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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

THE Annual Fall Meeting held in Chicago in conjunction with the celebration of a Centennial of Engineering brought forth a round of field trips and symposiums which did much to add to the store of information of the 240 who registered for the gathering. Instead of a scattered program, technical papers were grouped together in organized symposiums, where the particular importance of each report was enhanced by presentation in context. Despite the heavy accent on technical papers and informative field trips, those attending the meeting had ample time to enjoy the benefits of a visit to Chicago. The AIME dinner dance was held at the Palmer House, in the Red Lacquer Room. The Chicago Section played host Friday evening at dinner. The MBD held four sessions at the meeting headquarters, the Palmer House, September 4 and 5. Featuring the meetings was a review of taconite concentration and new theories on comminution. The first session opened with a paper on the Structural Features Which Effect the Concentration of Iron Formations, presented by F. J. Tolonen. The paper was centered upon the various members of the low grade iron formations of the separate Michigan districts. The study correlated macrostructure, microstructure, and concentration tests. [ ] Beneficiation Characteristics of Michigan Low Grade Iron Ores, presented by F. X. Tartaron, cochairman of the session, reviewed the work of his laboratory on the beneficiation of low grade ore taken from various strata of a deep shaft on the Marquette Range. The paper included data on flotation, gravity separation, magnetic separation, and combinations of these processes. The economics of low grade ore treatment generated great interest. Ty. Maki offered a compilation and correlation of field results with magnetic separators in ferrosilicon and magnetite medium recovery circuits. Following the morning session, 130 persons attended a luncheon, followed by a brief business meeting. Later, a film illustrating the grinding, separation, and pelletizing steps investigated by the Mines Experiment Bureau, was presented by H. H. Wade. T. E. Ban, and L. J. Erck gave a report on pelletizing which evoked much discussion. R. A. Limons presented a paper on the Mineralogy of Blast Furnace Sinter, for its author, H. M. Kraner. Friday sessions featured a new hypothesis for high speed drill rod milling and a new technical approach to comminution. Jack Myers commented that Consolidated's large rod mill was a hammer mill turned inside out. Steve Erickson described the use of Cyclones for Heavy Media Concentration of Iron Ore Fines. Bob Meaders gave a Progress Report on the Aerofall Mill. Shiou-Chuan Sun described an improved high frequency analyzer for studying the conductivity of suspensions of various minerals. L. A. Roe discussed a magnetic reflux condensor which enabled him to determine the degree of liberation of magnetic iron ores. Roy A. Johnson described a function of the hydroscilator in which the fan rake was eliminated in favor of a conical bottom. The Industrial Minerals Division sessions held September 5 and 6 and were well attended. The Friday morning session was particularly concerned with developments and advances in industrial minerals with special emphasis on the Chicago area. The first two papers dealt with transportation on the Great Lakes and fuel movement into the Chicago area. The third paper proved to be of great interest, turning the spotlight on the fairly new hydraulic mining methods introduced by a silica company in the Ottawa, Ill. field.

Jan 1, 1952

By C. Willard Hayes

One of the most productive iron-ore districts of the southern Appalachians lies in the vicinity of Cartersville, in northwestern Georgia, where the ore-deposits are so directly related to the stratigraphic and structural features of the region that a description of its geology possesses economic as well as scientific interest. Stratigraphy.—The area shown on the accompanying map, Fig. 1, occupies the southeastern portion of Bartow county, Georgia. It is about equally divided between the older crystalline and metamorphic rocks which occupy the Piedmont plateau and Appalachian mountains on the east, and the Paleozoic formations which occupy the Appalachian valley on the west. The line separating these two groups of formations enters the mapped area near the northeastern corner, and, pursuing a somewhat irregular diagonal course, leaves it, as shown on the map, near the southwestern corner. This line marks

Jan 1, 1901

By E. D. Cockrell, E. P. Hayes

The figures herein presented show that during the year 1938 drilling in the Texas Gulf Coast continued at a slightly lower rate than during 1937. In 1938 there were 21 new oil fields added to the Texas Gulf Coast; also numerous extensions and new sands in old fields. This report for 1938 cannot be compared with the report for 1937 in Volume 127 of the Transactions, because the area covered by this report is less than that covered last year. The cross-hatched area on Fig. 1 shows the limits of this report. Of the new fields, Cordele, in Jackson County, Eureka Heights and Fairbanks, in Harris County, Francitas, in Jackson County, LaRosa, in Refugio County, and League City, in Galveston County, have the greatest promise of prolific production. The 1938 production for the Gulf Coast area was 92,530,467 bbl. as compared to 94,019,355 bbl. for the same area in 1937. This shows a decrease of 1,488,888 bbl. during 1938, regardless of the increase due to the 21 new oil fields. This decrease was caused mainly by the Saturday and Sunday shutdowns (68 days during 1938) and by cut in allowables. The 68 shut-down days amount to approximately 18.6 per cent of the 365 days possible for production. The decrease in the 1938 production amounted to approximately 1.58 per cent. Therefore there was actually a potential increase in the year's production. During the past year, 1637 wells were completed as oil wells, 68 as gas wells and approximately 461 dry holes, as compared to 1672 oil wells, 83 gas wells and 448 dry holes in 1937 on the Texas Gulf Coast. Total wells drilled were 2166 in 1938 and 2203 in 1937. Condensate. sands in old fields and new fields are continuing to increase in importance from the standpoint of retrograde condensation and pressure maintenance. The following fields had major extensions during the year 1938 from the standpoint of increased areas of old sands and new deeper sands:

Jan 1, 1939

By E. D. Cockrell, E. P. Hayes

The figures herein presented show that during the year 1938 drilling in the Texas Gulf Coast continued at a slightly lower rate than during 1937. In 1938 there were 21 new oil fields added to the Texas Gulf Coast; also numerous extensions and new sands in old fields. This report for 1938 cannot be compared with the report for 1937 in Volume 127 of the Transactions, because the area covered by this report is less than that covered last year. The cross-hatched area on Fig. 1 shows the limits of this report. Of the new fields, Cordele, in Jackson County, Eureka Heights and Fairbanks, in Harris County, Francitas, in Jackson County, LaRosa, in Refugio County, and League City, in Galveston County, have the greatest promise of prolific production. The 1938 production for the Gulf Coast area was 92,530,467 bbl. as compared to 94,019,355 bbl. for the same area in 1937. This shows a decrease of 1,488,888 bbl. during 1938, regardless of the increase due to the 21 new oil fields. This decrease was caused mainly by the Saturday and Sunday shutdowns (68 days during 1938) and by cut in allowables. The 68 shut-down days amount to approximately 18.6 per cent of the 365 days possible for production. The decrease in the 1938 production amounted to approximately 1.58 per cent. Therefore there was actually a potential increase in the year's production. During the past year, 1637 wells were completed as oil wells, 68 as gas wells and approximately 461 dry holes, as compared to 1672 oil wells, 83 gas wells and 448 dry holes in 1937 on the Texas Gulf Coast. Total wells drilled were 2166 in 1938 and 2203 in 1937. Condensate. sands in old fields and new fields are continuing to increase in importance from the standpoint of retrograde condensation and pressure maintenance. The following fields had major extensions during the year 1938 from the standpoint of increased areas of old sands and new deeper sands:

Jan 1, 1939

By W. A. Tiller, S. O’Hara

Grain refinement in stirred melts has previously been shown to arise from dendrite segmentation. The present work discusses experiments capable of distinguishing between remelting and mechanical effects which result from fluid motion. Nucleation of still un-dercooled Sn-1 pct Pb melts with a single-crystal seed shows that the grain size of the resulting ingots decreases as the undercooling at nucleation increases up to about 1Z0C, then increases again for larger undercoolings. Pure melts exhibit little refinement as a result of nucleation at any undercooling up to 12°C. The presence of fluid motion gives rise to grain multiplication in pure melts, but the magnitude of this effect is partly obscured by solid-state pain growth. The results indicate that two grain-multiplication pvocesses can operate, one which involves dendrite remelt ing, and another associated with fluid motion. Small ingot experiments indicated that an equiaxed transition can be caused by fluid motion. THE presence of forced convection during recales-cence of undercooled Sn-1.3 pct Pb melts has been shown to give rise to extensive grain refinement during solidification of small ingots of this alloy.''2 In Ref. 2, this refining was shown to result entirely from dendrite fragmentation and not from any nucleation mechanism. The purpose of the present work is to establish what processes lead to dendrite segmentation. Experiments were therefore carried out to determine the resulting structure of both pure tin and Sn-1 pct Pb melts, nucleated at various undercoolings by single-crystal seeds in the absence of forced or natural convection. By comparing the information obtained from these experiments with the results of Refs. 1 and 2, the effects of fluid motion on the ingot structure, and the details of the segmentation mechanisms, should become clear. The results of these experiments should also be helpful in understanding the solidification structures of larger ingots since natural convection, which is known to play an important role in determining ingot structure13 differs only in degree from the fluid-motion effects studied here. I) EXPERIMENTAL PROCEDURE The apparatus shown in Fig. 1 was constructed to permit controlled nucleation of stirred or unstirred supercooled melts using a seed oriented in the tin dendrite growth direction. Because the melts, in all cases, were capable of larger supercoolings than the one used in each experiment, the structure observed always resulted from a single nucleation event at the surface. The sequential procedure was as follows: Tin was melted under purified hydrogen and the oxide removed at a temperature of 450°C . Electromagnetic stirring was then used to clear the surface completely and during this time the guide tube was lowered underneath the melt surface. A pointed Czochralski-like crystal was then propagated from a specially prepared tin dendrite seed4 inside the guide tube while the temperature of the bulk melt was held just above the melting point, ensuring a perfectly clean seed which was epitaxial with the original dendrite. The dendrite and epitaxial seed, still in the guide tube, were withdrawn from the melt which, in turn, was undercooled to 2C° below the temperature at which the nucleation experiment was to be performed. The melt was held there for several minutes, both in stirred and in still-melt experiments. The temperature was next raised to the required value and the melt nucleated by the carrot seed inside the guide tube, the heater power being shut off just after nucleation. In experiments where quenching after nucleation was required, a high-density graphite crucible was used, but otherwise the procedure was as described above. The temperature gradient in the melt before nucleation was kept below 1C° per cm by carrying the experiment out just below the center of the heater shown in Fig. 1.

Jan 1, 1968

By T. W. Peterson, J. W. White, E. E. Krist

In developing a minicomputer application for an industrial grinding circuit, the control program is usually coded and the compilation is debugged on a remote access computing system. Final debugging must wait for installation of the minicomputer. This work reports on an alternative. Here both compilation and execution bugs are eliminated before the hardware is installed by testing the control program against a dynamic simulation. Attention is directed toward development of a particular real-time control program for an industrial wet grinding circuit in a copper concentrator. Specific data were supplied by the Anamax Mining Co. for a grinding division consisting of a rod mill followed by two ball mills in parallel. This information was used to set up a plausible model structure.

Jan 1, 1977

By J. A. Bownocker

THE Pittsburgh is one of the most important coal beds of Ohio. It was the last of the great coal beds to be worked extensively in that State, has the largest area of virgin coal, and will in all probability be the last of the great deposits to be exhausted. The line of outcrop sweeps nearly southwest in a sinuous line from Jefferson County on the north to Lawrence on the south, a distance on a bee-line of at least 150 miles. (Fig. 1.) The maximum width of the area under which this coal is due is about 55 miles, but in most places it is less than half that and in the two southern counties it is in places restricted to narrow ridges. Here as elsewhere the Pittsburgh coal forms the base of the Monongahela formation, and the following section taken from Condit shows the position of this bed with reference to certain higher ones in this field:1 FEET INCHES Shales and thin beds of limestone 24 5 Coal, Meigs Creek, No. 9 4 0 Shale, sandy 11 0 Coal 0 8 Shale, clayey 6 0 Coal, Lower Meigs Creek 3 0 Shales,clayey 2 0 Limestones and thin layers of clay 25 0 Unseen 11 0 Coal, Redstone 2 0 Unseen 11 0 Coal, Pittsburgh, No. 8 8 0 Clay 5 0 Limestone 4 0 From the standpoint of continuity the Pittsburgh coal of Ohio must be classed with the patchy type. As the map shows, the coal is thin or wanting along many miles of the line of outcrop. The large deposits form three separate areas, which, in order of their importance, are generally known as (1) the Belmont, (2) the Federal Creek, and (3) the Gallia fields.

Jan 10, 1926

By D. S. Kingery, D. W. Mitchell

The authors attended the 11th International Conference of Directors of Safety in Mines Research held in France, July 1963. In addition to Conference discussions pertaining to control of coal dust they had the added assignment to study present European practices for neutralizing the coal-dust explosion hazard. Information was obtained through discussions with the Research Directors, by visits to testing stations and observations of operating mines in various countries. This paper tells what the current practice in this field is in Europe, and how effectively coal dust explosions are controlled. The method is rock dust barriers. CONTROL OF COAL DUST DISSEMINATION Experience in Europe indicates that the control of dust production and dissemination by water or foam systems is not successful except during undercutting. Cybulski, Dawes, and DeBraaf - respectively Director, Mines Research Establishment "Barbara", Katowice, Poland; Principal Scientific Officer, Safety in Mines Research Establishment, Sheffield, England; and Chief, Central Mines Research Establishment, Hoensbroek, Treebeek, The Netherlands - believe that wetted dust becomes readily dispersible and abatement measures should be considered only as a temporary means for reducing the health hazard. In an effort to reduce the health hazard, calcium chloride is used on the floor of main haulageways in Dutch mines and water infusion is practiced in Germany in mines where the coal is relatively porous. With respect to wet coal dust, the Belgians, British, Dutch, French, and Russians reportedly have accepted the results of research from the Polish and American experimental mines on the effectiveness of water as an inert in arresting explosion propagation. The Polish use the two test methods proposed by the U.S. Bureau of Mines1 for evaluation of the adequacy of wetness of mine dust; they require that water be added to the wet dust to maintain a minimum of 50% moisture by weight if dependence is placed on water alone. GENERALIZED ROCK DUSTING The general attitude with regard to protection against coal dust explosions throughout Europe is that generalized rock dusting is a vital primary step to inhibit initial ignitions but definite emphasis is also placed upon the efficiency of rock dust barriers. Those exceptions to generalized rock dusting are Germany and Austria where some rock dusting is done but principal reliance is placed upon rock dust barriers. The rock dust used in Belgium, Holland, Russia, and Poland is coarser than that used in the U. S.; 50% of the dust is through a No. 200 sieve (75 microns). Recent research by the Polish indicates that the portion finer than 20 microns is ineffective in arresting explosion propagation, and that the rock

Jan 1, 1964

By Roswell H. Johnson

What becomes of the water which must have filled the oil and gas sands at the time of deposition, has long puzzled students of oil and gas and has found expression in Munn's well-known article on the hydraulic theory. Both Munn and Clapp have pointed out that in the Appalachian field the deeper sands carry increasingly less proportionate amounts of water. It seems to me probable that the principal source of oil and gas has been in the shales in proximity to the sands which now contain these products. The sand spits which mark off the lagoons from the sea comply particularly with the requirements of a limited sand imbedded in shales rich in organic matter. Cunningham Craig has objected to this view that the rich organic muds of lagoons are found only at the surface. That such muds do extend to considerable depth 1 am assured by Prof. Douglas W. Johnson, who has made an extensive study of the Atlantic Coast marshes. As any particular sand body becomes weighted by a heavier and heavier overburden, the result of increasing deposition, a part of the very large percentage of water in the uncompacted sand and mud is forced out. The water percentage of freshly settled mud is vastly higher than that of the resultant shales, or even of a very porous sand. If beds of less compressible material meet or underlie the shales in question, there will frequently be a lateral motion along such beds to some point where the upward movement will be resumed. We find in our laboratory work here that oil, gas, and water have extremely slight capacity for gravitational sorting while in a state of rest, but when moving the gravitational sorting is readily accomplished. As the oil, gas, and water pass a body of larger pores, the gas, owing to its lack of capillary attraction, is retained in the large pores. This has been predicted by Washburne, Blatehley and others on the ground that the water has a higher capillarity and grips the finer pores in such a way that there will be a greater proportion of oil and gas in the large

Jan 1, 1915

Jan 1, 1961

By J. M. Dupouy, R. A. Rawe, M. B. Bever

The aging characteristics of a titanium alloy containing 13 pct V, I1 pct Cr, and 4 pct A1 have been investigated by hardness measurements, X-ray diffraction, and metallography. The P phase decomposes into 0 + a, and 0 + a, + TiCr, above about 1050°F; below this temperature a transition phase, believed to be w, precipitates first, followed by a, and TiCr,. The observed hardening is attributed to these reactions. Cold working of solution-treated specimens accelerates hardening and raises the hardness level attained. A TTT diagram is proposed. NEW titanium-base alloys, designated as "all-beta," have recently been developed. These alloys contain large amounts of P-stabilizing elements such as molybdenum, chromium, or vanadium. When cooled from the solution temperature, they consist only of P; in particular, the martensitic a,' phase does not form.

Jan 1, 1961

By William Colby

INCREASING governmental control of human activities seems inevitable. Within the present generation railroad rates and the public sale of water, gas and electricity have been subjected to rigid regulation. The field of control is slowly but surely being enlarged, and it is the object of this paper to outline in brief space this tendency toward increased governmental regulation, as far as mineral resources are concerned. Our, dual form of government complicates the problem. We must deal not only with the powers of the Federal Government, but also with those of the individual States. In order to approach this question intelligently we must have some conception of the powers and jurisdiction of the States and the United States, respectively, over mineral lands and mineral production. Starting with the Federal Government we find it never owned any public domain within the States that formed a part of the thirteen original colonies and, for historical reasons, the same is true of Tennessee and Texas. The Mid-Western States were erected out of the public domain which was acquired by the United States through cession from the original States or by purchase from foreign nations. Congress early in the last century adopted a policy of leasing public lands containing lead deposits in a portion of this Mid-Western territory, but later abandoned that policy and disposed of such public, lands, mineral and non-mineral, outright so that they long since have practically all passed into private ownership and become subject to the general jurisdiction of the respective State governments. In the great public domain lying west of the Mississippi River, and in portions of some of the Southern States, the Federal Government adopted a new mineral land policy following the discovery of gold in California. (Acts of Congress of 1866, 1870, and 1872.) The mineral lands within these States, instead of being disposed of on the game basis as agricultural lands, as occurred in the Mid-Western States, were segregated from agricultural lands and sold under special laws intended to encourage mining, giving the miner the free right to locate and work these mineral lands without paying any royalty to the Federal Government. A miner could also obtain at slight expense a complete

Jan 1, 1930

By R. G. Fenish

THE B-Ni system was chosen for this study because of the great interest being shown in boron-fiber-strengthened composite materials. Boron fibers were obtained from Texaco Experiment, Inc. They average 4.2 mils in diam with a 0.5-mil tungsten wire in the center. In order to make the diffusion couple, the fibers were included in the nickel matrix by electroforming. The samples were placed in a preheated furnace for the desired temperature and length of time. Sectioning and polishing the samples revealed concentric rings as shown in Fig. 1. The average penetration distance, X, was calculated by measuring the radius of the second phase (the white shell in Fig. 1) and subtracting the original radius. The second phase was identified as NiB by X-ray diffraction. This allows the kinetics of the formation of the phase NiB to be calculated by Eq. [I], which is taken from Hoffman:"

Jan 1, 1967

By John W. Cahn

Tile avevage value of the mean curvature of surfaces in a specimen can be precisely delermined by sitrlple measurements performed on random sections or on 1 vojectiotzs of these surfaces. For surjaces enclosing particles, the quanlity is sllown to be velated to the probable tlurrrhev ot particles intevcepted by a random platne and, under certain conditions, to the perimeter of their Projected image and to the increuse in surjace area when the particles grow. Many of the velalionsl~ips are valid for any shape or size of the particles. THE recent growth of the field of stereology or quantitative microscopy is largely the result of the discovery of a limited number of rigorously defined geometrical parameters that can be precisely measured on random sections or projections of a structure without assumption about particle shape.' Such parameters have been the volume fraction and surface area and line length in a unit volume. The present paper introduces the average of the mean curvature of surfaces in a volume, and shows that it can be rigorously measured by counting methods alone. AVERAGE CURVATURE ON A PLANE Consider a curve y = v (x) on the xy plane. The curvature Kp in the plane at any point is given by Kp = (dZy/dx2)/[1 + (dy/dx)2]3/2. The average curvature along the curve may be defined as Kp = (1/L) fKpdl |1] where dl = [(dx)' + {dy)2]1/2 is the length of an element of the curve and .(dl = L is the total length of the curve. The integral on the right-hand side of Eq. [l] will be called the total curvature, It is dimensionless and readily evaluated by substituting d = arctan (dy/dx) to give ah which is the change in direction of the tangents to the ends of the curve, Fig. 1. Hence, Kp = (1/L)(?h) [2] It can also be seen that Eq. [2] is applicable in the limit of sharp corners. Even though the curvature is infinite at a corner, f Kpdl remains integrable and equal to the change of angle. The signs of the quantities Kp and dl are arbitrary and, if the areas adjoining the curve are equivalent, there seems to be no compelling reason to fix the signs. For a closed curve, however, it becomes worthwhile to use the signs to distinguish among different types of areas or phases enclosed. For such a closed curve AO = t2r and As a convention, we shall take the direction of the integration along the curve in such a way that the area or phase under consideration (henceforth called a) is kept to the left side of the curve, Fig. 1. Then Kp is positive where the curve is concave and negative where the curve is convex. For a closed curve Ad - +2n if the curve encloses a, and Ad = —2n if the curve is surrounded by a. PLANAR SECTIONS OF THREE-DIMENSIONAL STRUCTURE OF ISOLATED a PARTICLES Consider next a planar section of a microstructure containing particles of a in a matrix. We place no restriction on shape of connectedness of these particles, and begin by considering the curvature of only the boundary between a particles and matrix' Clumps of contiguous a particles are then treated as a single a particle. The two-dimensional section will show in a unit area na simple closed curves enclosing a particles and nh closed curves of holes, in-

Jan 1, 1968

By J. P. Heller, H. B. Bradley, A. S. Odeh

A potentiometric model technique is presented for determining the areal sweep efficiency of a five-spot well pattern, at and beyond breakthrough. A sharp interface between displaced and displacing fluids is assumed. Although the prototype svstem is referred to as a waterflood operation, obvious changes in the notation and computations will adapt the results to other displacement processes. The results of the study include the following. 1. Areal sweep efficiencies for a five-spot well pattern, at and beyond breakthrough, for mobility ratios (displacing to displaced fluid) of 4:1, 2:1, 1:1 and 1:4. 2. Extension of potentiometric analysis to the investigation of the areal sweep efficiency beyond breakthrough in a five-spot pattern by the application of conformal mapping and conductive-solid models. 3. The use of layers of conductive fabric in representing mobility ratio changes in potentiometric models. 4. The development of a probe mechanism for probing conductive solids. The results obtained by conductive-cloth models agree with earlier areal sweep efficiencies at breakthrough obtained by Aronofsky and Ramey 1 on the potentiometric analyzer using electrolytic-tank models. Results beyond breakthrough differ from those obtained by the X-Ray Shadowgraph technique. Data from this study show that, for mobility ratios greater than one, water cut rises rapidly as fluid is produced after breakthrough. However, for mobility ratios smaller than one, a large increase in area swept resulted with only a small increase in water cut. INTRODUCTION In calculating reservoir performance of waterflood-ing operations and other fluid-injection programs, it is necesssary to estimate the areal sweep efficiency * before and after injected-fluid breakthrough into production wells. Influence of mobility ratio on oil-production history, before and after breakthrough for a five-spot well pattern, has been studied by X-Ray Shadowgraph techniques 2-5 and by gelatin models.6 In none of these investigations was the transition zone controlled experimentally. Steady-state anaiog techniques assume that a vertical and discrete interface exists between the displacing and displaced phase. Thus, when using a potentiometric analysis, it is assumed that no transition zone exists. To determine the areal sweep efficiency beyond breakthrough for a five-spot well pattern using the potentiometric analyzer, four principal problems had to be resolved. These were the following. 1. The laborious method of representing changes in mobility ratio in electrolytic tanks by means of contoured wooden blocks. 2. Vapcrization of the electrolyte solution during the study causing concentration changes and, thereby, variable conductivity. 3. The scale-limitation problem 7 that is accentuated by abrupt eiectrolyte depth changes. 4. A wellbore geometry problem. EXPERIhlENTAL EQUIPMENT AND PROCEDURES CONDUCTIVE-SOLID MODEL The theory, equipment and procedural techniques of the electrolytic-tank potentiometric model have been treaced excellently by Lee8 and by Muskat.9 By the use of a conductive solid to represent the fluid conductivity of the porous media, the need for contouring wooden blocks to represent mobility ratio was eliminated. It was found that a carbon-black coated fabric, Uskon D-16,** could be employed as a fairly uniform conductive media. This material, when stacked in appropriate layers and pressed together, can be used to represent changes in mo-

United Engineering Trustees, Inc. WILLIAM H. BASSETT H. G. MOULTON R. M. ROOSEVELT The Engineering Foundation GEORGE D. BARRON E. DEGOLYER R. M. ROOSEVELT Engineering Societies Library Board ROBERT PEELE H. K MASTERS A. B. PARSONS, Ex-officio F. F. SHARPLESS R. H. SWEETEST

Jan 1, 1934

By A. F. Peterson

MUCH has been said and written about the engineer shortage. The mining branch in engineering has lagged during the past several decades. I can think of two institutions, formerly prominent in that field, that have discontinued this department and another that has branched from a purely mining school into various forms of engineering. Conversely, I do not recall any institutions that have added mining to their curricula. I believe that this action is in direct response to the demands of incoming students. But I also believe that while there is a specific demand for civil, mechanical, and electrical engineers in the highly complicated mining operations of today, our need for mining engineers capable of assuming top responsibility for mining operations is unchanged.

Jan 3, 1957

By M. T. Abasov

The work suggests an approach to the problem of optimally planning the drilling and development of gas fields. The approach is based on systems analysis and allows a joint optimal choice of the total number of wells in the field, their spacing in the reservoir, the diameter of production tubing, drilling dynamics, the number and spacing of drilling platforms and well pattern schemes for each plat- form as well. The optimal solution satisfies the set of technical- economical requirements and provides a minimum value of discounted total expenditures (capital costs plus operating costs). A mathematical model of the problem is presented. This work represents an extension of the authors&apos; previous investigations that formulated and solved problems of optimal drilling of oil and gas deposits by directional wells [1] and problems of optimal control of the number of active wells in multi-reservoir oil and gas fields [2], [3]. For construction of the mathematical model we choose a range (Nmin, Nmax) of possible values of the total number of wells, N, which should be drilled in the deposit. Here Nmin, Nmax are minimum and maximum numbers of wells correspondingly, that should be drilled into the reservoir. N[€](Nmin = N1, ... N[o], ..., Nm = Nmax). For simplicity a one-reservoir gas field is considered. It is assumed that: (a) wells are spaced in the reservoir uniformly, (b) there is a certain algorithm providing a uniform spacing of the given number N[o] ([0]=l, . . . , m) of wells in the reservoir, (c) the diameters of the production tubing for all the wells are the same. The relation Qz (x), i.e. the dependence of the cumulative output of gas from the cumulative "well-years" of operations is constructed for each diameter dZ from the given range of diameters d1< ...< dr.

Jan 1, 1977

By W. F. Hosford, E. W. Kelley

By testing polycrystalline specimens from textured plates which had Previously been used to provide materials for growing single crystals, it has been possible to relate the plastic anisotropy of textured materials to the deformation behavior of single crystals. The deformation studies have been conducted at room temperature on textured polycrystalline magnesium and binary Mg-Th and Mg-Li alloys. Variously oriented specimens of the textured materials were deformed in plane-strain compression and in uniaxial tension and compression. The stress-strain curves are similar in their general jorm of anisotropy and stress levels to those obtained on single crystals of the same alloys. The degree of anisotropy is lower, however, in the polycrystalline materials and correlates with the intensity of the basal texture. Yield loci for the textured materials appear reasonable in terms of the deformation mechanisms, and deviate sharply from the form predicted by the Hill analysis for aniso-tropic material. A N earlier study1 of single crystals has shown that magnesium and magnesium alloys with thorium and with lithium deform at room temperature primarily by basal slip, {10i2) twinning, and (1011) banding. The (10i1) banding mode is a combination of {10ll) twinning followed by (1012) twinning and basal slip within the doubly twinned material.2, 3 Magnesium with lithium can also deform by {1010)(1210) prism slip.1&apos;4&apos;5 Still other deformation modes have been reported for magnesium6-11 but these are considered to play a minor role in room-temperature deformation. In a polycrystalline material, plastic deformation must occur in the individual grains through the operation of one or more of the various deformation modes. Because the critical shear stress for basal slip is very low compared to the activation stresses for the other deformation modes,&apos; basal slip accounts for much of the deformation in the polycrystalline aggregate. However, since there are only two mutually independent basal slip systems, and because five independent systems must be active for an arbitrary shape change in any material,&apos;&apos; modes other than basal slip must account for some of the strain. The deformation of textured magnesium, like that of other hcp metals, must be controlled by the same mechanisms observed in single crystals. In strongly textured material, the form of the anisotropy should be similar to that of single crystals, and the degree of anisotropy should depend on the intensity of the texture. EXPERIMENTAL PROCEDURE The anisotropy of deformation was investigated through the use of plane-strain compression tests, as well as uniaxial tension and compression tests. Materials. Test specimens were cut from the three textured plates of magnesium which had previously been used to provide material for single crystals.&apos; These plates, furnished by Dow Chemical Co., had been reduced about 80 pct during the process of being hot-rolled to their final 1/4-in. thicknesses. The plates had the three respective compositions, pure magnesium, Mg-0.5 wt pct Th (0.49 pct Th by spectro-graphic analysis), and Mg-4 wt pct Li (3.84 pct Li by chemical analysis). Impurities other than iron were less than 0.0005 pct Al, 0.01 pct Ca, 0.001 pct Cu, 0.0006 pct Mn, 0.001 pct Ni, 0.003 pct Pb, 0.001 pct Si, 0.001 pct Sn, and 0.01 pct Zn. Iron was 0.001 pct in the pure magnesium, 0.002 pct in the Mg-0.5 pct Th, and 0.014 pct in the Mg-4 pct Li. The textures of the three plates were determined by X-ray diffraction utilizing only the reflection technique out to an angle of 50 deg from the sheet normal. The resulting basal pole figures are presented in Figs. 1, 3, and 5. Grain sizes in the plates were ASTM number 4 in the pure magnesium and number 7 in each of the alloys. Plane-Strain Compression Tests. Plane-strain compression specimens approximately $ in. thick by 4 in. wide by $ in. long were prepared for each of the three compositions. These specimens were prepared in a manner similar to that used for the single-crystal specimens of the earlier study.&apos; All polycrystalline specimens were stress-relieved at 500°F for hr as the final step in their preparation for testing. The testing procedure was identical to that used for the single crystals, involving compression in a channel and using 2-mil Teflon film as a lubricant. The specimens were tested in six orientations of interest, these being the six combinations of the rolling, transverse, and thickness directions of the material serving as loading, extension, and constraint directions in the plane-strain compression test. Each of the six orientations was assigned a two-letter identifying code. These are combinations of the letters (thickness direction), R (rolling direction), and T (transverse direction) with the first letter signifying the loading direction and the second letter the extension direction. For example, ZR specimens were compressed in the thickness direction while extension was permitted to operate in the rolling direction of the textured material. To facilitate comparison of the present work with that of the single-crystal study1 the orientations used for single crystals are given in Table I along with the polycrystalline orientations that most nearly correspond. To insure reproducibility, at least three duplicate

Jan 1, 1969