalco, and U.S. Steel. The proprietary process employed in this operation consists of injecting an alkaline leaching solution into the ore-bearing formation through a pattern of injection wells. The uranium-bearing solution is then removed through producing wells using submersible pumps in central production wells. The produced solution is pumped through a pipeline to the plant area where the uranium is extracted. The barren solution is refurbished and returned to the pattern area for reinjection. The injection field and plant site are located in the drainage of Spring Creek, a small intermittent stream tributary to the Nueces River. Land use in the area is primarily agricultural cattle ranching and farming---but several producing gas fields are present in the areas as well. A nine month enviromental baseline study was conducted on the property beginning in Feb. 1975. Plants and animals of the Clay West area were identified and representative terrestrial and aquatic communities were analyzed. Physical and chemical parameters of the soils were described and analyzed. The surface and underground waters were analyzed chemically; radionuclides, heavy metals, nutrients, and pesticide concentrations were measured in the creek sediments; bacteriological measurements were made in creek water and sediments; radionuclide and chemical levels in plants and animals, both terrestial and aquatic, were measured. These studies, though not required by existing, state or federal laws, were considered necessary to assess the existing conditions before operations began on site. The in-place leaching technique for uranium mining eliminates the enviromental disturbances associated with open pit or underground mining. No grinding and crushing of ore is needed, nor are large tonnages of waste tailings produced. Surface subsidence is not expected since less than 5 lb of uranium is present per ton of rock and even complete removal of such small amounts should not cause subsidence. Solution mining has fewer environmental problems than conventional mining. Members of the Texas Water Quality Board recognized the differences which exist and have recently formulated new environmental control procedures which apply specifically to solution mining. Some of the solution mining activities which are of particular concern are discussed in the following pages. Process Description The produced uranium-bearing solution is pumped through a pipeline from the pattern area to the plant area. The first pattern area consists of a nest of 125 fluid injection, production, and monitor wells [(Fig. 1)]. Injection wells have 4-in. casings and are spaced 50 ft apart on a square grid. Production wells have a 6-in. casing and are located in the center of each square. A block flow sheet of the plant is given in [Fig. 2]. The produced solution goes through parallel trains, each consisting of a carbon column and an ion exchange column in series. The carbon column removes any sand present in the produced solution and the ion exchange column extracts the uranium. The depleted solution is treated with chemicals and returned to the field for reinjection. The uranium retained in the ion exchange column is removed periodically with a sodium chloride solution. Uranium-bearing solution from the ion exchange column is passed through a charcoal column for removal of impurities and then to a precipitation tank where the uranium is precipitated as yellowcake slurry. The yellowcake slurry is clarified, filtered and dried to produce a granular yellowcake product. Environmental Considerations Sources of waste solutions to storage reservoirs, the backwash reservoir and atmospheric discharges are shown in the block flow sheet [(Fig. 2)]. These waste solutions pose a relatively small problem and are adequately controlled by conventional means. There is one area, however,

Jan 1, 1978

By D. B. Jugle, J. B. Darby

The equilibrium solubility limits of the transition elements Ti, V, Cr, Fe, and Co in liquid tin were determined in the temperature range from 827" to 1211°K. Since the equilibrium concentration of Ti, V, or Cr in liquid tin is moderately dilute in the temperature range investigated, the solubility data were employed to estimate the partial molar enthalpy and the partial molar excess entropy of solution for the three solutes in liquid tin. The reference state s for titanium or vanadium were selected relative to the solute in an intermetallic compound. The thermodynamic quantities for chromium were calculated relative to pure chromium. RECENT experiments1 have shown that the rate of solution of several transition elements in liquid aluminum can be qualitatively predicted from a knowledge of the temperature dependence of the solvent-rich liquidus. In order to extend the analysis to binary tin systems,' it was necessary to know the equilibrium solubility of several of the first-long-period transition elements in liquid tin. Since solubility data for the tin-rich portion of binary systems are meager, the present investigation was undertaken to determine the equilibrium solubility limit of Ti, V, Cr, Fe, and Co in liquid tin in the temperature range from 850" to 1200°K. EXPERIMENTAL PROCEDURE A useful technique3 to determine the equilibrium solubility of a solute in a liquid-metal solvent consists essentially of placing a pure solute in contact with a pure solvent and allowing sufficient time for equilibrium to be attained at the temperature of interest. Subsequently, the solvent is removed and the equilibrium solute concentration in the solvent is determined by an appropriate analytical procedure. The technique can be applied very successfully to relatively simple systems such as the copper-germanium system.3 However, in many binary systems of transition elements with tin, several intermediate phases are known to exist and precipitation of the phases from solution, in solubility experiments, can lead to an erroneously large solubility. The difficulty was avoided in the present work by equilibration of the most solvent-rich intermediate phase with the pure solvent over a range of temperatures. The compounds employed in this investigation, and the temperature range over which each compound is in equilibrium with liquid tin are listed in Table I. No stable intermediate phases are reported in the chromium-tin system4 and, therefore, pure chromium was utilized as the solute. The stoichiometric compounds were prepared by arc-melting on a water-cooled copper hearth in a helium-argon atmosphere. The elemental tin employed in.this investigation was 99.998 pct pure, and typical lot analyses of the transition elements were reported elsewhere.' A sample of an appropriate solute, in the form of a button and in sufficient quantity to exceed the equilibrium solubility, and the pure tin solvent were placed in a high-purity recrystallized-alumina crucible. The crucible and contents were placed in a horizontal furnace under a high vacuum (10-6 torr) and held at temperature for periods varying between 24 and 72 hr. A water-cooled quench tank, partially filled with diffusion-pump oil, was attached close to one end of the

Jan 1, 1970

By Merlyn B. Buhle

FOR the past 20 years electrical earth resistivity exploration has been used in Illinois in many phases of study undertaken by the State Geological Survey, chiefly in locating and outlining deposits of water-bearing sand and gravel from which to obtain ground water for municipal and industrial supplies. At least 43 municipalities in the state derive their total water supply from deposits of sand and gravel discovered by resistivity methods. These deposits occur in both Quaternary and preglacial valleys and within much of the glacial drift which covers .a large portion of the state

Jan 4, 1953

ALABAMA Auburn.-Brown, R. L. Battelle.-Green, G. G. Bessemer.-Abbott, C. E. Dobbs, G. G. Ferguson, V. Birmingham.-Aldrich, T. H. Aldrich, T. H., Jr. Allen, A. W. Bonnyman, J. Bowron, J. Crawford, G. G. Crockard, F. H. Ellis, E. E. Fairbairn, C. T. Gambrill, G. T., Jr. Geismer, H. S. Hiller, E. McCormack, G. B. Maben, J. C.

Jan 1, 1917

Executive A R LEDUC, Chairman ARTHUR S DWIGHT R V NORRIS EDWIN LUDLOW E L DEGOLYER Membership J V W REYNDERS, Chairman E L DEGOLYER R M RAYMOND EDGAR RICKARD W Y WESTERVELT Finance WALTER H ALDRIDGE, Chairman GALEN H CLEVENGER J V W REYNDERS Library Chairman JOHN H JANEWAY GEORGE C STONES ROBERT LINTON ALEXANDER C HUMPHRLYS, - BRADLEY STOUGHTON

Jan 1, 1923

Arizona ROBERT E TALLY, Chairman CARL F MILLS, Secretary-treasurer, P O Box 1462, Jerome, Ariz W. S. BOYD THOMAS H O. O'BRIEN F. W MACLENNAN Boston Meets first Monday each winter month GALEN H. CLEVENCER, Chairman HOLCOMB J BROWN, Vice-chairman F LEROY FOSTER, Secretary-treasurer, Room 8-219, Mass. Inst of Tech, Cambridge, Mass A. E WELLS H A WENTWORTH

Jan 1, 1923

BRANCH COUNCILS Mining Branch E R Price, Chairman (Coal) Howard A Meyerhoff (Industrial Minerals) J V Beall, Secretary Richard M Foose (Industrial Minerals) Carroll F Hardy (Coal) Frank A Hardlaw (Mining, Geology, and Geophysics) S J Swainson (Minerals Beneficiation) Philip J Shenon (Mining, Geology, and Geophysics) Grover J Holt (Minerals Beneficiation) A C Callen (Mineral Industry Education) C H. Behre, Jr. (Mineral Economics)

Jan 1, 1952

While the production of this state has not realized the early hopes that this coal would replace eastern coal on the Pacific Coast, it has been steady though small. Nearly all of the tonnages given are from Goodyear's, The Coal Mines of the Western Coast of the U. s., a carefully com- piled and accurate account of the development of the industry along the Pacific. [ ]

Jan 1, 1942

E. O?C. Acker Jinzoc Adachi Truman H. Aldrich Walter H. Aldridge Anson W. Allen John H. Allen William R. Appleby W. Lawrence Austin W. S. Ayres David Baker John Henry Banks Henry C. Banon Alonzo F. Bardwell Wm de L. Benedict Robert Bentley Andrew A Blair Walter M. Brodie Elwin F. Brown Fredrick Burbidge H.H. Burden Charles Butters

Jan 1, 1942