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The Institute conducts jointly with the American Society of Civil Engineers, American Society of Mechanical Engineers and American Institute of Electrical Engineers, certain activities as listed below, and is joint owner with them of certain properties situated at 29 West 39th Street in New York City United Engineering Trustees, Inc. When Mr Carnegie made his gift, "for the erection of a suitable union home" for the engineering societies, United Engineering Trustees, Inc (then United Engineering Society) was chartered un¬der Chapter 703, Laws of the State of New York, 1904, for "the advancement of the engineering arts and sciences in all their branches, and to maintain a free public engineering library " The Corporation was further empowered to acquire real and personal property and to use, maintain and occupy it, with the provision that any building erected by the Corporation shall be used perpet¬ually as a meeting place and headquar¬ters for the Founder Societies Thus the Carnegie gift realized the ideal of bring¬ing the engineering societies together under one roof, and the Corporation through its members nominated in equal numbers by the four Founder Societies had the necessary authority to act for the Founder Societies in their joint in¬terests in owning and operating for them not only Engineering Societies Building, but in the course of time, Engineering Societies Library, and The Engineering

Jan 1, 1952

By R. Al-Hussainy, H. J. Ramey

Previous gas well test analyses have been based mainly upon linearizations of ideal gas flow results, although a method for drawdown analysis based upon real gas flow results has been proposed. Linearizations based upon ideal gas flow require estimation of gas physical properties at Tome sort of average pressure, and implicitly involve the assumption that pressure gradients are small everywhere in the reservoir. A new real gas flow equation has been developed by means of a substitution which couples presTure, viscosity and gas law deviation factor. This sub-stitution has been called the real gas pseudo-pressure. Use of the real gas pseudo-pressure leads to simple equations describing real gas flow which do not contain pressure-dependent gas properties, and which do not require the assumption of small pressure gradients everywhere in the flow system. Equations required to determine flow capacity, well condition and static formation pressure from pressure drawdown and build-up tests with the real gas pseudo-pressure concept are presented. Also shown are applications of the real gas pseudo-pressure to back-pressure testing, the gas materials balance and rigorous determination of average gas properties for previous gas flow equations. Included are sample calculations for well test analyses. INTRODUCTION A recent study' of the flow of the transient flow of real gases in ideal radial systems showed that it is possible to consider gas physical property dependence upon pressure by means of a substitution called the real gas pseudo-pressure. The substitution has the advantage that it enables engineering solutions for steady and transient flow of real gases that are more accurate and general than those previously available. The solutions are particularly important for the case of gas flow in tight, high-pressure formations under large drawdowns. Even for more ideal flow conditions, the real gas pseudo-pressure concept leads to important rules for finding average gas physical properties pertinent for older well test analyses. Ref. I provides a detailed study of the theory behind the real gas flow correlations to be used in this paper. The purpose of this paper is to provide necessary engineering forms for use of the real gas flow results, and to illustrate applications. The following considers flow of real gases in an ideal radial flow system. It is assumed that: (1) formation thickness, porosity, water saturation, absolute permeability, temperature and gas composition are constant; (2) gas compressibility and density are functions of pressure as described by the gas law pv = znRT; (3) gas viscosrty is a function of pressure; (4) effective permeability to gas may be a function of pressure to account for liquid condensation; (5) condensate is immobile; and (6) the formation has no dip.

Jan 1, 1967

By F. W. Osterwald, C. R. Dunrud

Coal mine bumps are a serious hazard to life and property in the mines of east-central Utah. Research into geologic factors associated with these bumps indicates that the bumps are spatially and genetically related to structural and stratigraphic features. Some bumps are directly related to stress accumulation along faults, either from natural causes or as a result of mining. Frictional properties of bedding planes between coal and roof rock, and between some rock units within the roof, directly affect the deformation of coal ribs, and hence the incidence of bumps. These frictional properties are related to the lithology of the roof rocks as well as to the sedimentary structures within the rocks. Commonly a sequence consisting of 1/3 ft of carbonaceous silt-stone, about 2/3 ft of rider coal, and several ft of massive siltstone or sandstone overlies the main seam. The sequence causes difficult roof conditions in the mines, difficult mining conditions and, directly or indirectly, many bumps. The U. S. Geological Survey has studied the relationships between geological features and coal mine bumps at Sunnyside, Utah, for about six years. The work, which was originally undertaken at the request of and in cooperation with the U.S. Bureau of

Jan 1, 1965

By Michael Perch, Charles C. Russell

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 stated1 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 conducted 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. Several attempts have been made to derive formulas for such predictions. The relations of both ultimate and proximate analyses to coke physical properties and byproduct yields have been studied. Lowry and co-workers1 correlated statistically the U. S. Bureau of Mines-American Gas Association assay test results with coal analyses, using 90 coals and coal blends. Parry,² Spooner,3 and Gabinskii and Krym4 made similar correlations. Lowry concluded that there were definite relationships between the proximate analyses of the coals and the yields and properties of the products. Although this statistical study was made on test results from carbonizing coal in a cylindrical steel retort, the conclusions are important and provided one of the first steps in the simplification of this complex subject. Studies should be made of other references on this subject just cited. Studies of the coking process reported in the literature frequently were confined to a small number of coals, and very few have included coals from various ranks. It would seem logical, however, that a program for studying factors involved in the formation of coke should be based on a number of coals selected from each of the various classes or types of coking coal. The possible use of the scheme of classifi-

Jan 1, 1950

By H. Ries

INTRODUCTION OF the several interesting physical properties of clay which have claimed the attention of investigators in recent years, none is more important than the behavior of the material when heated to temperatures above those of dehydration. Some of the problems to be solved are: 1. The mineralogical changes that take place in firing. 2. The relation between temperature and change in constitution, shrinkage, porosity, etc. 3. The importance of the time factor, as duration of firing, either in reaching a given temperature, or of exposure to a constant temperature. Mineralogical Changes As a result of fusion, reactions take place between the constituents of a clay, which results in a reorganization of the mass, and the formation of new compounds. Of the new minerals developed, sillimanite is the one usually recorded, and has been referred to by a number of observers.1 There appears to he a difference of opinion, however, regarding the temperature at which it is formed. Thus. Klein2 notes that sillimanite forms only above. 1300° C., while Mellor claims that it can develop below 1200° C., the difference in results being conditioned by the time factor. In Klein's experiments the test pieces were fired in 12 hr., while in Mellor's, the temperature rose from 800° to 1180° in 24 hrs., and occupied the same time in cooling back to 800°.

Jan 9, 1917

By P. C. Kapur

An approximate but simple and practical solution to the discretized batch grinding equation has been obtained. The solution is based on a new grind function, a combination of selection and breakage parameters and particle-size distribution of the feed. The grind function, which is readily computed from limited experimental data, has significant implications for analysis of the particle-size reduction processes. Using the practical solution, three ball-mill comminution systems—dry dolomite, wet quartz, and limestone—have been simulated with acceptable precision. The application of the discretized batch-grinding equation1 to routine comminution analysis is frustrated by two principal difficulties. First, the selection and breakage parameters of the grinding equation must be computed separately. This is usually a difficult and uncertain task although, recently, a number of experimentally and computationally efficient strategies have been proposed for determination of these parameters?" Second, for actual computation, the solution to the batch-grinding equation becomes progressively tedious and unwieldly for finer particle-size range.1,2 The purpose of this part of the report is to present an approximate solution to the batch-grinding equation, which is practical in that it seems to overcome the aforementioned obstacles. The solution involves the concepts of a new grind function, a lumped parameter of the selection-breakage functions, and particle-size distribution of the feed, which is readily computed from a limited amount of experimental data.

Jan 1, 1971

By Andrew B. Crichton

THE oft repeated statements of the United States Geological Survey and the Bureau of Mines that the coal reserves in the United States are sufficient for 3000 yr have given us all a sense of security hard to disturb. If we discount that statement 66 pct, which to the uninformed seems drastic, we would still have 1000 yr supply, and why should mortal man worry about the difference between 1000 and 3000 yr supply of coal. That is exactly the attitude which many who should be better in- formed have taken toward the problem. A recent brochure "How Strong is America," by the New York Herald Tribune, states there is "no end to coal * * The truth is staggering * * U. S. has enough coal to last 4000 years." What the statement actually means is that the calculator got as high as 4000 yr and decided it was pointless to go on. The President's ERP Committee on Natural Resources and others in high places continue to assure the country of our superabundance of coal. In the past few days the “Wall Street Journal" carried an item from Director Boyd of the Bureau of Mines saying that within a hundred years we would need to triple our annual coal production of 6oo,ooo,ooo tons, making it 1,800,000,000 tons annually, and at that rate we had coal reserves sufficient for 1000 yr. In my humble opinion, we cannot now or ever produce 1,800,000,000 tons annually, be- cause we do not have the reserves in the producing districts to do it. Past reckoning in geology may be, as in the Psalms, a thousand years are as yesterday, but the future must be considered more realistically, and "a thousand years" is really a "heck" of a long time. In most developed areas, mining engineers can count the coal reserves in terms of a hundred years or less, and in some important areas now producing large annual tonnages in much under fifty years. They think when they hear of thousands of years coal reserves, reference is made to distant fields and "the fields are always green far away." The estimates of our coal reserves upon which we are relying were made in 1907 under the direction of Marius R. Campbell, Director of the United States Geological Survey. It is apparent this work was not well done. It was necessarily based on rather meager data because of the little development and prospecting as of that date. There were mistakes in the correlation of seams, and they assumed the continuity of thick seams throughout large coal bearing areas where coal often did not exist. The overstatement of coal bearing areas in the Campbell figures are common. The 1907 survey includes all coals over 14 in. in thickness to a depth of 3000 ft. The total coal reserves according to Campbell were 3157.2 billion tons. The production and mining losses that year would amount to -570 million tons and

Jan 1, 1948

By R. D. Nelson, F. E. Bowman

Evidence has been found for a (010)a?(111)B[102]a /,11[341]/B crystallographic relationship between the monoclinic a and B phases of plutonium during the a?B transformation. The results of an X-ray diffraction study, where [010] fiber textured a samples were used in the absence of suitable single crystals indicate that the (OIO)a planes become (111)B planes upon transformation under near-equilibrium conditions. The transformation strain along the fiber axis, which was the [010] direction, was measured dila-tomekically; the measured 8.5 pct expansion compares favorably with the 8.44 pct expansion in the in-terplanar spacing represented by the (010)a?(111)B relationship. From plots of the atom positions in each of the related planes, a correspondence was deduced between the [102]a, direction and the [341]B direction. Further analysis of the two lattice structures in the light of this relationship revealed a rotation about the [102] direction of 1 deg 43 min and a slight shearing in this same direction of about 30 min. THIS paper discusses the (B crystal structure of plutonium and the orientation relationship existing between the monoclinic a and B phases during the a?ß transformation. The kinetics of the a?ß and (3 — a transformations have received extensive consideration, and because of the crystallographic complexity of these phases, the question of the mechanisms by which these transformations occur is especially intriguing. Nelson and Shyne1 evaluated the existing experimental evidence and concluded, from the indirect evidence available, that both the ß ? a and a ? ß transformations occur by a martensitic process. Their data reveal the anisotropic nature of these transformations which suggests the existence of specific crystallographic relationships between the parent and product phases. In this paper, we are concerned with the confirmation of the existence of such a relationship resulting from the a ? ß transformation and the derivation of the crystallographic details necessary to specify it. EXPERIMENTAL RESULTS X-ray diffraction and dilatometric data were obtained from samples of a plutonium having a [010] fiber texture. These cylindrical specimens, approximately 1 cm in diam, were prepared by transforming the ß phase to a under the influence of a uniaxially applied compressive load.' The [0l0] direction is parallel to the direction of applied stress; it is also perpendicular to the (010) planes. This correspondence between the plane normal and the direction having the same indices is, in the monoclinic a plutonium structure, restricted solely to this (010)[010] combination. Such a specimen was mounted in an evacuated, elevated temperature specimen holder on an X-ray dif-fractometer so that the diffracting surface was perpendicular to the fiber axis. The a diffraction pattern, Fig. 1, taken at about 115ºC, revealed the predominance of the (020) reflection. This monoclinic, P 21/rn space group yields no (0k0) reflections when k is odd. The temperature was raised slowly to 160°C to effect the complete transformation to the phase; then it was lowered to 120°C so that a diffraction pattern of the ß could be obtained near the a = ß equilibrium temperature for direct comparison with the a at the same temperature. The (3 diffraction pattern, Fig. 2, obtained under these conditions showed a (222) reflection relatively much more intense than in the random pattern. The other reflections appearing with sig-

Jan 1, 1970

By Eric Jette

THE literature on the binary alloys of iron and silicon has been reviewed by Stoughton and Greiner.1 Another even more extensive and detailed survey of the present knowledge has been prepared under the auspices of the Alloys of Iron Research Committee by Greiner, Marsh and Stoughton. Since the latter survey has already been issued in its preliminary form, it will be unnecessary to review the literature in the present article. However, in this connection there should be noted the important work on the crystal structures of the iron-silicon alloys by Phragmén,2 who investigated the entire system, identified the various phases and determined the homogeneity ranges of these phases. It was evident in the surveys cited above that in the range from 0 to 15 per cent silicon, which includes the commercially most' important alloys, the results obtained by thermal analysis, microscopic examination and the determination of electrical, magnetic and mechanical properties were extremely confusing. From time to time various compounds between iron and silicon have been postulated to account for the results yielded by the classical methods, and much argument has ensued. It was presumed that if compounds occurred which are sufficiently diverse in their properties to account for the characteristics of the alloys, they should be recognizable as separate phases but satisfactory proof of this sort has not been found by thermal or microscopic methods. Contrib-uting to the confusion is the fact that the electrical, the magnetic and some of the mechanical properties are "structure sensitive"; i. e., they are influenced to a marked degree by the presence of minute amounts of impurities, the specific characters of these impurities, the grain size, the character of the grain boundaries, small general or local strains, etc. Thus interpretations of the discontinuities in the various property versus composition curves that identified these discontinuities with phase changes or compound formation have always been open to question.

Jan 1, 1933

By B. D. Cullity

AS methods for measuring fiber textures become more exact, it becomes justifiable to scrutinize an observed pole-density curve for evidence of minor texture components. These are disclosed by minor maxima or abnormally broad major maxima. One possible source of these minor components is twinning of the main component. In cubic metals and alloys, there are two kinds of twins: 1) Annealing twins in face-centered cubic metals. These are reflection twins on {Ill), and they can be expected to be present in recrystallization textures. 2) Deformation twins in body-centered cubic metals. These are shear twins on (112). Although usually formed only by impact, they might conceivably be present in the deformation texture of severely cold-drawn wire. Fortunately, both kinds of twinning lead to the same orientation relationships. It thus becomes possible to prepare a single list of angles between various planes in parent crystal and twin, which is helpful in examining pole-density curves for evidence of twinning in any cubic metal or alloy. Such a list of interplanar angles is given in Table I. This table consists of three parts, corresponding to the three major texture components—<100>, <110>, and <111>-most commonly found in the fiber textures of cubic metals. The table lists the angle between the pole of {hkl}, in either the parent crystal P or the twin T, and the fiber axis <uvu>. The crystals with <uvw> parallel to the wire axis are here

Jan 1, 1959

Large scale mining of Mesabi taconites may have moved nearer to realization with the arrival of the latest model Linde Jet-Piercing machine at Reserve Mining Co.&apos;s Babbitt, Minn. property. When the machine is placed in operation it is expected to pierce blast holes in the hard taconite beds up to 10 times faster than is possible with existing drilling equipment. The new primary blast hole drilling machine has been designated the JPM-3, and is the successor to the JPM-1, in operation at Erie Mining Co.&apos;s taconite mines at Aurora, Minn. The size of primary blast holes which can now be pierced has increased from a nominal 61 in. diameter to 71 in. diameter and maximum hole depth has increased from 35 ft to 47 ft. Development has progressed to where 71/2 in. holes can be pierced with the same speed as 61/2 in. holes. Piercing progress is controlled by electronic blowpipe descent controls. Other features of the JPM-3 include: automatic burner ignition from the operating cab; heated and air conditioned operating cab designed for all-year operation; mechanical improvements for sub-zero operation common to the Mesabi, and redesign of wearing parts for longer service with minimum maintenance. The 40-ton machine is self-propelled. Power, oxygen, and cooling water lines trail from the machine. Jet piercing is based on combustion products of oxygen and a liquid fuel such as kerosene. The flame, jetting from a burner at speeds of about 6000 ft per sec, disintegrates layers of spallable rock. The burner is cooled by water which is then directed through orifices around the periphery of the burner. The water changes to steam and carries the spallings out of the hole. The equipment used in Jet-Piercing is essentially a tractor-mounted blowpipe containing a combustion chamber and nozzle, which is in effect a miniature rocket motor, from which the supersonic combustion gases emerge to do their work.

Jan 1, 1952

By Sir James Kitson

By the courtesy of the President and Council of the American Institute of Mining Engineers, I have been invited to take the chair and open the proceedings of this congress. It is a graceful compliment to those members of the Iron and Steel Institute who are your honored guests at this moment—an acknowledgment of high consid-

Jan 1, 1891

By H. F. Moore

This paper gives a preliminary summary of results of tests on the resistance to fatigue under reversed stresses of steel subjected to cold-working and of tests to determine the effect of rest on the endurance of steel under reversed stresses. The tests of cold-worked steel were undertaken as part of an investigation by the National Research Council Committee on Fatigue Phenomena of Metals and were made by Mr. Moore; the tests to determine the effect of rest are part of an investigation now being made by Mr. Putnam. Both series of tests were made in the Materials Testing Laboratory of the University of Illinois. The preliminary results of these tests are reported now. because it is believed that test data on fatigue strength should be available at the earliest possible moment; however, it should be clearly kept in mind that this paper gives preliminary results and is intended to encourage discussion rather than to give final conclusions. Before giving the data of the tests, the writers will explain the term "fatigue strength" as used in this paper and will discuss briefly the method used in interpreting the test data of repeated-stress tests. The term fatigue strength, as applied to a material, may be defined as that maximum fiber stress that will cause fracture of the material after the repetition of any given number of cycles of stress, each cycle involving the variation of stress from a minimum to the above maximum. The fatigue strength, then, varies with the number of repetitions occurring in the lifetime of a structural or machine member and with the range of stress for each cycle of stress. The fatigue strength will be lower for a member in which the stress is completely reversed than for one in which the stress varies from zero to a maximum. In interpreting test data from fatigue tests under reversed stress, the stresses and corresponding numbers of repetitions required for failure are plotted on logarithmic cross-section paper. In 1910, Professor

Jan 2, 1919

By AIME AIME

This section contains announcements of general interest to the members of the Institute, but not always of sufficient permanent value to warrant republication in the volumes of the Transactions.

Sep 1, 1906

By R. M. Rose, C. S. Tedmon, J. Wulff

It is frequently of interest to study the influence of small quantities of interstitial impurities on the properties of various refractory metals and alloys.

Jan 1, 1964

By Samuel G. Lasky

FAULTING at Kennecott, with its attendant fracturing, is unusual, complex, and important. As study and knowledge of the various fault systems have progressed, appreciation of that importance has helped in the selection of proper horizons for exploration and in the avoidance of useless crosscutting and drifting. During the study of this faulting and fracturing, a suggestion concerning the formation of the ore-bearing fissures occurred to me. Further study in the available portions of the approximately 45 miles of workings in the Kennecott mines for the purpose of checking up the the suggestion led to the hypothesis which this paper will attempt to present. Briefly, the hypothesis may be stated as follows: The formation of transverse faults that stop against a main system is connected with changes in the strike or dip of the main fault, and such cross faults or fractures lie in the moving block of the main fault system and indicate a change in strike or dip of the main fault. It has been found that each kind of change tends to produce definite effects and that careful study of the evidence can often suggest the exact type of change. Outline of Kennecott Mines Geology The mines at Kennecott are on the northeast flank of a broad anticlinell where erosion has exposed the Upper Triassic Chitistone limestone resting conformably on the Permian or Triassic Nikolai greenstone.2 These two are the only formations exposed in the immediate vicinity of the mines that bear relation to the ore deposits. The Nikolai greenstone is a series of altered basaltic lava flows, the actual thickness of which is unknown. The Chitistone limestone is the ore-bearing formation. At its base is a bed of about 5 ft. of red, green, or black shale which shows strong evidence of movement wherever it is exposed underground—one of the

Jan 1, 1929

By W. A. Mudge, Paul D. Merica

One of the most prominent features of our present-day industrial development is the ever-increasing demand put upon materials of construction. Engineering ingenuity, within the past 25 years, has been unusually active, and in some fields at least engineers frankly say that engineering design has progressed as far as the limitations imposed by the properties of the present materials of construction will permit. Consequently, they are today demanding improvement in their working materials and seeking new ones, through the aid of which the present limitations of design may be overcome. The activity of this search is evident in all fields, but it is particularly so in that of structural materials required to be resistant to corrosion. The corrosion resistance of metals and alloys is never absolute and all-inclusive; a particular alloy will withstand some corrosive conditions well and fail utterly under others. Furthermore, other properties, physical and mechanical, required in conjunction with corrosion resistance vary considerably for different commercial applications. One wants a soft, ductile sheet metal resistant to atmospheric corrosion; another, a high-strength alloy resistant to sulfuric acid. The last decade has witnessed active and definite progress in the development of high-strength, corrosion-resisting alloys. In June, 1924, a symposium by the American Society for Testing Materials, on Corrosion-resistant, Heat-resistant and Electrical-resistance Alloys, disclosed no less than 60 commercial alloys the properties of which were described as being suitable for industrial service where corrosion resistance was a feature. Today the number of these alloys has been doubled, at least. In addition, economy in design and construction through decreased weight has given considerable impetus to the improvement of alloys of which the mechanical propprties may be improved by heat-treatment.

Jan 1, 1935

By Paul D. Merica, W. A. Mudge

One of the most prominent features of our present-day industrial development is the ever-increasing demand put upon materials of construction. Engineering ingenuity, within the past 25 years, has been unusually active, and in some fields at least engineers frankly say that engineering design has progressed as far as the limitations imposed by the properties of the present materials of construction will permit. Consequently, they are today demanding improvement in their working materials and seeking new ones, through the aid of which the present limitations of design may be overcome. The activity of this search is evident in all fields, but it is particularly so in that of structural materials required to be resistant to corrosion. The corrosion resistance of metals and alloys is never absolute and all-inclusive; a particular alloy will withstand some corrosive conditions well and fail utterly under others. Furthermore, other properties, physical and mechanical, required in conjunction with corrosion resistance vary considerably for different commercial applications. One wants a soft, ductile sheet metal resistant to atmospheric corrosion; another, a high-strength alloy resistant to sulfuric acid. The last decade has witnessed active and definite progress in the development of high-strength, corrosion-resisting alloys. In June, 1924, a symposium by the American Society for Testing Materials, on Corrosion-resistant, Heat-resistant and Electrical-resistance Alloys, disclosed no less than 60 commercial alloys the properties of which were described as being suitable for industrial service where corrosion resistance was a feature. Today the number of these alloys has been doubled, at least. In addition, economy in design and construction through decreased weight has given considerable impetus to the improvement of alloys of which the mechanical propprties may be improved by heat-treatment.

Jan 1, 1935

By R. W. Snyder, H. J. Ramey

This paper presents the results of applying the Buckley-Leverett&apos; displacement theory to petroleum reservoirs consisting of a finite number of layers. The layers are assumed to communicate only in the wellbores, and the reservoir may be represented as a linear system. Most previous investigations of this nature were limited by assumptions and by inconsistent calculation techniques. This study improves on previous work by applying the Buckley-Lev-erett displacement theory to a noncommunicating layered system where permeability, porosity, initial saturation, residual saturation and relative permeability vary from layer to layer in a logical and consistent manner. Gravity and capillary-pressure effects are neglected. A modification of the Higgins-Leighton calculation method was used in this study. Waterflood predictions were made with all properties varying, and then with only permeability varying using several inability ratios. These results were compared with the Stiles and Dykstra-Parsons predictions. It is shown that the latter methods generally give poor values for the breakthrough recovery and pessimistic predictions for the performance after breakthrough. Similar results were obtained for a gas-displacement case. lNTRODUCTION Field experience with immiscible displacement usually shows constant producing conditions until breakthrough of the displacing fluid. Then oil production continues at increasing displacing-to-displaced fluid ratios until the economic limit is reached. Three different ideal mechanisms are known that will produce this behavior: (1) relative permeability effects as described by Buckley-Leverett frontal advance theory,&apos; (2) vertical stratification as considered by Stiles,2 Dykstra and Parsons5 and others and (3) different path lengths involved in areal (two-dimensional) flow between wells as described by Dyes et al.4 Without question, a combination of these factors modified by formation heterogeneity and other known and unknown factors actually does control the behavior of real systems. This paper presents results of an investigation of certain factors that should affect performance but which have received little attention to date. In 1944, Law5 demonstrated that porosity and perme- ability are often found to have normal and logarithmic-normal distributions, respectively. throughout cored intervals in natural formations. This led to the concept of the noncommunicating, multilayered reservoir model for immiscible displacement. This model assumes that the reservoir is composed of a number of layers that communicate only at the wellbores. Each layer is individually homogeneous, but may be different from every other layer. Stiles&apos; presented one of the earliest applications of this model to waterflood performance. In addition, Stiles assumed that the initial saturations and relative permeabilities were the same for each layer, porosity was the same. displacement was piston-like, fluids were incompressible and injection into each layer was proportional to that layer&apos;s permeability capacity (permeability-thickness product). The last assumption would be true if the mobility ratio for the displacement were unity.21 Dykstra and Parsons" used the same model as Stiles, but rigorously included mobility ratios other than unity for piston-like displacement. Dykstra and Parsons used their general result to produce charts for log-normal permeability distributions between layers. Similarly, Muskat6 Pub1ished analytical solutions for linear and exponential permeability distributions. In 1959, Roberts&apos; described a scheme for calculating water-drive performance for the noncommunicating, layered reservoir model which considered two-phase flow in the displaced region. Roberts used the same model and assumed that the injection rate into a layer was proportional to that layer&apos;s permeability capacity, but that flood front locations could be evaluated from the Dykstra-Parsons results. These assumptions are inconsistent, and a material balance cannot be maintained except for a mobility ratio of unity. At the same time, Kufus and Lynch8 coupled Buckley-Leverett displacement theory with the layered model to provide an improvement of the Dykstra-Parsons method that was consistent. In 1960, Higgins and Leighton9 resented a numerical method for calculating waterflood performance also considering two-phase flow in the displaced region. The result was used to investigate variation in absolute permeability and oil viscosity. An excellent, detailed history of using the noncomrnunicating, layered reservoir model was presented by Nielsen.&apos;" The preceding techniques (and many related ones) were similar in that differences in initial saturations, residual saturations and relative permeabilities from layer to layer were neglected. It is well known that the irreducible water saturation is an important function of absolute permeability. Calhoun11 showed that the irreducible water saturation

By A. E. Nash

This title is somewhat of a misnomer, because it does not accurately describe the phase of heat generation and application coming within the scope of this discussion. This paper is concerned primarily with that particular phase of radiant-heat transfer sometimes erroneously referred to as "shielded" radiant heat, to differentiate it from the open radiant heat of either flame or settings, in which the actual source of the radiant heat is a small incandescent furnace composed of a highly conductive superrefractory, within whose walls the combustion of the fuel is completed. This small furnace is usually located directly in the furnace proper, and although its refractory walls do shield the heat-absorbing surfaces from contact with the gases of combustion, there is no interference with the radiant heat given off by the furnace itself. We do not believe it either necessary or advisable to shield or screen radiant heat when properly controlled and applied. We do believe it essential to prevent the excessively hot gases of combustion from coming in contact with those parts of the heat-absorbing structure that are already receiving heat at high rates by radiation. In connection with any process for the refining of oil with which we are familiar, we are convinced that it is most advantageous to transfer the maximum of the heat generated in the form of radiant heat, applied directly to the heat-absorbing surfaces without the interposition of any form of shield or screen to prevent or reduce the radiant-heat transfer. While the term radiant heat is broadly used to cover all heat energy transferred from one body to another by radiation, in contradistinction to heat given up by gases in direct contact with the heat-absorbing structure (convection) or transmitted simply by conduction, in furnace work it is perhaps more often limited to the heat rays given off either by

Jan 1, 1928