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By P. E. Hildebrand, S. W. Mao, C. N. Crain

Hydrologic and economic criteria figure in many obvious ways in water resources development, but they are rarely linked quantitatively, and most of the applications are pertinent only to the case in point. In the preparation of a regional plan for the massive program of groundwater development in the Punjab, situations have arisen where the choice among two or more alternatives was made by analyzing the economic implications of critical hydrologic parameters. Two of these situations which are of more or less general interest are described herein. The first involves basic development policy, i.e., the question of whether groundwater development should be based on the demand of the economy, or the conservation concept of safe yield. The analysis demonstrated that mining of groundwater is clearly indicated for areas where alternative supplies are unavailable. The second problem involves integrating hydrologic data into an economic model to determine optimum well design. From an analysis of all pertinent factors, a simple nomograph was derived for determining well specifications on site during construction. The nomograph can be modified for use in any alluvial terrain. In the Northern Zone of the Indus Plains —the region known as the Punjab- Pakistan is proceeding with integrated development of water and land resources on a scale never before contemplated. The heart of the development plan is a massive program of groundwater development to supplement canal irrigation supplies and to provide drainage relief to the irrigated lands. By the close of 1966 about 2500 high-capacity wells were in operation and furnishing the water supply and drainage requirements for nearly two million irrigated acres. The development plan calls for the construction of a total of nearly 30,000 wells with an aggregate capacity of 120,000 cfs by 1980. This is part of an integrated program eventually affecting over 20 million acres of irrigated lands. [This development program is administered by the West Pakistan Water and Power Development Authority (WAPDA) for which the firm of Tipton and Kalm-bach, Inc. serves as regional planning consultant for the Northern Zone. The material presented herein is derived from planning studies which have been made in connection with the preparation of a regional development plan for the Northern zone.] Pakistan is proceeding with this large-scale development of land and water resources at a time when she is at the threshold of an almost calamitous population growth. Furthermore, she is attempting this development at a time when most of her usable land is already occupied and her food demands exceed current production. Here in the Northern Zone is one of the largest continuous areas of irrigated land in the world, easily irrigated, with a warm, dry climate and ample potential supplies of surface water and groundwater. Except for an abundance of land and labor, other primary resources are lacking or in very limited supply. The agriculture sector so dominates the economy that only by means of an effective development of the agricultural resources can other sectors grow and contribute to a viable economy. Because of inadequate irrigation, farming here has not effectively participated in the twentieth century revolution in agriculture, and only by means of massive development of potential supplies can Pakistan catch up. Capital for any kind of mass development must come from the outside. But the overriding restraint to development of the land and labor resources is the availability of water. ECONOMICS OF DEVELOPMENT The decision-making process in planning regional development becomes increasingly complex as the various sectors of the economy become more highly developed. Where, as in this case, one sector dominates the economy and its development can be considered the key to development of other sectors, the decision-making process is simplified and it is easier to identify alternatives and to trace the prob-

Jan 1, 1970

By R. L. Skaggs, D. T. Peterson

The effect of carbon in solid solution on the plastic behavior of thorium was studied by measuring the flow stress of Th-C alloys from 4.2" to 573°K and at several strain rates. Carbon was found to strengthen thorium primarily by increasing the thermally activated component of the flow stress. The strengthening due to carbon was directly proportional to the carbon content and decreased rapidly with increasing temperature up to 423" K. The flow stress also increased with increasing strain rate. The strengthening appears to be due to a strong short-range interaction between carbon atoms and dislocations. A yield point was observed in the Th-C alloys which increased with increasing carbon content. JTREVIOUS study of the mechanical properties of thorium has been confined largely to the measurement of the engineering properties. Work prior to 1956 has been summarized by Milko et al.1 who reported that additions of carbon to thorium sharply increased the room-temperature strength. In addition, the yield strength was observed to decrease rapidly over the temperature range from 25" to 500°C. In 1960, Klieven-eit2 measured the flow stress of thorium containing 400 ppm C. He found that over the temperature range from 78" to 470°K the flow stress was strongly dependent on temperature and rate of deformation. A drop in the load-elongation curve, or a yield point, was observed over most of the above temperature range. Above 470°K, the flow stress was nearly independent of temperature and strain rate. This strong temperature and strain rate dependence of flow stress is not generally observed in fcc metals. It is, in fact, more typical of the behavior reported for bcc metals. Bechtold,3 Wessel,4 and conrad5 have pointed out the striking difference between the commonly studied bcc metals and fcc metals in regard to the effect of temperature and strain rate on the flow stress. Zerwekh and scott6 studied the plastic deformation of thorium reported to contain 12 ppm C. They found that this material did not obey the Cottrell-Stokes law as expected for fcc metals. In addition, they found values of the activation volume smaller by an order of magnitude than expected for an fcc metal. They concluded that thorium was strengthened by a randomly dispersed solute. Thorium differs from many other fcc metals that have been studied extensively in that it shows a relatively high carbon solubility at room temperature. Mickleson and peterson7 report the solubility limit at room temperature to be 3500 ppm C. The lowest value reported is that of Smith and Honeycombe8 who report the limit to be 2000 ppm C at 350°C. The pres- ent investigation was a systematic study of the flow stress and yield point phenomenon of thorium over a broad range of carbon content, temperature, and strain rate. EXPERIMENTAL PROCEDURE The thorium used in this investigation was produced by the reduction of thorium tetrachloride with magnesium as described by Peterson et a1.' Chemical analysis of the original ingot after arc melting and electron beam melting is shown in Table I. Alloys were prepared by arc melting this thorium with high-purity spectrographic graphite. Threaded specimens with a gage length 0.252 in. diam by 1.6 in. long were used for the constant stress or creep measurements. These specimens were machined from rod which had been cold-rolled and swaged to % in. diam. Tensile specimens were prepared by swaging annealed 3/8 -in.-diam rod to 0.102 *0.001 in. The as-swaged wire was cut to lengths of 2 in., annealed, and the center 1-in. gage length elec-tropolished to 0.100 ±0.001 in. The specimens were gripped for a length of 3 in. at each end by a serrated four-jaw collet which was tightened by a tapered compression nut. No slipping occurred in the grips and negligible deformation was observed outside the 1-in. gage length. Both the creep and tensile specimens were annealed at 730°C under a vacuum of 1 x X Torr. The resulting structures consisted of equiaxed recrystallized grains with a grain size of 3200 grains per sq mm for the tensile specimens and 2200 grains per sq mm for the creep specimens. After the specimens were prepared, samples were analyzed for nitrogen, oxygen, and hydrogen. The results of these analyses are given in Table 11.

Jan 1, 1969

By G. W. Nabor, M. Mortada

The effects of anisotropic or directional permeability on the areal sweep efficiency and the flow capacity are examined. The paper points out the importance of taking directional permeability into consideration in planning a flood. It analyzes the two-dimensional flow pattern associated with the skewed line drive for a unit mobility ratio. The direct and staggered line drives are treated as special cases of the skewed line drive. Analytical expressions are developed for the areal sweep efficiency at breakthrough and the flow capacity. They are related to the spacing between like wells, the distance between a row of injectors and the nearest row of producers, and the degree of skewness of the line drive. The latter quantity is defined such that it is equal to zero for the direct line drive and equals one-half for the staggered line drive. The areal sweep efficiency and the flow capacity depend also on the orientation of the flood pattern with respect to the principal axis of anisotropy. The paper provides a simple method for determining the areal sweep efficiency and the flow capacity for a formation in which the permeability in the bedding plane is anisotropic. INTRODUCTION Directional or anisotropic permeability is manifested by the ability of the formation to conduct fluids more readily along certain preferred directions. This situation occurs in many producing formationsl-4 and is usually attributed to depositional features in which the sand grains are oriented in a preferred direction. In some cases it results from the formation of a major and a minor fracture system. 4 Directional permeability should be taken into account in many phases of the production and exploration activities. Recognizing its existence in the formation of interest and planning accordingly can lead to increased recovery and substantial savings. For instance, the areal sweep efficiency in a water flood depends to a great extent on the orientation of the flood pattern with respect to the principal axis of permeability. Anisotropic5 permeability is specified by the directions of its three principal axes and the permeability along each axis. The principal axes of permeability are mutually perpendicular. This paper deals with the areal sweep efficiency at breakthrough and the flow capacity for formations with aniscltropic permeability. The flood pattern considered consists of alternate rows of injecting and producing wells. The rows of wells are parallel and form a developed, skewed line drive which is illustrated in Fig. 1. The staggered and direct line drives are treated as special cases of the skewed line drive. PRELLMINARY CONSIDERATIONS The formations considered in this paper are assumed to be of uniform thickness and porosity. The permeability is uniformly anisotropic, with each principal axis of permeability maintaining

By V. Carlson, J. A. Rowe, E. O. Bennett

This report concerns the microbial flora found throughout the surface facilities of six water-injection systems in Texas and Oklahoma. Each system is described in detail and water quality data are presented when available. Pseudomonads and sulfate-reducers (Desulfovibrio) were the predominate organisms found in the systems. The genera Sphaerotilus, Bacillus, Achromobacter, Minococcus, Clostridium, Flavobacteriurn, and Sarcina were also isolated in significant numbers. Molds, iron bacteria, sulfur bacteria and soil bacteria were found less frequently in the systems. It is concluded that a complex microbiological flora exists in oilfield water-injection systems. A tendency for waters to deteriorate in passage through solid bed filters is also noted. INTRODUCTION The injection of water into a subsurface formation is often accompanied by numerous problems, the origin and nature of which are only partially understood. During the past few years, investigators have indicated that bacteria are involved in some of these problems even though very little specific information is available concerning this matter. It is surprising that investigators working on microbiological problems in water injection have never made a complete study of the flora of these systems. The logical course to pursue is that of identifying the microbial flora and then examining each organism individually and in combination with others to determine if they produce a particular problem. The objective of the present investigation is to identify the microbial flora in water-injection systems. In addition. the quality of the water in most of the systems was determined and some observations made on the extent to which passage through surface-handling facilities affects water quality. The information derived from this study can serve as a foundation for additional basic investigations. EXPERIMENTAL PROCEDURE The microbial flora of six water-injection systems were studied at 50 sampling points. These systems are experiencing problems which may be attributable to micro-organisms, and two were being treated with antimicrobial agents at the time of this study. The samples were obtained by inoculating 1.0 ml of the water onto the different media at the sampling point. The media used for primary isolation included nutrient agar, Strokes agar, M-10-E medium and semi-solid thioglycollate medium. The cultures were returned to the laboratory, incubated at 30°C until growth occured; then, pure cultures were obtained from individual colonies. The pure cultures were identified according to standardbacteriologica1 procedures. Those organisms not fitting identification criteria exactly, even though exhibiting close similarities to known species, are listed as unidentified organisms. Membrane filters were used to make water-quality tests at intervals before and after collection of the microbiological samples. The filter discs were 47 mm in diameter with a 0.45-micron particle-size retention, and the tests were done under closed conditions at 20) psi. Membrane flow rates are plotted as increasing filtrate volumes, and the total solids contents arcs given when available. An effort was made to sample at each place in a system where a change in environment occurred. In this manner, the effect of passage through filters, tanks, hay sections, etc., on the microbial flora and water quality could be observed. RESULTS SYSTEM A This waterflood system (Fig. 1) is about four years old and daily pumps approx&ately 110,000 bbl of oil-free sour water from a 3,700-ft deep reef. The

By AIME AIME

THE organization of the Board of Directors was effected Tuesday afternoon in ' executive session. Messrs. Bassett,. Buehler, Cates, Daveler, Eavenson, Eilers, Elliott, Evans, Guess, Lovejoy, Moulton, Rickard, Tally, Turner,, Wraith and Wright being pres¬ent. Messrs. Tally, Bassett, Rickard, Mathews and Cates were chosen to form the Executive Committe with Mr. Tally as Chairman, and Messrs. Krumb, Guess and Moulton for the Finance Committee with Mr. Krumb as chairman. Karl Eilers was reelected as Treasurer and H. Foster Bain as Secretary, after which the Directors adjourned for the usual dinner reported elsewhere. At the open session of the Board, at which in addition Messrs. Allen and McAuliffe were present, the work of organization was continued with appointments to committees as listed herewith. Various actions of the Executive and Finance Committees were confirmed, the budget for 1931 formally approved, the meeting dates for the year adopted, 34 new Members and Associates, 13 Junior Members and 31 Student Associates admitted by election and transfer and 29 resignations accepted.

Jan 1, 1931

By W. F. Kieschnick, and W. J. McGuire&apos, Eugene Harrison

This paper concerns the induction and extension of fractures into rock formations as involved in drilling, completing, and production stimulating operations on wells. Conclusions concerning formation breakdown are derived from (I) a review and extension of published analyses relating to mechanical theories of rock stress and the state of stress in the earth's crust and (2) a correlation of field data from fracturing operations. Conclusions concerning the mechanics of fracture extension, which indicate the relationship between fracture dimensions and rock properties, depth, and volume of injected fluid, are tentative and largely establish limits of relationships. These conclusions are derived from stress calculations, limited field data, and laboratory experimental studies. The experimental work involves the study of the stresses at the fracture boundaries and the geometry of pressurized fractures by means of photo-elastic modeling methods. Results of this investigation indicate that a large majority of pressure induced wellbore fractures are vertical, particularly in deeper wells; and variations in the pressures necessary to create and extend fractures can be explained largely on a basis of established rock properties. It is also shown that variations due to tectonic forces should usually be expected to be slight. Other results indicate that during that extension of fractures rather large fracture volumes are temporarily created by the parting of the formation. The purpose of this paper is to present the results of calculations and laboratory experiments concerning the mechanics of fracture induction and extension with a view to broadening existing knowledge relating to these phenomena. It is believed that continued progress in developing knowledge of this type is important to the further development of techniques for drilling and completing wells. When a wellbore is subjected to sufficiently high pressure, fracturing of the formation surrounding the well occurs. This phenomenon is a common cause of lost circulation during drilling operations, is a deliberately planned factor in most squeeze cementing operations, and is the controlling factor in many productivity stimulation operations. The exploitation of formation fracturing in recent years has been particularly impressive in sand-viscous fluid well stimulation treatments which were first introduced to the industry by the Stanolind research group1,2,3 several years ago. The borehole fracturing phenomenon has been analyzed mathematically by application of the principles defining the elastic and inelastic behavior of thick-walled cylinders of homogeneous, isotropic, and impermeable material.1,5,6 This basic argument is re-presented in this paper along with new considerations which strengthen it. In addition to these arguments relating to fracture induction some calculations and experimental results relating to the mechanics of fracture extension are presented. Since the nature of the pressure induced fracture at distances from the well is of great importance in considerations of well stimulation procedures there appears to be a need for an integrated approach which deals with the mechanics of fracture extension as well as with wellbore rupture.

Jan 1, 1955

By R. E. Boehler, N. C. Ludwig

At Buffington Station, Gary, Ind., Universal Atlas Cement operates fourteen 8 x 101/2 x 155-ft cement kilns in mill 6 and two 11 x 360-ft kilns in the Harbor plant. The No. 11 and 12 kilns in mill 6 are equipped with Manitowac recuperator sections. This report describes studies in measuring exterior shell temperatures on several of these kilns and the development of a traveling radiation pyrometer with certain novel features. Preliminary Work: At first various temperature-sensing devices were placed on the steel shell: 1) crayons with calibrated melting points, 2) colored paints with temperature-calibrated pigments, 3) aluminum paints with temperature-calibrated binders, and 4) metal-stem dial thermometers. The colored paints and aluminum paints failed to indicate the temperatures correctly. The crayons and thermometers did indicate fairly correct temperatures, but it proved impossible to apply enough of these on the shell to detect all the potential areas where hot spots might develop. Furthermore, considerable labor was required to apply these sensors and read the temperatures. Consequently no further work was done with these devices. Formation of Hot Spots: In the burning or clinker-ing zone of a cement kiln, the thickness of the protective coating and thickness of the brick govern the amount of heat transmitted to the steel kiln shell. Usually the protective coating consists of 4 to 8 in. of fused cement clinker. The formation of a hot spot is usually caused by loss of coating? that is, localized areas of the coating become thin or fall away from the refractory. This is generally caused by excessive temperature in the burning zone over a fairly long period of time. It may also be caused by a sudden thermal change in the burning zone. Variations in raw feed composition and in feed rate require changes in the fuel and air rates, and when these are not appropriately altered, conditions may develop in the kiln that will result in loss of coating. Luminescence on the kiln shell indicates that a hot spot has developed to a point that usually alters the refractory's thermal conductivity properties. When this thermal weakness zone occurs in the burning zone of the kiln, constant vigilance is required to protect it by maintaining proper coating. Even so, it has been the writers' experience that within a period of several days to about four weeks the hot spot usually recurs with greater severity. This necessitates shutting down the kiln and re-bricking the affected area. One of the prerequisites of a good burnerman is the ability to maintain a protective coating despite the many variables in operation. When he knows that it is getting thin or that an area has dropped off, he reduces the firing rate and kiln speed and brings feed into the affected area in an effort to rebuild the coating. But when powdered fuel is burned, the atmosphere of the kiln may prevent the burnerman's observing the condition of the coating closely at all times without taking off the fire. It is not considered good practice to do this frequently, as it imposes a thermal shock on the coating and upsets operation of the kiln. To help the burnerman scan the shell of the kiln along the burning zone, therefore, a radiation pyrometer, connected to a potentiometric recorder, was mounted on a slowly moving steel cable. The theory of operation, construction details, and adaptability of the radiation pyrometer are included in an excellent monograph' and also in a textbook.' Shell temperatures of the Atlas Cement kilns were measured with a Brown Instruments Div. low intermediate range Radiamatic unit, of range 200" to 1200°F, and a circular chart Electronik potentio-metric recorder, of range 500" to 1000°F. In Bulletin 59095M the supplier publishes standard calibration data (millivolts vs degrees Fahrenheit) for this radiation pyrometer, These data, however, apply only to flat surfaces having emissivities of unity. Calibration of Radiation Pyrometer for Use on Curved Surfaces: When applied to surface temperature measurements, the radiation pyrometer reading depends on the nature of the surface, the material of which it is composed, and also to some extent on the temperature of the surroundings. Although the present radiation pyrometer is designed to give a calibrated response under ideal (black body) conditions when used commercially, it must be calibrated empirically. The calibration procedure, given below, follows that described by Dike (Ref. 1, pp. 38-39). Calibration tests on plane and curved surfaces showed that the response of the radiation pyrometer was very

Jan 1, 1961

By N. De Nevers

A calculation method has been developed for carbonated water flooding. This method takes into account the effects of oil viscosity reduction and oil swelling, due to carbon dioxide transferred to the reservoir oil from the carbonated flood water. It shows the effect of changes in carbonation pressure and carbonated water slug size. The method is based on a Buckley-Leverett-type linear flow model. The mathematical approach is similar to that developed by Welge, et al, for enriched gas drives. However, it contains a very important advance over the previous papers in its solution to the problem of injection of a "slug" of carbonated water rather than continuous injection of fluid of constant composition. The method also shows the chromatographic nature of the transport of Co 2 in a carbonated water flood. Sample calculations indicate that viscosity reduction is the most important source of incremental oil recovery. Swelling contributes to a lesser extent. Raising the carbonation pressure increases recovery, but this effect diminishes as pressure is increased. increasing the slug size also increases recovery, but again this effect diminishes as slug size is increased. INTRODUCTION In recent years there has been considerable interest in carbonated water flooding as a secondary recovery method. Several carbonated waterflood field tests are now in progress.1'3 Yet there is no published method for predicting the results of a carbonated water flood. This paper presents a method for predicting the oil recovery for ; carbonated water flood. In a carbonated water flood. a carbonated water slug is injected into the reservoir. Then this slug is driven forward by injecting plain water behind it. The field operator must choose the carbonated water slug size and the CO2:water ratio in the slug. The calculation method presented here shows the effects of both slug size and CO2:water ratio on oil recovery. The calculation assumes that the addition of carbon dioxide to flood water increases the oil recovery by two mechanisms: 1. Carbon dioxide transfers from the flood water to the oil, thereby reducing the viscosity of the oil. At the lower viscosity, the oil flows more readily and is more easily swept out by flood water. 2. The carbon dioxide which transfers to the oil phase causes the oil phase to swell. Assume that the residual oil saturation (volume per cent of pore space) is the same whether the oil is carbonated or not. Then the same volume will contain less stock tank oil if it is carbonated, due to oil swelling. The plain water driving the carbonated water slug forward will strip the CO2 out of this residual oil., causing this oil to shrink. This swelling-followed-by-shrinking leaves behind a lower residual oil saturation than would have been left behind by a plain water flood. Since some oils swell to almost twice their original volume at reasonable CO2 pressures, this effect may be large. Two additional benefits sometimes claimed for carbonated water flooding are: 1. Adding CO2 to flood water greatly increases the water injectivity in some cases.1 (Injectivity = BPD of water injected/ft of sand x differential bottom-hole pressure, psi.) CO2 forms a weak acid in water; injecting carbonated water is, therefore, somewhat like acid treating. If a formation responds to acid treating, it will probably have a higher injectivity for carbonated water than for plain water. Although the increased injectivity increases the profitability of a carbonated water flood over a plain water flood, it does not change the production curve based on total fluid injected. Therefore, the method presented here does not show any effect of increased injectivity. 2. It is claimed in one patent4 that carbon dioxide will react with some constituents of the oil to form detergents. These detergents are expected to increase the oil recovery. There is little data available to support this idea. The calculation method presented here takes no credit for extra oil recovery due to the formation of any such detergents.

Jan 1, 1965

By M. A. Torcaso, P. Raimondi

To study mass transport in systems simulating oil recovery processes, different porous media were saturated with a mobile (carrier phase) and a stationary phase. Slugs of carrier phase containing a small amount of solute were displaced with pure carrier phase. By analogy to the chromato-graphic processes, the velocity of the solute can be predicted from a knowledge of the partition coefficient and the saturation provided that equilibrium between the two phases exists. Equilibrium was found to exist for different porous media, solutes and rates. The conditions were varied over the range normally encountered in the laboratory and in the field. The longitudinal dispersion of a solute undergoing interphase mass transfer was also investigated. INTRODUCTION The production of hydrocarbons by gas cycling, enriched gas drive and C02 or alcohol displacement involves, among other factors, relative motion between two phases and compounds, hereafter called solute, which are soluble in both phases. The solute is carried forward by the faster flowing phase at a lower velocity than the average velocity of that phase. Retardation of the solute is caused by chromatographic absorption and desorption in the slower flowing phase and by the degree of departure from equilibrium. At equilibrium the concentration of solute in the two phases can be related by the equation* CSw = K Cso ,............(1) where C, and C are the concentration of solute in the aqueous and oleic phases respectively and K is the equilibrium ratio, or partition coefficient. Displacement theories must contain an explicit assumption with regard to equilibrium, i.e., whether the compositions can be related by Eq. 1. The existance of equilibrium depends, in general, on the relative velocity between the phases. Unfortunately, other factors such as gravity segregation and viscous fingering, also depend on velocity. For this reason, whenever effects of rate on displacement were observed,2-4 it was practically impossible to discern what caused them — lack of equilibrium or the factors mentioned above. Equilibrium between phases has been the subject of extensive studies in fields such as extraction or chroma to graphy. It has received only small attention in flow through the type of porous media encountered in oil production.5 For this reason a method was developed which makes it possible to study the movement of a solute as it is affected by rate, type of porous media, partition coefficient and carrier phase, but in the absence of segregation or fingering. The information obtained enables one to determine when the assumption of equilibrium can be made. Briefly, the method consists of (1) saturating the core with a mobile and an immobile phase, (2) injecting a slug made up of the same fluid as the mobile phase and a small concentration of mutually soluble solute, (3) measuring the lag and the peak height of the slug at arrival and (4) correlating these variables with fluid properties such as partition coefficient and mixing constants of the medium. PROPOSED MECHANISM The principles of chromatography are combined with the equation of longitudinal mixing to predict the velocity of a solute slug compared to the bulk velocity and the peak height of a slug.6-9 The equation so obtained is valid under equilibrium conditions only. Therefore, a comparison between experimental and predicted results will give a measure of departure from equilibrium. This work was done with either the oleic or the aqueous phase being immobile. For simplicity, the following development is based on the case where the oleic phase is immobile. However, the treatment is the same in either case.

Jan 1, 1966

By T. K. Redden

Protective coatings based on the formation of a surface coating of nickel aluminide (NiAl) were applied to the nickel-base superalloys IN 100, SEL 15, and U-700. Coated specimens were exposed to an oxidizing environment at temperatures between 1600 and 2200 F for times up to 1000 hr. The oxidation resistance and stability of the coating were evaluated by weight gain measurements, metallographic examination, and X-ray diffraction study of surface oxides and coating. The composition of the coating and diffusion zone was determined by electron microprobe traverse of samples before and after high-temperature exposure. Intermediate phases formed in the coating and diffusion zone were identified by X-ray diffraction in situ and after electrolytic extraction. The outer coating was found to consist of the inter-metallic compound, NiAl, while the diffusion zone contained MC, M23C6 or M6C carbides, and a phase in a matrix of NiAl + Nidl. Oxidation resulted in formation of an A1203 n'ch scale containing some Tz02. Depletion of aluminum during oxidation resulted in degradation of the outer coating to Ni3Al and the nickel alloy matrix. Diffusion of aluminum into the base metal was found to be slight and did not influence coating life significantly. The o formed in the diffusion zone during coating decomposed during elevated-temperature exposure to form stable carbide phases characteristic of the base metal. Diffusion zone phase changes were found to have no effect on the life of the aluminide coating in the oxidizing envzron?nent. THE oxidation resistance of many high-strength nickel-base superalloys is inadequate for extended exposure at temperatures above about 1600°F. In addition, some applications for these materials require that they be exposed to environments containing sulfur compounds and sodium salts which can cause surface attalk known as sulfidation or hot corrosion. In order to provide the necessary corrosion resistance to the high-strength alloys, protective coatings based on an aluminizing process have been developed. These processes, usually based on a pack cementation technique, result in the formation of a NiAl-rich outer coating layer either during the coating process or by a subsequent diffusion treatment. The performance of the aluminide coatings is affected by interactions between the coating layer and the base metal both during the coating process and during subsequent exposure at elevated temperatures. Knowledge of these interactions is required to guide the development of coatings capable of longer life and improved reliability. Goward et al.' recently reported the metallurgical factors which influence coating per- formance on MAR-M200. The present work is concerned with correlating the interactions and performance of coating compositions on several representative materials. EXPERIMENTAL PROCEDURES Materials. Three cast nickel-base superalloys which are used for turbine buckets in air-breathing engines were studied: IN 100, U-700, and SEL 15. Their chemical compositions are given in Table I. The alloys were vacuum-induction-melted and cast to slabs approximately 0.3 in. thick from which rectangular specimens 0.25 by 0.5 by 1 in. were machined. Coating Procedures. The machined specimens were coated by CODEP processes which were developed at the author's laboratory. These are based on pack cementation in various media to deposit either aluminum or aluminum in combination with titanium. The coating process which deposits only aluminum is designated CODEP-C, while the CODEP-D process deposits titanium in combination with aluminum. The CODEP-D process was applied only to IN 100. Both CODEP processes are applied at 1950" or 2000°F for 4 hr without need for a subsequent diffusion treatment. An outer coating about 1 mil in thickness is produced by these processes. Test Procedures. Coated specimens were exposed to static oxidation for periods ranging from 24 to 1000 hr at temperatures of 1600" to 2200°F. Terminal weight gain measurements and visual examination were used to evaluate oxidation resistance. including oxide spalling and coating failure. Both as-coated and exposed specimens of each alloy were studied by metallographic examination, electron microprobe analysis (EMA), and X-ray diffraction analysis either of the exposed surfaces or of phases extracted from the coating and diffusion zone. RESULTS As-Coated Condition. The microstructures of as-coated conditions were generally similar, irrespective of base materials or the particular coating process. They are typified by IN 100 coated by CODEP-D as shown in Fig. 1. The predominately single-phase outer layer, area A, Fig. 1, was identified by X-ray diffraction as the intermetallic compound NiA1. The NiAl zone extended inward to the original base metal interface. The diffusion zone, area B, Fig. 1, included carbide phases, a lamellar phase oriented perpendicular to the base metal surface, and a matrix phase consisting of a mixture of NiAl and Ni3Al. The phases in the diffusion zone were electrolytically extracted using a 10 pct HCl in methanol solution at approximately 1.3 amp per sq cm. The extracted phases were found to be M6C, MC, or M=C6 carbides and o as shown in Table I1 for each of the alloys. The d spacings from a typical diffraction pattern are

Jan 1, 1969

By T. E. Leontis, J. P. Murphy

During the last few years, the trend in the aircraft and automotive industries has been toward higher and higher operating engine temperatures. This has created considerable interest in the effect of temperature on the properties of alloys. In the magnesium field, it has been recognized for many years that the addition of cerium imparts high strength and good resistance to creep at elevated temperatures. Beck,' in his treatise on magnesium, has summarized the work of German investigators. This includes the unpublished data of Menking, showing the increase in strength and hardness of extruded alloys containing 2 to 20 per cent Ce at temperatures from 20' to 300°C. (68" to 57z°F.) and the results of Vosskiihler, who demonstrated the improved resistance to creep of alloys containing 6 per cent Ce plus 2 per cent Mn and 0.5 per cent Ce plus 2 per cent Mn at 150°C. (302°F.). Wellinger and Kei12 have also reported the creep properties of a forged magnesium-cerium-man-ganese alloy at 200' and 250°C. (392' and 482°F.). Haughton and Prytherch have determined the tensile properties of various forged magnesium alloys containing cerium, cerium plus manganese, cerium plus calcium, cerium plus nickel, cerium plus nickel plus manganese, and cerium plus cobalt plus manganese at temperatures up to 290°C. (554OF.). Magnesium-cerium alloys have been used in some commercial applications. It is reported that an alloy containing 3 per cent Ce plus 0.5 per cent Mn plus 0.5 per cent Ca is being used on a forged impeller in Great Britain. Two forged parts made from an alloy with a nominal composition of 5 per cent Ce and 2 per cent Mn have been found on the German BMW-8o1D aircraft engine. These two forgings consist of a supercharger impeller and a rear cam-follower guide. In this country, several types of pistons have been made experimentally in both the cast and the forged conditions from an alloy containing 6 per cent Ce plus 2 per cent Mn and in the cast condition from an alloy of magnesium plus 10 per cent Ce. The cast pistons have been tested in various types of internal-combustion engines, with promising results. This paper presents the results of an extensive investigation on the properties of various cerium-containing magnesium alloys in both the cast and the forged conditions. Data are presented to show the beneficial effects of increasing amounts of cerium on the mechanical properties of magnesium at at temperatures' The effects of heat-treatment on the properties of these alloys and the attendant changes in the microstructure are discussed. The alloys investigated most extensively are

Jan 1, 1946

By J. P. Murphy, T. E. Leontis

During the last few years, the trend in the aircraft and automotive industries has been toward higher and higher operating engine temperatures. This has created considerable interest in the effect of temperature on the properties of alloys. In the magnesium field, it has been recognized for many years that the addition of cerium imparts high strength and good resistance to creep at elevated temperatures. Beck,' in his treatise on magnesium, has summarized the work of German investigators. This includes the unpublished data of Menking, showing the increase in strength and hardness of extruded alloys containing 2 to 20 per cent Ce at temperatures from 20' to 300°C. (68" to 57z°F.) and the results of Vosskiihler, who demonstrated the improved resistance to creep of alloys containing 6 per cent Ce plus 2 per cent Mn and 0.5 per cent Ce plus 2 per cent Mn at 150°C. (302°F.). Wellinger and Kei12 have also reported the creep properties of a forged magnesium-cerium-man-ganese alloy at 200' and 250°C. (392' and 482°F.). Haughton and Prytherch have determined the tensile properties of various forged magnesium alloys containing cerium, cerium plus manganese, cerium plus calcium, cerium plus nickel, cerium plus nickel plus manganese, and cerium plus cobalt plus manganese at temperatures up to 290°C. (554OF.). Magnesium-cerium alloys have been used in some commercial applications. It is reported that an alloy containing 3 per cent Ce plus 0.5 per cent Mn plus 0.5 per cent Ca is being used on a forged impeller in Great Britain. Two forged parts made from an alloy with a nominal composition of 5 per cent Ce and 2 per cent Mn have been found on the German BMW-8o1D aircraft engine. These two forgings consist of a supercharger impeller and a rear cam-follower guide. In this country, several types of pistons have been made experimentally in both the cast and the forged conditions from an alloy containing 6 per cent Ce plus 2 per cent Mn and in the cast condition from an alloy of magnesium plus 10 per cent Ce. The cast pistons have been tested in various types of internal-combustion engines, with promising results. This paper presents the results of an extensive investigation on the properties of various cerium-containing magnesium alloys in both the cast and the forged conditions. Data are presented to show the beneficial effects of increasing amounts of cerium on the mechanical properties of magnesium at at temperatures' The effects of heat-treatment on the properties of these alloys and the attendant changes in the microstructure are discussed. The alloys investigated most extensively are

Jan 1, 1946

By Samuel G. Lasky

In a recent discussion of the mineral resource position of the United States, published in the September 1946 issue of Mining and Metallurgy, I expressed my conviction that ore deposits of major magnitude remain to be found in this country and that they can be found without undue cost or risk. I stated with equally strong conviction, however, that if the search for such deposits is to be notably successful there must be, among other things, a reorientation of philosophy and mental habits on the part of many who would be connected with the search. I would now like to enlarge upon that statement. For such a purpose. we may consider that the search for concealed deposits involves four steps: (I) the selection of areas for further study; (2) the geologic study of those areas in order to verify their general favorableness and in order to choose specific patches worthy of being tested; (3) the decision whether exploration of the patches chosen should actually be undertaken; and (4) the exploration itself. The first two steps and the last rest upon the judgment and skill of geologists. The third step—the decision whether exploration should be undertaken—rests upon management. In my opinion, the philosophies or principles that have guided these steps in the past are now inadequate. Philosophy of Appraisal If concealed deposits are to be looked for, how are the places of their possible concealment to be recognized? Every known mineralized area still in the prospect stage has already been repeatedly examined and condemned. As for those deposits concealed under later rocks, there may be not even the clue of a near-by outcrop for engineer or geologist to consider. flow then, are we to know where to look? Geologic Probability In the early days of our mining industry, ore deposits were found mainly by "following the ore." Later, as such opportunities decreased, and as geologic concepts became accepted, deposits were found more and more through use of the notion of geologic probability. Many instances can be cited wherein a courageous operator ignored the implications of the unsuccessful efforts of predecessors and, solely by "following the ore," converted a discredited prospect into a good mine. Similar experience doubtless will occur in the future, but "following the ore" will no longer in itself find new deposits in the amount needed. Nor can enough new ore be expected from further use of the notion of geologic probability, for, as mentioned above, our known prospects have already been ex-

Jan 1, 1949

By Samuel G. Lasky

In a recent discussion of the mineral resource position of the United States, published in the September 1946 issue of Mining and Metallurgy, I expressed my conviction that ore deposits of major magnitude remain to be found in this country and that they can be found without undue cost or risk. I stated with equally strong conviction, however, that if the search for such deposits is to be notably successful there must be, among other things, a reorientation of philosophy and mental habits on the part of many who would be connected with the search. I would now like to enlarge upon that statement. For such a purpose. we may consider that the search for concealed deposits involves four steps: (I) the selection of areas for further study; (2) the geologic study of those areas in order to verify their general favorableness and in order to choose specific patches worthy of being tested; (3) the decision whether exploration of the patches chosen should actually be undertaken; and (4) the exploration itself. The first two steps and the last rest upon the judgment and skill of geologists. The third step—the decision whether exploration should be undertaken—rests upon management. In my opinion, the philosophies or principles that have guided these steps in the past are now inadequate. Philosophy of Appraisal If concealed deposits are to be looked for, how are the places of their possible concealment to be recognized? Every known mineralized area still in the prospect stage has already been repeatedly examined and condemned. As for those deposits concealed under later rocks, there may be not even the clue of a near-by outcrop for engineer or geologist to consider. flow then, are we to know where to look? Geologic Probability In the early days of our mining industry, ore deposits were found mainly by "following the ore." Later, as such opportunities decreased, and as geologic concepts became accepted, deposits were found more and more through use of the notion of geologic probability. Many instances can be cited wherein a courageous operator ignored the implications of the unsuccessful efforts of predecessors and, solely by "following the ore," converted a discredited prospect into a good mine. Similar experience doubtless will occur in the future, but "following the ore" will no longer in itself find new deposits in the amount needed. Nor can enough new ore be expected from further use of the notion of geologic probability, for, as mentioned above, our known prospects have already been ex-

Jan 1, 1949

By H. Hooykaas

A few years ago Marsal published a method of predicting oil recovery as a function of time for an edge-water-drive reservoir with several rows of wells.' The method is based solely on oil- and water-production data obtained during a short period for the first row of wells and the gross productions (past and future) of all wells. This paper presents a streamlined version of the original publication and experimental evidence showing the reliability of this version. For this purpose scaled experirnents were performed in a large model (750 X 500 X 23 cm, 24.4 ft X 16.2 ft X 8.9 in.) in which edge-water-drive reservoirs with three rows of production wells were simulated. From the results of the experiments it is concluded that the method gives a fairly accurate prediction of the future production behavior of the reservoir and enables us to select the most profitable production plan. Results obtained with the method were always slightly conservative. INTRODUCTION The calculation method developed by Marsal aims at forecasting future reservoir behavior.' It can be applied to floods in which a number of down-dip wells are rapidly going to water. Essentially it is a method for predicting the future behavior of the up-structure wells on the basis of the observed behavior of the down-structure wells. As such, the method is especially useful for predicting behavior of edge-water drives toward several rows of wells. The requirement to be met for justifying the approach is identity of production mechanism in all regions of the reservoir. The attraction of the method then lies in the fact that it applies even when we have no complete description of the prevailing production mechanism. The original publication was in the German language and for this reason, perhaps, did not attract widespread attention. In our opinion it deserves to do so because it does offer in a simple way results which are in fair agreement with observed data. The aim of the present paper is to bring the method to the attention of a wider audience. The method in its most simplified form is reviewed and experimental data in support of it are presented. PRINCIPLES To show Marsal's principle. we will first write the continuity equation for very simple conditions, linear flow (in the positive x-direction) in an incompressible porous body [cross-section A(x), porosity +(x)], saturated with incompressible fluids (oil saturation S). When the oil in this formation is displaced by water, injected at x = 0 (inlet face), we get where q(t) is the total gross displacement rate and f the fractional oil flow. The equation can be solved if we make the assumptions: (1 ) that the fractional oil flow (f) is a univalent function of saturation (S); and (2) that the function is the same throughout the porous medium. Then: f = f(S) Solving this equation with the method of characteristics, we obtain

Jan 1, 1966

By J. P. Murphy, T. E. Leontis

DURING the last few years, the trend in the aircraft and automotive industries has been toward higher and higher operating engine temperatures. This has created considerable interest in the effect of temperature on the properties of alloys. In the magnesium field, it has been recognized for many years that the addition of cerium imparts high strength and good resistance to creep at elevated temperatures. Beck,1 in his treatise on-magnesium, has summarized the work of German investigators. This includes the unpublished data of Menking, showing the increase in strength and hardness of extruded alloys containing 2 to 20 per cent Ce at temperatures from 200 to 300°C. (68° to 572°F.) and the results of Vosskühler, who demonstrated the improved resistance to creep of alloys containing 6 per cent Ce plus 2 per cent Mn and 0.5 per cent Ce plus 2 per cent Mn at 150°C. (302°F.). Wellinger and Keil2 have also reported the creep properties of a forged magnesium-cerium-manganese alloy at 200° and 250°C. (392° and 482°F.). Haughton and Prytherch have determined the tensile properties of various forged magnesium alloys containing cerium, cerium plus manganese, cerium plus calcium, cerium plus nickel, cerium plus nickel plus manganese, and cerium plus cobalt plus manganese at temperatures up to 290°C. (554°F.). Magnesium-cerium alloys have been used in some commercial applications. It is reported that an alloy containing 3 per cent Ce plus 0.5 per cent Mn plus 0.5 per cent Ca is being used on a forged impeller in Great Britain. Two forged parts made from an alloy with a nominal composition of 5 per cent Ce and 2 percent Mn have been found on the German .BMW-801D aircraft engine. These two forgings consist of a supercharger impeller and a rear cam-follower guide. In this country, several types of pistons have been made experimentally in both .the cast and the forged conditions from an alloy containing 6 per cent Ce plus 2 per, cent Mn and in the cast condition from an alloy of magnesium plus 10 per cent Ce. The cast pistons have been tested in various types of internal-combustion engines, with promising results. This paper presents the results of an extensive investigation on the properties of various cerium-containing magnesium alloys in both the cast and the forged conditions. Data are presented to show the beneficial effects of increasing amounts of cerium on the mechanical properties of magnesium at elevated temperatures. The effects of heat-treatment on the properties of these alloys and the attendant changes in the microstructure are discussed. The

Jan 1, 1946

By John P. Dolan, Charles A. Einarsen, GiIman A. Hill

his paper discusses how the following formation characteristics can be determined mathematically from drill-stem test pressure charts: true formation pressures, effective permeability of the entire section tested, well productivities, wellbore damage, and possible detection of barriers (faults, pinchouts, etc.). This paper also presents a practical method for im-mediate determination of eflective permeability and well-bore damage from successful double shut-in pressure tests. A list of recommendations for improving the reliability of drill-stem rest pressures is also presented. INTRODUCTION A drill-stem test is a temporary completion designed to sample the formation fluid and to establish the possibility of commercial production. Early pressure recording devices were used merely to verify proper operation of the testing tool. Until recently the accuracy of the pressure gauges has been insufficient for any reliable quantitative use of the recorded pressures. In view of the need for more reliable formation evaluation and as a result of the recent interest in exploration work employing the concept of hydrodynamic en-trapment,1,2,3,4 better pressure recording gauges are now in use. These devices can record pressure within 1 per cent above 1,000 psig and can detect differential pressures as low as 1/2 psig. In addition to formation pressure, several other reservoir characteristics can be determined from DST charts; namely, well productivity, formation permeability, wellbore damage, and the possible existence of bar- riers (faults, pinchouts, changes in permeability, etc.). This paper presents a practical method to interpret DST pressure charts for formation pressures and many other reservoir properties, a method that has been developed in analyzing approximately 4,000 DST charts during the last five years. The techniques used are a composite of published articles on drill-stem testing5,6, together with well-known pressure build-up analysis methods. THEORY It has been shown7,8 that the following equation may be used for analysis of pressure build-up curves: Po - Pw = 162.6 qu/kh log ( to + ?/?) .....(1) When this equation is applied to the curves obtained in drill-stem testing, the assumptions and boundary con-ditions are more nearly realized than in conventional flow and build-up tests on producing wells. Zak and Griffen9 have recently discussed in detail the use of this equation in analyzing DST charts. One of the problems with DST curves is the lack of reservoir data for precise analysis. Therefore, it is necessary to develop empirical rules and field methods for analyzing DST charts in quantity. For this reason, the empirical methods presented in this paper have been developed, and their derivation is found in Appendices A and B. METHOD USED FOR ACCURATE READING OF DRILL-STEM TEST CHARTS In order to apply the pressure build-up theory to DST charts, it is necessary to obtain a digitized expression for the pressure and time data recorded by the pressure gauge. These data may be either provided by the service company or interpolated by projecting a

Jan 1, 1958

Jan 1, 1935

By J. M. Tobin, L. H. Cadoff, L. M. Adelsberg

The reaction between liquid zirconium and graphite at temperatures above 2000 °C has been investigated. The reaction products were found to be carbon-saturated zirconium metal and ZrC which formed between the graphite and the metal. Parabolic growth behavior was observed for the ZrC Phase at all temperatures of this investigation. The parabolic growth constant at temperatures between 2000° and 2860°C was measured to be 1.83 exp 84,300/RT) sq cm per sec. The reaclion mechanism was proposed to be the rapid carbon saturation of the liquid metal and the formation of ZrC at the metal-carbide interface with diffusion of carbon through the ZrC, the "rate - determining step" of the reaction. The concentration-independent diffusion coefficient of carbon in ZrC, (DZrC), was expressed as 0.95 exp? 78,700/RT) sq cm per sec. This value mas calculated using the temperature-invariant ZrC phase fields proposed in the literature. The [ZrQiq)] — [ZYQiq) + ZrC] phase boundary over the temperature range 2000° to 2800°C was determined and the ZrC + C eutectic temperature was found to be 2890° ± 50°C. ThE Group IV and VB transition-metal refractory carbides are of interest because of their high melting points, high temperature strength properties, and relative inertness in certain corrosive environments. The present-day understanding of these materials, however, is limited by the general unavailability of accurate and reliable physical and chemical property data. This is due primarily to the difficulties associated with the preparation of suitable, high-density, high-purity carbide samples, and the achievement and control of uniform high-temperature environments. Accurate measurement of temperature is also an important factor limiting the reliability of reported data. The Zr-C reaction was selected for investigation because of the high melting point (>34000C) and favorable nuclear properties of the reaction product, ZrC. The direct reaction method afforded an opportunity to obtain kinetic data on the fully dense carbide. In this paper, layer-growth techniques were used to estimate the diffusivity of carbon in ZrC and to investigate the phase equilibria in the Zr-C system at temperatures above 2000°C. EXPERIMENTAL PROCEDURES AND DATA Crystal bar zirconium (99.9 pct Zr), purchased from the Nuclear Materials and Engineering Corp., and ZTA graphite (99.9+ pct) were used in this study. The analyses of the materials are listed in Table I. A schematic of the high-temperature carburization apparatus is shown in Fig. 1. The sample was a zirconium metal charge in a 1/2 -in.-ID graphite crucible which was capped with a tightly fitting graphite stern. The crucible and stem were designed to closely approximate black-body conditions. The graphite crucible was packed in lampblack (outgassed 1 hr at 2100°C) which provided insulation and thermal stability to the system. The inert atmosphere was maintained by a constant flow of high-purity argon or helium gas. The nozzle-diffuser section on the top flange was sufficient to prevent back-diffusion of air into the system. Chemical analysis of the carburized samples revealed oxygen and nitrogen concentrations of less than 44 and 20 ppm, respectively. The sample was heated by induction with a Westing-house 5 kw-450 kc power source. Temperature was measured with a Milletron two-color pyrometer which was sighted into the crucible by reflection from an overhead front surface mirror. Optical losses due to glass absorption and light reflection at air-glass interfaces were minimized by the employment of the dynamic-gas seal. It was found that no correction was required for the front surface reflector. The pyrometer was calibrated periodically against a U.S. Bureau of Standards tungsten ribbon secondary standard. Temperatures inside the crucible were also calibrated against the Zr-ZrC eutectic (1850°C)1 and the Nb-Nb2C eutectic (2335°C)2,3 temperatures and agreed to within ±10°C of these values. The temperature was controlled by manually adjusting the power input; variations of

Jan 1, 1967

By I. Fatt, D. N. Saraf

A method is described for measuring two- and three-phase relative permeabilities in sandstones or sand packs using a nuclear magnetic resonance (NMR) technique to determine fluid saturations. Two- and three-phase relative permeabilities have been determined on Boise sandstone using the NMR technique of saturation measurement. Three-phase relative permeability to water was found to depend only on the water saturation, whereas three-phase permeability to oil depended on both the water and oil saturations. Relative permeability to gas in three-phase flow was found to depend only on the total liquid saturation. INTRODUCTION Three-phase relative permeabilities are extremely useful in calculating field performance for reservoirs being produced by simultaneous water and gas drives. Three-phase relative permeability data are also needed for analyzing solution gas-drive reservoirs which are partially depleted and are being produced by water drive. Some thermal recovery processes involve three-phase flow which require three-phase relative permeability data for predicting reservoir behavior. Unfortunately, three-phase relative permeability measurements have rarely been made. Also, because of the scarcity of three-phase data, it has not been possible to date to relate other measured rock characteristics to the relative permeabilities with a great certainty. Leverett and Lewis,l Reid2 and Snell3 have reported three-phase relative permeability data on unconsolidated sands. Leverett and Lewis used ring electrodes spaced along the length of the sand sample to measure the resistivity of the sample which was assumed to be monotonically related to brine saturation. Gas saturation was determined from pressure-volume measurements. Oil saturation was obtained by material balance on the cell containing the sand sample. This method is involved and time consuming. Another difficulty arises from the fact that the resistivity of the sand is a function not only of saturation of brine but also of the distribution and saturation history of the brine in the pore spaces. Reid2 used a gamma ray absorption technique for measuring liquid saturation. This method has the disadvantage that total liquid saturation rather than oil or brine saturation is all that can be measured and still another method is required to determine the saturations of individual components. snel13 used a neutron bombardment method which also required a separate determination of the individual component saturations. Caudle et al.4 measured three-phase relative permeability on consolidated sandstones using vacuum distillation for determining fluid saturations. Distillation after each reading makes this technique very lengthy and time consuming. Corey et a1. 5 and Naar and Wygal 6 measured three-phase relative permeability on sandstones by the capillary-pressure method. Semipermeable diaphragm assemblies were used at each end of the core specimen to keep the water phase in the core. Gravimetric methods were used to determine fluid saturations. Sarem7 recently reported an unsteady-state method for measuring three-phase relative permeability on sandstones. This method is an extension of Welge's method8 for measuring two-phase relative permeability. Although Sarem's method is simple and comparatively fast, the assumptions involved may oversimplify the problem. Sarem's assumption, that in all rocks relative permeability to each fluid will depend only on the saturation of that fluid, seems to be rather unrealistic. Neglecting capillary effects at the end of the core is also a weak assumption. Donaldson and dean9 measured three-phase relative permeability using a method similar to Sarem's.