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By F. M. Lewis, E. C. Johnson

Used as a classifier in a plant expanding capacity or changing to closed-circuit operation, the liquid-solid cyclone offers the advantage of being adaptable to existing conditions. This paper presents the costs involved and experience gained from operating a unit of this kind. BY now application of the liquid-solid cyclone to various classification problems in the chemical and metallurgical fields is more or less familiar. A less publicized application receiving wider consideration as time goes on is its use as a classifier in closed-circuit grinding operations. This paper presents the costs involved and the experience gained from operating a unit of this kind. In May 1951 the Tennessee Copper Co. installed in its London mill at Copperhill, Tenn., a liquid-solid cyclone in closed circuit with a 6x12-ft ball mill. The circuit in which this cyclone is used is the regrind or secondary grinding circuit of a copper flotation plant. Originally it consisted of a 7x1-ft conical ball mill in closed circuit with a bowl classifier. Changes made in the primary grinding circuit of the mill necessitated a regrind circuit of greater capacity. The bulk concentrate to be ground was raised from 900 or 1000 tpd to 1200 or 1300 tpd, and to accommodate this increase a 6x12-ft ball mill which had been in the primary grinding circuit was moved into the regrind circuit. When this was done it was found that the classifier was too small to give efficient operation. Space in the plant was at a premium, and since use of the cyclone offered considerable economy the installation shown in Figs. 1-3 was made. The unit installed is a 24-in. diam cyclone classifier with a 20" cone angle. Diameter of the vortex finder is 8 in., the feed entrance area 20 sq. in. Maximum diameter of the adjustable apex valve is 6 in. and minimum diameter approximately 3.5 in. To refer again to Figs. 1 and 2, the cyclone* is mounted motor. It is charged with 18 tons of 1-in. balls. The overflow, or fines, passes by gravity directly to the copper flotation plant. The ball mill discharge and the new feed combine in a sump from which they are sent to the cone by an 8x6 SRL pump at a rate of 497 gpm. Pressure at the cyclone is 5 psi. For reasons dictated by the nature of the ore treated, particularly the bonding of fine grains of chalcopyrite to pyrrhotite, the froth from the second cell of the copper rougher circuit is returned to the regrind mill. This flow, which somewhat complicates the standard closed-circuit calculation, is seen in Fig. 1 to be 156 tpd of solids. This combines with the cyclone classifier underflow to constitute the ball mill feed. The requirement of the regrind product is that it be 77 to 80 pct —200 mesh. The liquid-solids cyclone operating in conjunction with the 6x12-ft mill adequately met this requirement. Of primary importance is the fact that this arrangement provided sufficient classification capacity to replace the undersized classifier and was capable of building up a circulating load to 87 pct, large enough to give an efficient grind. In this instance the circulating load is taken as the ratio of sands to new feed. Any comparison of performance between this liquid-solid cyclone and the replaced classifier would of course be unfair, since the bowl classifier was

Jan 1, 1955

By T. A. Rickard

The notion prevails that writing is a knack, that the skilful use of the pen is a gift of nature. This is an error. Dogberry may be responsible for it; he said: "To be a well-informed man is the gift of fortune, but to write and read comes by nature". Because Dogberry said it, we may be sure that Shakespeare thought otherwise. Ability of any sort may be partly innate, but my own observation and experience lead me to conclude that most of the easy writers have become so by constant practice. As I recall the names of men successful with the pen, I remember that most of them have written a great deal and have taken particular pains to improve their style. The suggestion that proficiency in the difficult art is a happy accident provokes a sardonic smile. The larger part of the great writing in our literature is the result of persistent effort. An easy fluency has been the undoing of many; their flamboyant and fantastic scribbling has proved as perishable as froth. This criticism applies to technical writing also; in order that a technical description or discussion may hold the interest of the reader, at least long enough to cause him to read it to the end, the writing must be done carefully and systematically; otherwise it will fail in its purpose of conveying information. Clearness is absolutely essential. "It is not enough to use language that may be understood; it is necessary to use language that must be understood."* The purpose of writing, at least of that which is meant to be read by others, is not only to express ideas but to communicate them. Lack of perspicuity may prove as %ad as

Jan 1, 1931

By R. C. Gould, A. M. Skov, L. F. Elkins

Comparison of long term decline in oil production during cyclic waterflooding or pressure pulsing of part of the Driver Unit with steady injection-imbibition flooding in the Tex Harvey area led to large expansion of flood in the Driver Unit on the steady injection basis. While the flood has been successful, the major problem has been attainment of satisfactory oil production rates in most of the wells. Large volume fracture treatments of low capacity wells were unsuccessful in achieving sustained increases in production. A two-section area in the Driver Unit has already recovered 620 bbl of oil per acre by waterflood but other areas have not performed so well. Sun Andres water containing 300 to 500 ppm H,S is sweetened to 0.5 to 1 ppm H,S by extraction with oxygen-free flue gas. This prevents contamination of gas produced in the area and apparently it has reduced corrosion in minimum investment, thin-wall, cement-lined water dktribution systems. Cement-lined tubing in injection wells has mitigated corrosion as effectively as thick polyvinyl chloride films have, and at less cost. Introduction As reported in the literature the Spraberry field of West Texas has presented unusual problems for both primary production and waterflood ing. Earlier information from the Spraberry Driver Unit included conception and evaluation of cyclic waterflooding or pressure pulsing in a nine-section pilot test as an aid to extraction of oil from the tight matrix rock and as a boost to normal capillary imbibition forces An additional 5 years' operation in that area, and performance of expanded steady injection water-flood, now covering a total of 68 sq miles, are reported herein. In addition, since the Driver Unit is one of the largest waterfloods in areal extent in the U. S., many operating experiences are presented for the benefit of engineers concerned with operation of other Spraberry floods or with other waterfloods where this reservoir technology and/or water handling technology may be adaptable in part. These include: (1) attempts to improve producing well capacity through large volume fracture treatments, (2) long-term performance of water treating plants utilizing oxygen-free flue gas to extract H,S from sour San Andres water, (3) performance of thin-wall cement-lined pipe in water distribution systems including comparison between those sections carrying raw San Andres water and those carrying treated water, and (4) comparison of performance of various lining materials and subsurface equipment in water supply and water injection wells. These experiences are reported without regard to whether results are good, bad or indifferent. Since the operations reported are limited to the techniques, materials, and equipment actually used in the Driver Unit, no comparison is possible with results of other approaches used in other Spraberry floods or in waterfloods generally under different conditions. However, an attempt is made to quantify these experiences as much as possible in the space available to permit other engineers to select those parts applicable to eheir problems. Background The Spraberry, discovered in Feb., 1949, is a 1,000-ft section of sandstones, shales and limestones with two main oil productive members—a 10- to 15-ft sand near the top and a 10- to 15-ft sand near the base, having permeabilities of 1 md or less and porosities of 8 to 15 percent. Extensive interconnected vertical fractures permitted recovery of oil on 160-acre spacing from this fractional-millidarcy sandstone, but they made capillary end effects dominant. Primary recovery by solution gas drive is less than 10 percent of oil in place, with most wells declining to oil production of a few barrels per day when reservoir pressures are still in the range of 400 to 1,000 psi. Partial closing of the fractures with declining reservoir pressure is believed to be the cause of such low production rates at these relatively high reservoir pressures. In 1952 Brownscombe and Dyes proposed that displacement of oil by capillary imbibition of water from the fractures into the matrix rock might significantly increase oil recovery from the Spraberry, overcoming otherwise serious channelling of water through the fractures." A pilot test conducted by the Atlantic Refining Co. during 1952 through 1955 indicated technical feasibility of the process; but low oil production rates averaging I5 to 20 bbl/well/D failed to create significant interest in large-scale waterflooding at that time." Humble Oil & Refining Co. conducted a highly successful 80-acre pilot test during 1955 through 1958 with

Jan 1, 1969

By John C. Martin

The discovery of a new gas reservoir demands that the planning of a sottnd well-spacing program be initiated early in the development stage. It is the purpose of this discussion to illustrate by actual field examples the application of basic well-spacing principles, previously developed for oil reservoirs, to the problem of well spacing in natural gas fields. These studies are presented for the field use of geologists and engineers who are concerned with the initial planning of the proper development of the newly discovered gas reservoir. INTRODUCTION The phenomenal growth of a vigorous natural gas industry emphasizes the increasing importance of natural gas as a source of energy, fuel, and raw materials to our nation's economy. Since 1945 marketed production of natural gas for the U. S. has increased 21/2 times to a record high of 10.6 trillion cu ft during 1957. As major participants in the gas industry, we share an added interest to develop and produce our natural gas reserves with constantly improved efficiency. The subject of well spacing is vitally important to the gas industry, for the well itself plays a significant role in the development of the natural gas reservoir and in control of the recovery process. Maximum utilization of wells is an integral part of sound conservation practices. The discovery of a new gas reservoir demands that careful choice of well location and well spacing be made and that the planning of a sound well spacing program be initiated early an the development stage. With the drilling of the first development well, efforts of the geologist and engineer must be directed toward acquisition of adequate technical evidence upon which a firm recommendation for a spacing program may be based. With this technical appraisal as a foundation, operators and state regulatory agencies jointly can go far in providing a framework for sound development of gas fields to achieve a program of conservation that avoids the unnecessary well. WELL-SPACING CONCEPTS Through laboratory and field investigations of the mechanism of the recovery of oil and gas, of fluid behavior, and of effective control of reservoir and well, a crystallization of ideas regarding reservoir behavior has emerged as a well-developed technology. Associated with a better understanding of the fundamental principles underlying reservoir and well behavior has been the growth of concepts concerning the role of wells and their spacing in the development and operation of an oil or gas reservoir. In addition to serving as outlets for the withdrawal of fluids from the reservoir, wells are recognized as having two other important functions: (1) providing access to the reservoir to obtain information concerning the characteristics of the reservoir and its fluids, and (2) serving as a means by which the natural or induced recovery mechanism may be effectively controlled. Beyond a minimum number of wells required to fulfill these two functions, additional wells will not increase recovery. With particular emphasis upon well spacing in oil reservoirs, many studies of the well spacing-recovery relationship have evolved the concept that the ultimate oil recovery is essentially independent of the well spacing.' These fundamental concepts are no different when regarding the role of wells and their spacing in the natural gas reservoir. They are equally applicable to the consideration of well spacing in gas reservoirs. For the gas reservoir, the problem of well spacing then revolves around the question of drainage and the degree or extent to which a well may drain gas from its surrounding reservoir environment. Theoretical and Experimental Work During the past 30 years, theoretical and experimental work carried on to study the physical principles involved in the flow of fluids through porous media has shed light upon the matter of drainage. Fundamental mathematical equations have been derived to describe the mechanism of flow of oil and gas through porous rocks. With the recent advent of high-speed digital computers, attempts have been made with mounting success to develop solutions, employing numerical techniques, to mathematical expressions that describe more rigorously the physical behavior and mechanism involved in the unsteady-state flow of compressible fluids, such as a gas, through porous rock. In 1953, Bruce, Peace-man, Rachford and Ricez published a stable numerical procedure for solving the equation for production of gas at constant rate. The results of these calculations are significant with respect to this matter of drainage, for they indicated (1) that depletion of the gas reservoir resulted in a drop in pressure at the extremity of the

By G. S. Ansell, J. Weertman

The creep behavior of an aluminum alloy hardened with a finely dispersed phase of aluminum oxide was investigated. The as-extruded alloy shows an approximate steady-state creep in which the creed rate depends exponentially on the applied stress. The activation energy of creeb is abbroximately 150,000 cal per mole. The recrystallized alloy shows no steady-state creep. ONE method of improving the creep resistance of a metal is to introduce a finely dispersed second phase into the metal matrix. The improvement of the creep resistance has been qualitatively explained by assuming that the dispersed second-phase particles act as obstacles to dislocation motion. If the main effect of second-phase particles is simply to hinder dislocation motion then it is possible to derive a high-temperature creep equation for a dispersion-hardened alloy in a straightforward manner. In the Appendix of this paper such an equation is derived from a creep model which works very well for pure metals. Recently, F. V. Lenel has fabricated, for the first time, powder extrusions of aluminum-aluminum oxide in a large-grained recrystallized form. This alloy, designated as MD 2100, consists of a fine dispersion of aluminum oxide plates in a matrix of commercial purity aluminum. A considerable amount of investigation has been carried out concerning the microstructure and physical properties of this alloy.&apos; ) The aluminum oxide is present in the form of flakes 130A units thick and 0.3 u on edge. They are dispersed in the aluminum matrix with an average spacing of approximately 0.5 jx. The spacing varies in the range of 0.05 to 1.5 µ. The alloy structure is extremely stable at high temperatures. For this reason the alloy offers a unique opportunity for a fundamental study of creep of a very finely dispersed two-phase alloy. Lenel supplied specimens in both the unrecrystallized and recrystallized condition. This paper reports high-temperature creep experiments carried out on these specimens. The results obtained were rather unexpected. No steady-state creep was observed in the recrys-tallized material. In fact, after some transient creep which takes place upon loading, the creep rate is essentially zero ( < 10-8per min). If the second-phase particles acted solely as obstacles to the motion of dislocations, measurable steady-state creep would be expected. Since none is observed it appears that the main effect of the fine dispersion in the recrystallized material is to inactivate the dislocation sources themselves, rather than hinder the motion of dislocation loops created at these sources. EXPERIMENTAL DETAILS Specimens were tested in wire form, 0.087 in. in diam for the as-extruded alloy, and 0.035 in. in diam for the recrystallized alloy. These samples were held in friction-type wire grips; a gage length of 2.5 cm was used for all the creep tests. The specimens were held at 600°C in the test apparatus for at least 15 hr prior to each test. The tests were run under the condition of constant loading and, since the creep strains were small, can be considered as constant stress tests. The temperature of testing was held constant within 3°C. Elongations were measured with an optical cathetometer which was capable of measuring strains as smaIl as 0.00012. This allowed the measurement of strain rates as low as l0-8&apos;per rnin. In addition to the creep tests optical micrographs were made in order to determine both the grain size and microstructure of these materials. RESULTS Fig. 1 shows a few typical creep curves obtained from the as-extruded material. The elongations were somewhat erratic, but each curve shows a region of quasi-steady-state creep from which an approximate steady-state creep rate can be obtained. In general the higher the stress at a given temperature, the greater the total elongation before fracture. The lower the applied stress, the longer is the region where the creep rate is almost constant. Summary data from the creep tests of the as-extruded material are listed in Table I. The steady-state creep data of the as-extruded material for a range of stresses at a constant temperature follow a creep equation of the type creep rate = K&apos; = A exp (&) [11 where A and B are constants, k is Boltzmann&apos;s constant, T is the absolute temperature, and a the stress. The standard error of estimate of the data received is less than one order of magnitude. As shown in Fig. 2, if one compensates the creep-rate data for the effect of temperature over the range of test temperature, the steady-state creep data roughly follow a creep equation of the type Temperature compensated creep rate = K* = A exp

Jan 1, 1960

By Ralph B. Stevens

INTRODUCTION Underground fires continue to be one of the most serious hazards to life and property in the mining industry. Although underground mines are analogous to high-rise buildings where persons are isolated from immediate escape or rescue, application of technology to locate and control fire hazards while still in their controllable state is slow to be implemented in underground mines. Even in large surface structures such as hotels, often only fire protection systems which meet minimal laws are implemented due to the high cost of adding extensive extinguishing systems, isolation barriers, alternate ventilation, escape routes and alarm systems. Incomplete and ineffective protection occasionally is evidenced where costs would not seem to be a factor, such as the $211 million MGM Grand Hotel fire November 21, 19801. Paramount in increasing fire safety and decreasing the threat of serious fire is early warning followed by proper decision analysis to perform the correct action. However, very complex fire situations can be produced in structures such as high-rise buildings and underground mines simply because of the distances between the numerous fire-potential locations and fire safe areas. Other complexities arise when normal activities occur that emit products of combustion signaling a fire condition to a sensitive fire/smoke sensor. For example, the operation of diesel equipment or the performance of regular blasting can produce combustion products that reach the sensitive alarm points of many sensors2. Smoke detectors for surface installations provide fire warning when occupants are at a distant location or when sleeping, thus greatly reducing injuries and property damage. However, when installed in the harsh environments of underground mines, fire and smoke detection equipment soon becomes inoperative, unreliable, or requires excessive maintenance. The U.S. Bureau of Mines has performed many studies and tests to improve fire and smoke protection for underground mine workers3. This paper describes several USBM safety programs which included in-mine testing with mine fire and smoke sensors, telemetry and instrumentation to develop recommendations for improving mine fire safety. It is hoped that the technology developed during these programs can be added to other programs to provide the mining industry with the necessary fire safety facts. By recognizing fire potentials and being provided with cost-effective, proven components that will perform reliably under the poor environmental conditions of mining, mine operators can provide protection for their working life and property equal to that which they provide for themselves and their families at home. The basis of this report is two USBM programs for fire protection in metal and nonmetal mines4,5 and one coal program6. The data was collected beginning in May 1974 and continuing through the present with underground tests of a South African fire system installed at Magma Mine in Superior, Arizona, and a computer-assisted, experimental system at Peabody Coal Mine in Pawnee, Illinois. The conduct of each program was as follows: • Define the problem and its magnitude in the industry • Develop concepts to solve or diminish the problem • Review available hardware or systems approaches to fit the concepts • Install and demonstrate the performance of a prototype system through fire tests in an operating mine. MINE FIRE FACTS Whether in coal or metal and nonmetal mines, the potential severity of fire hazard is directly related to location. As shown in Figure 1, fire in intake air at zones A, B, C or D can cause contamined air to route throughout the mine quickly if not detected, isolated or rerouted. Causes and location of former metal and nonmetal fires are represented in Table 1; the cause and location of fatalities and injuries is shown in Table 2. Coal-related fires and their impact on deaths and injuries are graphed in Figure 2; their locations are described in Table 37. Significantly the table shows that the hazard to personnel was three times greater for fires occurring in shaft or slope areas, and the percentage of deaths and injuries was four times that of other areas. Number of Persons Affected A 129-mine sample indicated that from 8 to 479 employees per shift work in underground metal and nonmetal mines, and that deeper mines have larger populations, as shown in Figure 3. Coal mining relates similar employment, and a 16-state sample of 670 mines employing at least 25 persons shows the distribution in Figure 4. Drift mines accounted for 58 percent of the sample but employ only 45 percent of the underground workers.

Jan 1, 1982

By Elwood G. Haney, R. N. Parkins

Stress corrosion cracking of two heats of 18 pct Ni maraging steel in rod form immersed in an aqueous solution of 0.6N NaCl at pH 2.2 has been studied on un-notched specimens stressed in a hard tensilf machite. Austenitizing temperature in the range 1830 to 1400 F has been shown to have a marked influence on the propensity to crack, the loulest austenitizing- temperature producing the greatest resistance to failure. In the nzosl susceptible conditions, the cracks followed the original austenile grain boundaries; but when tlze steels zcere heal treated to inproze their resistance to stress corrosion, the cracks becatne appreciably less branched and slzouqed significant tendencies to become trans granular. Electron metallography of the steels indicated the presence of snzall particles, possibly of titanium carbide, along- the prior austenite grain boundaries and these particles u:ere more readily detectable in the structures that were most susceptible to cracking. Crack propagation rates, which appeared to be dependent upon applied stress and structure, were usually in tlze reg-ion of 0.5 mm per hr and may, therefore, be e.xplained on tlze basis of a purely electrochetnical ,nechanism. However, there is some ezliderzce from fractography that crack extension may be assisted by ttlechanical processes. Anodic stit)zulation reduced the tiwe to fracture, although cathodic currents of small magnitudes delayed cracking-; further increase in cathodic current resulted in a sharp drop i,n fracture litne, possibly due to the onset of hydrogen ewbrittlement. THE use of the high strength maraging steels, with their attractive fracture toughness characteristics, is restricted because of their susceptibility to stress corrosion cracking in chloride solutions. Although this limitation has resulted in investigations of the stress corrosion susceptibilities of these steels, there have been few systematic studies aimed at defining the various parameters that determine the level of susceptibility. It is the case that the usual tests have been performed with the object of defining some stress or time limit, on unnotched or precracked specimens, within which failure was not observed,&apos; but while such results may be of some use in design considerations, they are necessarily concerned only with the steels as they currently exist and not with their improvement to render them more resistant to stress corrosion failure. This omission may be considered unfortunate because the indications are that stress corrosion in maraging steels shows dependence on structure in following an intergranular path, and since experience with other systems of intergranular stress corrosion crack- ing is that susceptibility may be varied by modifying heat treatments, a similar effect may be expected with maraging steels. It is sometimes from such observations that a fuller understanding of the mechanism of stress corrosion crack propagation begins to emerge, leading in time to the development of more resistant grades of material. The present work was undertaken to study only one aspect of the influence of heat treatment upon the cracking propensities of the 18 pct Ni maraging steel, namely the effect of austenitizing temperature, although certain ancillary measurements and experiments have been undertaken. EXPERIMENTAL TECHNIQUES Most of the measurements were made on a steel, A, having the analysis shown below, although a few results were obtained on a steel, B, having a slightly different composition. Both steels were supplied in the austenitized condition, A as 3/8-in-diam rod and B as 1/2-in.-diam rod. Cylindrical tensile test pieces were machined from the rods: the overal length was 2 1/2 in., the gage length 1 in. and the diameter 0.128 to 0.136 in. The stress corrosion tests were carried out with the specimens strained in tension in a hard beam testing machine, the necessary total strain being applied to the specimen over a period of about 30 sec, after which the moving crosshead was locked in position and the load allowed to relax as crack propagation proceeded; the load relaxation was recorded. The load was applied after the specimen had been brought into contact with the corrosive solution, the latter being contained in a polyethylene dish having a central hole through which the specimen passed, leakage being prevented by the application of a film of rubber cement. The specimen was in contact with the solution for over half of its gage length and the solution was exposed to the air during testing. The solution was prepared from distilled and deionized water to which NaCl was added, 0.6N, and the pH adjusted to 2.2 by HCl additions. The composition of the solution

Jan 1, 1969

By K. A. Slagle

Hydraulic analysis of the wellbore has become increasingly inzportant for designing cementing operations and selecting equipment, materials and techniques to complenzent modern well-c-ompletion practices. Non-Newtonian fluid technology has advanced beyond the point where former empirical methods of analysis adequately define the hydraulic system and fluid properties. In view of these factors, this paper describes a series of rheological calculations which have been found practical, through field usage, for assistance in selecting a cementing program. A relatively simple laboratory method using standard viscometric equipment is suggested for determination of the rheological properties of slurries, and clrrta are presented on some of the more common cementitrg conzposition.A. A criterion for divergence from laminar-flow characteristics has been proposed. Usefulness of the calculations is indicated by examples of cementing operations where they have been used. INTRODUCTION With the changing aspects of well-completion practices during the past few years, it has been increasingly important to have a relatively simple method of analyzing the flow conditions existing in the well during cementing operations. This is particularly true in view of the improved economics toward which most of the changes have been directed. Rheological characteristics of slurries used for cementing should be a major consideration in the trend toward smaller casing sizes, either single or multiple strings. Receiving increased attention is the practice advocated in 1948 by Howard and Clark&apos; of attaining turbulent flow with the fluids circulated during a primary cementing operation. While there may still be a difference of opinion concerning this technique, most available information indicates that superior primary-cementing results are generally obtained when high displacement rates are employed. Fluid properties of the slurry to be used must be available, as well as calculation methods, to determine what flow rates should be attained and the probable consequences in terms of frictional pressure and horsepower utilization. It would certainly be inappropriate to attempt high displacement velocities if sufficient pressure might be developed to create lost circulation. Since cementing slurries are non-Newtonian fluids, it is not possible to define their rheological or fluid properties by the single factor of viscosity and then make calculations for the quantities just described. Because the shear stress-shear rate ratio is not constant: it becomes necessary to establish at least two parameters for adequate fluid-flow calculations. It is not the purpose of this paper to delve into the mathematical development of non-Newtonian technology, nor to discuss the arbitrary classification system under which a single fluid may resemble two or three different classes depending upon experimental conditions. Rather, the intention is to present a useful series of calculations based on a concept applicable to both Newtonian fluids and to the preponderance of non-Newtonian fluids encountered in the oil-producing industry. Development of this approach was begun some 32 years ago,&apos; and has most recently been brought to fruition by Metzner and his co-workers at the U. of Deleware. Some non-Newtonian fluids encountered in the petroleum industry, other than cementing slurries, have also had the benefit of this method of analysis."&apos; The two parameters required to define the fluid are usually denoted by the symbols n&apos; and K&apos; and, for the purposes of this discussion, are called "flow behavior index" and "consistency index", respectively. These two slurry properties permit calculation of the Reynolds&apos; number and the "critical" velocity, or the velocity at which departure from laminar flow begins. EXPERIMENTAL DETERMINATIONS The two principal instruments used for rheological studies are the pipeline (capillary-tube) viscometer and the rotational viscometer. When conveniently possible, a capillary-tube viscometer (where the pressure drop and flow rate of the material can be measured) is the better method for rigorous determination of the flow behavior index and consistency index for non-Newtonian fluids. With pressure-drop data at various flow rates, it is then possible to prepare a logarithmic plot of shear rate as the abscissa-shear stress as the ordinate. For fluids which do not exhibit time-dependency, these data will usually produce a straight line. The flow behavior index n&apos; represents the slope of this line, while the consistency index K&apos; becomes the intercept of this line at unity shear rate in accordance with the mathematical derivations associated with this concept of rheology. Due to the difficulties anticipated in maintaining a uniform, pumpable cement slurry for the time interval required to obtain measurements from the pipe viscometer, the n&apos; and K&apos; data reported herein were obtained using a direct-indicating rotational viscometer (Fig. 2). The

By A. H. Heim

A method and apparatus for measuring gas porosities of rocks are described. The apparatus can be assembled from commercially available components. In principle, measurements are made by volume substitution at constant pressure. The maximum error is not more than 0.3 porosity per cent. Typical results are given. INTRODUCTION Determining the porosity of rock samples is one of the most important and yet most varied types of measurement in core analysis. Among the many techniques devised are the so-called "gas porosity" methods. An old and well known example is the Washburn-Bunting method.&apos; The U. S. Bureau of Mines2-&apos; described and later improved the apparatus for a now widely used method generally known as the "Boyle&apos;s law" method. In the present form of the Washburn-Bunting method,&apos; the volume of air in the pores of a rock sample at atmospheric pressure is extracted and then collected in a graduated burette at atmospheric pressure. The volume of air is read directly as the pore volume of the sample. The absolute error in reading the collected volume of gas is independent of the total volume; thus, the relative error is larger when the volume is small, as it is for rocks of low porosity. In addition, the sample after measurement contains mercury, which limits its use for other analyses. The Bureau of Mines (or Boyle&apos;s law) method measures directly the solids volume of a sample from which the pore volume and porosity are derived, using a separate measurement of the bulk volume. Gas at a few atmospheres pressure is introduced into a sample chamber of known volume containing the rock sample. The pressure is accurately measured. Following, the gas is expanded into a burette at 1 atm, and the gas volume is read directly. From the initial pressure p, and the final pressure p2 and volume v,, the initial gas volume v1 is calculated using Boyle&apos;s law; that is, p1v1 = p2v2. Volume v, minus the volume of the empty sample chamber is the solids volume of the sample. The accuracy of the method is limited, unless corrections are made, by deviations of the gas from the "ideal" gas-law behavior assumed in the simple form of Boyle&apos;s law. The purpose of the present paper is to describe a method for measuring the gas porosity of a rock which avoids many of these difficulties. Gas volumes are measured directly with the same accuracy as the bulk volumes. Pressures of at least an order of magnitude larger than those of previous methods are employed to insure rapid penetration of the gas into the sample. While special equipment may be built to apply the method, the porosimeter may be constructed as well from commercially available components. For simplicity, the apparatus described will be referred to as the "Constant-Pressure gas porosimeter". THE CONSTANT-PRESSURE METHOD Fig. 1 shows schematically the arrangement of components comprising the present Constant-Pressure porosimeter. Briefly, the method is one of volume substitution and may be considered a null measurement. Omitting (for the present) some of the operational details, the method of measurement consists of the following three steps. 1. After evacuation, the volume of the measuring system (a ballast chamber, a manifold, two gauges and their connections) up to the sample chamber is filled with gas to a high pressure (- 1,000 psi). A sample of the gas at this pressure is trapped in one side of a sensitive differential pressure gauge to serve as the reference pressure for subsequent steps. 2. The evacuated sample chamber containing the rock sample is opened to the measuring system. As the gas expands into the chamber, the resulting decrease in pressure unbalances the differential pressure gauge. 3. The pressure is restored by means of a mercury volumetric pump. The volume of mercury injected exactly equals the free or void volume of the sample chamber (volume of empty chamber minus the solids volume of the rock within). From the injected volume and the known empty chamber volume, the solids volume is obtained and the porosity calculated. The pressure and the volume occupied by the gas are the same before and after opening the sample chamber. Expansion and compression of the gas are incidental operations and do not enter into the calculation of porosity. By the pressure balancing or nulling, the free volume of the sample chamber is merely substituted by an equal and measured volume of mercury. Since the measurements are at constant pressure, there are no compressibility corrections necessary for the sample chamber.

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

By N. J. Olson, G. W. Toop

A series of equations previously derived for calculating ternary thermodynamic properties using binary data has been applied to the problem of predicting ternary phase diagrams and quaternary excess free energy. The methods are considered to be rigorous for regular ternary and quaternary systerns and empirical for nonregular systems. The equations have been used to predict ternary phase boundaries in the Pb-Sn-Zn system at 926°K and the Ag-Pd-Cu system at 1000ºK. Calculated quaternary excess free-energy values are presented for the Pb-Sn-Cd-Bi system at 773°K. A method for predicting the location of ternary phase boundaries would be a useful supplement to experimental measurements in ternary systems. This has been recognized with the considerable work that has been done to find models to predict or extend thermodynamic properties and phase diagrams in binary and ternary systems1-18 for which direct experimental measurements are limited. With the access to highspeed digital computers and mechanical plotting devices, it is currently rather easy to compare mathematical models with experimental data. The regular-solution model is consistent with systems which exhibit negative heats of mixing, positive heats of mixing, and miscibility gaps, and therefore it is applicable to simple phase diagrams. The purpose of this paper is to illustrate the use of regular-solution equations to predict, empirically, phase equilibria in some types of nonregular ternary systems. Corresponding equations for regular quaternary systems are given and used to calculate empirical quaternary excess free-energy data. METHOD FOR PREDICTING THE LOCATION OF TERNARY PHASE BOUNDARIES USING BINARY DATA Meijerin1,6 has used the regular-solution model to calculate common tangent points to ternary free energy of mixing surfaces and hence to determine phase boundaries in ternary systems involving miscibility gaps. He used the following equation to calculate ternary excess free energy of mixing values: stants characteristic of the binary solutions, and Ni is the mole fraction of component i. An alternate expression which gives for regular solutions as a function of binary values of along composition paths with constant N1/N2, N2lN3, and N1/N3 may also be derived:15 ternary r xs 1 ?c-*n.Ti*.U*. This expression for is more useful for the empirical calculation of ternary excess free-energy values for nonregular systems because actual binary AFXS data may be used in the expression rather than attempting to find suitable constants for Eq. [I]. The results of this feature of Eq. [2] are illustrated in Table I where calculated excess free-energy values for the Ni-Mn-Fe system at 1232°K are compared with experimental data of Smith, Paxton, and McCabe.19 Although regular-solution equations have been shown to give calculated thermodynamic quantities which agree quite well with experiment for single-phase nonregular ternary systems,14,15 care should be exercised in the use of the equations to predict thermo-dynamic properties of multiphase ternary systems in which strong compound formation is suspected. This precaution is consistent with the simple regular-solution model which for negative values of ai_j will indicate a tendency toward compound formation but even for very large negative values of ai-jwill not give multiphase binary or ternary systems involving a distinct stable compound. Hence, calculated ternary free-energy data using Eq. [2] might be expected to vary between being rigorous and poor, in the following order, for ternary systems which are: a) regular solutions, b) nonregular single-phase liquids in which random mixing is nearly realized, c) nonregular single-phase solids, d) nonregular multiphase systems exhibiting miscibility gaps, e) nonregular multiphase systems with binary compounds but no ternary compounds, f) nonregular multiphase systems with highly stable binary and ternary compounds. The calculated data will be expected to be least accurate for the last two cases. The general method adopted in this paper involves two-dimensional plots of ternary activity curves. The principle used is that tie lines indicating two-phase equilibria join conjugate phases a and B for example, for which a1(a) = a1(B), a2(a) = a2(B), and a3(a) = a3(B). Tie lines may be determined by plotting the ternary activities of two components along an isoactivity line for the third component and the unique points where the above equalities hold may be found graphically.

Jan 1, 1970

By B. G. Matson, M. A. Whitfield, G. R. Dysart

This paper describes the development of u computer program to calculate changes that occur in the length of tubular goods due to temperature and pressure changes during stimulation operations. Due to the numerous variables involved and the uncertainty of all static and dynamic conditions that could exist, it becomes a staggering task for individuals charged with completions to perform the necessary mathematical calculations. The computer program permits advance calculations for several sets of conditions. INTRODUCTION In the Delaware basin of West Texas alone, 50 wells were contracted or drilled to 15,000 ft or deeper in 1965. Deep well activity is continuing in this and other areas on an expanding scale. Many of these deep wells require extensive stimulation for successful commercial production, and during these operations, pressures and temperatures are encountered that have a pronounced effect on the length of tubular goods. This length change during a large-volume, high-pressure stimulation treatment utilizing fluids considerably cooler than bottom-hole temperature can be of such a magnitude that permanent damage to casing and tubing will result unless mechanical design, pressures and fluid temperatures are evaluated and controlled. These pressure and temperature effects can be calculated. However, the process lends itself well to computer solutions because of the mathematical nature of the problem and the calculating hours involved in arriving at an answer. The engineering-hour demand becomes more severe as tapered strings are involved. On initial treatments on a given well, surface pressure and injection rate conditions are unknown, and offset well conditions have not proven to be a reliable method for making predictions. For these reasons, it has become rather standard procedure for operators to compensate for these uncertainties by placing unnecessary pressure and fluid temperature restrictions on stimulation design. On a number of occasions treating fluids have been preheated to as much as 160F as a means of compensating for thermal contmction resulting from pumping cool fluids. The maintenance of packer seals has been treated by Lubinski, Althouse and Logan&apos;,&apos; and the problem of therma1 effects on pipe has been explored by Ramey." These works were expanded and the results made applicable to everyday oilfield terminology before submitting them to computer programming. The pressure and temperature effects on tubing movement previously mentioned occur simultaneously as fluid moves through the pipe. The pressure changes, for purposes of explanation, are categorized here as to the various effects these pressures have on a tubing string. These divisions are (1) the piston-like results of forces acting on horizontal surfaces exposed to pressure, (2) swelling or ballooning of the tubing along its entire length due to the forces of pressure acting against the tubing walls, (3) the elongation of tubing due to frictional drag and (4) corkscrewing of the pipe due to internal pressure. Thermal changes are also of great importance, as their results may be more significant than any of the pressure effects. Steel is an excellent conductor of heat and the earth is a relatively poor conductor. It has been calculated that pipe temperatures at depths of more than 20,000 ft approach within as little as 25" the temperfature of the surface fluid after pumping for 2 hours, or a drop in temperature in some treatments of more than 220F. The equations presented in this paper were developed for computer programming and simplicity of input information; therefore, numerical constants such as Young&apos;s modulus for steel (28 X 10\ si), the coefficient of thermal expansion of steel (6.9 X 10."IF) and Poisson&apos;s ratio for steel (0.3) are included with unit conversion factors. The moment of inertia of tubing cross-sectional area with respect to its diameter was changed to a constant times (D&apos; — d&apos;) where D is outer diameter and d is inner diameter. Units in the equations are length in feet, diameter in inches, density in pounds per gallon, pressure in psi, rate in barrels per minute and time in hours. PISTON-LIKE REACTIONS A change in tubing internal dimensions and the exposure of other horizontal surfaces to different pressures on the inside and outside of the tubing result in a reaction much like a piston under pressure. Such is the case when the internal diameter changes in a combination string of pipe, when seals of a slick joint assembly are subject to pressure and in the end effects of a tubing string. The change in tubing length due to the piston effects of a slick joint packer is affected by the various diameters involved, the tubing pressure Ap,, the casing pressure ,Ap,, length of pipe L, densities of fluid in the tubing before and during pump-

By W. B. Dancy, A. Adams

Laboratory test work on heavy liquid separation of sylvite from halite is reported. Numerous tests were run on sylvite ore sized in the ranges of 4x20 mesh, 10x65 mesh, 8x100 mesh, -8 mesh and -10 mesh with heavy liquids in the range of 2.05 to 2.15 sp gr. From the test results, it was concluded that, with the type of ore under study and a size in the range of -8 mesh, a recovery as high as 90% could be achieved with a product grade of 70% KCl. However, a final product at an acceptable recovery cannot be made with one pass, and the float must either be further processed with heavy liquids or dried and sent to a conventional froth flotation circuit. Potash ores occurring in this country consist essentially of sylvite and halite plus minor amounts of magnesium sulfate salts and montmoril-lonite-type clays. Recovery of potash minerals from evaporite ores in the North American potash fields is accomplished almost exclusively by use of amine flotation. European practice involves froth flotation as well as solution-crystallization processes. Laboratory and pilot plant test work has been reported in Europe and the U. S. on the application of heavy media separation to potash ore beneficiation. Work was probably discontinued because of lack of ore with the required very coarse liberation characteristics (1/8 to 1/2 in. liberation size). Sylvite, with a gravity of 1.99, and halite, with a gravity of 2.17, appear to be ideal for separation by heavy liquids, which are now available in gravities from 1.59 to 2.95. This paper reviews preliminary results obtained from laboratory test work on heavy liquid separation of sylvite from halite. TEST WORK The heavy liquids used in the tests under discussion were chlorobromethane, with a specific gravity of 1.923, and dibromethane, with a gravity of 2.490. These liquids, completely miscible, were combined in the proportions needed to give a mixture having the desired specific gravity. Feed for the laboratory tests was mine-run ore screened to the desired mesh sizes. In conducting the tests, the sample was fed at a constant rate into a stream of heavy liquid and the mixture directed into a small separatory vessel. The float overflowed into a collecting pan while the sink collected in the bottom of the separatory vessel and was removed at the end of the test. Approximately 500 g of feed constituted a charge. Pulp density of the feed was kept low to prevent particle to particle interference in separation. With feed in the range of 8x100 mesh, a pulp density of under 10% solids by weight was found advisable. With coarser feed the pulp density could be carried as high as 15% solids. Time of separation was very rapid. In the case of 4x20-mesh material, separation was effected in 15 to 30 sec; with -10-mesh feed, separation required about 1 to 2 min. SPECIAL EQUIPMENT Since heavy liquids are toxic to varying degrees, all separatory work was carried out in a standard laboratory fume hood. It was noted that complete removal of fumes was not being effected; therefore the hood construction was modified, resulting in a completely satisfactory arrangement for heavy liquid test work. In the interest of safety, details of this fume hood are reported here. Unlike most fumes, heavy liquid fumes tend to settle and flow like water, rather than to rise like a gas. Working on this assumption, a standard water drain was installed in the hood. Across the front of the hood a 1-in. barrier was constructed. In the rear of the hood a false back was installed, with an adjustable sliding door on both the bottom and top of this panel. As shown in Fig. 1, the exhaust fan pulled a vacuum behind the barrier, sucking the heavy fumes from the bottom of the hood. Another addition was the drying box, shown to the right of the hood. This is simply a box covered on top with hardware cloth and connected by a 6-in. inlet to the hood. Sample trays made of fine mesh wire filter screens were found ideal for drying samples. With this arrangement, air flowed completely through the sample and all fumes were drawn into the hood. In use, it was found effective to cover with a

Jan 1, 1963

By S. D. Baumer, P. M. Hulme

IN the late thirties, the National Carbide Co. cooperated with C. E. Wood, of the U. S. Bureau of Mines, in his investigation of the relative merits of various desulphurizers, including soda ash, caustic soda, and calcium carbide. Laboratory tests showed that carbide, when it could be made to react, is an excellent desulphurizing agent for molten iron. Sulphur content can be driven to lower levels and higher extractions obtained with carbide than with actionsany of the more common reagents. Wood&apos;s results1 are shown in Table I. Unfortunately, as the Handbook of Cupola Operation puts it, the chemical fact that carbide is a good desulphurizer was of only academic interest because it was found to be extremely difficult to devise a practical means to make it react with molten iron. Calcium carbide is formed in the electric furnace at 4000°F and above, and its softening point is probably at least 500 °F above the usual working temperatures encountered in iron and steel practice. Consequently, carbide does not form a true slag but floats as a dry powder on top of the metal and only a very small portion of it ever comes in actual contact with the iron. Stirring with a rabble, or pouring the metal over the carbide, increases the efficiency only slightly. Extractions of 20 to 30 pct can be obtained in this manner, but conventional soda slag treatment can do better than this and do it more cheaply. All attempts to lower the melting point of carbide in order to obtain a reactive, liquid slag have so far proved fruitless. Directly under the arc in a metallurgical electric furnace, carbide becomes highly reactive. Excellent sulphur removal can be obtained without any slag other than a thin layer of carbide." imilarly, good results are obtained by adding small amounts of carbide to the finishing slag in double-slag arc furnace practice. To react a liquid with a solid, it is axiomatic that the liquid has to wet the solid before anything can happen. If the solid is heavier than the liquid, the problem is easy, but it becomes more difficult when the solid is much lighter than the liquid, as in the case of carbide and liquid iron. Wood recognized this problem and solved it in a unique fashion. The results shown in Table I were obtained by spinning the carbide beneath the surface of the molten iron by means of a refractory centrifuge. This technique allowed each particle of the finely divided carbide to come into intimate contact with the metal and to be wetted thereby. Wood&apos;s centrifuge technique was successful in the laboratory where it achieved excellent and consistent results. Some attempts were made to expand this method to commercial practice, but serious difficulty was encountered in obtaining a refractory centrifuge head that would be economically feasible. About this time the war intervened and the project lay dormant for several years. In 1944, it was revived. It was suggested that the carbide could be blown into the metal with a carrier gas in an attempt to eliminate the necessity for the expensive and brittle centrifuge. The idea was first tried out in a fairly large ladle of iron using natural gas as the carrier. Considerable sulphur was removed, but it was quite obvious that the use of natural gas was not practical. Attempts then were made to blow carbide into molten iron using, in turn, nitrogen, argon, carbon dioxide, air, and oxygen. The latter two gases proved unsatisfactory. Calcium evidently prefers oxygen to sulphur because in the tests calcium oxide and carbon dioxide were produced, the sulphur still being untouched in the iron. Nitrogen, argon, and carbon dioxide gave much better results, although the efficiencies and extractions were erratic, and only a few isolated tests approached the results obtained by Wood. Table II shows typical results obtained with these gases. The sulphur removals were interesting, sometimes even encouraging, but it is evident that such erratic behavior could not be tolerated in commercial practice. A number of different types of equipment, such as sand blasting machines, refractory guns, and the like can used to blow the solid into the metal. All types required relatively large quantities of gas in order to maintain the flow of solid carbide through the system and into the metal. It was observed that the bubbles of gas breaking through the surface of the metal contained quantities of unreacted carbide. The liquid metal never came in contact with these particles and if it cannot wet them it cannot react with them. The initial work had shown that carbide had great possibilities as a desulphurizer. In practice

Jan 1, 1952

By F. A. Forward, J. Halpern

A new process for extracting uranium from ores with carbonate solutions is described. Leaching is carried out under oxygen pressure to ensure that all the uranium is converted to the soluble hexavalent state. By this method), alkaline leaching can be used successfully to treat a greater variety of ores, including pitchblende ores, than has been possible in the past. The advantages of carbonate leaching over conventional acid leaching processes are enhanced further by a new method which has been developed for recovering uranium from basic leach solutions. This is achieved by reducing the uranium to the tetravalent state with hydrogen in the presence of a suitable catalyst. A high grade uranium oxide product is precipitated directly from the leach solutions. Vanadium oxide also can be precipitated by this method. The chemistry of the leaching and precipitation reactions are discussed, and laboratory results are presented which illustrate the applicability of the process and describe the variables affecting leaching and precipitation rates, recoveries, and reagent consumption. THE extractive metallurgy of uranium is influenced by a number of special considerations which generally do not arise in connection with the treatment of the more common base metal ores. Perhaps foremost among these is the very low uranium content of most of the ores which are encountered today, usually only a few tenths of one percent. A further difficulty is presented by the fact that the uranium often occurs in such a form that it cannot be concentrated efficiently by gravity or flotation methods. In these and other important respects, there is evident some degree of parallelism between the extractive metallurgy of uranium and that of gold and, as in the latter case, it has generally been found that uranium ores can best be treated directly by selective leaching methods. It is readily evident that this parallel does not extend to the chemical properties of the two metals. Unlike gold, which is easily reduced to metallic form, uranium is highly reactive. It tends to occur as oxides, silicates, or salts. Two ores are of predominant importance as commercial sources of this metal: pitchblende which contains uranium as the oxide, U3O51 and carnotite in which the uranium is present as a complex salt with vanadium, K2O-2UCV3V2O5-3H2O. These ores may vary widely in respect to the nature of their gangue constituents. Some are largely siliceous in composition, while others consist mainly of calcite. Sometimes substantial amounts of pyrite or of organic materials are present and these may lead to specific problems in treating the ore. Further complications may be introduced by the presence of other metal values such as gold, copper, cobalt, or vanadium whose re- covery has to be considered along with that of the uranium, or whose separation from uranium presents particular difficulty. In general, there are two main processes for recovering uranium in common use today.&apos;.2 One of these employs an acid solution such as dilute sulphuric acid to extract the uranium from the ore. A suitable oxidizing agent such as MnO, or NaNO, is sometimes added if the uranium in the ore is in a partially reduced state. The uranium dissolves as a uranyl sulphate salt and can be precipitated subsequently by neutralization or other suitable treatment of the solution. The second process employs an alkaline leaching solution, usually containing sodium carbonate. The uranium, which must be in the hexavalent state, is dissolved as a complex uranyl tricarbonate salt, and then is precipitated either by neutralizing the solution with acid or by adding an excess of sodium hydroxide. The latter method has the advantage of permitting the solutions to be recycled, since the carbonate is not destroyed. This is essential if the process is to be economical, particularly with low grade ores. With each of these processes, there are associated a number of advantages and disadvantages and the choice between using acid or carbonate leaching is generally determined by the nature of the ore to be treated. In the past, more ores appear to have been amenable to acid leaching than to carbonate leaching and the former process correspondingly has found wider application. With most ores, acid leaching has been found to operate fairly efficiently and to yield high recoveries. One of the main disadvantages has been that large amounts of impurities, such as iron and aluminum, sometimes are taken into solution along with the uranium. This may give rise to a high reagent consumption and to difficulties in separating a pure uranium product. Excessive reagent consumption in the acid leach process also may result

Jan 1, 1955

By A. B. Cook

Gas cycling is generally considered a much less efficient oil recovery mechanism than water flooding. HOWever, recoveries from some fields have been exceptionally high as a result of gas cycling. Recovery from the Pick-ton field, for example, was calculated to be 73.5 perceni of the stock-tank oil originally in place. In evaluating pressure maintenance projects, determining how much of the recovery is due to displacement by gas and determining how much is due to vaporization of the imrnohile oil in the flow path of the cycled gas is very difficrilt. Even though most of the oil is recovered by displacetr~ent, the success of a project may depend on the amount of oil vaporized. A limited number of experiments have heen performed with a rotating model oil reservoir that simulates gas cycling operations and allows a separation of the oil from, tile free gas flowing into the laboratory wellbore at reservoir conditions, thus revealing which is displaced oil and which is vaporized oil. It Iras been determined that the amount of varporizatio&apos;n is .significant if proper conditions exist These experiments show that oil vaporization depends on pressure, temperature, volatility of the oil and amount of gas cycled. Increases in each of these conditions increase the volume of oil vaporized. Data from six experiments affecting vaporization are presented to illustrate reservoir condition that range from favorable to unfavorable. 111 these eaperitnenis recovery by vaporization ranged from 73.6 to 15.3 percent of /he immobile oil (oil not produced by gas displacerrlt). INTRODUCTION Between 1930 and 1950, gas cycling was a popular. oil recovery practice. especially for the deeper reservoirs. Later, with many case history-type studies published for both gas cycling and waterflooding, it was generally believed that waterflooding was far superior to gas cycling, even when gas cycling was conducted as a primary production procedure by complete pressure maintenance. A good example illustrating the advantage of water-flooding over gas cycling is given in a paper by Matthews&apos; on the South Burbank unit where gas injection was followed by waterflooding. The author concluded in part that "Early application of water injection, without the intervening period of gas injection, would have recovered as much total oil as ultimately will be recovered by waterflooding following the gas injection, and total operating life would have been shortened". This appears to be a logical conclusion. However, it should not be applied to all fields. Pressure maintenance with gas in the Pickton field, as reported by McGraw and Lohec;&apos; will result in a much larger percentage of oil recovery than was obtained in the South Burbank unit. The great success in the Pickton field resulted partly from vaporization of the immobile oil in the flow path of the cycled gas. The amount of vaporization is related to the following conditions: volatility of the oil as reflected by the APT gravity of the stock-tank oil; reservoir temperature; reservoir pressure during gas cycling; and the amount of gas cycled. Therefore, the U. S. Bureau of Mines is investigating these effects on vaporization in a research project using a model oil reservoir. Three different stock-tank oils having 22, 35 and 45" API gravities are being used as base stock to synthesize reservoir oils. Experiments are being performcd to determine vaporization at 100, 175 and 250F and at 1,100, 2,600 and 4,100 psia. This is a progress report showing the results from six experiments. Other Bureau of Mines reports"- concerning vaporization are listed. LABORATORY EQUIPMENT AND PROCEDURES The equipment &apos; consists of an internally chromium-plated steel tube packed with finely sifted Wilcox sand. The tube is approximately 44 in. long and has an ID of 13/4 in. The sand section contains approximately 570 ml of voids, has a porosity of 32 percent, and a permeability to air of 4.3 darcies. A unique feature of the laboratory reservoir (Fig. 1) permits the tube part to rotate at 1 rpm while the outlet and inlet heads are held stationary. The outlet end contains diametrically opposed windows to permit observatlon of the flowing fluids, and two valves, one on the top and the other at the bottom. Oil and free gas. when being produced simultaneously, can be separated by manipulating the two valves to keep a gas-oil interface in view through the windows. Thus, only gas is produced through the top valve and only oil flows through the bottom valve. The laboratory equipment was designed to study vaporization. Therefore, a uniform reservoir was made using dry sifted sand as opposcd to using a consolidated sand core with interstitial water. Furthermore. the reservoir was tilted to minimize fingering of gas. This tilting also in-

By E. Kendall Cork

The traditional financial objective for a single mine company has been to operate as frugally as possible and to pay out most of the earnings as dividends. If the business is cyclical (as it is for most metals) the dividends might fluctuate quite widely. When the mine is exhausted the company disappears. This is still quite a viable strategy for a single mine company. It is not however a viable strategy for the world as a whole. The mining industry is built by mine development companies who can mobilize the people and capital to bring new mines into production. Their skills must include marketing, engineering, finance and other politics. It is very rare for a property to be brought in without the support of a major company that can provide all these services. The exceptions will usually have some other form of big brother support, for example the U.S. government uranium contracts at guaranteed generous prices. The mine development company will seek as a minimum to perpetuate itself by developing new mines in order to replace those which are running out. The more common and more ambitious objective is to grow -- that is to add to its ore reserves and current production by developing more new mines. The financial objectives for that company are very different. Obviously if all the earnings were paid out in dividends there would be nothing left to work with. The first financial policy then is to spend an appropriate amount on exploration for new properties. The next is to retain enough of the earnings to provide the capital for new projects at least sufficient for the equity. There is no magic formula as to what proportion of earnings should properly be distributed as dividends by a growth-oriented mine development company. As a rough rule of thumb distributing half or more will probably leave too little to work on and 30% or so is probably a good balance. However the circumstances differ widely from company to company. It may be useful to set an objective for the rate of growth of a company&apos;s earnings. Some have picked rates such as 15% per annum compounded. Others have set a target in real terms which might appear as 10 or 11% plus inflation. Obviously the arithmetic of compound interest is very attractive; however in practice there is much variation. Indeed current returns from existing operations swing widely with the business cycle and there is no assurance that economic new properties will be found according to someone&apos;s arbitrary time schedule. For example, Western Mining Corporation Limited in Australia explored for 30 years with little to show for it, but then found the great Australian nickel deposits and more recently the huge Roxby Downs copper. That long dry spell could not have fitted anyone&apos;s arbitrary calendar of growth and yet they would not have found such orebodies without that long period of effort. Should they have abandoned the search? Once a new property has been found or acquired there has to be a threshold rate of return on the new capital to be invested against which to evaluate the property&apos;s economics. Conventionally this seems to be 15% after tax, a number common in other heavy industries as well. In some cases it is expressed as a lower number plus allowance for inflation. Discounted cash flow analysis is a very useful tool but it does not make the decision. In the end a "go" decision depends on judgment of many factors some of which are numbers used in the DCF calculation whose credibility must be examined. It is curious how frequently investment proposals come in with the rates of return very close to 15%. The project advocates know that a number much less than 15% will not fly and that a number much more is not necessary. With much higher nominal and real interest rates of recent years, even though before tax, logic suggests that the hurdle rate should also rise. The power of compound interest is so great that 20% is very hard to achieve in any cash flow projection but 18% may be a sensible yard - stick. Once again it is remarkable how many project proposals come in with an 18% return. On the record the mining industry as a whole has not been overly restrictive in choosing its hurdle rates of return. This is shown by the abundance of metals in recent years and the failure of metal prices to keep up with inflation. All of the foregoing is standard text book stuff.

Jan 1, 1985

By R. A. Garling

INTRODUCTION Since the infancy of in situ uranium mining, a growing number of hydrometallurgical processes have been incorporated into pilot and commercial scale flowsheets. Although initial design efforts were geared toward maximizing uranium recovery and minimizing plant and wellfield flow circuit maintenance, recent emphasis has shifted to improved means of water conservation and aquifer restoration. As mining units approached depletion, evaporation ponds reached minimum freeboard, and state and federal agencies demanded proof of groundwater restoration, processes including mixed bed and conventional ion exchange, reverse osmosis and electrodialysis were adopted by the industry. These units served the additional function of reducing process bleed flows during mining in states where the deep disposal well permitting ice remains unbroken. This report concerns the use of electrodialysis as an alternative to the more conventional processes used in in situ mining. In addition to a brief history and description of the process, a comparison to reverse osmosis and operational data derived from testing an Ionics, Inc. 1.31 x 10-3 m /s (30,000 gallon/day) unit at the Teton-Nedco Leuenberger Research and Development pilot will be presented. HISTORY Commercially practicable electrodialysis was contingent upon the development of synthetic ion exchange membranes in 1940&apos;s. In 1952, Ionics Inc. demonstrated that the process was amenable to the treatment of salt and brackish water and, in 1954, made their first commercial sale. The following decade saw several major electrodialysis unit sales which were generally targeted for use on private or municipal potable water treatment. Major increases in membrane desalting unit capacities, facilitated by technological advances in the reserve osmosis industry, were noted during the 1970&apos;s. The development of polarity reversing electrodialysis equipment which reduced feed pretreatment requirements, increased water recovery rates, and simplified unit operation, kept Ionics Inc. competetive in the water treatment industry. Engineering advances which incorporated automated equipment, non-corrosive construction materials, and improved ion exchange membranes allowed the electrodialysis process to compete in industrial waste treatment among other commercial markets. PROCESS AND APPARATUS DESCRIPTION The electrodialysis process utilizes direct electrical current passed across a stack of alternating cation and anion selective membranes in order to achieve an electrochemical separation of ionized materials in an aqueous solution. The membrane stack has the appearance of a plate and frame filter press and auxilliary equipment includes solution pumps, electrically actuated valves, filters, piping and a direct current power source. The ion separation membranes are thin sheets of synthetic cation or anion selective resins. Attaching sulfonate or quaternary ammonium groups to the cross linked copolymer structure determines the ion selectivity of the membrane. The membranes are separated from each other in the stack by non-conductive spacers that house flow channels which route the flow tortuously and parallel to the membranes. Direct electrical current passing perpendicularly to the membranes and solution passages attracts cations toward the cathode and anions toward the anode (Figure 1). As the ions from the feed stream pass through the ion selective membranes, they become concentrated in the adjacent brine channel and are retained there by the combined attractive force of the electrode and the repelling force of the next membrane toward the electrode. Limiting factors on the degree of demineralization possible include chemical solubilities in the brine flow and the current density that will produce an unacceptable degree of polarization (Figure 1). Feed or brine solution treatment with complexing agents or acids has been successfully applied to prevent membrane scaling. Polarization can occur when sufficient current density is applied to dissociate water in the ion depleted region of the diluting compartments near the membrane surfaces. Significant polarization is evidenced by large electrical resistances across cell pairs and notable pH differences between diluting and concentrating streams. Limiting current densities have been increased in U.S. manufactured equipment by utilizing tortuous flow paths of relatively high linear velocities thereby promoting continous solution mixing. Energy consumption is due to separating electrolytes and solutions, oxidation and reduction reactions occurring in electrode compartments, overcoming electrical resistance, conversion from AC to DC power, solution pumping and auxiliary equipment actuation. A major improvement to the basic electrodialysis process was applied in 1970 which resulted in frequent, automatic cleaning and descaling of membrane surfaces. The process, polarity reversal, incorporates alternating the cathode and anode on a periodic basis while exchanging product and brine flow channels via electrically actuated values. The reversal reduces the potential of stack plugging with CaCO3 (calcite), CaSO4 (gypsum), and colloidal materials and, in most waters, eliminates feed pre-treatment requirements. For approximately two minutes during and following the reversal, off spec. water is flushed to waste or reintroduced to the feed supply. The usual feed treatment on polarity reversing electro-

Jan 1, 1982

By R. I. Jaffee, R. M. Evans

IN recent years, the interest in liquid metals as heat-transfer media for power plants has been very great. The possibility of the development of nuclear power plants has increased this interest and served as the impetus behind much research on low melting metals and alloys for such purposes. The principal reasons for consideration of liquid metals as heat-transfer media lie in their high thermal conductivity and consequent high heat-transfer coefficients, stability at high temperatures, and the high ranges of temperature possible. The element gallium possesses some of the requisite properties for a heat-transfer liquid. It is a unique material, having a low melting point and a high boiling point. Pure gallium melts at 29.78oC, and suitable alloying will produce a metal which melts below room temperature. The boiling point is about 2000°C. As it is a liquid metal, the heat-transfer characteristics would be good. Gallium is not now readily available, due in part to a lack of uses for the metal. Nevertheless, it is not a rare element, and a sufficient supply of gallium exists to permit its consideration for this use. Since gallium has some promise as a heat-transfer liquid, owing to its unique properties, research on the subject was carried on at Battelle Memorial Institute at the request of the Bureau of Ships, U.S.N. The research had as its objectives the determination of the effect of alloying on the melting point of gallium, and the study of the corrosion of possible container materials. In this research, alloys were found which had significantly lower melting points than pure gallium, but none which simultaneously fulfilled other additional requirements, chiefly the corrosion problem. Neither was it found possible to reduce the melting point of certain otherwise suitable alloys appreciably by small additions of gallium or gallium alloys. The results gave little hope that gallium alloys can be developed which enhance the good properties and minimize the undesirable characteristics of elemental gallium. Thus, gallium now appears less promising than other metallic heat-transfer media. The experimental thermal-analysis techniques used in this work have been described.&apos; Experimental Results As a first approximation, the development of low melting gallium alloys was based on alloying elements suitable for use in a nuclear power plant, which also lowered the melting point of gallium. Information from the literature, summarized in Table I, indicates that. tin, aluminum, and zinc are the only suitable elements which cause a lowering of the melting point of gallium. Indium and silver also lower the melting point of gallium, but are of little interest for use in nuclear power plants. Of the elements reported not to lower the melting point of gallium, there is some ambiguity on the behavior of copper. Weibke3 obtained solidus arrest temperatures of 29°C for Cu-Ga alloys from 60 to 90 pct Ga, 0.8C lower than the generally accepted melting point. This may be the effect of a eutectic close to gallium, or, more likely, the result of impurities, or experimental error. The seven elements listed in Table I whose effects were not known were of potential interest if they lowered the melting point of gallium. Their effects were determined experimentally for this reason. Binary alloys containing nominally 2 pct of each of these elements were prepared in the form of 2-g melts by placing the components in a graphite crucible and holding them in an argon atmosphere at 370°C for 5 hr. These melts were then subjected to thermal analysis. In all cases. the solidus temperature was the melting point of gallium. Since these elements (As, Ca, Ce, Mg. Sb, Si, and T1) did not lower the melting point of gallium, they were not considered further as components of a eutectic-type alloy. Ga-Sn-Zn Alloys Preliminary considerations of this system for low-melting alloys were encouraging. All three binary systems were of the simple eutectic type. The composition and melting points of the eutectics were as follows: Sn-9 pct Zn (199°C), Ga-8 pct Sn (20°C), and Ga-5 pct Zn (25°C). Therefore, the probability of a ternary eutectic was high. For reasons to be discussed later, aluminum could not be used as an alloying constituent, leaving the Ga-Sn-Zn system as the only one of interest for low-melting gallium-

Jan 1, 1953

By K. C. Hong, R. B. Jensen

The problem of determining the optimum set of steam volumes and cycle lengths for a single well undergoing multicycle steam stimulation in order to maximize the cumulative discounted net income has been formulated mathematically and programmed for a digital computer. The mathematical fonnulation of the problem and the method for its solution are discussed in this paper. The oil production performance during each stimulation cycle was simulated by either a constant percentage or a harmonic decline. Using simple analytical expressions for production performance, the cumulative discounted net income and cumulative time of operation were related to the pertinent process and cost parameters and two principal process control variables (cycle length and steam injection volume). The discrete maximum principles was used to transform the equations for cumulative time of operation and cumulative discounted net income into a set of simultaneous equations. The simultaneous equations then were solved by trial and error on a digital computer to determine the set of cycle lengths and stem injection volumes that gives maximum cumulative discounted net income over the project life. INTRODUCTION Steam stimulation is a process for improving the oil recovery rate from wells producing high-viscosity crudes. The process is applied on an individual well basis and is executed in a series of cycles, each consisting of three phases: steam injection, soaking (steam condensation), and production. Significant increases in production rate following the stimulation operation result from heating the reservoir around the wellbore. As heat is removed with produced fluids and dissipated into nonproductive formations, the production rate declines, usually to near the prestimulation value. Typical production responses are given in case histories reported by Owens and Suter,l and are depicted in Fig. 1. Duration of the production phase is equal to the time for the oil production rate to decline to some specified value and is called the cycle length. (Cycle length is defined as the producing portion of the cycle and does not include the downtime required for steam injection and soaking operations.) Termination of the production phase coincides with the start of steaming for the next cycle. The process is continued, cycle by cycle, until it becomes unprofitable. Models 2-4 have been developed to simulate behavior of a single well during one cycle of steam stimulation and have been used to investigate the effects of system and operating conditions on the production responses. However, these investigations have not shown how the models can be used to determine a most profitable set of operating conditions for a multicycle stimulation project. Perhaps these models are too complicated mathematically to be adapted readily to an optimization study. This paper presents a method for optimizing a multicycle steam stimulation project based on simple production performance models. First, the performance of a steam-stimulated well during each cycle was simulated by either a constant percentage or a harmonic decline model. Using these simple analytical expressions for production performance, the cumulative discounted net income (before tax) and cumulative time of operation for each cycle were related to the pertinent process and cost parameters and two process control variables—the cycle length and the steam injection volume. Finally, the profit function to be maximized was formed. The analogy between the above problem and problems of optimizing multistage decision processes that have been reported extensively in the chemical engineering literatures5-10 in recent years has led this investigation to the use of the discrete maximum principle.5-7 This principle was used to transform the equations for cumulative discounted net income and cumulative time of operation into a set of simultaneous equations characterizing the optimum operating conditions in terms of the two control variables. These equations

Jan 1, 1970