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By R. E. Jenkins

The Bell Canyon member of the Delaware Mountain group has yielded quite a large number of fields in which completion and production problems have been numerous and complex. Reserves are difficult to estimate due to the problem of evaluating the formation water saturation, and the feasibility of water flooding is questionable. Extensive laboratory investigations were undertaken to determine if normally measured rock and contained fluids properties could account for many of the peculiar characteristics of the formation. A statistical study or routine core-analysis data was made. Capillary-pressure data were obtained by several techniques. Fresh-water and brine permeabilities were measured and relative permeabilities of oil, water and gas were determined. Some qualitative wetta-bility tests were performed, and the petrography of a few thin sections was studied. The results of this work are presented, with typical or average data shown for each test. The permeability -to- water characteristic of the Delaware was found to be abnormally poor. Correlations of laboratory and field performance data indicate high water saturations in much of the formation. Pore geometry is highly uniform. INTRODUCTION The Delaware formation has undergone extensive exploration and development in the past few years. This has resulted in the discovery of quite a number of fields—producing oil for the most part. A large percentage of the productive wells have produced water along with the oil. Often there is no apparent pattern for the percentage of water cut experienced. In several instances vertical displacments of over 200 ft have been established between communicating wells in which the formation appears to be about the same, yet the structurally high wells yield a much higher water cut than the lower wells. Drill-stem tests have contributed little to well completion because they nearly always show small amounts of water (usually mud filtrate), regardless of what is produced later in the life of the well. Other formation evaluation methods have had no more than limited success in indicating ultimate productivity. Consequently, predicting the type of fluid productivity of Delaware wells has been very difficult. Hydraulic fracture treatments are almost universal, and unstimulated Delaware wells have not exhibited the productivity that normally would be expected of wells with the specific permeabilities encountered. Some operators have indicated that their Delaware wells need frequent re-stimulation. The uncertainty of reservoir water saturations reported for the Delaware has made difficult the task of evaluating oil in place in the reservoirs and estimating primary recovery. The unreliability of this data also will cause feasibility studies for water flooding or other secondary-recovery methods to be problematical. Several opinions have been voiced to explain why the Delaware performs as it does. Chronically poor well completions, dynamic water and tilted water tables, capillary inequi-libria, peculiar relative permeability characteristics and oil-wetness are among the suggested reasons. The dual purpose of this paper is (1) to describe the principal rock characteristics, and (2) to present an evaluation of those characteristics so that approaches can be made to explain the irrational behavior of wells completed in the Delaware. STUDY OF ROUTINE CORE-ANALYSIS DATA A statistical study of routine core-analysis data has been made to relate fundamental rock properties and characteristics of the formation to well productivity. For the most part, well production data were obtained from operators and augmented by production data from commercial information services. Only data which were available in detail and which were considered to be accurate were used. The core data used were obtained on samples from the perforated or open interval only and, thus, may not always represent the total productive interval in a well. All the core-analysis data included in this study are from the Bell Canyon member of the Delaware and were obtained by "plug-type" techniques, as opposed to whole-core or full-diameter techniques. Porosity values were obtained by the summation-of-fluids technique, permeability values are air permeabilities corrected for slippage to an equivalent liquid permeability, and the oil and water contents were determined by means of a high-temperature downdraft retort. All the procedures used are discussed at length in Ref. I. The core-analysis data were sorted

By Theodore Simons

(Butte Meeting, August, 1913.) DURING the last half century a great amount of ingenuity and energy has been devoted to the invention of appliances for the recovery of valuable minerals from very fine sands and slimes. The reason for this is that in almost every dressing plant the greatest losses of values, considered relatively as well as absolutely, occur in the treatment of slimes. The natural aim of mill operators to minimize these losses has in recent years received another impetus, from the fact that the gradually diminishing occurrence of high-grade ores makes a more intense recovery of values from existing resources absolutely necessary for profitable operation. The results of such attempts are found in the appearance of a great number of machines and appliances which make it profitable to-clay to rework old dumps, containing the tailings of older processes. A constantly growing difficulty of obtaining skilled labor and the increase in wages made it prohibitory to employ those types of machines which required much attention, and in the middle of the nineteenth century the various concentrating tables of the percussion type, which automatically discharge their products, began to take the place of the intermittent tables, on which, when the bed had reached a certain thickness, operation had to be stopped in order to allow the skimming by hand of the separate layers formed on the table. In the course of years, two general types of machines evolved for the treatment of fine sands and slimes : The so-called concentrators and vanners, on the one hand, and the buddies and round tables on the other.1 For the profitable treatment of the very finest slimes, round tables have as a last resort proved more satisfactory and economical than other machines.

Jan 7, 1913

By Matti J. Saarivirta

The relative machinabilities of the precipitation-hardenable Cu-0.9 pct Cr, Cu-0.25 pct Zr, and Cu-0.9 pct Cr-0.25 pct Zr alloys are improved from 18 to 80 pct by 0.75 to 1.25 pct Pb. The Lead also improves the tensile strength, hardness, ad resistance to softening of the Cu-Cr and Cu-Cr-Zr alloys. When the alloy containing 0.7 to 2.2 pct Cr, 0.10 to 0.25 pct Zr, 0.75 to 1.25 pct Pb, and balance copper is solution-annealed at 1000°C (1830°F) and then aged at 525°C (Y75°F), tensile strength of 65,000 psi, 16 pct elongation, 62Rb hardness, and 84 to 87pct IACS electrical conductivity are obtained. The copper base Cu-Cr, Cu-Zr, and Cu-Cr-Zr alloys have high electrical and thermal conductivities, high strength and resistance to softening at elevated temperatures, but their machinability is poor, i.e., close to that of the pure copper. In the manufacture of various components such as welding electrodes or electrical and thermal conductors it is ofter desirable that the alloy have good machinability for high production rates and long tool life. Thus, alloys that combine these properties may be used not only for existing applications, but for new ones where good machinability is a requirement. This investigation was undertaken to improve machinability without impairing other desirable characteristics of the Cu-Cr, Cu-Zr, and Cu-Cr-Zr alloys. These commercial alloys contain about 0.4 to 1.2 pct Cr, 0.10 to 0.25 pct Zr, and balance copper. Lead was selected as an element that should improve the machinability and possibly other characteristics of the alloy. WORK PROCEDURE This investigation began with a study of the effect of lead on the hardness, tensile strength, electrical conductivity, and machinability of the binary alloy containing 0.10 to 1.30 pct Cr and balance copper. This was followed by an investigation of the effect of lead on the Cu-0.1 to 0.4 pct Zr and Cu-Cr-Zr alloys. The alloys were made from initially oxygen-free copper and for comparison some castings were made from phosphorus-deoxidized Lake Copper. Commercially pure chromium, zirconium, and lead were used for alloying. In melting the chromium was added to molten copper at 1400°C (2550°F), the heat held for 15 min at temperature, and the temperature then lowered to 1350°C (2460°F) when the other elements were added. The alloys were held for 15 min at this temperature and cast into a cast-iron mold. One-kilogram, 3-in.-diam castings were made. An argon cover was maintained during melting and casting to prevent oxidation. The chemical compositions of the alloys are shown in Table I. The micro structure and properties of the alloys were studied in the cast and wrought conditions prior to and after various solution-annealing and heat-treating cycles. The relative machinability was determined as a function of the lead content and compared with the free-machining Cu-lpct Pb alloy. To determine the machinability, 13/16-in.-diam cast specimens were cut by a machine hack saw using a constant cutting speed of 50 fpm, a fixed feed force, and a new blade for each alloy specimen. Molybdenum highspeed steel saw blades, 0.032 in. thick with 14 teeth per in., were used in all tests. No cutting fluid was used. Five tests were made on each specimen and the average elapsed time per test was taken as a measure of the relative machinability for that alloy. The variation of cutting time for each alloy was less than 110 pct.

Jan 1, 1969

By J. W. Eckerd, P. S. Lewis, N. H. Coates

USBM designed, constructed, and operated an 18-in.-diam fluidized-bed combustor for highly caking coals to evaluate the method for possible application to power generation. In initial tests, combustion was carried on successfully, with carbon losses as low as 0.8%+ Coal ash was not satisfactory as a bed material, but mullite proved to be acceptable. Overall heat-transfer coeffients from the bed (-20 t 50 mesh mullite) to a water-cooled tube were about 75 Btuper hr-sq ft. Fluidized-bed combustion is being investigated by the U. S. Bureau of Mines (USBM) as a potentially cheaper method of firing power plant boilers. Lower combustion temperatures in fluidized beds—only 1400" to 1800°F-—should reduce fireside deposition and corrosion and nitrogen oxides production. Fluidized-bed combustion also offers possible advantages in the use of additives to control SO, emissions and amenability to processing of high-ash, high-moisture coals without special preparation. This paper describes development of a fluidized-bed combustor and the results of preliminary tests. Equipment and Procedure Fig. 1 shows the 8-ft-high combustor. A cone-shaped plate perforated by I/8-in.-diam holes supports the fuel bed and admits the fluidizing air; water passing through the 3/4-in. pipe extracts heat from the combustion bed. Fig. 2 is a flow diagram of the system. Coal is fed pneumatically to the base of the fuel bed. Combustion products are passed through two centrifugal separators to remove most of the entrained solids, then to a water

Jan 1, 1971

By A. E. Powers, J. F. Libsch

THE simultaneous influence of time and temperature upon the tempering process in steel is well known. Hollomon and Jaffe¹ have expressed the effect of time and temperature upon the progress of tempering by a single parameter, T (c + log t); where T is the absolute temperature; t, the tempering time; and c, a constant characteristic of the steel and treatment. It was found that when hardness data for plain carbon and low alloy steels were plotted vs. this parameter, a master tempering curve was obtained which satisfied all the data for a given steel and a given hardening treatment. Roberts, Grobe, and Moersch² successfully applied the tempering parameter to various tool steels, including high speed steel for tempering times ranging from 6 min to 100 hr. The influence of tempering time and temperature upon the physical properties of high speed steel has also been extensively investigated.'" Recently, the use of induction heating for very rapid tempering treatments has received attention. The authors% have shown that tempering treatments of only a few seconds duration may be successfully applied to plain carbon and low alloy steel. However, the influence of such short tempering treatments in high speed steel has not been explored. Since high speed steel is a highly alloyed steel exhibiting physical reactions during tempering that are often relatively slow and large in magnitude, it is an interesting steel for the study of tempering reactions. It was the purpose of the present investigation, therefore, to study the early progress of reactions leading to secondary hardness in high speed steel, type 6-5-4-2, and to determine if induction-tempering treatments of a few seconds duration are able to produce results equal to those of more conventional long-time tempering cycles. Experimental Details The chemical compositions for two different heats of W-Mo high speed steel used in this study are given in Table I. Table II summarizes the heat treatment given various groups of specimens cut 21/2 in. long and centerless ground to ¼ in. diam. Hardening treatments consisted of preheating to 1600°F (870°C) for V2 hr and then oil quenching from 2250°F (1230°C). Heat I was subjected to the high temperature in a salt bath for 3 min, while specimens of heat II were austenitized in a carbon-block muffle furnace for 10 min. Specimens of series E were immediately refrigerated to — 318°F (— 195°C) in liquid nitrogen following the hardening treatment to transform the major portion of the retained aus-tenite. Specimens of series F and G were subzero cooled to — 100°F (-75°C) in a dry ice-alcohol mixture. Induction tempering was performed with a Lepel high frequency converter operating at a frequency of approximately 300,000 cycles per sec. Heating cycles were controlled and recorded for each specimen using a chromel-alumel thermocouple, percussion welded to the surface of the specimen, and a modified high speed instrument with a timer previously used and described.' Temperature oscillation of the specimens, while being held at the tempering temperature, was ± 15°F (8°C). Tempering Treatments: After hardening, specimens were tempered between 900" and 1500°F (480" and 815°C) to study the progress of retained austenite decomposition and secondary hardening. The specimens tempered in salt for 1 hr (series C, G, and I) were considered to represent conventional treatment and are used for comparison with rapid tempering treatments. Several induction-tempering cycles were employed: 1—flash tempering, i.e., induction heating to the tempering temperature and immediately cooling (series A, E, and F); 2—induction heating for 60 sec at temperature (series B); and 3—double-induction tempering by two successive heating and cooling cycles (series D). All specimens tempered by induction were heated at an initial rate of 450°F (250°C) per sec except those of series E, which were heated at an initial rate of 1300 °F

Jan 1, 1952

By A. S. Richardson

THE recent installation of a high-pressure propeller type fan at the Moose shaft of the Anaconda Copper Mining Co. at Butte, Mont., is of interest on account of novelty of design and also because an appreciable saving was made over the cost of a reversible centrifugal fan such as is ordinarily used where a high pressure is required. The lower cost is due solely to the fact that by means of controls on the power supplied to the three-phase, alternating-current, induction motor, directly connected to the propeller it is possible to reverse the direction of rotation of the propeller and thus reverse the direction of air flow. The extra air ducts and reversing doors required for this purpose with centrifugal fans are not necessary, and their elimination greatly reduces these construction charges, which form a great part of the total expense. The Badger State mine for which the Moose shaft is used as the main outlet air course is now being developed to the 4100-ft. level. The old centrifugal fan, formerly used at the collar of the shaft, was installed 15 years ago at a time when most of the stoping was being done above the 2400-ft. level, and when the temperature of the rock was much lower than it is now on the bottom levels recently opened. The old fan, therefore, became inadequate to maintain desirable ventilation conditions, on account of the increase in resistance to air flow incident to the greater depth of the mine workings and because a much larger volume of air is required to offset the higher rock temperatures. Propeller, or disk, fans commonly used in the ventilation of mines are not suited to high-pressure work, but economies in the cost of their installation have long been recognized. In South Africa use has been made of a number of propellers placed in series along a common shaft, the number of propellers used being varied with requirements for meeting different conditions of mine resistance, but the mechanical efficiency is described as being low. In Butte, experimental work was done by the writer along similar lines under somewhat different conditions, but with poor results as to both pressure capacity and mechanical efficiency. Tests were also made of two different types of propeller fans of moderate size, which were said by the manufacturers to be suited to high-pressure mine ventilation.

Jan 1, 1932

By Richard V. Hughes, Rudolf J. Pfister

The necessity for getting more water into sands of low permeability in any secondary-recovery water-flood operation in order to recover all the available oil always has been a major problem. In the early days of water-flooding the addition of soda ash and caustic soda to fresh input waters was recommended and tried without success in the Bradford field. The most frequent difficulty was sand plugging. The use of natural and artificial brines often has been suggested for water-flooding, in the belief that laboratory observations of decreasing fresh-water throughput rates in measuring water permeabilities of consolidated sand cores might be partially explained by swelling of clays. A review of available literature bearing on the subject and related laboratory experiments are presented herein, offering an explanation for failure in use of soda ash and caustic soda waters and supporting the recent concept that every water used for input purposes in the secondary recovery of oil should possess such physical and chemical characteristics as to keep the clay content of the producing sands in a permanently flocculated condition. Produced brines meet this requirement. Their use is recommended as a means of increasing intake rates of tight sands and oil recoveries, as a solution to brine-disposal problems, and as a means of conserving a natural resource. Introduction There is a general belief among those engaged in the secondary recovery of oil by water-flooding that one of the most important requirements for the success of any such project is an adequate supply of good, fresh water. Fresh waters have the advantages of being more easily stabilized than salt waters and of being usable about the lease for all purposes. The use of brines for water-flooding never has been given much consideration in the Pennsylvania Grade area. The use of brines in Mid-Continent operations has been considered largely as a substitute for fresh waters, which were economically unobtainable for many operations. Estimated recoveries for some water-drive fields indicate that less of the original oil in place will be left upon abandonment than with the above-average practices used in Pennsylvania Grade water-flood operations. Lower residual oil saturations than 25 pct of the pore space following the water-flooding of Third Bradford sand cores in the laboratory are unusual. In comparison, water-flushed sands surrounding any virgin oil pool are found to be practically devoid of oil. Such lower natural residual oil saturations may be the result of a time factor much longer than economic under artificial water-flood operations, but neither the producer of primary oil nor the producer of oil by secondary recovery can obtain maximum recoveries unless full advantage is taken of all natural forces and

Jan 1, 1947

By M. E. Wadsworth, C. H. Pitt

Nickel corrosion in sulfuric acid solutions at elevated temperatures and oxygen wer-pressures was imestigated. Weight loss was 1inear with time and varied directly with oxygen concentration. Independent variation of the possible active species in solution indicated that the undissociated sulfuric acid molecule plays an important part in the corrosion mechanism. The rate determining step was considered to be the adsorption of oxygen on a site containing adsorbed H2SO4. THE tendency for a metal to go into solution depends on a number of factors some of which are: 1) the position of the metal in the electrochemical series; 2) the type and concentration of corroding species in solution; 3) the concentration of oxygen in solution; 4) the type of film formed at the liquid-metal interface; and 5) the physical state of the metal. The corrosion of a metal in an aqueous solution may be considered to be a heterogeneous reaction that occurs at the liquid-metal interface. The reaction is generally considered to occur as a result of electrochemical potential differences within the system. Little work has been published in the literature concerning the corrosion of pure nickel. A great deal has been publistled dealing with the experimental and theoretical aspects of the over-all corrosion process. Evans,1 Uhlig,' and recently Todt 3 and Tomashoff,4 have published books which review the results of experiments which have been conducted on corrosion, and have developed some of the basic ideas of the more widely accepted theories of corrosion. Friend5 states that. nickel does not readily discharge hydrogen from any of the common nonoxidiz-ing acids and that a supply of some oxidizing agent is necessary for appreciable rates of corrosion. He further notes that at temperatures between atmospheric and close to boiling, corrosion rates tend to vary with concentration, temperature, and aeration in acid concentrations up to 25 pct. Whitman and Russel6 studied the effect of dissolved oxygen on a number of metals in acid solutions and found that oxygen accelerates the rate of corrosion of nickel in sulfuric acid. Flowers and Kelley7 in studying the action of dissolved CO, on electroplated nickel postulated that nickel dissolves as NiHCO3 in the presence of CO, and air. It was found that oxygen was necessary for corrosion to take place and that the rate increased with increasing amounts of oxygen in solution. Flowers and Kelley attributed the oxygen effect to cathodic depolarization. MacGillavry, Rosenbaum, and wensson' determined metal solution potentials of nickel in various electrolytes. They found that nickel has no tendency to corrode in alkaline solutions in the presence or absence of air. In acid solutions in the presence of air, metal solution potential increases in the order of 1/2 v were observed. This increase was attributed to probable chemisorption of oxygen on the nickel surface and the corrosion mechanism suggested was the interaction of H+ ions with the nickel oxide formed at the surface. Delahay9 observed the reduction of oxygen on various metals. A polarograph was used to measure the course of the reaction. With some metals hydrogen peroxide was produced as an intermediate compound. However, nickel was not considered to be a hdrogen peroxide producer. Van Rysselberghe 10,11 and associates attributed the accelerating effect of carbon dioxide on the corrosion process to the presence of percarbonic acid produced in solution reacting with the hydrogen peroxide. The percarbonic acid can be reduced at less negative potentials than hydrogen peroxide and as a result accelerates the reaction. EXPERIMENTAL Since a complete description of the apparatus used can be obtained elsewhere,12'13 no attempt will be made here to describe the equipment other than to note that it consisted essentially of an autoclave unit from which samples could be withdrawn periodically without disturbing the interior state of the autoclave. A titanium autoclave liner was used to protect the autoclave from the solution.

Jan 1, 1961

By G. O. Prickett, P. Somasundaran

An experimental progmm based on statistical principles is used for optimizing a flotation operation for the separation of minerals. In this case, flotation of sylvite from sylvinite ore with amine and starch as the flotation reagents was studied to find the optimum reagent levels at various slime levels. The experiments were first done on a two-level three-factor design. Analysis of the results showed that the interactions between various factors were significant. Hence, a first-order linear model of the flotation response would not be accurate. The two-level three-factor design was expanded into a composite design in order to test the fit of a higher-order model. Data were treated to obtain an expression for flotation response as a function of the different variables, to predict the optimum reaaent levels at various slime levels, and also to determine the path of steepest ascent. Tests around the predicted optimum and along the path of the steepest ascent were done until a near-optimum region was obtained. Exploration of the nature of the response surface in that region established the actual location of the maximum response. The optimum amine level was found to be 0.20 lb of amine per ten of ore at all slime levels, while the optimum starch level varied as a function of the slime present. Computer access at the laboratory by means of a teletype terminal on a commercial time-sharing system enabled efficient and accurate treatment of experimental data. The efficiency of experimental investigations can be improved significantly by the use of experimental design and data analysis based on statistical principles. The common approach used in experimental research is to study a property of a system as a function of "one-variable-at-a-time". Several authors'-4 have pointed out the inadequacy and deceptiveness of this method. Results obtained for the effects of a variable on the measured response of the system using

Jan 1, 1970

By Walter H. Bruckner, George B. Clark

Since the end of World War 11 interest has been increasing in the use of shaped charges in the mining industry and in other industries using explosives for blasting purposes. Shaped charges employ the principle known as the "Munroe effect," which was discovered by Charles E. Munroe more than 50 years ago (in 1888). Details of their design have been explained elsewhere.1,2,3 Fig I shows the essential features of design of two types of shaped charges (with conical and hemispherical cavities) and a schematic sketch of their action upon detonation. The following discussion deals with the behavior of the metal in the cavity liners when they are subjected to intense Pressures exerted when the explosive charge is detonated. Among the conclusions reached in research on shaped explosive charges, the following have been established conceming cavity liners:1'2 I. The optimum wall thickness of a conical cavity liner is dependent upon the apex angle of the cone as well as On the base diameter of the charge. Acute apex angles require thinner walls for optimum perfonnance and more obtuse angles require thicker walls for the same base diameter. '. Cones were more effective in forming a penetrating jet when the walls were tapered; that is, the thickness of the wall of the cone increased from the apex down. 3. The physical and mechanical properties of metals have a marked effect upon their performance as cavity-liner material. Boiling point, ductility, malleability, ten-sile strength, and hardness are among the properties that influence the effectiveness of a metal used as a cavity liner. Lead, for example, makes a wide, flat crater in steel plates. Aluminum makes a deeper crater than lead, and an aluminum alloy having a high tensile strength makes a deeper hole, but slightly smaller in diameter. Cast iron makes a deep, narrow hole. These findings, together with the following analysis under Metallographic Survey of slug, offer solutions to many of the problems involved in solving the mechanism of the formation of Munroe jets. It has been fairly well established that cavity liners collapse in a manner similar to that indicated in Fig 2, Conical liners are known to collapse upon themselves while hemispherical liners are believed to turn inside out in the process of jet formation. The first has been definitely proved by recovery of collapsed portions of cones, while liners from partly detonated charges show that hemispheres may turn inside out. Fig 3 shows a sketch of a recovered slug from a 6-in. shaped charge using a 45" cone made of cast iron. (This size of charge drilled holes up to 3 ft in depth in solid granodiorite.)

Jan 1, 1949

By J. D. Forrester, Erich Sarapuu, T. C. Cheasley

Electrocarbonization of coal will produce cheap fuel for electric power plants. The complete electrification of industry and domestic power consumption of gas generated as fuel in situ is a worthwhile goal for the coal industry. Production of synthetic oils, gasoline, and coal chemicals from coal gas will create additional new markets for the coal industry. RANKING high in the nation's wealth of natural resources, readily available liquid and gaseous hydrocarbons are nevertheless falling steadily in supply, while industrial requirements for hydrocarbon compounds are greater today than during the peak period of World War 11. Theoretically, several processes will increase the future supply of liquid and gaseous fuels, but the practical application of these methods depends on two controlling factors: 1—that enough carbon-bearing material be available to warrant industrial exploitation, and 2—that the given process be physically, chemically, and economically applicable. With regard to the first factor, the Western Hemisphere is fortunately well supplied, see Table I. Table I not only shows the extensive occurrence of many fuel sources, but also the wide discrepancy among quantities of fuel substances in various materials. Great quantities of potentially available fuel have not been recovered. Many coal seams and other hydrocarbon-bearing deposits are so situated that production is uneconomical by present-day mining or oilwell pumping methods, and even in many exploitable deposits where the most efficient production methods are used a large proportion of material is never recovered. Industrial production of hydrocarbon liquids and gases must be better balanced, and processes must be developed which will convert coals, oil sand, and oil shales into fabricated commodities. Among the techniques employed by scientists and engineers to secure fuel masses not economically available at present are several processes of underground gasification. These are all concerned with converting raw materials into gaseous products by thermal treatment of source substances while they are still in the ground and therefore require that a subsurface heat (fire) zone be induced to affect pervasively the buried raw fuel deposit. This is possible only where sufficiently high temperature exists and where the fuel material is satisfactorily opened or channelized. Also, to compete successfully with common mining or oilfield practices, a given method must be controllable and must not involve greater operational expense than regular methods. Preferably, it should be less expensive. Since the close of World War 11, England has continued field studies of underground gasification methods. Experiments have also been conducted in Sweden, Estonia, France, Belgium, Italy, and Germany. The U. S. Government has sponsored field studies at Gorgas, Ala., and because gasification in situ is vitally important to establishment of the nation's fuel resources, the mining engineering department at the Missouri School of Mines has been actively interested in developing the process of underground electrocarbonization. Research was conceived by Erich Sarapuu, and preliminary experiments in treating bituminous coal were begun at the school in September 1947. The work consisted of laboratory experimentation until June 1948, at which time, through a cooperative agreement with the Sinclair Coal Co. of Missouri, pilot plant studies were instituted at the Tiger mine of the Hume-Sinclair Coal Co. near Hume, Mo., to test the encouraging laboratory findings. This comprehensive field program was pursued continuously until the beginning of 1952."'" The broad term underground electrocarbonization describes a unique gasification process that releases by electricity the desired economic constituents from a raw carbon-bearing material, converting the substance of such deposits into deliverable form and greatly reducing the cost-of-mining factor. Underground electrocarbonization is not subject to the major limitations of many other underground gasifi-

Jan 1, 1955

By R. J. Blackwell, A. L. Pozzi

Scaled laboratory-model studies provide a powerful method for evaluation of a proposed oil-recovery process. In recent years, models have been used extensively to evaluate processes in which solvents displace oil, both for general cases and for specific reservoir conditions. Since the performance of a miscible flood in a horizontal reservoir can be significantly affected by transverse mixing between solvent and oil, this displacement mechanism must be accurately simulated in the scaled model studies. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long times for experiments. If scaling requirements for miscible displacements could be relaxed while accurate simulation of essential displacement mechanisms is maintained, the utility of model studies would be greatly enhanced. The purpose of the work reported herein was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascer tain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. These studies were performed with completely miscible systems in linear, horizontal models packed with unconsolidated media. From the experimental results, a set of relaxed scaling criteria was formulated which allows the requirements of geometric similarity and equality of the ratio of viscous to gravity forces to be omitted for specified conditions. The relaxed criteria are valid whether transverse mixing is by molecular diffusion or by convective dispersion. Correlations which permit prediction of vertical sweep efficiencies in linear, horizontal reservoirs were developed from the experimental data when transverse mixing is by molecular diffusion. These same correlations may be used when transverse mixing is by convective dispersion if an empirically defined, effective, transverse dispersion coefficient is used in the description of the mixing process. The effective transverse dispersion coefficient correlation essentially duplicates the dispersion coefficient correlation for equal-viscosity, equal-density fluid systems. Experimental values for the effective transverse dispersion coefficient can be measured readily. INTRODUCTION One of the most effective methods for evaluation of miscible-displacement oil-recovery processes is that of displacements in laboratory models scaled to simulate reservoir conditions. For these laboratory studies to be meaningful, however, the essential displacement mechanisms affecting reservoir performance must be accurately simulated. Since the performance of a miscible flood in horizontal reservoirs, or in dipping reservoirs at high rates, can be significantly affected by transverse mixing of solvent and oil, this mechanism must be considered in the design of laboratory experiments. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long experiment times. This difficulty seriously limits the utility of laboratory model studies. Craig,et al,1 demonstrated that geometric similarity is not required when mixing is unimportant. Their experimental data indicate, for the cases studied, that the displacement is sufficiently characterized by scaling the ratio of viscous-to-gravitational forces. This work suggests that relaxation of the requirement of geometric similarity and, possibly, other criteria might also be permissible when mixing is important, provided suitable groups describing the mixing process are scaled. The purpose of the work reported here was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascertain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. Consequently, laboratory investigations were made of the dependence of recovery on dispersion and other variables,

By E. J. Koval

Practical miscible displacement processes will be characterized by lingering of the solvent into the oil. The lingering process is brought on by viscosity differences, and can be accentuated by channeling and longitudinal dispersion. The effects of these factors on the efficiency of unstable completely miscible displacements are combined in what is called the K-factor method. This method, analogous to the Buckley-Leverett method, predicts recovery and solvent cut as a function of pore volumes of solvent injected. Experimental data are included and show excellent agreement with theory for a wide variety of sandstone cores and viscosity ratios. INTRODUCTION Theoretical considerations,1 laboratory experiments,2 and pilot tests3 lead to the conclusion that miscible displacements in the field will be unstable In an unstable miscible displacement, the solvent fingers through the oil. This fingering leads to early breakthrough of the solvent and an extended period during which both oil and solvent are produced. For such a system, there appear to be four principal factors which bring about or accentuate the effects of instability: longitudinal dispersion (including geometrical effects), channeling, viscosity differences and gravity differences. Other factors, such as diffusion and flooding rate, can also influence the effects of instability, but at the flooding rates considered in this report, circa 15 ft/D, they are unimportant. Longitudinal dispersion can be thought of as a spreading of the solvent front caused by the presence of microscopic inhomogeneities. Channeling of the solvent occurs when a porous medium has macroscopic inhomogeneities; i.e., gross permeability variations. Viscosity differences lead to fingering of the less viscous solvent. This difference in viscosity accelerates the growth of fingers along paths previously developed because of permeability variations. Gravity differences lead to overriding by the usually less dense solvent. Al- though gravity effects are generally small at a flooding rate of 15 ft/D, they would, nevertheless, unnecessarily complicate the interpretation of flooding experiments. For this reason, all the experiments reported herein were done with matched density fluids. Fingering and the resultant poor areal sweep were recognized early as the dominant influences on the efficiency and the economics of miscible displacement processes. Much research effort has been spent on ways to minimize fingering and increase areal sweep such as the use of graded viscosity slugs4 or water slugs. Some researchers attempted to work out ways to prevent fingering completely; i.e., to achieve a stable displacement through gravity or latitudinal dispersion stabilization. l Others did not attempt to control fingering but obtained an economic process by merely recycling the solvent and sweeping pattern by pattern.6 During this period, all aspects of fingering came under close scrutiny. Some researchers reported on how fingering looks2 and how it is affected by viscosity ratio,7 geometry,7 and slug size.2,* Peaceman and Rachfordg suggested a mathematical approach to the prediction of unstable miscible displacements in relatively homogeneous sand packs, but their work cannot be extended conveniently to heterogeneous systems. Hence for a heterogeneous system, no method is presently available for predicting solvent cut and recovery as functions of pore volumes of solvent injected. The purpose of this investigation was to attempt to fill in the gap in our knowledge concerning the prediction of performance of unstable miscible dis placements. Necessarily, the system selected for study was a relatively simple one. The restrictions placed on the system were: (1) The system was linear; (2) The solvent was miscible in all proportions with the oil in place; (3) The solvent was continuously injected into the porous medium; (4) Gravitational effects were eliminated by matching densities and (5) All the flood rates were high and constant at 15 ft/D to avoid any small rate effect and to minimize any diffusion effects. To simplify and to indicate that both longitudinal dispersion and channeling arise from permeability variations, the effects which they cause or influence have been termed heterogeneity effects. The use of

By J. E. Burke

Recent investigations have elucidated many of the phenomena of the grain growth process, but have also revealed some conflicting and unexplained results. Beck and his co-workers 1,2,3 have shown that grain growth continues with continued heating at one temperature until the average grain size approaches the thickness of the specimen. Plotting the logarithm of the average grain diameter, D, against the logarithm of the annealing time, t, they find the straight line relationship given by the equation: D = Ktm [,] with possible small deviations at short annealing times. K and n are constants at constant temperature. On the other hand, Wa1ker4 finds that, in alpha brass) the rate of growth falls off more rapidly than indicated by Eq i after long annealing, so that an equilibrium grain size is approached. Burke5 showed, using Walker's data, that time and temperature for grain growth are apparently related through an activation energy, H, according to the relationship: ] where h and tz are the annealing times necessary for the average grain size to increase from Do to D at temperatures T1 and T2 and R is the gas laws constant. In the case quoted, H had the value 60,000 cal per mol. The apparent validity of this relationship, at least up to 700°C, and the approximate value of H were later confirmed by Beck3 The results obtained by Beck Kremer, Demer and Holzworth2 for aluminum and aluminum-magnesium alloys could not be satisfied by such a relationship, since the slope of the isothermal curves increased with increasing temperature. These data indicate and Beck, Holzworth and HuV ater demonstrated expcrimentally that the only apparent factor controlling the rate of grain growth at constant temperature is the grain size. While many of the phenomena have been elucidated, a reasonably quantitative explanation of the process is lacking. There exists uncertainty even as to the primary driving force for grain growth, although there is a considerable body of indirect evidence that the interfacial energy of the grain boundary is responsible.7,8,io Making implicit use of this assumption, several authors14,16 have pointed out that grain boundaries should migrate toward their center of curvature. Harker and Parkerg have advanced this concept furthest, and show that one can expect grain boundary migration to occur only when the grain faces are curved, or when they meet at non-equilibrium angles. When the face is curved toward a grain A, for example, the atoms in the surface of grain B, on the other side of the boundary7 are on the average more surromded by the atoms of their lattice than the atoms on the surface of grain A. Because of thermal motion, the atoms at the interface will sometimes be attached to grain A and

Jan 1, 1949

By D. Turnbull, J. H. Hollomon

THERE is a large body of evidence'" indicating that solidification during the liquid-solid transition is usually induced by heterogeneities present in the liquid. By dispersing liquid metals into small droplets, the impurities responsible for catalyzing solidification are isolated within a small number of these droplets. The effect of the foreign body therefore is restricted to a single drop by this technique. Thus upon cooling below the melting temperature, solidification is initiated by homogeneous nucleation in the majority of the droplets that do not contain impurities. In the case of solidification of liquid metals, the activation energy for nucleation is so great that its rate changes by orders of magnitude for a change in temperature of only several degrees centigrade.' Effectively homogeneous nucleation occurs at a critical temperature upon continuous cooling. Thus by microscopic observation of single particles during cooling, a temperature at which the rate of homogeneous nucleation becomes sensible can be determined.3 since at the temperatures at which nucleation occurs in the absence of impurities the rate of crystal growth is extremely rapid, the temperature at which the entire particle solidifies is very nearly the temperature at which the nucleation of the solidification occurs. Thus for liquids that freeze at high temperatures the onset of nucleation can be established by simply observing the temperature at which the marked heat evolution and increase in brightness of the particle occur. For liquids that freeze at lower temperatures the onset of nucleation can be determined by a rumpling and change in shape of the particle resulting from its solidification. The microscopic technique for observing the solidification of small particles has already been described." In earlier papers the nucleation of solidification of pure metals 5,6 and of alloy systems7 showing complete liquid and solid solubility have been described. In the present paper, the observations are extended to a simple eutectic system (Pb-Sn) where the possibility of the formation of two solid phases exists. Metals for the investigation were obtained from the American Smelting and Refining Co. in the form of pure lead and pure tin, 99.8 and 99.9 pct purity, respectively. An ingot of each of the pure metals was made into shot by heating the metals at a temperature about 50 °C in excess of the melting point and pouring the liquid slowly into a container of water at 15°C. Samples of the shotted pure metals were weighed out to make alloys containing 5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, and 90 atomic pct Pb. Samples of each alloy were then melted in separate beakers. Each melt was poured through a pyrex funnel into a cylindrical mold (% in. ID). The casting solidified in 10 to 20 sec. The inside of the mold as well as the funnel through which the metal was poured were coated with graphite to eliminate adherence of the metal. Analyses were performed on some of the compositions and are given in Table I. The compositions also were checked for these samples and for those that were not analyzed by determining the spread between the liquidus and the solidus upon melting the small metal particles. These measurements agreed as well with the nominal compositions as the analyses listed above. Results The results of the supercooling experiments for the several alloys are summarized in Table II and plotted on the constitution diagram in Fig. 1. Data for the pure lead and pure tin were taken from earlier investigations. The values for the maximum supercooling of the several alloys are the average of several determinations on a number of drops of each alloy. The maximum value in any determination was within about 2 pct of the average. For the alloys containing from 20 to 60 atomic pct Sn, inclusive, two marked changes of the surface structure were observed upon cooling. At the higher temperature, after the first appearance of the solid phase it continued to grow slowly at a constant temperature and then stopped. At the lower temperature the alteration of surface structure was abrupt. For the alloys containing from 70 to 95 atomic pct Sn, inclusive, an abrupt change in surface structure was observed at a single critical temperature.

Jan 1, 1952

By John T. Eash

During the course of the war the supply of tin in this country has steadily decreased and a continued effort has been made since the beginning of the emergency to use alloys that are either tin free or contain appreciably lower quantities of it. Even with the use of emergency materials, the tin supply has become particularly acute, and it is estimated that after recovery of the far eastern mines probably one to two years will be required before our normal annual supply is attained. One of the major tin-consuming fields is the bronze industry. Recommendations were made several years ago by the War Production Board toward the use of bronzes of lower tin content and manganese bronze and yellow brass for the customarily used tin-bronze alloys. The substitution of 88-5-5-2 copper-nickel-tin-zinc for composition G received considerable attention before the war, and consequently this alloy and modifications of it have been adopted for some current structural and pressure castings requiring high mechanical properties. Another of the commonly used bronzes is the 10 per cent tin 10 per cent lead copper alloy for heavy-duty bearings. It has been known for some time that about 2.5 per cent nickel could be substituted for an equal amount of tin with retention of equivalent casting and tensile properties; however, it was desirable that a still greater conservation of tin be made. Consequently the present paper deals with the development of an alloy of low tin content that could be used for bearings. Selection or Composition While the final criterion of the suitability of an alloy for a bearing must of course be determined by practical applications where all the ramifications of service conditions are encountered, certain short cuts in the initial selection of compositions are necessary to avoid an extensive and time-consuming investigation. The present program has been to match certain metallurgical properties of the 80-10-10 bronze that have been shown by previous investigations to be related to good bearing qualities. Such properties as microstruc-ture, hardness, compressive yield strength, ductility, and castability have been considered, and certain simple wear tests have been made. Of the readily assessed characteristics desired in a good bearing alloy, one can be certain that a uniform distribution of lead is required in a leaded bronze. It has generally been found that segregation of lead is one of the chief difficulties with this type of material. Tin has a powerful effect on lead distribution, and with 10 per cent present produces a random distribution of chunky particles, such as are shown in Fig' 1. I' In the tin bronze contains the hard alpha + delta

Jan 1, 1946

By Pradeep K. Rohatgi, Clyde M. Adams

Dendritic aggregate of ice formed on freezing of aqueous soluitions has been studied. Chlorides of sodium, potassiutn, lithiunz , and hydroget1 were used as solutes. The spacing between ice platelets or den-drites was experimenlally found proportzonal to the square root of freezing time when the freezing rate was constant from beginrting to end of solidification; the constant freezing rates were obtained during freezing of small droplets of aqueous soliitions surrounded by relatively large heat sinks. The transverse growth velocity of the ice platelets is proportional to the square root of the freezing rate. During unidirectional freezing from a constant temperuture chill, the solution at each location is subjected to a spectrum of freezirtg rates. The freezing rate is ini- FREEZING of solutions has been a subject of investigation in many disciplines. Aqueous solutions offer the advantage of transparenty; their study is of special significance due to the increasing interest in freezing processes for desalination. In addition dendritic solidification of aqueous solutions is in many ways analogous to freezing of metallic solutions. Aqueous solutions of most ionic salts freeze with tially low, passes through a maximum, and then decreases until solidificatimz is complete. The den-drite spacing increases linearly with the distance from the chill surface; it is inversely profiortional to the square root of the maximum freezing rate. The dendrite spacings in the two systems (the constanl freezing rate and the varying freezing rate) are equal, when the maximum freezing rate of the varying freezing rate system equals the average freezing vale of the constant freezing rate system. Mass transport in interdendritic liquid duriug solidificatiotz is analyzed; the experimental observations indicate that maximum concentration difference (AC) and supercooling (AT) in the interdendritic liquid are indepexdent of freezing rate. the separation of practically pure ice crystals from the liquid phase; with very few exceptions there is no solid solubility of ionic salts in ice. As an ice crystal grows there is rejection of solute from the moving interface into the liquid. Since the rejected solute moves primarily by diffusion, concentration gradients are established in the liquid. The highest solute concentrations are found in liquid immediately adjacent to liquid-solid interfaces and lowest concentrations farthest from the interface. Two-phase equilibrium obtains only at the solid-liquid interface; at other locations the liquid becomes supercooled because temperature gradients are negligible compared to concentration gradients. This is an immediate consequence of the fact that thermal diffusivities are considerably higher than mass diffusivities.

Jan 1, 1968

By E. G. Woods, A. G. Comer

A mathematical model is presented and solved for determinution of the saturation distribution and pressure in a radial gas-storage reservoir. The model consists basically of two parts: (I) the growing gas-bubble core, and (2) the surrounding aquifer. Since the total pressure at the injection well is a function of the two-phase flow in the gas bubble and the unsteady single-phase flow in the aquifer, the resistance to flow in both zones was taken into consideration. The assumptions involved for both the radial equivalent of the Buckley-Leverett two-phase-flow equation and the injection-pressure equation are as follows: (I) the geometry is radial, (2) the gas bubble is free to expand or contract, (3) compression or expansion of the gas within the bubble may occur at the beginning of a time step, (4) the fluids are immiscible, (5) water is incompressible within the gas-storage region whereas it is compressible outside of this region, (6) a stable gas-water interface exists and (7) gas injection occurs at a constant rate or a series of constant rates. The mathematical model was solved numerically using an IBM 650 computer. A comparison is presented between the predicted results of the model, the results assuming steady-state flow and the actual initial injection-pressure history of an operating reservoir. Using the initial field pressure for a basis, the average deviation between the predicted pressure and the actual field pressure was less than 4.3 per cent. INTRODUCTION Underground storage of natural gas in abandoned oil fields, in abandoned coal mines, in caverns and in aquifers has had varying degrees of success. The lack of these first three facilities in the vicinity of most major gas marketing areas is leading more and more to storage in virgin aquifers. For the most part, this storage in aquifers has led to the study upon which this paper is based. Several excellent papers have been published discussing the problems involved in the underground storage of natural gas; however, to these writers' knowledge, none of them considered the two-phase flow of fluids in the gas bubble and the fact that the gas bubble will grow or shrink in size depending upon the injection and withdrawal history of the reservoir. Not only will both of these factors influence the required injection pressure, but also they will have a definite bearing upon the amount of water production occurring upon withdrawal from the storage area. To solve this problem on an IBM 650 computer, several simplifying assumptions were made. Only the drainage portion of the relative-permeability curve was considered, thereby neglecting any hysteresis effects introduced during an imbibition cycle. The quantity of gas withdrawn during the period of the field study was only a small percentage of the total gas in place; therefore, this assumption is justified. For the problem studied in this case, the combined effects of capillarity and gravity were assumed to be negligible. This assumption becomes less valid as the formation thickness or the average pore diameter increases markedly. The justification of these assumptions should be studied in each case. THEORY This mathematical model for the prediction of saturation distribution and pressure for a radial gas-storage aquifer is based upon the equations for radial two-phase fluid flow'.' and for radial, unsteady-state, single-phase fluid flow.' The two-phase flow is considered to take place in a "core" whose radius is equal to the maximum radius that the gas zone will attain, as indicated in Fig. 1. The injection-withdrawal history is approximated by a series of constant flow rates. Within the "core", gas is assumed to behave as a semi-compressible fluid; that is, the gas is assumed to have a constant density based on the average gas-zone pressure for the flow period. Between each constant-rate time increment, the gas density is allowed to change. This involves an iterative solution of the pressure equation. The liquid phase in this zone is considered to be incompressible, whereas it behaves as a compressible liquid outside of this region. The equations of incompressible flow in the "core" may be written for the gas phase

By G. R. Speich, S. A. Kulin

The isothermal formation of martensite at subzero temperatures has been studied in an austenitic stainless steel. The amount of martensite formed isothermally in a given time was found to follow a C-curve behavior with decreasing temperature. Since isothermal rnartensitic transformation occurs at temperatures above the true M. temperature of the olloy, the observed M. temperature is dependent on the cooling rate. It is believed that a general martensite theory must include the basic concepts of the strain embryo theory, and also the important role of thermal fluctuations. UNTIL recently the isothermal component of the martensitic transformation had been considered as a trivial effect in theoretical considerations of this type of transformation. One of the postulates used in defining a martensitic transformation was that the reaction was temperature dependent but not time dependent. Cohen and his associates1'2 were the first to report the isothermal formation of mar-tensite. They obsel-ved the time dependency of the martensite reaction at room temperature in plain carbon steels and certain tool steels. They found that a small amount of additional transformation occurred after the specimen reached the quenching temperature and that the rate of this isothermal transformation decreased rapidly with time. These authors considered this phenomenon to be a "tailing-off" of the main athermal reaction. Kurdjumov and MaksimovaL 5 studied the isothermal formation of martensite at subatmospheric temperatures in steels containing 0.6 pct C-6 pct Mn, 1.6 pct C, and in an iron-base alloy containing 23 pct Ni and 3.4 pct Mn. In each case it was found that both the initial rate and the total amount of isothermal transformation exhibited sharp maxima with decreasing temperature. They stated that it was possible to completely suppress the martensitic transformation in the 0.6 pct C-6 pct Mn steel by drastic quenching in liquid nitrogen. They interpreted their results in terms of a thermally activated process. The maximum in the rate of nucleation vs. temperature curve was assumed to be a result of the temperature dependence of the rate of growth of the martensite plates. It has been demonstrated," however, that martensite plates can form with great rapidity even at temperatures approaching absolute zero. In addition," attempts to confirm the reported suppression of the martensitic transformation by rapid cooling of a 0.6 pct C-6 pct Mn steel have proved unsuccessful. On this basis, and on other theoretical grounds, the validity of some of Kurd-jumov's results and conclusions is open to serious question. Cohen, Machlin, and Paranjpe' have proposed a theory of martensite formation based on the nucleation of strain embryos and a growth mechanism involving cooperative atomic displacements. According to this theory thermal fluctuations can make a strain embryo supercritical and thereby produce martensite isothermally. Das Gupta and Lement' have investigated the isothermal formation of martensite in a 17 pct Cr-0.7 pct C steel at temperatures below the ambient. They found that partial suppression of the martensitic reaction occurred on quenching into liquid nitrogen. That part of the reaction which can be suppressed is taken to correspond to the isothermal rather than the athermal part of the rnartensitic transformation. The initial rate of isothermal transformation for this steel was found to go through a maximum with decreasing temperature. This is in conformity with the findings of Kurdjumov and Maksimova for the steels used in their investigation. Das Gupta and Lement conclude that isothermal martensite formation occurs by the nucleation of new plates and is always preceded by some athermal transformation. An iron-base alloy containing 14 pct Cr-9 pct Ni was used in this investigation to study further the kinetics of the austenite to martensite transforma-

Jan 1, 1953

By J. Lohrenz, C. R. Clark, B. G. Bray

Procedures to calculate the viscosities of in situ reservoir gases and liquids from their composition have been developed and evaluated. Given a composition expressed in methane through heptanes-plus, hydrogen sulfide, nitrogen and carbon dioxide together with the molecular weight and specific gravity of the heptanes-plus fraction, the procedures are capable of calculating the viscosity of the gas or liquid at the desired temperature and pressure. The procedure for reservoir liquids was developed using the residual viscosity concept and the theory of corresponding states, and was evaluated by comparing experimental and calculated results for 260 different reservoir oils ranging from black to highly volatile. The average absolute deviation was 16 per cent. This is the first known procedure for calculating the viscosity of reservoir liquids from their compositions as normally available, i.e., including the heptanes-plus fraction. The procedure for reservoir gases uses a sequence of previously published correlations. Evaluation of the procedure was accomplished by comparison of 300 calculated and experimental viscosities for high-pressure gar mixtures in the literature. The average absolute deviation was 4 per cent. The calculations are useful for (I) determining viscosities in compositional material balance computations and (2) predicting the viscosity decrease which occurs when gases, LPG, or carbon dioxide dissolve in reservoir oils. INTRODUCTION Methods to predict viscosities of reservoir fluids from the normally available field-measured variables have been presented. Beal,1 Standing,2 and Chew and Connally3 orrelated oil viscosities with temperature, pressure, oil gravity and gas-oil ratio. Carr, Kobayashi, and Burrows4 and Katz et al.5 have presented correlations for reservoir gas viscosities as a function of temperature, pressure and gas gravity. Lie all intensive physical properties, viscosity is completely described by the following function: Eq. 1 simply states that viscosity is a function of pressure, temperature and composition. These previous correlations1- hay be viewed as modifications of Eq. 1, wherein one assumes more simple functions may be used. The assumptions are practical, because the composition is frequently not known. Further, the assumptions are sufficiently valid so that these correlations are frequently used for reservoir engineering computations. In compositional material balance"' computations, the compositions of the reservoir gases and oils are known. The calculation of the viscosities of these fluids using this composition information is required for a true and complete compositional material balance. For reservoir gases, Carr, Kobayashi and Burrows4 have presented a suitable compositional correlation. For reservoir oils, no correlation is available, and data from reservoir fluid analyses have been used7-9 for compositional material balance calculations.* From a theoretical point of view, this is entirely invalid. The reservoir fluid analysis, whether flash, differential, or other process, does not duplicate the compositions which occur during the actual reservoir depletion process, therefore the viscosities measured during reservoir fluid analysis are not those which occur in the reservoir. From a practical point of view, the "error" of using viscosities from reservoir fluid analysis is of varying and unknown significance. One can say qualitatively that the error is greatest where compositional effects are greatest, i.e., for volatile oil and gas condensate reservoirs and pressure maintenance operations. The first requirement to obtain a quantitative estimate of the significance of the error is to develop a reliable compositional correlation for the viscmities of reservoir oils. No such correlation has been available. Consistent with this requirement, the objective of this study was to develop a procedure to predict the viscosity of reservoir fluids from their compositions. Normally, the compositions of reservoir fluids are available expressed as mole fractions of hydrogen sulfide, nitrogen, carbon dioxide and the hydrocarbons methane through the heptane-plus fraction, with the average molecular weight and specific gravity of the latter. The final correlation was to use the composition in this form. While the more challenging objective of the study was the development of a correlation for the viscosities of reservoir oils, the viscosities of reservoir gases were also studied. The end result of the study was a procedure to calculate the viscosities of reservoir gases and liquids suitable

Jan 1, 1965