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By Leonard R. Weisberg

HE procedure of directional freezing by the Bridgman technique1 is frequently used in crystal preparation. On those occasions where the crystal is regrown, it can be advantageous to Crop part of the ingot before regrowth to achieve purification. This note describes some simple, yet interesting, observations concerning the effects of cropping an ingot between successive freezes. First, it is not effective to Crop the front end of an ingot, whether or not the distribution coefficient, k , of the impurities is greater or less than unity. This can be shown as follows. The concentration C, of an impurity in a directionally frozen ingot of length d with a uniform cross section is given by where x is the distance along the ingot, and C0 is the initial concentration per unit length. It is assumed in deriving this equation that diffusion is negligible in the solid, is complete in the melt, and that k is constant. Consider that a section of the ingot Ad is removed from the front end. Then the average impurity concentration in the remaining (d- Ad) section of the ingot can be shown by integration to be given by When the ingot is remelted and refrozen, the new impurity distribution is given by where xl is the distance along the refrozen ingot. Substituting the value of c into Eq. [3], one finds This is identical to Eq. [11 when x = (x, Ad), which represents the original impurity distribution in the (d - Ad) section of the ingot after the first directional freeze. Therefore, the cropping and re-freezing accomplished nothing. This can also be seen physically by realizing that the average impurity content in the melt after the first Ad section is frozen, is identical to that after the resulting ingot has been cropped and remelted. Hence, it is assumed in the following sections that only the tail end of the ingot is cropped. However, it must be realized that for impurities with k greater than one, the pieces cropped from the tail end are purer, and are therefore saved. After cropping an amount Ad from the tail end of an ingot, the average impurity concentration of impurities in the remaining portion of the ingot is given by wheref= d/d. For the case of k < 1, the purification is defined as c,/c. It is obvious from Eq. [5] that the purification increases asf increases, but the increase in purification is not large. For example, iff is doubled from 0.1 to 0.2, the purification increases by only 10 pct for k = 0.5, by only 24 pct for k = 0.1, and by 32 pct for k =0.01. Much smaller values off than 0.1 are not desirable since insufficient purification is achieved. These figures indicate that much larger values off do not lead to substantial improvement, especially considering that much of the original ingot is lost. Therefore, it is generally useful to Crop about 1/10 of the ingot to achieve purification. As compared to doubling the value off, it is much more helpful to remelt, refreeze, and crop the ingot twice. Using Eq. [51 reiteratively, and assuming f= 0.1, it is found that the purification after this process is found to be increased over the purification after a single freeze and cropping by 33 pct for k= 0.5, 450 pct for k = 0.1, and 4100 pct for k = 0.01. This indicates that considerable purification can be obtained by this procedure. However, if purification is the main goal, one should resort to zone refining,3

Jan 1, 1962

By M. C. Udy, P. C. Rosenthal

The use of minute boron additions to steel has been given considerable attention in recent years. Comparisons made between boron-free and boron-containing heats of otherwise identical analysis have indicated, beyond a doubt, the potent effect of boron for increasing hardenability. The actual hardenability increase has been expressed as a multiplying factor, or in terms of the percentage of other alloying elements boron might replace. The present study presents the results of a systematic survey of the use of boron as an addition to two types of alloyed steels and as a replacement for various percentages of molybdenum in these steels. Both cast and wrought steels of the two basic compositions were prepared. Molybdenum, because of its scarcity at the time the investigation was started, was selected as the element to be replaced by boron. Attention was also given to the effects of boron on other properties of the steels, particularly their notched-bar toughness, to investigate other advantages or limitations of this element as an alloy addition. Experimental Work Steels Investigated The two basic compositions used in this survey of boron as a replacement for molybdenum are given in Table I. The cast steels were higher than the wrought steels in silicon content to improve the casting quality. Table i.—Nominal Composition of the Two Base Alloy Steels composition. Per Cent. steel Mn Si Ni Cr Xi-Cr-Mo Wrought 0.28-0.70-0.15-o.45—o.45-0.32 0.90 0.25 0.55 0.55 Cast 0.28-0.70-0.35-0.45-o.45- 0.32 0.90 0.45 0.55 0.55 hln-&lo Wrought 0.28-I .go-o.0.15-0.32 1.70 0.15 Cast o. 28- I.40- 0.35- 0.31 1.70 0.45 a Sulphur was 0.040 per cent maximum and phosphorus 0.030 per cent maximum. Each of these base steels, both cast and wrought, was made with molybdenum contents of o, 0.10, 0.20, 0.30, or 0.40 per cent, the total comprising 20 steels. In addition, each of these 20 compositions was prepared with boron additions in amounts of o.oo15, 0.003, and 0.006 per cent as ferroboron; and in amounts of 0.002 and 0.005 per cent as two commercial intensifier alloys, designated alloys A and B. The boron-treated steels totaled 100, and the entire series 120. Test Procedure Each steel was melted as an individual heat in a 50-lb., magnesia-lined induction furnace. Ingot iron scrap or mixtures of ingot iron and steel. scrap were used for melting stock. Deoxidation was carried out in the furnace with 0.10 per cent aluminum. The aluminum addition was

Jan 1, 1948

By B. M. Larsen, T. E. Brower

An increasing amount of attention is being paid to the possible influence of oxygen, in its several modes of occurrence in steel, upon some of the properties of the metal; but clearly investigations along this line are unlikely to yield significant results until reliable analytical methods for the determination of oxygen have been established. This paper presents some results of a study of an improved Ledebur method which aims to determine a definite portion of the oxygen; namely, that which presumably is present in diffusible form in the solid steel. These more or less preliminary results lead us to believe that the oxygen so determined has some significance; their presentation at this time will, we hope, stimulate discussion of, and focus attention upon, certain rather neglected aspects of the problem. Considerable work has been done recently on methods of estimating inclusions and on the vacuum-fusion method for oxygen; with results which, however, are of somewhat questionable significance. It is commonly presumed that the oxygen in a bath of molten steel in a furnace is present partly as a separate phase consisting of suspended particles of oxides or silicates, partly in solution, the latter being probably the more important. Upon addition of a deoxidizer, it reacts with some portion of the dissolved oxygen and precipitates it as additional suspended particles; the oxygen not eliminated in this way, which remains in solution in the liquid steel, may be regarded indifferently either as dissolved oxygen or as dissolved FeO. When the steel is poured, some of the suspended particles rise towards the surface, others remain trapped in the finished steel, appearing as nonmetallic inclusions in amounts corresponding usually to about 0.01 to 0.03 per cent Oz in the steel. The dissolved oxygen may be partly eliminated as CO during freezing of the ingot, but some remains either in solution or in part precipitated as FeO. Finished steels may thus contain oxygen in several forms: (1) In non-metallic inclusions which are probably quite insoluble in the solid metal at all temperatures; (2) in solid solution which at lower temperatures may be supersaturated; (3) in FeO particles produced by relief of this

Jan 1, 1932

By H. H. Rachford

This work presents a first-order analysis of the instability underlying viscous fingering in adverse viscosity-ratio water floods. It extends previous analyses of frontal instabilities, which were carried out with equations for parallel plate models, by including effects of the saturation transition zone observed behind the front in water floods in water wet systems. This zone tends to insulate incipient fingers from the high-mobility watet;. thus conditions for the onset of fingering differ from those in the parallel plate theory. Finite-difference solutions of the two-dimensional equations of displacement in porous media exhibited the predicted stability characteristics in six hypothetical field- and laboratory-scale floods in rectangular reservoirs. In contrast to results with parallel plate systems, this paper concludes that for waterwet reservoirs, laboratory models scaled by the usual criteria are also correctly scaled for frontal instability. Further, fingering in the systems studied can occur in any saturation range behind the front, and may occur at an intermediate saturation even though stability obtains both at the saturation corresponding to the Buckley-Leverett front and near residual oil saturation. Other points of contrast are that the likelihood of occurrence of fingering may not increase as flow rate or viscosity difference increases, but my be sensitive to changes in he relative permealdlity and capillary pressure functions. INTRODUCTION The recovery of oil by water flooding frequently involves displacing the oil by water of a lower viscosity. Displacement of a fluid by a less viscous one may lead to gross channeling or fingering like that observed in solvent floods, in which it severely lowers recovery efficiency.1 In addition to adverse effects on recovery, it has been suggested that the unstable move- ment causing fingering may interfere with interpretation of scaled model studies of proposed water floods, since the instability in the model might not be faithfully scaled to that in the reservoir prototype. In view of the serious implications of this possible breakdown of widely used scaled model techniques4-6 it is the purpose of this paper to examine the question further. Instabilities in the solutions of systems of differential equations imply a loss of smooth dependence on initial and boundary conditions. Thus, the possibility exists that in using models whose scaling is based on the differential system there may arise size- and rate-dependent factors which are not properly scaled. This possibility was examined in detail by Chouke et al., who analyzed the instability of frontal advance in a related problem, water-oil displacement in parallel plate models,2 in which a moving interface separates two regions of constant, unequal mobilities. First-order perturbation theory predicts the existence of a critical wave length for the growth of perturbations: and a wave length of maximum instability of A, = The interpretation is that wave lengths in a perturbation which are longer than A, will grow. Thus, if the width of a two-dimensional channel is greater than A,, fingers will grow, and the spacing of the fingers which grow at the maximum rate will be approximately It is important that the higher the velocity and/or the difference in flow resistance, the lower is A,, and thus the greater the number of fingers that can grow in a given model. In applying these conclusions to porous media, a pseudo-interfacial tension, , was assumed for the invasion front. Since this would not necessarily be equal to the liquid-liquid interfacial tension, an unknown constant was substituted for the foregoing expression for A, This was determined

Jan 1, 1965

By H. E. Cline, T. H. Alden

A study zvas made of rate-sensitive plastic deformation and superplasticity in alloys of lead and tin. These alloys (lead, PO-19 pct Sn, Sn-38 pct Pb, Sn-2 pct Pb, tin) were extruded, aged at room temperature, or melted and resolidified to produce a variety of ~nicrostrnctures. Flow stress us strain rate data were obtained frorn tension tests for strain rates between 10-6 and 1 min-1. The curve log o .us log £ was S-shaped jor fine-grained materials and approxinzately linear for coarse-grained nzaterials. At constant grain size, the behavior was relatively insensitive to conposition. High rate sensitivity (d log o/d log k) and superplasticity occurred at intermediate strain rates in fine-grained materials and are believed to be associated with a transition with strain rate in the mode of plastic flow. This transition was shifted to higher strain rates with increasing temperataire or decrensing grain size. The high rate rneclzanisrn is presunzed to be slip, while rnetallographic evidence sug-gests that the low rate lnechanism is pain boundary sliding. PEARSON&apos; discovered that extruded eutectic alloys of Pb-Sn and Bi-Sn could be elongated as much as 2000 pct in tension. The ability for stretching decreased with aging time or annealing to increase the grain size. At high strain rates, or if the material was in the cast condition, normal ductility was observed. Following deformation of the extruded Pb-Sn eutectic at low rates, Pearson observed an equiaxed granular structure on an initially flat surface, while rapid straining produced elongated grains. He attributed the large deformation in the extruded alloys to the persistence of extremely small grains to a temperature sufficiently high for inter granular flow. Avery and backofen2 measured the strain rate sensitivity of the flow stress, m = d In old In 6, in the Pb-Sn eutectic and established a correlation between m and the tensile elongation. In the extruded eutectic alloy the strain rate sensitivity was 0.1 to 0.2 at rapid rates and the elongation was small, while at low rates m increased to 0.4 to 0.6 and superplastic elongation was observed. They also noted a grain size effect. In the case of the cast Pb-Sn eutectic the strain rate sensitivity remained at 0.1 over the range of strain rates of their experiment (3 x 10"3 to 2 min-I). These authors suggested that diffusional (Nabarro-Herring) creep was the mechanism by which deformation occurred at low strain rates, while climb-controlled creep occurred at high rates. Two predictions of this model are that, at low strain rates, the strain rate sensitivity approaches 1, i.e., Newtonian viscosity, and that the strain rate at constant stress varies as D/L2, where D is the coefficient of self-diffusion and L the grain size. More recently, a mechanical and microstructural investigation of the dilute superplastic alloy, Sn-5 pct Bi, has been done.3 The results show that the high strain rate sensitivity is associated with a transition with strain rate of the mechanism of plastic flow. At low strain rates, grain boundary sliding and its associated accommodation processes were evident, while at high strain rates quasi-uniform slip was concluded to be the dominant deformation process. The following experiments were performed to extend our knowledge of the phenomena of superplasticity to a larger range of strain rates, compositions, temperatures, and microstructures in the Pb-Sn alloy system. The question of why a cast structure does not exhibit viscous behavior although it appears to have a fine microstructure2 was investigated.

Jan 1, 1968

By Edward Saibel

The various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure,&apos; no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3&apos;4 or on the energy required to form new surfaces.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agree- ment between calculation and experiment. It has been pointed out by several observers&apos; that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermodynamic theory of the tensile strength of isotropic bodies based on work of Born relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melting phenomenon, Fürth obtains an expression for the rupture stress a, in the form where Q is the melting energy per unit mass, p is the density, and is Poisson&apos;s ratio. Furth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By George P. Chapman

Mica is a platy mineral occurring in a variety of complex hydrous aluminosilicate forms with differing chemical composition and physical properties. Principal minerals in the mica group include: Muscovite-potassium mica (colorless or pale green/ ruby) Phlogopite-magnesium mica (dark brown or amber) Biotite-magnesium-iron mica (black or dark green) Lepidolite-lithium mica (lilac) Selected properties are given in Table 1. Muscovite is most important commercially with phlogopite of lesser use. The laminated structure of mica enables it to be split into very thin films which are transparent and tough as well as having outstanding dielectric and insulating properties. Commercially, mica is used in a number of forms (Chowdbury, 1941; Rajgarhia, 1951; Skow, 1962). Sheet mica consists of flat sheets mined from naturally occurring books of mica, free from defects and capable of being punched or stamped into required shapes. Sheet mica is separately classified into blocks, films, or splittings according to thickness. Built-up mica, or micanite, is made by arranging overlapping splittings in layers , cemented with a binder and pressed together at high temperature. Reconstituted mica, or mica paper, is made by depositing fine flakes of high-quality scrap mica in a continuous film impregnated with binder. Scrap and flake mica are normally unsuitable in quality or size for making sheet mica. Originally the term scrap mica referred to the waste byproduct of mining and fabricating sheet mica, and distinct uses were developed for this material. Subsequently it became economically feasible to mine lower quality mica for these uses, and the term flake mica was introduced. Although the two terms are still used somewhat synonymously, it is considered better, at least in the United States, to use the term flake mica in referring to mica mined for uses other than as sheet mica; and to restrict the term scrap mica to mica mined for or with sheet mica, but which will not meet the specifications. Synthetic mica, such as fluorophlogopite, is produced by slow crystallization of a melted blend of pure raw materials. Mineralogy In the true sense the term mica does not relate to, a particular mineral, but to a group or family of minerals of similar chemical composition and to some extent similar physical properties. These minerals are predominantly potassium aluminum silicates with varying amounts of magnesium, iron, and lithium. The precise formulas and isomorphic relationships of the various group members have been studied, but general agreement has not been reached (Grimshaw, 1971; Hurlbut, 1952; Skow, 1962). The general formula describing the chemical composition of micas is [X2Y4-6Z8020(OH, F)4, where X is mainly K, Na, or Ca; Y is mainly Al, Mg, or Fe; Z is mainly Si or Al (Deer, et al., 1962).] These minerals have an internal structure of the layered lattice type where the silicon atoms are in the center of a tetrahedral grouping of oxygen atoms. The groups are linked together in a single plane by three oxygen atoms that lie within the common plane. Each of these oxygen atoms is shared by two tetrahedra. These linked tetrahedral groups, when continually extended, produce a hexagonal network within the plane. This internal structure of the mica has been used to explain the ex-

Jan 1, 1983

By Ira B. Joralemon

Neighboring mines, like men who live in the same environment, often assume similar characteristics. In the Bridge River area of the Lillooet district in central British Columbia there is a remarkable exception to this rule. The Pioneer mine has a simple fissure over 3000 ft. long, with no faults of more than a few feet and with only minor variations in width; the Bralorne mine, 2½ miles away at the other end of the same intrusion, has developed one of the most intricate vein and fault systems in the West. Hinged faults displace the main vein for hundreds of feet, and sometimes become valuable veins themselves. The width of ore varies in a few yards from 2 to 60 ft. Changes in grade of ore are just as abrupt. The rocks that follow the veins or are cut by them often grade into one another or into the ore with no definite contacts. Although the complexity of the structure has left many problems unsolved, the development has indicated a fascinating geological pattern. The Bralorne is in the eastern portion of the Coast Range, 55 miles by spectacular mountain road from the Pacific Great Eastern Railway station of Bridge River. The adit tunnel runs easterly from Cadwallader Creek, a tributary of Bridge River that flows into the Fraser River. Steep mountains rise from 3300 ft. elevation above sea level at the creek to peaks and ridges at 8000 to 9000 ft. altitude. The lower slopes are heavily wooded while above 5000 ft. bare rocks, glaciers and snow-fields extend far above timber line. See Fig. 1. Story of the Bralorne The Lorne claim, staked in 1897, was one of the earliest lode locations in the Bridge River district. At that time it was 70 miles by steep and treacherous trail from the railway. For the next 15 years Arthur Noel, Will Haylmore and other local prospectors mined the small, irregular, oxidized quartz veins to a maximum depth of 200 ft., and treated the ore in arrastres and later a five-stamp mill. The total production to 1912 was only $55,000. Noel and associates later formed the Lorne Amalgamated Mines Co., which they worked in a desultory way until 1925. Increasing sulfide and arsenide content in the veins

Jan 1, 1935

By F. N. Rhines, B. H. Alexander

MUCH attention has been directed to the effects of grain size upon the properties of alloys, but there has been scant study either of the conditions that determine the pattern and dimensions of den-drites in metal systems, or of the influence of their shape and size upon the overall properties of cast-ings. The aim of the research that is about to be described has been to investigate the effect of vari-ous factors upon the mode of formation of dendrites in alloys by measurements of the distance between adjacent dendrite arms (dendrite spacing). Early investigators, including Grignonl and Tschernoff,2 showed that a metal dendrite is com-posed of a tree-like system of stalks and branches arranged in a simple geometrical pattern. North-cott and Thomas3 demonstrated that, in the face-centered cubic solid solutions of copper-base, these stalks and side arms all lie in (100) directions in the crystal. Several investigators, including Sauveur and Chou,0 Sauveur and Reed,&apos; and Martin and Mar-tina have reported that the addition to steel of alloy-ing elements, such as nickel, chromium, and molybdenum, not only makes the dendrites easier to reveal by etching, but makes them coarser. The latter authors8 proposed that the coarsening of the dendrites is roughly proportional to the increase in the temperature range of freezing, caused by adding the alloying elements. Sauveur and Chou6 showed, in addition, that the dendrites are coarsened by a decreased rate of cooling of the casting. Measurement of Dendrite Arm Spacing Among the physical conditions that could be ex-pected to have an influence upon the dendrite arm spacing, that appears in a cast metal, are: composi-tion, rate of freezing, crystal structure, and type of constitution. The relationships obtaining between these variables and the dendrite dimensions have been examined, in the present research, by measur- ing the arm spacing in a wide variety of alloys, listed in tables II through VI. Alloy compositions are recorded in the tables by showing the symbol of the major metal followed by the percentage and symbol of the alloying agent; thus, "Al-10Ag" is an aluminum-base alloy containing 10 pct of silver. Although none of the alloys were analyzed, an im-pression of their degree of purity may be obtained from that of their component metals given in table I. Five hundred grams of each alloy was made by melting in small clay-graphite crucibles in an elec-tric muffle furnace. After alloying the temperature was adjusted to 50" to 75°C above the liquidus and the melts were poured into cast iron molds, at room temperature, the molds having a wall thickness of 1 in. and a cavity 11/2 in. sq in cross-section. Each ingot, thus cast, was sectioned at mid-height and the sectioned surface was polished and etched for metallographic examination. Dendrite spacing meas-urements were made at three positions, namely, ad-jacent to the mold wall, midway between the wall and the center of the ingot, and at the center (desig-nated e, m, and c respectively, in the tables). A typical series of microstructures is presented in fig. 1. For each measurement, the average was taken of the dendrite spacing of several grains covering a zone about 2 mm wide. Only those grains which had a major dendrite axis nearly in the plane of polish were selected in order to eliminate corrections for orientation differences from grain to grain. Although the dendrite spacings were measured to the nearest thousandth of a millimeter, the values listed in the tables are thought to be significant only to the nearest hundredth of a millimeter. The larg-est difference in readings found, when various ob-servers rated the same specimens, was 0.012 mm; the largest difference between corresponding meas-urements upon duplicate specimens was 0.027 mm.

Jan 1, 1951

By Frederick N. Rhines, William A. Anderson

The investigations of Wymanl have demonstrated that copper deoxidized with several of the commonly used agents that confer immunily to ordinary hydrogen em-brittlement can still be embrittled if it is annealed alternately under oxidizing and reducing conditions. During the oxidizing cycle, oxygen diffuses into the copper and frequently deposits a subscale composed of the oxide of the residual deoxidizing agent. Upon subsequent reduction with hot hydrogen, the copper becomes ruptured along the grain boundaries to a depth sharply limited by the previous penetration of oxygen as delineated by the inner boundary of the subscale. Obviously the sensitivity to this kind of hydrogen embrittlement is engendered by the introduction of oxygen during the oxidizing anneal, but beyond this the mechanism of the process, and hence the controlling factors, remain obscure. There are several possibilities: (I) oxygen dissolved in the copper matrix of the subscale may, upon cooling prior to the hydrogen anneal, precipitate as cuprous oxide which is subsequently reduced by hydrogen as in the familiar case of hydrogen embrittlement; (2) oxygen in solid solution in copper may itself confer susceptibility to embrittlement by hydrogen; (3) the normally refractory oxides such as those of aluminum, silicon and titanium may themselves be reduced by hydrogen when in contact with copper; or (4) the precipitated oxides of the subscale may be complex compounds such, perhaps, as SiO2.Cu2O, which are partially reduced by hydrogen. These possibilities have been examined, and it has been concluded that the first three and possibly the fourth are operative collectively or individually under more or less predictable conditions. Effect OF Precipitated Cuprous Oxide and Dissolved Oxygen The literature provides no definite proof that oxygen in solid solution in copper can confer susceptibility to hydrogen embrittlement; indeed, the research of Leiter2 seemed to indicate the opposite—that to produce the effect, cuprous oxide must be present in massive form and in a more or less continuous network along the grain boundaries. To test this point, pure copper has been annealed in hydrogen under conditions designed to ensure the presence in various samples of: (I) precipitated cuprous oxide, (2) dissolved oxygen only, and (3) no oxygen in any form. Very pure copper" said to contain no oxygen and no spectro-scopically detectable traces of any other element (that is, no individual detectable impurity in quantity greater than 0.0001 per cent) was used. Strips of this material cold.-rolled 75 per cent to 1/8 in. in thickness were subjected to the following treatments, the results of which are noted:

Jan 1, 1941

By H. L. Overton, J. B. Lipson

The concept of sodium single-ion equivalent activity as developed by Gondouin, Tixier and Simard,&apos; was used to determine the filtrate resistivity-activity relationships for 150 laboratory and 49 field drilling muds. With the exception of the native and phosphate high-resistivity muds and the calcium-treated muds, the filtrate resistivity-activity relationships were found to be within 20 per cent of that for pure sodium-chloride solutions. Gondouin, et al,* previously suggested a method of treating the high-resistivity muds in quantitative electrical log analysis. A new treatment is presented which uses the P-alkalinity of the filtrate as a correlating parameter in handling the calcium-treated muds in quantitative electrical log analysis. INTRODUCTION Gondouin, Tixier, and Simard in 1957 introduced new interpretive procedures for analyzing the self-potential curve of electric logging. They re-emphasized the previous work of the Schlumberger brothers, Wyllie and others, and re-defined the activity concept in terms of a number which they termed the effective resistivity. Their procedures are particuarly effective when the connate-water resistivities are less than 0.08 ohm-m or greater than 0.3 ohm-m. For gyp muds where the calcium content is known, a procedure was presented which allows calculation of the connate-water resistivity with improved accuracy. These procedures assume that one of the fluids in the system is a pure sodium-chloride solution, but they are not limited by the assumptions. For the fresh and saline connate waters, for instance, it is assumed that the drilling mud filtrate is a pure sodium-chloride solution. For the gyp mud interpretive procedure, it is assumed that the connate water is a pure sodium-chloride solution. Brown,&apos; on the other hand, has suggested that it would be extremely fortuitous if drilling mud filtrates could all be treated electrochemically as sodium-chloride solutions, and he cites some examples where discrepancies exist. A study has been made of the deviations of sodium single-ion equivalent activities, an of drilling mud filtrates from that of pure sodium-chloride solutions. Drilling fluids in common use on the Texas and Louisiana Gulf Coast and laboratory-controlled muds were investigated. Using a cell patterned after Gondouin, et al, (Fig. I), the equivalent activities were measured. It should be remembered here that the activity measured is merely an index which uses numbers that represent the sodium single-ion equivalent activity a,., of the mud filtrate. The membrane potential developed across the cell was determined with a null-type potentiometer. The resistivities of the solutions were measured by the four-electrode method. The resistivity system was calibrated by using saturated KC1 solution as a standard. Chemical properties of the drilling fluids studied were measured with standard API-approved equipment for the particular property in question. For the activity measurements, two shale discs were chosen to serve as cationic membranes. These two discs were both 1 1/4 in. in diameter and, respectively, 1/4 and 1/8 in. in thickness. The membrane potential, Em, was determined using the shale discs as cationic selective membranes separating two standard sodium-chloride solutions of known mean activity. Then by comparing the constant Km in the following equation, with the theoretical value of — 59 mv at 75OF, the perfection of the membrane was determined. The variation of Km for the two membranes used in this experimental work, as well as one of the many unsuitable membranes, is shown in Fig. 2. The measurement of the activity of mud filtrate involves the balancing of its combined individual activities against a standard solution of known mean activity. At the point where there exists zero potential across the membrane cell, the activity effects may be assumed equal for all practical purposes. The mechanics of making a null reading of this sort requires having a large number of different mean activity solutions. A more practical method involves

By Albert B. Horn, J. J. McKetta, O. L. Culberson

Since water is present in natural gas and petroleum reservoirs, it is of engineering value to have accurate experimental data regarding the behavior of water in hydro-carbon systems. Since experimental data of this nature are so scarce in literature, a program is under way at the University of Texas to obtain experimental data regarding the distribution of water in petroleum hydrocarbons. This initial paper is subdivided into three parts: A. The apparatus and analytical procedure are discussed. B. The equipment has been checked by comparing the experimental data with data of literature on the solubility of methane in water at 77°F and pressures to 10,000 psia. C. Experimental data are presented at 100, 160, 220, 280, and 340°F on the solubility of ethane in water at pressures to 1200 psia. As the temperature is increased the solubility of ethane in water first exhibits a minimum and then a maximum solubility. The range of applicability of Henry&apos;s Law is discussed. INTRODUCTION Although considerable experimental data have been published on water-hydrocarbon systems in the hydrate region, the information on these systems in the vapor-liquid and the vapor-liquid- &apos;References are given at end of paper. Manuscript received at the office of the Petroleum Branch August 31. 1949. liquid regions at elevated pressures is extremely scarce. A survey of the literature on hydrocarbon-water systems at elevated pressures was presented by McKetta and Katz12,13,14 showing the systems and phases investigated. In addition to these existing published data, Poettman and Dean" have reported the water content of propane in the three-phase region (only the propane-rich liquid and the vapor phases were studied) and Michels, et al.15 have reported the solubility of methane in water at pressures to 6800 pounds per square inch at 77°F and at pressures to 1500 psia at temperatures to 300°F. It has been shown12,14 that the presence of water will materially affect the phase equilibrium of hydrocarbon systems. In order to make experimental studies on the quantitative effect of the presence of water in naturally-occurring hydrocarbon systems, it is desirable to have data available on binary hydrocarbon-water systems. A program is underway at this laboratory to determine the phase relations of the hydrocarbon-water systems. Initially the investigation will be limited to binary systems with water as one of the components. Later ternary and complex systems will be investigated and reported. EQUIPMENT AND ANALYTICAL PROCEDURE Apparatus In order to avoid a description of the methods employed in each subsequent paper, a description of the apparatus and the analytical procedure will be given here. The apparatus is shown schematically in Fig. 1. The numbered items in Fig. 1 represent the high pressure valves. The equilibrium cell is of the totally enclosed type, with a volume of 550 cubic centimeters. The cell is mounted in an air bath which in turn is mounted on pillow blocks and connected to a rocking mechanism so that the cell and bath will oscillate approximately 30 degrees above and below the horizontal at 35 oscillations per minute. The air bath is heated by two resistance heaters. The first or primary heater is 250 watts and is controlled by a thermoregulator; the second heater is of 500-watt size and is manually controlled to aid in bringing the cell to equilibrium temperature. Air circulation in the bath is accomplished by means of a fan. the shaft of which is concentric to the heaters. The walls of the bath are insulated with 2-in. thick blocks of 85 per cent magnesia. Temperature observations are made with three calibrated thermocouples. One couple is sealed in a well provided within the equilibrium cell, and is used as the criterion of the cell being at the equilibrium temperature. The other two thermocouples are located on opposite sides of the cell to indicate temperature uniformity within the air bath. The thermoregulator, used in conjunction with a relay, gives a variation in the temperature of the air in the bath of plus or minus one degree Fahrenheit. However, since the equilibrium cell weighs approximately 55 pounds, the

Jan 1, 1950

By M. N. Pathasarathi, P. A. Beck, T. J. Koppenaal

EARLIER work1 indicated that in rolled and annealed copper the volume fraction of the cube-texture component may increase on continued isothermal annealing. Merlini found2 that in rolled copper the well-known increase in the amount of cube-oriented material with increasing annealing temperature3 is concurrent with grain growth, which takes place after recrystallization is complete. It was found that both in copper2 and in aluminum4 the texture resulting from primary recrystallization, even if this is followed by some grain growth, may in general comprise, in addition to the cube-texture component, four symmetrical texture components of the general type (123)[412], i.e., components not very far from the ideal orientations of the rolling texture. The volume fraction of the cube-texture component increases on further annealing at the expense of these four components.&apos; The present work was undertaken to study quantitatively the increase in the volume fraction of the cube-texture component in the course of normal grain growth, under varying conditions. Since the grain-gr3wth behavior of A1-Mn alloys has been already investigated in some detaiL5 an A1 + 0.8 pct Mn alloy was chosen for this work, in which the extent of normal grain growth can be effectively controlled by the inhibiting effect of a dispersed second phase. EXPERIMENTAL PROCEDURE High-purity aluminum of the following composition was used: A1 99.997 pct, Cu 0.0004 pct, Fe 0.0005 pct, and Si 0.001 pct. A high-purity A1-Mn master alloy was prepared by dehydrating manganese chloride at 500°C and reacting it with molten high-purity aluminum at 750°C in a graphite crucible.5 The Mn metal reduced from the salt by the molten aluminum goes into solution in the latter. The master alloy? containing 13 pct Mn, was solidified under conditions suitable for minimizing segregation. An ingot of the final alloy, to be used in the experiments, was per pared by melting high-purity aluminum and the necessary amount of master alloy in a graphite crucible, and by pouring the molten alloy into a graphite mold preheated to 700°C through a box containing graphite baffles designed to intercept most of the aluminum oxide films floating in the melt. The melt was then solidified by placing the mold on a water-cooled copper plate and by keeping the top of the mold hot, in order to minimize piping. The 6 1/2 in. long, 11/4-in.diam ingot consisted largely of a single crystal. Chemical analysis showed that there was little segregation from the bottom (0.83 pct Mn) to the top (0.81 pct Mn). Spectrographic analysis of the ingot showed that the impurity content remained essentially the same as that of the aluminum used. The ingot was processed so as to obtain a uniformly small grain size. without banding. The ini-tial steps of rolling in the form of a flat bar and of annealing, down through a thickness of 0.4 in., are shown in Table I. At this point the bar was cut into four sections, each approximately 3 in. long, which were processed separately as shown in Table If. The table also gives the penultimate grain sizes obtained in each section by annealing prior to the final rolling of 90 pct RA. During the final rolling the strips were reversed end to end between passes. Annealing treatments were given in a salt pot furnace, with the temperature controlled to 1°C. All annealing of section "6s" was carried out above the solvus point to avoid the formation of second-phase precipitate. The penultimate annealing was sufficiently short to give a relatively fine grain size in spite of the high temperature. Section "6L" was processed in a similar manner, except that the penultimate annealing was much longer, so as to allow considerable grain growth. Section "4" was given the two final

Jan 1, 1961

By C. C. Clark, J. S. Iwanski

The purpose of this investigation was to study mi-crostructural changes that take place in a commercial nickel-chromium-iron alloy, such as Incoloy "901," over long periods of time at temperatures up to 13 50°F and to correlate such changes with creep-rupture properties. of the alloy. In the course of the investigation, some microstructural changes were observed which correspond to microstructural alterations found in previous studies of Inconel "X." Microstructural phases have been identified in both alloys with the aid of electron and X-ray diffraction and an electron probe microanalyzer. The materials used in this investigation were from commercial heats of the following chemical composition: Pct Cr Pct Ni Pct Mo Pct Fe Pct Cb Incoloy "901" 12.51 43.67 5.72 Bal. -Inconel "X" 14.61 73.44 - 6.61 1.02 Pct A1 Pct Ti Pct Mn Pct Si Pct C Incoloy "901" 0.10 2.46 0.46 0.24 0.05 Inconel "X" 0.70 2.43 0.51 0.36 0.04 Long-term creep-rupture tests were conducted on Incoloy "901" at temperatures of 1000°, 1200°1 and 1350°F. A summary of these results is shown in Table I along with the results of a long-term creep-rupture test conducted on Inconel "X" at 1500°F. The heat treatments given the specimens are also shown in Table I. When the creep-rupture results on Incoloy "901" are compared with shorter-tertn data, there is no evidence of any undue deterioration of the creep-rupture strength with time, nor is the elongation decreased more than would be expected from the influence of time alone. INCOLOY "901" PHASE IDENTIFICATION Microscopic examination of the Incoloy "901" specimens reveals a dark etching grain boundary constituent in the specimen which was under test for about 11,500 hr at 1000°F. This grain boundary constituent was seen to increase in size as the test temperature was increased to 1200" and 1350°F, Figs. 1, 2, and 3. Simultaneously, an acicular structure of definite crystallographic orientation appears within the grains of the 1350°F specimen, Fig. 3. Under examination with the electron microscope, a fine precipitate is observed in the 1200 °F specimen. Fig. 4. It becomes considerably larger in the 2850-hr 1350°F specimen, Fig. 5. In a few areas the precipitated particles have been replaced by, or transformed to, small needles or platelets. After 7380 hr at 1350°F, Figs. 3 and 6, the needles are much larger and have replaced nearly all of the fine precipitate. X-ray diffraction studies detected the presence of hexagonal Laves phase and hexagonal n phase (Ni,Ti) in the 1350°F specimens, Table 11. Only the Laves phase was detected by X-ray diffraction in the 1200°F specimen and none was detected in the 1000°F specimen. In this latter specimen, however, the small quantity of precipitate in the grain boundaries (presumed to be Laves phase) precludes its detection by X-ray diffraction. Composition of the hexagonal Laves phase is not yet known, although its diffraction

Jan 1, 1960

By D. E. Peacock, B. Harris

Thermal-expansion and electrical-resistivity measurements have been carried out below 400°K on niobium and two niobium alloys containing tungsten. For anonaly in the expansion us temperature curve below aboct 300°K. This reslt is consistent with an earlier obsercation that Young&apos;s modilus joy Cb-132 lms an unusiully strong -tenperati-e dependence below roon temperature. No anonulous behavior was observed in the resistiuity vs temperature curve for either alloy or in the magnetic susceptibility us tenperature curve for Cb-132. These results are disclssed in terms of various electronic and bonding theories of the transition metals and their alloys, but it has not been possible to reach any definite conclusion as to the cause of the results obtained. ALONG with investigations of the low-temperature mechanical behavior of niobium and its alloys, some of the physical properties of these materials have also been studied. In the work described here, thermal expansion and electrical resistivity were measured below 400°K for niobium and two of its alloys, Cb-132 and D-43. In addition, the magnetic susceptibility of Cb-132 was measured over the same temperature range. The alloys are representative of two distinct tion-hardened alloy such as might find service as a turbine blade, while D-43 (Nb, 5.3 at. pct W, 1.1 at. pct Zr. and 0.08 at. pct C) is a solution- and dispersion-hardened alloy, of considerably lower strength than Cb-132. which is a potential vane material. Their significant common feature is the presence of tungsten as the principal source of solution hardening. EXPERIMENTAL TECHNIQUES Thermal-expansion measurements were made with a quartz-tube dilatometer using baths of liquid nitrogen, liquid bromoethane, and a liquid polyalkylene glycol derivative to cover the range 80 to 400 K. Results are recorded as expansion relative to that of quartz, and the probable maximum error in any value of relative expansion. All, is about il pct. The metallurgical condition of the specimens, which were in rod form. will be discussed in the section dealing with experimental results. Resistivity was measured on recrystallized wires 0.030 in. in diam using a potentiometric technique. The same baths were used for temperatures between 80&apos; and 400°K as were used for the expansion measurements. and in addition the resistance of D-43 and Cb-132 was measured at 4.2 K by immersion in liquid helium. The maximum expected experimental error in any resistivity value is about 3 pct and that in any change in resistivity about i0.05 pct. Temperatures in both sets of experiments were measured with liquid-in-glass thermometers with an accuracy usually better than 1°K. EXPERIMENTAL RESULTS 1) Thermal Expansion. In Fig. 1 is shown the relative linear expansion of recrystallized niobium. D-43. and Cb-132. The curve for Cb-132 is composed of results from several runs on three different samples. Two of the samples were annealed for an hour at 1500°C to cause recrystallization and the third was annealed for an hour at 2000&apos;C to remove some mi-crosegregation of tungsten which was known to be present in the wrought alloy received from the manu-

Jan 1, 1967

By W. H. Emmons

Although gold is one of the rarer metals, it is widely distributed; it is found on all of the continents and in each of the grand metallogenic provinces of the earth. It is prominent particularly in the shield areas of the earth; these areas have produced a large part of the world&apos;s lode gold and in most of them gold lodes are more important than the lodes of other metals. The Scandinavian shield is the only one that has not produced much gold. Nearly all of the world&apos;s gold has been derived from lodes and from sands and gravels where gold placers formed by the destruction of lodes. The gold derived from magmatic segregations, from pegmatites and from contact metamorphic deposits is quite subordinate to that derived from auriferous lodes. The lodes include all veins and related deposits that are formed by hot waters that move along fissures or other openings and that deposit vein &apos;matter :in the fissures and by replacement of the country rocks along the fissures. All of the shield areas of the earth are characterized by large areas of granitic rocks including granitic gneisses, granodiorites and other acid intrusives which here are included in the general term "granite." The granites are intruded into schists, ancient lavas and other rocks which here are designated as the "invaded" rocks. The granites are parts of what once were great batholiths: that is, they are the remaining portions of great deep-seated bodies that slope outward, have very irregular roofs and so far as known have no floors but extend downward to great though unknown depths. Some of them are scores or hundreds of miles across and contain islands or "roof pendants" of the invaded rocks at places where the roofs of the batholiths were low—that is, where erosion has not yet completely unroofed the batholiths. It is in these islands of older rocks and in the narrow marginal belts and cupolas of the batholiths that practically all of the gold lode deposits of the shields are found. Valuable lodes are lacking generally in the granites themselves except in grahite within a mile or less from .the contacts with rocks of the islands (Fig. 1). It is probable that the great areas of granites and gneisses that surround the islands are not all of the same age, and that at places unmapped granite intrudes gneiss or older

Jan 1, 1932

By W. D. Kruger

Methods for analyzing flooding or cycling projects by means of two-dimensional flow calculations are presented in the literature. The use of these methods allows the determination of optimum operating conditions for such projects and provides information on pattern efficiencies, relative flow rates, pressure distributions and floodout histories. The accuracy of such analyses depends on the basic reservoir data employed, especially the absolute permeability distribution in the reservoir; however, absolute permeability data normally are determined from well flow tests and/or core measurements and are so limited in quantity and quality that they do not adequately describe the reservoir flow properties. A calculation procedure is presented for determining the areal permeability distribution in the reservoir. Use of the procedure allows verification of the basic reservoir data through the matching of past reservoir conditions, thereby providing proper data for reliable predictions of future operations. The calculation procedure is a numerical technique based on a mathematical model of the reservoir and is designed for solution by means of an electronic digital computer. Results from field application of this procedure are presented. Permeability distributions from measured data are compared to those calculated to indicate the need for the analysis. Comparisons of field-measured and calculated pressure distributions are given to establish the validity of the calculation procedure. The conclusions of this paper are (I) use of the calculation provides data that allow a match of past reservoir conditions and thus reliable prediction of future operations; and (2) the procedure should, where applicable, be used to provide adequate reservoir data for use in two-dimensional flow calculations and related reservoir analyses. INTRODUCTION One means of providing more precise engineering control over reservoir operations during all stages of depletion is to develop some type of model to simulate the reservoir, using information developed from the behavior of the prototype to predict the performance of the actual reservoir. The use of mathematical rather than physical models for this purpose has been gaining in importance recently because of the application and availability of electronic computers. Mathematical models avoid instrumentation difficulties and allow easier handling of large-scale problems. At present, analyses employing two-dimensional models are common, and thought is being given to the use of models in three dimensions. The use of multi-dimensional models is necessary to show not only what is occurring in the reservoir, but also where in the reservoir the phenomena of interest are taking place. Methods for analyzing flooding or cycling projects by means of two-dimensional numerical models are presented in the literature. The use of these methods allows the determination of optimum operating conditions for such projects and provides information on pattern efficiencies, relative flow rates, pressure distributions and floodout histories. The applicability of numerical models and the results of using such analyses have been presented through field examples. The references indicated here discuss fully the data necessary to build the mathematical reservoir model and the way the model is used to study or predict the future performance of the reservoir. The accuracy of the analysis of such projects depends on the basic reservoir data employed in the construction of. the model. In order to be sure the model represents the reservoir, it must be used to match some known set of reservoir conditions, i.e., to match past reservoir performance. The accuracy of the model is directly dependent upon the absolute permeability distribution in the reservoir; however, absolute permeability data are normally determined from well flow tests and/or core measurements, and are so limited in quantity and quality that they do not adequately describe the reservoir flow properties. There is always the need for better data and for verification of existing data. The purpose of this paper is to show the use of the mathematical model to match past performance in flooding or cycling projects, the use of numerical techniques to adjust the basic absolute permeability data if necessary so that a match is obtained, and in this way to generate the effective areal permeability distribution of the reservoir. A review of the basic concepts of the numerical model will be given, followed by a discussion of the data-adjusting technique for matching past performance. TWO field examples will be cited to show

By Robert E. Ogilvie, Zvonimir Ban

Oxidation experiments were conducted above 600°C to investigate the oxidation products formed on the surface of MoSi2. Results are presented which indicate that minor iron impurities play a key role in the oxidation behavior of MoSi2 above 600 °C. Based on considerations of the crystal chemistry of the oxidation products, MoSi2 with rhenium and iron additions was found to be resistant to oxidation in the pesting temperature range. AS early as 1914, Honigschmidtl observed that some silicides of molybdenum exhibited high resistance to oxidation at elevated temperatures. This fact did not arouse much interest until 1950, when Kieffer and cerwenka2 examined this property in more detail. They found that Mo-Si alloys with approximately 70 pct Mo (by weight) could be heated to 1600°C in an oxidizing atmosphere without any significant damage. The surface was found to be protected by the formation of an extremely thin silica glass layer which had no tendency to spa11 during subsequent thermal cycling. In 1955, Fitzer3 discovered that even solid bodies made of MoSi2 completely oxidized within a relatively short time when exposed to the air in the temperature range from 300° to 600°C. To describe this phenomenon he proposed the name "molybdenum disilicide &apos;pest&apos; ", clearly analogous to the previously observed "tin plague" ("tin pest") which, however, arises as the result of a phase transformation. Studies performed by Fitzer and, in particular, one published recently by Berkowitz, Blackburn, and Fel-ten,&apos; comprise the most extensive research to date on the pest phenomenon in MoSi2, as far as the fundamen- tal mechanism of the process is concerned. The first of these studies revealed the existence of a crystalline phase which appeared at the surface at 750°C and dissolved in the glassy silica layer at 1150°C. The logical assumption was that this phase was some reaction product of MOO3 and SiO2. The formation of a reaction product of this type seemed probable since it had been mentioned by Glemser and Lutz6 in a paper describing their studies of molybdenum oxides; however, this assumption was later disproved.8 It is our belief that information concerning the exact nature of this crystalline phase may be important for a better understanding of both pesting and the protection mechanism. Therefore, since the only available general description of the pest phenomenon was that of Fitzer, it was decided to reproduce his experiments. These experiments established that, in addition to the "pest" and "nonpest" temperature range, an intermediate region exists between 600" and approximately 650°C. This region is characterized by the appearance of a variable amount of yellow to orange colored crystals. The electron-beam microanalyzer was used to qualitatively determine their composition. Iron and molybdenum were found to be major constituents. This result can be explained based on the following facts: 1) iron, according to literature data,* is the most common impurity in molybdenum powder, and its content can be as high as 0.25 pct; 2) technical silicon powder usually contains iron; 3) steel ball mills are often used for the crushing and grinding of MoSi2. In order to clarify the exact role of iron, it was deliberately added to a stoichiometric mixture of molybdenum and silicon. The observed results corroborated the previous experiment, proving that iron (probably as some silicide phase) concentrates along the grain boundaries. I) EXPERIMENTAL PROCEDURE A) Oxidation of MoSi2 with Iron Additions. 1) Specimen Preparation. Specimens were prepared by both

Jan 1, 1967

By T. D. Mueller, F. C. Miller, Jr. Earlougher R. C.

In analyzing pressure buildup tests for field wells producing both oil and gas, the common practice is to use a modification of single-phase flow theory. Validity of such an approximation has been demonstrated for single-well solution-gas-drive systems. This paper indicates that such approximations are also valid for two-well solution-gas&apos;-drive systems. From this it is inferred that the technique can be used for multiple-well systems. A computer was used to simulate the behavior of a two-well solution-gas-drive reservoir to test the validity of the above type of analysis. Simulation results indicate that pressure buildup tests in such a system can be analyzed within engineering accuracy for formation permeability and pressure. A rule of thumb is given for estimating the length of time a well must be shut in for the pressure in a nearby producing well to increase significantly. To observe such an increase, the shut-in well would have to be left shut in much longer than normal. INTRODUCTION An important technique for obtaining data concerning a producing petroleum reservoir is the pressure buildup test. Such a test, when properly conducted and analyzed, provides information on the average reservoir pressure and the permeability in the major drainage area of a well. The theory upon which the analysis of a pressure buildup test is based assumes that the behavior of the fluid in the reservoir is adequately described by the diffusivity equation.1 Use of the diffusivity equation implies that a single fluid of small and constant compressibility is flowing. To analyze a pressure buildup test in situations which involve more than one fluid phase, the single-fluid analysis is extended. This paper verifies the extension of pressure buildup analyses to two-phase, two-well systems. Miller, Dyes and Hutchinson1 have presented a technique for analyzing pressure buildup tests in circular bounded reservoirs. Their method requires that the reservoir be producing at pseudo-steady state (constant pressure gradients) prior to shut-in. An alternate reservoir model, presented by Horner,2 assumes that the reservoir is infinite. The Homer model does not assume a Pseudo-steady state prior to shut-in, but the assumption that the reservoir is infinite implies that the average pressure can be determined only if the total production prior to shut-in is small compared to the total fluid originally present. Limitations imposed by the pseudo-steady state and infinite reservoir assumptions are avoided by the technique proposed by Matthews, Brons and Hazebroek.3 Their method can be used to calculate both the Permeability and the average pressure in bounded single-well systems which are not necessarily at steady state. They also suggested determining the average pressure of a multi-well reservoir producing from pseudo-steady state by volumetrically averaging the static pressures of the individual wells. Matthews and Lefkovits4 used numerical simulation techniques to verify that this method does produce adequate results for single-phase, multiple-well systems. Perrine5 proposed modifications to the single-phase theory so that pressure buildup tests in multiple-phase systems could be analyzed. He suggested replacing the single-phase mobility (k/µ) by the sum of the mobilities of the individual phases, and replacing the fluid compressibility by an average compressibility weighted by the saturations of the separate phases. By using numerical techniques to solve the two-phase flow problem for a single-well system, he concluded that this approximation gives results within engineering accuracy. More recently, Weller6 has shown that, for a gas-oil system with a single well at the center of a circular reservoir, pressure buildup tests can be analyzed adequately by using the modification proposed by Perrine. Feller&apos;s results also indicate that, as the gas saturation increases, this analysis becomes less accurate. To date, no evidence is available to show that the Perrine approximations can be combined with the Matthews-Brons-Hazebroek technique to calculate the average pressure of a multi-well,

For many years it has been known that large bodies of iron ore existed in Iron and Washington counties in Utah. The ore is chiefly hematite-both hard and soft-though some magnetite is found. No definite and complete estimate of the iron ore reserves of the state have been made. The U. S. Geological Survey estimated that 40,000,000 tons of ore were disclosed by development work averaging only 35 feet below the surface of the ore. The ore is found along an area about one and a half miles wide by twenty miles long, and for the most part on the eastern and southern slopes or foothills of Three Peaks. Granite Mountain and Iron Mountain. Later estimates by others have gone as high as ore in sight 164,000,000 tons, probable ore 300,000,000 tons and possible ore 1,000,000,000 tons. Whether this last estimate is too great or not there is sufficient iron ore in Utah to justify the starting of an iron industry. Two companies are now mining iron ore in Utah, the Columbia Steel Corporation and the Utah Iron Corporation. The mine of the Columbia Steel Corporation is at Iron Springs a few miles west of Cedar City. About 650 tons, of ore a day is being shipped to the blast furnace at Ironton. The ore is mined by the glory hole method. After being drilled it is blasted to the bottom of the several glory holes and is dropped through chutes into cars on the ore haulage level below. It is then hauled by electric locomotives to the crushing plant, where it is crushed to blast furnace size before going to storage bins. Some of the softer ore is brought to the chutes by Fresno scrapers.

Jan 1, 1925