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By Rollin Farmin

Rock pressure against the supports for underground workings in certain mines becomes sufficiently severe to crush sound timbers. The cost of maintenance of these mines increases critically as the workings are extended. "Heavy ground " and "swell-jng ground" are terms commonly applied to a condition of excessive pressure from the wall rock. Defined for the purposes of this paper, "heavy ground" delivers gravi-tative pressure on the supports of a mint opening; "swelling ground" delivers pressure arising from expansion of the wall rock. Mining problems created by heavy ground have been studied extensively by mining engineers, as in the recent Symposium on Block caving.' A parallel study of rock bursts2 attacks the field of ground that ruptures under strain. The problem of swelling ground, which has received less current attention, is the subject of this paper. An ExaMPLe of Swelling Ground Severe cases of swelling ground are found in the gougy shear zones in mines along the western Sierra Nevada, where the veins are accompanied by faults through altered serpentine, schist and slate. For example, along troublesome stretches in the ldaho Maryland mine, Grass Valley, California, swelling ground continues to crush drift timbers, with diminishing intensity, for 3 to 10 years after entry. During this period, from five to nine generations of crushed timber sets must be replaced and a large additional tonnage of scaly rock and wet gouge must be removed from the drift to make room for this succession of new timbers. After "the squeeze has been taken out of the ground" the timbers will stand for years, until they collapse from decay. Heaving of floor and footwall along drifts develops soon after the timber sets are placed and frequent grading down of the track is necessary to keep it serviceable and to maintain headroom. If sills are placed under the drift posts, the sets break more quickly and the track becomes impassable at once. When the floor is left Open? and the bottoms of posts and stulls are pencil-pointed, the scaly ground of the fault zone swells up around the timbers (Fig. I) instead of breaking them (Fig. 2). A foot or two of this encroaching ground is trimmed from the floor and lower sides of the drift several times before complete retimbering is necessary. when a set of timber fai1s under the Pressure of swelling ground, there is no immediate fall of timber and broken rock to fill the drift, as is customary in heavy, caving ground. Instead, ground swelling from sides, top and bottom gradually closes the opening, over a period of weeks or months, and no especial hazard to workmen is present while they have room to walk through the narrowing drift. Most

Jan 1, 1946

By Horace Knerr

The term. "high-yield-strength," used in the title of Dr. Gillett's paper (p. 40) is obviously relative. His discussion is limited to improved steels intended to compete with the low-cost, low-carbon, hot-rolled, sheet and plate steels of commerce made and used on a tonnage basis, without heat-treatment. In his list of about three dozen steels, only three have a yield strength of 70,000 lb. per sq. in., or over. Double such values are not uncommon in aircraft steels. Dr. Jeffries (p. 21) refers to "light-weight metals," obviously meaning strong alloys of low specific gravity; namely, aluminum alloys of the duralumin type and certain magnesium alloys. In a structural material, "lightness" is determined by two factors, strength and specific gravity. They must always be considered jointly. The basis of comparison is a strength-weight ratio, obtained by dividing the desired strength value, such as tensile strength, yield strength, or endurance limit, by weight per unit of volume, such as specific gravity or pounds per cubic inch1. For example, aluminum is a heavy metal, structurally, unless alloyed and heat-treated to give it high strength. When the strength of a structural metal is raised by heat-treatment or by cold-work, its specific gravity is not appreciably changed, but it is made lighter in direct proportion to the increase in strength because less of it will be required to carry the load. The lightness of the finished structure of adequate strength is the real point of interest. This structure must not only carry designed load, but "stand the gaff" of service, which includes the effects of accidental overload, fatigue, corrosion, loosening of joints, and so forth. Neither Dr. Gillett nor Dr. Jeffries mentions the true "lightest material of construction," which is alloy steel, tubular in form (Fig. 1), assembled by welding and heat-treated to a yield strength in excess of 150,000 lb. per sq. inch.

Jan 1, 1936

By B. M. Larsen

SEVERAL articles have recently been published discussing the conditions necessary for accurate measurements of temperatures in the open-hearth steel furnace. In the course of a study of refractories service conditions in steel furnaces, the present writers have taken tempera; tunes in several open-hearth shops in the Pittsburgh district. The conclusions, as to conditions necessary for accurate measurements of temperature, are somewhat at variance with those of other investigators. The subject is closely connected both with the close-control of steel-making and the prevention of overheating of the silica refractories used in roofs and walls. It is becoming more and more important to obtain furnace temperatures of fairly definitely known accuracy. At present, the most useful instrument for such measurements is the disappearing-filament type of optical pyrometer. This method of measurement has formed the basis of most other discussions on the. subject and was also used by the writers.

Jan 8, 1926

Jan 1, 1955

LINN BRADLEY, H.' D. EGBERT and W. W. STRONG (communication to the Secretary*).--In the discussion of the paper, a request was made for a further explanation of the curves given on Chart I. In preparing the curves given on this chart, a typical blast-furnace top gas having the following composition by weight was assumed: Per Cent. C02 21.00 CO 24.00 Hz 0.25 CH4 0:25 N2 54.50 For any given top-gas temperature, Curves A, B, C, D, and E indicate in British thermal units the sensible heat lost in cooling the top gas to 60° F. by wet-cleaning methods. Top-gas temperatures are plotted as abscissae, sensible heats above 60° F. in British thermal units are plotted as ordinates, and separate curves are drawn for top gases carrying various amounts of moisture. For any given stove exit-gas temperature, curves A1,-B1, C1, D1, and E1, indicate in British thermal units the sensible heat carried out of the stoves by the moisture which is left in the top gas when it is dry-cleaned and enters the stoves hot. This moisture is removed when the gases are wet-cleaned and the sensible heat which it carries out of the stoves is therefore saved. As before, separate curves are drawn for top gases carrying various amounts of moisture. The curves in Fig. 1, therefore, indicate graphically how much more sensible heat is conserved by cleaning the top gases by the dry-hot method than is conserved by cleaning the top. gases by a cold-wet method and thus removing the greater part of the moisture carried by them. They also show of how little moment it is from a heat conservation standpoint whether or not the moisture carried by the top gases is removed before they enter the stoves. That wet cleaning secures the removal of this moisture and is thus to be recommended from a heat conservation standpoint is an argument often advanced by advocates of wet cleaning. The curves of Fig. 1 show how fallacious such an argument is.

Jan 6, 1917

Jan 1, 1882

By R. H. Hiltz, R. W. Douglass

Large-grain specimens of iodide titanium prepared metal-lographically were stain etched using the technique of New York University as modified by Watertown Arsenal Laboratories. Orientations of grains showing an abnormal response to stain etching were determined by back-reflection X-ray techniques. X-ray results showed that a-titanium grains, oriented such that their basal planes were parallel to the polished surface, have a slower reactivity to stain etching than any other orientation. Grains oriented such that their basal planes made small angles with the polished surface exhibited reaction rates between that of the true basal orientation and the normal rate. As the angle with the surface increases the reactivity increases up to a maximum angle of 14 deg. Basal planes making an angle with the surface of greater than 14 deg show normal reactivity to stain etching. These data, plus work on polycrystalline specimens, indicate that the oxidation rate of titanium might be reduced by correct alignment of crystal planes. ThE earliest observed phenomenon in the micrography of titanium was the occurrence of a grains which exhibited no birefringency. Even though a titanium possesses a hexagonal-close-packed structure and should be optically anisotropic, it can appear optically isotropic, when the crystal is so oriented that its intersection with the polished surface is perpendicular to the axis of symmetry. During the develoment of color staining techniques for titanium: it was noted that the a phase did not stain uniformly. Staining of specimens of commercially pure titanium resulted in a micro-structure of blue-colored grains, among which were randomly oriented a few grains exhibiting colors between the initial yellow and the final blue color. Under polarized light, these off-colored grains appeared to be optically isotropic. More intense study with polarized light, however, showed only the yellow grains to be isotropic. The intermediate colored grains exhibited weak birefringency, which at first glance is not detectable due to the strong birefringency of the surrounding structure. Aminoff2 and Straumanis3 have previously shown that in zinc the basal orientation is less reactive than other orientations. Leidheiser4 showed the same thing to be true for the hexagonal-close -packed configuration of cobalt. Thus, it would appear that the basal-plane orientation is responsible for the abnormality in stained titanium. Later work by Leidheiser5 on cobalt has shown that other planes besides the basal plane exhibited reaction rates slower than the normal rate. Reported planes were the (100), the (1011) and several planes making small angles with the basal plane. The last observance appears not to be due to the reactivity of the reported plane but due to the reactivity of the basal plane which is very close to being parallel to the surface. There are, then, two possible explanations for the range of colors observed in stain-etched a titanium. Since extensive research on the effect of orientation on surface reaction has failed to provide any definite trend, these two explanations are not adequate in themselves. Planes showing the retarded reactivity differ not only for different crystal structures but for metals of the same crystal structure and even for different reactions of the same metal. Tragert,6 Leidheiser,7 Tammann,6 and wagner9 have shown copper to exhibit retarded reactivity on the (111) plane. However, Leidheiser10 has shown that under other conditions the retarded reactivity of copper is associated with the (100)

Jan 1, 1960

By R. A. Anderson, O. D. Sherby, J. E. Dorn

Solid solution alloying increases the plastic properties of aluminum at elevated temperatures by solid solution strengthening, by restraining recovery and recrystallization, and by a Cottrell effect. When binary aluminum alloys are strained and aged at 1940° to 300°K they develop a yield point. This is attributed to a migration of dislocations to solute atoms during aging. IN view of the ever expanding interest in applications of metals and alloys to high temperature service conditions, it becomes increasingly important to be cognizant of the effect of various metallurgical factors on the strength of alloys at elevated temperatures. One problem of wide interest, not only because of its engineering significance but also due to its fundamental scientific importance, is the elucidation of the effect of alloying elements on the plastic properties of homogeneous a solid solutions at elevated temperatures. It is indeed astonishing to note that in spite of its importance, and in spite of extensive random testing of alloys at elevated temperatures, no systematic investigation has been reported yet on the effect of alloying additions on the plastic properties of a solid solutions at elevated temperatures. This deficiency in our knowledge prompted the investigation described in this report. Rather extensive data are currently available on the effect of alloying elements on the plastic properties of a solid solutions at atmospheric and sub-atmospheric temperatures. Such data might be ex- trapolated to higher temperatures and reasonable guesses might be made regarding the influence of such factors as recovery and recrystallization in order to hazard a qualitative estimate of the effect of alloying elements on the plastic properties of a solid solutions at elevated temperatures. Such

Jan 1, 1952

The following is an incomplete list of members and guests who called at Institute headquarters between Nov. 10 and Dec. 10, 1917. Harlan H. Bradt, Duluth, Minn. Lt. Geo. H. Morgan. Albert Burch, San Francisco, Cal. F. W. Osborn, Ajo, Ariz. J. A. Daniel, Institute of Mining & Metal- J. C. Ray, 2d Lt., 0. M. C., N. A. lurgy, London. A. E. Ring, Creede, Colo. Martin Fishback, Benson, Ariz. Geo. B. Rodgers, Dobbs Ferry, N. Y. E. L. Foucar, San Francisco, Cal. Forest Rutherford, Pueblo, Colo. I. A. L. Henderson, Institute of Mining & J. G. Scrugham, Reno, Nev. Metallurgy, London. A. F. Shurick, Forest Hills, L. I., N. Y. Jerome A. Hilbert, Santa Monica, Cal. Arthur C. Spencer, Washington, D. C. B. B. Hood, Chrome, N. J. Robert C. Sticht, Mt. Lyell, Tasmania. J. C. Hoyt, Jerome, Ariz. A. Perry Thompson, San Francisco, Cal. A. F. Kennedy, Duluth, Minn. J. B. Tyrrell, Toronto, Canada. Paul S. King, Wilmington, Del. Thor. Warner, Phoenix, Ariz. Alfred C. Levis, Golden, Colo. S. F. Wellman, Cleveland, 0. A. F. Lucas, Washington, D. C. Gardner F. Williams, San Francisco, Cal. B. E. McKechnie, Sharon, Pa. W. G. Woolf, Salt Lake City, Utah.' A. N. Mackay, Barranquilla, Colombia. C. W. Merrill, San Francisco, Cal. P. G. Beckett expects to be located in New York for some time, and may be addressed care of the Phelps, Dodge Corporation at 99 John Street. Corey C. Brayton and E. R. Richards have temporarily closed their San Francisco offices in order to give more time to their operations at Midvale, Utah.

Jan 1, 1918

By Perry Olcott .

THE Taka oil field is in the northern part of Titus and Franklin Counties, in north- eastern Texas. The small town of Talco, from which the field derives its name, is on the P. & Mt. P. R. R., about 15 mi. north of Mt. Pleasant, the county seat of Titus County. The oil field extends east and west from the town of Talco, the approximate center. In May, 1924, R. L. Cannon, while doing surface geology for the Humble. Oil & Refining Co., mapped the surface trace of this fault structure as evidenced by Upper Midway faulted down against Lower Midway. In the interval of sixteen years between the original surface work and the recent productive well completion, approximately eight wells were drilled into the Woodbine sand without success. The structure was well defined by those tests and all of the wells en-

Jan 1, 1936

By R. F. Jones, N. E. Truitt, M. Prats

In most published discussions and theories of in situ combustion, the combustion fronts are assumed to be vertical. However, evidence from field tests leaves no doubt that combustion fronts often advance more rapidly along the top than near the bottom of a formation as a result of difference in density between injected air and formation liquids. The approximation proposed in this paper to determine the movement of the resultant tilted combustion surfaces states that the vertical rate of movement of combustion surfaces is proportional to the horizontal oxygen flux. Where self-ignition is possible, the proposed method demands that a secondary combustion surface exist around production wells which produce some oxygen. These secondary combustion surfaces may be formed long before the primary combustion surface can advance from injection to production wells. Heat liberated near production wells at these secondary combustion surfaces can contribute to an early increase in production rate. Results indicate that significant oil recoveries cannot be obtained from the usual flood patterns (five-spots, seven-spots, etc.) without producing large volumes of unused oxygen. Ideally, to increase oxygen- consumption efficiency, well patterns should allow oil production from a first line of production wells and gas production from more distant lines of producers. However, it may be desirable to produce some gas at all wells to support (and benefit from) active secondary combustion surfaces. Results indicate that the well spacing through which combustion can be advanced is larger than that predicted by other methods. A large number of production wells may still be desirable to take quick advantage of gravity drainage. From a comparison with results at South Belridge field, California, it appears that this method adequately describes oxygen concentration and temperature histories and combustion-front shapes. However, this method does not accurately locate the most advanced point of the combustion surface. There is some field evidence to substantiate the actual presence of secondary combustion surfaces at South Belridge. Use of the proposed method appears warranted at this time when lay-over of the combustion surface can be anticipated. INTRODUCTION The assumption of vertical combustion fronts has been embodied in all previous publicationsl-6 which use the movement of combustion fronts away from injection wells to determine the temperature and fluid distributions in the reservoir. The only paper concerned with a mathematical model of the combustion process in which a nonvertical combustion front is used was written by Gottfried.11 Actually, nonvertical combustion fronts have been observed in most in situ combustion field tests for which adequate data are available.7, 8, 6 In practice, the typical vertical extent of the burned zone decreases with distance from the injection well, and this burned zone is at or near the top of the sand body. In some cases, such as at South Belridge field near Taft, Calif., the combustion surface is almost horizontal over a very large area.8 Thus, for some years an obvious and serious gap has existed between theory (vertical fronts) and practice (tilted fronts). This is indicated in Fig. 1. Tilted combustion fronts such as observed at South Belridge8 sometimes result from the natural tendency of injected gases to rise to the top of an oil sand. An initially present gas cap, even if thin, would make apparent the effect of gravity segregation from the first, particularly since formations considered for in situ combustion field operations are generally selected for their

Jan 1, 1969

Edward K. Landis, Philadelphia, Pa.: In studying Mr. Thackray's paper it seemed that a critical comparison of the results from different methods therein reported would he of interest. For this purpose Table I. was constructed by grouping all determinations made by the same method, and the probable errors were calculated. In this table all chemists titrating with permanganate (A1, E, F, G and 0 of Mr. Thackray's paper) are classed under "Emmerton;" those titrating with nitric acid (C, J, S and Y) under " Handy; " those re Probable error of result: a, ±0.0008996; b, ±0.000694; c, ±0.00107; d, ±0.00115; e, ±0.000674; f, ±0.000473; g, ±0.003675; h, ±20.0007959; i,0.000.5098; k, ±0.0008303. Probable error of single determination: a, ±0.001989; b, ±0.001547; c, ±0.00214; d, ±0.0023;e, ±0.00116;f, ±0.000818;g, ±0.0019;h, ±0.00224; i, 40.00143; k, ±0.00234. The formula for calculating the probable error is 0.6745, where N (N— 1)' S is the sum of the squares of the differences from the mean and N is the number of determinations.

Jan 1, 1897

UNITED ENGINEERING TRUSTEES, INC James L Head, '51 E C Meagher, '52 Gail F Moulton, '53 ADVISORY COMMITTEE TO REAL ESTATE COMMITTEE Cleveland Dodge Herbert Hoover Paul D Merica HOOVER MEDAL BOARD OF AWARD Scott Turner, '56, Chairman Cadwallader Evans, Jr , '52 Paul D Merica, '54

Jan 1, 1951

By J. A. MacLellan, John C. Bowling, J. R. Davenport, G. M. Ellis

Six months out of the year the cold is always there, and it seems to be waiting for someone to make a mistake. The simplest things can shut down a multi-million dollar plant besieged with -40°F temperatures and a 40 mph wind. It takes only one man-door improperly latched to feeze up all the pumps on the bottom floor. Someone can poke a one inch hole in an outside wall in July and six months later, the whole plant is flooded because the main water line just froze up and burst. Some important things must be remembered in plant design for cold and remote areas. For one thing, everything in these areas is more expensive due to long and difficult supply lines. Fuel is expensive and would be a major cost item even if it were not expensive, due to the extended periods of low temperatures. Building volumes should therefore be kept to an acceptable minimum. Service areas, on the other hand, must be adequate, because maintenance generally has to be conducted inside in a heated area. Supply vehicles, for instance, have to get completely inside the building to unload. If you try to unload a supply vehicle with the door open at -50°F, you won't be able to find the vehicle for fog and if you take more than 5 minutes half the water lines in the plant will freeze UP.

Jan 1, 1972

By C. B. Dudley

IN the spring of 1877, the Pennsylvania Railroad Company became so dissatisfied with the average life and wear of the steel rails it was then able to procure, that it determined to make an investigation into the chemical composition and physical properties of steel rails, with a view, first, to answering the question why one steel rail has to be removed from the track after, perhaps, eight months' service, while another lasts ten years ; and, secondly, if this investigation succeeded in throwing light on this important subject, to use this information in securing better rails in the future. The results

Jan 1, 1879

By Bunting S. Crocker

Bunting S. Crocker (Executive Vice President, Kilborn Engineering Ltd., Toronto, Ont., Canada)-This is an interesting report on laboratory-scale testing with pebble charges in 12-in.-diam mills, and the author correctly concludes that useful laboratory testing can be done. In the opening paragraphs he states, "laboratory pebble-milling tests have been considered too difficult to perform and not relevant enough to the actual grinding situation"!! This is definitely not so! The writer published detailed tests done in a 12-in.-diam mill comparing pebble and steel balls in 1952 6 and again in 1954 7. We note that our review paper in 1963 was the only one mentioned in the References. The author states that "a smooth lining is more frequently used in commercial-scale pebble grinding." The writer has designed some 22 plants treating 134,000 tpd in North America and Australia. He has also visited pebble installations in Norway, Sweden, Finland, and South Africa. All these plants correctly use heavier lifters than would be considered standard for ball mills of a similar size. Smooth liners are not recommended in wet ore treating plants. In the 1952 paper6 it was clearly demonstrated in the test work that the individual ore pebbles had to be the same weight-not the same diameter or size-as the steel balls if comparable grinding results were to be obtained. In the tests performed in this study most of the pebbles "passed 50-mm round hole screen openings and remained on a 40-mm round hole sieve. Correspondingly most of the ball mill experiments were performed with 50 or 40-mm steel balls". Thus, the balls and pebbles were essentially the same size or diameter. This means we are comparing apples and oranges. When the feed being ground is fine enough the pebbles will be superior. When the feed is coarse the steel balls will be the better. This is similar to grinding tests in which two sizes of steel balls are compared. In the middle of the article, "Crocker5 has reported that equal weights of pebbles and steel balls achieve the same grinding capacities under similar conditions …", then he proceeds to question this postulate. In the eight reports that I have published, I have never made this statement. What I have said is "for comparable grinding, the individual pebbles in the mill charge should be the same weight as the individual steel balls." This is not the first time that I have been misquoted on this point! It is most unfortunate that this test work has been done with a ball and pebble of the same diameter and not the same weight. It is impossible to properly evaluate the results. I also regret the fact that the screen analyses of the tests were not shown. Many of us who have been 40 years or less in the grinding game can easily read screen analyses at a glance. We can tell whether the top meshes are being ground by the ball charge, etc., etc. The graphs are fine for the summary or to illustrate conclusions but are often misleading in the report itself. However, we do agree that useful pebble grinding tests can be done in a 12-in. mill.

Jan 1, 1973

By Frank E. Shepard

Electric power in mining-operations is now successfully applied to haulage, hoisting, lighting and pumping; and until lately, drilling was the one department of mining in which an electric source of energy had not been introduced. Drilling by electric power has been the field for much investigation and several forms of electric-drills have been tried; but in the severe service of rock-drilling many dieculties have been encountered, and the heavy cost of repairs has caused a deep prejudice against this system of drilling. In the majority of electric rock-drills previously placed on the market, two principal factors have been considered; first, a portable electric motor usually of heavy pattern, coupled to the driving-mechanism of the drill proper by means of a flexible shaft; and second, the coupling of some form of reciprocating cross-head to a piston by means of a spiral spring, the drill-bit being fastened to the piston-rod by some suitable form of chuck with fastening bolts and nuts. In this latter form of drill, the cross-head has a fixed stroke, while the piston with drill-bit attached is allowed a variable stroke through the

Jan 1, 1904

By H. Margolin, E. Ence

In order to understand the effect of zirconium on properties of Ti-Cu-A1 alloys, Ti-Zr alloys were examined for the presence of ordering or compounds at the following compositions in weight percent: 24.1 pct Zr (lZr:GTi), 32.2 pct Zr (lZr:4Ti), 38.8 pct Zr (lZr:3Ti), 49.0 pct Zr(1Zr:ZTi). Alloys were prepared as 15-g buttons by non- consumable arc melting under argon atmosphere from Bureau of Mines titanium (Bhn 63) and Reactor Grade zirconium (Bhn 150). Weight losses during melting did not exceed 1 pct of the initial button weight. Prior to heat treatment, buttons were hot-rolled at 600" to 700°C to rods of about 6 mm diam. Contamination after hot-rolling was found to extend to a depth of less than 0.5 mm. Specimens for heat treatment were wrapped in molybdenum sheet, annealed in argon-filled quartz capsules, and quenched by breaking the capsules under iced brine. Annealing times were as follows: 700°C — 7 days; 600°C— 14 days; 575°C-1 and 2 months; 525°C-2 months; 500°C-2 months. Prior to heat treatment, all Ti-Zr alloys were vacuum annealed at 900°C to remove hydrogen. The reanneal of 575°C specimens for an additional month produced no observable microstructure changes. The results obtained by microstructure and X-ray diffraction are shown in Fig. 1, together with data of Hayes et al.' No other phases than a or P were found. Small amounts of retained P were detected by X-ray in the 49 pct Zr alloy. The data of the present investigation suggests that ß and a transus boundaries are at considerably lower temperatures than those of Hayes et al. The work of Hayes et al. is based on sponge titanium and Bureau of Mines zirconium, both of which contained 0.15 pct 0. Since melting was performed in

Jan 1, 1962

By M. Sheffield

This paper presents a technique lor predicting the flow of oil, gas and water through a petroleum reservoir. Gravitational, viscous arid capillary lorces are considered, and all fluids are considered to be slightly compressible. Some theoretical work concerning the fluid flow in one-, two- and three-space dimensions is given along with example performance predictions in one- and two-space dimensions. INTRODUCTION Since the introduction of high speed computing equipment, one of the goals of reservoir engineering research has been to develop more accurate methods of describing fluid movement through underground reservoirs. Various mathematical methods have been developed or used by reservoir engineers to predict reservoir performance, 193-5,7,8 The work reported in this paper extends previously published work on three-phase fluid flow (1) by including a rigorous treatment of capillary forces and (2) by showing certain theoretical mathematical results proving that these equations can be approximated by certain numerical techniques and that a unique solution exists. DISCUSSION The method of predicting three-phase compressible fluid flow. in a reservoir can be summarized briefly by the following steps. 1. The reservoir, or a section of a reservoir, is characterized by a series of mesh points with varying rock and fluid properties simulated at each mesh point. 2. Three partial differential equations are written to describe the movement at any point in the reservoir of each of the three compressible fluids. All forces influencing movement are considered in the equations. 3. At each mesh point, the partial differential equations are replaced by a system of analogous difference equations. 4. A numerical technique is used to solve the resulting system of difference equations. Capillary forces have been included in two-phase flow calculations.1,4,8 The literature, however, does not contain examples of prediction techniques for three-phase flow that include capillary forces. Where capillary forces are considered, each of the three partial differential equations previously discussed has a different dependent variable, namely pressure in one of the three fluid phases. Therefore, three difference equations must be solved at each point in the reservoir. Where large systems of equations must be solved simultaneously, an engineer might question whether a unique solution to this system of equations actually exists and, if so, what numerical techniques may be used to obtain a good approximation to the solution. It is shown in the Appendix that a unique solution to the three-phase flow problem, as formulated, always exists. It is also shown that several methods may be used to obtain a good approximation to the solution. The partial differential equations and differenceequations used are shown in the Appendix. Matrix notation has been used in developing the mathematical results. Two sample problems were solved on a CDC 1604. They illustrate the type of problems that can be solved using a three-phase prediction technique. SAMPLE ONE-DIMENSIONAL RESERVOIR PERFORMANCE PREDICTION A hypothetical reservoir was studied to provide an example of a one-dimensional problem that can be solved. Of the several techniques available, the direct method of solution as shown in the Appendix was used. The reservoir section studied was a truncated, wedge-shaped section, 2,400 ft long, with a 6' dip. (A schematic is shown in Fig. 1.) This section was represented by 49 mesh points, uniformly spaced at 50-ft intervals. The upper end of the wedge was 2 ft wide, and the lower end was 6 ft wide. The section

Jan 1, 1970

By L. J. Murphy

The production of crude oil in the United States is exceeding consumption by one-quarter million barrels per day and, with the possibilities of West Texas, this condition of overproduction, unless controlled, is likely to continue for some time. The resulting low price of oil has caused the operator to observe closely his lease operating costs. The installation of more efficient and reliable machinery has followed and it can well be said that the art of producing oil is on the threshold of a new era. In this advancement electricity has played a leading part. This paper covers only the problem of electricity as applied to lease operation and does not consider other phases of the industry, such as drilling and pipe-line pumping, in which electric power has been utilized economically. In considering electrification of pumping wells, the first question the operator asks is whether or not his costs will be reduced and the second question is whether or not the production will be increased. The third question, although in effect it is closely allied to the first, is the cost of power. The last question can be answered only after a thorough analysis of operating conditions and a study of the power rates prevailing in the particular field under consideration. Within the past few years, the power companies have realized the desirability of a steady 24-hr, pumping load, have made their rates for oil-field service particularly attractive, and in general have shown splendid cooperation in assisting the oil companies in the satisfactory application of electric power to their leases. When everything is taken into consideration, the first cost is practically the same for electric drive as for gas engines when pumping on the beam with individual motors. This cost, at prevailing prices, should aver-age approximately $2200 to $2400 per installation when using 15 to 35-hp., two-speed pumping equipment, including motor and control, countershaft, motor house, belt, installation charges, and a prorated portion of the cost of transmission lines and transformers for serving a number of wells. Since there is practically no difference in the cost of the two installations, it is evident that electricity, to justify its consideration, must have a lower operating cost or produce more oil.

Jan 1, 1928