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By J. Douglas, W. T. Ford, G. E. Henderson, I. F. Roebuck

An implicit numerical method is presented for simulating the differential and algebraic relations governing one-dimensional three-phase flow in porous media. The method is based upon compositional representation of the hydrocarbon system. Variable physical properties and water-oil capillary forces are included in the formulation; however, the effect of gravity is ignored. The effects of changing composition and mass transfer are considered through the use of known phase behavior concepts and correlations. The differential and algebraic equations and the numeric approximations to these equations are presented, and the computing algorithm is discussed in detail. This method is used to simulate a single-phase, two hydrocarbon-component gas displacement laboratory experiment. The method is also applied in simulating a solution gas drive and a gas injection problem using a reservoir oil represented as a nine-component mixture. For comparative purposes, the latter two problems also are examined with a one-dimensional volumetric model. The results of the simulation of the laboratory experiment demonstrate the relevance of this method to problems wherein the effects of mass transfer significantly enter the displacement process. The comparison of the results of the volumetric and compositional methods applied to a reservoir system illustrates not only the advantages and benefits derived from examining the hydrocarbon system composition, but also the necessity of this approach in application to a general reservoir problem. INTRODUCTION The advent of large memory, high-speed digital computers enabled reservoir engineers and mathematicians to pool their knowledge in the development of sophisticated techniques for the prediction of oil and gas reservoir performance. These techniques have progressed from volumetric and trend analysis calculations to the development of "mathematical models", or reservoir simulators. These latter models, in general, utilize finite difference approximations to the rather complex partial differential equations that mathematically describe the physics and thermodynamics of fluid flow in porous media. Many forms of this "model" type are available today, and much of the recent literature has been devoted to either improving known methods or developing new techniques for use in these prediction methods. The more advanced techniques in use at this time consist of the solution of differential and algebraic relations that describe a reservoir geometry in one, two or three dimensions and that incorporate reservoir hydrocarbon and water fluid systems that obey specified physical laws, having properties that might easily be measured in the laboratory. This type of model utilizes formation volume factors and other volumetric data, expressed directly as functions of pressure, to represent the reservoir fluid system. Experience gained with this type of simulator, commonly known as a "beta-factor model", has indicated that the approach has many outstanding defects, most of them due to the assumption that those properties measured in the laboratory completely describe the behavior of the fluid system throughout the life of the project under study. The effects of varying hydrocarbon composition and mass transfer between the phases of this hydrocarbon system must, by definition, be ignored. These defects, which may often be ignored in

Jan 1, 1970

By P. W. Ramsey, G. L. Werley

THERE have been numerous examples in recent years of the similarity between aging behavior and diffusion behavior, where a plot of the logarithm of the aging rate versus the reciprocal of the absolute temperature yields an approximate straight line, analogous to a similar plot of the diffusion coefficient D (log D vs. 1/T). Austin and Rickettl have pointed out that this linear relationship holds empirically for the de- composition of austenite into pearlite and bainite in carbon steels, and Robertson' has shown similar trends in the aging of 24S-type aluminum alloys. Jenkins and Bucknall³ have also demonstrated the association between aging and diffusion rates for nickel-silicon-copper alloys. Jetter and Mehl,4 however, have shown that the maximum rate of dilation of a series of aluminum-silicon alloys does not show this linear relation and Mehl5 has pointed out that careful study of available knowledge indicates that "aging rates increase with temperature approximately exponentially, whereas D increases precisely exponentially." He further notes that "the rate of aging at a given temperature is the greater the lower the melting point of the alloy, which is also true for D." This paper describes the aging changes occurring in a zinc-25 pct manganese-15 pct copper-0.1 pct aluminum die casting alloy. It was found that this alloy does show this linear relationship and use was made of this relationship to estimate aging rates at low temperatures from data acquired at elevated temperatures. It should be noted that the aging reaction is being studied only indirectly, using changes in certain properties as criteria of the progress of the phenomenon. This alloy is purely an experimental one and is not available commercially. Zinc-Manganese-Copper System: The zinc-rich portion of the zinc-manganese-copper diagram which is of significance in the present work is quite uncertain. X ray examination of the alloy as die cast shows a phase similar to the epsilon phase (hexagonal close packed) of the copper-zinc system. All of the data accumulated indicate that the epsilon phase of the zinc-manganese-copper alloy is stable at high temperatures; that is, 500°C or above. Below this temperature a new phase is precipitated on annealing, and a decrease in specific volume occurs. At elevated temperatures this phase change occurs quite rapidly, while at room temperature the alloy has shown no change after several years. According to X ray data, this precipitated phase resembles the gamma phase (cubic) of the copper-zinc system, a hard and brittle structure. From examination of the microstructure and from X ray examination of the alloys annealed at

Jan 1, 1951

By Michael Perch

The fact that coal is a complex organic material and heterogeneous in composition has made its study extremely difficult, particularly in regard to obtaining a fundamental concept of the processes involved in the formation of coke. It has been stated recently that coals are natural polymers and that in a complex reaction such as occurs during carbonization the differences between coals are quantitative and not qualitative. Such being the case, it would be expected, therefore, that a series of coals subjected to exactly the same conditions of coking would produce results that should be related quantitatively to the chemical analyses of the individual coals. In the past, however, this fact was not generally recognized and consequently many empirical test methods were devised for testing coals. The interpretation of the results obtained depended upon comparing a set of data with other data on coals of known characteristics. The testing procedure had to be con- ducted in precisely the same manner each time and not the least requirement in making the interpretation was experience. The test methods varied from those utilizing a gram of coal to the plant-scale tests in which one or more ovens were charged with the test coal. The aim had been principally to find some simple, inexpensive means by which the coke-making and other properties of coal could be predicted. It is not necessary to emphasize the importance of these endeavors, for anyone acquainted with the problems involved in the selection of coals for making coke is well aware of the time and expense involved in making a series of definitive tests.

Jan 1, 1949

By L. Russell Van Wert

DURING an investigation in which the solubility relations of the phases in Muntz metal (60 per cent. copper, 40 per cent. zinc) were under study, certain phenomena that had no immediate connection with the main problem were observed, which were thought sufficiently interesting to study further. Because of lack of time, only a preliminary survey was made of two of these; namely, the cleavage structure developed under certain conditions in a 60:40 brass and abnormal grain growth in this alloy. CLEAVAGE STRUCTURE IN HEAT-TREATED MUNTZ METAL Carpenter noted many years ago that cold-working a brass of the Muntz metal type, which had been quenched previously from within the beta field, results in a partial breakdown of the supersaturated beta solution and the precipitation of the solute (the alpha solution) in the cleavage planes of the beta grains. This manner of rejection of a solute from a metastable solid solution is not peculiar to this particular alloy, for among others, it occurs in the cold-working of certain austenitic steels; for example, the austenitic nickel steels. In these ferrous alloys, cold deformation produces a partial decomposition of the austenite, with the formation of martensitic "needles" and zigzags in the austenitic poly-hedra. It is interesting to note that while the two solid solutions-austenite and quenched Muntz metal- are metastable and in their mode of decomposition behave quite alike when deformed in the cold, the metastability of each results from a different cause; viz., that of the austenite from the fact that it is a supercooled solution (its solvent, gamma iron, at ordinary temperatures is below its normal stable range) whereas the metastability of the quenched Muntz metal is the result of supersaturation.

Jan 1, 1929

By Gerald Edmunds

IN a paper1 before this Institute in 1940, the writer reported that the surface orientation texture of zinc and cadmium differed from the texture existing within the casting, in that basal planes were parallel to the surface. He was unable to rationalize the origin of this surface texture. It is conceivable that the surface orientation texture is influenced by the atomic force fields, which are different at the surface and within the body of metal. It was considered that a radical change in the surface against which the metal is cast might alter the surface texture. In trial of this, zinc has been cast against a surface of molten lead, but the same result has been obtained-i.e., (001) parallel, ±20°, to the surface-as was obtained when it was cast against air, Transite or iron.1 Into the bottom of an open cast-iron tray, 7 by 14 in. by 2 in. deep, preheated to about 275°C., about ¼ in. of lead, then) ½ in. of zinc was poured, and the whole was covered with an electric heater to enforce freezing from the bottom upward. After a lapse of time sufficient for the zinc but not the lead to solidify, the zinc slab was raised free of the molten lead. The bottom surface of the zinc casting was coated with a thin layer of lead. A specimen of the slab 1 ½ in. square was metallographically polished to flatten it and remove the slight film of lead, and the orientation was determined by the method used before,1 with the result stated above. Some determinations have also been made on other metals, as follows: Surface orientation determinations were made on the 3/8-in. diameter grip section of two ¼ -in, diameter aluminum-alloy die-cast tensile bars and on a 1/8 by ½ -in. flat aluminum-alloy die-cast tensile bar. None of these three aluminum die castings exhibited any preferred orientation at-the surface. A brass die casting (nominal composition: 60 Cu, 37.75 Zn, 1.00 Sn, 1.00 Pb, 0.10 Al, 0.15 Si) furnished by C. S. Smith was also examined. The surface showed a random orientation of alpha and beta. SUMMARY A zinc casting solidified against a molten lead surface was found to have the same surface orientation texture, (001) parallel to the surface, as other zinc and cadmium castings. Aluminum and alpha-beta brass die castings were found to have random grain orientation textures at the surface. ACKNOWLEDGMENT The X-ray determinations were conduced by M. L. Fuller.

Jan 1, 1945

By A. B. Parsons

AT the outset, the authors of this paper desire to file a disclaimer and an, explanation. They have no inside information from occult sources; neither of them feigns clairvoyant powers in the slightest degree. It is true that they have indicated on be graphs an approximate trend for the consumption of seven important mineral commodities up to the year 1954. At best this is a risky business; the figures do not pretend to be any- thing more than reasoned conjectures that are predicated on an attempt to evaluate some of the more obvious of the many factors that are likely to have a bearing on the future.

Jan 1, 1937

By Zay Jeffries

IT HAS been known for centuries that iron and steel could be hardened by cold hammering and that the metal could be restored to the normal condition by heating to a red heat and cooling either rapidly or slowly with nearly pure iron and slowly with steels containing considerable carbon. The art of tempering steels is also very old. When a medium- or high-carbon steel is quenched from a cherry-red heat, the hardness is increased; this hardness can be reduced by heating to various temperatures below the lower thermal critical point, which is near 700° C. The present paper will not consider these old and well-known changes in iron and steel below the thermal critical range but will confine itself to the more unusual changes, some of which have been studied recently. Stromeyer,1 for example, in 1886, reports that both working steel and heat treatment of steel in the blue-heat range are highly injurious. Recently, however, some metallurgists believe that the straightening of warped steel forgings at a blue heat produces a beneficial effect on the metal.2 The Engineering Division of the National Research Council has constituted a committee on Physical Changes -in Iron and Steel Below the Thermal Critical Range, which has the following personnel: R. R. Abbott, H. C. Boynton, William Campbell, J. V. Emmons, F. B. Foley, H. J. French, H. M. Howe, Zay Jeffries (chairman), F.C. Langenberg, J. A. Mathews, P. D. Merica, A. H. Miller, J. H. Nelson, G. A. Reinhardt, W. E. Ruder, H. F. Wood: This committee is studying several aspects of the physical changes in iron and steel. The results, reported in the literature and obtained by recent experimentation, will be given; this will be followed by a general theoretical discussion of the more important

Jan 2, 1920

I am much pleased by your presentation of my article and flattered to the extent that the cover design refers to it. Incidentally, as between folks who like to work with words, refer to line 6, second full paragraph, page 773 (August Mining Engineering) Would "for" preceding technological have changed the percentages in lines two and three of the bold-face heading on page 770? The intent was coequality among three, (studies of mankind, of science, and of technological empirics). Thirty-three pct for "man" studies is a pretty big bite for engineering schoolmen; 50 pct they won't even examine, let alone nibble at. Arthur F. Taggart For those of you without a copy of the August issue handy, the sentence referred to read: The plea herein is to make the overall time allotment for studies of mankind coequal with those, for science and technological empirics.... Professor Taggart suggests that insertion of the word "for" would clarify the intent of coequality among three divisions of study: The plea herein is ... for studies of mankind coequal with those for science and (for) technological empirics. Editor.

Jan 1, 1952

By Bert S. Sandell

Much has been said and written about the various uses of die castings, their applications in the various industries and their advantages and disadvantages. Examination of this literature, however, fails to disclose any data concerning the effect of temperature upon any of the physical properties of die-casting alloys. The uses and applications of die castings are so numerous, and of such a varied nature, that far too lengthy a manuscript would be required to list all of them. Brief mention of some specific cases will suffice to illustrate the temperature ranges in which certain die castings function. Automobile hardware, such as hub caps, door handles, radiator caps, etc., can be used as one example. Castings of this type are constantly exposed to varying climatic conditions, temperatures ranging from below zero to upwards of 100" F. Refrigerator parts, such as ice-cube trays, etc., form another example. Approaching the other temperature extreme, we encounter conditions such as are found in kitchens in which oven-heat indicator parts, cooking utensils, waffle grids, etc., embody use of die castings, where temperatures as high as 500" F. are often met with. Because of this variation in service temperatures, it was felt necessary to ascertain the effect of these temperatures upon the physical properties of die-casting alloys. The Charpy impact test was chosen first because of its simplicity, and because of the fact that brittleness is more likely to be objectionable in die castings than hardness or other physical properties. Alloys Investigated Two types of alloys were used in this investigation—zinc-base and aluminum-base alloys. Two alloys of each group were included. Those most generally employed in the industry at present were selected. Alloys A and B are of the same nominal composition, and correspond to A. S. T. M. alloy XXI, containing 4 per cent aluminum, 3 per cent copper, 0.1 per cent magnesium, and the balance zinc of 99.99 per cent

Jan 1, 1932

By E. C. Stephens

The eastern Washington— Idaho clay region stretches along the northeast margin of the Columbia basin for 150 mil es. The three better known and developed clay areas are Clayton, Wash., (2 miles north of Spokane); Mica, Wash., (10 miles southeast of Spokane); and Moscow-Deary-Bovill, Latah County, Idaho (about 80 to 90 miles southeast of Spokane) see Fig. 1. Clays from the eastern Washington— Idaho clay area have been mined for more than 50 years. At present Mica, Washington deposits are used by the Gladding—McBean & Co. to make a variety of bricks and ceramic products and Latah County, Idaho clays are used by the A. P. Green Fire Brick Co. to make refractories. The Anaconda Co. made an intensive investigation of the clay deposits in the northeastern Washington-!daho area in 1919 to determine the existence of a supply of raw materials from which alumina could be made. The greater part of the work, which included systematic drilling and shaft sinking, was concentrated at Mica, Wash. This was part of a research project carrted on by the Anaconda Metallurgical Research Dept. under the direction of Frederick Laist and F. Frick and it was terminated in 4920. V. D. Perry, Vice President and Chief Geologist for The Anaconda Co., in 1952 assigned the writer to make a preliminary study of clay and other potential sources of alumina ore in the Pacific Northwest with particular emphasis on those deposits which might be of future importance to The Anaconda Co9s. then new aluminurri plant at Columbia Falls, Mont.

Jan 1, 1961

By G. E. Frantti

UNDER the auspices of the Geophysical Committee of Michigan College of Mining and Technology, an investigation was made in Michigan's Upper Peninsula to obtain geophysical data" related to the regional subsurface geology in the area covered by Paleozoic sediments. The area surveyed includes that portion of the Upper Peninsula which lies between R18W to R26W and T41N and T49N, covering approximately 1300 square miles. On the index map, Fig. 1, it is represented by the cross-hatched zone west of Munising. Four of the five sites of detailed investigation are indicated by the letters A, B, C, and D. A detailed gravity and magnetic survey had previously been conducted by J. G. Wilsonz near Perkins, 8 miles north of Rapid River, on a local anomalous area. Results of his work, which showed a large positive magnetic anomaly associated with a gravity anomaly, aroused interest in the possible economic significance of the formations underlying the Paleozoic sediments in this part of the Upper Peninsula. Early in the 1900's the Michigan Geological Survey, as well as many private companies, had done a considerable amount of dip needle work near the southwest corner of the area discussed in this paper. Most of the information available to the writer was obtained from indicated magnetic anomalies on the geological map of the northern peninsula of Michigan. Results of the geophysical activities of mining companies in the vicinity of the Marquette range and Gwinn district were unavailable to the author. Physiography and Geography: The region under consideration has low to moderate relief. About half the area is comprised of swampy lowlands, and because of the swamps and forests much of the land is almost inaccessible. The major drainage system is dendritic, with streams flowing into Lake Michigan on the south and Lake Superior on the north. The general geology, shown in Fig. 2, indicates an overlay of Paleozoic sediments on pre-Cambrian formations along a line running approximately south from Marquette (not shown on the geological map). Actual contact between pre-Cambrian and Paleozoic sediments is not known because most of the area is covered with glacial till, and outcrops are very scarce. Exposures of the Paleozoic sediments show that these beds in the northern areas dip gently under Lake Superior and that in the southern areas they 'dip gently to the southeast. Outcroppings of the pre-Cambrian formations occur primarily to the west of the surveyed area except in the northwest corner where the Laurentian series outcrop as far east as the Gwinn district and also in T46N, R24W. Instrumentation: Gravity measurements were made with the Worden portable gravity meter. Since this was chiefly a reconnaissance regional survey, both the large and small dials were used. The instrument used had a constant of 0.0035 milligals per scale division, a working range of about 25 milligals.

Jan 1, 1957

By Kalervo Rankama

UNTIL a few years ago, geological mapping, the study of ore boulders, and different geophysical methods were the principal means used in the systematic search for mineral deposits covered by a layer of disintegration products or soil. These methods have been developed to a high stage of perfection as far as the geometrical definition of the conductor is considered. Use of geophysical methods in prospecting is based on the fact that an ore body differs from the country rock not only geologically but also in its physical properties. The general drawbacks and complications included in the use of geophysical methods are well known to everyone who has been using them, so need not be entered into here in detail. One of the more important ones is the fact that geophysical methods are unable to furnish information concerning the chemical composition of the ore bodies responsible for the indications. Further, the ores of many metals, such as silver, gold, beryllium, zinc, mercury, tin, lead, vanadium, antimony, chromium. molybdenum, tungsten, manganese, cobalt, nickel, and the platinum metals cannot be directly located by known geophysical methods, owing to lack of physical characteristics suitable for distinguishing them from the country rock. Thus it is quite natural that efforts have been made to develop direct methods for prospecting and locating ore bodies of the elements named. Known as chemical, biogeo-chemical, and geobotanical methods of prospecting, these have been much improved during recent years. A brief review of these methods and of some results obtained with them will be presented in the following, on the basis of available information and my own experience.

Jan 1, 1947

By Sherwin F. Kelly

THAT gold ores occur in Georgia is a fact apparently not widely known outside of that state, yet in the last hundred years nearly $18,000,000 worth of gold has been mined there. The discovery of gold-hearing quartz was made in 1823 on the "Forty Acre Lot" (which now belongs to the Columbia Mining Co.), in McDuffie County, and about seven years later the first stamp mill on record was erected near there. In recent years Georgia's gold production has dwindled to an insignificant figure. However, with the increase in gold price, interest in this district has been revived, so an electrical geophysical survey was undertaken to aid in discovering new quartz veins, on a part of the Forty Acre Lot, the adjoining Hamilton mine, and the nearby Woodall property.

Jan 1, 1934

By Robert Bakish, William D. Robertson

AFTER more than fifty years of investigation and continuing failure in service, a satisfactory mechanism to explain stress corrosion cracking in homogeneous alloys is still lacking. The relative chemical activity of grain boundaries and adjacent grains, inferred from the boundary structure, has been used to explain intergranular cracking in a brass.' This concept is probably correct as a general hypothesis, but it requires much more extensive development in order to explain satisfactorily the observed phenomena. For example, the specific function of the solute in an alloy must be considered, because intergranular failure does not occur in pure metals,' which are structurally similar to homogeneous alloys. Also, in this connection, an inter crystalline fracture path in binary copper alloys can be changed to a transcrystalline path by relatively small ternary additions.' The fracture path in ß brass is predominantly transcrystalline,' in contrast with an inter crystalline path in a brass. Whether the two different fracture paths are the result of a difference in composition, crystal structure, or the state of long range order is unknown and cannot be determined with ß brass, because only the ordered state can be obtained at room temperature. The study of chemical activity at structural sites in the Cu-Zn system is restricted by the formation of opaque films in an ammonia environment in which stress corrosion cracking is generally observed. Furthermore, both components of the alloy are chemically active and the interpretation of observations is therefore relatively complicated. The Cu-Au system is a better choice for the purpose of studying structural factors. In particular, CuAu is very susceptible to cracking in ferric chloride and opaque films are not formed in this solution; it may be obtained in different states of long and short range order; and, finally, only copper is oxidized in dilute ferric chloride, which considerably simplifies the chemical problem. To provide information necessary for a more general explanation of stress corrosion cracking in homogeneous solid solutions, the following structural factors have been investigated in a Cu-Au alloy having a composition corresponding to Cu,Au: 1) the effect of long and short range order; 2) the structural sites from which copper is removed from the annealed and cold worked polycrystalline alloy; and 3) the effect of annealing time and temperature on structural reactions in the cold worked alloy. Experimental Procedure A Cu-Au alloy of nominal Cu3Au composition was cast from cathode copper and high purity gold and fabricated into sheet and wire. Chemical analysis for copper and gold indicated 48.92 wt pct Cu and 51.01 pct Au. Quantitative spectrographic analysis indicated 0.01 pct Ag, 0.002 pct Pd, 0.001 pct Pb, and 0.002 pct Fe, with traces of magnesium, silicon, and zinc. Presumably most of the remaining 0.055 pct corresponds to the limits of analytical precision. Heat treatments of wire and sheet were conducted in argon or vacuum. Wire specimens, 0.064 in. diam, were heated for 1 hr at 850 °C to establish a definite

Jan 1, 1957

By J. B. Clark

In 1933, R. paris1 published a phase diagram for the entire Mg-Ca-Zn system. He reported the existence of a ternary intermetallic phase, Mg5Zn5Ca2, which formed a quasi-binary with the magnesium solid solution. Since then, no extensive work has been reported on the system. Recently however, indications of the existence of a second ternary in-termetallic phase in equilibrium with the magnesium solid solution led to a reinvestigation of the solid phase equilibria involving the magnesium solid solution. The 335°C (635°F) isothermal section was chosen for study. Metallography and powder X-ray diffraction were selected as the best mutually corroborating methods for determining the solid phase constitution. Seventy-six alloys were prepared from singly sublimed (99.95 pct) magnesium, electrolytic (99.95 pct) zinc and USP calcium. The analyses of some of the alloys are shown in Fig. 1. The alloys were melted in a graphite crucible under a chloride flu and chill cast in a split graphite mold. Dif-fusion couples (see Fig. 2) were prepared by casting molten Mg-20 wt pct Zn alloy around a cylinder of Mg-30 wt pct Ca alloy. The alloy samples and the diffusion couples were sealed under argon in Pyrex vials and annealed in a furnace capable of controlling within 1/2°C of 335°C. At the conclusion of the anneal, the alloy samples were quenched in ice water and the diffusion couples were air cooled. Procedures standard for magnesium alloys were used for metallographic examination. Powder X-ray diffraction patterns were taken on a G. E. camera with a 14.32 cm dim using nickel-filtered copper radiation. The redetermined 335°C (635°) section of the Mg-Ca-Zn phase diagram is shown in Fig. 1. TWO ternary intermetallic phases, designated w and

Jan 1, 1962

By Henry Louis

THE work performed by the Royal Commission on Mining Subsidence is likely to prove of permanent value, less perhaps for the conclusions it has reached and for the recommendations it has based upon these than for the admirable exposition which it affords of the law concerning mining subsidence and of the legal status of the person who has suffered damage by reason of such subsidence, as also of him whose working has caused the damage. The Commission was appointed by Royal Warrant in the middle of 1925 and delivered its final report in the middle of 1927. The terms of reference to the Commission were as follows: "To consider the operation of the law relating to the support of the surface of the land, and of buildings or works on or under the surface, by underlying or adjacent minerals; to enquire into the extent and gravity of the damage caused by subsidence owing to the extraction of minerals and the incidence of the resulting liability; and to report what steps should be taken, by legislation or otherwise, to remedy, equitably to all persons concerned, any defects or hardships that may be found to arise in existing conditions."

Jan 1, 1929

By Richard Miller

RECENT studies of creep have made it apparent that plastic deforma-tion may occur in metals under stresses less than the elastic limit as deter-mined from short-time tests. In summarizing conclusions drawn from creep tests by various investigators, Tapsell1 said: "It is evident that if a material has a true elastic range, the elastic limit must represent the maximum stress for no creep." The presence of a. definite elastic limit, represented in single crystals by a critical or threshold shearing stress, is claimed by Schmid2, Elam3 and others who have investigated the plastic deformation of single crystals. However, this "law of critical shearing stress" was deter-mined2 from short-time tests, and the measurement of the deformation was made with apparatus primarily designed to observe large amounts of plastic deformation, not to detect elastic changes. Experimental data recently obtained with highly sensitive instru-ments by A. W. Hanson4 on zinc and by Podaschowsky5 on rock salt indicate that the elastic range in single crystals is considerably narrower than formerly was supposed. Moreover, a theoretical possibility of permanent deformation, under the influence of even the smallest shear stress in single crystals above a certain temperature (Td), has been developed by G. I. Taylor6. This evidence seemed to warrant an examination of the elastic limit in large single crystals by means of creep tests. The first metal chosen for examination was zinc.

Jan 1, 1936

By P. D. White, J. T. Moss, J. S. McNiel

Results of experimental work on the in situ combustion process were first published in this country in 1953' when Kuhn and Koch described results of a three-well test in Jefferson County, Okla. Shortly there-after Grant and Szasz2 described field studies in Nowata County, Okla., in which several modifications of the basic combustion process were investigated by injection of various oxidizing gas mixtures other than air. In the past five years speculation concerning this method of oil recovery has continued, with a number of interesting papers on various aspects of in situ combustion appearing in the literature3,4,5,6,7. However, only one of these' provided actual engineering information on pattern-type field experiments. The primary objectives of the Oklahoma three-well test were to check operation of specially designed electrical ignition equipment and evaluate problems associated with initiation of combustion in a natural oil sand reservoir. Immediately following successful completion of this test in the Pontotoc sand, plans were activated for a second field experiment to be conducted in the same sand a short distance away. The objective of this second field test1 as to establish a relationship between field observations and information derived from laboratory experimentation and computations. Secondary objectives of the test were to develop operating tech- niques and define operating problems, and to obtain information that would assist in the economic and engineering appraisals of the process. Careful planning was required since this test was designed with the hope of providing basic information on the characteristics and operation of a combustion drive. It was necessary to include test facilities which would not only permit precise control and measurement of the process variables but would also provide sufficient flexibility of control to insure that variables in the combustion process could be studied during the course of the test under a wide range of conditions. In order to accomplish these objectives elaborate instrumentation and several control wells were included in the design of the test installation. This type installation was felt to be well suited for an experimental study, but was in no respect intended as a counterpart of a commercial-scale operation. PRELIMINARY LABORATORY WORK An important objective of the field experiment, as stated previously, has been to obtain reliable data on operating variables which might be compared with similar data obtained in laboratory combustion tests. The value of successful correlations between quantities that can be measured in the laboratory and those obtained in a full-scale commercial venture has been well established for other industrial processes. The difficulty of following a process underground should make such correlations even more essential here. Also. approaching the field test phase of development of in situ combustion, it was considered desirable to precede design of test equipment with laboratory combustion studies under a variety of conditions to establish likely ranges of variables. These included temperature, air injection rate, frontal advance rate and produced gas composition.

By R. C. Earlougher

Jan 1, 1970

By R. G. Bentsen, D. A. T. Donohue

The cyclic steam injection process has become the most widely applied and most successful thermal recovery technique in use today.1-4 Normally, steam stimulation is repeated several times during the life of a project. The problem is to select the optimum number and size of steam treatments so that the profits realized over the entire life of the project are maximum. Obviously, operating costs rise directly with the frequency and amount of steam injection. Operating efficiency, on the other hand, can be adversely affected if the amount and frequency of stimulation are insufficient. Thus arises a multistage decision problem; that is, a decision must be made at each sub-period (day, for example), as to whether steam should be injected, and, if so, how much. It is desirable that these decisions be made in such a way as to secure maximum net profit before taxes. This can be achieved by dynamic programming. To use dynamic programming, we must be able to predict not only the production rate-time curve resulting from a given stimulation, but also how changes in stimulation policy will affect this curve. In this study, the effect of steam injection on well performance is estimated on the basis of a simple model that takes into account both steady-state and transient flow. Oil production rate is calculated for both types of flow, and the larger of the two values is used. This allows the calculation to change to radial steady-state flow at such time as this mechanism becomes more effective than the transient mechanism. We propose to show how dynamic programming can be used to optimize the steam soak process with respect to net profit. For this, a mathematical representation of the steam soak technique is necessary. A further objective, therefore, is the formulation of a mathematical model capable of realistically simulating the physical process. Oil Production Response Model The advantage of using a mathematical model is its generality and ease of manipulation. However, the model must be an accurate representation of the physical process, for a solution derived from a model can be no better than the model itself. The question now arises as to how well the model should be expected to simulate reality. In general, the simplest model should be tried first, for additional accuracy is apt to require additional cost and time. Also, the search for a high degree of accuracy may yield only greater complexity and difficulty without yielding significantly better results. With this in mind, we kept our model as simple as possible, yet generally representative of the actual physical process. The number of state variables is limited to three, and stochastic variations in the parameters are ignored. As a consequence, use of this model should be restricted to cases in which the underlying assumptions are not severely violated. In

Jan 1, 1970