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By H. William Ahrenholz

The coal industry had another prosperous year in 1966. Since the turn of the decade, production has been climbing at an average rate of 6% per annum. Although the fast pace slackened somewhat, 1966 production showed a gain of almost 3 % over that of 1965. An impressive record can be drawn from the fact that output per man-day in 1966 was more than twice that of the early 1950's, and more than three times that of the early 1940's. And even though man-power requirements lessened, those men retained by the industry worked longer hours and benefited through higher hourly pay rates. However, cost to the customer increased a little. Such statements can only be made for a healthy industry -one that is constantly improving its efficiency. Coal currently provides more than 25% of the total U.S. energy output. About 50% of all U.S.- mined bituminous coal goes directly to the electric utility market. It should be noted that, now, well over one trillion kwh of electricity is generated annually. Dependence of the giant electric utility industry on coal is based on economy and an abundant, dependable supply of this fuel.

Jan 2, 1967

By Gill Montgomery

At this moment in the history of the world, the all- pervading and universally most important fact is that the world population is beginning to outgrow its food supply, and the United States has suddenly lost its ability to give away huge food surplus to any nation in the world with a food shortage problem. This, of course, means that, all of a sudden, our government must completely reverse its former bureaucratic stance regarding crop controls and agricultural price supports, to out-right incentives to increase farm production and bring more idle land into food-growing use.

Jan 2, 1967

By A. Z. Dimitroff

Immediate detection of methane buildup or of sudden liberation of large quantities of methane in the face area is essential to avert disasters in coal mines. Proper timely detection and handling of methane have always presented problems in extremely gassy mines, and these problems have been magnified by present accelerated mining methods. Strict rules and regulations have been established by coal-mining companies, States, and the Federal Government, which provide for periodic inspections for methane in face areas when electrical equipment is working. Other provisions require the operator' to shut down electrical face equipment and change or adjust ventilation when more than 1.0 percent of methane is detected. Nevertheless, human failure to detect such conditions has been responsible for numerous ignitions arid explosions Recognizing this fact, Marling J. Ankeny, former Director of the Bureau of Mines, proposed in 1958 the development of an automatic methane-monitoring device. He envisioned such a device as being entirely dependable, capable of giving a warning when a predetermined concentration of methane in air is reached, and capable of deenergizing the equipment and rendering it inoperative when a dangerous concentration of methane is present in the air. Such a device has been developed by the Bureau of Mines Health and Safety Research and Testing Center in Pittsburgh, Pa.

Jan 1, 1967

By Jack L. Henry

The monocarbide region of the ternary system U-C-O has been investigated at 1,700° C as the first phase of a more extensive study of a portion of the four-component system U-C-O-N. An area bounded by the following compositional limits in atomic percent was studied: U, 44 to 55; C, 30 to 60; 0, 0.2 to 20. Compacts composed of mixtures of uranium, graphite, and uranium dioxide powders were sintered at 1,700° C under an equilibrium pressure of carbon monoxide to produce uranium oxycarbide specimens having a variety of compositions. Sintered specimens were evaluated by X-ray, chemical analysis, and ceramographic techniques. Solid-solution boundaries and phase relations have been established, and the effects of composition on the lattice parameter as well as the decomposition pressure have been investigated. Oxygen can be substituted for carbon in stoichiometric uranium monocarbide to the extent of about 17 atomic percent at 1,700° C. The composition range of the oxycarbide solid solution extends from about 48 to 51 atomic percent uranium in the low oxygen region. Above 10 atomic percent oxygen the composition range narrows to less than 1 atomic percent uranium. Carbon monoxide exists as a gaseous phase in equilibrium with all compositions which contain oxygen. Five separate phase fields were found bounding the solid-solution area. Other phases within this portion of the system include uranium, uranium dioxide, uranium dicarbide, and uranium sesquicarbide. Decomposition pressures of oxycarbide compositions at 1,700° C have been found to vary from a few microns for stoichiometric and uranium-rich compositions to 35 torr for carbon-oxygen-rich specimens. Lattice parameters were found to depend upon the U to C + 0 ratio as well upon the extent of substitution of oxygen into the stoichiometric monocarbide lattice.

Jan 1, 1967

By Richard F. Link

The objective of this report is to explain a statistical method for the summarization, organization, and classification of multivariate assay and other data from the mineral industry. Multivariate data are those characterized by several measurements at each data point, such as assay data from a mixed metal mine, or blast furnace data. A specific method of linear discriminant analysis, the Mahalanobis d2 procedure, is explained, starting from elementary principles; the d2 procedure enables many measurements at many data points to be studied by investigating the interrelationships among the data. The relation of linear discriminant analysis to other statistical methods for treating multivariate data, in particular the eigenvalue technique of factor analysis, is also explained. Example analyses are made on data from the Frisco mine, San Francisco del Oro, Chihuahua, Mexico. The data comprise assay values for silver, lead, copper, and zinc taken at some 19,000 sample points distributed into 91 groups.

Jan 1, 1967

By Thomas C. Wilder

The concentration and activity of oxygen in liquid copper has been measured by the reversible galvanic cell: at 1100°and 1200°C for the concentration range of oxygen of 3 to 5600 ppm Measurements for approximately thirly alloys at each temperature indicate that the activity of oxygen roughly follows Henry's law, the activity coefficients of oxygen being 0.12 and 0.205 at 1100° and 1200°C, respectively. These results compare javorably with the results of seven other electrochemical and gaseous equilibrium studies on this system, the free energy of the solution reaction 1/2 O2 = O (7 at. pct in Cu, liq) being -18.10 * 0.30 kcal per gfw at 1200°C. Estimates of the standard molar free energy of formation of CupO(S) are also made. Praclicul consideration of this cell as an oxygen sensor for liquid metals is discussed briefly. SOLID mixed-oxide electrolytes which have a defect structure in the anion sublattice have recently become a very popular means by which the chemical potential of oxygen is measured at high temperatures. Since the pioneering work of Kiukkola and Wagner1 such electrolytes have been used in numerous cell studies for determining the thermodynamic properties of metallic oxides and oxy compounds, the partial pressure of oxygen in vacuum systems and other atmospheres, and the properties of oxygen dissolved in metals and alloys. The use of a solid electrolyte in a cell for a fast reliable method of oxygen determination in liquid metals would be a very important tool to the process metallurgist. In copper, for example, the oxygen content of the molten metal in the cathode furnace is a prime factor in determining the "set" or solidification profile of cast wire bars. In this investigation the activity of oxygen in liquid copper was measured by an electrochemical cell employing the electrolyte ZrO2 + 7 1/2 wt pct CaO. The cell used at 1100° and 1200°C was

Jan 1, 1967

By Leroy Dockter

The grinding characteristics of lignite in a ball mill were investigated. The variables studied were initial lignite moisture content, degree of in-the-mill drying, and lignite source. The mill tested was a pilot-p1ant-size conical ball mill which had a maximum output of from 80 to 180 lb/hr pulverized product depending on the lignite and test conditions. The capacity of the test mill ranged from 82 to 103 lb/hr depending upon mine source, in pulverization of as-mined lignite with minimum drying, The capabilities of the ball mill could not be correlated to Hardgrove index of the individual lignites or other observed physical properties. Predrying lignite from its 35 to 40 percent raw moisture content to about 10 percent moisture before grinding improved the mill capacity 87 percent, compared to an increase in capacity of 74 percent with in-the-mi11 drying to the same product moisture.

Jan 1, 1967

By W. B. Hickman, J. J. Pickell, B. F. Swanson

Many physical properties of the porous media-immiscible liquid system are dependent upon the distribution of fluids within the pores; this in turn, is primarily a function of pore structure, liquid-liquiri interfacial tcnsion and liquid-solid wetting conditions. The cnpillary pressure hysteresis process provides a means of investigating the influence of pore structure upon fluid distribution for consistent sur/acc conditions. Invcstigntiot2s indicate that residual non-wetting-phase saturations /ollozuir,g the imbibition process (i.e.,wetting phase displacing nor2-wctting phase) are dependent upon both pore structure and initial non-raetting phase saturation and suggest that residual fluid is distributed as Discontinuous ,globules, one to a few pore sizes in dimension, thrnugh the entire range 01 pore sizes originally occupied. It clppears that air-mercury capillary pressure dala adequntely rellect the distribution of fluiris in a water-oil system when strong wetting condition preliczil. An oil-air counter-current imbibition technique has also been found to provide a rapid rneans of obtaining residual-initial saturation data. In a majority of cnses, rcsidual saturations detf-rniinecl from the oil-air or air-mercury process reasonably approximate residual oil saturation following water drive of a strongly water-wet medium. INTRODUCTION A reliable estimate of recoverable reserves depends not only on the amount of original oil-in-place but also on pore geometry and distribution of fluids within the pores. A critical parameter determining the recovery from a reservoir under waterflood, for example, is the amount and distribution of residual oil within the various rock types present. The purpose of this paper is to investigate the mechanism of capillary trapping and assess its importance in laboratory measureqents of residual oil saturation. The degree of wettability of a reservoir rock is recognized as an important factor in waterflood or imbibition experiments. In this paper, however, only the water-wet case has been considered. Considerable experimental evidence1 suggests that for water-wet rocks, capillary forces predominate in tile distribution of fluids and that viscous forces in the range normallv of interest in the reservoir have a minimum influence on residual oil saturation. It follows that if the ultimate recovery is controlled by pore geometry, a unique residual non-wetting phase saturation should exist for a given set of initial conditions. Two laboratory procedures.found to be extremely useful in the study of pore structure and degree of fluid interconnection at various saturations are decribed. Although air-nercury capillary injection curves have been used2 previously to characterize the drainage case, the withdrawal or imbibition case can provide valuable supplementary data. The air-mercury process, however, has several disadvantages; it is difficult to run in a sufficiently accurate manner, mercury does not always act as a strongly non-wetting liquid and in the air-mercury process the sample is rendered unsuitable for future analyses. An alternative process is described in which air is the non-wetting phase and naptha, hentane, octane or toluene is the wetting phase. INTERFACIAL TENSION AND CAPILLARY PRESSURE Interfacial tension between immiscible fluids is due to the difference in attraction of like molecules as compared with their attraction to molecules of the neighbouring fluid. This net attraction results in a tension at the interface. To extend the interface; thus, interfacial tension s can also be thought of as free surface energy. Interfacial tension is normally expressed as dynes/cm, and interfacial energy is measured in ergs/cm2 hence, both have dimensions ml A 2 and are numerically equal.

Jan 1, 1967

By Thomas R. Bur

The strain and pressure gage methods for evaluating the relative performance of explosives in rock were compared. This comparison was based on a study of the responses of strain and pressure gages to explosion-generated seismic waves. Several explosives) representing a wide range of detonation pressures) were used. In general the relative performance of these explosives) as determined from amplitude) impulse parameter) and energy parameter measurements) is the same if the compressive portion of the strain pulse and the comparable portion of the pressure pulse are considered. Other similarities and differences of the two methods are also discussed.

Jan 1, 1967

By E. J. Murphy

The Bureau of Mines developed a fast, reliable modification of the Griess-Ilosvay procedure suitable for field analysis for NO2 in the fumes from explosives. Known concentrations of NO2-air mixtures were analyzed for the nitrous acid or nitrite formed in the reaction with three Griess-Ilosvay-type reagents by diazotizing and coupling. Comparison was made of the Rider-Mellon, Saltzman, and Patty-Petty procedures; the three procedures are in agreement if sufficient time of contact between NO2 and the reagents is allowed. In experiments to obtain an accurate factor for converting NO2 to nitrite, overnight contact was allowed in order to be sure conversion was complete. The factor was found to be 75 percent with a standard deviation of ±3.2. Low and erratic results were found using either the Saltzman or Patty-Petty reagents as absorbing liquids unless several hours' contact was allowed. If dilute NaOH solution was used as the absorbing liquid instead of a Griess-Ilosvay-type reagent, 92 percent of the overnight conversion factor was found after a 3-minute shaking time and a la-minute standby time. The Saltzman reagent was preferable for fieldwork with the dilute NaOH solution as the absorbent because of its easy application, rapid reaction, and intense color even at low NOB concentrations.

Jan 1, 1967

As part of its regular program to provide timely information on domestic mineral commodities, the Bureau of Mines conducted an engineering appraisal of more than 1,300 lode and placer gold deposits in the United States to deter-mine their gold production potential. While these deposits were estimated to contain over 400 million ounces of gold, only 9 million ounces, or slightly more than 2 percent, was found to be producible at $35 per ounce under prevailing mining and metallurgical technologies. The study revealed that any significant increase in available gold in the United States is most likely to come from the discovery of new sources, intensive exploration and development of the more promising known mineralized areas, and development of new or improved mining and metallurgical techniques.

Jan 1, 1967

By R. A. Friedel

THE IMPORTANCE of infrared and ultraviolet-visible spectrometry in studies of the structure of coal and similar substances is described. Special experimental techniques have been developed for these studies. Thin sections of coal are preferred, but halide pellets are easier to prepare. Information obtained from infrared spectra on chemical functional groups has been discussed; the importance of both intensities and wavelengths of absorption bands has been emphasized. Functional groups assigned include aliphatic and aromatic CH, methylene and methyl groups, hydrogen-bonded hydroxyls, hydrogen-bonded and chelated carbonyls, phenolic structures, minerals, and aromatic structures that are benzenoid or polynuclear. Infrared studies of structures of coal extracts, distillates, and reaction products of various processes, both chemical and physical, are discussed. Coallike infrared spectra of chars of model compounds have been utilized extensively in studies of coal structure. Ultraviolet-visible absorption spectra of coals show a lack of fine structure and low spectral intensities. These results have been applied to the questions of the chemical and physical structure of coal, particularly the question of polynuclear aromaticity of coals. The color of coal is also treated. The physical-chemical origin of the color of coal may be due to free radicals, as interesting correlations of ultraviolet-visible spectra with electron paramagnetic resonance have been obtained. The optical color of coal has been explained and simulation of the color changes observed in thin sections has been carried out, The spectra and structure of coal derivatives and other carbonaceous materials are also discussed. Possible sources of error in absorption spectral measurements are pointed out. Limited measurements of the ultraviolet-visible reflectance spectra of coal are described.

Jan 1, 1967

By Murray Weintraub

In an investigation of the incineration of combustible wastes, the Bureau of Mines studied the effect of dimensional parameters, process variables, and fuel properties on the operation of an incinerator that consisted of a single cylindrical combustion chamber in which all combustion air was supplied tangentially above the fuel. Construction and operation of three designs of such a device proved that the tangential overfire air design is effective in providing efficient combustion and low concentration of particulate matter in the effluent gas. A correlation was found that related burning rate with air rate, chamber diameter, and inlet port diameter. In one of the incinerator models, ignition was by radiation from a preheated surface. The temperature of this surface was required to be 1,400° to 1,600° F to insure ignition of moist refuse; however, this had little effect on combustion rates. In the combustion of moist refuse, evaporation of the water proceeded through the fuel bed as a wave, with an ignition wave following the evaporation.

Jan 1, 1967

By D. W. Bacon

Plant process optimization programs are often costly, both in technical effort and loss of production. Evolutionary Operation or "EVOP" is a mode of plant operation consisting of controlled cyclical changes in process conditions by which information is provided concerning potential process improvements while both volume and quality uniformity in production are maintained. Its conceptual simplicity and low cost of utilization have led to successful adoption in a variety of industrial manufacturing operations. This paper is an expository account of basic EVOP theory, the problems encountered and the organization required in applying it to a processing plant. Illustrations are provided which indicate the payoff that can result.

Jan 1, 1967

By Richard I. Petritz

A brief review of today's processing of integvated circuits is given. The major trends in the development of advanced integvated electronics are identified as 1) the broadening of the integvated circuit concept to a large class of circuit function, 2) the processing of more complex circuits within relatively small chips of silicon, and 3) the processing of very large electronic functions on complete slices of silicon. This latter trend, called array technology, is then developed in detail. Emphasis is given to defining the key tech-nological problems. Current progress being made is illustrated. THIS paper will endeavor to identify the major trends in advanced integrated electronics technology. One of these, array technology, will be developed in some detail. The array technology discussion will identify the key problem areas. Since it is the scope of the entire meeting' to present specific progress in the science and technology of integrated electronics, we shall indicate general directions being explored rather than discuss comprehensively solutions to the problems. In order to set the stage for the discussion of future trends in integrated-electronics technology, let us briefly compare the processes by which circuits are fabricated through discrete-device technology with that of integrated circuits technology. The reader is referred to the December 1964 issue of Proceedings of IEEE2 for a comprehensive review of integrated electronics. The article3 by Jay Lathrop is an excellent discussion of integrated-circuits technology. A discussion of the history of semiconductor technology is contained in Ref. 4. A) Current Status of Integrated Electronics. Fig. 1 (top) shows the process by which circuits are constructed from discrete devices. Key points are: 1) Slices containing large numbers of transistors or diodes are processed separately. 2) The slices are scribed into small chips (on the order of 15 mils on a side is about as small as can be conveniently handled) each chip containing one transistor. 3) Each device is specified separately—circuit -function specs are derived largely from device specs. 4) Circuits are formed by connecting together the discrete devices. 5) The number of circuit connections required is approximately equal to the number of devices. 6) There are potentially many more discrete devices per inch2 of semiconductor—only our lack of ability to handle them in discrete form prevents us from going to several orders of magnitude higher density iin Fig. 1, 400,000 transistors are discussed at 1.5 mils on a side). The bottom part of Fig. 1 illustrates the integrated circuit process. Key points are: 1) On the same slice of silicon, transistors, diodes, and resistors are processed grouped to do a complete circuit function. 2) While still in slice form, the components are interconnected into circuit functions by an evaporation process, eliminating the need for separate interconnection steps later. Dramatic improvements in cost and reliability are realized. With a simple flash of metalization thousands of interconnections are reliably made. 3) The slices are scribed into chips which contain complete circuit functions. 4) The circuit functions are specified-not each component in the circuit. This important point was missed by some of the early opponents to integrated circuitry. They argued that, with device yields at x pct, integrated circuit yields would be pct, where n is the required number of devices to make a circuit. This argument leads to extremely low yields for integrated circuits. The fallacy of the argument is that in integrated circuits each device is not specified separately. Furthermore, since a device is forever integrated into a specific circuit function, it need meet only the requirements for that particular function. Discrete devices, on the other hand, are tightly specified so that they can be applied to a variety of circuit functions. 5) Extremely high packing densities are achievable because one need only make the basic devices as large as the circuit demands. Their size is not dictated by handling requirements. A current example

Jan 1, 1967

By M. Vallée, J. -P. Charette, D. P. Gold

"The Oka Carbonatite and Alkaline Complex is a Lower Cretaceous intrusive body of the Monteregian petrographic province. Carbonate rocks of various types, and associated alkaline rocks of the ijolite and okaite suites, are distributed in a double ring-dyke structure 4 Yi miles long by 1 1/2 miles across. Alnoite and alrioite breccia pipes intrude all rocks of the Complex and indicate, from inclusions, that a cover of Palaeozoic rocks existed at the time of emplacement.The results of radiometric, magnetic and gravity surveys of the Complex are compiled and discussed both with respect to the regional pattern and, locally, the bed-rock geology. The Complex is characterized by high-intensity anomalies.Exploration activities started during 1953, and mining operations began in 1961 on the property of St. Lawrence Columbium and Metals Corporation, at one time the world's largest producer of niobium concentrates. Because of the boudinaged and fractured nature of many of the rocks and the variability in grade of the ore minerals, the role of the mining geologist is both demanding and exacting. Rock types are varied and their mutual relation-ships ambiguous, the minerals are rare and complex, and close geological control of the ore is needed in the mine and in the mill. Closely spaced diamond drill holes are needed for mining control, and the ore-waste contact is defined mainly by assay results.In the exploration for 'carbonatites' in Eastern Canada, aeromagnetic surveys are judged to be the best exploration tool, followed in decreasing order by the search for circular structures on aerial photographs, regional gravity surveys and radiometric surveys."

Jan 1, 1967

By Yoichi Ishida, Ching-Yao Cheng, John E. Dorn

Tile creep behavior of a iron was investigated over the range of temperatures from 375° to 1150°K. Apparent activation energies for creep, obtained by the effect of sudden changes in temperature on the creep rate, revealed the presence of- four distinguishable regions. The creep behavior of a iron in Regions II (480° to 774°K) and 111 (775° to 1045°K) was found to correlate well with a model where the creep rate is controlled by the nonconsevualive motion. of jogged screw dislocations. An anomalous increase in the apparent activation energy fur creep in Region III was found to be in harmony with the known decrease in the free activation energy for self-diffusion over the Curie transformation range. Furthermore, the creep rates in Regions II and III were found to increase with stress due not only to the effect of stress on the activation energy but also to an increase in density of mobile dislocations. The evidence suggests that pipe diffusion along moving dislocations could be a significant factor over the lower temperatures of Region II. ALTHOUGH the creep properties of iron and steel have been of interest to metallurgists for some time and an extensive literature is now available, most of the published information has not produced much toward understanding the fundamental dislocation processes controlling the creep behavior of these materials. Whereas the activation energy for high-temperature creep of metals usually agrees well with that for self-diffusion, Sherby, Orr, and Dorn1 deduced from the data of Tapsell -and c1enshaw2 that the activation energy for creep of Armco iron is about 78,000 cal per mole and more recently Lytton and sherby3 reviewed the data of Jenkins and Mellor4 and found an activation energy for creep of a iron of 80,000 cal per mole. Both values are substantially greater than the activation energy for self-diffusion in a iron. Because of the limited data suitable for purposes of identifying the controlling dislocation mechanisms of creep and the unusually high activation energies for creep quoted above, it was considered desirable to reinvestigate in detail the creep of a iron by more reliable techniques which would provide sufficient data for determination of the creep mechanisms. EXPERIMENTAL TECHNIQUE Creep specimens were prepared from 3/8 by 4 in. iron bar stock of the following composition by weight percent: 0.001 C, 0.0120 0, 0.001 N, 0.004 S, and 0.003 P. The as-received bars were cold-rolled to a thickness of 0.100 in., annealed under argon for 30 min at 1113°K, cold-rolled to a final thickness of 0.063 in., and machined into tensile specimens having gage section 0.250 in. wide and 1.70 in. long. Finally they were recrystallized under argon at 1113°K. Specimens to be crept above 1060°K were recrystallized at 1173°K. Both recrystallization treatments gave the same reproducible equiaxed ASTM No. 4 grain size. Creep testing was conducted in machines fitted with Andrade-Chalmers arms that maintained a constant stress to within ±0.2 pct of the reported values. Deformation over the specimen gage section was sensed with a linear differential transformer and recorded auto-graphically as a function of time. The strains deduced from these measurements were sensitive to ±5 x 10-5. During creep the specimens were contained in an argon-filled chamber which was immersed in a temperature-controlled molten tin bath. Creep temperatures, as measured by thermocouples attached to the specimen, were maintained to within ±10.25°K of the reported values. For activation-energy determinations rapid changes in temperature of about 12°K were obtained within 30 sec by direct resistance heating of the creep specimen, and maintained to ±1°K of the reported values. Observations of structural details of specimens before and after creep tests were made by electrolytic polishing and etching in acqueous ammonium persulfate. EXPERIMENTAL RESULTS A typical example of the determination of apparent activation energies, Q, by the effect of small changes in temperature is illustrated in Fig. 1. Q is defined by

Jan 1, 1967

By M. C. Makepeace

"It is the objective of designed experiments to obtain more information for less material and process cost than can be obtained by traditional experimentation. In this paper, the fundamental concepts on which the statistical design of experiments is based are briefly re-viewed according to the following outline: The Experiment The Design The Analysis Two simple 2"" factorial experiments are presented as examples."

Jan 1, 1967

By G. H. Charlewood, J. W. McBean

"One hundred years after being developed, the diamond drill is still an essential tool in mineral exploration. The basic principle is unchanged, but the technique has been revolutionized, particularly in the past fifteen years. The cost of core drilling has not kept pace with the rising cost of living. The price of machinery, supplies and labour in drilling has doubled and trebled since 1946. Some of the techniques which have made it possible to hold the price line are described."

Jan 1, 1967

By M. R. Tek, F. F. Craig, J. O. Wilkes, C. S. Goddin

The waterflood performance of a water-wet, stratified system with crossflow is computed by a finite difference procedure. The effects of five dimensionless parameters on tile oil displacement efficiency, water saturation con-tour.7 and crossflow rates are evaluated in the absence of gravity forces. Crossflow due to viscous and capillary forces is shown to exert a significant effect on oil recovery in a field-scale model of a two-layered. water-wet sandstone reservoir. The crossflow is at a maximum in the vicinity of the front advancing in the more permeable layer. Under favorable mobility ratio conditions, the comparted oil recovery with crossflow always is interrnerliate between that predicted for a uniform reservoir and that for a layered reservoir with no crossflow. INTRODUCTION The important erects of reservoir heterogeneity on waterflood performance are commanding increased attention in the technical literature. Much of this attention is centered on two categories of layered reservoirs: those in which layers are non-communicating and those in which crossflow of fluids occurs between the layers. In the first category, the reservoir is assumed to consist of discrete layers, each uniform within itself and differing from the others only in such properties as thickness, porosity and absolute permeability. The performance within each layer is calculated by one-dimensional flow theory, and the performance of the total reservoir is obtained by summing individual layer performances. Capillary and gravity effects usually are not considered. Representative publications dealing with thi5 type of reservoir are those of Stiles,' Dykstra and Parsons,' Hiatt,3 Warren and Cosgrove' and Higgins and Leighton." Prediction of performance for reservoirs in the second category is considerably more difficult since viscous, capillary and gravitational forces all play important roles in causing crossflow between layers. A number of authors have investigated the simpler problem of two-dimensional displacement flow in a stratified system with a mobility ratio of unity and negligible capillary and gravity effects.'; Others have considered two-dimensional, non-steady-state flow of a single, slightly compressible fluid in a stratified reservoir. A limited number of laboratory oil displacement tests in layered models with crossflow have been reported. Miscible floods (with resultant zero capillary forces) in layered five-spot models were conducted by Dyes and Braun," who studied the effect of mobility ratio with zero gravity forces, and by Craig et al. 12 who studied the effect of gravity forces at constant mobility ratio. Waterfloods in layered five-spot models (with cross-tlow due to capillary, viscous and gravity forces) were conducted by Gaucher and Lindley,"' who showed the effect of gravity forces in causing underrunning of the injected water and by Carpenter, Bail and Bobek, 14 who demonstrated the reliability of Rapoport's" dimension-less parameters for scaling layered systems. Waterfloods in rectangular layered models were conducted by Richardson and Perkins."' who investigated the effect of velocity at constant mobility ratio and with zero gravity forces, and by Hutchinson," who studied the effects of varying mobility, layer permeability and layer thickness ratios. The differential equations which rigorously describe waterflooding in a heterogenous porous medium are non-linear and do not facilitate analytical solution. By using finite difference approximations it is possible to obtain a solution to any desired degree of accuracy. Such a solution, using an alternating direction implicit procedure (ADJP), is described by Douglas, Peaceman and Rachford.18 In the present study, a computer program using ADJP explores systematically the effects of important parameters on waterflood performance of a two-dimensional, two-layered, field-scale model of a water-wet sandstone system. Particular attention is given to evaluation of the water saturation contours and crossflow rates at the interface between layers to gain improved understanding of the crossflow mechanism. PROCEDURE BASIC: FLOW EQUATIONS The basic flow equations for two-dimensional, two-phase, immiscible, incon~pressible flow in a porous medium are:

Jan 1, 1967