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By A. Satter, J. M. Campbell

Reported herein are the results of a careful and detailed study of the non-ideal behavior of pure gases and their mixtures. Included are: (1) new data on five ternary systems composed of methane, ethane and H2 S; (2) a simple compressibility factor correlation that is inherently superior to present correlations, particularly for gases containing H2S and CO2; and(3) a detailed study of combination rules and the effect of system composition on the choice thereof. This study makes use of the rather large mass of data already available in the literature. A complete re-examination of the data and ideas presented in the last 25 years was considered desirable as a prelude to our basic concern — the effect of diluents on gas behavior. A consideration of both the macroscopic and microscopic properties of gases provides a better insight which, in turn, gives a firmer basis for improved correlation techniques. Such a study has shown that expressing the compressibility factor Z as a function of acentric factor w, as well as reduced temperature and pressure, yields a correlation that is broader in scope. The study of various combination rules has shown that better results are obtained by "tailoring" the rule used to the system composition. To do so improves the basic reality of results by overcoming some of the anomalies often found when using Kay's rule alone. Tentative recommendations are made regarding the most reliable combination rule for use with a given class of gas. The data presented are useful for estimating the direction and magnitude of the expected deviation when using a given rule. Although more work is needed, particularly around the critical region and with CO2 mixtures, the advantage of the classification scheme proposed is apparent. INTRODUCTION When one attempts to write a PVT equation to fit the data for actual gases, greater precision is obtained by the use of a multiple number of empirical constants. This has lead to multiple-constant equations such as Benedict-Webb-Rubin, Beattie-Bridgman, Keyes, etc., which are capable of yielding very precise results for pure gases in a range for which data to get the constants are available. As a matter of practicality, though, the use of such equations for gas mixtures is limited. Because of the infinite number of gas analyses available, any attempt to compile the constants needed requires a prohibitive amount of experimental data. This could be overcome by the use of a combination rule, but there is no real advantage in doing so because the end result offers no practical impovement over the Z factor correlation. The most widely used method of predicting the volumetric properties of pure gases is based upon the "theorem of corresponding states". According to this theorem, "all pure substances have corresponding molal volume at corresponding temperature and pressure if the reference point of correspondence is the critical point". Generalized compressibility charts for gases were prepared first by Cope and associates1 in 1931 and later by Brown and co-workers2 in 1932. However, the most commonly used charts are those of Dodge,3 Nelson and Obert,4 Hougen and atsson: and Standing and Katz.6 The work of Katz and co-workers has provided us with basic data for the hydrocarbons most widely used today. Their original chart6 was compared with a relatively large amount of multi-component data for gases consisting almost entirely of normal paraffin hydrocarbons. A deviation of only + 1.2 per cent was obtained.39 In the 20 years following publication of this work it has been found that the behavior of most mixtures of paraffin hydrocarbons could be predicted by this correlation within at least 5 per cent. Where difficulty has been encountered it has largely involved one or more of the following circumstances: pressures above 4,000 psig, mixtures containing large amounts of heavy ends and/or aromatics, systems in the critical region and mixtures containing polar compounds and/or CO2. The abnormal error sometimes found with such gases, not too unexpected for this method, is

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

By O. D. Gonzalez, H. A. Wriedt

Alloys ranging from pure iron to pure nickel were saturated with nitrogen gas at 918°, 999°, and 1217°C and analyzed. The solubility of nitrogen at 1-atm pressure was obtained as a function of nickel content for the whole range of iron-nickel alloys and the temperature dependence of solubility is shown for the experimental alloy compositions. The heat of solution and the entropy of solution of nitrogen in the alloys as func-tiom of composition up to 41 pct Ni are given. 1 HE acquisition of more exact thermodynamic information for systems composed of iron with various alloying elements continues to interest ferrous metallurgists. The interstitial alloying elements, especially carbon, hydrogen, and nitrogen, comprise a field of particularly intense study. A recent investigation of carbon solubility in Fe-Ni alloys held at 1000°C in gases of fixed carbon activity showed an unpredicted minimum in the solubility near 72 pct Ni.1 The present investigation was undertaken to see if a similar anomaly in solubility existed for nitrogen in Fe-Ni alloys. The solubility of nitrogen in ? iron at known nitrogen activities has been measured several times.&apos;-&apos; Corresponding information for the solubility of nitrogen in solid Ni and Fe-Ni alloys is not available. Juza and sachsze9 reported that metallic nickel dissolved 0.07 pct N in equilibrium with Ni3N at 445°C. This result was regarded as dubious by Turkdogan and Ignatowicz10 who found less than 0.0004 pct N in nickel specimens equilibrated at 600°C with ammonia-hydrogen mixtures having fugacities of N2 gas up to 35,000 atm. Such fragmentary reports indicate only that nitrogen gas has a very much lower solubility in nickel than in iron. MATERIALS A purified iron from Battelle Memorial Institute was used for solubility measurements. This grade contained more than 99.95 pct Fe, the highest content of any measured individual impurity being 50 ppm for each of As, C, Cu, and Pb. The nickel and iron-nickel alloys, supplied by the International Nickel Co., contained 0.02 to 0.04 pct C, 0.17 to 0.19 pct Mn, 0.04 to 0.08 pct Si, < 0.01 pct P, <0.03 pct S, and <0.20 pct Co as principal impurities. The Fe-0.59 pct Mn alloy was of zone-melted quality, the highest concentration of any individual impurity being 15 ppm Al. The "prepurified" grade of nitrogen gas from Matheson Co. had a nominal nitrogen content of 99.996 pct. An "electrolytic" grade of hydrogen gas from National Cylinder Gas. CO. in which the principal impurity is water vapor was admixed with the nitrogen to prevent oxidation of these specimens. This grade was preferred to a purer grade because the presence of some oxygen helps in suppressing contamination of the specimens, for instance, by silicon from the porcelain furnace tube. EXPERIMENTAL PROCEDURE The specimens were equilibrated in vertical tube furnaces through which a 99 pct N2-1 pct H2 gas was passed at ambient pressure. For the 915", 918", and 999°C runs, a wound-resistance furnace was used, and for the 1217°C runs, a furnace with a tubular silicon carbide element was used. The temperature control system on both furnaces was similar: a Weston "Celectray" controller with a modulator, responding to the electromotive force of a thermocouple with its hot junction in the furnace, switched the furnace current between high and low settings. The temperature distributions in the working zones of the furnaces were determined with calibrated Pt/Pt-10 pct Rh thermocouples. The overall uncertainty in temperature was estimated to be ±3° at 915° to 999°C and ±5° at 1217°C . Consideration of the small temperature coefficients of the equilibria studied, together with the error limits in the method of analyzing for nitrogen, showed that further refinement in temperature uniformity would give no improvement in resultant accuracy. The reactive gas was generated by mixing together "prepurified" nitrogen and "electrolytic" hydrogen directly from cylinders commercially supplied. The flow rates of nitrogen and of hydrogen were fixed by setting with bleeders the pressure drops across the individual calibrated flow meters of constant resistance. For any given alloy, the solubility of nitrogen at 1-atm pressure (% N) was obtained from the analyzed nitrogen content of equilibrated specimens (% Na)according to Sieverts&apos; law, thus

Jan 1, 1962

By J. M. Uys, T. B. King

The solubility of water in silicate melts of various compositions was measured. The basicity of the silicate did not appreciably affect the water solu-bulity at low-base content (acid compositions). Near the orthosilicate composition the solubility increased with basicity for silicates in which the cation displayed a weak ion-oxygen attraction and apparently decreased for those in which the cation showed a strong ion-oxygen attraction; metasilicates of the former class dissolved more water than those of the latter. Temperature had little effect on water solubility. The experimental results are interpreted on the basis of two modes of solution, the contribution of one decreasing, and that of the other increas -ing, with increased melt basicity. In the former, solution occurs through interaction with doubly-bonded oxygen atoms and in the latter, through interaction with singly-bonded oxygen atoms, or, in very basic melts, through reaction with free oxygen ions. THE hydrogen content of a steel melt is in a large measure determined by water dissolved in the slag. In some glasses water may be a major cause of "seeds". Water vapor in the furnace atmosphere is the primary source in both instances. A knowledge of the mechanism of water solution in silicate melts should help in assessment of practical methods for its control in steelmaking and glass refining. Walsh et a1.l measured the water content, expressed as hydrogen, of 40 pct lime-20 pct alumina-40 pct silica and 62 pct manganese oxide-38 pct silica melts as a function of the steam partial pressure, in equilibrium with the melt. Tomlinson 2 and, also, Russell3 investigated this relationship for a molten 30 pct soda-70 pct silica glass. In all three investigations, the solubility of water was found to be proportional to the square root of the partial pressure of steam. Moulson and Roberts 4 confirmed this relationship for a silica glass. On the basis of the square root relationship, Tomlinson2 and Russell3 interpreted the solution reaction as "network-breaking", similar to that expected on the addition of metal oxides to silica. Walsh et al.&apos; postulated two possible modes of solution, one the mechanism suggested by Tomlinson and Russell and the other the reaction of the water molecule with an oxygen ion to form hydroxyl ions. These two modes of solution suggest opposite effects of melt basicity on water solubility. However, little appears to be known about the effect of melt basicity on water solubility. Walsh et a1.l found, in the lime-silica system, that the water content increased slightly with increased basicity. As these authors pointed out, this does not appear to be in accord with their further observation that slags containing little or no silica dissolve very little water. Kurkjian and Russell5 measured the effect of basicity on water solubility in alkali silicates in the composition range 15 to 45 mole pct alkali oxide. They found a minimum in the water content at about 25 mole pct alkali. This was interpreted on the basis of two concurrent solution reacZions; one in which solubility was proportional to the activity of doubly-bonded oxygen and, in the other, proportional to the activity of singly-bonded oxygen. The present work was aimed at establishing the effect of basicity on water solubility in silicate melts over as wide a range of compositions as practical. APPARATUS AND EXPERIMENTAL PROCEDURE The silicate melt was equilibrated with a "carrier-gas" of accurately known water content, quenched, and analyzed for water by a vacuum fusion technique. Some pertinent details of the equilibration procedure, analysis technique, preparation, and handling of the silicates are given below. Gas-Silicate Equilibration. The apparatus used to equilibrate the melt with the gas mixture was similar to that used by Walsh et al.&apos; but with some important modifications.6 Purification trains were provided for nitrogen and hydrogen; whenever air or oxygen was used as carrier gas the nitrogen purifiCation train was used with the copper furnace at room temperature. Gas flow rates were measured with capillary flow meters; bleeders filled with a mixture of dibromo and tribromo ethyl benzene (density about 2 g per cc) were used for convenience in controlling flow rates.

Jan 1, 1963

By Charles E. Mann, Douglas J. Lootens, Rufino B. Bomasang

INTRODUCTION The economy of the Philippines, like that of many other developing nations, has been severely strained by the rapid escalation of imported crude oil prices over the past decade. In an effort to reduce its dependence on imported crude, significantly increased emphasis, both in the public and private sectors, is being placed on the rapid development of Philippine coal resources. This paper is designed to present an overview of the Philippine coal industry, its historical development, present status, and future potential. COAL RESOURCES AND RESERVES In 1977, a British consulting firm collated all available data on Philippine coal resources and estimated the total coals potential at about 0.9 to 1.4 billion metric tons (mt). In 1981, using more recent data the Philippine Bureau of Energy Development (BED) estimated the potential at 1.7 billion mt. The BED estimated the proven coal reserves at 257 million mt. These coal resources are scattered throughout the major islands comprising the Philippine archipelago. However, about 52 percent of the currently proven reserves are located in the tiny island of Semirara between the islands of Mindoro and Panay. About 25 percent is located in the Cagayan Valley in northeastern Luzon while 13 percent is located in Mindanao. The remaining 10 percent is scattered in the islands of Cebu, Samar, Mindoro, Negros, Polillo, Batan, and Catanduanes. The bulk of Philippine coal is sub-bituminous in rank. Some bituminous coal with coking properties has been reported in Malangas, Zamboanga del Sur in western Mindanao, and in Catanduanes, but the exact tonnages have not been accurately established. It is believed, however, to be at most 5 million tons. A little semi-anthracite coal exists in Malangas with the remaining unmined reserves estimated at a little more than one million tons. Table 1 shows the quality ranges of Philippine coal deposits.. Figure 1 shows the distribution of known Philippine coal resources PHILIPPINE COAL PRODUCTION In 1981, total coal production was 330,720 mt. Though modest by world standards, this was the highest production figure in Philippine coal mining history. This came from 25 mines, mainly small scale underground mines of capacities varying from 10 to 100 tons per day (tpd). The actual production capability was about 800,000 mt in 1981, but the producers had to scale down production to the level of local demand. Even then, some 50,000 tons of coal remained unused by year-end. The 1981 production came from the following areas: Cebu 224,751 mt (68%) Zamboanga del Sur 57,095 mt (17%) Semirara 13,222 mt (4%) Polillo 17,132 mt (5%) Cebu has always been the main source of Philippine coal production. Coal mining has been carried out in Cebu for the last 50 years, although it has been characterized by a very crude mining technology. Due to the limited size of coal deposits and complicated geology, however, Cebu&apos;s share of the total national production is expected to go down to only 10 percent by 1985. Except for Semirara&apos;s open-pit production, the balance of Philippine coal production comes from underground mines. These underground mines generally use room-and-pillar methods, except for those at Zamboanga del Sur and Polillo which use modified longwall methods patterned after those used in Taiwan. Due to the much higher mining recovery, most underground mines are now planning on switching to longwall. At Semirara, an open pit mine is now being developed for a one million ton per year capacity by 1984, and will then be the largest Philippine coal mine. While present earthmoving work is done with bulldozers, loaders, and trucks, the main coal extraction equipment will be bucket wheel excavators imported from Austria. PRESENT COAL UTILIZATION Existing coal production is sold mainly to coal- fired cement plants and power plants. The balance is sold to a sugar central, a coconut oil mill, a food processing plant, and two plants producing carbide and ferro-silicon alloys.

Jan 1, 1982

By C. H. Li, R. D. Carnahan, R. J. Stokes, T. L. Johnston

When silver chloride deforms by pencil glide at temperatures of 26ºand 72°C, grain size has no effect upon the proportional limit and the material necks down to a knife edge under tension. At -196ºC, deformation takes place on fewer slip systems to produce straight slip traces, the flow stress becomes sensitive to grain size and fracture occurs by cleavage from an intergranular source without any reduction in area. THERE are significant differences between the appearance of the slip bands formed in silver chloride and in the alkali halides at room temperature. The bands in sodium chloride, e.g., are fine and geometrically straight, whereas in silver chloride they are coarse and wavy.&apos; Such differences in the slip behavior prompted us to inquire what the effects of grain boundaries might be on the mechanical properties of these solids. As an introduction to a general study of ionic poly-crystal behavior, we have investigated the effect of grain size on the stress-strain relationships in silver chloride at different temperatures. We have chosen silver chloride chiefly because polycrystals can be easily prepared free from cracks and macroscopic voids by conventional techniques. Moreover, as we shall see, the slip behavior can be readily modified by changing the temperature. It will be shown that the effect of grain size on the yield stress of silver chloride is strikingly dependent upon the temperature of deformation and that this temperature effect comes about through a change in the number of slip systems which operate at the onset of plastic flow. EXPERIMENTAL PROCEDURES Polycrystalline tensile specimens were made by recrystallizing cold-rolled AgCl sheet. Thirty-gram quantities of AR grade silver chloride powder were melted in a low heat capacity furnace, cast into cylindrical forms 3/4 in. in dim and approximately 1 in. in length and then extruded with a 16:l reduction ratio into rods 3/16 in. in dim. Extrusion temperatures were varied from room temperature to 350°C. In order to impart various degrees of cold&apos;work to the extruded rod. All extrusions were then cross rolled to sheet 0.040 in. in thickness at room temperature and machined to form tensile specimens having a gage length of 0.750 in. with a width of either 0.250 or 0.145 in.* Annealing was carried out in an air oven at 200°C for periods up to 20 hr. specimens having average grain diameters ranging from 0.024 to 0.40 mm were prepared by varying the extrusion temperature and annealing time in the conventional manner. To obtain specimens with grain sizes larger than 0.40mm, lightly deformed thin prisims of silver chloride single crystals (supplied by Harshaw Chemical Co.) were recrystallized. Grain size determinations were made by an intercept method and revealed that the grains were equi-axed. Laue back-reflection X-ray patterns showed little tendency to form a preferred orientation texture. Specimens which were to be used for the slip band studies were polished by immersion in fresh boiling concentrated NH,OH for 60 sec. They were then etch polished for 10 sec on each side by hand lapping on a stationary velveteen lap wetted with a dilute Hypo solution (5 g of Kodak Acid Fixer in 100 cc H20). Finally the specimens were rinsed in warm water and alcohol, blown dry and carefully mounted in the tensile machine for testing. Tensile tests were performed at three temperatures, namely, 26º, -72º, and -196°C. A screw-driven hard tensile machine was used at a constant strain rate of 0.006 in. per in. per min. Loads were determined with a light- proof ring fitted with A-18 strain gages and extensions were measured with a 0.0001 in. dial gage. Constant level baths of alcohol with dry ice and liquid nitrogen were used to maintain the two lower test temperatures. EXPERIMENTAL RESULTS Reproducibility—In view of the light sensitivity and reactive nature of silver chloride, it was necessary to determine whether reproducibility depended upon either exposure to light or to the condition of the surface. However, during the course of the work it became clear that variation of laboratory lighting

Jan 1, 1962

By G. Sandoz, D. A. Meyn

The fracture surfaces of specimens of titanium a1loys which exhibited susceptibility to subcritical crack growth in a wide variety of environments, including aqueous solutions, alcohols, hydrocarbon gases, carbm tetrachloride, and dry air, were examined. The dominant and characteristic fracture mode was cleavage. which became mixed with an increasing porportion of ductile fracture modes (dimples. and so forth) as the applied KI was increased. The cleavage plane in all the alloys was oriented at 15 deg from (0001) of the a phase. No indices could be assigned to the 15 deg cleavage Plane because of uncertainty as to which zone it belonged to. SLOW crack growth and delayed fracture take place in certain titanium alloys at stress intensity (KI) lower than the critical values for complete fracture (KIc) found in short-time tests for plane strain fracture toughness.&apos; Such crack growth may take place in very dry air on sustained loading if the alloy contains a sufficient amount of hydrogen and if the stress intensity factor is higher than a threshold value designated KIH.2 Similarly, a number of environments such as water, alcohols, and hydrocarbons may cause slow crack growth provided the stress intensity factor exceeds the threshold value KISCC. In this paper it is intended to examine some fracto-graphic and crystallographic details of this subcritical crack propagation process as related to alloy composition, environment, and stress intensity. It has been previously reported that subcritical crack growth takes place in titanium alloys in aqueous environments by cleavage.2"6 The observations to be described here indicate that in the alloys investigated the mode of subcritical crack propagation is more dependent on the stress intensity during cracking than on the environment. The fracture mode is illustrated with photographs of the fracture surfaces at a wide range of magnifications. The crystallographic character of the cleavage mode is also presented and the results discussed. EXPERIMENTAL APPROACH The studies were made on four titanium alloys— Ti-8A1-1Mo-lV, Ti-5A1-2.5Sn, Ti-7Al-1Mo-lV, and Ti-0.350. Of these four alloys the first two were mill annealed and fine grained. The latter two were noncommercial and coarse grained, having been prepared for other experimental purposes. The crystallographic studies required a large-grain size. Consequently the fine-grained alloys were an- nealed in a vacuum at 1950°F and furnace cooled to produce samples for these studies. This treatment did not alter the microstructure significantly except for grain size. All the aluminum-containing alloys showed primary a with a network of ß-phase particles within the a grains; Figs. 1 and 2 show this microstructure for the specific case of fine-grained Ti-8A1-1Mo-1V. The cracks in the figures will be discussed later. Fractographic studies were made on all the alloys, but the electron fractographs displayed herein are from the Ti-8A1-1Mo-1V alloy in the fine-grained condition. Emphasis was placed on this commercial alloy because considerable information was available on the stress-corrosion cracking characteristics in a variety of environments. Sufficient supplementary studies of the alloy after the anneal to produce large grains were conducted to establish that the stress-corrosion cracking susceptibility and fractographic characteristics were not changed significantly. Thus it could be inferred that the crystallographic data obtained exclusively on large-grained specimens would apply also to fine-grained specimens. Fracture surfaces for study were obtained using precracked cantilever beam specimens loaded as described by Brown. The precracked section of a specimen was immersed in the environment of interest. Values of initial stress intensity factor Kli were chosen slightly higher than KISCC in order to obtain a fairly extensive region of slow crack growth. Fracture surfaces representative of a variety of stress intensity levels could then be examined because in the cantilever beam test KI increases as the crack propagates.

Jan 1, 1970

MINING METHODS W. J. COULTER, Chairman P. B. BUCKY, Vice-Chairman CLYDE E. WEED, Vice-Chairman ROBERT S. PALMER, Secretary Alluvial Mining CLINTON BERNARD O. B. PERRY NORMAN CLEAVELAND C. M. ROMANOWITZ R. B. EARLING J. B. STAPLER BENERE H. GRANTCHARLES THURMAN Open-Cut Mining Iron. A. D. CHISHOLM EARL E. RUNNER G. E. DIEHL G. E. LEVEQUE P. G. HARRISON SIMPSON RICHEY W. A. STERLING

Jan 1, 1943

By R. V. Smith

The theory for unsteady radial flow of gas, as simplified by Aronofsky and Jenkins, has been reviewed and compared with actual well performance. This study indicated that the theory should be modified by the introduction of an empirical "rate of flow" function "Y(q)". The expansion of the theory on the flow of gas to include a Y(q) term bridges the gap between the theory of unsteady-state flow of gas and actual gas-well behavior. Apparently, the Y(q) term is a function only of the rate of flow for a given well. The completion factor or skin effect is associated with the Y(q) function in such a manner that at least two or more sets of drawdown or pressure build-up tests are needed to separate the Y(q) function and the completion factor. Since the Y(q) function used in this report represents an energy loss dependent on rate of flow near the well-bore of a gas well which is in addition to the loss required by Darcy&apos;s law, the Y(q) function is related to the exponent of the back-pressure curve for a gas well. Techniques and equations are presented which permit the estimation of stabilized and "short-time" deliver-abilities. INTRODUCTION The published theory of radial unsteady-state flow of gas through porous media may be divided into papers1-" which use Darcy&apos;s law as a premise and other papers4-7,16-10 which recognize that Darcy&apos;s law may not hold for flow into gas wells. Miller8 compared theory based on Darcy&apos;s law with actual gas-well behavior and concluded that flow into gas wells deviates from Darcy&apos;s law. Houpeurt4,5 in a thorough investigation of flow into gas wells concluded that the flow rate into a gas well is proportional to the difference between the squares of upstream and downstream pressures elevated to a power between 1.0 and 0.5. Houpeurt also concluded that the deviation from Darcy&apos;s law is caused by irreversible, kinetic energy exchange between the flowing gas and the porous media. Tek9 presented a complete evaluation of the flow problem in gas wells. Several investigators state that the inclusion of gas compressibility into flow equations based on Darcy&apos;s law does not begin to explain the flow problems suggested by gas-well behavior. For many years, natural-gas engineers have realized that gas wells by actual test exhibit behavior which cannot be explained entirely by Darcy&apos;s law. Many tests on gas wells have indicated that a value of 0.85 for the exponent in the back-pressure equation is a fair average for many wells. However, Darcy&apos;s law either for steady or unsteady-state conditions indicates that the exponent should be 1.0. The purpose of this paper has been to examine this deviation from Darcy&apos;s law and to present a reasonable mathematical means of evaluating the deviation. The method presented in this paper combines previous theory with an empirical function to provide a description of gas-well behavior. All equations in this report are for constant terminal-rate-of-flow conditions. While present methods of testing wells usually are not based on this concept, they are believed to approach the constant terminal-rate conditions closely in many tests. However, several gas wells were tested by holding the rates of flow constant in order to approach more closely the constant terminal rate of flow; the results confirm the concepts presented in this paper. REVIEW OF THEORY FOR UNSTEADY-STATE FLOW OF GAS The basic partial differential equation for the flow of natural gas has been given in technical literature; the equation for a cylindrical reservoir with the well in the center is

By C. L. Thornburg

FLANKING the Valley of Mexico on the northeast is a mountain range known as the Sierra de Pachuca. This northwesterly-trending range is about 30 miles long and 5 miles wide, its summit attaining an elevation of more than 10,000 feet above sea level, or 2000 feet above the valley floor. Pachuca, a town of 50,000 inhabitants, lies nestled at the southwest base of the range, 60 miles northeast of Mexico City. Three miles to the east, just over the summit and on the northeasterly slope, is the mountain town of Real del Monte with a population of about 20,000. These are the two principal towns in a 40-sq mile area whose yield has brought the district to its high rank among the world&apos;s silver producers. Total production probably exceeds 1.25 billion ounces of silver and 4.5 million ounces of gold. Exploitation by the Spanish was under way by 1530. As the mines were deepened operations became handicapped by the inadequate method of handling water with horse whims and bull skins. To offset this disadvantage a two-mile drainage tunnel was started in 1749 and completed ten years later. John Taylor of London acquired the mines from the third Count of Regla in 1824 and formed the Compania de Real del Monte y Pachuca. Two years later Cornish pumps were brought from England. A Mexican company purchased the British interest in 1848 and within a few years resumed an old project of driving a second, lower three-mile drainage tunnel, completing it in 1857. After Americzn interests acquired control of the property in 1906 operations expanded to an unprecedented scale, despite periods of political strife, unstable prices, labor problems, and a growing burden of taxation. An idea of the scale of operations may be gained from records of the last two decades prior to 1947, the last year for which production information is at hand, during which time production ranged from 1.4 million to 1.1 million tons per year, and the combined development and exploration, exclusive of diamond drilling, amounted to about 18 miles annually. Pachuca differs from Zacatecas and some other Mexican silver vein districts that flourished and de- clined in earlier centuries in that a substantial part of its total production was made after 1900. While the district&apos;s accelerated activity in this century was largely due to the successful application of the cyanide process to the treatment of the ores, improved pumping methods, and new mechanical equipment, it was at the same time stimulated by the opening up of important new orebodies as a result of active and extensive exploration of the vein system. Some of these orebodies were found on veins which terminate upward far below the surface, and though these particular veins do not crop out, they show relationship with a type of alteration which may be their surface expression. The district has been studied by many able geologists, and a large store of information has been accumulated, much of which is recorded in published as well as private papers. Wall Rocks Extrusive Rocks: The Sierra de Pachuca is a thick accumulation of Tertiary eruptive rocks consisting mainly of flows, breccias, and tuffs. Numerous recognizable volcanic vents within the range itself manifest that the range was built up by material ejected from these vents. The maximum thickness of the volcanic pile is not known, but from deep exploration and from relationship with Mesozoic sediments to the north and east it is inferred that the average thickness in the main part of the district may be at least 6000 ft. The extrusive rocks comprise four general types, which in ascending order of age are: andesite, rhyolite, dacite, and basalt. The veins are confined largely to the andesite, the dominant rock of the region. Characteristically this rock is augite andesite, but it includes comparatively acidic as well as basic layers, the acidic strata being

Jan 1, 1953

By C. L. Thornburg

FLANKING the Valley of Mexico on the northeast is a mountain range known as the Sierra de Pachuca. This northwesterly-trending range is about 30 miles long and 5 miles wide, its summit attaining an elevation of more than 10,000 feet above sea level, or 2000 feet above the valley floor. Pachuca, a town of 50,000 inhabitants, lies nestled at the southwest base of the range, 60 miles northeast of Mexico City. Three miles to the east, just over the summit and on the northeasterly slope, is the mountain town of Real del Monte with a population of about 20,000. These are the two principal towns in a 40-sq mile area whose yield has brought the district to its high rank among the world&apos;s silver producers. Total production probably exceeds 1.25 billion ounces of silver and 4.5 million ounces of gold. Exploitation by the Spanish was under way by 1530. As the mines were deepened operations became handicapped by the inadequate method of handling water with horse whims and bull skins. To offset this disadvantage a two-mile drainage tunnel was started in 1749 and completed ten years later. John Taylor of London acquired the mines from the third Count of Regla in 1824 and formed the Compania de Real del Monte y Pachuca. Two years later Cornish pumps were brought from England. A Mexican company purchased the British interest in 1848 and within a few years resumed an old project of driving a second, lower three-mile drainage tunnel, completing it in 1857. After Americzn interests acquired control of the property in 1906 operations expanded to an unprecedented scale, despite periods of political strife, unstable prices, labor problems, and a growing burden of taxation. An idea of the scale of operations may be gained from records of the last two decades prior to 1947, the last year for which production information is at hand, during which time production ranged from 1.4 million to 1.1 million tons per year, and the combined development and exploration, exclusive of diamond drilling, amounted to about 18 miles annually. Pachuca differs from Zacatecas and some other Mexican silver vein districts that flourished and de- clined in earlier centuries in that a substantial part of its total production was made after 1900. While the district&apos;s accelerated activity in this century was largely due to the successful application of the cyanide process to the treatment of the ores, improved pumping methods, and new mechanical equipment, it was at the same time stimulated by the opening up of important new orebodies as a result of active and extensive exploration of the vein system. Some of these orebodies were found on veins which terminate upward far below the surface, and though these particular veins do not crop out, they show relationship with a type of alteration which may be their surface expression. The district has been studied by many able geologists, and a large store of information has been accumulated, much of which is recorded in published as well as private papers. Wall Rocks Extrusive Rocks: The Sierra de Pachuca is a thick accumulation of Tertiary eruptive rocks consisting mainly of flows, breccias, and tuffs. Numerous recognizable volcanic vents within the range itself manifest that the range was built up by material ejected from these vents. The maximum thickness of the volcanic pile is not known, but from deep exploration and from relationship with Mesozoic sediments to the north and east it is inferred that the average thickness in the main part of the district may be at least 6000 ft. The extrusive rocks comprise four general types, which in ascending order of age are: andesite, rhyolite, dacite, and basalt. The veins are confined largely to the andesite, the dominant rock of the region. Characteristically this rock is augite andesite, but it includes comparatively acidic as well as basic layers, the acidic strata being

Jan 1, 1953

By J. S. Levine, M. Prats

Several methods are available for calculating the performance of solution-gas-drive reservoirs from the PVT properties of the oil and from the relative permeability and other properties of the formation. These methods require a number of simplifying assumptions. The present method of computation has made use of a high-speed computer to solve simultaneously the nonlinear partial differential equations that describe two-phase flow by solution-gas drive in order to calculate the performance of a reservoir. Some of the results obtained by the nonlinear partial differential equation solution are compared with those obtained with an approximate method, which has been called the semisteady-state solution. The pressure and saturation profiles from the wellbore to outer boundary calculated by the two methods are compared for one constant-terminal-rate case and two constant-teminal-pressure cases. The agreement in these profiles, as well as in the values of average reservoir pressure and cumulative recovery, leads to the conclusion that, for most engineering calculations, the semisteady-state method will give a reasonable approximation to the numerical solution of the differential equations describing solution-gas drive. An unfavorable (as regards ultimate oil production) set of relative permeability curves was used in the calculations in the belief that the effect of the parameters which were studied would be emphasized to a greater degree. Furthermore, the reservoir was assumed to be completely homogeneous, and these results should not be considered applicable to any other type of reservoir. Gravity effects are not considered. The absolute permeability was varied from 25 to 0.5 md. At an economic limit of 2 B/D, the recovery for a 25-md reservoir is about 1.8 times as great as that for a 0.5-md reservoir. The effect of permeability on the producing gas-oil ratio is minor. Once PVT properties of the oil and the relative penneability properties of the reservoir are fixed, the pro- during gas-oil ratio is found to be a function of the fraction of oil recovered. Well spacings of 10, 40 and 80 acres were considered. For the assumed homogeneous-reservoir properties, the effect of spacing on recovery at an economic limit of 2 B/D was very slight. Certain dimensionless groups can be used to extend the results to other fields having different penneabilities, spacings, reservoir thicknesses, well radii and porosities, so long as the PVT and relative permeability properties are similar to those used in this paper. INTRODUCTION An important aspect of reservoir engineering is the prediction of the performance of the reservoir based on the limited information normally available early in the life of a field. Usually, soon after a field has been discovered, it is necessary to decide upon the spacing to be employed and the production program to be used for most efficient utilization of reservoir energy. Where these decisions have not been dictated by legal or political considerations, they have frequently been based on experience factors which indicate that two fields with similar characteristics will probably have similar performances. To the extent that the industry has been successful in economically exploiting oil reservoirs, this rule-of-thumb method has been found to have merit. A large amount of theory has been developed with which it is possible to predict the performance of a reservoir by using certain known properties of the oil and the formation. Because of the difficulties of the mathematics involved for a drainage area having square or rectangular boundaries, the problem usually has been simplified and idealized by assuming each drainage area to have radial symmetry and the field to be represented by a number of these drainage areas. Muskatl was one of the first to formulate the theory for two-phase flow and to solve the equations for a few cases by numerical integration, using the relatively slow means of computing available at that time. His equations describing

By Lyman H. Hart

Some of the significant facts that will affect the supply and demand for metals during the next few decades are given in this presentation. This is important because the only hope for intelligent guidance of the national destiny depends upon presenting a consistent and accurate picture of basic problems. The metals problems now fomenting are only slightly less important than those precipitating the energy crisis. Admittedly, it is difficult to generate serious thinking on this subject when the world is enjoying easy access to all metals at modest prices. This is possible because of the current world capacity to over-produce, and United States credit standing, at least up to now, has permitted buying freely on world markets. Although both these vital conditions are subject to change, there is little doubt that if the U.S. financial house is kept in order, we can muddle along for a while on a generally expanding, metal-based economy. But should our credit standing be permitted to collapse, or should there be a tightening of world supplies of metals, the nation would immediately find itself in trouble. Unfortunately, clear signals indicate that both of these conditions are threatening. The metal age started many centuries ago, and with the exception of the noble metals, barely a dent was made in world reserves until the present century. Then, as a result of the pioneering ideas of D. C. Jackling and Paul Gemmel, and the willingness of the McNeals, Penroses and Guggenheims to back ideas with money, a virtual explosion of metal production was propagated throughout the world. It is important to examine the causes of this expansion to determine whether it is a trend that may be sustained or whether it is anomalous and therefore attributable to circumstances not likely to be repeated or continued. This period of plenty is a once only phenomenon. Vast metal resources have been sitting around here for eons, while the world was unaware of or unconcerned with their existence. But when population began to grow exponentially, and ways were discovered to use metals to develop machines to do the work of men and animals, the exploitation of raw materials increased at a staggering rate. And now the realization is dawning that minerals are a wasting asset and are beginning to present supply problems that should begin to be of concern. Two main factors have caused this condition; One is the population growth, and the other is the expanding demand for irreplaceable raw materials as nations become more developed. A group of systems analysts, at Massachusetts Institute of Technology in a book Limits of Growth, has warned that at present rates of population growth and resource consumption together with environmental constraints, a point will be reached within 100 years when the world population will become totally incapable of supporting itself. The authors conclude that this end result could be avoided if a planned equilibrium could be established at a lower rate of population growth and resource consumption. Fortunately, there is evidence that the population problem is moderating. The growth rate in the U.S. has decreased from 2.3% per year in 1900 to 1.1% in 1970. But, even at the lower rate, population will double in 70 years. The world rate is greater, and if it continues, world population will rise from 3.5 billion to nearly 10 billion in 50 years. All of these projections are questionable because the dangers of growing population are now being recognized. A marked decrease in growth rate has been noted in the more developed countries-in fact, it was zero in the U.S. in 1972. The other factor affecting consumption of raw materials is the increase in per capita use of most items as individuals become more affluent. Many economists believe that developing countries such as China and India represent a vast future potential market; but there are others, with whom the author agrees, who believe over-population tends to stagnate development. Nevertheless, it is a fact that vigorously developing societies increase consumption at a rate far above their population growth rate.

Jan 1, 1974

By G. A. Vissac

MoIstuRe in coal must be considered as an impurity, just the same as ash, from the standpoint of utilization of the coal. Being incombustible, it reduces directly the heating value of the coal, and in addition absorbs heat for its evaporation. Its presence means useless expenditures in handling and transportation. In coke plants, extra moisture reduces capacity and may cause damage to brick work and equipment. Accordingly, the removal of extra moisture can be considered just as important as the removal of other impurities, such as ashes, in the modern coal preparation plant. Moisture, which can be removed by heating the coal up to a temperature of 100°C, may be retained in various forms: 1. As a film, on the surface of each coal particle, and in the interstices between particles, retained by capillary forces. 2. Or "occluded" inside the coal particles. This occluded moisture may be either free moisture (as in a sponge), or hygroscopic moisture which varies with atmospheric conditions, (also called "regain"). These latter forms of moisture are particularly common in "young" coals (subbituminous and lignites); bloom coals (seam outcrops); fusain; and carbonized products. In our study of coal drying, we shall consider only the removal of free moisture, exclusive from hygroscopic moisture. Dewatering If we reserve the name of drying to the removal of water by evaporation, we must consider the initial phase of the mechanical removal of free moisture as a distinct operation covered by the term dewatering. In all cases the free water carried over the surface of the coal particles or in their interstices, or in their pores, is retained by capillary forces. Dewater-ing is accomplished by breaking or counteracting these capillary forces; removal of as much water as possible by dewatering methods is usually advisable, as the cost of these operations is generally much less than by evaporation. The most common methods of me-chanical dewatering are: 1. "Pressure piling," which reduces the interstitial spaces, accomplished in dewatering bins or over dewatering screens. 2. Or dynamic methods, such as used in centrifuges or over vibrating screens. We shall only mention the " preferential wetting" method, in which surface water can be displaced by hydrocarbons, as offering possibilities, but which, to our knowledge, has not reached yet a practical development. But we must point out that the capillary forces retaining water on the coal surfaces, decrease considerably with increased temperatures. This is the principle used in all modern dishwashing machines; by using very hot water, dishes are extracted almost dry. In line with this development, we favor the type of dryers including a dewatering section; as the coal enters the dryer and is gradually brought up to higher temperatures, its dewatering ability is increased and advantage can be taken of this conditioning, resulting in increased drying efficiencies and reductions in drying costs. Heat Drying In the final phase, the remaining moisture must be evaporated. Coal and water must be brought up to the chosen temperature of evaporation, and heat must be supplied to fill the requirements of the latent heat of evaporation of the water to be removed. Accordingly, drying becomes largely a problem of heat transfer, and drying methods can be classified accordingly, namely: 1. Radiant transfer. 2. Transfer by surface contact and conduction. 3. Transfer by hot gas contact. The first method is not applicable to coal drying; the second method is used in the old type rotary dryer. The third method, the most commonly used in modern coal dryers, will be the only one considered here; and, of course, we shall deal with continuous types of dryers only. The mechanism of complete drying is really very complex-—several phases are involved: 1. The constant rate period. 2. The uniform falling rate period. 3. The varying falling rate period. As most of our practical coal drying problems deal with wet coals (over 6 pct of moisture), and do not require complete drying (under 1.5 pct), we shall deal with the first condition only, namely the constant rate drying. Dryer Calculations Instead of presenting the algebraic formulas, we believe a concrete example will provide a clearer illustration. Assume a feed of wet coal at the rate

Jan 1, 1950

By R. D. Stover, F. O. Shuck

The variation of binary-diffusion coefficients with composition in the liquid Bi-Sn system at 300°C was measured using the capillary-reservoir technique. The experimental coefficients did not exhibit a simple composition dependence. A number of tests were also made to determine the effect of variation of density with composition on convection within the capillaries. These tests indicate that the density changes arising from composition duferences may give rise to high diffusion coefficients unless care is taken to maintain a stable configuration. In recent years there has been considerable interest in diffusion in liquid metals. However, the bulk of the work done to date has involved measurements of self-diffusion or diffusion of dilute concentrations of "solute" metals. Because there are possible applications to liquid phase processing of metal alloys and since additional data may help to clarify the nature of diffusion in liquid metals, investigations of the concentration variation of diffusion coefficients in binary alloys have been undertaken. Of past studies only two have covered large ranges of binary composition. Niwa et al.&apos; investigated the Pb-Sn, Bi-Pb, and Bi-Sn systems and Grace and Derge2 investigated the Bi-Pb system. Because of the discrepancy between the data of these investigators, it was deemed desirable to check the possibility of convection arising from the variation of density with composition. The capillary-reservoir technique of Anderson and saddington3 was chosen for the present investigation since it has been widely used for measurements involving dilute solute concentrations and it was the technique used by Grace and Derge.2 It was necessary, however, to modify the normal procedure of using a pure metal bath to avoid measurement of integral diffusion coefficients over large concentration ranges. The alloy system chosen for study was the Bi-Sn system for which there are some data available.&apos; EXPERIMENTAL PROCEDURE In order to utilize the capillary-reservoir technique for measurements of diffusion coefficients as a function of composition, it was necessary to modify the normal procedure slightly. This modification consisted of using a reservoir composition which was only slightly different from that in the set of capillaries, in order that the integral coefficients measured might be taken over a small composition range and might thereby be assumed to approximate the differential coefficient at some average composition between that of the capillary and that of the bath. It was found that a composition difference of approximately 0.10 mass fraction provided a satisfactory compromise between a small increment in composition and reasonable accuracy in measuring changes of composition. The alloys were prepared from tin and bismuth of 99.999 pct purity. The materials were first cleaned of surface oxides, then weighed and melted to form a homogeneous alloy in a Pyrex filling apparatus. The capillaries used were of precision bore Pyrex tubing 1.000 *0.005 mm bore. Capillaries of various lengths (from 2.85 to 5.85 cm) were cut and sealed at one end by fusing a 3-mm Pyrex rod to the end. The capillaries were filled by inserting them into the filling chamber, evacuating the chamber, submerging the capillaries, and pressurizing the chamber with argon. Two sets of capillaries were prepared for each run. One set contained an alloy more dense than the bath alloy and one set a less dense alloy. This procedure was followed so that the effect of density difference on the measurement could be determined. After filling one set of capillaries, these were placed open end up in a capillary holder and transferred to the diffusion chamber which consisted of a Pyrex tube inserted into a graphite block. The second set of capillaries was then filled and placed into the diffusion chamber. The reservoir alloy, which had been melted in a separate crucible, then was poured carefully into the diffusion chamber. Sufficient reservoir alloy was used to cover all capillaries to a depth of several centimeters. All of these operations: capillary filling, melting of alloys, and diffusion anneal, were carried out in a fused-salt bath which maintained a temperature of 300"*1°C. All capillaries were permitted to diffuse for approximately 48 hr. At the end of the diffusion period the capillary holder was removed from the bath and

Jan 1, 1969

By P. Datta, L. L. Handy

For a wetting phase displacing a nonwetting phase from a porous medium the distribution of the residual fluid may depend on displacement conditions. Although this subject has been debated in the literature, only a few experiments have been cited to support the various conclusions. Experimental results presented in this paper show that fluid distributions are dependent on imbibition pmcedures. Results agree qualitatively with predictions from the pore doublet model. If the rate of water imbibition is restricted, the nonwetting phase is trapped preferentially in .the larger pores as expected. But if the rate of water imbibition is unrestricted, trapping occurs somewhat more in the smaller pores. These conclusions were deduced primarily from relative permeability measurements. INTRODUCTION Relative permeabilities are known to depend on the saturation history of the porous medium. For either continuously increasing or continuously decreasing wetting phase saturations, however, they have normally been assumed to be single-valued functions of saturation. Severat investigators have compared relative permeabilities measured by different methods and have reported acceptable agreement.1-5 Studies of simple models of the displacement process suggest that the distribution of residual fluids can be influenced by the displacement method. If this is so, relative permeabilities also should depend on the method of displacement. These predictions have not been supported by experimental data. The object of this paper is to investigate experimentally some of the predictions of these model studies. The particular question of importance is whether steady-state and unsteady-state methods should be expected to give the same values of relative permeability. Much of the reported data showing agreement between steady-state and unsteady-state methods have been obtained on un consolidated sand. Johnson, Bossler and Naumann, however, compared steady-state and unsteady-state results for Weiler sandstone and found no significant differences.5 Levine made a detailed study of pressure and saturation distributions for a laboratory waterflood in a consolidated system but made no attempt to calculate performance from steady-state relative permeability data Bail and Marsden in a somewhat similar set of experiments did attempt a comparison of observations with predictions but the results were inconclusive.7 Excluding gravity, two forces affect the distribution of wetting and nonwetting phases during an unsteady-state, immiscible displacement: viscous and capillary forces. If relative permeabilities are indeed the same when measured by steady- or unsteady-state methods, the fluid distributions at the same fluid saturations must be similar for both methods. Furthermore, the implication is that the relation between capillary and viscous forces is the same for both methods insofar as the effect on microscopic fluid distributions is concerned. Unsteady-state displacements are normally run at high rates to maximize the ratio of the viscous to capillary forces. The objective is to reduce the effect of capillary forces on macroscopic fluid distributions. For floods in which the phase which wets the porous medium displaces the nonwetting phase, capillary forces compete with viscous forces in determining fluid distributions.8 The residual nonwetting phase is discontinuous. Competitive aspects of viscous and capillary forces and the resulting effect on water-oil distribution in porous media have been illustrated in an elementary way using a pore doublet model. This model and predictions from it have been discussed at considerable length by Rose and Witherspoon, Rose and Cleary and by Moore and Slobod.9-13 Rose and Witherspoon show that so long as water invades the model at a rate equal to or greater than the free imbibition rate, the water will move through the larger capillary of a doublet first and trap oil in the smaller capillary. On the other hand, if a negative pressure is applied to the water

Jan 1, 1967

By R. F. Mehl, C. E. Birchenall

SINCE Maxwell1 first considered the self-diffusion process in 1872 its importance in the kinetic theory of matter has been recognized. Until the discovery of isotopes in 1913, a direct measurement of this quantity seemed impossible. The only information that could be gathered indirectly was for gaseous systems for which the kinetic theory was well developed. When methods of direct observation be-came available, investigations on self-diffusion were carried out in condensed phases. In metals these data are presumably of potential importance in the study of recovery, recrystallization, creep, sintering, and related phenomena. Following the pioneer work of Von Hevesy2 and his collaborators, who determined the rate of self-diffusion in lead with the naturally occurring thorium B isotope, several metals have been investigated. Pb, Ag³, Au.6,5, and Cu6,7,8,9 are examples of isotropic crystals existing in only one phase modification. Anisotropy of diffusion has been demonstrated in Bil6 and Znll. This paper is a study of a single metal in two allotropic forms and also of self-diffusion in a body-centered cubic lattice. Despite the fact that the measurements in each of the papers cited on self-diffusion in copper seem to be internally consistent to about 10 to 15 pet, the curves reported by different authors differ by factors of 2 to 4 at the same temperatures. This uncertainty may account, in part, for the failure to establish a successful correlation between the self-diffusion rates and other physical characteristics of the metals. No satisfactory theory of metallic self- diffusion has as yet been proposed to account for all the existing data and to permit estimation in other metals. Experimental Part: Two units of radioactive iron were used in these experiments, each a mixture of Fe53 and Fe59 (12). Fe53 decays by K electron capture and the emission of an X ray with a half life of about 4 years. Fe59 emits two beta spectra, one with a maximum energy of 0.26 Mev, the other 0.46 Mev, and gamma rays of 1.1 and 1.3 Mev, with a half life of about 44 days. They were present in nearly equal concentration initially. The composite half life started at about 50 days and increased as the Fe59 decayed, leaving Fe55 relatively more abundant. After aging a year, the half life was too long to measure significant decay in a month. The absorption properties also changed with time. Because of the importance of the absorption coefficient in the diffusion calculations, it was necessary to determine this quantity frequently over the period during which these experiments were carried out. This correction was unsuspected at the time of publication of notesl3 on this work and accounts for the discrepancy in alpha iron and for part of the discrepancy in gamma iron.* * The data in the present paper supersede those given in the notes entirely. In one note the scale of log D was inadvertently reversed. In addition to the correction for the drift in absorption coefficient, the D values for gamma iron at low temperatures were high owing to insuficient correction for diffusion occurring during heating and cooling through the high temperature part of the alpha range at a rate much slower than that employed in the runs reported here. The high temperature alpha rates are much higher than the low temperature gamma rates and correspond to large equivalent times at these temperatures. These experiments were discarded and new measurements taken. Independent experiments with the same activity units indicated a radioactive contaminant in the iron, but exhaustive attempts to isolate and identify it chemically failed. These experiments? indicate † These experiments will be discussed in a later publication from this laboratory. that the contaminant represented only a trace of little importance in the diffusion results. The active iron was plated from an iron chloride solution. Enough of the solution was dropped on a 1% in. square of filter paper to wet it thoroughly.

Jan 1, 1951

By G. M. Schwartz, G. A. Thiel

THE first record of the quarrying of dimension stone in Minnesota dates back to 1820 when limestone was quarried locally for part of old Fort Snelling. Limestone quarries were operated at Stillwater, Mankato, and Winona as early as 1854. Granite was quarried first at St. Cloud in 1868, and within a few years thousands of tons were shipped to widespread points. Rough dimension stone for large buildings furnished the first important market, but beginning in 1886 paving blocks were in demand. The largest shipment was in 1888, when 1925 cars were shipped from the St. Cloud area. Quartzite was quarried first at New Ulm in 1859 and somewhat later at Pipestone and elsewhere in southwestern Minnesota: The productive dolomite quarries at Kasota were opened first in 1868 and have continued as large producers of a variety of stone to the present time. At present, the industry is controlled by relatively few operators, and for that reason detailed figures on dimension stone are not released for publication. A general idea may be obtained from the data in the Minerals Yearbook for 1948. The figures for total stone produced in Minnesota are 1,804,000 tons valued at $5,090,652. Probably the largest item in the latter figure is received from dimension stone. A better idea of the situation, in relation to the country as a whole may be gained by using the data for 1930 when more companies were operating in Minnesota, and complete figures were published. In that year Minnesota produced granite valued at $2,668,119 and ranked third among the states in value. Minnesota&apos;s production of granite was almost exclusively for dimension stone. In the same year Minnesota produced 300,000 tons of limestone (dolomite) valued at $840,860, and this likewise was mainly dimension stone. In finished limestone Minnesota ranked second among the states in 1930. Sandstone and minor amounts of quartzite are the only other dimension stones that have been produced in Minnesota, but the quarries are now inactive. The commercial stones of Minnesota have been described in two reports by Bowled and by Thiel and Dutton.2 The early history of quarrying in Minnesota and extensive notes on the various rocks are given by N. H. Winchell.3 Small limestone and dolomite quarries were numerous throughout the area of Paleozoic rocks in southeastern Minnesota. Early production was largely dimension stone. With the increased use of Portland cement, most of these ceased production, and today only those at Kasota and Winona remain in operation. In recent years many quarries have reopened and new ones started, but these are devoted to the production of crushed rock and agricultural lime. As the application of modern quarrying and finishing methods increased, small companies in the granite business have dropped out, and the remaining companies have modernized their plants, purchased old quarries, and opened up new ones, thus furnishing a wide variety of granites suitable for most of the customary uses. It is the purpose of this review to present notes on&apos; the geology and operations of each of the quarries now operating within the state. Granites and Related Igneous Rocks The term granite as used in this report includes granites, gneisses, diorites, gabbros, and other igneous rocks. The granites of greatest economic importance are found in three widely separated regions, see Fig. 1. 1-Central Minnesota in the region of the city of St. Cloud, 2-the upper Minnesota River valley region, 3-the northeastern portion of the state, commonly referred to as the Arrowhead region. The St. Cloud Region: The rocks of the St. Cloud region are mainly granites and related rock types such as monzonites and quartz diorites. The stones may be grouped into three major types, namely, pink granite, red granite and gray granite. Most of the pink granite occurs in the area to the southwest of St. Cloud. The rock is best described as stone with large pink crystals set in a finer grained black and white background. The minerals of the matrix occur in remarkably uniform sizes, and the pink crystals are sufficiently uniform in. their dis-

Jan 1, 1952

E. E. Olcott, New York City: Prof. Kemp&apos;s valuable description of the Lancaster Gap mine is in line with many other able contributions on the origin of mineral deposits that the Institute has lately brought forward. The splendid contribution that Prof.

Jan 1, 1895

By P. E. Busby, C. Wells, M. E. Warga

Fundamental data on the rate of diffusion of boron in austenite and solubility of boron in the a and y phases of iron and steel have been obtained from deboronizing experiments and provide partial explanations for some of the phenomena observed in boron steels. The rate of diffusion of boron is about the same as carbon in austenite. The solubility of boron in austenite at normal heat-treating temperatures is less than 0.001 pct. A partial tentative Fe-B phase diagram in the important low boron concentration ranges and an equation representing the diffusion of boron in austenite are presented. A LTHOUGH a search of the literature revealed ALTHOUGHthat boron diffusion had not been studied quantitatively and systematically prior to 1948, a few qualitative observations which were made by following the diffusion of boron into iron packed in ferro-boron1-3 suggest that boron obeys normal diffusion laws and that the rate of diffusion increases with increasing temperature. The claim of Cornelius and Bollenrath1 that boron does not appear to influence the rate of carbon diffusion has recently been substantiated by Wells, Batz, and Mehl.4 Calculations based on data from the paper by Campbell and Fayv indicated that the diffusion coefficient (D) for boron in iron at 900°C is approximately 3x10 sq cm per sec; a value of 2x10-7 sq cm per sec at 1038°C has been reported by Digges et al in connection with decarburizing experiments on a commercial boron steel containing 0.43 pct C. During the period 1948 to 1950 several diffusivity constant (D) values for the diffusion of boron in the y phase of iron and steel and a number of solubility values for boron in both a and y phases were reported. It was concluded tentatively as a result of Metals Research Laboratory studies that D values for boron in y and a phases are about the same as for carbon in the comparable phasesa and that carbon up to 0.4 pct did not affect the rate of diffusion of boron in y iron above 1000°C within the limits of experimental error. Whether saturation of the y or a phases with carbon would significantly affect rates of diffusion of boron through them was then and still remains in doubt. The best estimate of Q (activation energy) was reported to be about 25,000 cal, somewhat lower than that for carbon in y iron. The solubility of boron in y iron at 1000°C was thought to be higher than 0.004 pct B but not as high as a more recent analysis of available data shows it to be. The solubility of boron in a iron at 700°C was reported to be 0.0004 pct B, but it would not have surprised the authors if the true solubility value is actually lower than this. Breaks in diffusion curves which were not understood when first obtained prior to 1950 have now been recognized as indicating solubility limits, and these are included in the present paper. Experimental Procedure Two methods were employed in an effort to determine diffusion coefficients (D) for boron in austenite. Early experiments involved the use of welded couples prepared in accordance with the procedure of Wells and Mehl,&apos; but when the results of these experiments proved to be unsatisfactory for calculating D values, studies were continued by means of deboronizing experiments. In both cases, boron analyses following the diffusion anneal were carried out spectrographically and all D values were computed using the Grube solution of Fick&apos;s law. The precision of the spectrographic method used proved to be about equal to that reported by Corliss and Scribner" —average deviation from the mean about 5 pct of the amount present when the boron content is 0.003 pct. Concentration-penetration curves obtained from spectrographic analyses of welded couples generally indicated that practically no boron was transported across the weld interface during the diffusion anneal. Furthermore the concentration-penetration

Jan 1, 1954